Handbook of Nanostructured Materials and Nanotechnology [5 volumes in one]

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Foreword Nanostructured materials are becoming of major significance and the technology of their production and use is rapidly growing into a powerful industry. These fascinating matedais whose dimension range for 1-100 nanometer (1 nm = 10 -9 m, i.e., one billionth of a meter) include quantum dots, wires, nanotubes, nanorods, nanofilms, nanoprecision self assemblies and thin films, nanosize metals, semiconductors, biomaterials, oligomers, polymers, functional devices, etc. etc. It is clear that the number and significance of new nanomaterials and application will grow explosively in the coming twenty-first century. This dynamical fascinating new field of science and its derived technology clearly warranted a comprehensive treatment. Dr. Had Singh Nalwa must be congratulated to have undertaken the task to organize and edit such a massive endeavor. His effort resulted in a truly impressive and monumental work of fine volumes on nanostructured materials coveting synthesis and processing, spectroscopy and theory, electrical properties, and optical properties, as well as organics, polymers, and biological materials. One hundred forty-two authors from 16 different countries contributed 62 chapters encompassing the fundamental compendium. It is the merit of these authors, their contributions coordinated most knowledgeably and skillfully by the editor, that the emerging science and technology of nanostructured materials is enriched by such an excellent and comprehensive core-work, which will be used for many years to come by all practitioners of the field, but also will inspire many others to join in expanding its vistas and application.

Professor George A. Olah University of Southern California Los Angeles, USA Nobel Laureate Chemistry, 1994

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Preface Nanotechnology is the science and engineering of making materials, functional structures and devices on the order of a nanometer scale. In scientific terms, "Nano" means 10 -9 where 1 nanometer is equivalent to one thousandth of a micrometer, one millionth of a millimeter, and one billionth of a meter. In Greek, "nanotechnology" derives from the nanos which means dwarf and technologia means systematic treatment of an art or craft. Nanostructured inorganic, organic, and biological materials may have existed in nature since the evolution of life started on Earth. Some evident examples are micro-organisms, fine-grained minerals in rocks, and nanosize particles in bacterias and smoke. From a biological viewpoint, the DNA double-helix has a diameter of about 2 nm (20 angstrom) while ribosomes have a diameter of 25 nm. Atoms have a size of 1-4 angstrom, therefore nanostructured materials could hold tens of thousands of atoms all together. Moving to a micrometer scale, the diameter of a human hair is 50-100/xm. Advancements in microscopy technology have made it possible to visualize images of nanostructures and have largely dictated the development of nanotechnology. Manmade nanostructured materials are of recent origin whose domain sizes have been precision engineered at an atomic level simply by controlling the size of constituent grains or building blocks. About 40 years ago, the concept of atomic precision was first suggested by Physics Nobel Laureate Richard E Feynman in a 1959 speech at the California Institute of Technology where he stated, "The principles of physics, as far as I can see, do not speak against the possibility of maneuvering things atom by atom ...". Research on nanostructured materials began about two decades ago but did not gain much impetus until the late 1990s. Nanotechnology has become a very active and vital area of research which is rapidly developing in industrial sectors and spreading to almost every field of science and engineering. There are several major research and development government programs on nanostructured materials and nanotechnology in the United States, Europe, and Japan. This field of research has become of great scientific and commercial interest because of its rapid expansion to academic institutes, governmental laboratories, and industries. By the turn of this century, nanotechnology is expected to grow to a multibillion-dollar industry and will become the most dominant technology of the twenty-first century. In this handbook, nanostructures loosely define particles, grains, functional structures, and devices with dimensions in the 1-100 nanometer range. Nanostructures include quantum dots, quantum wires, grains, particles, nanotubes, nanorods, nanofibers, nanofoams, nanocrystals, nanoprecision self-assemblies and thin films, metals, intermetallics, semiconductors, minerals, ferroelectrics, dielectrics, composites, alloys, blends, organics, organominerals, biomaterials, biomolecules, oligomers, polymers, functional structures, and devices. The fundamental physical and biological properties of materials are remarkably altered as the size of their constituent grains decreases to a nanometer scale. These novel materials made of nanosized grains or building blocks offer unique and entirely different electrical, optical, mechanical, and magnetic properties compared with conventional micro or millimeter-size materials owing to their distinctive size, shape, surface chemistry, and topology. On the other hand, organics offer tremendous possibilities of chemical modification by tethering with functional groups to enhance their responses. Nanometer-sized organic materials such as molecular wires, nanofoams, nanocrystals, and dendritic molecules have been synthesized which display unique properties compared with their counterpart conventionally sized materials. An abundance of scientific data is now available to make useful comparisons between nanosize materials and their counterpart microscale or bulk materials. For example, the hardness of nanocrystalline copper increases with decreasing grain size and 6 nm copper grains show five times hardness than the conventional copper. Cadmium selenide (CdSe) can yield any color in the spectrum simply by controlling the size of its constituent grains. There are many such examples in the literature where physi-

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PREFACE

cal properties have been remarkably improved through nanostrucure maneuvering. Nanostructured materials and their base technologies have opened up exciting new possibilities for future applications in aerospace, automotive, cutting tools, coatings, X-ray technology, catalysts, batteries, nonvolatile memories, sensors, insulators, color imaging, printing, flat-panel displays, waveguides, modulators, computer chips, magneto-optic disks, transducers, photodetectors, optoelectronics, solar cells, lithography, holography, photoemitters, molecular-sized transistors and switches, drug delivery, medicine, medical implants, pharmacy, cosmetics, etc. Apparently, a new vision of molecular nanotechnology will develop in coming years and the twenty-first century could see technological breakthroughs in creating materials atom by atom where new inventions will have intense and widespread impact in many fields of science and engineering. Over the past decade, extraordinary progress has been made on nanostructured materials and a dramatic increase in research activities in many different fields has created a need for a reference work on this subject. When I first thought of editing this handbook, I envisaged a reference work covering all aspects of nanometer scale science and technology dealing with synthesis, nanofabrication, processing, supramolecular chemistry, protein engineering, biotechnology, spectroscopy, theory, electronics, photonics, and other physical properties as well as devices. To achieve this interface, researchers from different disciplines of science and engineering were brought together to share their knowledge and expertise. This handbook, written by leading international experts from academia, industries, and governmental laboratories, consists of 62 chapters written by 142 authors coming from 16 different countries. It will provide the most comprehensive coverage of the whole field of nanostructured materials and nanotechnology by compiling up-to-date data and information. Each chapter in this handbook is self-contained with cross references. Some overlap may inevitably exist in a few chapters, but it was kept to a minimum. It was rather difficult to scale the overlap that is usual for state-of-the-art reviews written by different authors. This handbook illustrates in a very clear and concise fashion the structure-property relationship to understand a broader range of nanostructured materials with exciting potential for future electronic, photonic, and biotechnology industries. It is aimed to bring together in a single reference all inorganic, organic, and biological nanostructured materials currently studied in academic and industrial research by coveting all aspects from their chemistry, physics, materials science, engineering, biology, processing, spectroscopy, and technology to applications that draw on the past decade of pioneering research on nanostructured materials for the first time to offer a complete perspective on the topic. This handbook should serve as a reference source to nanostructured materials and nanotechnology. With over 10,300 bibliographic citations, the cutting edge state-of-the art review chapters containing the latest research in this field is presented in five volumes: Volume 1: Volume 2: Volume 3: Volume 4: Volume 5:

Synthesis and Processing Spectroscopy and Theory Electrical Properties Optical Properties Organics, Polymers, and Biological Materials

Volume 1 contains 13 chapters on the recent developments in synthesis, processing and fabrication of nanostructured materials. The topics include: chemical synthesis of nanostructured metals, metals alloys and semiconductors, synthesis of nanostructured coatings by high velocity oxygen fuel thermal spraying, nanoparticles from low-pressure and lowtemperature plasma, low temperature compaction of nanosize powders, kinetic control of inorganic solid state reactions resulting from mechanistic studies using elementally modulated reactants, strained-layer heteroepitaxy to fabricate self-assembled semiconductor islands, nanofabrication via atom optics, preparation of nanocomposites by sol-gel methods: processing of semiconductors quantum dots, chemical preparation and characteriza-

PREFACE

tion of nanocrystaUine materials, rapid solidification processing of nanocrystalline metallic alloys, vapor processing of nanostructured materials and applications of micromachining to nanotechnology. The contents of this volume will be useful for researchers particularly involved in synthesis and processing of nanostructured materials. Volume 2 contains 15 chapters dealing with spectroscopy and theoretical aspects of nanostructured materials. The topics covered include: nanodiffraction, FT-IR surface spectrometry of nanosized particles, specification of microstructure and characterization by scattering techniques, vibrational spectroscopy of mesoscopic systems, advanced interfaces to scanning-probe microscopes, microwave spectroscopy on quantum dots, tribological experiments with friction force microscopy, electron microscopy techniques applied to study of nanostructured ancient materials, mesoscopic magnetism in metals, tools of nanotechnology, and nanometrology. The last five chapters in this volume describe computational technology associated with the stimulation and modeling of nanostructures. The topics covered are tunneling times in nanostructures, theory of atomic-scale friction, theoretical aspects of strained-layer quantum-well lasers, carbon nanotube-based nanotechnology in an integrated modeling and stimulation environment, and wavefunction engineering: a new paradigm in quantum nanostructure modeling. Volume 3 has 11 chapters which exclusively focus on the electrical properties of nanostructured materials. The topics covered are: electron transport and confining potentials in semiconductor nanostructures, electronic transport properties of quantum dots, electrical properties of chemically tailored nanoparticles and their applications in microelectronics, design, fabrication and electronic properties of self-assembled molecular nanostructures, silicon-based nanostructures, semiconductor nanoparticles, hybrid magnetic-semiconductor nanostructures, colloidal quantum dots of III-V semiconductors, quantization and confinement phenomena in nanostructured superconductors, properties and applications of nanocrystalline electronic junctions, and nanostructured fabrication using electron beam and its applications to nanometer devices. Volume 4 contains 10 chapters dealing with different optical properties of nanostructured materials. The topics include: photorefractive semiconductor nanostructures, metal nanocluster composite glasses, porous silicon, 3-dimension lattices of nanostructures, fluorescence, thermoluminescence and photostimulated luminescence of nanoparficles, surface-enhanced optical phenomena in nanostructured fractal materials, linear and nonlinear optical spectroscopy of semiconductor nanocrystals, nonlinear optical properties of nanostructures, quantum-well infrared photodetectors and nanoscopic optical sensors and probes. The electronic and photonic applications of nanostructured materials are also discussed in several chapters in Volumes 3 and 4. All nanostructured organic molecules, polymers, and biological materials are summarized in Volume 5. This volume has 13 chapters that include: Intercalation compounds in layered host lattices-supramolecular chemistry in nanodimensions, transition-metalmediated self-assembly of discrete nanoscopic species with well-defined shapes and geometries, molecular and supramolecular nanomachines, functional nanostructures incorporating responsive modules, dendritic molecules: historical developments and future applications, carbon nanotubes, encapsulation and crystallization behavior of materials inside carbon nanotubes, fabrication and spectroscopic characterization of organic nanocrystals, polymeric nanostructures, conducting polymers as organic nanometals, biopolymers and polymers nanoparticles and their biomedical applications, and structure, behavior and manipulation of nanoscale biological assemblies and biomimetic thin films. It is my hope that Handbook of Nanostructured Materials and Nanotechnology will become an invaluable source of essential information for academic, industrial, and governmental researchers working in chemistry, semiconductor physics, materials science, electrical engineering, polymer science, surface science, surface microscopy, aerosol science, spectroscopy, crystallography, microelectronics, electrochemistry, biology, microbiology,

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PREFACE

bioengineering, pharmacy, medicine, biotechnology, geology, xerography, superconductivity, electronics, photonics, device engineering and computational engineering. I take this opportunity to thank all publishers and authors for granting us copyright permissions to use their illustrations for the handbook. The following publishers kindly provided us permissions to reproduce originally published materials: Academic Press, American Association for the Advancement of Science, American Ceramic Society, American Chemical Society, American Institute of Physics, CRC Press-LLC, Chapman & Hall, Electrochemical Society, Elsevier Science Ltd., Huthig-fachverlag, IBM, Institute of Physics (IOP) Publishing Ltd., IEEE Industry Applications Association, Japan Society of Applied Physics, Jai Press, John Wiley & Sons, Kluwer Academic Publishers, Materials Research Society, Macmillan Magazines Ltd., North-Holland, Pergamon Press, Plenum, Physical Society of Japan, Optical Society of America, Springer Verlag, Steinkopff Publishers, Technomic Publishing Co. Inc., The American Physical Society, The Mineral, Metal, and Materials Society, The Materials Information Society, The Royal Society of Chemistry, Vacuum Society of America, VSP, Wiley-Liss Inc., Wiley-VCH Verlag, World Scientific. This handbook could not have reached fruition without the marvelous cooperation of many distinguished individuals who contributed to these volumes. I am fortunate to have leading experts devote their valuable time and effort to write excellent state-of-the-art reviews which led foundation of this handbook. I deeply express my thanks to all contributors. I am very grateful to Dr. Akio Mukoh and Dr. Shuuichi Oohara at Hitachi Research Laboratory, Hitachi Ltd., for their kind support and encouragement. I would like to give my special thanks to Professor Seizo Miyata of the Tokyo University of Agriculture and Technology (Japan), Professor J. Schoonman of the Delft University of Technology (The Netherlands), Professor Hachiro Nakanishi of the Tohoku University (Japan), Professor G. K. Surya Prakash of the University of Southern California (USA), Professor Padma Vasudevan of Indian Institute of Technology at New Delhi, Professor Toskiyuki Watanabe, Professor Richard T. Keys, Dr. Christine Peterson, and Dr. Judy Hill of Foresight Institute in California, Rakesh Misra, Krishi Pal Reghuvanshi, Rajendra Bhargava, Jagmer Singh, Ranvir Singh Chaudhary, Dr. Hans Thomann, Dr. Ho Kim, Dr. Thomas Pang, Ajit Kelkar, K. Srinivas, and other colleagues who supported my efforts in compiling this handbook. Finally, I owe my deepest appreciation to my wife, Dr. Beena Singh Nalwa, for her cooperation and patience in enduring this work at home; I thank my parents, Sri Kadam Singh and Srimati Sukh Devi, for their moral support; and I thank my children, Surya, Ravina, and Eric, for their love. I express my sincere gratitude to Professor George A. Olah for his insightful Foreword.

Hari Singh Nalwa

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About the Editor Dr. Hari Singh Nalwa has been working at the Hitachi Research Laboratory, Hitachi Ltd., Japan, since 1990. He has authored over 150 scientific articles in refereed journals, books, and conference proceedings. He has 18 patents either issued or applied for on electronic and photonic materials and their based devices. Dr. Nalwa has published 18 books, including Ferroelectric Polymers (Marcel Dekker, 1995),

Handbook of Organic Conductive Molecules and Polymers, Volumes 1-4 (John Wiley & Sons, 1997), Nonlinear Optics of Organic Molecules and Polymers (CRC Press, 1997), Organic Electroluminescent Materials and Devices (Gordon & Breach, 1997), Handbook of Low and High Dielectric Constant Materials and Their Applications, Volumes 1-2 (Academic Press, 1999), and Advanced Functional Molecules and Polymers, Volumes 1-4 (Gordon & Breach, 1999). Dr. Nalwa is the founder and Editor-in-Chief of the Journal of Porphyrins and Phthalocyanines published by John Wiley & Sons and serves on the editorial board of Applied Organometallic Chemistry, Journal of Macromolecular Science-Physics, International Journal of Photoenergy, and Photonics Science News. He is a referee for the Journal of American Chemical Society, Journal of Physical Chemistry, Applied Physics Letters, Journal of Applied Physics, Chemistry of Materials, Journal of Materials Science, Coordination Chemistry Reviews, Applied Organometallic Chemistry, Journal of Porphyrins and Phthalocyanines, Journal of Macromolecular Science-Physics, Optical Communications, and Applied Physics. He is a member of the American Chemical Society (ACS), the American Association for the Advancement of Science (AAAS), and the Electrochemical Society. He has been awarded a number of prestigious fellowships in India and abroad that include National Merit Scholarship, Indian Space Research Organization (ISRO) Fellowship, Council of Scientific and Industrial Research (CSIR) Senior fellowship, NEC fellowship, and Japanese Government Science & Technology Agency (STA) fellowship. Dr. Nalwa has been cited in the Who's Who in Science and Engineering, Who's Who in the World, and Dictionary of International Biography. He was also an honorary visiting professor at the Indian Institute of Technology in New Delhi. He was a guest scientist at Hahn-Meitner Institute in Berlin, Germany (1983), research associate at University of Southern California in Los Angeles (1984-1987) and State University of New York at Buffalo (1987-1988). He worked as a lecturer from 1988-1990 in the Tokyo University of Agriculture and Technology in the Department of Materials and Systems Engineering. Dr. Nalwa received a B.Sc. (1974) in biosciences from Meerut University, a M.Sc. (1977) in organic chemistry from University of Roorkee, and a Ph.D. (1983) in polymer science from Indian Institute of Technology in New Delhi, India. His research work encompasses ferroelectric polymers, electrically conducting polymers, electrets, organic nonlinear optical materials for integrated optics, electroluminescent materials, low and high dielectric constant materials for microelectronics packaging, nanostructured materials, organometallics, Langmuir-Blodgett films, high temperature-resistant polymer composites, stereolithography, and rapid modeling.

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List of Contributors Numbers in parenthesis indicate the pages on which the author's contribution begins. I. T. H. CHANG (501) School of Metallurgy and Materials, University of Birmingham, Edgbaston, Birmingham, United Kingdom K. L. CHOY (533) Department of Materials, Imperial College, London, United Kingdom JOSEP COSTA (57) Grup de Recerca en Materials, Departament de Fisica, Universitat de Girona, Girona, Spain S. P. DENBAARS (295) Departments of Chemical Engineering and Materials, University of California, Santa Barbara, California, USA DAVID J. DUVAL (481) Department of Chemical Engineering and Materials Science, University of California, Davis, California, USA K. E. GONSALVES(1) Department of Chemistry and Polymer Program, Institute of Materials Science U-136, University of Connecticut, Storrs, Connecticut, USA E. J. GONZALEZ (215) Ceramics Division, National Institute of Standards and Technology, Gaithersburg, Maryland, USA HONGGANG JIANG (159) Materials Science & Technology Division, Los Alamos National Laboratory, Los Alamos, New Mexico, USA CHRISTOPHER D. JOHNSON (251) Department of Chemistry and Materials Science Institute, University of Oregon, Eugene, Oregon, USA DAVID C. JOHNSON (251) Department of Chemistry and Materials Science Institute, University of Oregon, Eugene, Oregon, USA KRZYSZTOF C. KWIATKOWSKI (387) Department of Chemistry, Vanderbilt University, Nashville, Tennessee, USA AMIT LAL (579) Department of Electrical and Computer Engineering, University of Wisconsin, Madison, Wisconsin, USA MAGGIE LAU (159) Department of Chemical and Biochemical Engineering and Materials Science, University of California, Irvine, California, USA ENRIQUE J. LAVERNIA (159) Department of Chemical and Biochemical Engineering and Materials Science, University of California, Irvine, California, USA

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LIST OF CONTRIBUTORS

CHARLES M. LUKEHART (387) Department of Chemistry, Vanderbilt University, Nashville, Tennessee, USA

JABEZ J. MCCLELLAND (335) Electron Physics Group, National Institute of Standards and Technology, Gaithersburg, Maryland, USA MYUNGKEUN NOH (251) Department of Chemistry and Materials Science Institute, University of Oregon, Eugene, Oregon, USA B. Z. NOSHO (295) Departments of Chemical Engineering and Materials, University of California, Santa Barbara, California, USA R. I. PELZEL (295) Departments of Chemical Engineering and Materials, University of California, Santa Barbara, California, USA G. J. PIERMARINI (215) Ceramics Division, National Institute of Standards and Technology, Gaithersburg, Maryland, USA S. P. RANGARAJAN (1) Department of Chemistry and Polymer Program, Institute of Materials Science U- 136, University of Connecticut, Storrs, Connecticut, USA

C. M. REAVES (295) Departments of Chemical Engineering and Materials, University of California, Santa Barbara, California, USA SUBHASH H. RISBUD (481) Department of Chemical Engineering and Materials Science, University of California, Davis, California, USA ROBERT SCHNEIDMILLER (251) Department of Chemistry and Materials Science Institute, University of Oregon, Eugene, Oregon, USA

HEIKE SELLINSCHEGG (251) Department of Chemistry and Materials Science Institute, University of Oregon, Eugene, Oregon, USA VICTORIA L. TELLKAMP (159) Department of Chemical and Biochemical Engineering and Materials Science, University of California, Irvine, California, USA

J. WANG (1) Department of Chemistry and Polymer Program, Institute of Materials Science U- 136, University of Connecticut, Storrs, Connecticut, USA W. H. WEINBERG (295) Departments of Chemical Engineering and Materials, University of California, Santa Barbara, California, USA

QIAN YITAI (423) Department of Chemistry, University of Science and Technology of China, Hefei, Anhui, People's Republic of China

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List of Contributors Numbers in parenthesis indicate the pages on which the author's contribution begins. DOYEOL AHN (619)

The Institute of Quantum Information Processing and Systems, Department of Electrical Engineering, University of Seoul, 90 Jeonnong, Tongdaimoon-Ku, Seoul 130-743, Republic of Korea JORGE A. ASCENCIO (385) Instituto Nacional de Investigaciones Nucleares, Amsterdam No. 46-202, Hip6dromo Condesa, 06100 Mrxico, D. E, Mrxico MARIE-ISABELLE BARATON (89)

SPCTS-UMR 6638 CNRS, Faculty of Sciences, F-87060 Limoges, France STEPHEN BARNARD (665) NASA Ames Research Center, Moffett Field, California, USA R. BIRRINGER (155) FB 10 Physik, Geb~iude 43, Universit~it des Saarlandes, Postfach 151150, D-66041 Saarbrticken, Germany

ROBERT H. BLICK (309) Max-Planck-Institut fur Festkrrperforschung, 70569 Stuttgart, Germany C. E. BOTTANI (213) INFM, Dipartimento di Ingegneria Nucleare, Politecnico di Milano, Via Ponzio, 34/3-20133 Milan, Italy J. M. COWLEY (1) Department of Physics and Astronomy, Arizona State University, Tempe, Arizona, USA D. DOSSA (707) Lawrence Livermore Laboratory, Livermore, California, USA FEDOR DZEGILENKO (665) NASA Ames Research Center, Moffett Field, California, USA Vo GASPARIAN (513) Department of Physics, Yerevan State University, 375049 Yerevan, Armenia; Departamento de Electr6nica y Technologia de Computadores, Facultad de Ciencias, Universidad de Granada, 18071 Granada, Spain R. HABERKORN (155) FB 11 Chemie, Geb~iude 9, Universit~it des Saarlandes, Postfach 151150, D-66041 Saarbrticken, Germany

MIGUEL JOSI~-YACAMAN (385) Instituto Nacional de Investigaciones Nucleares, Amsterdam No. 46-202, Hip6dromo Condesa, 06100 Mrxico, D. E, Mrxico C. E. KRILL (155) FB 10 Physik, Geb~iude 43, Universit~it des Saarlandes, Postfach 151150, D-66041 Saarbrticken, Germany

R. LfJTHI (345) IBM Research Center Zurich, 8803 Rtischlikon, Switzerland

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LIST OF CONTRIBUTORS

MADHU MENON

(665)

Department of Physics and Astronomy, University of Kentucky, Lexington, Kentucky, USA E. MEYER (345) Institute of Physics, University of Basel, 4056 Basel, Switzerland J. R. MEYER (707) Naval Research Laboratory, Washington, DC, USA P. MILANI (213) INFM, Dipartimento di Fisica, Universit~ di Milano, Via Celoria, 16-20133 Milan, Italy M. ORTUlqO (513) Departamento de Ffsica, Universidad de Murcia, Murcia, Spain KAMEL OUNADJELA (429) ICPMS CNRS UMR46, F-67037 Strasbourg, France

L. R. RAM-MOHAN (707) Worcester Polytechnic Institute, Worcester, Massachusetts, USA SUBHASH SAINI

(665)

NASA Ames Research Center, Moffett Field, Califomia, USA G. SCHON (513) Institut fur Anorganische Chemie, Universitiit-GH Essen, Essen, Germany U. SIMON

(513)

Institut ftir Anorganische Chemie, Universitiit-GH Essen, Essen, Germany SUSAN B. SINNOTT (571) Department of Chemical and Materials Engineering, The University of Kentucky, Lexington, Kentucky, USA J. C. H. SPENCE (1) Department of Physics and Astronomy, Arizona State University, Tempe, Arizona, USA DEEPAK SRIVASTAVA (665)

NASA Ames Research Center, Moffett Field, California, USA R. L. STAMPS (429) Department of Physics, University of Western Australia, Nedlands, Western Australia 6907, Australia RICHARD SUPERFINE (271) Department of Physics and Astronomy, University of North Carolina, Chapel Hill, North Carolina, USA RUSSELL M. TAYLOR, II (271) Department of Computer Science, University of North Carolina, Chapel Hill, North Carolina, USA I. VURGAFTMAN (707) Naval Research Laboratory, Washington, DC, USA SISIRA WEERATUNGA (665) Lawrence Livermore National Laboratory, Livermore, California, USA

DAVID J. WHITEHOUSE (475) Department of Engineering, University of Warwick, Coventry CV4 7AL, United Kingdom; Metrology Consultant Taylor Hobson, Leicester, United Kingdom

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Chapter 1 CHEMICAL SYNTHESIS OF NANOSTRUCTURED METALS, METAL ALLOYS, AND SEMICONDUCTORS K. E. G o n s a l v e s , S. R R a n g a r a j a n , J. W a n g

Department of Chemistry and Polymer Program, Institute of Materials Science U-136, University of Connecticut, Storrs, Connecticut, USA

Contents 1. 2.

3.

4.

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Synthesis of Nanostructured Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.

Physical Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2.2.

Chemical Methods

1 2 . .

...........................................

3 4

Synthesis of Metals, Intermetallics, and Semiconductors . . . . . . . . . . . . . . . . . . . . . . . . . .

5

3.1. 3.2.

Chemical Synthesis of Metals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Synthesis of Intermetallics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5 22

3.3.

Synthesis of Semiconductors

34

Conclusions

.....................................

..................................................

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

52 52

1. INTRODUCTION Ultrafine microstructures having an average phase or grain size on the order of a nanometer (10 -9 m) are classified as nanostructured materials (NSMs) [ 1]. Currently, in a wider meaning of the term, any material that contains grains or clusters below 100 nm, or layers or filaments of that dimension, can be considered to be nanostructured [2]. The interest in these materials has been stimulated by the fact that, owing to the small size of the building blocks (particle, grain, or phase) and the high surface-to-volume ratio, these materials are expected to demonstrate unique mechanical, optical, electronic, and magnetic properties [3]. The properties of NSMs depend on the following four common microstructural features: (1) fine grain size and size distribution (

U1

r.~

bl

bl

['i"1

9

COSTA

2.3. Powders in Thin-Film Processing Plasmas The desire to maintain profitability motivates the semiconductor industry to improve manufacturing efficiency. These improvements typically include increasing the device speed and decreasing the cost per function. These require reduced device dimensions, increased wafer diameters, and increased device yields. One of the main causes of a reduction in the yield is the introduction of an unacceptable level of contamination in the course of the handling and processing of the wafer. Improvements in air filtration, clean room garments, and methods for wafer transport have dramatically reduced the contribution of the modern clean room environment to particle contamination. The largest source of contamination is now contributed by process-induced contamination [40, 41]. In high-volume manufacturing, approximately 75 % of all yield losses are due to particles and as many as 90% of these particles are induced by the process itself [42]. The concern of the microelectronics industry for "process-inherent" particle contamination may be illustrated with the advertisement shown in Figure 3. The publicized apparatus contaminates the wafer with a controlled amount of particles in order to calibrate the wafer inspection systems of a device fabricator. A review on the formation of particles in thin-film processing plasmas written by Steinbrtichel was published in 1994 [43]. Historically, plasma-generated particles during thin-film processing were first observed in situ in a silane-argon deposition plasma [ 1]. However, it became apparent that particles are also produced in etching plasmas, specifically in sputtering and in reactive ion etching

Fig. 3. The concern of the microelectronics industry about the contamination of devices from particles generated in the discharge is illustrated by this advertisement. This apparatus contaminates the silicon wafers with a selected amount of particles in order to calibrate wafer inspection systems.

66

NANOPARTICLES FROM LOW-PRESSURE, LOW-TEMPERATURE PLASMAS

(RIE) plasmas (see Section 2.3.1). Laser light scattering (LLS) techniques have been the most widely used to detect particles. The sensitivity of this technique to particle concentration and particle size depends on the geometrical configuration of the LLS setup, the laser intensity, and the detection method. Since the earliest studies, LLS showed that particles accumulate in a quite localized region of the discharge, near the sheath edge at the powered electrode of a parallel-platetype reactor [2]. This was the first indication that particles were negatively charged, and so they were suspended in the direction perpendicular to the electrodes. When the discharge was turned off, the particles fell onto the substrate or else they were swept out into the exhaust by the gas flow. The position of the particle cloud was strongly dependent on the discharge parameters, such as the reactor geometry, the gas pressure, the flow rate, the flow pattern across the electrode, and the temperature distribution in the reactor. We can briefly review some of the observations reported in sputtering, RIE, and deposition plasmas.

2.3.1. Particles in Sputtering Plasmas Particles have been observed in systems chemically as simple as the sputtering of an elemental target in a noble-gas discharge. Particles have been observed in Ar plasmas sputtering Si [44-49], SiO2 [50-52], graphite [53], Lexan and Teflon [50], as well as A1 and Cu [52-55]. In sputtering plasmas, the particles consisted mainly of the target material [44, 45], although atoms coming from the electrodes were also reported [45, 46]. Whatever the cause, it was clear that the particles must have nucleated and grown in the gas phase from atoms removed by the sputtering process. These studies showed that the electrical characteristics of the discharge have a marked effect on the appearance of a particle cloud [44]. Threshold behavior versus both rf power and pressure for the powder appearance was reported for sputtering of Si and SiO2 in Ar by Yoo and Steinbrtichel [47-49]. At the onset of cloud appearance, particles were typically approximately 200 nm in diameter and quite monodisperse. Further particle development led to larger particles and wider particle size distributions. Selwyn et al. [45, 51] reported the optical characterization of particle traps. In their reports, it was shown that particles were trapped not only on the plasma sheaths but also in a ring over the edge of the wafer. Figure 4 is a rastered LLS photograph showing trapped particle clouds over three Si wafers [56]. Selwyn et al. emphasized that any material or geometrical discontinuity on the wafer-holding electrode may give rise to a particle trap above it [57-59]. Further research on the particle traps induced by particular geometries of the electrodes was performed by other authors [60-64]. By the combination of LLS and a Langmuir probe, Carlile et al. [46] showed that the particle traps coincided with the localized maxima of the plasma potential above its surrounding value. Jellum et al. [55], in experiments on the rf sputtering of A1 and Cu, investigated the effect of the electrode temperature on particle formation and particle cloud position between electrodes. These authors demonstrated a thermophoretic effect on particles, as they tended to move to the colder electrode. 2.3.2. Particles in Reactive Ion Etching The first observations of particles on RIE plasmas were also reported by Selwyn et al. [57]. They reported particle clouds in CC12F2/Ar, O2/CC12F2/Ar, or SF6/C12/Ar. For the same discharge conditions however, no particle cloud appeared in C12/Ar, CF4/Ar of CC12F2/Ne. They combined LLS with laser-induced fluorescence (LIF) of C1 atoms and showed that both LLS and LIF signals were localized at the sheath edge. This led the authors to conclude that Si-halide etch products, with their propensity to form negative ions, may be involved in the formation or nucleation of particles.

67

COSTA

Fig. 4. A photographof a rastered laser light scattering image showingtrapped particle clouds overthree closely packed Si wafers on a graphite electrode. The particle cloudshave a ring shapethat reproduces the edge of the wafers. Reprinted with permission from G. S. Selwyn,Plasma Sources Sci. Technol. 3, 340 (9 1994Institute of Physics Publishing Ltd.).

Yoo and Steinbriachel [47] hypothesized, from observations of CC12/Ar etching of silicon, that the nucleating species must originate from the substrate as byproducts of the etching process. Stoffels and co-workers [65] reached similar conclusions, on the basis of infrared spectroscopy of 10% CC12F2/Ar discharges. SF6/Ar etching plasmas have been shown to generate particle clouds [66]. Garrity and co-workers [67] proposed mechanisms to explain the formation processes of particles, including gas phase precursor formation, nucleation, and coagulation. Kushner and collaborators developed a model for transport and agglomeration of particles in reactive ion etching plasma reactors [68]. 2.3.3. Particles in Deposition Plasmas

Studies on the occurrence of particles in rf glow discharges of silane-based gas mixtures will be analyzed in detail in Section 4 because most of the basic knowledge of particle formation and plasma-particle interactions is based on them. However, in this section, we review preliminary studies mainly concerned with the particle contamination effect during the processing of microelectronic materials and devices. The first detailed studies of particles on deposition plasmas were those of Spears and coworkers [ 1-3] starting in 1984. These authors investigated the position of the particle cloud in an Ar-diluted silane discharge and the influence of gas pressure, silane concentration, and flow rate on the appearance of the particle cloud. For the first time, they used LLS to gain information on the particle concentration and size distribution. Although later studies provided more accurate values, their measurements allowed them to argue that the particle size distribution was quite narrow. These authors, however, did not report the time course of the particle cloud development. Around 1990, Watanabe [69-71], as well as Lloret [72], Verdeyen [73, 74], and others [75, 76], examined the modulation of the discharge as a method to control the appearance of particles in the discharge and to modify the thin film microstructure. Watan-

68

NANOPARTICLES FROM LOW-PRESSURE, LOW-TEMPERATUREPLASMAS

abe et al. [70] showed that with a modulated discharge it was possible to reach higher rf powers and, thus, obtain much higher deposition rates, without forming particles. Bertran and co-workers [72, 75, 76] studied the microstructure of a silicon thin film grown under different plasma modulation frequencies, and claimed that negatively charged species such as anions and particles contributed to film growth during the plasma-off times. Later research on particle nucleation, growth dynamics, and plasma-particle interactions contributed to the present basic knowledge of the formation of particles in lowpressure, low-temperature plasmas and these will be discussed in Section 4.

3. T E C H N O L O G Y

3.1. Low-Pressure, Low-Temperature Plasmas Plasma is a state of matter that consists of electrons, negatively and positively charged particles, and neutral atoms or molecules moving in random directions. Matter in this state is more highly activated than in the solid, liquid, or gas state. Most of the matter in the universe is in a plasma state. Occasionally, particles may nucleate and reside in the plasma. The plasma is electrically neutral. Therefore, in the absence of charged particles, m

ne k- n i -- n +

(2)

where ne is the electron density, n~ the anion density, and n + the cation density. Low-temperature, low-pressure plasmas are the most often encountered, both in the microelectronics industries and in research laboratories. They are induced by applying an electric field to a low-pressure gas. This electrical excitation may be direct current (DC) or alternating current (AC). Commonly, the plasma is excited by a 13.56-MHz rf electrical field. This is the frequency allowed by the international authorities, because it does not interfere with communication signals. The electric field ionizes the gas and accelerates the electrons, which impact on neutral species and provoke their ionization. These new ionizations compensate for the loss of electrons and ions by mutual recombination or ambipolar diffusion to the walls. Laboratory plasmas are far from the equilibrium and the electron and ion temperature are markedly different. Although the electron temperature may be around 4 • 104 K (equivalent to 5 eV), ions are too heavy to follow the electric field and remain close to the gas temperature. For that reason, these discharges are referred to as low-temperature discharges or cold plasmas. As indicative values of the external parameters for a low-pressure, low-temperature discharge, pressure ranges between 1 and 200 Pa and the rf electrical power typically lies between a few mW/cm 2 and 500 mW/cm 2. Concerning the internal parameters of the plasma, the plasma-bulk positive ion and electron density, n + and ne, lie between 108 and 101~ cm -3. However, in Sill4 plasmas, the negative ion density, n~- (or negative charge density as powders), can exceed ne by an order of magnitude [77-79]. The ratio n+/N or ionized fraction of the gas ranges from 10 -7 (low power and relatively high pressure) to 10 -3 (high power and low pressure). The plasma chemistry of the discharge is a consequence of the inelastic collisions between electrons and neutral or charged species, and of their recombination. Positive ions, anions, neutral radicals, excited molecules, and photons are products of these inelastic collisions. For instance, Table III shows the main dissociative reactions of the silane molecule resulting from electronic impact. To quantify this plasma chemistry, it is necessary to determine the energy distribution function (EDF) of the electrons in the discharge and the effective cross section for each reaction. Many reports have been devoted to the determination of these reaction cross sections [81-83]. Among rf plasmas, the capacitively coupled discharges are the most widely used. In this case, the electrical field is driven to the electrode through a blockage capacitor. Figure 5

69

COSTA

Table III. Products of the Dissociative Collision of One Electron with the Silane Molecule [80] Threshold Products

energy (eV)

Sill2 + 2H + e -

8(?)

Sill 3 + H + e -

(?)

Sill + H2 + H + e -

10(?)

Si + 2H2 + e -

12(?)

Sill* + H2 + H + e -

10.5

Si* + 2H2 + e -

11.5

Sill + + H2 + 2e-

11.9

SiH~- + H + 2e-

12.3

Si+ + 2H2 + 2e-

13.6

Sill + + H2 + H + 2e-

15.3

e - + Sill 4 --+

Sill 3 + H

6.7

Sill 2 + H 2

7.7

V

plasma Vs2_L_

S2

m m

Sheaths

Fig. 5. Scheme of the distribution of potentials between electrodes at different instants of the rf cycle in a capacitively coupled rf discharge. The plasma is confined between electrodes. The surfaces of the electrodes are S 1 and S 2. VS1 and VS2 are the time-averaged potentials between the plasma and each electrode. VB is the resulting DC bias.

p r e s e n t s a s c h e m e o f the electric field b e t w e e n the e l e c t r o d e s at different instants o f the rf cycle. T h e e l e c t r o d e s are u s u a l l y p l a c e d inside the v a c u u m chamber. O n c e the p l a s m a is ignited, three different regions can be distinguished. In the central region, the p l a s m a is electrically quasi-neutral and the negative c h a r g e density c a u s e d by

70

NANOPARTICLES FROM LOW-PRESSURE, LOW-TEMPERATUREPLASMAS

electrons, anions, and charged particles equals the positive ion density. Between the plasma and the electrodes, there are space charge regions, the sheaths, that are mostly positive because of the difference in mobility between electrons and ions. The electric field in the sheaths tends to confine the negative species in the discharge and to accelerate the positive ions toward the walls. In capacitively coupled reactors, a DC self-bias, VB, may appear on the electrode connected to the rf generator, depending on the ratio between the area of the rf electrode and the effective area of the grounded walls. The time-averaged potential drops of each electrode through the sheaths, Vsl and Vs2, follow an inverse power law of $1/$2:

VS1 ._(S1) n Vs2

$22

1 ~

~-5oo E

'I:

> 400

300

-I

0.4

i

I

0.6

0.8

R

1.0

Fig. 53. Dependenceof the voltage peak shown in Figure 53 on methane concentration.

I

I

I

!

I

0.50

0.40

0.30

I

L

I

l

I

0.4

0.5

0.6 R

0.7

0.8

Fig. 54. Dependenceof the carbon concentration x (Sil-xCx) on the precursor gas mixture R, R -[CH4]/([CH4]-!-[SiH4]).

act as traps of negative charges and the electric field rises so as to balance the lost charges. The fact that this peak scaled with the silane concentration was in good agreement with the experimental evidence that the formation of powder diminished with the methane content on the precursor gas. The dependence of the carbon content, x, on the methane fraction was studied by means of elemental analysis [193, 194]. Figure 54 shows this dependence. To obtain a stoichiometric powder, x = 0.5, a methane-rich gas (R = 0.8) was necessary. This is related to the higher energy required to ionize the methane molecule compared to that needed for silane. In addition to carbon content, the elemental analysis measurements revealed that the hydrogen content was about 45%. X-ray photoelectron spectroscopy (XPS) analyses also provided a compositional factor, x [197]. The 1-s carbon peak of an Sil-xCx sample with x = 0.56 is shown in Figure 55, where it is compared to the experimental spectrum of commercial/~-SiC. The deconvolution of this spectrum showed that it was composed of peaks arising from carbon bonded to silicon, at 283.5 eV, and carbon bonded to carbon, at 284.6 eV. The dominance of Si-C bonds over C-C bonds was evident from their relative peak intensifies. No C - O was detected in spite of the presence of a significant amount of oxygen in the sample revealed by

120

NANOPARTICLES FROM LOW-PRESSURE, LOW-TEMPERATURE PLASMAS

Fig. 55. XPS spectra of C (1 s) core levels of Si0.44C0.54and commercial/3-SICpowders.

Fig. 56. A series of Sil_x Cx powdersamples obtainedin rf discharges of methane and silane mixtures. Sample color ranges from brownyellowfor silicon-rich samples to white for carbon-rich samples.

IR and elemental analysis. Therefore, this oxygen content was assumed to be bonded to only silicon atoms. The color of the samples was dependent on the carbon content [ 171 ]. Figure 56 shows a series of powder samples deposited on a glass substrate (R =0.4, 0.6, 0.7, 0.8, 0.95). The color ranged from red yellow for the silicon-rich samples to transparent white for the carbon-rich powders. These studies were mainly devoted to the structural characterization of the material but no effort was made to control the size of these powders. Therefore, to the author's knowledge, there is no report concerning the development of particle size in silane-methane mixtures. TEM investigations on the Sil_x Cx powder samples revealed a wide size distribution of particles, which ranged from 10 to 300 nm [ 193-198]. As explained for particles produced in silane discharges, specification of the plasma-on duration and the plasma conditions should allow for control of the particle size and size distribution. Raman measurements, as well as those of SAED and HRTEM, showed that the particles were amorphous. Moreover, Raman analysis provided evidence of the presence of Si-H and C-H vibrational modes, whereas those of Si-C could not be detected.

121

COSTA

I

T'

i

i

,

I

'

I

t

j

'1

a-Sil-x C'H x R=0.1

v

r t,-

R =0.45

.=_ E or) t'-L_.

R = 0.75

R=0.9

4000

3000

2000

1000

Wavenumber (cm "1) Fig. 57. IR transmission spectra of a series of samples produced in silane/methane discharges with different methane fractions.

The IR spectra of these samples, however, provided more detailed information on the Si-H, C-H, and Si-C bond configurations. Figure 57 shows the IR spectra for a series of samples, from silicon-rich to carbon-rich samples. The vibrational modes related to silicon-hydrogen bonds appeared in each spectrum, the wagging modes, at 650 cm -1, and the bending modes related to (SiH2)n and Sill2, between 870 and 910 c m - 1 [ 199, 200]. The stretching band, at around 2100 c m - 1, did not shift toward higher wavenumbers as the carbon concentration increased as expected from the electronegativity of carbon. Absorption contributions from the carbon-hydrogen groups did not appear in the silicon-rich samples. Stretching modes of the C-H arrangements (between 2875 and 2955 cm -1) as well as bending modes (around 1400 cm -1) were evident in samples with R -- 0.75 and R = 0.9. The absorption band at 1250 cm -1 was attributed to C-C skeletal vibrations or to C-H3 bending vibrations in the Si-C3 groups. In the spectral region between 700 and 1100 cm -1, several absorption peaks were superimposed on each other. Besides the bending modes of Si-H, the absorption at around 780 cm -1 was related to Si-C bonds, whereas that at around 1000 cm -1 might be due to Si-CH2 bonding arrangements or to silicon-oxygen bonds. Figure 58 shows the IR absorbance in the region between 425 and 1500 cm -1. Figure 59 describes the thermal desorption of hydrogen from the Sil-xCx sample with x - 0.28. Hydrogen evolution started at around 473 K and rose continuously to its maximum at around 930 K. The shape of the peak revealed that the evolution had two distinct contributions: The contribution of the low-temperature peak increased with the silicon content in the sample, as shown in the inset to Figure 59. Therefore, these two contributions,

122

NANOPARTICLES FROM LOW-PRESSURE, LOW-TEMPERATURE PLASMAS

t

I

I

1

I

I

I

I

I

I

I

I

i

!

I

!

I

I

I

I

I

i

I

I

i

v

rO

L__

O t~

n,"

i 600

R = 0.45

800

1000

Wavenumber

1200

1400

(cm4)

Fig. 58. IR absorption spectrain the range between 450 and 1450 cm-1 for the series of samples shown in Figure 57.

'''''' F'

I= ~i_~ It ~

'''~'''1 !

'

/\

,

J ,~

~

/

-I

I l~

JI

-

~Z

~_

s00

a00

700/

\

q

9

400

500

600 700 800 900 1000 Temperature (K)

Fig. 59. Thermaldesorption spectra of hydrogen for the sample produced in a discharge with a fraction of methane of R = 0.4. The figure inset shows that the low-temperattn'eevolution scales with the silicon concentration in the sample.

at low and high temperature, could be assigned to silicon-hydrogen bonds and to carbonhydrogen bonds, respectively. From the temperature of the maximum of the evolution, it was deduced that the free energy for the desorption of C - H was A G = 2.94 eV [171]. Although this value was slightly lower than that in amorphous carbon thin films [ 174], an energy balance equivalent to that presented in Section 5.2.1.4 allowed the determination of the C - H bond energy (3.73 eV), which was in very good agreement with that reported in the literature (3.7 eV) [201 ]. The free energy related to the evolution of Si-H was A G = 2.08 eV and therefore greater than that determined in silicon powder. This could be due to the increase in the Si-H bond strength as the carbon content increases.

123

COSTA

I

I

I

I

I

I

I

Si-O

0

800 ~

o .c>




SiC

I

,

~" ~ , , " ~ , . - ~ >

I ti

->s-pepared

i !

annealed

sick220> 't

't~

I/f I : I

/ i SiC

I

Si o~ 9-~ rY "O

-

type B

, ~

-

_

10 / I

10

20

I

30

I

I

40 50

Laser power (mW)

Fig. 70. Dependenceon laser power of the type-A and type-B emissions.Note the logarithmicscale on the emissionintensity axis.

type A, shown in Figure 69. The type-A emission was several orders of magnitude more intense than the type-B emission and its spectrum shifted to longer wavelengths. The A and B emissions corresponded to independent processes because of their different characteristics. For instance, the dependence of the type-A emission intensity on laser power was extremely supralinear: IA ~ I~

(22)

whereas that of type B was sublinear. As Figure 70 shows, an increase in the laser power by a factor of 2 resulted in an increase of nearly three orders of magnitude in the emission intensity. Another striking result was the behavior of Si powder emission with gas pressure inside the cryostat. The type-A emission intensity showed an exponential decrease with pressure below 15 Pa: IA=I0 exp(-p)

(23)

The type-B emission under vacuum could be observed only in the pellet sample and did not exhibit the pressure dependence shown by the type-A emission. Because of its high intensity and unusual features, the type-A emission was studied in detail in further reports [236-241 ]. The structural origin of this emission was related to the laser annealing of the powder. Figure 71 demonstrated that the type-A emission appeared after an irreversible structural change of the sample caused by relatively high-power laser irradiation [239]. Further evidence of the structural change was provided by the simultaneous monitoring of the hydrogen desorbed from the sample and its light emission [239]. In this experiment, the powder sample was mounted in a vacuum chamber connected to a quadrupole mass spectrometer, which detected the evolved molecular hydrogen. After a few seconds of laser irradiation, both H2 effusion and light emission began. Whether this laser annealing caused the crystallization of the sample is not clear. However, this was not an important question, as the emission was not related to quantum confinement effects in nanometric crystalline domains but to the heating of the sample.

139

COSTA

'

'

'

'

'

I

'

'

'

'

I

I

'

I

a)

xlO

B

30 mW (before)

v .,,i..a i car) t,(D

A

b)

t,t"-

I

. 1O oO r .i

E

B~

40 mW

(D > Ol .i.-, t~

iY

c)

iB II

30 mW (after) I

I

I

I

I

I

500

I

, I

I

I

1000

k

I

I

1500

Time (ms) Fig. 71. Plotsof the complete emission transient caused by a laser excitation pulse. (a) The emission of the as-grown sample before laser annealing; (b) associated with the structural change, a new emission appeared. The irreversibility of this light emission was evidenced with transient (c) taken at the same laser intensity as (a). Because the origin of the observed emission was the thermal emission of the sample, the laser-induced structural change leading to its luminescent structure may be easily understood. Laser irradiation caused the loss of hydrogen from the sample and the consequent reorganization of the particle structure. The increase in the number of Si-Si bonds increased the absorption coefficient of the sample in the visible region. Therefore, the light absorption in the annealed sample was more efficient than in the as-prepared powder. Higher absorption implies more intense heating. As has been explained, the type-A emission from silicon powders was first interpreted in terms of a particular energy level structure and specific excitation dynamics. To explain the supralinear dependence of the emission intensity on laser power in terms of photoluminescence, a multistep-multiphoton excitation process was proposed [236]. This model could satisfactorily explain both the complicated dynamics of the emission and the supralinear dependence of the emission intensity on laser power. Within the framework of this model, the quenching of the emission intensity with gas pressure was simply the result of a similar pressure dependence on the dynamic parameters (lifetime and optical cross section) of each level [237]. With this phenomenological model, all the observed features of the emission could be explained, although its physical origin remained obscure. The first insight into the physical origin of the light emission was provided by the experimental evidence that the effect of the gas on the emission intensity was linked to the energy that its molecules were able to extract from the powder after every collision with the particles [238, 240]. This was made clear by the dependence of the characteristic pressure, P0 in Eq. (23), on different gases [238].

6.2.2. Blackbody Emission In a final paper, it was demonstrated that the emission was simply due to the blackbody emission of the particles [241 ]. The energy absorbed from the laser beam can be dissipated through the surrounding gas by radiation. Under vacuum, energy dissipation by radiation is not efficient enough to avoid the heating of the particles, whereas at higher pressures the energy released by the gas molecules quenches the emission.

140

NANOPARTICLES FROM LOW-PRESSURE, LOW-TEMPERATUREPLASMAS

All the dynamic characteristics of the emission that had been previously explained in terms of multistep-multiphoton excitation dynamics were reinterpreted in this final paper as a consequence of the blackbody emission of these particles. Therefore, a theoretical study of the emission intensity dependence on pressure and laser intensity, and of its dynamic behavior was presented. New correlations were established that both highlighted the predictive power of the theory and permitted the unambiguous identification of a blackbody emission. The most relevant results concerning blackbody emission intensity in nanometric particles can be summarized as follows [241 ]. Consider the energy balance in an isolated particle suspended in a gas that is irradiated by a laser beam. The particle temperature will depend on the balance between the energy absorbed and that dissipated through the gas or by radiation. It will be assumed that there is no thermal conductivity between the particles. The particle is also assumed to be small enough to be at a homogeneous temperature. Therefore, the particle temperature would be governed by the following equation: 4

dTt

- rer 3pc - Jr r 2 QabsIL -- 4Jr r 2 (qR q- qK) 3 -h-7

(24)

where r is the particle radius, p its density, and c the specific heat; Qabs is the absorption efficiency and IL is the laser intensity. Finally, qR and qK are the heat fluxes caused by radiative emission and thermal conduction through the gas, respectively. The radiative emission is given by the Stephan-Boltzmann law:

q R - eirr(T;- T4)

(25)

where rr is the Stephan-Boltzmann constant and 8i is the integrated emissivity of the particle; TR is the radiation temperature around the particle. To find the heat dissipation caused by the gas, qK, we will consider the limiting case where the pressure is so low that the mean free path is greater than the particle size. Then, qK can be calculated approximately by multiplying the number of collisions by the mean energy per molecule in the gas. This procedure gives

1 cv ~8kB P q K - 4~/-ff R

m ,q/~ct(Tp - TG)

(26)

where kB is the Boltzmann constant, m is the molecular mass, TG is the gas temperature, cv is its specific heat at constant volume, and R is the universal constant of gases. The parameter ot is the "accommodation coefficient" that accounts for the fact that after one collision the gas molecules will not be thermalized to the particle temperature (c~ < 1). Once the temperature of the particle has been determined, the radiative emission at any wavelength can be calculated according to Planck's distribution:

8rrhc(hc) Ie(,k) -- e(~,) )5

exp

),kBTp

(27)

where it is assumed that exp(hc/~kBTp) >> 1. A similar model was used to determine the temperature of silicon particles suspended in the plasma [242], where the heating power was delivered by the collisions of ions existing in the plasma. In this case, the suspended particles were clearly independent. It is doubtful, however, whether the particles in the powder are completely independent. In fact, following the usual classification of ceramic raw materials, as the particle size of our powder is well below 1 /zm, the system is colloidal [243]. In such a system, the inertial forces on the particles are insignificant and the surface forces are dominant. This is the case here, given the low density of the powder (10 mg/cm 3 [236]). This value means that the particles occupy only about 1/200th of the powder volume. Consequently, the thermal conductivity of the powder is very small and its contribution to the energy balance is negligible. So, it has not been considered in Eq. (23). Another proof leading to this conclusion comes from

141

COSTA

Wavelength(nm) 2000

0.5

0.8

1000

1.0

1.3

600

1.5

1.8

;3.0

Energy (eV) Fig. 72. Emissionspectra of the silicon powder at two laser intensities.

the dependence of the radiative intensity on the cryostat temperature. From 14 to 300 K, the intensity experiences only a slight increase of a factor of 2. So, the particle temperature at the excitation conditions does not follow the variations of the cold finger to which it is glued, which indicates negligible thermal conduction. The comparison between the experimental results and the prediction of this simple model demonstrated the validity of this explanation of the physical origin of the type-A emission of silicon nanoparticles. To simplify the analysis, it was assumed that T4 , 03

c !, ~ L ~ r r ' __=

~SE~ 514 nm I t 420

I

I I 480

] I

I i 540

t 600

R a m a n shift (cm -1) Fig. 79. Raman spectra of silicon powder measured at different gas pressures. The shift of the TO peak is interpreted as being due to the heating of the powder.

15

I

e---_..__.

I

I .......... I

I

8O0

~10 E 0

600 o~"

v

0 h.

400

0

(8)

where Cp is the specific heat of the particles and ~.p is the heat conductivity of the particles. The boundary conditions describing the center and the surface of the particles are as follows"

OVp

(9)

Ox (0, t) -- 0

OVp

~p ---~-(Rp, t) = O~h(Tf -- Tp(Rp, t))

(10)

where Tp(x, 0) -- Tp0, and the coefficient of heat transfer, Oth, can be determined by the Ranz-Marshall semiempirical equation [60]" Nu - o~hdp __ 2 ~f

+0.6Rel/2pr 1/3

Pr --

(11)

Cfr}f ~f

It is thought that during the HVOF spraying process the surface temperature of a homogeneous particle can become as high as the melting temperature of that material [50]. Hence, subsequent propagation of the melting front toward the particle center is controlled by the Stefan heat balance condition [61 ]. Inserting the effective specific heat into the heat conductivity Eq. (8), Eq. (8) then becomes

OTp 1 0 ( OTp~ ppCpql(Tp) Ot -- x n Ox xn~'P-ff-f-xJ

0 ~ x ~ Rp

qJp (Tp)-- 1 + qPcp-l(1- k)-I (Tk - 7])-1( Tk-Tp T1T1)(2-k)/(1-k)

9 (Tp) -- 1

Tp>T1

t> 0

(12)

Ts + Mo>

800

,

0

10

. . . .

,

20

. . . .

,

30

. . . .

,

. . . .

40

,

50

. . . .

,

60

. . . .

,

70

. . . .

,

80

. . . .

,

90

. . . .

100

A t o m i c Percent M o l y b d e n u m

Fig. 14. The binary Mo-Cu phase diagram.

nary compound Mo6Se8, which contains Mo6 octahedra capped with selenium atoms, is not observed to form directly from a multilayer reactant. Mo6Se8 was only formed as the product of a reaction between MoSe2 and either Mo3Se or Mo. Schneidmiller et al. suggested that the nucleation behavior of this system reflects the complexity of the crystal structures, proposing the nucleation of Mo3Se involves the assembly of a relatively small number of atoms relative to that required to nucleate Mo6Se8. The second situation in which multilayer reactants can provide access to new compounds is in binary phase diagrams in which the elements have little, if any, mutual solubility in the liquid or solid state. An example of such a situation is the molybdenumcopper phase diagram shown in Figure 14. There are no binary compounds in this system. Investigating Mo-Cu multilayer reactants, Fister observed a reversible phase transformation (shown in Fig. 15) at 530~ in a DSC experiment. This behavior was observed in multilayer reactants with bilayer thicknesses less than 40 ,~ and copper-rich compositions. Presumably, the reaction that results in the formation of this compound is driven by the increased energy of the system as a result of the high density of unstable interfaces. The system eliminates this interfacial energy through interdiffusion of the layers. The area of the reversible transition of the DSC decreased with each additional cycle through the transition, indicating that the amount of the substance causing the phase transition decreased with each cycle. A diffraction study as a function of annealing temperature showed the growth and subsequent disappearance of a diffraction maximum midway between the 111 diffraction maximum of Cu and the 110 diffraction maximum of Mo. Fister proposed that the reversible transition was an order-disorder transition of a new binary compound [55]. However, further studies are needed to determine the structure of this new phase and confirm this hypothesis. Multilayer reactants also provide access to new binary compounds where the new compound is thermodynamically unstable with respect to known compounds. In this situation, the new binary compound can only be prepared if one can avoid the formation of any other binary compounds. Annealing a modulated reactant with a bilayer thickness less than the critical thickness results in the formation of a homogenous amorphous alloy. The

269

JOHNSON ET AL.

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compound formed from the amorphous alloy depends on the relative nucleation energies of potential compounds, not on their absolute thermodynamic stability. As discussed earlier, the composition of the amorphous intermediate can be used to control the relative nucleation energies. The formation of the binary skutterudite, FeSb3, is an example of this situation. This binary phase system has recently been investigated by Richter and Ipser [56], who showed that, at equilibrium, a sample containing 25 at% iron and 75 at% antimony consists of a mixture of FeSb2 and antimony below 624 ~ (see Fig. 16). Binary multilayer reactants of this composition with bilayer thicknesses less than 40 ]~, however, evolve into a homogeneous amorphous alloy below 100 ~ Annealing these amorphous alloys above 150 ~ results in the nucleation and growth of a new compound, FeSb3 [57]. Further annealing of FeSb3 above 350 ~ results in the exothermic decomposition of this new compound. The exothermic decomposition implies that FeSb3 is thermodynamically unstable with respect to a mixture of FeSb2 and Sb. If the bilayer thickness is greater than 40 A, FeSb2 nucleates at the reacting interfaces. If the bilayer thickness is less than 40 ]k and the composition of the initial multilayer is more iron rich than a 3:1 ratio of antimony to iron, FeSb2 is observed to nucleate from the amorphous intermediate. The targeted compound, FeSb3, can only be prepared by avoiding the more stable binary compounds.

3.4. Application of Multilayer Reactants to the Synthesis of New Ternary Compounds In the synthesis of temary and higher-order compounds, the need to avoid stable binary compounds as reaction intermediates is well recognized. As stated by Brewer many years ago, there are a multitude of undiscovered compounds that are thermodynamically stable with respect to the elements yet metastable with respect to a mixture of known binary compounds [58]. Discovering synthetic conditions and procedures to make these unknown compounds is an ongoing challenge.

270

KINETIC CONTROL OF INORGANIC SOLID-STATE REACTIONS

Fig. 16. The binary Fe-Sb phase diagram.

Fig. 17. A schematic of the expected reaction pathways of ternary reactants with different layer sequences. In a binary A-B multilayer,the phase AB is assumedto form at the reacting interfaces.

Multilayer reactants offer some significant advantages for the preparation of ternary and higher-order compounds by providing access to an amorphous reaction intermediate. A new experimental parameter, the order of the elemental layers within the repeating unit, can be used to control the reaction pathway. As an example, consider a ternary system ABC in which the elements A and B react to form the compound AB at the interfaces of binary A-B multilayers. In a ternary multilayer reactant with layer order ABC within the repeating unit, one would expect the compound AB to form at the reacting A-B interfaces. In a ternary multilayer with layer order ACBC within the repeating unit, there are no A-B interfaces where the binary compound AB can form. These various reaction sequences are illustrated in Figure 17. The different diffusion rates of the elements through the different layers also create opportunities to control the reaction sequence by adjusting diffusion lengths to control time and/or the sequence of layer mixing. For example, consider the ternary system ABC in which A diffuses into B 10 times faster than it diffuses into C. A ternary multilayer reactant with a simple ABC sequence in the repeating unit on annealing will form a mixed AB layer that will then react with the C layer. By preparing a multilayer reactant with a more complex repeating unit, for example ACBCBC, one can force C and B to interdiffuse before A can react with B. This ability to design the initial structure of the multilayer reactant provides several options to select and control reaction intermediates. One consequence of the differences in relative diffusion rates of elements through different layers is that the "critical thicknesses" are not transferable from the binary systems. The different diffusion

271

JOHNSON ET AL.

rates can be used to mix sequentially the reacting layers or force the layers to interdiffuse simultaneously, depending on the design of the initial reactant structure. The ternary metal-molybdenum-selenium system provides a convenient platform to illustrate the principles discussed previously. In a study of the binary Mo-Se system, the thermodynamically stable binary compound Mo6Se8 was not observed to nucleate from binary multilayer reactants, regardless of the repeat spacing or composition [59]. Schneidmiller et al. explored the evolution of temary reactants, M-Mo-Se, as a function of concentration and identity of the M atom. When the M atom was nickel, a slow diffusing species relative to the rate of Mo and Se, the binary compound MoSe2 was observed to nucleate interfacially at the Mo-Se interfaces. When the M constituent was a fast diffusing species relative to that of Mo and Se, for example, Zn, In, Sn, or Cu, a change in reaction pathway was observed as a function of M atom concentration. When M was below a critical concentration, MoSe2 was observed to nucleate interfacially. When M was above this critical concentration, the multilayer was observed to interdiffuse and form an intermixed amorphous intermediate. This is summarized in Figure 18. The low-angle diffraction pattem was observed to decay as a function of annealing temperature until the sample was no longer modulated in composition. The authors have proposed that this is due to the initial interdiffusion of the M and Se layers of the multilayer reactant to form an intermixed M-Se amorphous alloy, which then interdiffuses with the Mo layers. The interfacial nucleation of MoSe2 is inhibited by the large concentration of the M cation at the reacting interface. Further annealing of the resulting amorphous alloys in these systems leads to crystallization of a number of different compounds, depending on the ternary metal. When M was tin, a layered dichalcogenide compound was formed. When M was indium, ternary molybdenum selenides containing larger clusters than the Mo6Se8 phase were observed. When M was copper, the desired compound, CuxMo6Se8, exothermically nucleated at 250 ~ [60]. Further studies are required to understand the factors that control the nucleation behavior in these systems. We rationalize the difficulty in nucleating the desired cluster compounds as resulting from the large difference between the structure of the amorphous state and

Mo

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Cu

Fig. 18. A summary of the reaction behavior observed in the ternary Cu-Mo-Se system. For samples below 13% Cu, the binary phase MoSe2 was observed to nucleate interfacially, denoted by filled triangles and circles. Abovethis composition, the ternaryreactant was observedto form an amorphousintermediate, denotedby the empty triangles and circles. The samplesdenoted by triangles had an exothermin the DSC data corresponding to crystallization, whereas samples denoted by circles did not have an exotherm in their DSC scans.

272

KINETIC CONTROL OF INORGANIC SOLID-STATEREACTIONS

that of the desired cluster compounds. Although this idea will be explored in future experiments, the ternary amorphous state is clearly accessible via ternary elementally modulated reactants. More straightforward nucleation tendencies were found in the ternary iron-antimony systems. The ternary antimonides, known as "filled" skutterudites [61], with formulas MxM~Sb12 where M is a lanthanide and M t is either Fe or Co, have been recently touted as potentially useful thermoelectric materials [62]. The antimonides with this filled structure are promising thermoelectric materials because of an unusual structural property (see Fig. 19). They can be formed with cations that are significantly smaller than their interstitial site. As a result, these ions have unusually large thermal vibration amplitudes and, therefore, are strong phonon scatterers. The conduction, however, occurs in the transition metal and antimony framework and is not effected by the motion of the cations. The result is a suppression of the phonon thermal conductivity without adverse affects on the electrical properties [63]. The weak bonding of the ternary metal in the "filled" skutterudites makes many of the potential ternary skutterudites containing small ternary metal atoms thermodynamically unstable with respect to disproportionation to a mix of binary compounds. The size mismatches cause a reduction in the Madelung energy, which is important for the stability of the crystalline structure. Consequently, only the early rare-earth skutterudites from LaFe4Sbl2 to NdFe4Sbl2 have been prepared via traditional synthesis techniques. The basic structure of the skutterudites suggests that their nucleation from the amorphous state should be relatively straightforward. It consists of iron atoms octahedrally coordinated by antimony. Adjacent octahedra share comers to prepare a rather open structure, as shown in Figure 19. The ternary metal atom resides in the asymmetric cavities in this structure. An amorphous alloy with a 3:1 ratio of antimony to iron is likely to contain some of these structural features, aiding the formation of the critical nuclei of the skutterudite phase. The DSC of a La-Sb-Fe multilayer reactant, shown in Figure 20, contains two sharp exotherms. Low-angle X-ray diffraction indicates that the multilayer interdiffused before the first sharp exotherm and high-angle diffraction indicates that the sample is amorphous. Diffraction data collected after the first exotherm are consistent with the formation of a

Fig. 19. The filled skutterudite structure. The ternary M cation sits in a large and asymmetricsite.

273

JOHNSON ET AL.

Fig. 20. Calorimetrydata of the La-Sb-Fe ternary reactant. Two sharp exothermsare observed.

Fig. 21. The shaded elements have been successfully inserted into the ternary site of FeSb3, which has the skutterudite structure.

cubic skutterudite and a small amount of an impurity phase. After the second exotherm, the original cubic phase has decomposed into a mix of binary compounds and another cubic skutterudite with a smaller unit cell. The lattice parameters of the low-temperature skutterudite are larger than those previously reported. The lattice parameters of the hightemperature skutterudite agree with those of skutterudites prepared using conventional high-temperature synthesis. We suspect the difference between these two compounds is a rotation or tilt of the iron octahedra [57, 64]. Ternary M - S b - F e multilayer reactants have been prepared with approximately 20 different temary metals, as shown in Figure 21 [57, 64, 65]. All interdiffuse to the amorphous state and nucleate the filled skutterudite structure at low temperature. Rare-earth-Sb-Fe multilayer reactants nucleate the "filled" skutterudite structure around 150~ The lowtemperature skutterudite structure decomposes exothermically at approximately 450 ~ for all of the rare-earth cations. The heavier, later rare earths all decompose to a mixture of binary compounds. The early rare earths through gadolinium all show at least traces of a

274

KINETIC CONTROL OF INORGANIC SOLID-STATE REACTIONS

small unit-celled skutterudite on decomposition of the low-temperature phase. Ba, Y, and Hf containing multilayers also interdiffuse and nucleate the filled skutterudite structure. Posttransition metal (A1, Ga, In, Zn, Bi, Sn, and Pb)-containing multilayers form the filled skutterudite structure, but decompose at lower temperatures than observed for the rare earths. In all of the ternary systems studied, the multilayer reactant was observed to interdiffuse to an amorphous state below 150 ~ The nucleation temperature of the skutterudite phase was very low in all of the systems studied, varying from 120 to 250 ~ depending on the ternary cation. This suggests that all of the amorphous intermediates must be structurally similar to each other and contain the essential structural building blocks of the skutterudite structure. The ternary skutterudite system demonstrates the importance of being able to vary the diffusion length in the multilayer reactant. For multilayers with repeating trilayers less than 20 ,~ thick, the formation exotherm of the skutterudite compound is sharp. Doubling this thickness to 40 ~ broadens and adds considerable structure to the exotherm as shown in Figure 22. The compound nucleated is still the filled skutterudite. Tripling the trilayer thickness results in the interfacial nucleation of the binary compound FeSb2. Because a mixture of binary compounds is more stable than the ternary skutterudite, the formation of FeSb2 prevents the formation of the skutterudite. This highlights the importance of controlling reaction intermediates. Multilayer reactants provide a simple and systematic way to vary the diffusion distances to form an amorphous intermediate. The composition of the amorphous phase can then be used to control the subsequent nucleation. The design of the initial reactant avoids binary intermediates and permits the preparation of undiscovered compounds that are thermodynamically stable with respect to the elements yet metastable with respect to a mixture of known binary compounds.

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275

JOHNSON ET AL.

4. C R Y S T A L L I N E S U P E R L A T T I C E S F R O M M U L T I L A Y E R REACTANTS: CONTROL OF INTERFACIAL NUCLEATION

4.1. Background The key to the preparation of metastable compounds using multilayer reactants is the control of composition on an angstrom length scale. During the course of the preceding studies, we pondered what would happen to a multilayer reactant with a long (50 to several hundred angstroms) compositional period. There are at least three reaction pathways that would lead to a crystalline supeflattice product as shown in Figure 23. In the pathway to the lower left,

Fig. 23. A schematic of three proposed reaction pathways in which a multilayer reactant with a modulated composition could evolve into a crystalline supeflattice. The pathway to the upper right interfacially nucleates both components of the final superlattice at the reacting interfaces. The pathway to the lower left shows the initial reactant interdiffusion that forms an amorphous intermediate while still maintaining a long length scale composition modulation. The middle pathway is a combination of these two extremes.

276

KINETIC CONTROL OF INORGANIC SOLID-STATE REACTIONS

the initial reactant interdiffuses the elemental layers but maintains the long-range compositional period. Nucleation of this amorphous intermediate results in a crystalline product with the built-in compositional period. In the reaction pathway shown to the upper left, the initial reactant interfacially nucleates binary compounds at the reacting interfaces. Annealing at low temperature leads to the formation of the crystalline supeflattice because insufficient time or energy is available to interdiffuse the components. The center pathway is a combination of these two extremes, with one compound interfacially nucleating while the other interdiffuses. Low-temperature annealing again may produce a crystalline supeflattice. The ability to fabricate crystalline superlattices with controlled superstructure is a prime example of fundamental research leading to new technology. Several synthetic approaches based on epitaxial growth, including molecular beam epitaxy (MBE), chemical vapor deposition, and liquid phase epitaxy, have been developed to prepare these materials. In these techniques, the deposition rates and substrate temperature are carefully controlled such that epitaxial growth of the growing sample occurs in a layer-by-layer manner. MBE has emerged as the growth technique with the most control, able to prepare samples with atomic-scale control of composition and nearly ideal interfaces [66]. These synthetic advances have led to new physical phenomena, including the quantum Hall effect [67] and the fractional quantum Hall effect [68], as well as new high-performance devices through modulation doping [69] and band gap engineering [70]. Although most of the early efforts in MBE focused on semiconducting materials, more recently researchers have explored other systems in an effort to manipulate properties and discover new phenomena. In the early 1980s, researchers prepared crystalline supeflattices containing two metals with large differences in their lattice parameters and different crystal structures [71 ]. More recently, supeflattice structures containing high-temperature superconductor components such as SrCuO2-BaCuO2 and BaCuO2-CaCuO2 have been prepared using pulsed laser deposition onto heated substrates [72, 73]. Another recent synthetic development is called van der Waals epitaxy (VDWE). This technique is used to grow structures containing van der Waals gaps, resulting in interfaces with no dangling bonds. VDWE growth has produced high-quality epitaxial films on substrates that have both large lattice mismatches and different crystal structures than that of the deposited films [74, 75]. In spite of this success, epitaxial-based techniques have several drawbacks for the exploratory synthesis of new materials. Determining epitaxial growth conditions for new materials can be a daunting task, especially when the material being grown contains elements with a wide range of vapor pressures, surface mobilities, and surface residency times. This challenge increases as the number of elemental components in a material increases. If deposition conditions for two compounds are incompatible, it is difficult to toggle between deposition of these components in building the desired superstructure. The preparation of crystalline supeflattices using modulated reactants, if successful, would permit a rapid survey of new systems for unusual properties, providing targets for future MBE studies. Noh et al. [76] decided to initiate their studies using transition metal dichalcogenides. The dichalcogenides were chosen because they were known to nucleate interfacially and grow with the 001 direction perpendicular to the interfaces. The basic structure of the layered transition metal dichalcogenides contain hexagonal sheets of transition metal atoms with each sheet sandwiched between two hexagonal sheets of chalcogen. The transition metal bonds covalently to the six nearest-neighbor chalcogen atoms in the adjacent chalcogen layers, forming a tightly bound XMX trilayer sandwich. The XMX sandwiches are coupled together by weak van der Waals bonding. This two-dimensional structure results in anisotropy in many physical properties. The electrical properties of these layered materials vary from insulators to true metals, depending on the coordination of the metal atom and the degree of filling of the bands. The strong dependence of physical properties on stoichiometry results from excess transition metal atoms donating additional electrons to the nonbonding d bands [77].

277

JOHNSON ET AL.

4.2. The Growth of Crystalline Superlattices on Annealing Multilayer Reactants To explore the feasibility of preparing supedattices using interfacial nucleation and growth, a multilayer reactant with a composition modulation designed to yield three TiSe2 and three NbSe2 layers in the unit cell of the final superlattice was prepared [78]. The structure of the initial multilayer reactant is shown in Figure 24. The reactant shown in Figure 24 was annealed in a tube furnace in a nitrogen atmosphere. The evolution of its structure as a function of annealing time and temperature was studied using X-ray diffraction. Figure 25 shows the changes in the low-angle

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278

KINETIC CONTROL OF INORGANIC SOLID-STATEREACTIONS

diffraction pattern as the sample is consecutively annealed for 8 h at each of the indicated temperatures. The Bragg diffraction maxima in the low-angle diffraction patterns confirm the compositionally modulated nature of the as-deposited sample and clearly indicate that the modulated structure persists throughout the annealing process. There is little change in the intensity of the low-order superlattice diffraction maxima during annealing below 220~ At higher annealing temperatures, the fourth-order Bragg diffraction peak increases with time, indicating that the sample is developing sharper concentration gradients. In addition to developing sharper concentration gradients, the sample becomes smoother, as indicated by the increase in the intensity, regularity, and persistence with increasing angle of the subsidiary maxima. The subsidiary maxima result from a combination of incomplete destructive interference from the layers as well as interference between the front and back surface of the multilayer. The persistence of the subsidiary maxima is correlated to the roughness of the multilayer. Further evidence for the smoothing of the layers comes from rocking angle scans on the low-angle diffraction maxima. As shown in Figure 26, the low-angle rocking curve about the 002 Bragg maxima consists of a sharp specular peak on a broad nonspecular background. The intensity of this diffuse background depends only on the magnitude of the rms roughness of the interfaces. During low-temperature annealing, the intensity of this diffuse scattering decreases. This is shown in Figure 27, which plots the integrated area of the nonspecular scattering as a function of annealing temperature. The decrease in the roughness of the interfaces is probably related to the elimination of voids and defects in the structure, as the sample contracts by 3% during annealing. High-angle diffraction data collected during the annealing are shown in Figure 28. The diffraction patterns obtained on the as-deposited sample indicate that dichalcogenide nuclei

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279

JOHNSON ET AL.

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superlattice (TiSe2)6(NbSe2)6 based on the observed X-ray diffraction pattern is shown in Figure 34. The basic structure is as designed, containing six unit cells of each of the dichalcogenide components. The refined structure revealed that there are four niobium diselenide layers with little titanium content and one layer next to the titanium layers that is approximately 40% titanium and 60% niobium. The titanium diselenide layers all contain approximately 7% niobium substituted for titanium. The van der Waals gaps in both the TiSe2 and NbSe2 blocks are comparable to those of the pure dichalcogenides. The van der Waals gaps on either side of the 40% titanium and 60% niobium mixed layers are slightly larger because of the a-axis mismatch between the niobium and the titanium dichalcogenides [76]. The diffraction pattern normal to the surface contains no information about the bonding in the layers resulting from preferred orientation. To obtain information on the structure along the planes, a number of experiments were performed. To determine if the superlattice samples were crystalline in the plane and aligned between planes, off-specular diffraction data were collected. Figure 35 contains the diffraction map obtained on a (TiSez)12(NbSe2)9 superlattice. In addition to the 001 Bragg diffraction maxima, the

285

JOHNSON ET AL.

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complete family of 101 diffraction planes are observed, implying that this superlattice is crystallographically ordered in the ab plane. Pole figure measurements of the 101 diffraction planes show that these planes are completely isotropic. This suggests that the samples are composed of microcrystalline domains that are highly oriented along the c axis, but each domain has a random orientation in the ab plane. To confirm this hypothesis, Noh et al. [80] collected scanning electron microscopy (SEM) images of the (TiSe2)12(NbSe2)9 superlattice. The SEM image of this sample formed using secondary electrons, shown in Figure 36, reveals that most areas of the sample surface are very fiat without any topographic structure. Cracks are observed on the annealed samples that are not observed on the as-deposited samples. The authors suggested that the cracks result from shrinkage of the sample during annealing, leading to stress and fracture during cooling. The backscattered image of this sample, which is much more sensitive to the average atomic number, is shown in Figure 37. The significant contrast observed in this image suggests that the mean atomic number varies across domains of the sample. To confirm this result, electron microprobe data were collected. The light areas had an average composition of Nbo.88Ti].o2Se4, while the dark areas had average compositions of Nbo.93Til.03Se4 [80].

4.5. Metastability of the Crystalline Superlattices The interdiffused layers observed in the crystal structure at the interface between the NbSe2 and TiSe2 blocks suggest that the crystalline superlattices are only kinetically trapped. To test the stability of these compounds, a (TiSe2)6(NbSe2)6 superlattice was annealed at elevated temperatures and diffraction data were collected as a function of annealing, as shown in Figure 38. The data in Figure 38 show that, as the annealing temperature is increased, the superlattice diffraction pattern decays as a result of the intermixing of the TiSe2 and NbSe2 layers. The decay of the superlattice pattern is not that expected from a simple picture. If Fick's law for diffusion for a composition-independent diffusion coefficient holds, the nth-order diffraction peaks should decay n 2 times faster than the first-order diffraction peak as the composition profile approaches a sinusoidal modulation. The data in Figure 38 indicate a different picture, however, because both low- and high-order diffraction peaks decay at about the same rates. This suggests that the square-wave composition profile in the initial structure remains throughout intermixing. One explanation of these data is that

286

KINETIC CONTROL OF INORGANIC SOLID-STATEREACTIONS

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the electron density difference between the two regions decreases with annealing, as shown in Figure 39. The composition profile within each of these regions remains flat, however, because the rate limiting step in mixing is the motion of the transition metals across the boundary between them.

4.6. Preparation of Superlattices Containing Other Component Phases Using Multilayer Reactants To probe the generality of the reaction pathway observed for the evolution of multilayer reactants containing Nb/Seffi/Se layers into (TiSe2)m(NbSe2)n superlattices, several additional systems have been investigated. These are briefly discussed next.

287

JOHNSON ET AL.

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Fig. 36. SEM image of the [NbSe219[TiSe2112 superlattice formed using secondary electrons.

4.6.1. (TiSe2)6(TaSe2)6 Superlattice Formation from Ti/Se/Ta/Se Multilayer Reactants To determine whether it is possible to prepare other dichalcogenide superlattices using multilayer reactants, a Ti/Se/Ta/Se multilayer reactant was prepared. The composition of each

288

KINETIC C O N T R O L OF I N O R G A N I C SOLID-STATE R E A C T I O N S

Fig. 37.

SEM image of the [NbSe2]9[TiSe2]12 superlattice formed using backscattered electrons.

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289

JOHNSON ET AL.

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Distance Fig. 39. A schematic of the proposed interdiffusion of the [NbSe2]6[TiSe2]6 superlattice as it forms a uniform solid solution of composition NbTiSe4. The rate limiting step is the transfer of the transition metal cations across the boundary region between the NbSe2 and TiSe2 blocks.

'

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Fig. 40. The diffraction patterns of the [TaSe2]6[TiSe2]6 superlattice obtained by annealing a multilayer reactant. The numbers above the diffraction maxima correspond to the 001 index of the superlattice unit cell.

T i - S e and T a - S e period was chosen to be that of the desired dichalcogenide c o m p o u n d and the thicknesses of each elemental layer in the initial multilayer were chosen to form integral multiples of the dichalcogenide unit cells after annealing. Because the chemical properties of tantalum are similar to that of niobium, a similar superlattice formation was expected. The X-ray diffraction pattern collected on this sample after annealing is shown in Figure 40. The data contain all of the (00/) diffraction m a x i m a expected from the designed

290

KINETIC CONTROL OF INORGANIC SOLID-STATE REACTIONS

Fig. 41. A schematicof the initial multilayerreactant used to form the Wn[WSe2]8 superlattice.

repeat unit containing six TiSe2 layers and six TaSe2 layers. This result suggests that multilayer reactants can be designed to prepare superlattices with most of the dichalcogenide compounds as components.

4.6.2. W/WSe2 Superlattice Formation from W/Se/W/Se/W/Se Multilayer Reactants In the previous experiments, two layered transition metal dichalcogenide species were used as the components of the superlattice. To test the extension of the observed reaction mechanism to systems without both components having van der Waals gaps, the tungstentungsten diselenide system was explored. Tungsten is a hard metal with a body-centered cubic structure, whereas tungsten diselenide is a semiconductor with a layered structure of hexagonal symmetry. The lack of epitaxial relationships and structural similarities between the components of the proposed superlattice made it doubtful that long-range structural coherence would develop across many layers of the material. Previous research in a binary tungsten-selenium system revealed that WSe2 nucleated and grew at the internal W-Se interfaces. This information was used to prepare an initial reactant designed to evolve into a tungsten and tungsten diselenide superlattice. This reactant consisted of a thick tungsten and several thin tungsten and selenium layers in the repeating unit, as shown in Figure 41. The sample was cut into several pieces and each piece was annealed under different annealing procedures and examined using X-ray diffraction. The best result was observed when the sample was annealed at 250 ~ for more than 12 h at which point WSe2 nucleated. After the 600 ~ annealing, there was a significant increase in the intensity and a decrease in the line widths of both the tungsten and the tungsten diselenide high-angle diffraction maxima, suggesting crystal growth perpendicular to the substrate. Figure 42 shows the diffraction pattern collected on this sample after being annealed at 750 ~ for 23 h. The appearance of subsidiary peaks around the (002) diffraction peak of the tungsten diselenide near 13 ~ and the (110) diffraction maxima of the tungsten near 40 ~ clearly indicates the formation of a superlattice. The rocking curve data collected on these two Bragg diffraction peaks suggested that the alternating layers of tungsten and tungsten diselenide were crystallized preferentially: The (001) Miller planes of the dichalcogenide layer and the (110) Miller plane of the tungsten layer are parallel to the interfaces [81 ].

291

JOHNSON ET AL.

-

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Fig. 42. The diffraction patterns of the Wn[WSe2]8 superlattice obtained by annealing a multilayer reactant. The subsidiarydiffraction maximaresulting from the supedattice unit cell are apparent as shoulders of the 00l peak of the diselenide and the 110 peak of the tungsten.

5. Conclusions 5.1. Controlling Nucleation of Amorphous Intermediates Prepared Using Multilayer Reactants The ability to design the structure of multilayer reactants provides access to amorphous intermediates by avoiding interfacial nucleation of binary compounds. Multilayer reactants below a critical layer thickness interdiffuse, forming metastable amorphous reaction intermediates. In ternary systems, the order of the deposited layers and the ability to control the diffusion distances in the initial reactant provide additional parameters to control the reaction pathway. The composition of the amorphous intermediate controls the relative activation energies required to nucleate different crystalline compounds. A major challenge remains, however, in developing further techniques to control nucleation. The goal of these studies should be to develop control of the structure of the nucleated compound. Several techniques have been suggested as potential ways to achieve this control. The amorphous intermediate could be "seeded" with crystallites of the desired structure, templating the crystallization of the amorphous intermediate. The template for this seeding could be the substrate or a region within the initial multilayer having the composition of the desired seed compound. A second goal is to develop techniques to control the nucleation density. Rapid thermal annealing of the wafer to high temperatures for a short period of time followed by lowtemperature annealing might be an avenue to control nucleation density by the period of the high-temperature anneal. A second approach would be to prepare an isolated region on a wafer that is connected to the rest of the wafer by only a long and thin path. Nucleation would occur on one side of the path followed by crystal growth through the thin path. This would result in a single crystal region as only one crystallite would have the correct orientation to grow through the path. A third area of exploration is the use of other deposition techniques as well as codeposition for preparing amorphous reaction intermediates. Codeposition may be one option for preparing amorphous alloys in systems that interfacially nucleate binary compounds easily. A difficulty in this area will be the characterization of the amorphous reactant produced.

292

KINETIC CONTROL OF INORGANIC SOLID-STATE REACTIONS

Solid-state nuclear magnetic resonance (NMR) might be a powerful companion to X-ray diffraction and transmission electron microscopy for determining both the type and the frequency of local bonding arrangements within the amorphous precursors. Understanding the relationship between the structure of the amorphous intermediate and the activation energies for nucleating various compounds would add tremendous insight into the challenge of controlling nucleation.

5.2. Superlattice Formation from Multilayer Reactants The results published on the formation of crystalline superlattices from multilayer reactants suggests that the reacting interfaces control the nucleation process and the identity of the nucleating compounds. The "first phase rule" developed by Walser and Ben6 is useful as a guide to predict the compounds that will nucleate. The initial structure of the superlattice reactant controls the subsequent kinetics of the solid-state reactions. In many respects, the use of the structure of the initial multilayer reactant to guide the subsequent evolution of products is analogous to the use of "protecting groups" as diffusion barriers in molecular chemistry. Although the results to date clearly demonstrate the ability to prepare crystalline superlattices, further experiments are necessary to demonstrate that the properties of the extended compounds formed can be controlled by manipulating the superlattice structure. Work toward this goal is underway.

References 1. E J. DiSalvo, Science 247, 649 (1990). 2. H. Schmalzried, "Solid State Reactions," Vol. 12. Verlag Chemie, Deerfield Beach, FL, 1981. 3. J.D. Corbett, in "Solid State Chemistry Techniques" (A. K. Cheetham and P. Day, eds.), pp. 1-38. Clarendon Press, Oxford, UK, 1987. 4. H. Sch~fer, Angew. Chem.,Int. Ed. Engl. 10, 43 (1971). 5. G.M. Kanatzidis, Curr. Opin. Solid State Mater. Sci. 2, 139 (1996). 6. J. Rouxel, M. Tournmoux, and R. E. Brec, Mater. Sci. Forum 152-153 (1994). 7. R. Schollhorn, Angew. Chem., Int. Ed. Engl. 35, 2338 (1996). 8. J. DuMond and J. P. Youtz, J. Appl. Phys. 11,357 (1940). 9. L.A. Greer, Curr. Opin. Solid State Mater. Sci. 2, 300 (1997). 10. A. L. Greer and E Spaepen, in "Synthetic Modulated Structures" (L. C. Chang and B. C. Giessen, eds.), pp. 419-486. Academic Press, New York, 1985. 11. T. Novet, Ph.D. Thesis, University of Oregon, 1993. 12. T. Ishikawa, A. Iida, and T. Matsushita, Nucl. Instrum. Methods Phys. Res., Sect. A 246, 348 (1986). 13. D.L. Rosen, D. Brown, J. Gilfrich, and P. Burkhalter, J. Appl. Crystallogr. 21,136 (1988). 14. S.K. Sinha, E. B. Sirota, S. Garoff, and H. B. Stanley, Phys. Rev. B 38, 2297 (1988). 15. S.R. Andrews and R. A. Cowley, J. Phys. C 18, 6427 (1985). 16. D.G. Stearns, J. Appl. Phys. 65,491 (1989). 17. J.M. Elson, J. P. Rahn, and J. M. Bennett, Appl. Opt. 19, 669 (1980). 18. C.K. Carniglia, Opt. Eng. 18, 104 (1979). 19. D.E. Savage, J. Kleiner, N. Schimke, Y.-H. Phang, T. Jankowski, J. Jacobs, R. Kariotis, and M. G. Lagally, J. AppL Phys. 69, 1411 (1991). 20. W. Weber and B. Lengeler, Phys. Rev. B 46, 7953 (1992). 21. E Nava, P. A. Psaras, H. Takai, and K. N. Tu, J. Appl. Phys. 59, 2429 (1986). 22. P. Gas, E M. d'Heurle, E K. LeGoues, and S. J. La Placa, J. Appl. Phys. 59, 3458 (1986). 23. B. Coulman and H. Chen, J. Appl. Phys. 59, 3467 (1986). 24. C. Canali, E Catellani, G. Ottaviani, and M. Prudenziati, Appl. Phys. Lett. 33, 187 (1978). 25. C. Canali, G. Majni, G. Ottaviani, and G. Celotti, J. Appl. Phys. 50, 255 (1979). 26. R. W. Ben6, AppL Phys. Lett. 41,529 (1982). 27. R.M. Walser and R. W. Ben6, AppL Phys. Lett. 28, 624 (1976). 28. R. Sinclair and T. J. Konno, J. Magn. Magn. Mater. 126, 108 (1993). 29. K. Holloway and R. Sinclair, J. AppL Phys. 61, 1359 (1987). 30. K.L. Holloway, Ph.D. Thesis, Stanford University, 1989. 31. K. Holloway, K. B. Do, and R. Sinclair, J. Appl. Phys. 65,474 (1989). 32. R. Benedictus, A. Bottger, and E. J. Mittemeijer, Phys. Rev. B 54, 9109 (1996).

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33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43. 44. 45. 46. 47. 48. 49. 50. 51. 52. 53. 54. 55. 56. 57. 58. 59. 60. 61. 62. 63. 64. 65. 66. 67. 68. 69. 70. 71. 72. 73. 74.

75. 76. 77. 78. 79. 80. 81.

R. B. Schwarz and J. B. Rubin, J. Alloys Compd. 194, 189 (1993). R. B. Schwarz and W. L. Johnson, Phys. Rev. Lett. 51,415 (1983). R. B. Schwarz, K. L. Wong, and W. L. Johnson, J. Non-Cryst. Solids 61/62, 129 (1984). M. Van Rossum, M. A. Nicolet, and W. L. Johnson, Phys. Rev. B 29, 5498 (1984). B. M. Clemens, R. B. Schwarz, and W. L. Johnson, J. Non-Cryst. Solids 61/62, 817 (1984). B. M. Clemens, Phys. Rev. B 33, 7615 (1986). H. Schroder, K. Samwer, and U. Koster, Phys. Rev. Lett. 54, 197 (1985). R. W. Bene, J. Appl. Phys. 61, 1826 (1987). B. M. Clemens and R. Sinclair, Mater. Res. Soc. Bull 19 (1990). E. J. Cotts, W. J. Meng, and W. L. Johnson, Phys. Rev. Lett. 57, 2295 (1986). H. Beck and H.-J. Gtintherodt, in "Glassy Metals I: Ionic Structure, Electronic Transport, and Crystallization" (H. Beck and H.-J. Gtintherodt, eds.), Vol. 46, pp. 1-17. Springer-Verlag, New York, 1981. J. H. Brophy, R. M. Rose, and J. Wulff, "The Structure and Properties of Materials," Vol. 2. 1964. H. E. Kissinger, Anal Chem. 29, 1702 (1957). J. H. Brophy, R. M. Rose, and J. Wulff, "Thermodynamics of Structure," Vol. 2. Wiley, New York, 1964. H. J. Highmore, A. L. Greer, J. A. Leake, and J. E. Evetts, Mater Lett. 6, 40 (1988). U. G6sele and K. N. Tu, J. Appl. Phys. 66, 2619 (1989). W. J. Meng, C. W. Nieh, and W. L. Johnson, Appl. Phys. Lett. 51, 1693 (1987). L. Fister and D. C. Johnson, J. Am. Chem. Soc. 114, 4639 (1992). M. Fukuto, J. Anderson, M. D. Hornbostel, D. C. Johnson, H. Haung, and S. D. Kevan, J. Alloys Compd. 248, 59 (1997). C. A. Grant and D. C. Johnson, Chem. Mater. 6, 1067 (1994). T. Novet and D. C. Johnson, J. Am. Chem. Soc. 113, 3398 (1991). O. Oyelaran, T. Novet, C. D. Johnson, and D. C. Johnson, J. Am. Chem. Soc. 118, 2422 (1996). L. M. Fister, Ph.D. Thesis, University of Oregon, 1993. K. W. Richter and H. Ipser, J. Alloys Comp. 247, 247 (1997). M. D. Hornbostel, E. J. Hyer, J. Thiel, and D. C. Johnson, J. Am. Chem. Soc. 119, to appear. L. Brewer, J. Chem. Educ. 35, 153 (1958). R. Schneidmiller, M. D. Hornbostel, and D. C. Johnson, lnorg. Chem. 36, 5894 (1997). L. Fister and D. C. Johnson, J. Am. Chem. Soc. 116, 629 (1993). W. Jeitschko and D. Braun, Acta Crystallogr. Sect. B 33, 3401 (1977). B. C. Sales, D. Mandrus, and R. K. Williams, Science 272, 1325 (1996). G. S. Nolas, G. A. Slack, D. T. Morelli, T. M. Tritt, and A. C. Ehrlich, J. Appl. Phys. 79, 4002 (1996). M. D. Hornbostel, E. J. Hyer, J. H. Edvalson, and D. C. Johnson, Inorg. Chem., to appear. H. Sellinschegg, S. L. Stuckmeyer, M. D. Hornbostel, and D. C. Johnson, Chem. Mater., to appear. A. Cho, ed., "Molecular Beam Epitaxy," Vol. 1. AlP Press, New York, 1994. K. v. Klitzing, G. Dorda, and M. Pepper, Phys. Rev. Lett. 45,494 (1980). D. C. Tsui, H. L. Stormer, and A. C. Gossard, Phys. Rev. Lett. 48, 1559 (1982). N. Sano, H. Kato, and S. Chiko, Solid State Commun. 49, 123 (1984). E Capasso, Physica B 129, 92 (1985). I. K. Schuller, Phys. Rev. Lett. 44, 1597 (1980). X. Li, T. Kawai, and S. Kawai, Jpn. J. Appl. Phys. 33, L18 (1994). D. P. Norton, B. C. Chakoumakos, J. D. Budai, D. H. Lowndes, B. C. Sales, J. R. Thomson, and D. K. Christen, Science 265, 2074 (1994). A. Koma and K. Yoshimura, Surf. Sci. 174, 556 (1986). A. Koma, K. Saiki, and Y. Sato, Appl. Surf. Sci. 41/42, 451 (1989). M. Noh, J. Thiel, and D. C. Johnson, Science 270, 1181 (1995). J. A. Wilson and A. D. Yoffe, Adv. Phys. 18, 193 (1969). M. Noh and D. C. Johnson, J. Am. Chem. Soc. 118, 9117 (1996). M. Noh and D. C. Johnson, Angew. Chem. Int. Ed. Engl. 35, 2666 (1996). M. Noh, H. J. Shin, K. Jeong, J. Spear, D. C. Johnson, S. D. Kevan, and T. Warwick, J. Appl. Phys. 81, 7787 (1997). S. Moss, M. Noh, K. H. Jeong, D. H. Kim, and D. C. Johnson, Chem. Mater 8, 1853 (1996).

294

Chapter 6 STRAINED-LAYER HETEROEPITAXY TO FABRICATE SELF-ASSEMBLED SEMICONDUCTOR ISLANDS W. H. Weinberg, C. M. Reaves, B. Z. Nosho, R. I. Pelzel, S. P. DenBaars Departments of Chemical Engineering and Materials, University of California, Santa Barbara, California, USA

Contents I.

2.

3.

4.

5.

6.

Introduction

296

Trends in Semiconductor Nanostmctures: Smaller in All Dimensions . . . . . . . . . . . . . . .

1.2.

Processing: The Good and the Bad

1.3.

An Alternative: Self-Assembled Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1.4.

Outline of the Chapter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

..................................

296 297 298 299

Basics of Heteroepitaxy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

299

2.1.

Fundamental Processes during Epitaxy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

299

2.2.

Heteroepitaxial Growth Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

301

C o m m o n Experimental Techniques

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303

3.1.

Synthesis Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

303

3.2.

Characterization Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

304

Two-Dimensional Growth and Island Formation Before Transition to Three-Dimensional Gro~fth . . . 305 4.1.

Initial Stages of the Two-Dimensional Layer Formation . . . . . . . . . . . . . . . . . . . . . . .

4.2.

Transition from the Two-Dimensional Layer to Three-Dimensional Islands . . . . . . . . . . . .

308

4.3.

Effects of Surface Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

311

306

4.4.

Effects of Surface Orientation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

314

Three-Dimensional Islands . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

317

5. I.

Early Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

317

5.2.

Strain Relief from the Islands . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

318

5.3.

Different Types o f l s l a n d s

319

5.4.

Impact of Deposition Conditions

5.5.

Impact of Surface Orientation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

323

5.6.

Controlling the Location of Self-Assembled Islands . . . . . . . . . . . . . . . . . . . . . . . . .

324

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Physical Properties and Applications of Self-Assembled Islands 6.1.

7.

..................................................

I.I.

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321

325

Physical Properties: Some Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

325

6.2.

Self-Assembled Islands in Devices

327

6.3.

Use of Islands to Make Other Nanostructures

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328

Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

328

Acknowledgment

329

...............................................

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

329

Handbook of Nanostructured Materials and Nanotechnology, edited by H.S. Nalwa Volume 1: Synthesis and Processing Copyright 9 2000 by Academic Press All rights of reproduction in any form reserved.

ISBN 0-12-513761-3/$30.00

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1. INTRODUCTION 1.1. Trends in Semiconductor Nanostructures: Smaller in All Dimensions

In the study of physical properties, nanostructures often provide the best or the only testing ground for phenomena in fields such as quantum mechanics and condensed-matter physics. In electronic devices, there is a trend to use smaller numbers of electrons to get a task done. With devices that emit light such as laser diodes, the emission wavelengths must be controlled. To improve both types of devices, structures that exploit quantum mechanical behavior are an option. This is achieved by reducing the size of the structure. If only one dimension is made small, the electron will only be partially confined; it will still behave as a free electron in the remaining two large dimensions. Quantum structures are, therefore, classified by how many dimensions provide confinement or, inversely, how many dimensions allow free-electron behavior. If a structure provides confinement in one dimension, it is called a quantum well. If a structure provides confinement in two dimensions, it is called a quantum wire. If a structure provides confinement in three dimensions, it is called a quantum box or quantum dot. Although the quantum mechanics are well established, the creation of quantum structures, in particular, quantum dots, is difficult, This difficult work is pursued because quantum dots emulate a single atom, One atomic property is that an atom has discrete energy levels. If a nanostructure that confines electrons can be fabricated small enough, then discrete energy levels can be observed. This has been done with thin semiconductor structures for several decades [ 1], However, thin structures only provide quantum confinement, and discrete energy states, in one dimension. The goal with quantum dots is to achieve quantum confinement in all dimensions. One motivation for this arises from the concept of density of states. The total energy of an electron has kinetic energy components resulting from motion (momentum) in three Cartesian directions. To account for a particular amount of energy, there is usually a number of combinations of momentum components that can be considered. Even in a quantum well or a quantum wire, the discrete energy levels only partially define the energy; momentum in the unconfined dimensions can lead to a range of allowed states. A quantum dot provides confinement in all dimensions. The allowed energy states are completely defined by the quantum confinement, and the resulting density of states is, therefore, ~ delta function [2-4]. Why is this well-defined density of states so desirable? One reason is the increased accuracy in the energy. With the widely used quantum well, the energy of an electron c~n be narrowed down to a minimum of the lowest energy state. There are several instances where this uncertainty can be a problem. Quantum structures are often used in physical measurements to understand better quantum mechanics and the properties of materials. What if an external field (e.g., magnetic, electric, or stress) is applied to a sample and the experimentalist is looking for a shift in the quantized energy level? A shift in the measured energy of the electron could possibly be due to redistribution among allowed energy states, not just a shift in the level. Quantum structures are often used in electronic and optoelectronic devices. In the case of lasers, a partially continuous density of states may lead to the transformation of electrical energy into light at an unwanted energy. For many applications, the distribution of electronic energy resulting from thermal considerations can be a problem, yet would be nearly eliminated if the density of states were a delta function [5]. Other chapters in this book discuss the fabrication and use of many types of nanostructures, many of which use semiconductor epitaxy. One approach to nanostructure fabrication is to take advantage of the unique aspects of epitaxy to form self-assembled nanostructures. Such structures have several advantages. One major advantage is that they are formed during the epitaxial growth with no processing.

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1.2. Processing: The Good and the Bad Regardless of the technique, there are two key requirements in fabricating nanostructures: (1) achieving the desired size, shape, density, and spatial distribution and (2) maintaining high material quality. These requirements can be difficult to achieve. Producing structures that are nanometer sized in one dimension is relatively simple. Epitaxy grows material on an atomic level of a control. Thin layers such as quantum wells have been readily fabricated for about two decades [ 1]. They can be found in a number of commercial microelectronic devices and have been used in a range of physical studies. Thin semiconductor layers can be formed simply by epitaxy. What about nanostructures that are wires and boxes? These structures require control not only in the epitaxial growth direction but also laterally. There are several methods to achieve this. There are many successful approaches that involve common processing steps such as lithography and etching. Some of these techniques are illustrated in Figure 1. Other methods involve processing after growth. A semiconductor sample, often starting with a thin layer, is patterned by placing a patterned etch mask (often a photoresist or a dielectric layer) on the sample, as shown in Figure l a. The sample is then etched with either solution-based wet techniques or reactive-ion dry techniques such that the thin layer is laterally defined. This technique has been used to create a quantum box laser [6].

Fig. 1. Typicalmethods of semiconductor nanostructure fabrication via processing. A thin layer sandwiched between other layers is etched (a) to reduce the lateral dimensions. Epitaxial growth can occur over a patterned surface (b) where variations in thickness will occur, leading to a wirelike region at the bottom of the groove. Epitaxial growth can also occur over a masked surface (c) such that the new material is only deposited in the exposed region.

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A processed surface can also be used for semiconductor overgrowth to obtain laterally small nanostructures. For example, a V-shaped groove, shown schematically in Figure l b, can be etched into a semiconductor by taking advantage of the etch selectivity of different crystallographic planes. These crystallographic planes will often exhibit different behavior during growth. Some work with this approach has formed material that is thicker at the bottom of the groove than on the side wall. The electronic behavior of such a structure has been used to make quantum wires [7]. Another approach that involves processing before growth consists of placing a patterned mask, often a dielectric, over the surface, as shown in Figure lc. The growth can be done such that the new semiconductor material only deposits in the open area. The dielectric can later be removed to leave a laterally small semiconductor nanostructure. There are many advantages of processing approaches to achieve semiconductor nanostructures. They can be very good in determining the shape, density, and spatial distributions of the structures. In some cases, these are major concerns. The size of the structure can also be controlled down to a lower limit. Lithographic techniques are evolving to smaller and smaller sizes and the 100-1000-/~ range is readily achievable. In some cases, however, smaller nanostructures may be desired. One disadvantage with processing techniques is that the commonly used etching processes often cause damage to the remaining material [2]. This damage may lower the material quality of the nanostructure. Another problem is exposing the sample to air between steps. For example, growth is usually done in one chamber, the sample removed, taken to another chamber for dielectric deposition, then removed, taken to a lithography system, patterned, then etched either in a beaker or in a chamber, removed, and so on. These multiple steps are often done in different environments. Changes in environments can introduce oxidation and contamination, also compromising material quality. One approach is to connect a processing chamber to a deposition chamber such that oxidation and contamination are reduced [8]. Many of the problems with processing routes to nanostructures are being addressed with ongoing research. A complementary approach is to find methods to fabricate semiconductor nanostructures without processing. 1.3. An Alternative: Self-Assembled Structures Self-assembling approaches to quantum structures have the advantage that the structures are formed in the growth environment and no processing is needed either before or after the growth. There is no processing-related damage or contamination and the nanostructures can be smaller than lithographic dimensions, yet there is little direct control over the size, shape, density, and spatial distribution. There have been several different types of self-assembled quantum structures. One class that can be fabricated in situ during growth are lateral supeflattices. Two approaches have been demonstrated. One approach relies on the fact that some alloys undergo atomic ordering, leading to low band gap and high band gap regions [9]. This has been observed in the case of GaInP, which separates into gallium phosphide-rich and indium phosphide-rich regions that extend in one dimension within the sample. If the layer is thin, the resulting structures are quantum wires [ 10]. The other approach is to deposit fractional monolayers of one material alternately on a vicinal surface. During the step-flow growth mode [11, 12], new adatoms that adsorb on a terrace will attach to the up-step edge. Hence, if a half monolayer of material A is deposited on a vicinal surface followed by a half monolayer of material B and this process is repeated, a lateral supeflattice can be formed consisting of vertical regions of different materials. This technique has been used to form tilted superlattices [13] and serpentine supeflattices [14], which exhibited quantum wire behavior and have been used in laser structures [15].

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There has also been considerable work in forming self-assembled quantum dots not using traditional epitaxy, but solution chemistry and other techniques to form small clusters [ 16, 17]. Although there have been a number of successes with this work, including precise control of cluster size by selection of template molecules, there are several disadvantages with producing quantum dots with these techniques. Passivation steps are vital to prevent a significant fraction of the cluster from oxidizing, and these clusters would also be difficult to integrate with traditional semiconductor structures. The types of self-assembled quantum structures discussed in this chapter involve the formation of defect-free three-dimensional islands during strained-layer epitaxy. The previously mentioned techniques involving heteroepitaxy were demonstrated in lattice-matched materials systems.

1.4. Outline of the Chapter Because the formation of these island nanostructures is highly dependent on the growth process, the basics of heteroepitaxy will be reviewed next (Section 2). Then comments will be made on the common experimental techniques used to fabricate and study these structures (Section 3). During the growth, there is an abrupt transition between two-dimensional growth and three-dimensional growth. One way to classify the self-assembling islands is to divide them into those that form before the transition (Section 4) and those that form after the transition (Section 5). Before summarizing, a brief discussion of the properties and applications of these islands will be given (Section 6).

2. BASICS OF HETEROEPITAXY Heteroepitaxy is the process of depositing one crystalline material on a different material with an interface that is nearly perfect. The process is widely used, not only for research, but for manufacturing semiconductor devices such as lasers, light-emitting diodes, and transistors. With its well-established position in semiconductor research and manufacturing, using heteroepitaxy to fabricate nanostructures is a natural extension. Although epitaxy has been studied for many years, it is still not fully understood [ 18]. There have been several books, chapters, and reviews on the topic, a subset of which is listed here [ 19-24], and these can be consulted for more in-depth information. In this section, we review some basic concepts of heteroepitaxy that are important in understanding how self-assembled islands can be made. The basic surface processes will be reviewed and the most common growth modes will be introduced.

2.1. Fundamental Processes during Epitaxy The key surface processes that occur during epitaxy are shown schematically in Figure 2 [22]. Regardless of the growth technique, atoms (and molecules) are delivered to the substrate surface, and a large fraction of these species adsorb on the surface. Once adsorbed, there are three things that can happen to the adatom. It can either form a strong chemical bond to the surface where it is trapped, diffuse on the surface to find an energetically preferred location prior to strong chemical bonding, or desorb. Once adsorbed chemically, the adatoms can also diffuse on the surface, and this diffusion can be highly anisotropic, depending on the symmetry and nature of the surface. These chemisorbed adatoms diffuse until they either (1) desorb from the surface, (2) find another adatom and nucleate into an island, (3) attach, or aggregate, into an existing island, (4) diffuse into the surface, or (5) react at defect sites. The last two effects are often considered relatively minor occurrences in epitaxy but are mentioned here for completeness. Diffusion into the surface, or interdiffusion, can be significant at times. The extent of interdiffusion can be thought of

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Fig. 2.

Basic processes during epitaxy.

as the solubility of one material into the other and clearly has a strong dependence on the material system. The segregation of atoms into other layers can be seen, for example, in the case of In segregation into surrounding barrier materials [25] and also in atomic diffusion from delta-doped layers [26]. The reactions at defect sites are often important. For example, reactions at step edges (a defect with respect to a perfect surface) are the foundations of step-flow growth. The formation of clusters and the attachment of atoms to existing structures and clusters are important in the formation of self-assembled islands. When diffusing adatoms find each other, they can nucleate and form an island. Island growth continues either when other diffusing adatoms attach themselves or by direct impingement of gas phase atoms onto existing islands. Adatoms that directly impinge on an island can either incorporate into the island or lead to the next-layer growth, depending on the surface potential. Although the diffusion of adatoms attached to islands can be significantly reduced because of the local surface potential, it is still possible for adatoms to detach from the islands. Thus, islands have a "critical size" associated with them, at which they become "stable" with respect to "evaporation." Here, stable means that the islands are sufficiently large that the rate of attachment to the islands is the same or greater than the rate of detachment from the islands [27-31 ]. As the islands continue to grow further, and possibly migrate, they can find other islands and coalesce into one large island. The evolution of island formation can, therefore, be visualized as a progression through three different growth regimes. Initially, there is a high concentration of adatoms or monomers diffusing on the surface, resulting in a high probability of island nucleation. This is the nucleation regime, where the density of islands on the surface increases with coverage. The density continues to increase until the probability of a diffusing adatom finding an island is much higher than the probability of finding another adatom. The number of nucleation events is substantially reduced as the adatom diffusion length becomes large relative to the average island spacing, and, thus, the majority of events occurring are adatoms attaching to the existing islands, hence defining the aggregation regime. As further growth continues in the aggregation regime, the island density remains relatively constant while the islands continue to grow in size. Eventually, the islands will begin to merge with one another and enter into the coalescence regime, which is signified by a decrease in the island density with increasing coverage. There has been a considerable amount of work in the literature in trying to describe analytically the atomic processes involved in thin-film growth through the use of kinetic rate equations. In these equations, each of the atomic processes can be represented by writing expressions for the time-dependent changes in the densities of single adatorns, clusters of a given size, and stable clusters. The specifics of these equations will be not be discussed in detail here as comprehensive reviews on this topic are widely available in the literature [22, 23, 27, 32, 33]. To illustrate the point, however, a possible equation for the time rate of change of the single adatom density is given by

dnl dt

= gdep -]- gdis -- gevap - 2U1 - Ucap

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where similar expressions could be written for the rate of change of islands of a given size. The single adatom density can increase by the rate of deposition and dissociation (or detachment) from larger islands as embodied by Udep and Udis, respectively, or decrease by the rate of evaporation, the nucleation of two single adatoms, or the capture of a single adatom by a larger island as embodied by Uevap, 2U1, and Ucap, respectively. The factor of 2 in front of U1 is to account for the two adatoms that nucleation requires. Clearly, additional terms could be added to represent diffusion into the surface, or reaction at defect sites, or any other surface process one could imagine. To continue with this description, explicit expressions for the various elementary rates must be determined. The terms describing the deposition rate and the evaporation rate are fairly straightforward. The other terms involving the nucleation and aggregation of islands are functions of the diffusion coefficient, the densities of the single adatoms, the densities of islands of any given size, and a "capture number," which is a variable that takes into account the local distribution of adatoms around an island. To help discard some of the terms, certain regimes of the growth are studied to find terms that are minimal in that regime and, thus, reduce the rate equations. For example, in considering the aggregation regime of growth, an assumption could be made that the density of single adatoms on the surface is much smaller than the total density of islands, and the rate equations can be modified accordingly. By simplifying the rate equations sufficiently, the variables can be separated and then integrated to give general expressions for the densities. With the appropriate approximations, the equations describing the densities of the single adatoms and islands can be expressed as simple functions of the coverage and the ratio of flux to diffusion. This is the basis for the scaling relations derived for thin-film growth, and they have been used extensively in attempting to model epitaxial growth [28-30, 34-36].

2.2. Heteroepitaxial Growth Models There are three general ways in which one material, say B, can grow epitaxially on a dissimilar material, say A [ 19]. These growth modes can be described by the equilibrium morphology, as determined from the surface free energies [ 18, 19, 21 ]. Following the notation used by Tsao [21], the three surface free energies considered are the energies associated with the substrate-vacuum, substrate-epilayer, and epilayer-vacuum interfaces and are denoted by Ysub-vac, Ysub-epi, and Yepi-vac, respectively. The Ysub-vac term can be thought of as the initial energy term before the epilayer formation, and the remaining two terms, Yepi-vac and Ysub--epi a r e associated with the epilayer formation. Based on work by Bruinsma and Zangwill [37], a "spreading pressure" can be defined as S = Ysub-vac -- Ysub-epi -- Yepi--vac - - Ysub-vac -- (Ysub--epi -~" Yepi-vac)

It is evident that the relative contributions from these terms change as the epilayer evolves, resulting in a competition to determine the lowest-energy surface. We will start the discussion with the two extremes. If Ysub--epi+ Yepi-vac < Ysub-vac, then material B will grow in a layer-by-layer fashion. This means that the B atoms will try to cover completely the surface of A because this growth minimizes the surface free energy. During the growth of the first layer of B, new atoms landing on the bare A surface will diffuse on the surface until they attach to existing clusters of B atoms. If a new B atom lands on top of an existing cluster of B atoms, it will diffuse to the edge of the structure and jump down, attaching to the edge of the cluster. Growth occurs in a two-dimensional fashion. Thus, each complete layer is thermodynamically stable as a two-dimensional layer. This is known as the Frank-van der Merwe growth mode and is illustrated in Figure 3a. On the other hand, when J/sub--epi + Yepi-vac > Ysub-vac, it is thermodynamically unfavorable for the epilayer to be flat and the B atoms will cluster and form islands to try to minimize the interface between A and B. Water beading on a waxed car is a result of a high interfacial energy. New atoms that land on top of an existing cluster of B atoms will

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Fig. 3. Comparisonof Volmer-Weber(a) and Frank-Van der Merwe (b) growth modes.

Fig. 4.

Heteroepitaxy of lattice-mismatched materials. Note the (tetragonal) deformation of the epitaxial layer.

remain on top instead of jumping down. Growth occurs in a three-dimensional fashion; new material will add to the height of the existing islands more than the lateral size. This is known as the Volmer-Weber growth mode and is illustrated in Figure 3b. Before describing the third growth mode, we should discuss one important point that has been excluded from the previous discussion, namely, the concept of lattice mismatch. If the lattice structure or lattice constant of A and B is dissimilar, then elastic strain must be considered. The material in the layer being deposited must stretch or compress, as shown in Figure 4, to match the lattice of the underlying material. The fraction of lattice mismatch, f , is given by

f=

af - as as

where af is the lattice constant of the film and as is the lattice constant of the substrate. This definition is widely used [38] although other similar definitions do exist [39, 40]. There are two paths that lattice-mismatched films can take. For small lattice mismatches, approximately 2% or less, the growth will occur in a layer-by-layer fashion for many layers. At some point, the strain energy will build up and bonds within the sample, often at the heterointerface, will break. These patterns of broken bonds are known as dislocations. Dislocations in semiconductors and other materials are a widely studied field [40, 41 ]. Materials that contain dislocations and other crystal defects are often referred to as incoherent, in contrast to a coherent material with no defects. For moderate to large lattice mismatches, approximately 3% and larger, the growth also initially occurs in a layer-by-layer fashion. In some cases, the growth of the first layer is heavily impacted by strain, a topic that is discussed further in Section 4. Returning to our discussion based on thermodynamics, consider a material system where the initial stages of growth resemble the Frank-van der Merwe growth mode. Recall that in this scenario )"sub--epi + Yepi-vac < Ysub--vac. After the first layer is grown, we should now replace "substrate" terms with wetting layer terms, such that YWL--epi, Yepi-vac, and ~VL-vac are the relevant free energies resulting from the wetting layer-epilayer, epilayervacuum, and wetting layer-vacuum interfaces, respectively. These new terms take into

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account the strained wetting layer. As the film thickness increases and strain builds up, the contribution from the wetting layer-epilayer interface will begin to dominate such that YWL--epi -+" ~'epi-vac > ~VL-vac. As in the Volmer-Weber growth mode, the surface will form three-dimensional islands to minimize the free energy and accommodate the strain. This is known as the Stranski-Krastanov growth mode [ 19], and is the most often observed growth mode in the lattice-mismatched heteroepitaxy of semiconductors. The phenomenon of three-dimensional island formation during epitaxy has been documented for many decades [ 19]. However, there are two reasons why the islands so formed were not readily explored as potential quantum structures. First, there is a bias in semiconductor epitaxy toward flat (smooth) surfaces and interfaces. One reason behind this bias is that, with thin layers such as quantum wells and electron tunneling barriers, the thickness of the layer is critical to the performance of the device, such as the emission wavelength of a laser. If the interfaces are rough, leading to thickness variations of the layer, the emission energy will vary. Traditionally in semiconductor epitaxy, there has been an emphasis on developing and using flat surfaces and interfaces [1]. In more recent efforts, the formation of islands during strained-layer growth was seen as a problem, namely, a rough surface. In point of fact, considerable work has been done to suppress island formation by varying growth conditions [42] and by using surface treatments (surfactants) during growth [43, 44]. Second, the islands that were observed, often in metal epitaxy, contained dislocations and other defects. It was assumed that all such islands would be dislocated and, hence, not be suitable for quantum structures. However, many lattice-mismatched heteroepitaxial systems have been found to grow in a Stranski-Krastanov growth mode, where three-dimensional islands evolve after the formation of the two-dimensional wetting layer. Often, these systems possess a coverage range, or "window," in which defect formation is suppressed and three-dimensional coherent islands form. These coherent islands are the topic of Section 5. Eventually, the islands will dislocate; however, the coverage regime for coherent structures is easily obtained with current epitaxial growth techniques.

3. C O M M O N EXPERIMENTAL TECHNIQUES Before discussing the details of the self-assembled islands, a few comments will be made on the growth and characterization techniques commonly used. These techniques will be codified briefly with appropriate references. The techniques to be discussed will be molecular beam epitaxy (MBE) and chemical vapor deposition (CVD) for synthesis, and reflection high-energy electron diffraction (RHEED), transmission electron microscopy (TEM), scanning tunneling microscopy (STM), and atomic force microscopy (AFM) for characterization.

3.1. Synthesis Techniques 3.1.1. Molecular Beam Epitaxy [21, 45-47] Molecular beam epitaxy refers to the growth of a crystalline material in ultrahigh vacuum (UHV) using collimated gas phase reactants. The UHV environment facilitates the growth of extremely pure materials. The sources for growth can range from solids to gases and can be either elemental or compound. If the precursors are solid or liquid, they are heated in crucibles and their vapor is used to generate a molecular beam, or gaseous sources can be used directly. The geometry of the MBE system is such that there is a line of sight between the source and dopant beams and a temperature-controlled rotating substrate. Because growth occurs in UHV, the mean free path of the molecules is rather large, ensuring that the source molecules impinge onto the substrate directly. Growth is controlled by varying such parameters as substrate temperature, source flux, the sequence and duration of source beam(s) [i.e., alternating beam epitaxy and migration-enhanced epitaxy (MEE)],

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and group V overpressure (for III-V growth). Fluxes are controlled by modulating the molecular beams, usually through the use of high-speed mechanical shutters. These shutters provide the control necessary to deposit the desired quantity of material with better than 0.05 monolayer (ML) accuracy.

3.1.2. Chemical Vapor Deposition [48-50] In chemical vapor deposition, growth occurs at a much higher pressure (1-760 torr) than in MBE. Often, the sources for growth are organometallic compounds (e.g., trimethyl gallium and arsine or tertiarybutylarsine for GaAs growth). These CVD techniques using organometallic sources go by a variety of names, two of the most common of which are organometallic vapor phase epitaxy (OMVPE) and metalorganic chemical vapor deposition (MOCVD) [48]. During growth, precursor compounds are flowed (using an inert carrier gas) over a substrate located on a heated susceptor. Flow rates are usually such that transport is governed by mass transport within a boundary layer that is present near the substrate surface. Growth usually occurs at relatively high temperatures (600-1000 ~ such that the metalorganic precursors are cracked in the boundary layer, facilitating the diffusion of the alkyl fragments through the boundary layer (away from the surface) into the free-stream flow of the carrier gas. Growth is controlled by varying such things as substrate temperature and reagent flow rates. Flow rates are controlled by metering the gaseous sources through flow controllers and fast switching valves.

3.2. Characterization Techniques

3.2.1. Reflection High-Energy Electron Diffraction [51-541 One distinct advantage of MBE growth in comparison to CVD techniques is the ability to monitor MBE growth (in situ) using reflection high-energy electron diffraction. RHEED can be used to infer information about surface cleanliness, surface order and smoothness, and the growth rate. For RHEED, monoenergetic electrons (3-15 keV) are diffracted from the substrate (angle of incidence < 1~ onto a fluorescent screen. The small angle of incidence used in RHEED corresponds to a relatively small penetration depth (a few monolayers), making RHEED a very surface-sensitive technique. In essence, RHEED is similar to X-ray diffraction for a surface. (The theoretical analysis for RHEED is identical to the formalism used to explain X-ray diffraction.) Thus, RHEED offers insight about the periodicity present at the substrate surface. Furthermore, by monitoring the intensity of the oscillations of a single RHEED spot, one is able to determine the growth rate because a single oscillation corresponds to the deposition of one monolayer.

3.2.2. Transmission Electron Microscopy [55-57] The foundation of TEM is the wave behavior exhibited by electrons. In an experiment, periodic atomic planes within a thin crystalline sample (--~1000 A) diffract a monochromatic electron beam, typically accelerated by a 60-200-kV potential. Because TEM is sensitive to variations in the spacing of atomic planes [58], it is a useful technique for the study of islands formed during strained-layer epitaxy. Strain effects can be clearly seen as well as the presence of crystal defects [59, 60].

3.2.3. Scanning TunnelingMicroscopy [61-66] As the name suggests, STM relies on the quantum mechanical phenomenon of electron tunneling. In an STM experiment, a sharp metallic tip is brought sufficiently close to a conducting surface that electron tunneling between the sample and the tip will occur. A bias voltage (either positive or negative) is applied to the tip, and a tunneling current flows from

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the surface to the tip (for negative sample bias) or from the tip to the surface (for positive sample bias). In the constant-current mode, the tip is rastered in the plane of the surface and the tip-sample separation is altered, using a feedback circuit, such that the tunneling current is maintained at a constant value. The tip position in this rastering procedure follows a constant density of electronic states topograph of the surface. It is important to realize that an STM image is not a map of atomic position. Rather, it represents a constant density of electronic states contour of the surface for a given bias voltage. Even so, by varying the bias voltage, the electronic states of the surface involved in tunneling are changed. Furthermore, both negative and positive sample biases can be used to probe the filled and empty states. Thus, bias-dependent imaging can be used to infer details about the atomic structure and electronic nature of the surface. In practice, STM has been an invaluable technique used in the study of surface reconstructions and atomic scale features, providing information at resolutions unavailable by almost any other technique. 3.2.4. Atomic Force Microscopy [64, 67-69] In an AFM experiment, a sharp tip mounted on the end of a flexible cantilever is brought into sufficiently close proximity with the sample that a detectable force is generated. Detection of the tip-sample force has been achieved in different ways. One common method involves the deflection of a laser beam reflected from the back of the cantilever. The tip is rastered above the surface and a feedback loop is used to keep the separation between the tip and the sample at a constant value through the actuation of a piezoelectric translator that moves the sample (in the z direction perpendicular to the sample). As mentioned, the AFM relies on force detection. Depending on the tip-sample separation, the type and magnitude of the tip-sample force will vary. In the so-called contact mode, the separation distance between the tip and the sample is small, and the detected force is a result of core-core repulsion (the Pauli principle). Although contact mode AFM can provide atomic resolution, it requires a very rigid substrate. In the noncontact mode, the tip-sample separation is larger than for contact mode AFM, and the gradient of the van der Waals potential is the relevant force. Generally, the spatial resolution of noncontact mode AFM is inferior to the resolution achievable with contact mode AFM. Yet, noncontact mode AFM is less susceptible to imaging artifacts resulting from deformation of the sample by the tip. To image a surface nonintrusively and still achieve a high level of spatial resolution, tapping mode AFM was developed. In the tapping mode, the cantilever of the AFM is forced to oscillate at a certain distance from the sample while the probe is scanned laterally. When the tip encounters a surface feature, the resonant frequency of the cantilever changes. A change in the resonant frequency of the cantilever will result in a change in the amplitude of oscillation, which is detected by the laser reflecting from the back of the cantilever. When this happens, the feedback loop lowers the sample so that the original amplitude of cantilever oscillation is restored. An on-line computer records the voltages applied to the z-direction piezoelectric actuator for feedback control and converts them into a topographic map of the surface.

4. TWO-DIMENSIONAL G R O W T H AND ISLAND FORMATION BEFORE TRANSITION TO THREE-DIMENSIONAL GROWTH There has been much recent interest in creating reduced-dimensional structures with cartier confinement in two and three dimensions by self-assembling mechanisms in latticemismatched heteroepitaxy. It is hoped that the in situ formation of these low-dimensional structures can be utilized as a suitable alternative to damage-inducing ex situ processes such as etching and lithography [70-74]. Many lattice-mismatched heteroepitaxial systems follow the Stranski-Krastanov growth mode, where at least one monolayer grows in

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a layer-by-layer mode, forming a two-dimensional layer, sometimes known as the twodimensional layer. The strain from the lattice mismatch is accommodated in elastic deformation and, thus, determines the critical thickness of the two-dimensional layer. In the layer-by-layer regime of growth, two-dimensional islands (islands that are one monolayer in height) can form as a mechanism to help minimize surface energy. As the film thickness increases beyond the critical thickness, three-dimensional islands form on the twodimensional layer. Considering that high-quality materials preclude dislocation formation, a given heterostructure is limited by the amount of coherent material that can be deposited before dislocation formation becomes energetically favorable. Hence, it is of great importance to determine the mechanisms of strain relief for various technologically important semiconductor systems because a better understanding of the initial stages of strained-layer heteroepitaxy is crucial for the further development of this technology. The importance of two-dimensional islanding should also be extended to the understanding of interfaces. Interfaces can play a critical role in the device performance of heteroepitaxial systems. As relevant length scales decrease, the importance of morphological issues at these interfaces becomes even more crucial. For example, resonant tunneling devices (RTDs) are currently of considerable interest because of their potential use in highspeed terahertz devices. RTDs are double-barrier heterostructures, where the barriers are typically on the order of 5 to 10 monolayers (ML) thick. A theoretical study examined the effects of islands at the interface on the performance of RTDs, as predicted by the peakto-valley ratios determined from calculated I-V curves as a function of terrace sizes [75]. A modest amount of lattice mismatch can be tolerated because the barrier thickness can be substantially smaller than the critical thickness to three-dimensional growth. However, new issues arise when two compounds with different group-V components are grown together. As an example, consider the case of InAs and A1Sb, which are used in RTDs. A1Sb has a lattice constant slightly larger than InAs (1% mismatch) and also a significant band offset, making it an ideal candidate as a barrier material to InAs. The interface bonds for this system must be either In-Sb or A l A s . Most MBE growths occur under group-V overpressures, and the traditional approach is to "soak" the surface under the new group-V flux when changing materials at an interface. In either case, the InSb-like or AlAs-like material on the InAs is significantly lattice mismatched to the InAs substrate, thus making strain issues relevant. In this section, we will review the issues relating to the initial stages of StranskiKrastanov growth. In particular, we will first discuss the beginning stages of latticemismatched heteroepitaxial growth as the two-dimensional layer forms up through the transition from two-dimensional to three-dimensional growth. Furthermore, the effects of reconstruction and surface orientation on the formation and morphology of twodimensional islands will be discussed. Clearly, the literature is far too rich to attempt to review every material system that has been studied throughout the years. Rather, we will discuss specific examples from the literature that we believe are representative of the concepts we bring forth. What we wish to emphasize are concepts, because the ideas are general for lattice-mismatched heteroepitaxy. We will focus this discussion on elemental or compound semiconductor systems with the diamond or zincblende structure.

4.1. Initial Stages of the Two-Dimensional Layer Formation Insight into the mechanisms involved in the formation of the two-dimensional layer is needed to understand some of the fundamental aspects of lattice-mismatched heteroepitaxial growth. Figure 5 shows STM images of the initial stages of InAs growth on GaAs(001)(2 • 4) at various submonolayer coverages. Parts a and b of Figure 5 show a coverage of 0.15 and 0.29 ML, respectively. The InAs forms two-dimensional islands, which are one monolayer in height above the GaAs surface. Higher-resolution STM images show that these islands also exhibit a c(4 • 4) reconstruction, which further distinguishes the islands

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Fig. 5. Filled-stateSTM images of InAs islands on GaAs(001)-(2 x 4): (a) 30-nm x 15-nm image of 0.15 ML of InAs deposition and (b) 100-nm x 70-nm image of 0.29 ML of InAs deposition. The islands in both images are elongated in the [i 10] direction and exhibit a c(4 x 4) reconstruction and easily distinguishable from the (2 x 4) reconstruction still observed on the bare substrate. Reprinted with permission from V. Bressler-Hill et al., Phys. Rev. B 50, 8479 ( 9 1994 American Physical Society) and from J. Tersoff and R. M. Tromp, Phys. Rev. Lett. 70, 2782 ( 9 1993 American Physical Society).

from the initial (2 x 4) reconstructed surface (cf. Fig. 5c). In addition, the islands are observed to be anisotropic and elongated in the [ 110] direction at all submonolayer coverages studied. Qualitatively, there appears to be a difference in the energetics of the two types of island edges. The edges that run along the [i 10] direction are relatively straight compared to the edges that are parallel to the [ 110] direction, which are seen to have more kinks (cf. Fig. 5b). This indicates that rearrangement along the steps in the [i 10] direction is relatively rapid. A statistical analysis on the island dimensions shows that the InAs islands maintain a most probable width of approximately 4 nm in the [ 110] direction at all coverages examined, whereas the islands appear to grow freely in the [110] direction with increasing coverage. From this, it follows that the aspect ratio of these islands will significantly increase with coverage until the onset of coalescence. It should be mentioned

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that anisotropic island shapes are common in semiconductor systems, and are even seen in homoepitaxial systems. Several factors could lead to this observed anisotropy, including an anisotropy in the step energies, a preferential growth direction resulting from different step edge reactivities, anisotropic barriers to surface diffusion, or some combination of them all [76-78]. Strain, in addition to the other possible anisotropies mentioned, is clearly expected to influence the surface morphology for the case of lattice-mismatched heteroepitaxial growth. One other noteworthy result seen in the aforementioned InAs/GaAs study was found when growing InAs islands on a 1o vicinal, B-type (anion-terminated steps running parallel to the [110] direction) GaAs(001)-(2 x 4) surface [79]. On this substrate, the steps limited the In diffusion in the [ 110] direction and, hence, the extent of growth possible in the [ 110] direction. Moreover, the B-type steps were found to be more reactive than the A-type steps (cation-terminated steps running parallel to the [ 110] direction) and to act as adatom sinks. Even with these growth constraints, the islands still showed a preferred width of around 4 nm in the [110] direction, indicating that the strain is likely being accommodated in that crystallographic direction. The observation of a preferred two-dimensional island size is consistent with work done by Massies and Grandjean [80], who considered the effects of nontetragonal elastic distortion at the edges of two-dimensional islands. A simplified version of the valence force field model was used in which the shape of a one-dimensional island on top of a completely rigid substrate could be calculated. For a surface coverage of 0.5 ML of In0.49Ga0.51As islands on GaAs (lattice mismatch of 4%), the model predicted a preferred island size of 11 unit cells, or 4.4 nm. This preferred size would be expected to be smaller for the increased lattice mismatch of InAs on GaAs(001). The observation of islands with a preferred size is also consistent with the theoretical predictions of Tersoff and Tromp [81], who proposed a shape transition for coherently strained islands. From their model, small islands initially evolve in a compact shape, but at a critical size, the islands take on a rectangular shape and become progressively elongated, where the width of these islands approaches a constant. The islands can then minimize their energy by keeping the optimal size in one direction, while continuing to grow in the other direction. The question then arises as to what determines which direction will elongate. On a surface terminated with group-V atoms, dimers form with the dimer bonds aligned in the [110] direction. Deposition of group-III atoms will form bonds between the group-III and the group-V atoms that will also be aligned in the [110] direction. If the atoms wish to move to help accommodate strain, they could modestly move perpendicular to the directions of their back bonds to the surface; that is, they could move in the [ 110] direction. Thus, strain energy could be partially relieved by the same nontetragonal deformation model of Massies and Grandjean [80] in the [110] direction. 4.2. Transition from the Two-Dimensional Layer to Three-Dimensional Islands

Following the Stranski-Krastanov growth mechanism, the two-dimensional layer will eventually give way to the formation of three-dimensional islands. The exact mechanism of this transition is presently not well understood and is a subject of much study [82-93]. It is reasonable to believe that the size and spatial distribution of the two-dimensional islands formed in the two-dimensional layer of these systems is somehow related to the distribution of three-dimensional islands formed after further material deposition. In other words, the two-dimensional islands, or platelets, are precursors to three-dimensional islands and, ultimately, grow into the larger structures. Priester and Lannoo [90] have proposed a model that follows this line of reasoning in an attempt to describe the formation of three-dimensional InAs islands on GaAs(001). In their model, a complete monolayer of InAs would first cover the surface forming the two-dimensional layer. At a total coverage of 1.4 ML, the model predicts the formation of large two-dimensional islands that are ran-

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domly distributed across the surface. These two-dimensional islands are uniform in size and are a single monolayer in height. This prediction of uniformly sized two-dimensional islands is reported by Chen and Washburn [84], who believe that the increase in strain at island edges affects the surface potential near the island edges and, subsequently, makes it increasingly difficult for adatoms to aggregate further into existing islands. Similarly, in kinetically driven models, such as Monte Carlo simulations, the detachment probabilities of adatoms from islands as a function of island size have been studied [30, 36]. As more material is deposited, the islands continue to grow and eventually evolve into uniformly sized three-dimensional islands. In an attempt to study the two-dimensional-to-three-dimensional morphology transition, Heitz et al. [85] have examined this same InAs/GaAs system at InAs coverages ranging from 0.87 to 1.61 ML on the GaAs(001)-c(4 x 4) surface. Images from their study are shown in Figure 6. There is no evidence of the large platelets that were predicted by Priester and Lannoo, but rather a surprising result regarding the two-dimensional-tothree-dimensional transition. At a coverage of approximately 1.15 ML, features 2-4 ML high begin to appear on the surface. The density of these features increases until an approximate coverage of 1.35 ML, whereupon these three-dimensional features disappear. Upon further deposition to 1.45 ML, the three-dimensional islands reappear, but at a much higher density. This type of appearance, disappearance, and subsequent reappearance of three-dimensional islands at coverages below the critical film thickness has not been previously reported for systems evolving in the Stranski-Krastanov growth mode. To study this phenomenon further, samples were grown for photoluminescence (PL) measurements with InAs deposition ranging from 1 to 2 ML. Peaks attributed to three-dimensional islands are observed at 1.15 and 1.25 ML, where the peak at 1.25 ML is shifted toward lower energies because of the larger island sizes. However, at 1.45 ML, this peak disappears and does not reappear until about 1.55 ML of deposition, whereupon it evolves into the peak typically observed at the critical point. Other examples of the transition from two-dimensional to three-dimensional growth can be found in the growth of antimony-based materials on GaAs. Thibado et al. [91 ] studied GaSb on GaAs(001)-c(4 x 4), and found that, after 1 ML of GaSb deposition, the surface was covered with two-dimensional islands, or platelets, which were approximately 10 nm in diameter, although slightly anisotropic in the [ T10] direction. An image in a related study of the same material system is shown in Figure 7, where the islanded two-dimensional layer is clearly observed. Furthermore, they found that adding a second monolayer of material primarily added onto the existing platelets, making them 2 ML high while approximately maintaining the same diameter. After 3 ML of deposition, they observed the formation of three-dimensional islands. Imaging the areas between the three-dimensional islands showed that the two-dimensional layer composed of the network of two-dimensional islands (2 ML in height) was still intact. Furthermore, a rough calculation based on the apparent island dimensions (neglecting convolution effects from the tip) showed that approximately 0.6 ML of material was incorporated into the three-dimensional islands, which is consistent with the two-dimensional layer remaining intact and not necessarily incorporating itself into the three-dimensional islands. Voigtl~inder and K~istner [92] have also tried to address the issues of three-dimensional island formation from two-dimensional growth by studying Ge growth on Si using in vivo STM during growth. They concluded that there did not appear to be any type of special morphology (e.g., step edges, large or high islands in the two-dimensional layer, domain boundaries, etc.) where the three-dimensional islands would nucleate and evolve, but rather it simply appeared to occur at random locations on the surface. Based on these experimental observations, it appears that the large two-dimensional platelets are not the precursors to three-dimensional islands as predicted by equilibriumbased theoretical models [90]. In an earlier and related work to that of Heitz et al. [85], Ramachandran et al. [86] considered mass transfer and kinetics in the formation of

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Fig. 6. Filled-state STM images showing the surface evolution for InAs deposition on GaAs(001)-c(4 x 4) at coverages of (a) 0.87, (b) 1.15, (cl, c2) 1.25, (d) 1.30, (e) 1.35, (f) 1.45, and (g) 1.61ML. The labels represent small two-dimensional islands less than 20 nm in width (A), large two-dimensional islands greater than or equal to 50 nm (B), small multilayer (2--4 ML) clusters up to 20 nm wide (Ct), larger multilayer clusters up to 50 nm wide (C), three-dimensional islands (D), atomic steps (S), and 1-ML-deep holes (H). Reprinted with permission from R. Heitz et al., Phys. Rev. Lett. 78, 4071 ( 9 1997 American Physical Society).

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Fig. 7. Filled-stateSTM images of GaSb on GaAs(001)-c(4 x 4) at coverages of (a) 1.0 and (b) 3.5 ML. The image in (b) shows a region between three-dimensional islands that has already formed by that coverage. Reprinted from J. Cryst. Growth, 175/176, 888, B. R. Bennett et al. (9 1997), with kind permission of Elsevier Science-NL, Sara Borgerhartstraat 25, 1055 KV Amsterdam,The Netherlands. three-dimensional InAs islands on GaAs. Again, no direct relationship between the large two-dimensional islands and the three-dimensional islands was observed. The major observation was that the highest observed density of the coherent three-dimensional islands was approximately an order of magnitude greater than the highest density of the twodimensional islands. Some hints of a possible precursor to the three-dimensional islands were observed and denoted "quasi"-three-dimensional islands, or islands 2-4 ML in height (cf. Fig. 6, the features labeled C). These features are relatively high in density, nearly twice that of the coherent three-dimensional islands. These "quasi"-three-dimensional islands appear about 0.2 ML before the formation of the true three-dimensional islands, where upon they quickly disappear within about 0.2 ML prior to additional deposition. Thus, the changing densities of these different types of islands over very small changes in the total coverage indicate a mass transfer mechanism from the two-dimensional to the threedimensional islands, which leads to a significant reorganization of mass on the surface. The authors conclude that to study and understand the formation and evolution of threedimensional islands, the strain-dependent kinetics of the system must be considered [86]. Clearly, this is plausible as epitaxy by nature is a kinetically driven process. Furthermore, there may be island-island interactions that affect the surface morphology and that result from strain-related phenomena [86, 94].

4.3. Effects of Surface Reconstruction Semiconductors often have a different symmetry at the surface compared to the bulk solid. This change of symmetry at the surface is a result of the displacement of atoms with respect

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to their bulk positions, thus creating a new unit cell on the surface. This rearrangement of surface atoms is referred to as a surface reconstruction, and significant effort has been devoted to understanding this phenomenon [95]. The motivation for the restructure itself is to minimize its free energy by forming bonds at the surface and maintaining charge neutrality. It should be noted that the reconstruction that is observed is not necessarily the lowest-energy surface, but rather the lowest-energy surface that is obtainable under the given set of kinetic conditions. Because the surface reconstruction represents a surface energy and symmetry (geometry), it is reasonable to believe that it will influence subsequent deposition of materials on the surface. To illustrate the effects that surface reconstruction can have on the formation of islands, consider the study by Belk et al. [96] of InAs deposition at various coverages up to 1 ML on the GaAs(001)-c(4 x 4) surface at a substrate temperature of 420 ~ A number of STM images showing the progression of island formation from 0.1 to 1 ML are shown in Figure 8. At 0.1 ML of InAs, new domains of (1 • 3) reconstruction are observed at the step edges, and it appears that the (1 x 3) areas are on the same layer as the c(4 x 4) ones. As the coverage is increased to 0.3 ML (cf. Fig. 8b), two-dimensional islands be-

Fig. 8. InAs islands grown on GaAs(001)-c(4 x 4) shown at fractional coverages of (a) 0.1, (b) 0.3, (c) 0.6, and (d) 1.0 ML. The image sizes are (a) 50 nm x 50 nm and (b)-(d) 40 nm x 40 nm. Reprinted from Surf. Sci., 365,735, J. G. Belk et al. (9 1996), with kind permissionof Elsevier Science-NL, SaraBurgerhartstraat 25, 1055 KV Amsterdam, The Netherlands.

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gin to appear on the surface, which, at this point, is a mixture of (1 x 3) and c(4 x 4) domains. These islands are 1 ML in height and show the same (1 x 3) reconstruction. In contrast to the highly anisotropic, two-dimensional InAs islands formed on the (2 x 4) surface and shown in Figure 5, the islands formed on the c(4 x 4) surface have a different reconstruction and appear to be much more isotropic. At 0.6 ML (cf. Fig. 8c), the surface is entirely covered by the (1 x 3) structure. The RHEED pattern in the [110] direction at 0.3 ML showed a mixture of 1/2- and 1/3-order spots, corresponding to the c(4 • 4) and the (1 • 3) reconstructions, respectively. By 0.6 ML, the 1/2-order spots were gone and the RHEED showed a clear (1 x 3). At 1.0 ML (cf. Fig. 8d), the surface is composed of large islands and terraces as some of the smaller islands have coalesced and the growth has proceeded in a reasonable, layer-by-layer fashion. Further study of the system revealed that the amount of InAs required to fill the surface completely with the (1 • 3) reconstruction varied with surface temperature. On this basis, the authors postulated that the (1 x 3) domains were actually composed of an (In, Ga)As alloy. The exact mechanism for this reconstruction/transformation remains unknown. Bennett et al. [82, 83] have studied the deposition of InSb on different reconstructions of GaAs(001). In particular, they deposited 1.5 ML of InSb on both a (2 x 4) and a c(4 x 4) reconstructed surface. Because of the significant lattice mismatch between InSb and GaAs (14.6%), this deposition is beyond the critical thickness and three-dimensional islands are present. The differences resulting from deposition on the different initial surface reconstructions can be seen in Figure 9. Figure 9a shows 1.5 ML of deposition on GaAs(001)c(4 x 4), whereas Figure 9b shows the equivalent deposition on GaAs(001)-(2 • 4). The islands were observed to be anisotropic in both cases, with the elongation in the [ 110] direction. The island separations, as determined from an autocorrelation analysis, were found to be 50 ,~ for growth on the c(4 x 4) surface and 40 ,~ for growth on the (2 x 4) surface. The islands formed in the two-dimensional layers of these systems appear to be somewhat dependent on the reconstruction of the initial growth surface. Islands that are formed on the (2 x 4) surface are highly anisotropic (cf. Figs. 5 and 9b), whereas islands that are formed on the c(4 x 4) surface appear to be slightly more isotropic (cf. Figs. 8a-d and 9a). This dependence on the initial surface reconstruction could be due to several different factors. To consider how the reconstruction of the initial surface could play a part in subsequent island formation, it would be sensible to consider first differences in the atomic structure of the reconstructions. Although there have been several different proposals for the (2 x 4) reconstruction [97, 98], the commonly accepted structures of the (2 • 4) surface are shown in Figure 10a [95, 99]. The surface is composed of two As dimers and two missing dimers on the top level, with the exposed As atoms in the third layer forming dimers. There is a missing row of gallium atoms in the second layer, leaving 0.75 ML of Ga atoms in that layer. A proposed model for the c(4 • 4) reconstructed surface is shown in Figure 10b [ 100]. There is no missing row of gallium atoms in this case, but rather a complete layer of cations with 1.75 ML of arsenic on top of it. The top layer, composed of 0.75 ML of arsenic, forms the characteristic "brickwork" pattern of the c(4 x 4) reconstruction. Clearly, there are significant differences in the concentrations of group-III and group-V elements present at the surface for the different reconstructions. There are a number of possibilities concerning how these differences could affect subsequent island morphology. Because these structures are typically grown in a group-V overpressure, it would seem that the concentration of group-III material could be the key variable. As previously noted, the (2 • 4) reconstruction has an incomplete layer of cations at the surface. Thus, significant variations in the energy barriers for diffusion on the surface may well result from the different atomic structures. These variations could lead to changes in the rate of diffusion of cations on the surface and also along step edges. Furthermore, the variations in the surface potential could easily produce sites of varying reactivity. This can be seen clearly in a study by Krhler et al. [88] in which Ge was deposited on the Si(111)-(7 • 7). When the deposition was at room temperature, Ge clusters with various

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[110]

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Fig. 9. Filled-stateSTM images of 1.5 ML of InSb deposition on (a) GaAs(001)-c(4 x 4) and (b) GaAs (001)-(2 x 4). The islands in (b) are slightly more elongated in the [110] direction than in (a). Monolayer-high steps are also observed in both images. Reprinted from J. Cryst. Growth, 175/176, 888, B. R. Bennett et al. (@ 1997), with kind permission of Elsevier Science-NL, Sara Burgerhartstraat 25, 1055 KV Amsterdam, The Netherlands. sizes were observed to be randomly distributed on the surface. However, the clusters rarely occupied a comer hole in the (7 x 7) reconstruction, indicating a different reactivity at that site. Along this same line of reasoning, there may be differences in the structures that the surface will try to form to minimize the surface energy; that is, the equilibrium structures of the surface may be different.

4.4. Effects of Surface Orientation Lattice-mismatched heteroepitaxy on a number of different (001) surfaces has been shown in many systems to follow the Stranski-Krastanov growth mode and eventually form coherently strained three-dimensional islands. Because the growth mode is dependent on the surface energy and reconstruction, another variable that can be used to affect the strainedlayer growth of heteroepitaxial systems is the surface orientation. Obviously, the electronic structure and symmetry of the surface can lead to different reactivities and island shapes.

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For example, the Si(111) surface has threefold symmetry in the surface plane. Both Si homoepitaxy [88, 92] and Ge deposition [101] on the Si(111) surface result in triangularly shaped islands, reflecting the symmetry of the surface. On the other hand, both the (001) and the (110) surfaces are rectangular, with in-plane nearest neighbors in the [110] and [ 110] directions. In GaAs homoepitaxy on the (001) surface, anisotropic islands elongated in the [ 110] direction are observed. These islands are random in shape apart from their anisotropy [76, 102]. However, GaAs homoepitaxy on a (110) surface results in triangularly shaped islands pointing in the [110] direction with elongated sides running in the (113) and (115) directions. This island shape indicates a preference for adatoms to attach at the base of existing islands (edges that run in the [110] direction) and illustrates the difficulty in predicting the shapes that islands will form on a given surface from surface symmetry alone [ 103]. In zincblende structures, certain crystal planes can actually have two types of surfaces because of the different ways in which the surface can be terminated. This is simply a result of the bilayer nature of zincblende structures. Diamond structures, such as silicon, do not exhibit this type of dependence because of their higher symmetry. To illustrate these differences, consider the { 111 } surfaces of a diamond and a zincblende structure. Figure 11 a shows the unit cell of a zincblende structure. For the sake of discussion, let the white dots represent the anions and let the black dots represent the cations. The diamond structure, on the other hand, would have the same atomic positions, but, obviously, there would be no distinction between the types of atoms. The models for the (111)A and (111)B surfaces shown in parts b and c of Figure 11, respectively. For the unreconstructed compound surface, it can be seen that a surface will be either cation rich for the (111)A surface or anion rich for the (111)B surface. Clearly, different reactivities can be expected between the Aand B-type surfaces. For the diamond structure, the (111) surface would appear identical in either case because of its symmetry. In some heteroepitaxial systems, growth on different surface orientations can dramatically change the growth mode. For example, in the case of InAs deposition on GaAs(001), which was discussed earlier, the growth was shown to proceed in a layer-by-layer manner, to the formation of coherent three-dimensional island and then, finally, to dislocated threedimensional islands. When InAs is deposited on GaAs(110) and GaAs(111)A, however,

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no coherent three-dimensional islands are observed [104-106]. On both surfaces, twodimensional islands are observed in a layer-by-layer growth mode, but the formation of three-dimensional islands is replaced by the introduction of misfit dislocations as a strainrelieving mechanism. Interestingly, on the G a A s ( l l l ) A surface, Gonzalez-Borrero et al. [ 107] report quantum dot formation for InGaAs deposition. Altogether, these authors grew In0.sGa0.sAs quantum dots on (n 11)A/B surfaces, where n was 1, 2, 3, 5, and 7, and compared the samples by PL measurements. In their work, they demonstrated that the (n 11)B surfaces had a higher integrated PL intensity compared to the (n 11)A surfaces, with the (311)B surface showing the most uniformity in island sizes as judged from PL. Nishi et al. [108] studied the In0.sGa0.sAs quantum dot formation on the (311)B surface and found the dots to have an approximate diameter of 25 + 2 nm and a height of 13.7 4- 2.2 nm, as determined from AFM. Luminescence peaks resulting from dots grown on the (311)B surface were shown to be much narrower than those measured from dots on a (100) surface. Germanium deposition on different silicon surface orientations has been an area of recent interest because of its potential uses in optoelectronic devices. High-index silicon surfaces have been of particular interest because of their unusual density of states, which results in promising optical [109, 110] and transport properties [111, 112]. One drawback of high-index surfaces is that they tend to be high-energy surfaces and, consequently, form low-index facets upon annealing [ 113, 114]. One high-index surface that has been of particular interest is the (113) surface. One study by Gibson et al. [ 115] showed that annealing Si(110) produced various low-index planes, as well as (113) facets. Also, the Ge "hut clusters" that have been observed are faceted structures composed primarily of { 113 } planes [88, 89]. Thus, it appears that the Si(ll3) surface is a relatively low-energy surface and may be suitable as an MBE growth surface. One example of Ge growth on Si(113) was reported by Knall and Pethica [87]. In this work, a number of STM images were presented at various coverages ranging from clean Si(113) up through 5 ML, by which point threedimensional islands had begun to evolve on the surface. Furthermore, they performed similar growths on Si(100) to contrast the differences resulting from the initial growth surface. The Ge growth on the (113) surface was predominantly two dimensional up to coverages of approximately 3 ML, whereas on the (100) surface second-layer growth of Ge islands began at submonolayer coverages. By 2.5 ML of deposition, at least four distinct levels could be observed on a given terrace. The differences in the growths were attributed to the preferred nucleation of islands at antiphase domain boundaries in the (100) surface reconstruction. Other studies have also shown that the nucleation of islands at antiphase domain boundaries can be a dominant growth mechanism [ 116, 117].

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5. THREE-DIMENSIONAL ISLANDS In the previous sections, the Stranski-Krastanov mode was introduced and the transition from layer-by-layer growth to three-dimensional island growth was discussed. In recent years, these islands have been utilized as nanostructures. These self-assembled islands will be the focus of this section.

5.1. Early Work Although the Stranski-Krastanov growth mode has been known for many decades, it was not considered until relatively recently as a method to fabricate useful nanostructures. As previously mentioned, there is an emphasis in epitaxy on the creation of smooth surfaces and interfaces. Moreover, much of the early work in studying growth modes was done with metal-on-metal epitaxy (e.g., Ag/Mo) or metal-on-semiconductor epitaxy (e.g., Ag/Si) [ 19, 24]. These structures were not considered to be useful nanostructures because defects readily formed in these islands. With more work in strained-semiconductor epitaxy, evidence evolved that these islands were not defected. One early report that showed evidence of island formation was presented by Goldstein et al. in 1985 [ 118]. They were studying InAs/GaAs superlattices and some samples exhibited three-dimensional nucleation. During growth, the RHEED pattern changed from a diffuse pattern to a spotty pattern, indicating three-dimensional growth for an InAs thickness greater than 2 ML. In TEM images, they observed localized strain fields that, in retrospect, were caused by the InAs islands that were present. Because the islands were surrounded by other material, direct observation of the islands was not possible; yet there was no evidence of dislocations. In 1990, two important reports were published that peaked interest in the field of selfassembled semiconductor islands. In the first report, Eaglesham and Cerullo [59] examined Ge deposition onto Si(100). Their goal was to disprove the assumption that islands formed during Stranski-Krastanov growth are always dislocated. Using TEM, which is sensitive to dislocations and structural defects, they explored the islands. In plan-view images, they observed a strain contrast feature (cf. Fig. 12), consistent with a coherent particle within a lattice-mismatched matrix [58]. From their work, they developed the concept of the coherent Stranski-Krastanov growth mode. Similar results were reported later in this material system by Krishnamurthy and co-workers [ 119]. The second paper, by Guha and co-workers [60], presented coherent Ga0.5In0.sAs islands formed on GaAs, examined by cross-sectional TEM. Many of the islands, as shown

Fig. 12. Plan-viewTEM image showing Ge islands surrounded by Si. The strain contrast features indicate that the islands are defect free. Reprinted with permission from D. J. Eagleshamand M. Cerullo, Phys. Rev. Lett. 64, 1943 (9 1990 American Physical Society).

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Fig. 13. Cross-sectionalTEM image showingInAs on a GaAs surface. No defects are observedin these islands. Reprinted with permissionfrom S. Guha et al.,AppL Phys. Lett. 57, 2110 (@ 1990American Institute of Physics).

in Figure 13, were found to be defect free. Those that were defected exhibited dislocations and stacking faults that were injected from the edge of the islands. These results not only support those seen for Ge on Si, but extend the phenomenology to results for compound semiconductor systems. Semiconductor nanostructures are often considered candidates for quantum structures such as quantum dots. Such structures are discussed in detail elsewhere in this book as well as in the literature [ 16, 70]. Leonard et al. [ 120] first demonstrated the application of coherent Stranski-Krastanov islands as quantum dots in 1993. In this work, Ga0.5In0.sAs was deposited on GaAs. As in the case of the previous work, the GalnAs was deposited by MBE until the RHEED pattern indicated a three-dimensional growth. The quantized properties of the islands were determined from photoluminescence. This work was the precursor to additional studies of these self-assembled islands as quantum dots, which is ongoing today, because it is extremely promising for many applications. Additional comments concerning applications of such islands are discussed in the following section. Many additional reports have more recently disclosed self-assembled semiconductor islands during multilayer strained heteroepitaxy. The remainder of this section will address some topics in this field, including how the islands provide strain relief, different types of three-dimensional islands, the impact of deposition conditions, and the formation of islands on different surface orientations. This section will finish with a few unique approaches to arranging the islands.

5.2. Strain Relief from the Islands Islands form as a way for the system to relieve strain. The complete details of how this occurs are not known, but a few observations and theories exist. In the Stranski-Krastanov growth mode, the material will begin to grow in a layer-by-layer fashion. At some point, the strain energy can be initially relieved by surface roughening, as shown in Figure 14 [ 121].

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Fig. 14. Stranski-Krastanov growth mode. The growth is initially two dimensional. As the strain energy increases, the surface starts to roughen. With additional deposition, three-dimensional islands form to provide additional surface area to relieve strain. In many cases, the roughening cannot be clearly observed before island formation.

Fig. 15. Schematicdiagram showing nontetragonal deformation of three-dimensional islands. The layer relaxes toward its natural lattice constant with distance from the heterointerface. Reprinted from J. Cryst. Growth 134, 51, N. Grandjean and J. Massies (9 1993), with kind permission of Elsevier Science-NL, Sara Burgerhartstraat 25, 1055 KV Amsterdam, The Netherlands.

A rough surface has a larger surface area than a smooth surface; free surfaces can provide strain relief [ 122]. This roughening has been observed to occur in some material systems. In other material systems, the growth goes directly to the formation of three-dimensional islands at a low coverage without a clear roughening stage. Regardless of whether a layer undergoes roughening, the islands form to relieve strain. This relief results most likely from a combination of two effects. First, three-dimensional islands have a larger surface-to-volume ratio than a flat layer. Although this increased area has a related increase in the total surface energy, there is more freedom for the lattice within the island to relax. This relaxation is often referred to as nontetragonal deformation [80, 121]. In a strained two-dimensional layer, there is tetragonal deformation, as shown in Figure 4. The lateral or in-plane lattice constant is constant in each layer. In an island, however, the in-plane lattice constant may be different on the top of a unit cell than on the bottom; that is, the cell is trying to return to its natural lattice size, as shown in Figure 15. In a study of GalnAs islands on GaAs, Guha et al. [60] measured the lattice spacing within the islands and found that it increases with the distance from the base or interface. Second, the material surrounding the islands can accommodate some of the strain [59]. The lattice constant of the material surrounding the island deviates from its natural value; the strain energy is distributed over a larger area. A schematic representation of this is shown in Figure 16, where the substrate lattice is locally deformed. This has been observed in several transmission electron microscopy studies [59, 123].

5.3. Different Types of Islands Several stages of islanding have been observed in heteroepitaxial growth. These stages are often overlapping with different types or sizes of islands coexisting. The three types of islands are the following: (1) small islands, also known as precursor [90] or quasitwo-dimensional [86] islands; (2) medium-sized three-dimensional islands, which are still lattice-matched to the substrate (i.e., which are still strained); and (3) large, defected islands, which are no longer lattice matched to the substrate (i.e., which have relieved their strain by defect formation). One example of these different types of islands was observed in the work by Reaves et al. [123] for InP islands formed on GalnP/GaAs(100) surfaces (cf. Fig. 17). The small

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Fig. 16. Schematic diagram showing deformation of the substrate resulting from concentration of the strain by a three-dimensional coherent island. Reprinted with permission from D. J. Eaglesham and M. Cerullo, Phys. Rev. Lett. 64, 1943 ( 9 1990 American Physical Society).

Fig. 17. Example of the three different types of islands. In this atomic force micrograph of InP growth on GalnP/GaAs(100), small islands are labeled A, medium-sized islands are labeled B, and large defected islands are labeled C. Reprinted from Surf. Sci., 326, 209, C. M. Reaves et al. ( 9 1995), with kind permission of Elsevier Science-NL, Sara Burgerhartstraat 25, 1055 KV Amsterdam, The Netherlands.

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SELF-ASSEMBLED SEMICONDUCTOR ISLANDS

Fig. 18. Deducedshape of coherent InP islands. Reprinted with permission from K. Georgsson et al., Appl. Phys. Lett. 67, 2981 (9 1995 American Institute of Physics).

islands, an example of which is labeled A, are about 20 A high and have a base width of 1200 A. The medium-sized islands, an example of which is labeled B, are about 240 A high and have a base width of 1200 A. The defected islands, an example of which is labeled C, can vary in size, depending on the extent of deposition. The defected islands continue to grow with deposition, with each new dislocation in an island allowing a significant jump in the island size [124]. These islands become more obvious after they have grown to be much larger than the other islands that are present. Note that, for a given type, the islands appear to be similar in size. Size distribution studies for this and other material systems illustrate this [120, 125]. The exact shape of self-assembled islands is difficult to measure. One study discussing the shape of these islands was presented by Georgsson et al. [126] for InP islands. Many reports of islands observed by AFM or low-resolution electron microscopy conclude that the islands are cap-shaped and featureless. As shown in Figure 18, however, the islands are polyhedral. The tops are flat and the side walls consist of { 110 } and { 111 } planes. The shape varies according to the different crystallographic orientations that are present.

5.4. Impact of Deposition Conditions In fabricating nanostructures for a particular application, the size is often important. What determines the size of self-assembled islands? Because they form as a way for a heteroepitaxial layer to relieve strain, one thought would be that only the lattice mismatch and the elastic properties of the layers should matter. This is not the case, however, because the island size can vary for the same material system deposited under different conditions. This implies that the formation of the islands is kinetically controlled under technologically relevant growth conditions. A few observations on these variations in island size and density will be discussed next. One interesting observation is that the size of the islands for a given material system and set of deposition conditions will lock into a defined size. Only defected islands increase in

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10

D e p o s i t i o n Time, s Fig. 19. Island size vs deposition time for different types of InP islands. Note that the size of the small (type A) and medium-sized (type B) islands does not change with additional deposition. Reprinted from Surf.. Sci., 326, 209, C. M. Reaves et al. (9 1995), with kind permission of Elsevier Science-NL, Sara Burgerhartstraat 25, 1055 KV Amsterdam, The Netherlands.

size as additional material is deposited. This was quantified for the InP/GalnP/GaAs(100) system [ 123]. The height and base width of the small and medium-sized coherent islands are constant with additional deposition, as shown in Figure 19. Such observations indicate that coherent islands have a preferred size and remain at that size until they develop dislocations. As indicated by the error bars in Figure 19, the size distributions for the coherent islands, particularly for the medium-sized islands, are narrow. If the islands are not getting bigger, then where is the newly deposited material going? Although some of this material goes into the growth of defected islands, the primary result is that the density of the islands increases. Reports in the literature show that the onset of three-dimensional islands, that is, the medium-sized islands, is abrupt. For the case of InAs/GaAs(100), the critical coverage for this transition is around 1.5 ML [86, 127]. Within 0.1 ML of additional coverage, the density of the medium-sized islands is already 109 cm -2. This density continues to increase throughout the deposition [123, 128, 129]. Hence, the formation of these islands is governed by kinetics. With this in mind, the substrate temperature is expected to be a major influence on the size and density of the islands. Indeed, this has been observed to be the case. At low temperatures, island formation can be suppressed; diffusion is insufficiently rapid for islands to nucleate and grow [ 129]. The island size, in particular, the height, increases with increasing substrate temperature [ 125, 128, 130]. One explanation for this observation is that adatoms have a larger diffusion range at higher temperatures. They are more likely to find an existing island and add to that island rather than nucleate a new island. As a result, a lower density of larger islands

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SELF-ASSEMBLED SEMICONDUCTOR ISLANDS

is expected at higher temperatures. This is observed to be the case in reports where both island size and density are tracked as a function of substrate temperature [ 125, 128, 130]. Another deposition condition that can influence island size is the deposition rate or, equivalently, the arrival flux of the growth species. If the deposition rate is relatively high (relative to the rate of surface diffusion), the number of unattached adatoms on the surface is high and, therefore, the probability of nucleation of a new island is high. This would lead to a higher density of smaller islands. Surprisingly, there have been few studies of the impact of deposition rate with few consistent trends having been observed to date [ 128, 131 ].

5.5. Impact of Surface Orientation As discussed in the previous section, the surface orientation will impact many of the processes occurring during epitaxy. A large fraction of semiconductor epitaxy is carried out on the (100) surface. The dominance of this surface extends into self-assembled islands formed during strained-layer epitaxy. Studies of growth on other surface orientations have, in general, shown some interesting results such as unique reconstructions [ 132] and different step-flow growth modes [133, 134]. Interesting results have also been observed in the case of self-assembled islands. One of the more interesting results for island growth on higher-index surfaces has been demonstrated by Nrtzel, Temmyo, and their co-workers [135-139]. For example, on a GaAs(n 11)B substrate, with n = 1-5, GaInAs has been deposited on A1GaAs layers. What happens is that the GaInAs moves below the A1GaAs surface and forms coherent disks. Such structures, as shown in Figure 20, are uniform in size and often well aligned. The selfassembled nanostructures formed on (311)B surfaces have exhibited the best alignment. Similar disks have also been formed on InP(311)B surfaces. Several reasons have been suggested for these phenomena, based on the high surface energies of these surfaces [ 140]. These structures have been used for several optical studies as well as the active region of injection lasers [ 141 ]. Self-assembled islands, produced by the coherent Stranski-Krastanov growth mode, also form on high-index planes. The (311) surface, for example, has been used to form coherent islands in several systems [ 108, 142]. One of the more obvious differences with

Fig. 20. Self-organized quantum disks formed by interlayer mixing of A10.5Ga0.5As on top of In0.2Ga0.8As on a GaAs (311)B surface. Reprinted with permission from R. Nrtzel, Semicond. Sci. Technol. 11, 1365 (9 1996lOP Publishing).

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WEINBERG ET AL.

respect to the (100) surface is that the islands are smaller and denser on the (311) surface. For example, with InP islands on GaInP/GaAs, the density of islands on the (311)A surface is 1010 cm -2, whereas, on the (100) surface, it is 109 cm -2 [108, 142]. The height of these islands decreases from 240 A on (100) to 60/k on (311)A. Island growth has also been observed for InAs on GaAs(111)A. These islands appear, however, to be incoherent from the initial stages of growth [106]. As self-assembled islands are used more frequently for physical studies and device applications, the ability to adjust their size and density will become increasingly important. One of the disadvantages of self-assembled approaches with respect to lithographic avenues is the lack of direct control on sample morphology. The situation with self-assembled islands is not hopeless, however. There is clear tunability of island morphology, not just with deposition parameters, but also with surface orientation. 5.6. Controlling the Location of Self-Assembled Islands

There have been several interesting phenomena observed with respect to where selfassembled coherent islands are located on the growth surface. These phenomena can readily be traced back to basic epitaxial processes. One case is the vertical alignment of islands grown in sequential layers. If an array of islands is formed and then overgrown with buffer materials, the next layer of islands that is formed will be positioned directly above the first array of islands. This will continue to occur with additional layers of islands, as shown in Figure 21. This phenomenon has been observed by several groups [143-148]. Because

Fig. 21. Verticalalignmentof InAs islands formedduring sequential layers of island growth.Reprinted with permissionfrom Q. Xie et al., Phys. Rev. Lett. 75, 2542 (9 1995AmericanPhysical Society).

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SELF-ASSEMBLED SEMICONDUCTOR ISLANDS

the strain fields from the islands extend into the surrounding materials, the thickness and modulus of the spacer layer are important. For the case of InAs islands separated by GaAs layers, spacers thinner than 150 A lead to good vertical alignment [144]; for Ge islands separated by Si, spacers thinner than 1000 ,~ are needed [ 147]. This alignment arises from the impact of strain on surface diffusion [ 144]. The strain fields from an island can extend into the capping layer. One simple picture is that for a compressively strained island, the strain field in the spacer layer will make the local lattice constant larger. Adatoms for the next layer of islands will preferentially locate in these regions above previous islands. One result of this strain propagation is that the islands may grow larger because of less local lattice constant mismatch. This can be seen clearly in Figure 21. Surface morphology will also impact where islands form. Vicinal surfaces with monolayer steps are common as epitaxial growth substrates. Two reports for InAs islands on GaAs(100) have presented evidence that these steps are impacting island formation. Ikoma and Ohkouchi [149] found islands aligning along [110] steps on a surface that had a 1~ vicinal miscut towards [ 110]. A similar preferential nucleation of islands at step edges was observed by Leonard et al. [127] for a nominally flat surface. Moison et al. [150], however, have observed that the majority of islands nucleate on the terraces away from the step edges. It is known that surface steps influence surface diffusion and attachment [ 151,152]. These influences may provide local variations in adatom concentrations that increase the probability of island formation. Such variations in the basic epitaxial growth process would also arise from surface features larger than monolayer steps. Under certain growth conditions, various surface features will form. These are commonly identified as bunches of monolayer-high steps [133, 134, 153]. When these step bunches are present, they will act as nucleation sites for self-assembled islands. This has been observed for InAs/GaAs(100) [127, 154], for InGaAs/GaAs(100) [155], and for InP/GalnP/GaAs(100) [ 156]. In these reports, strings of several islands were found to be aligned along these surface features. Large surface features can also be formed by patterning a substrate. Several groups have demonstrated various results. Mui et al. [ 157] performed InAs deposition on a GaAs(100) surface that had etched ridges. For [011 ] ridges, the islands only formed on the (100) planes at the top of and in the valleys between the ridges. The islands were observed to form along the side wall of [011] ridges with no islands formed on the (100) top and valley planes of the ridges. Saitoh et al. [158] etched tetrahedral pits into a GaAs(111)B surface and then formed InAs islands. Depending on the deposition temperature, the islands were observed to form either on the side wall of the pit or only in the bottom vertex.

6. PHYSICAL PROPERTIES AND APPLICATIONS OF SELF-ASSEMBLED ISLANDS In this chapter, there has been a focus on the formation and structural properties of selfassembled semiconductor islands formed during heteroepitaxy. One motivation for work on this topic is the unique physical properties of the islands. These properties are discussed in detail elsewhere in this book and in other reviews [159, 160]. In this section, a few properties and uses of self-assembled islands will be discussed.

6.1. Physical Properties: Some Examples As previously mentioned, semiconductor nanostructures are of interest for their often unique physical properties. These structures can be engineered such that they can confine electrons into small regions, leading to potentially useful effects. A few studies and applications of these effects will be discussed here. Luminescence is the optical emission resulting from an electronic relaxation [ 161, 162]. The electrons can be initially excited with higher-energy photons as in photoluminescence

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WEINBERG ET AL.

or with higher-energy electrons as in cathodoluminescence. Such techniques are commonly used to study the properties of solids and engineered structures. They also provide some insight into how materials will behave in some applications such as lasers and light-emitting diodes. There has been some effort to study the luminescence from a single quantum dot. As previously discussed for self-assembled islands, the sizes have a narrow, yet finite, distribution. The quantization of energy levels in these nanostructures is a function of size. Even small variations in size will lead to a range of electron energy levels. The resulting luminescence from an ensemble of islands is, therefore, broadened. This convolution can hide the true properties of the nanostructures. There were two early reports in the literature regarding luminescence from small ensembles of self-assembled islands. Marzin et al. [163] have studied self-assembled InAs quantum dots with photoluminescence. Using electron beam lithography, the authors were able to pattern a sample containing the nanostructures into separated mesas. Because each mesa had a limited number of islands, the luminescence spectrum, shown in Figure 22, exhibits isolated peaks. Grundmann et al. [164] have made similar studies with cathodoluminescence in which the size of the excitation electron beam could be decreased to a 50 nm diameter. Their results from a self-assembled InAs island sample, shown in Figure 23, also exhibit isolated peaks. Both studies conclude that the narrow peaks ( Spontaneous emission

Laser excitation

Ig> Fig. 3. Opticalpumping. A laser is used to excite an atom from the ground state [g) to the excited state le). While the atom is in the excited state, there is some probability that it will fall into the metastable state Im) by spontaneous emission. Once in Im),the atom can no longer interact with the laser.

The Doppler shift is especially important in experiments where atoms are being slowed by a counterpropagating laser beam. As the atoms slow, their velocity component along the laser beam changes by enough to shift them completely out of resonance very quickly. To counteract this effect, a number of approaches can be taken. For example, a spatially varying magnetic field can be used to keep the atoms in resonance by the Zeeman shift [23], the laser frequency can be varied in time ("chirped") to slow repeatedly one group of atoms after another [24], or very broad band laser light can be used [25]. So far, our discussion of the spontaneous force has tacitly assumed only two atomic levelsnthe ground state and the excited state. If there are other states in the atom, a possible pitfall arises as a result of what is referred to as optical pumping (see Fig. 3). Optical pumping occurs if somewhere below the excited state there is a metastable state that has even a small probability of receiving an atom by spontaneous decay. Over many excitationdecay cycles (required if the spontaneous force is to have a significant effect on the atomic motion), a sizable fraction of the atoms can get trapped in the metastable state. As this happens, these atoms will stop participating in the spontaneous force process and become a potentially troublesome background unaffected by the laser light. For example, in the case of sodium, the 32S1/2 ground state is split into two hyperfine levels separated by 1772 MHz. If the spontaneous force is exerted by tuning a laser from one of these levels to a hyperfine level of the excited 32p3/2 state, there is a finite probability that some atoms will decay into the other ground-state hyperfine level. If nothing is done to prevent this, eventually all the atoms will be optically pumped into an off-resonance state and the spontaneous force will cease acting. Another example is chromium, where the spontaneous force can be applied by tuning 425-nm laser light from the 47S3 ground state to the 47p4 state located at 23,500 cm -1 (~2.9 eV). About 8000 cm -1 ( ~ 1 eV) above the ground state lie the 45D metastable levels, which are weakly coupled to the excited state with a transition rate of about 6000 s -1. Here, too, if the atoms are exposed to resonant radiation too long they will be lost and the spontaneous force will cease to have an effect. In many cases, optical-pumping population traps can be remedied by the addition of laser frequencies to pump the lost atoms back into the ground-to-excited-state loop. For sodium, an acoustooptic or electrooptic modulator can be used to put sidebands on the main frequency, and, for chromium, laser beams in the 660-nm range can be introduced. In some cases, however, the problem can become quite difficult if, for example, there are no lasers available at the necessary wavelengths or if there are too many metastable states. This latter situation occurs, for instance, if an attempt is made to apply the spontaneous force to molecules. Because of the manifolds of vibrational and rotational levels that exist

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McCLELLAND

in even the simplest molecular spectra, it is very unlikely for a given molecule to return to the original ground state and absorb more than one photon from the laser.

2.3.2. Dipole Force The other significant form of interaction between an atom and laser light is the dipole force. In this case, the force arises from a shift in the energy of the atom induced by the presence of the light field. If there is a spatial dependence in this shift, that is, a gradient in the energy, there will be an associated force. This force can be many times larger than the spontaneous force because it does not rely on the rate of spontaneous emission, but rather on how strong the laser-atom coupling is and how steep a gradient in light intensity can be achieved. As will be seen later, it is the interaction of choice in a majority of the atom-optical implementations involving laser light. To get some sense of the origin of the dipole force, a classical picture is helpful as a starting point. Consider the atom to be a charged harmonic oscillator (electron on a spring) with resonant frequency COo.One can then ask what happens when this atom is placed in a near-resonant oscillating electric field, that is, a laser field, with frequency co. The effect of this field is to induce an oscillating electric dipole moment on the atom with magnitude that depends on the atomic polarizability and how close o9 is to 090. The phase of the oscillating dipole relative to the phase of the electric field will vary from 0 ~ (in phase) to 180 ~ (out of phase) as o) goes from below the atomic resonance to above. Just as in the case for an atom in an electrostatic field, there will be an energy - l p . E associated with the induced dipole in the presence of the external field. This energy will, however, be positive for detuning above resonance (positive detuning) and negative for detuning below resonance (negative detuning). Thus, if the electric field has a gradient, the atom will feel a force away from high field strength for positive detuning or toward high field strength for negative detuning. Although the classical description gives a good physical picture for the qualitative behavior of the dipole force, to model the interaction correctly, a fully quantum treatment must be implemented. This can be done fairly easily via the dressed-state formalism for a two-level atom interacting with a monochromatic light field [26]. To determine the force on the atom in this approach, the energy shift as a function of laser intensity is derived, and then a spatial derivative can be taken. The energy shift in the atom is obtained by forming the two dressed-atom wave functions I1) and 12), each a linear combination of the ground state and excited state. For positive detuning, the state I1) consists of mostly the ground state, with an increasing admixture of the excited state as the laser intensity increases, and the state 12) is mostly the excited state with an increasing admixture of the ground state. The energies of states I1) and 12) are given by E1 =

h

h = 5([a

+ +

1/2 1/2

- A)

(5)

+ A)

(6)

where f2 = F(I/2Is) 1/2 is the Rabi frequency and A = COo- o9 is the detuning of the laser light from resonance. E1 and E2 are often referred to as light shifts of the atomic energy levels. In situations where the laser is tuned relatively far from resonance (i.e., when A >> ~2), nearly all the population is in the state I1), and this state is nearly identical to the ground state. At this limit, the energy of the atoms in the field is approximately equal to h f22/(4A). If the detuning is relatively small, however, the situation is a little more complex. Ignoring spontaneous emission, one simply has atomic populations in two states, with possible coherence between them, and the motion of the atoms is governed by the two distinct potentials [27]. Taking spontaneous emission into account, one can consider the limit in which the atom stays at rest while many spontaneous photons are emitted. In this case, one

342

NANOFABRICATION VIA ATOM OPTICS

can speak of a mean potential felt by the atoms, weighted by their relative populations in I1) and 12). This potential is given by [26]: hA In 1 + U : -~ 1_,2+ 4A 2

(7)

We note that in the limit A >> f2, the expression for U approaches the same limit as Eq. (5), that is, U ~ h~22/(4A). Although the potentials given in Eqs. (5) and (7) provide a simple basis for calculating the effects of a light field on the motion of an atom, often the real situation is more complicated. Most atoms are not two-level atoms, because, at a minimum, they will have some magnetic sublevels in the ground or excited state (or usually both). Considering that the laser light will have some definite polarization state, one must take into account which transitions between magnetic sublevels are allowed by optical selection rules and what their relative strengths are, as governed by the Clebsch-Gordan coefficients. The dressing of such a multilevel atom is possible, and it leads to an array of potentials, each associated with a state that is a linear combination of the various magnetic sublevels of the undressed atom. The motion of the atom on these potentials can be calculated, but, in practice, this must be done numerically because there are too many level populations and potentials to keep track of analytically. The situation is further complicated when the atoms move across the potentials too quickly for the population to settle into the dressed levels, thereby inducing nonadiabatic transitions between the dressed levels. More complexity is introduced when spontaneous emission is taken into account, as this introduces random transitions between the dressed levels. To account fully for all these effects and, hence, calculate exactly the motion of actual atoms in a light field, quantum Monte Carlo calculations are performed [28]. These consider the time evolution of the density matrix of the atoms, tracing many wave packets and allowing random spontaneous emission events to occur. After accumulating a large number of wave packets, the resulting distribution of atoms can be determined with fairly high accuracy. In the context of atom optics, these calculations find their most utility in providing confirmation of approximate models and modeling subtle experimental effects.

2.3.3. Laser Cooling One of the most dramatic forms that laser manipulation of atoms can take is the cooling of an ensemble of atomsmthat is, the reduction of the width of its velocity distribution. Laser cooling can be remarkably efficient, reducing the effective temperature of a cloud of atoms to as low as 200 nK or, in some cases, even lower. In addition to being a very useful tool for atom optics, laser cooling has a number of other applications, ranging from the development of very high precision atomic clocks [29] to the generation of a BoseEinstein condensate [30]. The simplest form of laser cooling is referred to as Doppler cooling [31 ]. In this version, counterpropagating laser beams tuned below resonance are directed at the ensemble of atoms (see Fig. 4). If an atom in the ensemble has a velocity component toward any of the incoming laser beams, it will see the laser frequency of that beam as being shifted higher because of the Doppler effect. Thus, the incoming laser will appear to be closer to resonance and the atom will feel a stronger spontaneous force from this beam. The force will be greater the closer the frequency is shifted toward resonance, or, equivalently, the larger the velocity component toward the incoming laser beam is./'he result is a velocitydependent force in a region of space sometimes referred to as "optical molasses" [32]. In such a region, the atoms move exactly as if they are in a viscous medium that dissipates their kinetic energy and results in a narrower velocity spread; in other words, they become cooled. The limits of Doppler cooling are set by a balance between heating caused by continued spontaneous emission, which adds random momentum kicks to the atomic velocities, and

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McCLELLAND

Spontaneous emission

j" Fig. 4. Dopplercooling. Counterpropagating laser beams, tuned below the atomic resonance, interact with a population of atoms with random velocities. Those atoms with velocity component Vx towardone of the laser beams will be Doppler-shifted closer to resonance and, hence, will feel a stronger spontaneous force from that laser. Thus, atoms feel a velocity-dependentforce, whichreduces the velocity spread of the population.

cooling from the optical molasses. The minimum achievable temperature is given by [33]: kB Tmin "-

hF 2

(Doppler cooling)

(8)

where kB is Boltzmann's constant and F is the spontaneous decay rate. For most atoms, this value is in the range of a few hundred microkelvins. Since the discovery of Doppler cooling, a number of new mechanisms that produce even colder atoms have been uncovered. Polarization-gradient cooling, in particular, has been shown to cool atoms below the Doppler limit [34, 35]. In this form of laser cooling, use is made of the potential hills created by the light shifts induced by the laser light. Atoms repeatedly climb these hills only to find themselves optically pumped to the bottom againm hence, the term "Sisyphus cooling" is often applied, after the character in Greek mythology who was forced to push a stone continually up a hill only to see it roll down again. The necessary configuration of potential hills is created by giving the counterpropagating laser beams different polarizations; for example, they may be linearly polarized perpendicular to each other (lin _1_lin configuration), or one could be tr + while the other is or-. The other necessary ingredient, besides a laser tuned below resonance, is that the atom must have some magnetic sublevel structure in the form of at least two Zeeman levels in the ground state. When such an atom is placed in a lin _k lin field, it can be viewed as moving on two light-shift-induced potentials, one for each Zeeman level. Each potential is sinusoidal in shape, but they are shifted by a half period relative to each other (see Fig. 5). As an atom in a given Zeeman level moves along the light-shift potential starting at the bottom of a hill, it must go up the potential and give up a corresponding amount of kinetic energy. At the peak of the hill, it is closest to resonance with the laser and, hence, has the greatest chance to be optically pumped to the other Zeeman level. If this pumping takes place, the atom finds itself at the bottom of the hill again because it is now on the other potential. As this process is repeated over and over, the atoms gradually lose energy and the ensemble can become cooled well below the Doppler limit. The minimum temperature obtainable in polarization-gradient cooling is conveniently expressed in terms of the recoil energy ER = h 2 k 2 / m , which is the kinetic energy associated with the absorption and emission of a single photon. The smallest values seen experimentally are in the range of 10ER to 15 ER, and these are reasonably well explained by detailed theoretical calculations [36]. Although it may seem that the recoil limit would represent an absolute minimum for any laser cooling process, recent research has shown that even this limit can be surpassed. Two schemes of interest that have demonstrated subrecoil velocity spreads have been velocity-selective coherent population trapping (VSCPT) [37, 38] and stimulated Raman cooling [39]. Both these processes are not, strictly speaking, cooling processes, but rely instead on creating a situation in which atoms can fall into a state that for a very narrow

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NANOFABRICATION VIA ATOM OPTICS

ii ii ii B

iiiii

~=m.=,,

..........

Laser.~..,,~

)Spontaneous

l~emission (

Light-shift

potentials

Energy l

Atomic motion

= Position Fig. 5. Polarization-gradient cooling. In a lin 2. lin laser field, an atom with two Zeeman levels in the ground state experiences two sinusoidal light shift potentials offset by one half period. As the atoms move along these potentials, optical pumping from one potential to the other occurs more readily at the peaks because the laser is red-detuned. Thus, atoms are forced to travel "uphill" more frequently, resulting in a net loss of kinetic energy.

(a)

Io>

(b)

le>

......

A.~ ..........

031

~"~

032

Ig~ ~ Ig,)

Ig~

Ig,)

,i~L~,772 MHz

Fig. 6. (a) Velocity-selective coherent population trapping (VSCPT). In a A configuration, an atom with two degenerate ground states Igl) and Ig2) interacts with counterpropagating tr+ and or- laser beams via a single excited state le). If the atom has momentum 4-hk, a coherent superposition state results that cannot absorb photons, Over time, atoms with momenta in very narrow ranges around +hk accumulate in the superposition state, resulting in cooled populations. (b) Stimulated Raman cooling. In a sodium atom, counterpropagating laser pulses with frequencies differing by the hyperfine splitting of the ground state (1772 MHz) generate Raman transitions with a detuning A from the excited state le). By adjusting the frequency width, detuning, and propagation direction of the pulses, selective population transfer for only atoms with near-zero velocity can be achieved. The result is an accumulation of cold atoms in one of the hyperfine states.

velocity range does not interact with the laser. By repeatedly giving atoms a chance to fall into this state, population can be accumulated with a very narrow velocity spread. In VSCPT, use is m a d e of a coherent superposition of two degenerate ground states coupled through an excited state in a " A configuration" (see Fig. 6a). Such a configuration is realizable, for instance, with the metastable helium 23S 1-23p1 transition, where the M -+ i and M = - 1 sublevels of the 23S1 lower state can be coupled to each other through the M = 0 sublevel of the 23P1 excited state [37]. The coherent coupling between the two M sublevels is created by counterpropagating lasers of opposite circular polarization, which results in a superposition state that cannot absorb photons (i.e., is "dark") if the atom has translational m o m e n t u m +hk. Thus, if atoms fall into states with m o m e n t u m + h k during a r a n d o m - w a l k process, they will remain there without being heated by scattering photons. The result is an accumulation of atoms in two very narrow velocity bands around

345

McCLELLAND

the velocities +hk/m or -hk/m. Using this scheme, temperatures (referring now to the width of the velocity distributions around 4-hk/m) well below the recoil limit have been observed. In the stimulated Raman process, cooling below recoil is achieved by making use of the "recoil-less" nature of stimulated Raman transitions. This type of cooling has been demonstrated in sodium, where Raman transitions are induced between the F -- 1 and F - 2 hyperfine levels by pulses of two counterpropagating laser beams differing in frequency by the spacing of the hyperfine levels (1772 MHz) (see Fig. 6b). By varying the frequency width, detuning, and propagation direction of the Raman pulses, all atoms except those in a very narrow velocity band around zero are transferred from the F = 1 to the F = 2 hyperfine level. From there, they are optically pumped back to the F = 1 level, in the process randomizing their velocity and giving them a chance to have zero velocity again. After several Raman pulse-optical pumping cycles, a population of very cold atoms is accumulated, and this has been shown in one dimension to have a velocity spread as small as 1/10th the recoil limit [39].

2.4. Atom Trapping Another important development involving the manipulation of atoms is atom trapping. Motivated in part by the opportunities for extremely high resolution spectroscopy, and also the study of collective effects such as Bose-Einstein condensation, there has been a great deal of research recently into ways to generate potential wells that will trap neutral atoms. Although, to date, the trapping of atoms has not been employed in any form of nanofabrication, the degree of control over atomic motion that it affords suggests that applications might be forthcoming in the near future. In principle, all the interactions discussed in the earlier part of this chapter can be put to use to trap atoms, with varying degrees of success. Generally speaking, because any interactions with neutral atoms tend to be weak, atom traps tend to be quite shallow. For this reason, the study of atom traps has historically been intimately connected with the study of atom cooling. An atomic population must be made very cold before it will be confined by the types of potentials available for trapping. Whereas electrostatic fields are generally too weak to trap atoms, magnetostatic traps have been used with considerable success. Considering the energy - / t . B of an atom with a magnetic dipole moment # in a magnetic field B, one can see that atoms whose moment is aligned along the field will have a minimum energy at a minimum in the magnetic field strength. Such a local magnetic field minimum can be produced in three dimensions in a number of ways. For example, a quadrupole trap for sodium atoms has been demonstrated using a pair of coils in a Helmholtz geometry, but with current flowing in opposite directions in the two coils (anti-Helmholtz configuration) [40]. This type of trap generates a magnetic field that increases linearly in all directions from a value of zero at the center and, hence, can have a relatively narrow confinement. It has a disadvantage, however, in that very cold atoms can escape in a very small region around the zero of magnetic field at the center of the trap by flipping their spins (i.e., they undergo Majorana transitions). Another scheme, demonstrated with spin-polarized hydrogen atoms [41 ], employs a "pinch"-type trap made from a superconducting quadrupole magnet for radial confinement and two auxiliary solenoids for axial confinement. Still another scheme uses six permanent magnets oriented along three mutually orthogonal axes around a region in such a way as to create a local minimum at the center and a quadratic dependence of the field in the radial direction. This arrangement has been used to trap lithium atoms with good efficiency [42]. Although magnetostatic traps are simple in concept and are usable when no optical means are available (such as with hydrogen), by far the most popular atom trap has proven to be the magnetooptical trap (MOT) [43]. This trap makes use of the spontaneous force from resonant laser light to confine atoms. It relies on there being some magnetic sublevel

346

NANOFABRICATION VIA ATOM OPTICS

Fig. 7. Magnetoopticaltrap (MOT). (a) A magneticfieldthat increases linearly from zero in all directions is produced by two coils with current I flowing in opposite directions (anti-Helmholtz configuration), and three pairs of oppositely, circularly, polarized laser beams counterpropagate through the center. (b) Energy of a J = 0 --+ J = 1 atom in the presence of the magnetic field of an MOT. The magnetic sublevels M = - 1, 0, 1 are shifted in opposite directions on opposite sides of the center. When the laser frequency Wlaser is tuned below resonance, atoms at negativepositions are closer to resonance with the tr + laser beam, while atoms at positive positions are closer to resonance with the tr- laser beam. Thus, all atoms feel a net spontaneous force toward the center.

structure in the atom, and also on the fact that tr + light excites only A M -- + 1 transitions, whereas o r - light excites only A M = - 1 transitions. The atoms are placed in a quadrupole magnetic field generated by a pair of coils in the anti-Helmoltz configuration, and irradiated with three pairs of counterpropagating laser beams along three mutually orthogonal axes (see Fig. 7). The restoring force necessary to keep the atoms in the center of the trap is generated by a combination of (a) a laser tuned below resonance, (b) opposite circular polarization in the counterpropagating laser beams, and (c) a radially increasing Zeeman shift of the atomic energy levels resulting from the magnetic field. Referring to Figure 7b, which shows the energy levels of an idealized J - 0 --+ J = 1 atom along one dimension of the trap, we see that with a laser tuned below resonance the M -- + 1 state is Zeemanshifted closer to resonance for negative positions, whereas the M -- - 1 state is Zeemanshifted closer to resonance for positive positions. Thus, for negative positions, the atoms will interact most strongly with the cr + light, which is incident from negative to positive, and vice versa for positive positions. The result is a restoring force that keeps atoms trapped at the minimum of the magnetic field. Magnetooptic traps owe their popularity to their relative simplicity of construction and their relative robustness of operation. Typically, up to 108 atoms can be confined with peak densities up to approximately 1011 atoms/cm 3. An added advantage of the traps is that the negative detuning of the laser contributes some velocity damping to the force, and, hence, the atoms are cooled as well as confined while in the trap. Temperatures around 1 mK can be readily achieved, and with some care even sub-Doppler cooling is possible [44]. Atoms can also be confined with laser light alone. Making use of the dipole potential (see Section 2.3.2), a trap for sodium atoms has been demonstrated by tightly focusing a single red-detuned laser beam into a region of optical molasses [45]. The tuning below resonance of the trapping beam creates a dipole potential with a minimum at the highest laser intensity. Because the laser is a focused Gaussian beam, an ellipsoidal potential well is formed with its long axis along, and short axis transverse to, the laser beam. This concept has been further developed by making use of the fact that, for large detuning, the potential depth is proportional to I/A and the excited state fraction is proportional to I/A 2. Thus, a reasonable trap depth can be had with a very large detuning by using a very high laser intensity, all the while keeping the excited state population, and, hence, spontaneous emission and the associated heating, to a minimum. Such a trap has been demonstrated for rubidium atoms with a detuning up to 65 nm below the D1 resonance at 794 nm [46].

347

McCLELLAND

An intriguing example of dipole force atom trapping is the transverse confinement of atoms inside a hollow optical fiber. In the first demonstration of this [47], rubidium atoms were guided down the bore of a hollow optical fiber in which red-detuned laser light also propagated. The laser light in the fiber had a maximum along the axis, so the atoms felt a radially inward dipole force that prevented them from sticking to the fiber walls. Successful guiding was seen through a 31-mm length of fiber with a hollow-core diameter of 40/zm. Recently, a similar guiding has been accomplished using blue-detuned laser light coupled into the shell of the hollow fiber [48]. This allowed the atoms to be confined in a lowintensity region, thereby reducing the effects of spontaneous emission.

2.5. Bose-Einstein Condensation One of the ultimate goals of atom cooling and trapping research has been the formation of a Bose-Einstein condensate. For many years, it has been theoretically predicted [49] that a gas of atoms with the correct nuclear spin, if cold and dense enough, would undergo a phase transition, coalescing into a macroscopic occupation of a single quantum state with unique properties. Recently, this phenomenon has been demonstrated for three different atoms: Rb [30], Li [50], and Na [51 ]. In each case, a population of trapped atoms is cooled and compressed to the point where the predicted phase transition occurs, as evidenced by measurements on the spatial and velocity distributions of the atoms. In the case of Rb, the atoms were first trapped and cooled in an MOT. Then the MOT was shut off and the atoms were retrapped in a quadrupole magnetic trap that had an additional transverse rotating magnetic field component. The time orbiting potential (TOP) created by this configuration prevented the atoms from undergoing Majorana transitions at the trap center, The trapped atoms were then subjected to evaporative cooling by turning on a radio frequency (rf) field, which selectively allowed hotter atoms to escape the trap. It was this evaporative cooling step that provided enough reduction in temperature and increase of phase space density for condensation to occur. The experiments with Li were similar, except the trap was purely magnetostatic, formed by six permanent magnets arranged to produce a magnetic field minimum at the center and a quadratic radial dependence. The Na experiments used a quadrupole trap as in the Rb experiments, but the leak at the zero field point was sealed by focusing a far-off-resonant blue-detuned laser beam into the center of the trap. Bose-Einstein condensation is of interest to atom-optical methods for nanostructure fabrication mainly because of the type of atomic source it represents, As will be discussed in more detail later, thermal beams of atoms present some serious restrictions on what kind of atomic focusing can be achieved because of their spatial incoherence and broad velocity distributions. A Bose-Einstein condensate, on the other hand, represents an extremely coherent group of atoms that could, in principle, be focused with much higher precision, or even diffracted to generate complex patterns. Just as the laser, which in a way represents a Bose-Einstein condensate of photons, has introduced a wide range of new optical applications, we can imagine that a Bose-Einstein condensate of atoms could open many new possibilities for atom optics. Although these possibilities may be far in the future, progress is presently encouraging, as evidenced by the very recent demonstration of an "atom laser" produced by coupling Na atoms out of a Bose-Einstein condensate [52],

3. Atom Optics We now turn to a more specific discussion of the types of atomic manipulation that can generally be grouped under the concept of atom optics. As the name implies, atom optics is concerned with producing "optical" elements for beams of neutral atoms. These optical elements include, for example, lenses, mirrors, or gratings that manipulate atoms in ways analogous to the ways photons or charged particles are manipulated by similarly named

348

NANOFABRICATION VIA ATOM OPTICS

Source

Optics

size, divergence

(~ li ~~

Fig. 8.

Image Spot

[~aberraationceJ ~ns,.1 ~accept

Components of an optical system, illustrating the separation into source and optics characteristics.

objects in other forms of optics. We give here a summary of some of the various types of atom-optical elements that have been discussed in the literature. A number of reviews of this subject have also been published; in particular, references [17] and [53] are quite useful. The analogy between atom optics and ordinary optics, which has both classical and quantum mechanical aspects, is a very useful concept. On the classical trajectory level, the analogy arises from the fact that the motion of any particles traveling predominantly in one direction and affected relatively weakly by a conservative potential can be treated with a paraxial approach. This allows the separation of longitudinal motion from transverse motion and makes the concept of lenses useful. On the quantum level, there is a fundamental similarity between the time-independent Schr6dinger equation for a particle traveling in a conservative potential and the Helmholtz equation for an electromagnetic wave traveling in a dielectric medium [ 17]. Because these two take the same functional form, most of the results of scalar diffraction theory developed for light optics can be applied directly to atom optics. Thus, many insights can be had into the behavior of atom optics just by considering the light or charged-particle analog. Another advantage to using the concept of atom optics is that the analysis of atom beam manipulation can be separated into the roles played by the object (i.e., atom source) properties and the optical system properties (see Fig. 8). One can then concentrate on two separate problems: (1) developing the best optical system, assuming the source to be, for example, a perfect plane wave; and (2) developing the best possible source. This simplifies the analysis and often points to where the weakness of a system is. Having separated the problem in this way, one can then go a step further and see if there is a way to modify the optical system to accommodate the atom source, such as is done, for example, in light optics with achromatic lenses.

3.1. Atom Lenses

Because nanofabrication with atom optics is naturally concerned with concentrating atoms into nanoscale dimensions, atom lenses are of central importance for this field. Quite a few types of atom lenses have been discussed or demonstrated, utilizing a wide variety of atom manipulation methods. Although, so far, the application to nanofabrication has only been done with a limited subset of the types of lenses available, it is nevertheless useful to consider what possibilities exist, because future developments may broaden the field. To construct an atom lens, the most important requirement is a force that is exerted radially toward the axis of the optical system with a magnitude proportional to the distance from the axis, that is, F = -kr, where k is a constant (see Fig. 9). This is the necessary condition for Gaussian optics to hold, and it is the situation in which pure imaging takes place according to the elementary laws of optics, for example, the Gaussian lens law [54]: 1

1

1

s1

$2

f

349

(9)

McCLELLAND

~

F =-kr

_ r :Z

~

F=-kr

Fig. 9. The essential property of a Gaussian lens: A transverse force F must be exerted that is proportional to the distance r from the axis, so that all initially parallel rays cross the axis at the same point.

where S1 is the distance from the object to the lens, se is the distance from the lens to the image, and f is the focal length of the lens. In general, it is only necessary for the linear radial force dependence to hold in the vicinity of the axis of the optical system. In fact, nearly all optical systems deviate from linear dependence away from the axis, but as long as there is linearity near the axis these deviations can be treated as aberrations. If the radial force acts only over a short axial distance (compared to the focal length), the additional approximation of a thin lens can be made. If this is not the case, though, formalisms exist for treating the lens as a thick and possibly an immersion lens without undue complications. The construction of an atom lens then reduces to the production of a linear radial force dependence in the vicinity of an axis. Such a force can be achieved for neutral atoms using basically the same interactions that are used in atom trapsmthat is, either magnetostatic or optical forces [55]. Many arrangements of laser or magnetic fields that form atom lenses have been discussed in the literature; we discuss a few of them here to illustrate the variety of possibilities available.

3.1.1. Magnetic Hexapole Lens One of the earliest demonstrations of an atom lens utilized a magnetic hexapole field [56]. The radial dependence of such a field is quadratic near the center of the lens, resulting in the necessary linear dependence of the force on a spin-polarized atom. A recent demonstration of this type of lens [57] used NdFeB permanent magnet pole pieces arranged as shown in Figure 10. Using a laser-slowed atom beam, this experiment showed imaging of a pattern of holes drilled in a screen placed at the object plane of the lens. The focal length of the lens is governed by the velocity v of the atoms and the second derivative of the magnetic field B at the center of the lens, and is given in the thin-lens approximation by f --

my2 21zBf (oeB/oze) dz

(10)

where m is the mass of the atom. Typical focal lengths of 40-50 mm were obtained with Cs atoms slowed to 60-70 m/s and a magnetic field second derivative of 2.66 x 104 T/m 2.

3.1.2. CoaxialLaserLens The first demonstration of the use of laser light to focus atoms was done using a Gaussian, red-detuned laser beam copropagating with a thermal sodium atom beam [58]. Because

350

NANOFABRICATION VIA ATOM OPTICS

,p

Fig. 10. Poleconfigurationfor the magnetic hexapole lens discussed in [57]. Arrowsindicate the direction of magnetization.

of the red detuning, the atoms felt a dipole force toward higher laser intensity and were, therefore, attracted toward the center of the laser beam. Concentration of the atoms was observed by comparing the transverse atom beam profiles with the laser on and off. Using a 200-/zm laser beam diameter, focusing of the atom beam to a spot size of 2 8 / z m was achieved [59], demonstrating for the first time the concentration of atoms by laser light.

3.1.3. "Doughnut"Mode Laser Lens A major limitation on the spot size for atoms focused by a copropagating Gaussian laser beam is the diffusion of the atom trajectories caused by spontaneous emission. An alternative approach is to use a "doughnut"-mode, or TEMPi laser beam, which has a hollow center [60-62]. In this case, the laser is blue-detuned so the atoms are concentrated in the lower intensity regions of the laser beam and, hence, experience less spontaneous emission. Calculations of the behavior of such a lens have shown that, if the laser beam is brought to a diffraction-limited focus of approximately 1/zm, and if the atoms are constrained to travel through the center of this focus, focal spot sizes of 1 nm or less are, in principle, possible (see Fig. 11). An intriguing aspect of this "doughnut"-mode atom lens is that the axial dependence of the potential is such that the first-order (paraxial) equation of motion takes on exactly the same mathematical form as the equation of motion of an electron in a magnetostatic lens in the Glaser bell model [63]. This model, which allows an analytic solution to the equation of motion, has been analyzed in detail in the context of electron optics, so results can be transferred directly to the atom-optical case. The result provides an opportunity to analyze an atom-optical lens in great detail, examining all the common aberrations such as spherical aberration, chromatic aberration, and diffraction, as well as some unique ones such as spontaneous emission and dipole force fluctuations [62].

3.1.4. Spontaneous Force Lens Although the dipole force seems a natural choice for high-resolution focusing, it is also possible to focus atoms with the spontaneous force. Such a lens has been demonstrated using four diverging near-resonant laser beams aimed transversely at a sodium atomic beam from four sides (Fig. 12) [64]. The approximately linear force dependence in this case comes from the fact that the laser beams are diverging as they propagate toward the atom beam. Atoms traveling through this light field experience a higher laser intensity the farther away from the axis they are, and so the spontaneous force is greater (as long as the atomic transition is not saturated). With this lens, it was possible to create an easily discernible image of a two-aperture atomic source, demonstrating the imaging capability of

351

McCLELLAND

Fig. 11. Schematic of atom focusing in a "doughnut"-mode (TEM~I) laser beam. Atoms traveling coaxially through the focus of the laser beam feel a dipole force toward the axis, focusing them into a very small spot. Analysis of aberrations indicates that focal spots in the few-nanometer regime are possible.

,'-" Atoms

Laser-~l

F

Laser

~ .'%

-i ~ Laser

t'

Laser

Fig. 12. Spontaneous force lens. Four diverging resonant laser beams propagate transversely to the atom beam. Because the laser light becomes more intense as a function of distance from the axis, atoms feel a radially increasing spontaneous force, resulting in first-order focusing.

the technique. T h e two oven apertures were 0.5 m m in d i a m e t e r and the resulting i m a g e spot sizes w e r e 1.3 m m in diameter. The spot size was found to be limited by chromatic and spherical aberrations, as well as the r a n d o m c o m p o n e n t of the spontaneous force.

3.1.5. Large-Period Standing. Wave Lens A n o t h e r lensing t e c h n i q u e d e m o n s t r a t e d recently involved sending m e t a s t a b l e h e l i u m atoms t h r o u g h a l a r g e - p e r i o d standing wave [65]. The large-period standing wave was

352

NANOFABRICATION VIA ATOM OPTICS

I! stand,n0ave Atoms 25 l~m Laser

Fig. 13. Large-periodstanding-wavelens. A below-resonance laser beam reflects at grazing incidence from a substrate, creating a standing wavewith a 45-/zm-wideantinode. Atoms, aperturedby a 25-/zmslit aligned with the peak of the antinode, feel a dipole force towardthe highest intensity, resulting in focusing.

formed by reflecting a laser beam, tuned just below the 23S1 --+ 23p2 transition at 1083 nm, at grazing incidence from a substrate placed transversely to the atom beam (see Fig. 13). The atom beam was apertured to 25/zm, so that it filled only a portion of a single antinode of the standing wave, which was 4 5 / z m wide. Clear imaging, at unity magnification, of a 2-/zm slit and also a grating with 8-/xm periodicity was observed with this cylindrical lens. An image spot size of 6 / z m was observed under optimal focusing conditions. The major contribution to this spot size was considered to be diffraction, arising from the long focal length (28 cm) and small lens aperture (25/zm). Chromatic aberrations were held to a minimum because the atomic beam in this case was produced in a supersonic expansion. An additional interesting feature of this lens is that it was formed under conditions of relatively high intensity and small detuning. Ordinarily, spontaneous emission would be a major effect under these conditions, but, in this case, the transit time through the lens was too short for any significant amount to occur. Thus, the atomic motion in the lens was governed by the two potentials given in Eqs. (5) and (6), with a fair fraction (15%) of the atoms in the state that feels a repulsive potential.

3.1.6. Standing-Wave Lens Array An atom-focusing technique that has seen a great deal of attention recently is the focusing of atoms in an array of lenses created by a laser standing wave. This technique has been used successfully for nanostructure fabrication [66-69], and will be discussed in detail later on in this chapter. The principle of the approach is to make use of each node of a near-resonant, blue-detuned laser standing wave as an individual lens, so that the entire standing wave acts as a large lens array (see Fig. 14). Near the center of the nodes of the standing wave, the intensity increases quadratically as a function of distance from the node center. This intensity variation leads to a quadratically varying light-shift potential (as long as the excited-state fraction is low), and, hence, the force on the atom is linear and conditions are consistent with first-order focusing. Because of the high intensity gradient inside the node (the intensity goes from zero to full value in a fourth of an optical wavelength), it is relatively easy to get quite short focal lengths (on the order of a few tens of micrometers) with a standing-wave lens and, hence, small spot sizes, reaching into the nanometer regime.

353

McCLELLAND

Fig. 14. Standing-wavelens array. An above-resonance laser standing wave propagates parallel to and as close as possible to a surface. Collimated atoms, incident perpendicular to the surface, are focused in each of the nodes of the standing wave by the dipole force. Nanometer-scaled focusing has been demonstrated with this lens (see Section 4.1).

Fig. 15. Near-fieldlens. Below-resonance laser light propagates through a subwavelength-sized aperture. The longitudinally and transversely decaying transmitted laser light produces a light-shift potential that can focus atoms on the nanoscale.

3.1.7. Near-Field Lens Another recently proposed way to achieve nanometer-scale spot sizes makes use of the intensity pattern found in the vicinity of a small aperture irradiated by near-resonant reddetuned laser light [70]. In this scheme, atoms are passed through an aperture that is illuminated with light copropagating with the atoms (see Fig. 15). The aperture is typically made smaller than the optical wavelength, so the intensity pattern of the light on the far side of the aperture is dominated by near-field effects. Close to the aperture, the intensity falls off rapidly in both the radial and the axial directions. The radial dependence of the intensity approaches a quadratic form near the axis, so, again, the correct spatial variation of the light-shift potential for focusing is obtained. Because of the small size of the lens, short focal lengths can be obtained, and calculations involving the standard aberrations result in predicted spot sizes of 4-7 nm.

354

NANOFABRICATION VIA ATOM OPTICS

3.1.8. Channeling Standing-Wave Lens Although a laser standing wave can be used to construct an array of lenses for nanoscale focusing as discussed previously, it is also worth noting that it can be used in a macroscopic sense as well. A recent demonstration has shown that a diverging sodium atom beam passing through a standing wave can be concentrated by making use of the channeling that occurs in the nodes of the standing wave [71]. In this arrangement, the laser intensity is high enough to cause the atoms to be confined by the dipole potential and oscillate within a node as they traverse the standing wave. As they emerge from the standing wave, their trajectories are concentrated into groups traveling either toward the axis or away from the axis. Those atoms approaching the axis can be considered to be focused.

3.1.9. Fresnel Lens Although the bulk of atom lenses make use of magnetostatic or light forces, there is another type of focusing that has also been represented in atom optics. Fresnel lenses create focusing conditions by relying on a diffraction phenomenon. Typically, a mask is fabricated that transmits incident radiation or particles in a pattern of concentric rings, the radii of which increase as the square root of the ring number, counting from the center out. Diffraction from this pattern of rings creates a spherical wavefront that is convergent on a spot beyond the lens, resulting in focusing (see Fig. 16). The focal length is given by f = r21/)~dB,where rl is the radius of the innermost ring and )~dB is the De Broglie wavelength of the atoms. Such a lens has been demonstrated for atoms [72] using a freestanding Fresnel zone plate 2 1 0 / z m in diameter microfabricated from gold. The plate had 128 zones and a first zone diameter of 18.76/zm. Focusing of metastable He atoms in the 21S0 and 23S1 states was observed, as a result of diffraction caused by the atomic De Broglie wavelength. The atoms were produced in a cooled supersonic expansion, so the velocity spread was narrow and the mean velocity was variable (by varying the source temperature). The De Broglie wavelength of the atoms was, therefore, well defined, and was variable from 0.055 to 0.26 nm. Clear images of a single and a double slit were observed with approximately 1:1 imaging and a focal length of 0.45 m. The observed images of the 10-/zm slit were 18 lzm wide, in agreement with numerical calculations of the expected diffraction limit. Whereas the advantages of a Fresnel lens include no requirement for near-resonant laser light and, hence, no restriction on the atomic species that can be focused, the disadvantages include multiple focal lengths arising from multiple diffraction orders and spot sizes limited to no smaller than the smallest feature that can be fabricated in the zone plate.

Atoms ~

Fig. 16. Fresnel lens. A transmission mask diffracts atoms to form a converging spherical wavefront, thereby focusing them. The mask consists of concentric rings that increase in radius as the square root of the ring number, in accordance with the Fresnel zone formula.

355

McCLELLAND

3.1.10. Atom-Optical Calculations Whatever particular geometry of laser or magnetic fields is chosen to make an atom-optical lens, it is usually of interest to perform some calculations of the behavior of atoms in the lens to find out what focal lengths and resolutions might be expected. With the exception of the Fresnel lens, which must be treated with diffraction theory, most atom lenses can be treated quite successfully with a particle optics approach. Diffraction comes into play only in determining a limit on focal spot size. As long as the dimensions of the lens are large compared to the De Broglie wavelength, the spot size is well approximated by the diffraction limit formula used in conventional optics: 0.61Z~B d = (11) O/

where d is the full width at half maximum of the spot, LOB is the De Broglie wavelength, and c~ is the convergence half-angle of the beam at the focus. To trace the trajectories of atoms in a lens, the starting point is with the basic equations of motion derived from classical mechanics. In a cylindrically symmetric potential, these reduce to

d2r 1 0 U (r, z) dt----~ + -m ~ Or

= 0

(12)

d2z dt 2

- 0

(13)

!

1 OU(r, z) m Oz

where r is the radial coordinate, z is the axial coordinate, m is the mass of the particle, and U(r, z) is the potential. We note that Eqs. (12) and (13) are also applicable in a onedimensional focusing geometry, such as is found in a one-dimensional laser standing wave, with the substitution of the coordinate x for r. Thus, the following discussion also applies for this geometry. One approach to analyzing an atom-optical lens is simply to integrate Eqs. (12) and (13) numerically. This approach certainly gives useful information [73], but for motion that is generally axial it is often useful to eliminate time in these equations and write them as a single equation for r as a function of z. This is done by using the conservation of energy to reduce Eqs. (12) and (13) to ~zz[(ld

U(r,_~o + ) z1/2) (1 1(1

rt2)-l/2r']

U(r' z) ) -1/2 (1-+- rt2) l/2 OU(r' Z) = o

(14) E0 Or where prime denotes differentiation with respect to z and E0 is the initial kinetic energy of the atom. To simplify Eq. (14), it is very useful to make the paraxial approximation. This concentrates on trajectories that are not affected too greatly by the potential, that is, those that are near the axis, and is made by taking the limit r I 0.89) is of importance as a hydrodesulfurization catalyst and for its magnetic properties [53, 54]. Conventionally, it is synthesized through the direct reaction of elements [53, 55] (>500~ Some low-temperature routes are known. Reactions between anhydrous hexamine cobalt(II) and hydrogen sulfide at room temperature produce poorly crystalline CoS2 [56]. When anhydrous cobalt sulfate salt is exposed to a mixture of hydrogen and hydrogen sulfide at 525 ~ Co9S8 is formed [57]. We successfully prepared nanocrystalline Co9S8 and its serial compounds by the toluene thermal reaction between Na2S3 and COC12.6H20 in the temperature range of 120 to 170 ~ The phase formation can be controlled under appropriate reaction conditions. In a typical reaction, appropriate amounts of COC12-6H20 and Na2S3 (excess 50%) are added to an autoclave that is filled with toluene and maintained at 120-170 ~ for 12-24 h and then cooled to room temperature naturally. The different reaction conditions are shown in detail in Table I.

432

CHEMICAL PREPARATION OF NANOCRYSTALLINE MATERIALS

Table I.

Reaction Conditions of Cobalt Sulfides Temperature

Time

Reagent

Solvent

(o C)

(h)

Na2S 3 + COC12.6H20

Toluene

110-130

24

Co9S 8

Na2S 3 + COC12.6H20

Toluene

150-170

12

Co9S 8 +Co3S 4 +CoS 2

Na2S3 + COC12.6H20 + Zn

Toluene

170

12

Co9S 8

Co9S 8 + I2a

Toluene

170

12

CoS 2 +Co3S 4

Na2S 3 + anhydrous C o C 1 2

Toluene

140-170

12

CoS 2

Product

(Source: Data from X. E Qian et al., Inorg. Chem., 1999.) a Co 958 is first formedby the toluene thermal process at 120~ for 24 h, without any posttreatment,

12 is added, and then the autoclaveis continually maintained at 170~ for 12 h to form CoS2 and Co3S4.

In the preparation process, toluene is chosen because of its appropriate boiling point (110.6 ~ and pressure (about 5 atm at 178 ~ which is much lower than that of water (about 10 atm at the same temperature). So the toluene thermal process is much safer in comparison with the hydrothermal process. Furthermore, toluene is a poor polar organic solvent; it can avoid the immediate reaction of Na2S3 and COC12.6H20 at room temperature, which is beneficial to controlling the rate of the reaction and forming nanocrystalline materials. The toluene thermal process may be a liquid-solid reaction according to the theory of Gouw and Jentoft [59]. Because of the coexistence of S 2- ions, which have a weak reduction property, with water at high temperature [60], there is a redox reaction. The equation can be written as follows: 9COC12.6H20 + 9Na2S3 --+ Co9S8 + 18NaC1 + 19S + 54H20 Figure 11 a shows the XRD pattern of a typical sample prepared by the toluene thermal process. All the peaks can be indexed to the single phase of Co9S8 with lattice parameter a = 9.92 ,~, which is close to the reported data. The crystalline size of Co9S8 estimated by the Scherrers equation is about 20 nm. The TEM micrograph of the as-prepared Co9S8 particles shows the Co9S8 particles consisting of uniform spherical crystallites. The average size is about 20 nm, which is consistent with the result from the XRD pattern. In the preparation process of Co9S8, the water of crystallization in the precursor COC12-6H20 is very important. If we use anhydrous COC12 as the precursor, we only obtained the single phase of CoS2 (Fig. 1 lc) and no Co9S8 occurred. The average size of the particles is about 30 nm. In the anhydrous atmosphere, ionic sulfur may be present mainly as S 2- and it is difficult to disproportionate into S and S 2-. The reaction may be written as COC12 + Na2S3 --+ Co52 + 2NaC1 + S The reaction temperature and time have an important effect on the preparation processes of cobalt sulfides. The optimum condition for preparing Co9S8 is about 110-130 ~ for 24 h. If the temperature is lower than 100~ or the time is shorter than 12 h, the reaction is very slow and incomplete. If the reaction temperature is higher, 150-170 ~ a mixed phase of Co9S8, COS2, and Co3S4 results (Fig. 1 lb), which may be caused by the high reactivity of Co9S8 and an enriched sulfur environment in the autoclave. The process may be written as follows: NazS3 + 2H20 --+ HzS + 2NaOH + 2S Co9S8 + (9x - 8)H2S ~

9CoSx + (9x - 8)H2

433

x > 1.06

YITAI

P L+P

"2".

=.

v

--'-=--------

C

P

B C L ~ ~

L

C+L+P[I C+L "A

A t

20

30

40

50

60

20 (deg.) Fig. 11. XRD pattern of nanocrystaUine cobalt sulfide powders. (C = Co9S 8, L = Co3S4, P = COS2.) (a) Co9S8 prepared by the reaction of COC12.6H20and Na2S3 at 120~ for 24 h. (b) A mixedphase of Co9S8, COS2, and Co3S 4 prepared by the reaction of COC12.6H20 and Na2S3 in the range of 150 to 170~ for 12 h. (c) CoS2 prepared by the reaction of anhydrous COC12and Na2S3 at 140~ for 12 h. (d) A mixed phase of Co3S4 and CoS2 prepared by the reaction of Co9S8 and 12. (Source: Reprinted with permission from [52]. 9 1999 American Chemical Society.)

The process can be demonstrated by adding Zn and 12, respectively. As we add Zn to the autoclave with COC12.6H20 and Na2S3, we only obtain a single phase of Co9S8, even though the temperature reached 170 ~ for 24 h. This is due to the H2, which results from the reaction of the zinc and the water of crystallization and which shifts the equilibrium toward Co9S8. At the same time, if we add 12 to the Co9S8 (which is prepared according to the preceding procedure with no posttreatments) and react the solution at 170 ~ for 12 h, we obtain a mixed-phase C o 3 5 4 and CoS2 (Fig. 11 d). No Co9S8 phase occurs. This may be due to the formation of HI, which makes the equilibrium transfer to CoSx (x > 1.06) in accordance with the literature [61 ]. The sulfur contents of the as-prepared single phases of Co9S8 and CoS2 are determined by heating the samples to constant weights in a stream of oxygen [53]. The sulfides are converted to CoO at a temperature that does not exceed 900 ~ in order to prevent overoxidation of CoO. Products prepared by this procedure correspond to Co9S7.93 and CoS 1.97, respectively.

2.2.3. Cadmium Sulfide [621 CdS is an important material in nonlinear optics [63], quantum size effect semiconductors [64], electroluminescent devices [65], and other interesting physical and chemical technological applications [66-68]. Many methods have been developed to synthesize solid nanocrystalline CdS [63-69], but they all produce solid semiconductor particles or small clusters with morphologies. CdS nanorods were first prepared in ethylenediamine nonaqueous solvent systems with the reaction of cadmium metal powder and sulfur under pressure in an autoclave: Cd + S ~ CdS An appropriate amount of sulfur in ethylenediamine and cadmium powder were added to an autoclave filled with ethyleneamine. The autoclave was maintained at 120-190 ~ for 3-6 h and cooled to room temperature. A bright-yellow product was obtained.

434

CHEMICAL PREPARATION OF NANOCRYSTALLINE MATERIALS

C'|

.....

.--.

~

r

'

- ~ . -

,.~

-

~

~,,i ~

_J C ~

r~

t"! t"l

N 9

--

~

-.,

c-,!

.-,/-

er

~

~

D

t

i

,

~

~

II

II II IL.__ __J

t,,a

N

"

JL.______j

l

~

-

m N

k.

20

30

40

50

60

70

g0

20 (deg.) Fig. 12. XRD patterns of obtained samples: (a) CdS (prepared with Cd and S), (b) CdS (prepared with CdC12 and S), (c) CdSe, and (d) CdTe (W, wurtzite structure, ZB, zincblende structure). (Source: Reprinted with permission from [62]. 9 1998 AmericanChemical Society.) In the XRD pattern (Fig. 12), all the peaks can be indexed by the hexagonal cell of CdS (wurtzite structure) with lattice parameters a = 4.141/~ and c = 6.72/~. The unusually strong (002) peak in the pattern indicates a preferential orientation of [001 ] in CdS crystallines. Elemental analysis of the sample confirmed the element composition of CdS: Cd:S in 50:50 atomic ratios. This was also confirmed by energy-dispersive spectrometry (EDS) analysis. TEM images showed that the CdS crystallites synthesized in ethylenediamine solvent appear to display rodlike monomorphology with lengths of 300-2500 nm and widths of 25-75 nm (Fig. 13). Figure 13 shows that the CdS nanorod is a single crystal. The nanorod axis (growth direction) was [002], which is consistent with the XRD pattern (Fig. 12). In this synthetic system, the result of CdS nanorod formation indicated that the nucleation and growth were well controlled. The ethylenediamine plays an important role in controlling the nucleation and growth of the CdS nanorod. It was supposed that, owing to the ethylenediamine intermolecular interactions including hydrogen bond, van der Waals force, and electrostatic interaction, a supermolecular structure [70] was formed that provided a template for inorganic atom or ion self-assembling. Thus, the nanorod growth mechanism can be viewed as a templating mechanism. Using a similar process, CdSe and CdTe nanorods can also be prepared.

435

YITAI

Fig. 13. TEM imageof CdS nanorods. (Source: Reprintedwithpermissionfrom [62]. 9 1998American Chemical Society.)

2.2.4. Bismuth Sulfide [711 Av~vI 2 ~"3 ( A - - S b , Bi, As and B = S, Se, Te) group semiconductors have potential applications in television cameras with photoconducting targets, thermoelectric devices, electronic and optoelectronic devices, and in IR spectroscopy [72]. Bismuth sulfide (Bi2S3) has a direct band gap of 1.3 eV [73] and is useful for photodiode arrays or photovoltaics [74, 75]. The preparation methods of bismuth sulfide usually include direct reaction, chemical deposition, and thermal decomposition. Direct reaction and thermal decomposition need high reaction temperature. The products obtained by chemical deposition are amorphous or poorly crystallized. Here, we prepared Bi2S3 through a solvothermal reaction of BiC13 and thiourea in ethanol. In a typical synthesis, thiourea was dissolved in the ethanol in the autoclave, and then an appropriate amount of BiC13 was added with stirring. The autoclave was sealed and maintained at 140 ~ for 12 h and then cooled to room temperature. The dark-brown product was washed and dried in vacuum. The XRD pattern of the product is shown in Figure 14. All the peaks can be indexed with orthorhombic cells with a = 11.128, b = 11.264, and c = 3.978 ~, which are close to the reported data. A TEM micrograph (Fig. 15) shows that the particles have a size of 500 nm x 30 nm on average, which indicates that the morphology of Bi2S3 is rodlike. In comparison, nanocrystalline Bi2S3 prepared by the hydrothermal process also displays a rodlike shape with a particle size of only about 150 nrn x 40 nm. This means that the solvothermal method can control the growth of nanorods, which has been observed in IIVI group semiconductor nanorods. The formation of the bismuth sulfide in ethanol may be through two steps: (i) the formation of Bi-thiourea complex in ethanol and (ii) the thermal decomposition of Bi-thiourea complex in ethanol at appropriate temperature and the formation of bismuth sulfide. The influence of thermal treatment temperature and time on the formation of Bi2S3 in ethanol was investigated. The appropriate temperature for the preparation is 140 ~ If the temperature was lower than 100 ~ the product was poorly crystallized and some unidentified phases were detected. If the time was shorter than 6 h, there was some amorphous phase in the sample.

436

CHEMICAL PREPARATION OF NANOCRYSTALLINE MATERIALS

&

&

"7",

("4 r~

cO

15

25

"'~

35

'~1"

t",l

""

tt~

45

O

55

20 (deg.) Fig. 14. XRD pattern of Bi2S3. (Source: Reprintedfrom [71] with permissionof Elsevier Science.)

Fig. 15. TEM image of Bi2S3. (Source: Reprintedfrom [71] withpermissionof Elsevier Science.)

The IR spectrum of Bi2S3 showed no peaks of Bi203 and no evidence of organic impurities in the compound. The absorption peaks ranging from 3600 to 3000 cm-1 correspond to the - O H group of H20 absorbed in the sample. The absorption peaks centered at approximately 1630 cm-1 correspond to CO2 absorbed on the surface of the particle. In fact, the absorbed water and CO2 are common to all powder samples that have been exposed to atmosphere and were more pronounced for high-surface-area particles.

3. y-IRRADIATION SYNTHESIS AND CHARACTERIZATION OF NANOMETER MATERIALS Fujita et al. [76] began the synthesis of metal aggregates by the radiolytic reduction of metal cations in solution. In recent decades, this method has been developed further [77-80]. The technique of pulse radiolysis has been used to study the yield of short-lived clusters and

437

YITAI

their optical spectra in dilute aqueous solutions of about 10 -4 M metallic ions [81-83]. By this method, silver cluster and colloidal silver could form [84, 85]. The formation of other colloidal metals from correspondent ions such as Cu 2+ [86-88], Ti 4+ [89, 90], Pb 2+ [91, 92], and Pd 2+ [93] has also been studied. By high-energy electron irradiation of 1.7 x 104 M NaAu(CN)2 solution, Mossed et al. [94] prepared ultrafine Au particles. Marignier et at. [95] prepared ultrafine Ni and Cu-Pd alloy particles by separate y-irradiation of NiSO4 solution and CuSOn-PdC12 solution. However, the solutions used in the aforementioned studies are about 10-4 M metal ions, and the ultrafine particles produced are in the colloidal state. We have developed a new method--v-irradiation of solutions containing 10-2-10 -3 M metal ions--to prepare nanometer-sized powders of not only metals, but also nonmetals, alloys, metal oxides, metal sulfides, and nanocomposites. This method with relatively high yield of product and low cost can process under normal pressure at room temperature. During F-irradiation, the formation of hydrated electrons can be shown as follows [96, 97]: H20 --->e~q, H30 +, H, H2, OH, H202 Then the radiation reduction of metal ions by hydrated electrons leads to the formation of metal nanoparticles: eaq +Mm+ ~ e~q + M + ~ nM 0 ~

M(m 1)+ M~ M2 --+ Mn --+ Magg

where n is a number of aggregation of a few units and Magg is the aggregate in the final stable state [87].

3.1. Nanocrystalline Metals

3.1.1. Nanocrystalline Silver [981 Highly pure silver powders of fine, narrowly distributed, and uniform particles are very important in many fields of technology. For example, ultrafine silver powders constitute the active part of conductive ink pastes and adhesives used in the manufacture of various electronic parts [99]. Conductive silver pastes and inks form the bases for thick-film technology, for producing electronic components such as hybrid microcircuits [ 100], and for the internal electrodes of multilayer ceramic capacitors [ 101 ]. The stability of Ag42+ and colloidal silver has been investigated [ 102]. After 5 min of y-irradiation of a solution containing 5 • 10 -2 M AgNO3, 1.0 M (CH3)ECHOH, and 1.0 • 10 -2 M C12H25NaSO4 at a dose of 18.5 Gy/min (sample 1), the result is as shown in Figure 16. From this figure, it is obvious that the absorption at about 290 nm (due to the Ag42+ cluster [103]) decays very slowly. The Ag42+ cluster can exist for more than 1 month in y-irradiated concentrated AgNO3 solution in air. This is much longer than that in dilute Ag + ion solutions previously reported [103-109]. On the other hand, the absorption band of colloidal silver (around 400-410 nm [ 110]) broadens and shifts toward longer wavelengths at longer aging time, indicating a slow increase in the size of the colloidal silver. Because the colloid was stable, the hydrothermal treatment method was used to aggregate the colloid to metal powders. Solutions were prepared with silver nitrate of analytical grade in distilled water. Sodium dodecyl sulfate, poly(vinyl alcohol), and sodium polyphosphate were chosen as the surfactants, and isopropanol was used as a scavenger for hydroxyl radicals. Both the surfactant and the scavenger were added to solutions in various concentrations. All solutions were deaerated by bubbling with nitrogen for 1 h and then irradiated in the field of a 2.59 x 1015-Bq 6~ y-ray source with different doses. Then the irradiated solutions were put into autoclaves with Teflon inners and heated in an oven at different temperatures ranging from 105 to 200 ~ for different periods of time. After cooling to

438

CHEMICAL PREPARATION OF NANOCRYSTALLINE MATERIALS

tl) t~

.~ 1.0 O oo d~

:,,._t>-

~

,,~,\

460

660

goo k [nm]

700

Fig. 16. Aging effect in open air on the solution containing 5 x 10-2 M AgNO3, 1.0 x 10-2 M C12H25NaSO4, 1.0 M (CH3)2CHOH with 5 minutes of },-irradiation at a close rate of 18.5 Gy/min. Aging time after irradiation: ( .... ) just after irradiation, (. . . . ) 38 h, (..... ) 73 h, (--) 144 h, (--) 240 h. (Source: Adapted from Zhu et al. [ 102].)

A

t"4

t"q t",l

_

___JL

_

L B

__/ 30

40

50

60

70

80

20 (deg.) Fig. 17. X-ray diffraction pattern of the product prepared by the y-irradiation-hydrothermal treatment combined method: (a) sample 1 and (b) sample 4. (Source: Reprinted from [98] with permission of Elsevier Science.)

room temperature, the products were separated and washed with distilled water and 25% ammonia aqueous solution. The final product was a black powder. X R D patterns show the products are metallic silver (Fig. 17). The average crystallite sizes calculated from the peak broadening of X R D patterns by the Scherrer equation [ 111 ] are listed in Table II, from which one can see that the smallest average particle size of silver powder is 8 nm for sample 4, which was prepared by irradiating a mixed solution

439

Table II.

Experimental Conditions and Silver Particle Diameters [98] Temperature (~

Sample Solution

number

Irradiation dose (• 104 Gy)

and time (h)

Silver particle

of hydrothermal treatment

size (nm)

1

0.1 M AgNO 3 + 4.0 M (CH3)2CHOH

1.8

105, 3

47

2

0.1 M AgNO 3 +4.0 M (CH3)2CHOH+0.1 M C12H25NaSO4

4.3

105, 2

13

3

0.05 M AgNO3 + 6.0 M (CH3)2CHOH +0.1 M C12H25NaSO4

3.0

105, 1

15

4

0.05 M AgNO3 + 6.0 M (CH3)2CHOH +0.1 M C12H25NaSO4

2.4

105, 1

8

5

0.05 M AgNO3 + 6.0 M (CH3)2CHOH +0.1 M C12H25NaSO4

1.1

105, 1

9

6

0.05 M AgNO3 + 6.0 M (CH3)2CHOH +0.1 M C12H25NaSO4

0.77

105, 1

10

7

0.05 M AgNO3 + 6.0 M (CH3)2CHOH +0.1 M C12H25NaSO4

1.1

Precipitation

23

8

0.05 M AgNO3 + 6.0 M (CH3)2CHOH +0.1 M C12H25NaSO4

1.1

105, 1

31

9

0.05 M AgNO3 +6.0 M (CH3)2CHOH +0.1 M C12H25NaSO4

1.1

105, 26

35

10

0.05 M AgNO3 + 6.0 M (CH3)2CHOH +0.1 M C12H25NaSO4

1.1

210, 1

43

11

0.05 M AgNO3 + 6.0 M (CH3)2CHOH +0.2 M C12H25NaSO4

3.0

105, 1

13

,

(Source: Data from Y. Zhu et al., Mater Lett., 1993.)

CHEMICAL PREPARATION OF NANOCRYSTALLINE MATERIALS

Fig. 18. TEM microphotographs of silver particles produced by the g-irradiation-hydrothermaltreatment combined method: irradiation solutionof sample 5. (Source: Reprinted from [98] with permission of Elsevier Science.)

Fig. 19. Particlesize distribution of sample 2. (Source: Reprinted from [98] with permission of Elsevier Science.) of 0.05 M AgNO3, 6.0 M (CH3)2CHOH, and 0.1 M C12H25NaSO4 with a dose of 2.4 x 104 Gy and hydrothermally treated at 105 ~ for 1 h. The TEM image (Fig. 18) shows that the silver powders consist of quasispherical crystallites. The particle size distribution was determined by the photographic image microstructure densitometry analysis method. The distribution of particle sizes of sample 2 is shown in Figure 19, from which we can see silver particle sizes ranging from 6 to 40 nm, and the largest percentage is about 35% in the size range 10 to 15 nm. The average particle size is 16 nm calculated from this figure. The experiments reveal that the surfactant, the y-irradiation dose, the hydrothermal temperature, and time influence the silver particle size, as shown in Table II and Figure 20. The shape of the silver particles produced by ),-irradiation depends on the surfactant used. For example, when sodium dodecyl sulfate is used as a surfactant, the silver particles are quasispherical. However, when poly(vinyl alcohol) is used, the silver particles have various shapes (Fig. 21). The yield and radiation chemistry yield (G value) [112] were studied and the results are given in Table III. Table III shows that the yield increased on increasing the irradiation dose when the concentration of AgNO3 was fixed. On the other hand, the G value had little

441

YITAI

Fig. 20. TEM images of silver particles produced by the F-irradiation method. Solution: (a) 0.01 M AgNO3, 0.01 M C12H25NaSO4, and 1.0 M (CH3)2CHOH; (b) the same solution as in (a); and (c) 0.05 M AgNO3, 0.01 M C12H25NaSO4, and 1.0 M (CH3)2CHOH. Dose rate (Gy.min-1) and radiation time: (a) 18.4, 5 min; (b) 59.3, 30 min; and (c) 72, 5.5 h. (Source: Reprinted from [98] with permission of Elsevier Science.)

relation to the irradiation dose when the AgNO3 concentration was fixed. However, the G value increased rapidly from 2.6 to 9.65 when the AgNO3 concentration increased from 0.01 to 0.05 M. With further increase in the AgNO3 concentration, the G value increased slowly. This implies that the mechanism of radiolytic reactions in the solutions containing 1 0 - 2 - 1 0 -3 M metal ions is different from the mechanism in the dilute solutions (about 10 -4 M metal ions) that contain only primary free-radical reactions [ 104-108]. In concentrated Ag + solutions, Ag + ions could go into the spurs in which they reacted with primary radicals produced during radiolysis, and this led to the higher G value.

442

CHEMICAL PREPARATION OF NANOCRYSTALLINE MATERIALS

Fig. 21. TEM image of silver particles produced by the F-irradiation method. Solution: 0.1 M AgNO3, saturated poly(vinyl alcohol), and 1.0 M (CH3)2CHOH. Dose rate: 76.3 Gy.min-1 9radiation time: 12 h. (Source: Reprinted from [98] with permission of Elsevier Science.)

Table III. Effectof Experimental Parameters on the Yield and G value of Silver Produced from AgNO3 Solution Irradiation dose ( 104 Gy)

Yield (%)

G value

0.01 M AgNO3 + 2.0 M (CH3)2CHOH

3.09

95.1

2.66

0.01 M AgNO3 + 2.0 M (CH3)2CHOH

2.50

84.5

2.91

0.01 M AgNO3 + 2.0 M (CH3)2CHOH

1.34

40.9

2.64

0.05 M AgNO3 + 2.0 M (CH3)2CHOH

3.09

69.3

9.62

0.1 M AgNO3 + 2.0 M (CH3)2CHOH

3.09

37.4

Solution

10.3

3.1.2. NanocrystaUine Copper [113] Figure 22 shows XRD patterns of the products prepared from solution containing sodium dodecyl sulfate as the surfactant. One can see that the products only washed with distilled water contain the impurity copper(I) oxide. The impurity could be removed by washing with 25 % ammonia aqueous solution. Because of the formation of Cu(NH3)+, pure copper powders could be obtained. The process of reducing the copper ions in the solution may be understood as follows: Cu 2+ ions are rapidly reduced to Cu + ions by hydrated electrons and organic radicals produced by F-ray radiation. Cu + ions can be further reduced in reaction with eaq, giving atomic copper. The copper atoms are generators of small clusters (Cu~- and others), which then form aggregates (Cun). The clusters also may act as nuclei on which the dismutation of monovalent copper ions takes place: Cun + 2Cu + = CUn+l + Cu 2+ This results from the extremely negative reduction potential for the copper atoms [ 114]. The two simultaneous processes of the growth of the metallic aggregates through

443

YITAI

O O cq

.,..~ = ~D =

O t",l c,l O

I

,!

o

I

35

45

55

I

I

65

I

75

20 (deg.) Fig. 22. XRD pattern of the product prepared by y-irradiation combined with hydrothermaltreatment. Solution: 0.01 M Cu(NO3)2, 0.1 M C12H25NaSO4, and 3.0 M (CH3)2CHOH; dose: 8.6 x 104 Gy; o copper(I) oxide. (Source: Reprinted from [113] with permission of Elsevier Science.)

dismutation and coalescence result in the formation of colloidal copper. There is a competitive reaction with the reduction and dismutation of monovalent copper ions, that is, the formation of poorly soluble copper(I) hydroxide (CuOH). As a result of the competition of the preceding reactions, the products consist of both copper and copper(I) oxide9 When the pH value is greater than 4, CuOH is very unstable in solution and decomposes rapidly to copper(l) oxide (Cu20). To obtain pure copper powders, the pH value of solution should be smaller9 Although poly(vinyl alcohol) is used as the surfactant instead of sodium dodecyl sulfate, copper(l) oxide could not form in the solution for the lower pH value. The experimental result shows that copper powders produced by F-irradiating copper salt solutions without ethylenediaminetetraacetic acid (EDTA) as a complex agent consist of relatively large particles. When EDTA was added to the solution, the final product consists of much smaller copper particles. Thus, the complexation of copper ions with EDTA is favorable for preparing nanocrystalline copper powders. This may be due to a dramatic decrease in the reduction reaction rate caused by the complexation of copper ions with the EDTA ligand. Also, the ligand on the copper ion may act as a bridge for electron transfer from the solvent to the copper ions. Copper powder prepared from a solution of 0.01 M CuSO4, 0.01 M EDTA, 0.1 M C]2H25NaSO4, and 3.0 M (CH3)2CHOH with a radiation dose of 3.6 • 104 Gy consists of quasispherical particles with an average particle size of 16 nm (Fig. 23a). In addition to the quasispherical shape, acicular copper particles (Fig. 23d) were observed in the sample prepared from a solution of 0.01 Me Cu2SO4, 0.01 M EDTA, 0.02 M C]2H25NaSO4, and 3.0 M (CH3)2CHOH. Therefore, by controlling the conditions of the experiment, different-shaped copper particles can be obtained. The growth process of nanocrystalline copper to single crystals induced by electron irradiation was observed by TEM, as shown in Figure 23a--c. Figure 23a shows the original nanocrystalline copper particles with an average particle size of 16 nm. After electron irradiation under the electron microscope, the particles became larger. Finally, after 12 s of electron irradiation, the particles became a large spheroid about 1.5 /zm in diameter (Fig. 23b). The electron diffraction result is shown in Figure 23c, from which one can see that it is a single crystal of copper. Because of the thickness of the single crystal, Kikuchi

444

CHEMICAL PREPARATION OF NANOCRYSTALLINE MATERIALS

Fig. 23. TEM image of the sample prepared by y-irradiation combined with hydrothermal treatment: (a) solution: 0.01 M CuSO4, 0.01 M C12H25NaSO4, and 3.0 M (CH3)2CHOH; dose: 3.6 • 104 Gy; (b) after 12 s of electron irradiation under an electron microscope; (c) electron diffraction of the sample in (b) in the [001] direction; and (d) solution: 0.01 M CuSO4, 0.01 M EDTA, 0.02 M C12H25NaSO4, and 3.0 M (CH3)2CHOH; dose: 3.6 x 104 Gy. (Source: Reprinted from [113] with permission of Elsevier Science.)

lines can be observed in its electron diffraction microphotograph (Fig. 23c), where the beam of electrons was incident in the [001 ] direction. From the occurrence of the Kikuchi lines, we may conclude that the thickness of the single crystal is more than 100 nm.

3.1.3. NanocrystaUine Ruthenium [115] Ultrafine powders of metal could also be obtained from acid group ions. Nanocrystalline Ru(12) has been prepared successfully from RuO 2-. The mechanism of the reduction of ruthenate ions during ?,-irradiation may be explained as follows. The hydrated electrons react with RuO 2- to form Ru v" R u O 2 - + e~q --+ Ru v The dismutation of pentavalent ruthenium occurs [ 116]: Ru v + Ru v ~ Ru TM+ Ru vI The tetravalent ruthenium reacts further with hydrated electrons to form ruthenium atoms.

3.1.4. Nanocrystalline Nickel [117,118] and Cobalt In nickel salt solutions, Ni 2+ ions are rapidly reduced to Ni + ions by hydrated electrons (e2q) and organic radicals produced by ?,-irradiation. Ni + ions can further react with eaq and organic radicals [119]:

eaq + Ni + --+ Ni ~ Ni + + C(CH3)2OH -+ NiC(CH3)2OH + NiC(CH3)xOH + reacts in the following ways: NiC(CH3)2OH + + H + --+ Ni 2+ + (CH3)xCHOH NiC(CH3)eOH + + Ni + --~ Ni 2+ + Ni ~ + (CH3)eCHOH NiC(CH3)eOH + + (CH3)2COH -+ Ni ~ + (CH3)2CO + (CH3)eCOH + H + The metal atoms are the generators of small clusters, which may act as nuclei on which aggregates form, resulting in the formation of colloidal nickel. However, the zero valence state of nickel, which resulted from the two-electron transfer, could also undergo oxidation: Nin + H 3 0 + --+ Nin-1 + Ni + + 1H2 + H20

445

YITAI

In the presence of NH3-H20, which acts as an alkalizing agent, the pH of the solution is kept in the range of 10 to 11, so the reoxidation of atoms or aggregates of nickel in solution is greatly suppressed. The product produced by )/-irradiating a solution containing 0.01 M NiSO4, 0.1 M NH3.H20, 0.1 M C12H25NaSO4, and 2.0 M (CH3)2CHOH with a dose of 6.0 x 104 Gy is a single phase of nickel with an average particle size of 8 nm. Figure 24 shows the differential thermal analysis (DTA) curve of the sample, from which it can be seen that two exothermic peaks appeared in the temperature range of 40 to 1040 ~ because of the oxidation of metallic nickel, which began at approximately 220 ~ in air. The maximum of the first exothermic peak, located at approximately 340 ~ corresponds to the formation of NiO in the oxidation of metallic nickel. The second exothermic peak, located at approximately 385 ~ corresponds to the formation of Ni203 because of the oxidation of NiO. The irradiated solutions were black and stable in air. When Ni(NO3)2 was used instead of NiSO4, no nickel powder product was formed. This may be due to the reaction of NiO 3 ions with hydrated electrons during )/-irradiation. The yields and G values are given in Table IV. From Table IV, it can be seen that the weight and G value of the product increased on increasing the concentration of NiSO4. However, the yield of nickel powder decreased as the NiSO4 concentration increased. This was because more Ni 2+ ions were left unreduced in the solution with larger concentration when the irradiation dose was fixed. The G value increased rapidly from 2.17 to 5.91 when the NiSO4 concentration increased from 0.01 to 0.03 M, but with further increase in the NiSO4 concentration, the G value increased slowly. This implies that the mechanism of

T a~ o

40

240

440

640

840

1040

Temperature (~ Fig. 24. The DTA curve of the sample prepared by the y-irradiation method. Solution: 0.01 M NiSO4, 0.1 M NH3.H20, 0.01 M C12H25NaSO4, and 2.0 M (CH3)2CHOH; dose: 6.0 x 104 J.kg-1 . (Source: Reprinted from [117] with kind permission from Kluwer Academic Publishers.) Table IV. Effectof Experimental Parameters on the Yield and G Value of Nickel Produced from NiSO4 Solution (Dose: 2.78 x 104 Gy) [118] Solution (in molar concentration) NiSO4

NH3.H20

Weight of product in

Yield

(NH4)2SO4

(CH3)2CHOH

200 mL solution/g

(%)

G value

0.01

0.16

0.1

3.0

0.088

75.2

2.17

0.03

0.28

0.1

3.0

0.241

68.7

5.91

0.05

0.28

0.1

3.0

0.261

44.6

6.36

0.1

0.7

0.1

3.0

0.280

23.9

7.72

0.01

0.16

0.1

0

0

(Source: Data from Y. Zhu et al., Chin. Sci. Bull., 1997.)

446

0

0

CHEMICAL PREPARATION OF NANOCRYSTALLINE MATERIALS

Table V. Effectof the Concentration on the Yield and G Value of Nickel Produced from Ni(CH3COO)2 Solution (Dose: 2.71 x 104 Gy) Solution (in molar concentration) Ni(CH3COO)2

NH3.H20 CH3COONH4

Weight of product in

Yield

(CH3)2CHOH

200 mL solution/g

(%)

G value

0.01

0.16

0.2

3.0

0.106

90.6

2.68

0.03

0.28

0.2

3.0

0.117

33.4

2.94

0.05

0.4

0.2

3.0

0.174

29.8

4.35

0.1

0.7

0.2

3.0

0.175

15.0

4.31 ,

i

(Source: Data from Y. Zhu et al., Chin. Sci. Bull., 1997.)

radiolytic reaction was different in dilute and concentrated solutions. In concentrated solutions, Ni 2+ ions could go into the spurs where they reacted with primary radicals produced during radiolysis, and this led to the higher G value. The maximum G value in these experiments is as large as 7.72, much larger than that previously reported 0.03 [87]. On the other hand, in the absence of isopropanol, nickel powder failed to form. Table V shows the trends of the yield and G value with the change of Ni(CH3COO)2 concentration. The G value increased from 2.68 to 4.35 corresponding to a Ni(CH3COO)2 concentration increase from 0.01 to 0.05 M. However, further increase in the concentration did not lead to an increase in the G value, indicating the maximum G value was reached (Fig. 25) at a dose of 2.71 x 104 Gy. The G value and yield of nickel decreased on decreasing the dose rate at a given irradiation time (Table VI). This may be due to a positive effect of the nucleation of crystallites caused by an increase in the reduction reaction rate at a larger dose rate. The anion in the salt had an influence on the yield and G value of nickel produced (Table VII). Our experiments showed that the optimum G value of nickel produced was reached by using nickel sulfate. In this way, nanocrystalline cobalt with an average particle size of 22 nm was prepared by y-irradiation of a solution containing COC12 instead of NiSO4.

4.5-

4.0

3.5

3.0

.5

i

0.00

i

0.02

i

i

l

i

I

i

0.04 0.06 0.08 Concentration of Ni(CH3COO)2M

i

!

0.10

Fig. 25. The effect of the concentration on the G value of nickel. Solution: Ni(CH3COO)2; dose: 2.71 x 104 Gy. (Source: Adapted from Zhu etal. [118].)

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Table VI. Effectof Dose Rate of y-Irradiation on the Yield and G Value of Nickel Produced from the Solution Containing 0.05 M Ni(CH3COO)2, 0.4 M NH3-H20, 0.5 M CH3COONH4, and 1.0 M (CH3)2CHOH (Irradiation time: 6.5 h) Weight of product in 300 mL solution/g

Yield (%)

G value

80

0.200

22.3

3.12

45

0.065

7.4

1.83

30

0.038

4.4

1.67

Dose rate/Gy.min- 1

(Source: Data from Y. Zhu et al., Chin. Sci. Bull., 1997.) Table VII. Yieldsand G Values of Nickel Produced from Solutions of Different Nickel Salts (Dose: 3.02 x 104 Gy) Solution (in molar concentration)

Weight of product in

Yield

NH3.H20

(CH3)2CHOH

300 mL solution/g

(%)

G value

0.05 M NiSO4

4.0

2.5

0.277

31.5

3.88

0.05 M NiC12

4.0

2.5

0.235

26.7

3.29

0.05 M Ni(CH3COO)2

4.0

2.5

0.224

25.5

3.14

0.05 M Ni(NO3)2

4.0

2.5

0

0

0

Salt

(Source: Data from Y. Zhu et al., Chin. Sci. Bull., 1997.)

3.1.5. Nanocrystalline Cadmium [120], Tin [121], I n d i u m [122],

Antimony [1231, and Lead Nanocrystalline metals with low melting points are difficult to prepare because of their lower melting points (Table VIII). Some methods such as electrolysis and reduction with more active metals have been developed for the manufacture of these fine particles. However, the particle sizes of the powders prepared by these methods are relatively larger [ 124126]. By using the y-irradiation method, we have successfully prepared nanocrystalline Cd (20 nm), Sn (28 nm), In (32 nm), Sb (8 nm), and Pb (45 nm) under ambient pressure at room temperature. The mechanism of Cd 2+ reduction during y-irradiation may be understood as follows: The hydrated electrons form in the aqueous solution during ),-irradiation. Then the hydrated electrons react rapidly with Cd 2+ to form Cd + [127,128]: eaq + Cd 2+ --+ Cd +

(1)

The OH radicals react with isopropanol to yield organic radicals: O H - + (CH3)2CHOH --+ H 2 0 + (CH3)2COH

(2)

Subsequently, these intermediates react among each other: Cd + + Cd + --+ Cd~2+ --+ Cd ~ + Cd 2+ Cd + q- (CH3)2CHOH -+- H20 --+ Cd 2+ -k- (CH3)zCH2OH -k- O H -

(3) (4)

Reaction (3) competes with reaction (4), and reaction (3) is much faster than reaction (4). Colloidal cadmium is finally formed via dismutation and association reactions of Cd 2+. By y-irradiating a solution containing 0.01 M CdSO4, 0.01 M (NH4)2SO4, 1 M NH3.H20, 0.01 M C12H25NaSO4, and 6.0 M (CH3)2CHOH with a dose of 1.6 • 104 Gy,

448

CHEMICAL PREPARATION OF NANOCRYSTALLINEMATERIALS

Table VIII. MeltingPoints of Metals Metal Melting point (~

Cd

Sn

Pb

In

Sb

302.9

231.9

327.5

156.3

630.0

nanocrystalline Cd with an average particle size of 20 nm is obtained. Similarly, nanocrystalline Sn, In, Sb, and Pb can also be obtained. 3.2. Alloys [129] Ultrafine powders of alloys are important in many applications such as coatings, conductor pastes, and parts requiring good electrical and thermal conductivity. Various methods are used to prepare the Ag-Cu alloy [130-135]. The gas-condensation method is commonly adopted, but a high temperature is needed and the product yield is relatively low. We have prepared the Ag-Cu alloy by the y-irradiation method. We dissolved analytically pure Cu(NO3)z.3H20 and AgNO3 in distilled water and added NH3.H20 as a complex agent. A surfactant, scavenger, and bubbling were also necessary. To obtain a Ag-Cu alloy, a NH3 ligand was used to adjust the condition of the solution. In the absence of the NH3 ligand, the product is a mixture of metallic silver and copper. When the solution contains the NH3 ligand, the single phase of the Ag-Cu alloy is obtained. This may be caused by the change in the rate of reduction reactions of Ag + and Cu + ions during y-irradiation resulting from the complexation of metal ions with the NH3. On the other hand, the NH3 ligand on metal ions may act as a bridge for electron transfer from the solution to the metal ions. The product prepared by y-irradiating a solution containing 0.01 M AgNO3, 0.05 M Cu(NO3)2, 0.3 M NH3.H20, and 2.0 M (CH3)zCHOH at a dose of 2.3 • 104 Gy does not contain the phase of metallic copper, and all the diffraction peaks shift toward larger diffraction angles compared with those of metallic silver, indicating the formation of the Ag-Cu alloy (25 nm). From the XRD data, the cell parameter a of the product is calculated to be 4.0395/k, which is smaller than that of metallic silver (a - 4.0862 A.). Figure 26 is the TEM micrograph of the sample. The composition of the Ag-Cu alloy was analyzed using X-ray photoelectron spectroscopy (XPS), and the results are listed in Table IX.

3.3. Nanocrystalline Nonmetals We extended the y-irradiation method to the preparation of ultrafine powders of nonmetallic elements.

3.3.1. Tellurium [136] The XRD pattern of the product prepared by y-irradiating a solution containing 0.0063 M TeO2, 0.05 M C12H25NaSO4, 0.7 M HC1, and 1.6 M (CH3)2CHOH with a dose of 2.32 x 104 Gy indicates that the product is a single phase of hexagonal tellurium. Figure 27 shows the TEM micrograph of the sample. It shows that the tellurium powder consisted of aciculate particles of size ranging from 10 nm x 80 nm to 40 nm x 300 nm.

3.3.2. Selenium [137] It is difficult to prepare nanometer-sized selenium powders because of its low melting point (217 ~ We have successfully prepared nanometer-sized powders of both amorphous and crystalline selenium at room temperature by y-irradiation. We dissolved analytically pure SeO2 in hydrochloric acid, or in distilled water, or in NaOH solution, and added a surfactant (ClzHz5NaSO4) and a scavenger (C2H5OH) for hydroxyl radicals. After irradiation,

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Fig. 26. The TEM micrograph of the Ag-Cu alloy prepared by the ),-irradiation method. (Source: Reprinted from [ 129] with permission of Elsevier Science.)

Table IX. Composition of the Ag-Cu Alloy Prepared by the ),-Irradiation Method Element

at%

wt%

Ag

84.97

90.56

Cu

15.03

9.44

(Source: Data from Y. Zhu et al., J. Alloys Comp., 1995.)

Fig. 27. TEM micrograph of the sample prepared by the ),-irradiation method. Solution: 0.0063 M TeO2, 0.05 M C12H25NaSO4, 0.7 M HC1, and 1.6 M (CH3)2CHOH; radiation dose: 2.32 x 104 Gy. (Source: Reprinted from [136] with kind permission from Kluwer Academic Publishers.)

450

CHEMICAL PREPARATION OF NANOCRYSTALLINE MATERIALS

0

20

30

40

50

60

70

20 (deg.) Fig. 28. XRD pattern of the products prepared by ),-irradiation (dose: 3.32 x 104 Gy) of the solution containing 0.01 M SeO2, 0.46 M HC1, 0.01 M C12H25NaSO4, and 2.6 M C2HsOH. (a) The product dried at room temperature, and (b) the product dried at 80 ~ (Source: Reprinted from [137] with permission of Elsevier Science.)

Fig. 29. TEM micrograph of the same sample as in Figure 28a. (Source: Reprinted from [137] with permission of Elsevier Science.) the powders were dried at room temperature or at 80 ~ The powders obtained from the irradiated solution containing hydrochloric acid and dried at room temperature were amorphous selenium (Fig. 28a) with a uniform particle size of 70 nm (Fig. 29), whereas the product dried at 80 ~ was crystalline hexagonal selenium with an average particle size of 8 nm, as calculated using the Scherrer equation (Fig. 28b). On the other hand, the product prepared in an irradiated solution containing NaOH and dried at room temperature was nanocrystalline hexagonal selenium with an average particle size of 17 nm.

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Table X. Yieldsand G Values of Selenium Powders Prepared by v-Irradiation Sample number

SeO2

Solution (in molar concentration) Dose HC1 C2HsOH C12H25NaSO4 NaOH (104Gy)

Yield (%)

G value (atoms/100eV)

1

0.01

0.46

2.6

0.01

0

1.31

39.6

2.25

2

0.01

0.46

2.6

0.01

0

1.74

47.8

2.71

3

0.01

0

2.6

0.01

0

1.74

31.0

1.78

4

0.01

0

2.6

0.01

0.05

1.74

14.3

0.82

5

0.1

0.46

2.6

0.01

0

1.74

6

0.01

0.46

2.6

0.01

0

3.32

84.3

7

0.01

0.46

0

0.01

0

3.32

0

5.60

3.14 4.79 0

(Source: Data from Y. Zhu et al., Mater. Lett., 1996.)

Table X shows that the yields and G values of the selenium powders prepared in hydrochloric acid (sample 2) are much larger than those obtained from solutions of water (sample 3) and sodium hydroxide (sample 4). This is due to the different mechanisms involved in radiation reduction of selenium(IV) by the hydrated electrons produced during ?'-irradiation in acidic and alkaline solutions. Selenium(IV) exists as Se 4+ ions and SeO32ions in hydrochloric acid and NaOH solutions, respectively. The reduction of SeO~- ions was more difficult than that of Se 4+ ions. This is due to the stability of SeO~- ions caused by the strong covalent bonding between selenium and oxygen. The G value increased with increasing concentration of SeO2 when other conditions were fixed. The yield and G value of selenium prepared increased with increasing irradiation dose. From Table X, it can also be seen that, when there was no ethanol as a scavenger for hydroxyl radicals in the solution, no selenium powder was obtained. In the absence of ethanol, the zero valent state of selenium resulting from the four-electron transfer could undergo oxidation by the hydroxyl radicals.

3.3.3. Nanometer-Sized Amorphous Powders of Arsenic [138] After y-irradiation of the hydrochloric acid solution of analytically pure arsenic(III) oxide in the absence of sodium dodecyl sulfate, a deeply red precipitate of arsenic formed immediately. The product produced from a solution containing 0.05 M CH3CH2OH and 1.0 M HC1 with a dose of 3.32 • 104 Gy and dried at 60 ~ in air was amorphous. Electron diffraction also confirmed the amorphism of the product. However, the product treated at 350 ~ in N2 consisted of single-phase crystalline arsenic particles (average size: 20 nm) with a hexagonal structure. The average particle size increased with heat-treated temperature and time. For example, when the sample was heated at 500 ~ for 48 h, the average particle size increased to 25 nm. Figure 30 shows the TEM micrographs of the samples. The particle size of arsenic powder prepared by y-irradiation from the alkaline solution is 10 nm on an average (Fig. 30c), which is much smaller than that from the acidic solution, 30 nm on an average (Fig. 30a), or the water solution, 40 nm on an average (Fig. 30d).

3.4. Nanometer-Sized Metal Oxides [139-142] Metal oxides can be prepared by the reaction of solvated electrons and high-valence multivalent metal ions. In a previous section, copper was obtained from a CuSO4 solution after y-irradiation. Now, by controlling the conditions, a nanocrystalline powder of cuprous oxide can also be obtained after y-irradiation with a dose of 2.4 • 104 Gy of a 0.01 M

452

CHEMICAL PREPARATION OF NANOCRYSTALLINE MATERIALS

Fig. 30. TEM micrograph of the products prepared by y-irradiating the solution containing 0.05 M As203, 0.5 M C12H25NaSO4, 0.5 M C2H5OH, and 1.0 M HC1. (a) The product dried in air at 60~ (b) the product heat-treated at 350~ in N2 for 15 h; (c) the sample prepared from an alkaline solution; and (d) the sample prepared from a solution of water. (Source: Reprinted from [138] with permission of Elsevier Science.)

Cu2804 solution containing 0.01 M C12H25NaSO4, 2.0 M (CH3)2CHOH, and a 0.02 M CH3COOH/0.03 M C H 3 C O O N a buffer. Without the C H 3 C O O H / C H 3 C O O N a buffer pair, the pH of the solution is about 3.0-3.5 and the final product is a mixture of copper and cuprous oxide. However, when the solution contains a C H 3 C O O H / C H 3 C O O N a buffer pair that keeps the pH in the range of 4.0 to 4.5, the final product is pure cuprous oxide. In this case, the reduction and dismutation of cuprous ions are completely suppressed. Because cuprous hydroxide is very unstable in a solution of pH > 4.0, it decomposes rapidly to cuprous oxide immediately after its formation. On the other hand, the precipitate of cupric hydroxide forming in the solution should be controlled in the range of 4.0 to 5.0 in the preparation of cuprous oxide. This can be achieved by using the C H 3 C O O H / C H 3 C O O N a

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Table XI. ExperimentalConditions, Products, and Particle Sizes of Cuprous Oxide Sample number

Irradiation dose (x 104 Gy) Product Particle

Solution 0.01 M CuSO4 + 0.01 M C12H25NaSO4 + 0.02 M CH3COOH +0.03 M CH3COONa+ 2.0 M (CH3)2CHOH

2.4

Cu20

14

0.01 M CuSO4 + 0.01 M C12H25NaSO4 + 0.02 M CH3COOH + 0.075 M CH3COONa+ 2.0 M (CH3)2CHOH

2.4

Cu20

20

0.01 M CuSO4 + 0.05 M C12H25NaSO4 + 0.05 M CH3COOH + 0.075 M CH3COONa+ 2.0 M (CH3)2CHOH

2.4

Cu20

19

0.01 M CuSO4 + 0.1 M C12H25NaSO4 + 0.05 M CH3COOH +0.075 M CH3COONa+ 2.0 M (CH3)2CHOH

2.4

Cu20

16

0.01 M CuSO4 + 0.05 M CH3COOH +0.075 M CH3COONa+ 2.0 M (CH3)2CHOH

2.4

Cu20

50

0.1 M CuSO4 + 0.1 M C12H25NaSO4 + 0.05 M CH3COOH +0.075 M CH3COONa+ 2.0 M (CH3)2CHOH

2.4

Cu20

28

0.05 M Cu(CH3COO)2 + 0.05 M C12H25NaSO4 + 2.0 M (CH3)2CHOH

2.4

Cu20

36

2.4

Cu + 12% Cu20

0.01 M CuSO4 + 1.6% poly(vinyl alcohol)+0.02 M CH3COOH +0.03 M CH3COONa+ 0.2 M (CH3)2CHOH

2.4

Cu20

28

0.01 M CuSO4 + 0.05 M C12H25NaSO4 + 0.05 M CH3COOH +0.075 M CH3COONa+ 2.0 M (CH3)2CHOH

6.2

Cu20

24

0.01 M CuSO4 + 0.1 M C12H25NaSO4 + 2.0 M (CH3)2CHOH

3.6

Cu + 30% Cu20

0.05 M CuSO4 + 0.05 M C12H25NaSO4 + 0.05 M CH3COOH + 0.075 M CH3COONa+ 0.05 M EDTA + 2.0 M (CH3)2CHOH

10

(Source: Data from Y. Zhu et al., Mater. Res. Bull., 1994.)

buffer solution. The experiment shows that other conditions also influence the particle size (Table XI): (1) The particle size of cuprous oxide increases as the concentrations of acetic acid and sodium acetate increase. (2) The particle size of cuprous oxide decreases as the concentration of sodium dodecyl sulfate increases. (3) In the concentration range of 0.01 to 0.1 M of cupric ions, the particle size increases with the concentration of cupric ions. (4) In the case of using a higher dose, the product consists of relatively larger particles. Similarly, we can obtain nanometer-sized Cr203 powders from a solution containing 0.05 M K2Cr207, 0.05 M C12H25NaSO4, and 3.0 M (CH3)zCHOH at a dose of 1.0 • 104 Gy. After heat treatment at 500 ~ the amorphous Cr203 turned into a single phase of crystalline Cr203, and the particle size increased from 6 to 15 nm. Cr203 powders were not produced from ?,-irradiated solutions containing C r 2 0 2- ions. This may be due to the difference in the structure of these two ions. In the case of the CrO 2- ion, there exists a tetrahedral arrangement in which a chromium atom is located at the center. However, in the dichromate ion, there are two tetrahedral units linked together by one oxygen atom. The C r - O distance for the bridging oxygen is greater than that for the other oxygen atoms. The cr-zr donor properties of the bridging oxygen atom are much less compared with the terminal oxygen atoms. Thus, the Cr-O bond for the bridging oxygen in the C r 2 0 2- ion could break down to form a CrO3 radical in the process of y-irradiation. The CrO3 radical is unstable and is reduced rapidly by hydrated electrons to form Cr203.

454

CHEMICAL PREPARATION OF NANOCRYSTALLINE MATERIALS

MoO2 and Mn203 have been successfully prepared by ?'-irradiation of an aqueous solution of [(NH4)6Mo7024.4H20] and KMnO4 [ 141,142], respectively.

3.5. Nanocomposites 3.5.1. OxidelMetal Nanocomposites Nanocomposite materials are very important because of their interesting electrical and optical properties, their possible commercial exploitation, and their importance in improving the stability of nanometals and providing models for understanding the physics of nanocrystalline particles. We have developed a new methodmsol-gel ?'-irradiationmto prepare titania-silver and silica-silver nanocomposites.

3.5.1.1. Si02/Ag [143] First, a solution of colloidal silver was obtained by y-irradiation. Then the sol-gel method was used to prepare silica-silver nanocomposites. Tetraethoxysilane [(C2H50)4Si, 5 mL] was dissolved in isopropyl alcohol (10 mL) with water (5 mL), and dilute nitric acid (2N) was wadded to keep the pH close to 2, after continuous stirring for 1.5 h. For gelation, the pH of the solution was increased to 8 by the addition of aqueous ammonia under mild stirring. The hydrogels obtained were dried overnight in air. Figure 31 gives the XRD pattern of a typical sample containing metallic silver particles prepared by ?'-irradiation of a solution containing 0.01 M AgNO3, 0.01M C 12H25NaSO4, and 2.0 M (CH3)2CHOH with a dose of 8.1 x 103 Gy. This shows that the sample consists of two phases, namely, metallic silver (6 nm) and noncrystalline silica. The amount of silver present as a metallic species in the composite glass is 1.24%, as measured by atomic absorption spectroscopy. A TEM micrograph of the sample is shown in Figure 32. The silica glass contains a dispersion of fine metallic silver grains that are quasispherical and well separated.

3.5.1.2. 7i02/Ag [144] In the preparation of titania-based nanocomposites, the formation of particulate materials occurs because of the vigorous hydrolysis of titanium alkoxides with water. This can

~


1), the analytical solution becomes T

Ts

n

2cos(-~)exp(-

82/r

Ct pX 2

1

where Bn = (n + 0.5)rr. Figure i shows the calculated average cooling rates e as a function of thickness X and heat transfer h for the solidification of A1 in contact with a Cu chill. The cooling rate increases with increasing heat transfer coefficient and decreasing thickness. The measured cooling rates of 104-106 K/s during rapid solidification are associated with heat transfer coefficients of 104-105 W/m 2 K, which correspond to cooling conditions intermediate between Newtonian and ideal cases. Typically, in rapid solidification processing, the cooling rate can reach in excess of 104 K/s for a layer thickness less than 100/zm. This implies that the solidification is completed within a few milliseconds.

1012

1010

108 E K/s 106

104 10 -6

102

0.1 prn

1 pm

10 pm

0.1 mm

1 mm

10 mm 0.1 m

Fig. 1. Calculatedaverage cooling rate e as a function of thickness X and heat transfer coefficient h (W/mm2 K) for A1 in contact with a Cu chill, together with experimental data points. (Source: Reprinted with permission from [6]. 9 1982 Institute of Materials.)

503

CHANG

The average solidification rate R can be approximated by equating the latent heat released to the heat removed to the cooling medium [6]. This gives the following expression: R-

dX dt

Ao -- B ~ h Af

(6)

but n

m

T f - Ts Lp

Ao

Af Ao

=1

for a slab-like geometry

Ao

Z-X Z2

Af

( Z - X) 2

Af

for a cylinder for a sphere

where Tf is the liquidus (freezing) temperature and Z is the radius of a cylinder or sphere.

2.2. Rapidly Solidified Microstructures The rapid extraction of thermal energy associated with RSP permits a large deviation from equilibrium, as evidenced by the extension in solid solubility limits; the reduction or elimination of the detrimental effects of segregation; the development of new nonequilibrium crystalline, quasicrystalline, or noncrystalline (amorphous) phases; and the sharp reduction of grain size to the micrometer or nanometer scale. Jones [6], Liebermann [8], Cahn [9], and Suryanarayana [10] have reviewed the rapid solidification processing technology. A range of rapid solidification processes have been developed to produce the metastable microstructure in materials. There are three main types of rapid solidification processes: (1) chilled, (2) spray, and (3) weld methods. The most common RSP methods used in the manufacture of nanocrystalline metallic alloys and composites are chill-block melt spinning and gas atomization.

2.3. Chill-Block Melt Spinning In chill-block melt spinning [ 11], the molten material is forced through a nozzle to form a liquid stream, which is then spread continuously across the surface of a rotating wheel (or drum) under an inert atmosphere, to manufacture strip and ribbon products, as shown in Figure 2. The thickness of the ribbon varies from 10 to 100/zm. The heat flow from the liquid stream to the cold substrate under certain conditions can be treated as a Newtonian cooling mechanism [ 12], which gives an expression for the thickness of the ribbon, t, as (~ t--

AT)./

(7)

VR'AH

where C~Tis the empirical heat transfer coefficient, VR is the linear velocity of the substrate (i.e., the speed of the rotating wheel), A T is the temperature difference between the opposite sides of the ribbon and A H is the latent heat per unit volume of the liquid metal, and l is the length of the contact zone between the liquid metal and substrate. The thickness of the ribbon is proportional to the cooling conditions and they depend on the substrate material (aT). All process parameters for a given chill-block melt-spinning apparatus are adjusted to preserve the stability of the liquid metal. These parameters are nozzle size, nozzle-to-substrate distance, melt ejection pressure, and substrate speed, all of which, in concert, control the puddle length of the molten metal. This length limits the time available for the solidification of the ribbon and, therefore, governs the ribbon thickness. The width of the ribbon varies from 1 to 3 mm and is governed by the size of the nozzle.

504

RAPID SOLIDIFICATION PROCESSING OF NANOCRYSTALLINE METALLIC ALLOYS

Gas pressure

Heatin ribbon

Fig. 2. Chill-blockmelt-spinning apparatus.

Chill-block melt spinning is a simple technique and it can produce fully dense samples directly. However, it is predominantly used for metals because these materials can easily be melted by induction heating. There have been some cases where melt spinning has been employed in the rapid solidification of semiconductors [ 13]. 2.4. Gas Atomization

In gas atomization, a fine dispersion of droplets is formed when molten metal is impacted by a high-energy fluid (i.e., inert gas), as shown in Figure 3. Atomization occurs as a result of the transfer of kinetic energy from the atomizing fluid to the molten metal. In general, the droplets are formed from Rayleigh instabilities and they grow on the surface of torn molten ligaments [ 14]. Further breakdown of the droplet may occur as a result of interactions with the atomizing gas if the dynamic pressure resulting from the gas stream velocity exceeds the restoring force resulting from the surface tension of the droplet [ 15]. This is followed immediately by the spheroidization of the individual droplets [ 16], as shown in Figure 4. The spherical or near-spherical droplets continue to travel down the atomization vessel, rapidly losing heat as a result of convection to the atomizing fluid. The disintegration of a molten metal by high-energy gas jets has been reported to obey a simple correlation to give the mass mean droplet diameter [17] (i.e., the opening of a screening mesh that lets through 50% of the mass of the powder resulting from an atomization) ds0 as dso-

Kd[(lZmdotYm/lZgV2ePm)(1 + Jmelt/Jgas)] 1/2

(8)

where Kd is an empirically determined constant with a value between 40 and 400;/Zm, am, ,Om, and Jmelt are the viscosity, surface tension, density, and mass flow rate of the melt, respectively; mg, Vge, and Jgas are the viscosity, velocity, and mass flow rate of the atomizing gas, respectively; and do is the diameter of the metal delivery nozzle. During flight, heterogeneous solidification occurs in all but the smallest droplets because of the following: (a) bulk heterogeneous nucleation within the droplet, (b) surface oxidation processes, or (c) interparticle collisions. A high cooling rate is readily achieved during atomization

505

CHANG

Fig. 3. V- or cone-jet gas atomization apparatus.

Fig. 4. Schematic diagram showing particle formation during atomization. (Source: Reprinted with permission from [14]. 9 1983 ASM International.)

506

RAPID SOLIDIFICATION PROCESSING OF NANOCRYSTALLINE METALLIC ALLOYS

where fast interfacial growth velocities (0.5-3.5 m/s) and, therefore, microstructural refinement are maintained as a result of (a) particles with large surface/volume ratios and (b) an efficient convective heat flux to the surrounding atomizing gas [ 18, 19]. Gas atomization is an ideal method to produce a large quantity of nanocrystalline alloy powder for subsequent hot consolidation to form bulk samples. However, it is limited to metals because they can easily be molten.

3. DEVELOPMENT OF NANOCRYSTALLINE METALLIC ALLOYS 3.1. Formation of Nanocrystalline Microstructure Recently, the development of nanocrystalline metallic alloys using rapid solidification processing has focused on four main categories of nanoscale microstructures consisting of (1) crystalline plus amorphous phases, (2) quasicrystalline plus crystalline phases, (3) multiple crystalline phases, and (4) single crystalline phases. Chill-block melt spinning is a simple technique and it can produce (a) porosity-free samples and (b) samples of different grain size by controlling the processing parameters. Furthermore, because no artificial consolidation process is involved, the interfaces are clean and the product is dense. However, gas atomization has been employed to produce either fully amorphous alloy powders or partially crystallized alloy powders with nanocrystalline phase embedded in an amorphous matrix. The size of the crystal in the rapidly solidified microstructure is controlled by the nucleation rate I and growth rate G during manufacture [20, 21]. The growth rate G and nucleation rate I both depend on the degree of undercooling A T of the melt prior to solidification according to the following expressions: G -- avexp - ~

1-exp

( Q) I -- nvexp - ~ - ~

kT

( ) 16~rcr3f(0) n D exp - 3 A G 2kT

o

~ --(1 - e x p ( - A AT)) a ~(

~

Bexp ) -

AT 2

(9) (10)

but

AG= f(O) -

LAT Tm 1 (2 - 3 cos 0 + cos 3 0)

where a is the interatomic spacing, v is the atomic vibration frequency, Q is the activation energy required for an atom to transfer across the solid-liquid interface, A Gv is the driving force for solidification, Tm is the melting temperature, D is the diffusion coefficient in the liquid, 0 is the contact angle for a solid nucleus on the substrate surface, n is the nucleation site density, (r is the solid-liquid surface energy, and A and B are constants. Cantor [20] has derived the following relationship between crystal size d, nucleation rate N, and growth rate G based on columnar solidification through the melt spun ribbons: d-

((8o) ~

(11)

This gives the following relationship between the crystal size d and the undercooling A T" d3 = 8a(1 - e x p ( - A AT))

Jrn exp(_ B/ A T2)

(12)

Figure 5 shows the variation of crystal size with undercooling. Crystals cannot nucleate above the nucleation onset temperature Tn and they cannot grow below the glass transition temperature Tg. The crystal size reaches a minimum value with increasing undercooling.

507

CHANG

log d b~ r,r

.=.

I

I

I

Tg

Tn

Tm

Temperature T Fig. 5. Plot of grain size versus temperature. (Source: Reprinted with permission from [20]. 9 1997 Cambridge UniversityPress.)

Therefore, nanocrystalline grain structures can be obtained by rapid quenching to a high undercooling during solidification of a liquid alloy.

3.2. Nanoscale Mixed Structure of Crystalline and Amorphous Phases

3.2.1. Nanocrystalline Light Metals The need for high-strength and lightweight materials has led to the development of A1TM-Ln (TM = Ni, Cu, Ag, Co, Fe, Zr, Ti; Ln = Ce, La, Y, Mm, Nd) alloys [22-29] prepared by melt spinning and gas atomization processes. These materials are based on a composition of about 85-94 at% A1 and exhibit a tensile strength (crf > 1200 MPa) greater than conventional high-strength A1 alloys. The typical microstructure of a melt-spun A1-YNi-Fe alloy is shown in Figure 6. It consisted of 10-30-nm-sized defect-free or-A1 particles embedded in an amorphous matrix [22a]. The volume fraction of the ct-A1 particles varies from 0.1 to 0.3. These microstructures can be produced either directly from melt spinning at low rotating speed or by subsequent annealing of the fully amorphous structure produced by melt spinning at high rotating speed. A similar nanoscale mixed structure has also been found in gas-atomized A1-Ni-Mm-Zr [30] alloys. It has been reported [31 ] that the Al-rich amorphous alloys with low concentration of solute elements has a two-stage crystallization process involving: (1) Am ~ c~-A1 and (2) Am I (remaining amorphous phase) ~ intermetallic compounds, as evidenced by the two exothermic peaks found in the differential scanning calorimetry (DSC) trace in Figure 7. This type of crystallization is known as primary crystallization in which the amorphous phase decomposes into a crystalline phase with different composition. This provides a two-stage continuous cooling transformation behavior where an or-A1 phase field is located at the lower-temperature side, as shown in Figure 8. The control of the cooling rate during RSP or annealing to primary crystallization for this type of Al-based alloy is expected to cause the production of a nanoscale mixed structure of or-A1 particles embedded in an amorphous phase. This can be illustrated by the continuous cooling transformation

508

RAPID SOLIDIFICATION PROCESSING OF NANOCRYSTALLINE METALLIC ALLOYS

Fig. 6. Bright-field TEM micrographs and selected-area diffraction patterns showing the change in microstructure of melt-spun A188Ni9Ce2Fe 1 ribbons produced at different rotation speeds. (Source: Reprinted with permission from [22b]. 9 1992 Japan Institute of Metals.)

AI88Ni9Ce2Fel

=

0.67 K/s

vt= o ~

__

,

V~ = 12%

v, = 25%

/! It \

i I~ ~k~

431K

20s1

V~ = 30% ,, ~/

I L ~

t

472K

1

1 350

,i 400

I 450

/ I ,I 500 550 600 Temperature, T/K

1 650

[ 700

Fig. 7. Differential scanning calorimetry (DSC) traces of melt-spun A188Ni9Ce2Fe1 ribbons produced at different rotation speeds. (Source: Reprinted with permission from [22b]. 9 1992 Japan Institute of Metals.)

(CCT) behavior of amorphous A1 alloys, as shown in Figure 8. Because the nose of a C C T curve corresponds to the m i n i m u m time for the onset of crystallization from the melt, at high quench rates, the cooling curve misses the noses of both C curves of the

509

CHANG

T~

~t 13

Supercooled

Tg

W (:1

E

Ice-At . . . . . . . . . . . .

Time

Fig. 8. Schematicdiagramof two-stage continuous coolingtransformation(CCT)behavior for M-rich amorphous alloysand two kinds of coolingcurves. (Source: Reprintedwithpermissionfrom [31]. 9 1995Japan Institute of Metals.) crystalline a-A1 and compound phases. This implies that crystallization is prevented during the quenching from the melt and a fully amorphous structure is developed. On the other hand, at lower quench rates, the cooling curve cuts the C curve of the c~-A1 phase and leads to the formation of or-A1 particles. However, the transformation is incomplete and the remaining liquid is quenched into the amorphous structure. Alternatively, when an amorphous alloy is heated to sufficiently high temperature, thermal motion becomes sufficient for the nucleation and growth of the crystalline phase. To develop the nanocrystalline microstructure, a high nucleation rate together with a slow growth is required. In practice, annealing of the fully amorphous structure is commonly used because the volume fraction and size of the c~-A1 particles can be controlled more readily. The primary crystallization of amorphous A1 alloys involves transient heterogeneous nucleation, which is influenced by the quench rate. This provides a fine dispersion of quenched-in nucleation sites, giving a population of or-A1 particles on the order of 1023 m -3 for A190Ni6Nd4 alloys and 1021-1022 m -3 for A185NisY10 alloys [32]. The growth behavior of c~-A1 particles in the primary crystallization is very unusual. For the A188Ni4Y8 alloy [33], the growth shows a sharp transition from a high coarsening rate in the first few minutes of annealing at temperatures between 190 and 220 ~ to a much slower coarsening rate at longer annealing times, as shown in Figure 9. A similar growth behavior has also been observed in the primary crystallization of the amorphous A190Ni6Nd4 alloy [32, 34]. The particle size did not agree with the square-root dependence on the annealing time. This implies that the growth kinetics is not a simple diffusion-controlled growth of an isolated particle. There appears to be impingement of diffusion fields around the particle (i.e., soft impingement) during the growth process. The reduction in the growth rate at long annealing times may be due to the presence of a diffusion barrier between the or-A1 particles and the matrix. Field ion microscopy (FIM) has been employed to study the local composition of the nanocrystalline microstructure produced after primary crystallization of the amorphous A1 alloys. Hono et al. [31 ] have shown through FIM measurements that the Ln element diffuses more slowly than the TM element in A1-Ni-Ce alloy. In the partially crystallized A187Ni10Ce3 alloy, the Ni and Ce atoms are rejected from the a-A1 particles and the concentration of cg-A1 is approximately 98% A1. The rejected Ni and Ce atoms are partitioned into the amorphous matrix phase and its composition is approximately 25% Ni and 3% Ce,

510

RAPID SOLIDIFICATION PROCESSING OF NANOCRYSTALLINE METALLIC ALLOYS

14

12

i~

8

-..~.-r

~

!

I

i

I

280 ~

-

,,

250 ~ ~

220 200 "c

~-#r/" i

" 190~

6

U

4

O--

0

1

I

1

1

50

100

150

200

250

Annealing Time, min. Fig. 9. Plot of a-A1 particle diameter versus time at different annealing temperatures in melt-spun A188Y8Ni4 ribbons. (Source: Reprinted with permission from [33]. 9 1997 Minerals, Metals, & Materials Society.)

amorphous (x-A!{ amorptmus

Co 5, Ni

.

.

.

.

.

.

.

! I !

! I

'

'

I I

! I

! '

I I

Fig. 10. Schematicdiagram of the concentration profiles of A1, Ni, and Ce across the interface between the a-A1 and the amorphous phases for an amorphous AI87Ni10Ce3 alloy annealed for 180 s at 553 ~ (Source: Reprinted with permission from [31]. 9 1995 Japan Institute of Metals.)

respectively, as shown in Figure 10. The Ce atoms are enriched within a distance of less than 3 nm at the c~-Al/amorphous interface. Although both Ni and Ce are rejected from the c~-A1 phase, only Ce is enriched at the interface because of the lower diffusivity of large Ce atoms. Hence, during the growth of the c~-A1 particles, the rejected Ce atoms are enriched at the interface and the particle has to drag Ce for further growth. This effectively controls the grain growth. Therefore, the small interparticle spacing together with the gradual pileup of the slow-diffusing solute species around the c~-A1 particle quickly arrests the growth of the particles. The resistance against crystallization of the surrounding residual amorphous matrix is due to a combination of increasing TM contents [23] and the presence of a sharp concentration gradient produced by the pile-up of the Ln atoms [35]. This results in the suppression or reduction of the thermodynamic driving force for the nucleation of intermetallic compounds ahead of the growing particles, thereby stabilizing the residual amorphous matrix. Eventually, a metastable equilibrium state between the primary c~-A1 phase and the residual amorphous phase is reached. The metastable equilibrium composition of the amorphous

511

CHANG

Fig. 11. Schematicdiagram showing the refinement of c~-A1particles by the addition of Cu. (Source: Reprinted with permission from [28]. 9 1994Japan Institute of Metals.) matrix can be affected by the curvature of the crystallite/matrix when the crystal size becomes so small that the Gibbs-Thomson effect [36] is significant. The addition of Cu, Ag, Ga, and Au to the A1 alloys increases the or-A1 particle density, leading to finer particles [28]. It was proposed that the addition of these soluble elements into A1 changes the amorphous structure to one that contains a high number of small A1rich regions distributed homogeneously in the disordered structure, as shown in Figure 11. These Al-rich regions are the preexisting nuclei of c~-A1. However, recent X-ray absorption fine structure (XAFS) measurements have shown that the addition of Cu to the amorphous A1 alloy induces the formation of Cu-rich regions and increases the inhomogeneity of the amorphous matrix [29]. Furthermore, the diffusivity of the A1 element in the c~-A1particles doped with solute atoms becomes more difficult because of the necessity of the solute redistribution. This suppresses further grain growth of the or-A1 particles. This proposed mechanism is supported by the result that the addition of insoluble elements such as Fe does not have any effect on the refinement of the or-A1 particles. Experimental evidence indicates that the amount of precipitation from the amorphous matrix is strongly influenced by the concentration of solute elements and the size of the particles decreases gradually with decreasing solute concentration. A similar microstructure of 30-50-nm-sized c~-A1 particles surrounded by a 10-nmthick amorphous phase, as shown in Figure 12a, has been achieved directly from the melt spinning of the A197TisFe2 alloy. The solidification involves the nucleation of the c~-A1 phase and the solidification of the remaining liquid to the amorphous phase. The formation of the amorphous phase is believed to be caused by the low diffusivity of the Ti element [25]. A new type of nanoscale mixed structure of nanocrystalline and amorphous phases has been found in melt-spun A194V4Fe2. The typical melt-spun microstructure consisted of homogeneously mixed 20-nm-sized granular amorphous and 7-nm-sized or-A1 phases, as shown in Figure 12b [25]. It has been proposed that the solidification takes place through the primary formation of an amorphous phase, followed by the nucleation of c~-A1 from the remaining liquid. Usually, the addition of V to A1 alloys tends to promote the formation of a quasicrystalline phase (i.e., icosahedral) during solidification. In this case, the supercooling in rapid solidification processing may suppress the formation of a long-range icosahedral phase and lead to the development of a nanoscale granular amorphous phase.

512

RAPID SOLIDIFICATION PROCESSING OF NANOCRYSTALLINE METALLIC ALLOYS

Fig. 12. Bright-fieldelectron micrographs and selected-areadiffraction patterns of nanocrystalline meltspun A193Ti5Fe2 (a, b) showing a mixedmicrostructure of 30-50-nm-sized or-A1particles embedded in an amorphous matrix and nanocrystalline melt-spun A194V4Fe2 (c, d) showing a mixed microstructure of 20-nm-sized granular amorphous and 7-nm-sized c~-A1phases. (Source: Reprinted with permission from [25]. 9 1997 Minerals, Metals & Materials Society.)

Another nanoscale mixed structure consisting of Mg particles embedded in an amorphous matrix has also been found in the annealing of melt-spun amorphous M g - Z n - L n alloys [37, 38]. The Mg particles have a hexagonal closed-pack (hcp) crystal structure. These annealed Mg alloys exhibit a tensile strength of approximately 920 MPa (i.e., three times that of commercial Mg-based alloys [ 19]). It has also been reported that primary crystallization of amorphous Ti60Ni30Sil0 or Ti56Ni28Si16 alloys produced 20-30-nm spherical Ti2Ni or lozenge-shaped Ti5Si3 particles embedded in an amorphous matrix, respectively [39]. The Ti2Ni phase has a cubic crystal structure, whereas TisSi3 has a hexagonal crystal structure. However, the annealing atmosphere during primary crystallization can affect the formation of the nanosized particles. This is most important to base elements that are prone to oxidation (e.g., Tibased alloys). During the annealing of a Ti38.5Cu32Co14Al10Zr5.5 alloy in vacuum [40], the amorphous alloy appears to be more resistant to crystallization. This implies that the transformation kinetics is reduced in a clean environment. The resultant partially crystallized microstructure consisted of 20-nm-sized particles with a body-centered structure and a lattice parameter very close to that of TiCo and TiNi intermetallic compounds (A2 type).

3.2.2. Nanocrystalline Nickel Alloys A nanoscale mixed structure of crystalline and amorphous phases has also been found in a partially crystallized amorphous melt-spun Ni58.5Mo31.5B10 alloy [41]. The primary crystallization of this amorphous alloy produces a microstructure of a 10-28-nm Ni(Mo)

513

CHANG

solid-solution phase embedded in an amorphous matrix. The maximum amount of Mo dissolved into Ni was found to be 20%. The remaining Mo and B segregate to the surrounding amorphous matrix, thereby increasing its crystallization temperature. Hence, the thermal stability of the nanocrystalline structure is increased because the intergranular amorphous layers prevent further grain growth.

3.2.3. Mechanical Properties At present, detailed investigation of the mechanical properties of these nanoscale mixed structures has only been carded out on Al-based alloys. The mechanical properties of nanocrystalline A1 alloys are very sensitive to the volume fraction of the ct-A1 phase and the solute contents, as shown in Figure 13. With increasing volume fraction Vf of the nanoscale ct-A1 particles, Young's modulus E and the hardness Hv increase, and the elongation decreases almost monotonically, while the tensile strength shows a maximum value of 1200 MPa for a volume fraction of 10% to 30% [22b]. The highest strength obtained is about 1200 MPa for an A188Ni10Y2 alloy. Similar results were obtained in the quaternary alloys with the highest strengths varying from 1460 to 1560 MPa, as shown in Table I. The exceptionally high tensile strength is attributed to the presence of these nanoscale particles [27]. The nanoscale or-A1 particles are too small to contain internal defects. The interface between the ct-A1 and amorphous phases has the following characteristics: (1) no faceted phases with stress concentration regions, (2) a highly dense atomic configuration, and (3) a relatively low interfacial energy between the amorphous (liquid-like) and c~-A1 phases. This interface structure enables a good transfer of applied load between the amorphous and ct-A1 phases, thereby suppressing the failure at the interface. Consequently, an

Alloo-x.yYxNb,

500 400

2

Y

-

~

.

-

e-~-r

~-.~ 300

5Y-6Ni

"T

200 c-

1200

2 Y - 10Ni lilt

,,=_,,

= 1000 ( D .-,.

~.

800

~

t._

"6 u_

600

o~

70

~.~

50

e-

o >_ ,o

~ "

400

~

*

-

6Y-4Ni

_.

A

^

t~_

_

-

o LU

* BdHle

*-2Y-10Ni

30 2

"

-L

2Y-10Ni. 9

'1.

-5Y-6Ni

6Y-4Ni ,i

0

I

I

I

I

I

10 20 30 40 50 Volume Fraction ( % )

Fig. 13. Changesin trf, E, Hv, and ef as a function of the volumefraction of the t~-A1phase for rapidly solidified AllOO_x_yYxNiy alloys. (Source: Reprinted with permission from [27]. 9 1992 Japan Institute of Metals.)

514

RAPID SOLIDIFICATION PROCESSING OF NANOCRYSTALLINE METALLIC ALLOYS

Table I. TypicalAlloy Systemsand Highest Tensile Strengths of Nanocrystalline A1-Based Alloys Obtained by Rapid Solidification

Alloy

Structure

Preparation method

trf (MPa)

A188Y2Ni8Mn2

Nano. or-A1+ amorphous

Melt spinning

1470

A188Ce2Ni9Fe3

Nano. ct-A1+ amorphous

Melt spinning

1560

A187Ni7Nd3Cu3

Nano. t~-A1+ amorphous

Annealingof melt-spun ribbons

1460

i

(Source: Data from A. Inove et al., Sci. Rep. Res. Inst. Tohoku Univ., 1996.)

Fig. 14. Schematicdiagram of the tensile deformationmodeof an amorphoussingle-phase alloy and an amorphous phase containing nanoscale ct-A1particles. (Source: Reprinted with permissionfrom [22b]. 9 1994 Japan Institute of Metals.) increase in rye is achieved by capitalizing the high-strength t~-A1 particles with a perfect crystal structure. Furthermore, the presence of the nanoscale ct-A1 particles can influence the shear deformation of the amorphous matrix. As shown in Figure 14, it is known that an amorphous alloy is deformed along the maximum shear plane with a thickness of 1020 nm, which is inclined by about 45 ~ to the direction of the tensile load. Therefore, only when the particle size is comparable or smaller than the thickness of the shear deformation band can the particle act as an effective barrier against the subsequent shear deformation of the amorphous matrix. Recently, Zhong et al. [33] have reported that the microhardness of the partially crystallized A186Ni12Y2 alloys obtained after primary crystallization is comparable to fully amorphous alloys of composition matching that of the residual amorphous matrix in the crystallizing alloys. This suggests that the contribution to the hardening is due to chemical solution hardening of the residual amorphous matrix resulting from solute enrichment. The same hardening mechanism is presumed to operate when nanophase composites are produced directly by quenching. Therefore, the improved strength in these nanocrystalline A1 alloys is caused by a combination of particle strengthening and solution hardening mechanisms.

515

CHANG

3.2.4. NanocrystaUine Soft Magnet A new class of soft magnetic materials has been developed by exploring the primary crystallization of melt-spun amorphous Fe-based alloys with Fe content between 70 and 85 at%. Yoshizawa [42] found that the Fev3.sSi13.sB9Nb3Cu1 (known as FINEMET) amorphous alloys transform from an amorphous structure to a mixed structure of c~-Fe and residual amorphous phases on annealing at temperatures slightly above the onset of the primary crystallization (~520 ~ and the crystallized products exhibit good soft magnetic properties (i.e., high permeability, high magnetization, low core loss, and low coercivity). The c~-Fe phase exists as 5-20-nm-sized particles. The crystalline volume fraction Vcryst ranges from about 50% to 80%, depending on the alloy composition and heat treatment. The amorphous layer thickness d can be estimated from the following simple geometric relationship between d, Vcryst, and the ot-Fe crystal size D: (1

D (13) 3 Typically, this gives a thickness of d ,~ 1-2 nm. The local chemical composition in the nanocrystalline Fe-Cu-Nb-Si-B alloy has been studied using FIM. Hono et al. [43] have reported that the Si partitioned into the ot-Fe particles forming an Fe(Si) solid solution with a Si content of about 20 at% Si during primary crystallization. The Nb and B content segregate to the residual amorphous regions. This results in a positive magnetostriction (~.s). The slow-diffusing Nb atoms lead to a sharp concentration profile, whereas the fast-diffusing B atoms give a flat concentration profile in the amorphous regions ahead of the growing c~-Fe particles. Once again, the primary crystallization of amorphous Fe-Cu-Nb-Si-B alloys involves the heterogeneous nucleation of the ot-Fe phase. This is brought about by the addition Cu, which causes a chemical inhomogeneity of the amorphous matrix through cluster formation at the incipient stage of annealing. This is because Cu atoms have strong repulsive interatomic interactions with both Fe and Nb atoms, which provides a thermodynamic driving force for Cu clustering [35]. XAFS measurement on the formation of the nanocrystalline microstructure in Fe73.5Si13.5B9CulNb3 showed that the local structure around the Cu atoms in the alloy changes from an amorphous to a face-centered cubic structure prior to the precipitation of the ot-Fe phase. The Cu-rich clusters can serve as nucleation sites and they trigger massive nucleation of c~-Fe(Si) particles [44]. Subsequent growth of these particles involves the redistribution of elements. The Nb and B atoms are excluded from the crystallized region and they are enriched in the remaining amorphous phase, because they possess little solubility in the c~-Fe(Si) phase. Thus, the additional Nb and the sharp concentration profile stabilize the amorphous phase against the formation of an intermetallic phase. Concurrently, grain growth of the c~-Fe phase is suppressed. However, Naohara [45] has reported that quenched-in c~-Fe(Si) nuclei can also be produced in Cu-free Fe84-xSi6BloNbx melt-spun alloys when the addition of Nb is in excess of 3 at%. The addition of Ga has also been reported to assist the massive nucleation of the ot-Fe phase in the primary crystallization of a melt-spun amorphous Fe73SillB9Nb3Ga4 alloy [46]. At present, the nucleation mechanism for an alloy containing Ga is still unclear. The addition of a refractory metal (X = Zr, Nb, Mo, V) to the alloy has been reported to influence the size of the u-Fe(Si) particles in partially crystallized Fe73.sSi13.5B9Cul Nb2X2 alloys [47]. The average particle size and the volume fraction of c~-Fe(Si) decrease in the order V > Mo > Nb > Zr for a given annealing condition. This is because of the increase in the thermal stability against crystallization with the addition of Zr. The addition of Mo and V, on the other hand, diminish the thermal stability of the amorphous phase. Since then, other nanocrystalline Fe-M-B (M = Zr, Hf, Nb) alloys (NANOPERM) with a higher Fe content between 85 and 90 at% have been developed that exhibit superior d-~

-

Vcryst)

516

RAPID SOLIDIFICATION PROCESSING OF NANOCRYSTALLINE METALLIC ALLOYS

5x10 5 Co-Based Amorphous Alloys

2x10 5 1 xlO 5 -

•

Nanocrystalline -B based Allo~

4

2 xlO 4

\ Nanocrystalline (~s) Fe-Si-B-Nb-CuAlloys ~

Silicon Steels

2x10 a

1x l 0 3 0

Mn Zn/erriteF

I

I

0.5

1.0

1.5

I

I

2.0

2.5

Bs (T) Fig. 15. Correlationbetween effective permeability(~e) at 1 kHz and saturation magnetization (Bs) for nanocrystalline Fe-M-B (M = Zr, Hf, Nb)-based alloys. The data on conventional soft magnetic alloys are also shown for comparison. (Reprinted with permission from [51]. 9 1996 Institute for Materials Research Tohoku University.)

soft magnetic properties, as shown in Figure 15. In these alloys, the c~-Fe phase is nearly pure Fe and the ~,s becomes negative. In Fe-Zr-B alloys, the nucleation of ct-Fe particles is assisted by the formation of small medium-range ordering structure domains with no compositional fluctuation at temperatures below the crystallization temperature (~400 ~ The domain size increases with annealing time and these domains act as nucleation sites for primary ct-Fe particles. At the nucleation and growth stage of ct-Fe, it is clearly confirmed by FIM that the Zr and B atoms segregate to the amorphous matrix because they are not completely soluble in the c~-Fe phase. Although Zr atoms are almost completely rejected into the amorphous matrix, some B atoms still remain in the particles. Eventually, this results in the enrichment of Zr and B in the remaining amorphous matrix. However, a sharp concentration gradient of Zr has been observed at the ot-Fe/amorphous interface because Zr is the slowest diffusing species compared with other alloying elements. Consequently, a metastable local equilibrium is developed at the growing crystalline front and the growth kinetics of the ot-Fe particles is predominantly controlled by the diffusion of Zr atoms. The maximum content of B near the interface appears to result from the enrichment of Zr at the interface because of the strongly attractive interaction between Zr and B atoms. The small addition of Cu or Pd to F e - M - B alloys has been found to reduce the size of the ct-Fe particles [48]. For example, as shown by FIM, the Cu atoms in the Fe89ZrTB3Cu1 alloy form clusters but do not affect the redistribution of both Zr and B atoms. Hence, it is concluded that the addition of Cu to the Fe-Zr-B alloy plays a role similar to that in the F e - S i - B - N b - C u alloy and the formation of Cu clusters enhances the massive nucleation of ct-Fe particles. Varga et al. [49] have also studied the role of other nucleating additives (M = Cu, Ag, Au, Pd, Pt, Sb, Gb) in the formation of nanocrystalline structures and soft magnetic properties in Fe86ZrTB6M1. It was reported that Cu is the most effective nucleating agent. The addition of boron has been found to suppress the coarsening of the ot-Fe phase because of the increased thermal stability of the residual amorphous phase and the suppression of the second stage of crystallization to form compound phases [50].

517

CHANG

'

I

A

[..

"-

L

.3. 5 j

-5

!

. . . .

i

I

oas-Q

9

.o "'~

.qp..~

,

I

....

I

I

IP--.-~ e

d~ ~.0

-

Fe so.x Z r 7 B 3 A I x

0.5-

.

10 3 ~

.

I

.

.

.

.

.

.

I

t

f-lkHz Hm~0.8AIm

9

-

! 10~1

.

0

I . . . . I 5 10 AI content ( a t e )

I . 15

Fig. 16. Changesin Zs, Bs, and/Ze as a functionof A1content for the nanocrystallineFe90-xZr7B3Alx annealed for 3.6 ks at 600~ (873 K). (Reprinted with permission from [51]. 9 1996 Institute for Materials Research TohokuUniversity.) Recently, there has been some investigation into fabricating nanoscale c~-Fe phases with a near-zero magnetostriction ~.s by forming Fe(A1) and Fe(Si) solid solutions in the FeZr-B alloys using the small addition of A1 or Si elements, respectively [51]. Figures 16 and 17 show the changes in the soft magnetic properties as a function of the A1 and Si contents in the rapidly solidified Fe-Zr-B-A1 and Fe-Zr-B-Si alloys, respectively. The advantages of quaternary Fe88ZrTB3A12 and Fe86ZrTB3Si4 soft magnetic alloys consisting of a nanoscale c~-Fe phase embedded in the amorphous matrix include the achievement of zero ~.s and improvement of permeability/Ze to 1.7 x 104 and saturation magnetization Bs > 1.5 T. In the partially crystallized Fe86ZrTB3Si4 alloy, the c~-Fe phase contained approximately 96 at% Fe, 2 at% Zr, 1.5 at% Si, and less than 1 at% B, whereas the amorphous phase consisted of 7 at% Si, 17 at% Zr, and 2 at% B. The enrichment of Si in the residual amorphous phase is presumed to be caused by the strong interaction between Si and Zr atoms compared to that between the Si and Fe. The enthalpy of mixing between the Si and Zr is twice as high as that between Si and Fe [52]. When Zr is rejected from the c~-Fe, Si would be attracted to the Zr-enriched amorphous phase although Si has high solubility in ot-Fe.

3.2.5. Soft Magnetic Properties The characteristics of good soft magnetic properties are high initial permeability/Ze, high saturation magnetization Bs, low coercive force Hc, low core loss, and near zero ~.s. This is closely associated with the nanoscale grain size of the c~-Fe phase and the intergranular amorphous phase. Typical measured magnetic properties of this type of nanocrystalline Fe-based alloy are summarized in Table II. In the scale where the grain size is less than

518

RAPID SOLIDIFICATION PROCESSING OF NANOCRYSTALLINE METALLIC ALLOYS

J~ 20 F

i

'"

i ..... ~

/

A o2a< ,~, 3.~,,

/

9 873K for 3.6ks

-10

f

oa,-O

....

-

oii"/

/

i

I

~e....L. 1.5-

.. t

_

Fego-xZrTSixB3

a3 ~.o05..........

I

,,

i

i

10" ~

I o 10~

--

10=

-

e,.

Hm,,O.SAIm

.

0

.

~

. ,I

e

I

.

5

-

10

~ 9

15

content (at%)

Fig. 17. Changes in ~.s, Bs, and/Ze as a function of Si content for the nanocrystalline Fe90_ x Zr7B 3 Six annealed for 3.6 ks at 550~ (823 K) and 600~ (873 K). (Source: Reprinted with permission from [51]. 9 1996 Institute for Materials Research Tohoku University.) Table II. Magnetic Properties of Nanocrystalline Fe-Based Alloys and Other Conventional Soft Magnetic Alloys Bs

/Zs at

Core loss a

Alloy

(T)

1 kHz

(W/kg)

Fe73.5 Si ] 3.5 Nb3 B9 Cu 1

1.24

100,000

Fe84Nb3. 5zr3.5B8Cu]

1.53

100,000

Fe84Nb7 B9

1.59

Fe90Zr 7B 3

Dfe b ~.s x 106

(nm)

2.1

12

0.06

0.3

8

50,000

0.1

0.2

9

1.70

29,000

0.17

-1.1

15

Fe83Nb7B9Cul

1.52

57,000

1.1

8

Oriented Si-steel

1.80

2,400

0.73

(Source: Data from A. Makino et al., Sci. Rep. Res. Inst. Tohoku Univ., 1996.) a At f = 50 Hz and Bm = 1.4 T. b Df e is the average size of the ot-Fe particles.

the ferromagnetic exchange length (i.e., where the exchange interaction starts to dominate), Hc and the inverse initial permeability (1//Ze) are directly proportional to the average anisotropy (K) (i.e., they essentially determine the soft magnetic properties of the materials). This is expressed in the following equation [54a]:

Hc,~ pc(K)/Bs

519

(14)

CHANG

where pc is a dimensionless prefactor with a typical value of 0.1-0.2. Herzer [54b] has evaluated the average anisotropy (K) for nanocrystalline soft magnetic alloys on the basis of the random anisotropy model in which the randomly oriented grains are perfectly coupled through the exchange interaction. Accordingly, the (K) value for a three-dimensional sample can be written as

(K) ,~ K4D6 A3

(15)

where K1 is the magnetocrystalline anisotropy constant of the grains, D is the grain size, and A is the exchange stiffness. The preceding expression shows that the (K) value is mainly dominated by D. It is believed that the existence of the residual amorphous phase in nanocrystalline Fe-based alloys can decrease the effective exchange stiffness between ot-Fe particles, leading to a higher (K) value. This is because the residual amorphous phase can inhibit the exchange coupling between the ot-Fe particles. However, the effective stiffness of the residual amorphous phase varies with the measurement temperature. It increases with decreasing measurement temperature because of the increasing magnetization of the amorphous phase at low temperature, leading to a decrease in the (K) value. Therefore, the soft magnetic properties of the nanocrystalline Fe-M-B alloys are also dominated by D and )~s, together with the existence of the residual amorphous phase that affects the effective A value. 57Fe M6ssbauer spectrometry of the nanocrystalline in Fe86.sCulZr6.sB6 alloys [55] has revealed that the nanosized ot-Fe particles are separated by a paramagnetic amorphous residual phase at the initial stage of primary crystallization. The chemical inhomogeneity in the structure caused by the clustering of Cu increases the Curie temperature. The relative content of the atoms inside these crystalline and amorphous zones is almost stable during the primary crystallization because the grain size does not change substantially. However, further crystallization at elevated temperatures reduces the fraction of the amorphous matrix and increases the portion of atoms with higher magnetic fields because of the propagation of ferromagnetic exchange interactions through the paramagnetic amorphous regions. This leads to high saturation magnetization Bs in the nanocrystalline Fe-based alloys. The magnetostriction )~s decreases significantly in nanocrystalline Fe-Cu-Nb-Si-B and Fe-M-B (M -- Zr, Nb, Hf) alloys. The alloying elements in the ct-Fe particles have a strong effect on the sign and value of )~s, as shown by the addition of A1 or Si to Fe-Zr-B alloys. It has been found that the magnetostriction of Co-doped ot-Fe crystals in nanocrystalline Fe57Co21NbTB 15 is increased, leading to a higher coercive force. In the nanocrystalline microstructure, Zs can be evaluated by the sum of the contributions from both the crystalline ot-Fe and the residual amorphous phases using the following expression [56]: ~.s ~ Vcryst~.s fe + (1 - Vcryst)~.sam

(16)

where L~e and L~un are the magnetostriction of the ot-Fe and amorphous phases, respectively. A low magnetostriction is required to overcome the magnetoelastic anisotropy arising from internal mechanical stresses. Therefore, the small magnetostriction of the nanocrystalline state is closely related to the increase of initial permeability. The high initial permeability (/Ze) of the nanoscale t~-Fe phase is caused by the following four factors: (1) formation of the ct-Fe phase with nearly zero magnetostriction (~.s), (2) achievement of high magnetic homogeneity because of the small ot-Fe particles in comparison to the magnetic domain walls, (3) small apparent magnetic anisotropy of the ot-Fe phase resulting from ultrafine grain size, and (4) effective interaction of magnetic exchange coupling through a small amount of the thin intergranular residual amorphous layer. Nanocrystalline Fe-based alloys exhibit low core loss. The classical eddy current loss Wc [57] is calculated by Wc -

(rctf am) 2 6pDm

520

(17)

RAPID SOLIDIFICATION PROCESSING OF NANOCRYSTALLINE METALLIC ALLOYS

where t is the thickness of the sheet, f is the frequency, Bm is the maximum flux density, r is the electrical resistivity, and Dm is the density. However, the total eddy current loss Wet [57] is expressed as Wet-- Wa -+- Wc

(18)

where Wa is the anomalous eddy current loss, which varies with the frequency and the static hysteresis loss [57]. The anomaly factor 77is calculated by 77=

Wet We

(19)

The anomaly factor r/at 50 kHz and 1.0 T is evaluated to be 1.4 for the Fe-Zr-B nanocrystalline alloy with a direct-current (dc) remanence ratio of 0.44 and 5.7 for the amorphous alloy with a dc remanence ratio of 0.37 [57]. The small r/comparable to that for the Cobased amorphous alloy appears to be a major reason for the low core losses of the nanocrystalline Fe-M-B (M = Zr, Hf, Nb) alloy. It is known that the 0 value is closely related to the magnetic domain structure of alloys, particularly the spacing of domains with 180 ~ walls. At present, there is no report on the domain structure of the nanocrystalline Fe-M-B alloys. However, the curved domains with a width of about 100 # m separated by 180 ~ walls have been observed in nanocrystalline Fe73.5Si13.5B9Nb3Cul alloys with low core losses comparable to those of Co-based amorphous alloys with zero magnetostriction. Similar curve domains separated by 180 ~ walls have been observed in nanocrystalline Fe91Zr7B2 alloys using magnetic force microscopy (MFM). The domain wall thickness was estimated to be less than 2/zm from the MFM image. This result is consistent with the exchange correlation length (0.5/~m) evaluated from the measured magnetic properties. These results reveal that excellent soft magnetic properties are due to the averaging of the effects of the magnetocrystalline anisotropy over the order of 104 grains [58]. The nanocrystalline Fe-based alloys have other unique magnetic properties such as good piezomagnetic [59] and giant magnetoimpedance effects [60]. The piezomagnetic properties have been studied by the magnetic field dependence of the modulus of elasticity and magnetomechanical coupling measurement. The maximum value of the magnetomechanical coupling coefficient of the nanocrystalline Fe73.5Cul Nb3Sil3.5B9 alloy was found to be 0.7 and the maximum elastic modulus changed from 50-60 to 170-180 GPa as a function of the applied magnetic field. This is believed to be due to the reduction of magnetostriction associated with the formation of a nanocrystalline structure. The giant magnetoimpedance effect (GMI) gives rise to large changes in the complex impedance upon the application of a dc magnetic field. The basic mechanism responsible for GMI is generally considered to be the skin depth, which is strongly dependent on the frequency of the exciting magnetic field, the transversal permeability, and the electrical resistivity [61 ]. The GMI ratio resulted from a combination of large permeability and high electrical resistivity, as found in a nanocrystalline microstructure [62]. The GMI effect has been found in many nanocrystalline Fe73.5CulNb3Si13.5B9 and Fe86Zr7B6Cul alloys [63, 64]. The GMI effect, together with a very high sensitivity at low fields, has opened up enormous potential applications in the field sensing and magnetic recording heads [65]. For nanocrystalline Fe73.5Cu 1Sb3 Si 13.5B9 alloys, a maximum magnetoimpedance ratio of - 227 % is obtained in the amorphous melt-spun ribbons after annealing at 550 ~ for 3 h with alternating current (ac) at 300 kHz. The mechanism of the GMI effect in nanocrystalline materials is still a subject of further investigation. However, it has been found that the GMI is correlated with the high effective permeability associated with nanocrystalline structures. These new quaternary soft magnetic alloys have tremendous potential applications including power transformers, data communication interface components, electromagnetic interference (EMI) prevention components, magnetic heads, sensors, magnetic shielding, and reactors. Furthermore, the soft magnetic materials are expected to be used in various kinds of magnetic parts of transformers, saturable reactors, choke cores, and so on [66].

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One drawback of nanocrystalline alloys is their extreme brittleness. No winding or any kind of materials handling is possible on the final ribbons and the sample has to be encased in any thermal treatments. By replacing conventional annealing in an oven with Joule heating, where the ribbon is supplied with a current density on the order of some 107 A m -2 for times ranging between 10 and 100 s, it is possible to obtain high bending strains at fracture and higher initial permeability in Joule-heated Fe73.5Cu1Nb3Si13.sB9 alloys [67, 68]

3.2.6. Nanocrystalline Permanent Magnet A new class of nanocrystalline permanent magnetic Fe89Nd7B4 alloys has been produced after heat treatment of the rapidly solidified amorphous structure at 800 ~ for 60 s. The resultant microstructure consisted of three phases: 20-30-nm-sized ot-Fe and 20-nm-sized tetragonal Fe14Nd2B particles surrounded by the remaining amorphous phase with a thickness of 5 to 10 nm, as shown in Figure 18. The volume fractions of constituent phases in the F e - N d - B alloys are about 60% for the c~-Fe phase, 20% for the remaining amorphous phase, and 20% for the Fe14Nd2B phase. The Nd content is about 0.5% for the c~-Fe phase and about 14 at% for the Fel4NdaB phase as measured using energy dispersive spectroscopy (EDX) [51 ]. The Nd content in the remaining amorphous phase is about twice that of the nominal Nd content, indicating that Nd is significantly enriched in the amorphous phase. The distribution of B in the nanocrystalline Fe-Nd-B alloy is similar to that in the Fe-Zr-B alloy because of a similar alloy composition. The enrichment of Nb and B elements near the interface causes the formation of a nanoscale mixed structure. It has been postulated that the formation of the Fe14NdaB phase is initiated by the enrichment of B in the preexisting Fe3B phase that has been nucleated preferentially at the interface between the c~-Fe and the surrounding amorphous matrix [51 ].

Fig. 18. High-resolutiontransmission electron micrograph of the Fe90Nd7B3 alloy annealed for 60 s at 800 ~ showing a triplex microstructure consisting of 20-30-nm-sized c~-Fe, 20-nm-sized Fel4Nd2B, and 5-10-nm-thick residual amorphous region. (Source: Reprinted with permission from [51]. 9 1996 Institute for Materials Research Tohoku University.)

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RAPID SOLIDIFICATION PROCESSING OF NANOCRYSTALLINE METALLIC ALLOYS

Table III. Comparisonof the Hard Magnetic Properties for the Nanocrystalline Fe-rich Fe-Nd-B Magnet Containing an Intergranular Amorphous Phase with Those for Conventional Permanent Magnets

System

Br (T)

Hc (kA/m)

(BH)max (kJ/m3)

Ferrite magnet

0.4

312

30

Alnico magnet

0.9

112

42

SmCo5 magnet

0.89

1360

151

Sm2Co17 magnet

1.14

800

239

Nd2Fel4B magnet

1.31

999

319

Nanocrystalline Fe89Nd7B4

1.3

252

146

Nanocrystalline Fe88Nb2Pr5B5

1.23

270

110

(Source: Data from A. Inove et al., Sci. Rep. Res. Inst. Tohoku Univ., 1996.)

3.2.7. H a r d M a g n e t i c Properties

Both the c~-Fe and the amorphous phases exhibit soft magnetic properties, whereas the Fel4Nd2B exhibits hard magnetic properties. In this triplex nanostructure [69-71 ], the intergranular amorphous network phase has dual functions: (1) to provide an effective exchange magnetic coupling medium between the ot-Fe and the ot-Fe or tetragonal Fel4Nd2B phases, leading to an increase in remanence; and (2) to suppress the reversion of the magnetic domain walls in the central region of the soft magnetic ot-Fe phase, leading to the achievement of a high coercive force Hc. The suppression may be the result of a combination of the inhomogeneity of the constituent elements at the crystalline/amorphous interface and the inhomogeneity of the ferromagnetic properties of the ot-Fe and remaining amorphous phases. Consequently, one can regard the present Fe-rich F e - N d - B hard magnetic alloys as a multiple exchange-coupling-type magnet. Table III shows a comparison of the hard magnetic properties of the nanocrystalline Fe-rich F e - N d - B magnet containing an intergranular amorphous phase with those of conventional permanent magnets. Recently, nanocrystalline Fe88Nb2PrsB5 alloys produced from the crystallization of the melt-spun amorphous phase [72] have also been shown to exhibit superior hard magnetic properties. This is due to the fine nanoscale composite structure of the ot-Fe and Fe14Pr2B phases with a grain size of 10-20 nm, which was achieved by the existence of the Nb- and Pr-enriched intergranular amorphous phase.

3.3. Nanoscale Mixed Structure of Quasicrystalline and Crystalline Phases 3.3.1. Nanocrystalline A l u m i n u m Alloys

The icosahedral phase is formed in a number of rapidly solidified A1-TM (TM = Mn, Cr, V, Fe, Cu, Pd) alloys and it exhibits limited ductility at room temperature. The icosahedral phase has been reported [73] to comprise the Mackay icosahedral cluster containing 55 atoms, as shown in Figure 19, which are arranged through glue atoms to the threedimensional quasiperiodical lattice. Consequently, by utilizing the large unit volume and a number of constituent atoms in the icosahedral structure, it is believed that nanoscale control of the icosahedral structure can improve the ductility and toughness at room temperature. This type of nanoscale mixed structure is predominantly based on nanosized icosahedral phases. This new type of microstructure was first reported in the melt-spun

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CHANG

Fig. 19. Schematicdiagram of the Mackayicosahedral cluster containing 55 atoms. (Source: Reprinted with permission from [73]. 9 1995 AmericanPhysical Society.)

A1-Mn-Ln and A1-Cr-Ln (Ln = lanthanide metal) temary alloys [74]. It consisted of nanoscale icosahedral (i.e., quasicrystalline) particles and an a-A1 phase. Since then, other melt-spun A1-TM-Ln (TM = V, Cr, Mn, Fe, Mo, Ni) alloys have been found to have a similar nanoscale mixed structure. Recently, the application of high-pressure gas atomization to A1-Mn-TM and A1-Cr-TM (TM = Co, Ni) ternary alloys has caused the formation of a coexistent c~-A1 and quasicrystalline structure [75]. Figure 20 shows a typical nanoscale mixed microstructure of A192Mn6Ce2 that consists of 30-50-nm spherical icosahedral particles surrounded by a 10-nm layer of or-A1. The icosahedral particles appear to be distributed homogeneously and the surrounding A1 phase has no high-angle grain boundary. The structural features of the homogeneous dispersion of the icosahedral particles and the absence of any high-angle grain boundaries are believed to result from the unique solidification mode. It is presumed [76-78] that the following solidification sequence occurred: liquid ~ primary icosahedral particles plus remaining liquid --+ primary icosahedral particles and a-A1 phase. The primary precipitation of the icosahedral phase takes place as a result of the high homogeneous nucleation rate and low growth rates. Furthermore, the appearance of distinct reflection tings analogous to halo tings suggests that the nanoscale icosahedral particles have a slightly disordered structure. Further high-resolution transmission electron microscopy (TEM) investigation shows that icosahedral particles with a size of 10-30 nm have a disordered atomic configuration on a short-range scale less than 1 nm and an icosahedral atomic configuration on a long-range scale above about 3 nm.

3.3.2. Mechanical Properties These mixed-phase alloys exhibit tensile fracture strengths sf exceeding 1000 MPa combined with good ductility. This is believed to be the first evidence of the simultaneous achievement of high crf and good ductility in Al-based alloys containing more than 90 at% A1 and the icosahedral phases as a main component having a volume fraction above 50%. The achievement of the high crf is independent of the kind of transition elements. The origin of the high tensile strength and good ductility in these alloys is attributed to the nonequilibrium short-range disorder and long-range icosahedral structure with the following characteristic features: (1) the existence of a natural affinity between the major (A1) and

524

RAPID SOLIDIFICATION PROCESSING OF NANOCRYSTALLINE METALLIC ALLOYS

Fig. 20. (a) Transmissionelectron micrographand (b) selected-areadiffraction pattern of a rapidly solidified A192Mn6Ce2 alloy. (Source: Reprinted with permission from [26]. 9 1996 Institute for Materials Research Tohoku University.) other minor elements, (2) the absence of a slip plane, (3) the existence of voids that enable the local movement of the constituent atoms, (4) an unfixed atomic configuration, leading to structural relaxation, and (5) the existence of A1-A1 bonding pairs because of the Al-rich concentrations. These characteristic features are similar to those for metallic glasses with high tensile strength and good ductility. Furthermore, the existence of a ductile A1 thin layer surrounding the icosahedral particles improves the ductility in these alloys because it provides an ease of sliding along the interface between the icosahedral and approximant crystalline phase. The icosahedral-based structure produced by rapid solidification can be maintained up to 3.6 ks at 550 ~ on annealing. The high thermal stability of this structure enables the production of bulk icosahedral-based alloys by extrusion of atomized icosahedral-based powders in the temperature range of 300 to 400 ~ well below the decomposition temperature of the icosahedral phase [75].

3.4. Nanoscale Mixed Crystalline and Crystalline Structure

3.4.1. Granular Nanocomposite Direct production of nanocrystalline composite materials by melt spinning has been demonstrated successfully in the monotectic alloy systems exhibiting a liquid miscibility gap [79-81 ]. Melt spinning of near monotectic alloys leads to undercooling of the alloys followed by phase separation in the liquid phase, thereby producing a nanodispersed emulsion. Subsequently, solidification of the continuous liquid traps the liquid inclusions, producing a nanodispersed microstructure (also referred to as a granular nanocomposite). The nanodispersed solid phase in this case was formed by the heterogeneous nucleation during solidification of these trapped nanoscaled liquid inclusions. Therefore, these phases show an orientation relationship with the matrix. A typical microstructure of dispersion of

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CHANG

10-50-nm-sized Pb particles embedded in an ct-A1 matrix obtained by melt spinning of an AI-10 wt% Pb alloys is shown in Figure 21. The immiscible granular nanocomposite represents an interesting class of materials. Other examples of melt-spun granular nanocomposites have been fabricated from A1-Bi, A1-Pb, Cu-Pb, Zn-Pb, and Zn-Bi [79] in which the nanoparticle comprises the low-melting-point phase while the crystalline matrix comprises the high-melting-point phase. Table IV shows the size range of the nanoparticles in various systems as a function of the wheel surface velocity during melt spinning [79]. The matrix phase can be modified by selecting the appropriate type of alloying and this provides a great potential for alloy design. For example, melt spinning has been used to produce granular nanocomposites with Bi embedded in an amorphous A1-Fe-Si matrix [80]. Other granular nanocomposites that have attracted interest are based on Cu-Co [82, 83], C u - C o - X (X = Fe, Ni, Mn) [84], Cu-Fe [85], Fe-Au, and C o - A u [86] alloys. These

Fig. 21. Transmissionelectron micrographof a melt-spun AI-10 wt% Pb alloy showing nanodispersion of Pb particles in an A1 matrix. (Source: Reprinted from [81], with permission of Elsevier Science.) Table IV. SizeRange and Average Size of the Nanoparticle in Various Systems as a Function of the Wheel Surface Velocity during Melt Spinning

System

Wheel velocity (m/s)

Size range (nm) 8-200

Average size (nm)

Zn-10 wt% Pb

30

Zn-2 wt% Bi

15

Zn-10 wt% Bi

15

8-160

10

AI-10 wt% Pb

30

20-200

30

A1-2 wt% Pb

30

4-15

5

A1-8 wt% In

15

20-160

80

Cu- 10 wt% Pb

15

100-400

100

15-75

8 25

(Source: Data from R. Goswami and K. Chattopadhyay, Mater Sci. Eng., A, 1994.)

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RAPID SOLIDIFICATION PROCESSING OF NANOCRYSTALLINE METALLIC ALLOYS

alloys exhibit giant magnetoresistance (GMR) when prepared by a combination of rapid solidification to form a supersaturated solid solution and subsequent heat treatment to cause decomposition into a granular nanocomposite structure. In the as-melt-spun state of the Cu70Co30 alloy, two types of face-centered cubic (fcc) Co-rich particles are present: large 100-300-nm-diameter particles, with a Cu-rich shell, formed by liquid phase separation; and smaller 15-40-nm-diameter disks formed via a monotectic reaction. These particles play little or no part in the magnetoresistance (MR) of these materials. On annealing, a very fine distribution of 5-7-nm-diameter disk-shaped precipitates, coherent with the matrix, is formed by a spinodal mechanism. It is these precipitates that are responsible for the large MR observed in the sample annealed at 450 ~ However, a different microstructure is found in the as-melt-spun Cu80Fe20 alloy. Such a binary system has been reported to exhibit GMR in Cu-Fe multilayers. However, the meltspun microstructure consisted of 0.1-0.5-mm droplet-shaped particles embedded in the Cu matrix. The droplet-like particles have an inner fine-scale nanostructure with particle size on the order of 20 nm. The occurrence of these nanostructured droplet particles can be explained as follows. As the liquid alloy of the composition Cu80Fe20 is rapidly quenched from T = 1500 ~ down through the two-phase liquid + y-Fe region, the liquid phase decomposes to Fe-rich droplets within a Cu-rich liquid matrix. These Fe-rich droplets then solidify before the surrounding matrix. Because they are rich in iron, y-Fe nucleates more easily within the droplets while rejecting excess Cu, thus generating the nanostructure within the solidified droplets, as shown in Figure 22. Solidification of the Cu-rich liquid matrix occurs subsequently, followed by the expected transformation of y-Fe into ot-Fe. The addition of boron to the Cu-Fe alloy suppresses the formation of ot-Fe regions during the quench from the melt but not that of the droplet-type structures. During the decomposition of the undercooled liquid solution, boron atoms, which have a stronger affinity to Fe than to Cu, are redistributed preferentially in the Fe-rich zone. It appears that boron atoms stabilize the y-Fe and suppress the ot-Fe phase formation. Boron trapped in the metastable y-Fe crystallites during the quench seems to retard their transformation into ot-Fe. Our present understanding of the GMR in layered structures is based on spin-dependent scattering at the interface between magnetic and nonmagnetic layers, as well as spindependent scattering in magnetic layers [87]. It is emphasized that high-density interfaces between magnetic and nonmagnetic materials give rise to GMR in the granular alloys. Song et al. [83] have reported that the melt-spun Cu70Co30ribbon developed a maximum 4.2-K magnetoresistance of 22% following annealing for 1 h at 450 ~ The addition of a small amount of Ni to Co-Cu alloys is found to improve the GMR effect. Because Ni dissolves in both Co and Cu, the enhancement of the magnetoresistance ratio by the replacement of Ni may be due to the increase in the solubility limit of Co(Ni) in the Cu-rich matrix in the as-quenched state.

3.4.2. Equiaxed Nanocomposite The production of equiaxed multiphase microstructures with an average grain size in the nanometer scale can be achieved by complete crystallization of rapidly solidified amorphous precursors. As referred to in a previous section, the primary crystallization of A1and Fe-based alloys retains some residual amorphous phase. However, further heat treatment of the partially crystallized materials at elevated temperature provides sufficient thermodynamic driving force to complete the crystallization process by transforming the residual amorphous phase to a crystalline compound phase. Several workers have adopted this approach of complete crystallization of amorphous precursors to generate fully dense microstructures with an average grain size less than 50 nm in various Fe, Pd, and Ni alloys. In all cases, the amorphous precursors are transformed into a nanocrystalline equiaxed microstructure consisting of multiple crystalline phases either by primary crystallization or eutectic crystallization processes. Table V gives a summary of the minimum grain size achieved by complete crystallization of the amorphous alloys.

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Fig. 22. Transmission electron micrographs of melt-spun Cu80Fe20 (a, b), (CusoFe20)99B1 (c, d), and (Cu80Fe20)97B3 (e, f). (Source: Reprinted with permission from [85]. 9 1996 Trans Tech publications Ltd.)

Table V. Minimum Average Grain Size in Equiaxed Nanocomposites Produced by Complete Crystallization of Amorphous Precursors

Crystalline phases

Minimum grain size d (nm)

Ta/Tm a

Reference

0.5

88

0.46

89

System

Type

Ni80P20

Eutectic

Ni3P + Ni(P)

6-7

Fe80B20

Eutectic

Fe3B + Fe(B)

8

Fe40Ni40P14B6

Eutectic

(FeNi)3+ FeNi(PB)

Fe78B13Si9

Primary

Fe(Si) + Fe3B

9

0.55

90

21-22

0.51

91

Fe60Co30Z10

Primary

Fe(Co) + (FeCo)2Zr

15

0.51

92

Pd78.1 Cu5.5Si16.4

Primary

Pd(Si) + (PdCu)3Si

19

0.62

93

(Source: Data from K. Lu, Phys. Rev. B, 1995.) a Ta = annealing temperature, Tm = melting point.

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RAPID SOLIDIFICATIONPROCESSING OF NANOCRYSTALLINEMETALLIC ALLOYS

The thermodynamic aspects of the solid-state transformation from an amorphous phase to a nanocrystalline phase have been reviewed by Lu [88a-c]. This is based on the idea that the transformation involves the decomposition of the amorphous phase into nanometer crystallites and the interfaces. The interaction between the interface and the nanometersized crystallites is assumed to be negligible. The maximum fraction of the interface component can be calculated by equating the Gibbs free-energy change for the overall transformation to zero. If we let the atomic fraction of the interface be inversely proportional to the average grain size and assume the thickness of the interface to be independent of the grain size, the minimum grain size (d*) can be deduced from the maximum interface fraction, which is related to the excess Gibbs free energies for the interface A G i and the amorphous phase A G a relative to the crystalline phase(s) according to the following expression [88c]: AG i d* = c~~ AG a

(20)

where c~ is a constant. The A G i is found to be dependent on the excess volume of the interface according to the quasiharmonic Debye approximation. The thermodynamic analysis has shown that the decrease in the excess volume of the interface can result in a significant refinement of the grain size in the crystallized products. The previous experimental data in Table V have shown that eutectic crystallization products consisted of smaller minimum grain size than the primary crystallization products. The reason is presumably due to the different crystallization mechanism. In eutectic crystallization, the amorphous alloy decomposes into a mixture of two equilibrium or metastable crystalline phases. The proportions of these phases give an overall eutectic composition. Such a transformation is controlled by the interface movement and no long-range diffusion ahead of the growing crystals. The two crystalline phases usually have a defined orientation relationship and the interface between these crystalline phases is either coherent or semicoherent such that the excess energy is small and the excess volume is low. However, primary crystallization, as described in the previous section, produces a different interface structure. The primary crystallization is a diffusion-controlled process and this leads to compositional pile-up ahead of the growing crystal front. Therefore, the crystallization of the residual amorphous phase involves heterogeneous nucleation and growth processes. The interface formed in primary crystallization is believed to be a high-energy state compared with other crystallization mechanisms. This implies that the interface has high excess volume. This is believed to be the reason for the larger grain size limits in primary crystallization than that in eutectic crystallization. Therefore, nanocrystalline alloys with small grain size can be achieved by crystallization from an amorphous phase when the interfacial excess volume is small. A nanocrystalline Fe73B13Si9 alloy has been found to exhibit enhanced oxidation resistance at a temperature range of 200 to 400 ~ over its amorphous and coarse-grained crystalline counterparts with the same composition. The nanocrystalline microstructure consisted of an equiaxed mixture of ot-Fe(Si) and Fe2B phases with an average grain size of 30 nm. This microstructure is achieved by complete primary crystallization of the amorphous precursor. It has been proposed that the enhanced oxidation resistance can be attributed to the large fraction of interphase boundaries and the fast-diffusion character of the nanocrystalline materials. At elevated temperature, Si atoms in the ot-Fe(Si) phase segregate to the interface and diffuse quickly to the surface of the sample along these interphase boundaries. Consequently, a large amount of Si atoms accumulate at the surface, where they oxidize to form a continuous SiO2 film that prevents further oxidation [94].

3.5. Nanoscale Single-Phase Structure So far, only nanoscale mixed structures with various phases produced by a combination of rapid solidification and thermal treatment have been reviewed. Currently, it is difficult to

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produce single-phase microstructures with average grain sizes less than 50 nm directly by rapid solidification processing. The most successful route to achieve a nanoscale singlephase structure is by polymorphous crystallization of an amorphous alloy. Polymorphous crystallization is similar to that found in eutectic crystallization. The process is controlled by the interface movement and there is no long-range diffusion ahead of the growing crystalline phase. Examples include NiZr2 [95] and (Fe, Co)33Zr67 [96] alloys. The polymorphous crystallization of the amorphous (Co)33Zr67 alloy produces a single phase consisting of a tetragonal (Fe, Co)Zr2 phase with an average grain size of 10.5 nm after annealing for 80 s at 478 ~ (i.e., above the crystallization temperature). This type of microstructure provides the basis for the study of the grain growth mechanism [96] and Hall-Petch relationship [97] in the nanometer scale. The experimental data have shown that the grain growth kinetics for the nanocrystalline (Fe, Co)Zr2 phase is as follows for the average grain size D: O-

r

- tcryst)1/3

(21)

where Cgg is the constant dependent on certain physical parameters (i.e., mobility, grain boundary free energy) and tcryst is the time for complete crystallization (i.e., until the entire volume is composed of very small grains in contact with one another). However, the microhardness measurement of the nanocrystalline microstructure has shown some controversial evidence of a negative Hall-Petch slope as the grain size approaches to the nanometer scale [97]. The reason for the softening in nanocrystalline alloys is still inconclusive.

4. CONCLUSIONS Rapid solidification has been and continues to remain an important processing approach for materials. One of the main attractions is the flexibility that RSP offers for new approaches to material design and the fabrication of components with superior performance. Rapid solidification processing combined with controlled heat treatment is a powerful approach to generate novel nanocrystalline materials with unique high mechanical strength, excellent soft/hard magnetic properties, and enhanced oxidation resistance. It has become clear that processing conditions play a major role in the achievement of nanocrystalline metallic alloys. Furthermore, the selection of a suitable solute element is essential to cause the appearance of nanoscale mixed structures of fine particles embedded in an amorphous matrix produced by either direct rapid solidification or primary crystallization of the amorphous precursor. These effective solute elements have the following characteristic features: (1) high melting temperature, (2) large atomic size or large atomic size ratio among constituent elements, (3) large negative heat of mixing against the major element, and (4) nearly zero solubility limit against the major element. Recent progress has yielded an improved comprehension of the nucleation and growth processes that enables a better understanding of the alloying effects on the formation of nanocrystalline microstructures. This provides new opportunities for the synthesis of unique microstructures in both structural and functional materials. It is, therefore, believed that new advanced materials exhibiting other novel properties can be fabricated by the modification of atomic configuration on a nanoscale. A variety of nanocrystalline microstructures have been reviewed and their exciting properties have been highlighted. As the microstructure reduces to the nanoscale, the physical properties deviate from those found in coarse-grained materials. This opens up questions on the validity of conventional theories to describe these physical properties. So far, on a laboratory scale, these nanocrystalline alloys have exhibited superior performance than their coarse-grained counterparts. To capitalize on their unique properties, it is essential to maintain the stability of the nanocrystalline microstructure during material processing and in service. The next challenge will be to focus on the processing of these materials in large quantity and economically without losing the nanocrystalline microstructure.

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Kataoka, H. Takeda, I. J. Kim, and K. Fukamichi, Sci. Rep. Res. Inst. Tohoku Univ., A 39, 121 (1994). 87. D.M. Edwards, J. Mathon, and R. B. Muniz, IEEE Trans. Magn. 27, 3548 (1991). 88. (a) K. Lu, J. T. Wang, and D. Wei, J. Appl. Phys. 69, 522 (1991). (b) K. Lu, J. T. Wang, and D. Wei, Scr. Metall. Mater 24, 2319 (1990). (c) K. Lu, Phys. Rev. B 51(1), 37 (1995). 89. A.L. Greer, Acta MetalL 30, 171 (1982). 90. D.G. Morris, Acta Metall. 29, 1213 (1981). 91. H.Y. Tong, J. T. Wang, B. Z. Ding, H. G. Jiang, and K. Lu, J. Non-Cryst. Solids 150, 444 (1992). 92. H. Q. Guo, T. Reininger, H. Kronmiiller, M. Rapp, and V. Kh. Skumrev, Phys. Status Solidi A 127, 519 (1991). 93. P.G. Boswell and G. A. Chadwick, Scr. MetalL 70, 509 (1976). 94. H.Y. Tong, E G. Shi, and E. J. Lavemia, Scr. Metall. Mater. 32, 511 (1995). 95. M.G. Scott, in "Amorphous Metallic Alloys" (E E. Lubrosky, ed.), p. 144. Butterworths, London, 1983. 96. T. Spassov and U. K6ster, J. Mater Sci. 28, 2789 (1993). 97. X.D. Liu, M. Nagumo, and M. Umemoto, Mater Trans., JIM 38, 1033 (1997).

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Chapter 12 VAPOR PROCESSING OF NANOSTRUCTURED MATERIALS K. L. Choy Department of Materials, Imperial College, London, United Kingdom

Contents 1. 2. 3. 4. 5.

6.

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Selection Criteria of the Appropriate Processing Technique . . . . . . . . . . . . . . . . . . . . . . . . Why Vapor Processing Techniques? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Classification of Vapor Processing Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Physical Vapor Deposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1. Process Principles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2. Advantages and Disadvantages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3. Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4. Evaporation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.5. Sputtering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Chemical Vapor Deposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1. Process Principles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2. Advantages and Disadvantages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3. Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.4. Chemical Vapor Deposition Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.5. Thermally Activated Chemical Vapor Deposition . . . . . . . . . . . . . . . . . . . . . . . . . . 6.6. Photo-assisted Chemical Vapor Deposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.7. Plasma-Assisted Chemical Vapor Deposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.8. Metalorganic Chemical Vapor Deposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.9. Atomic Layer Epitaxy Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Aerosol-Based Processing Routes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.1. Process Principles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2. Characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.3. Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.4. Aerosol Generation Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.5. Deposition Mechanism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.6. Aerosol-Assisted Sol-Gel Thin-Film Deposition . . . . . . . . . . . . . . . . . . . . . . . . . . 7.7. Spray Pyrolysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.8. Pyrosol . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.9. Aerosol-Assisted Chemical Vapor Deposition . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.10. Electrospraying-Assisted Deposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Flame-Assisted Deposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.1. Process Principles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.2. Advantages and Disadvantages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.3. Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.4. Counterflow Diffusion Flame Synthesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Handbook of NanostructuredMaterials and Nanotechnology, edited by H.S. Nalwa Volume 1: Synthesisand Processing Copyright 9 2000 by Academic Press All rights of reproduction in any form reserved.

ISBN 0-12-513761-3/$30.00

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8.5. CombustionFlameChemical VaporCondensation . . . . . . . . . . . . . . . . . . . . . . . . . 8.6. Sodium/HalideFlame Deposition with in situ Encapsulation Process . . . . . . . . . . . . . . . 9. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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1. INTRODUCTION Nanocrystalline materials are solid-state systems constituting crystals of sizes less than 100 nm in at least one dimension. In general, nanostructured or nanophase materials can be classified into four categories according to the shape of their structural constituents and to their chemical composition. These include (1) nanophase powder; (2) nanostructured film (including single-layer, multilayer, composite film, compositionally graded film, etc.); (3) monolithic nanostructured material; and (4) nanostructured composite. The nanocrystalline materials can be metals, ceramics, or composites containing crystalline, quasicrystalline, and/or amorphous phases. Nanophase materials exhibit many exciting extraordinary properties, which are not found in conventional material. These include superplasticity, improved strength and hardness, reduced elastic modulus, higher electrical resistivity, and lower thermal conductivities. They also exhibit improved soft ferromagnetic properties and giant magnetoresistance effects. The significance of nanostructured materials is found in electrical, electronic, magnetic, superconductor, catalytic, structural ceramic, and functional applications. The quantum effects observed are the results of materials at the atomic and nanometer levels. However, for many of these cases, it still needs to be ascertained whether the improved properties are due to new physical phenomena at small dimensions or to an extension of larger-scale systematics to small sizes [1 ]. The understanding of the extraordinary behavior of nanostructured materials requires detailed studies of the correlations between the processing, structure, and properties. These studies rely on the identification and development of appropriate (i) processing methods and (ii) suitable characterization methods and analytical tools for the nanocrystalline materials. This chapter focuses on the processing aspects of nanocrystalline materials and provides a brief review of the methods used and highlights the emergent technologies.

2. SELECTION CRITERIA OF THE APPROPRIATE PROCESSING TECHNIQUE

There are several criteria that one should consider when selecting the appropriate technique for the processing of nanostructured materials. The selected processing methods should be able to meet the following requirements: 1. Fabrication of nanocrystalline materials into useful sizes, shapes, and structures without loss of desirable nanometer-sized features 2. Production of large quantities of nanometer-scale materials cost effectively 3. Assurance of process reproducibility and ease of process control 4. Optimization of the process For the processing of nanosized powders, the capability of the technique to control the particle agglomeration and particle size distribution is essential. The efficiency and the selectivity of the particle collection and the handling of ultrafine powders safely still need to be addressed. Nonetheless, for the processing of nanocrystalline films, additional criteria such as the processing technique should not impair the properties of the substrate and the capability

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of coating the engineering components uniformly with respect to both size and shape, thus yielding improved end product quality. The ability to produce nanocrystalline materials with well-controlled structure cost effectively will provide improved understanding of the process/structure/property relationships and pave the way for the successful exploitation of nanocrystalline materials commercially with improved properties.

3. W H Y V A P O R P R O C E S S I N G T E C H N I Q U E S ?

Since Gleiter [2] first drew attention to the extraordinary properties of nanocrystalline materials fabricated using an inert-gas condensation method, many diverse methods for processing nanocrystalline materials have been reported. These include vapor processing routes, liquid phase/molten state methods, and wet chemical and solid-state routes. Figure 1 summarizes the different processing techniques available for the processing of nanostructured materials. There are atomic and morphological differences between the materials manufactured by the various techniques. Each method is particularly suited for particular nanocrystalline systems with specific shapes and volume. Solid-state processing routes such as the mechanical milling-based methods involve mixing, grinding, calcination, and sintering. Although these methods involve relatively simple techniques, they are tedious and time consuming because of prolonged milling times and multiple cycles of processing, which are also prone to contamination from the milling media. However, these powders require further hot consolidation to form bulk sampies. Furthermore, these powders can suffer from chemical and phase inhomogeneities. Extensive milling is expensive and limited to the processing of ultrafine powders. Nanostructured films and multilayer and functionally graded coatings cannot be produced using solid-state processing routes. Wet chemical routes, such as the sol-gel, hydrothermal, and electrodeposition methods, require a high number of processing steps, including pretreatment, mixing, chemical reactions, filtration, purification, drying, and calcination during the fabrication of

Processing route

Processingmethods

Nanocrystalline materials

Solid-state

9 Mechanical Milling

powder

Liquid

9 Sol-gel 9 Sonochemistry 9 Hydrothermal 9 Electrodeposition 9 Gas Atomization 9 Laser BeamMelting 9 Melt Spinning

powder/film powder powder powder/film powder film continuous ribbon

Vapor

9 Chemical VaporDeposition 9 PhysicalVaporDeposition 9 AerosolProcesses 9 Flame-AssistedDeposition

powder/film powder/film powder/film powder

Fig. 1. Classificationof different processing techniques available for the processing of nanostructured materials.

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ultrafine powder. These methods are tedious and can cause contamination. Waste treatment is difficult, especially when producing large quantities. Moreover, some wet chemical routes such as the hydrothermal method are limited to powder processing and cannot be used to produce nanostructured films and multilayer and functionally graded coatings. This chapter aims to provide a brief overview of the vapor processing of nanostructured materials. There exist many distinctive advantages of using vapor processing techniques over other methods in the processing of nanostructured materials. It is obvious that vapor processing methods seem to be the only method that can provide highly pure materials with structural control at the atomic level or nanometer scale. Moreover, vapor processing routes can produce ultrafine powders, multilayer and functionally graded materials, and composite materials with well-controlled dimensions and unique structures at a lower processing temperature. The classification of vapor processing methods, including the recent discoveries of new vapor processing technologies, will be outlined in this chapter. The process principle, description of the processing technique, apparatus used, range of nanomaterials synthesized, and properties will be presented. Their advantages and limitations will be discussed, and their applications will be briefly reviewed.

4. CLASSIFICATION OF VAPOR PROCESSING TECHNIQUES Vapor processing techniques can be classified into physical vapor deposition (PVD), chemical vapor deposition (CVD), aerosol-based processes, and flame-assisted deposition methods as shown in Figure 1. There are several variants of these techniques as summarized in Figure 2. For example, PVD can be subdivided further into evaporation, sputtering and ion plating processes based on the different ways of generating the gaseous species. Similarly, the classification of CVD processes can be based on different heating methods (e.g., thermally activated, photo, plasma, etc.) for the deposition reactions to occur or the type of precursor used. These have led to the development of different variants of CVD such as plasma-assisted CVD, laser-assisted CVD, metalorganic-assisted CVD, and so forth. Aerosol-based processing techniques can be subdivided into spray pyrolysis, electrostaticassisted vapor deposition, and so on, based on the different aerosol generation methods used. All of the preceding vapor processing methods have been used to produce films and coatings. There are numerous papers in the Journal of the Electrochemical Society, Thin Solid Films, Chemical Vapor Deposition, Journal of Applied Physics, and Journal of Vacuum Science and Technology that describe the process and applications of vapor processing techniques, giving further insight into recent developments. These techniques can be adapted to the manufacture of nanostructured materials in the form of either films or powders. Some of these techniques are better than others in providing precise control of the production of nanocrystalline materials and have the capability of scaling up for large-area or large-scale production. The advantages and disadvantages of these vapor processing techniques will be compared and discussed in the subsequent sections. Bulk nanocrystalline materials can be produced by in situ consolidation of the deposited powders.

5. PHYSICAL VAPOR DEPOSITION 5.1. Process Principles The PVD process involves the creation of vapor phase species through (i) evaporation, (ii) sputtering, or (iii) ion plating. During transportation, the vapor phase species undergo collisions and ionization and subsequently condense onto a substrate where nucleation and

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Variants of vapor processing techniques for the fabrication of nanophase materials

1. PhysicalVapor Deposition (i) Evaporation (a)

Inert-Gas Condensation

(b) Electrical explosion wire (c) Laserablation (d) Molecular beam epitaxy (ii) Sputtering 2. ChemicalVapor Deposition (CVD) (i) Thermallyactivated CVD (ii) Photo-assistedCVD (iii) Plasma-assistedCVD (iv) MetalorganicCVD (v) AtomicLayer Epitaxy Process 3. Aerosol-BasedProcessing Routes (i) Pyrosol (ii) Aerosol-assistedchemical vapor deposition Off) Electrospraying-assisteddeposition (a) Coronaspray pyrolysis (b) Electrostaticspray pyrolysis/electrostatic spray deposition (c) Electrosprayorganometallic chemical vapor deposition (d) Gas-aerosolreactive electrostatic deposition (e) Electrostaticspray-assisted vapor deposition 4. Flame-AssistedDeposition (i) Counterflowdiffusion flame synthesis (ii) Combustionflame-Chemical vapor condensation (iii) Sodium/halideflame deposition with in situ encapsulation process Fig. 2. Variantsof the vapor processing techniques.

growth occur, leading to the formation of films. The process principles of PVD are summarized in Figure 3. For the formation of powders, the neutral and/or ionized vapor phase species will collide with the inert-gas molecules and undergo homogeneous gas phase nucleation to form powders that are eventually being removed and collected. Figure 4 shows the different methods of generating the vapor species, which give rise to a variety of PVD techniques such as evaporation, sputtering, and ion plating. The PVD processes take place in a vacuum. The vacuum environment plays an important role in the vapor flux and the deposition and growth of films. The three important aspects of the vacuum environment to thin-film deposition are: the pressure, expressed as the mean free path; the partial pressure ratio of reactive and sputtering gases in inert working gases; and the ratio of film vapor arrival to reactive gas impingement rate. Detailed descriptions of the PVD deposition mechanism are available in the literature [3-5].

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evaporation

sputtering ion plating

collisions

Vapor transportation

ionizations condensation nucleation

Film or powder formation

growth ion bombardment Fig. 3. Processprinciples of PVD.

5.2. Advantages and Disadvantages 5.2.1.

Advantages

The vacuum environment in the PVD process provides the ability to reduce gaseous/vapor contamination in the deposition system to a very low level. Therefore, ultrapure films or powders can be produced using PVD methods. During the fabrication of nanosized powders, the powders can be collected and compacted in situ into a bulk material with a high degree of cleanliness. PVD is an atomistic deposition method that can provide good structural control by careful monitoring of the processing conditions. Moreover, the as-deposited materials are already nanocrystalline in nature and do not require any further milling to reduce the particle size or heat treatment to burn out the precursor complexes.

5.2.2. Disadvantages In general, the disadvantages of PVD processes are as follows: 1. The deposition process needs to operate in the low-vapor-pressure range. Therefore, a vacuum system is required, which increases the complexity of the deposition equipment and the cost of production. 2. The synthesis of multicomponent materials is difficult, except for the laser ablation method. This is because different elements have different evaporation temperatures or sputtering rates. Many compound materials partially dissociate on thermal vaporization producing nonstoichiometric deposits. However, highly

538

VAPOR PROCESSING OF NANOSTRUCTURED MATERIALS

Fig. 4. Threebasic PVD techniques: (a) evaporation, (b) sputtering, and (c) ion plating.

nonstoichiometric materials are beneficial for defect-related applications such as in sensors, fuel cells, ceramic membrane reactors, and oxidation catalysts. 3. PVD is a line-of-sight deposition process, which causes difficulty in producing nanocrystalline films on complex-shaped components, and has poor surface coverage.

5.3. Applications The science of PVD can be traced back to the 1850s. During the 1950s, PVD techniques were widely used for the deposition of thin films for resistors and capacitors for telecommunications, microelectronic circuits, and optical coating applications. Today, PVD covers a wider range of commercial applications that include the deposition of various of metals, alloys, and compounds in the form of coatings and films for (i) optics (e.g., antireflection coatings), (ii) electronics (e.g., metal contacts), (iii) mechanics (e.g., hard coatings on tools), and (iv) protective coatings (e.g., corrosion, oxidation).

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5.4. Evaporation The basic evaporation process is shown in Figure 4a. The sources are generally made of refractory metal (e.g., W, Ta, and Mo) in the form of coils, rods, boats, or special-purpose designs. Material to be evaporated can be in the form of wires, rods, sheets, or powders placed in the evaporation sources. An intense heat is used to vaporize the source from a solid or molten state to a vapor state. The heat is provided by resistance, induction, arc, electron beam, or laser, which give rise to a variety of evaporation methods such as Joule heating evaporation, cathodic-arc deposition, electron beam evaporation, laser ablation, and so on. The vapor flux of the desired material condenses either onto the cooler substrate to form a solid film or onto a cool finger to form powders. The process requirements that need to be considered are the compatibility of the evaporant and the power and the capacity availability. The evaporant compatibility seems to be the most difficult to achieve because many important evaporants (e.g., A1, Fe, Inconel, and Pt) dissolve all refractory metals to some extent. The pressure in the vacuum must be sufficiently low (< 10 -4 mtorr), so that the mean free path (~.) of the vapor species is large; that is, evaporated atoms essentially travel in a straight line from the source to the substrate without colliding with the ambient gas molecules. This relationship can be written as

Z = (1/4~-~a )(kT/P)

(1)

where a is the collision cross section of the gas and T and P are the temperature and pressure of the gas, respectively. The advantages of evaporation, in addition to those outlined in Sections 3 and 5.2.1, are as follows: 1. 2. 3. 4.

The material to be vaporized can be in any form and purity. The residual gases and vapors in the vacuum environment are easily monitored. The rate of vaporization is high. The line-of-sight trajectories and point sources allow the use of deposition onto defined areas. 5. The cost of thermally vaporizing a given quantity of material is much less than that of sputtering the same amount of material.

The limitations of the evaporation method are the utilization of material may be poor. Many compound materials may partially dissociate on thermal vaporization, producing nonstoichiometric deposits. Evaporation has been used by researchers to produce nanocrystalline films or powders. For example, Goodman and co-workers [6] deposited epitaxial MgO(100) films with thicknesses ranging from 2 to 100 monolayers by evaporating Mg onto Mo(!00) at 300 K in 1.0 • 10 -6 torr oxygen. Sasaki et al. [7] synthesized nanocrystalline Ni using the evaporation method. Small particles (10 nm in diameter) and aggregates were produced. The aggregation and coercivity were reduced with a lower evaporation temperature and a higher pressure in the evaporation chamber. They found that the evaporation rate was clearly dependent on the evaporation temperature; however, the particle size was almost independent of it.

5.4.1. Inert-Gas Condensation Inert-gas condensation (IGC) involves the evaporation of materials using fumace or Joule heating sources into vaporized gaseous species, which are subsequently condensed onto a cold surface. Gleiter [10] adapted this technique to the fabrication of nanostructure materials. Figure 5 shows a schematic diagram of the IGC for the production of nanocrystal!ine powders. During the IGC process, the vaporized gaseous species lose their kinetic energy by colliding with the inert gas (e.g., He) molecules. The short collision mean free path

540

VAPOR PROCESSING OF NANOSTRUCTURED MATERIALS

Fig. 5. Schematicdiagram of the inert-gas condensation apparatus for the production of nanocrystalline powders.

resulted in efficient cooling of the vapor species. Such cooling generates a high supersaturation of vapor locally, which leads to the homogeneous gas phase nucleation followed by cluster and particle growth through a coalescence mechanism [ 11 ]. The particles are transported via natural gas convection to a rotating cold finger, where they are collected via thermophoresis [ 12]. The particles are subsequently removed from the cold finger and assembled and compacted in situ into three-dimensional nanostructure compacts with an ultrahigh volume fraction of grain boundaries. The common processing conditions for the production of the smallest particle size while maintaining a high evaporation rate are a few hundred pascals of He and an evaporation temperature that corresponds to a vapor pressure of approximately 10 Pa for the evaporants [ 13]. Under such process conditions, the clusters formed normally have diameters within the range of 5 to 15 nm. Guillou et al. [ 14] reported the preparation of nanocrystalline Ceria powders with narrow crystallite size distributions (3-3.5 nm diameter) by inert-gas condensation using thermal evaporation. No significant differences were observed between the powders collected in the different parts of the ultrahigh vacuum chamber. Particles develop cubic/octahedral shapes during annealing in the temperature range of 400 to 800 ~ The crystallites grow individually by a binary coalescence process and only very few grain boundaries were observed. The size of about 25% to 30% of all crystallites is not affected by sintering at 600 ~ Significant changes occur in the sample annealed at 800 ~ when two populations of crystallites are formed. Fougere et al. [ 15] developed a new consolidation device that was built to reduce the processing defect population inherent in samples and to minimize contamination. The Vickers microhardness of nanocrystalline Fe samples produced by a combination of inert-gas condensation and a new consolidation method is three to seven times higher than that of coarse-grained Fe. The inert-gas condensation technique has also been used to produce nanocrystalline intermetallic compounds (Ni3A1, NiA1, TiA1) with crystallite sizes in the range of 5 to 20 nm [16]. The as-prepared nanocrystalline Ni3A1 samples (24 at% A1) exhibited no superlattice reflection in X-ray diffraction (XRD) and transmission electron microscopy (TEM). Ordering occurred during annealing starting at 400~ As-prepared nanocrystalline NiA1 samples (50 at% A1) were at least partially ordered. Vickers hardness measurements showed that nanocrystalline samples were substantially harder than polycrystalline, indicating that grain refinement caused strengthening. Grain growth could be inhibited

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using hot pressing at temperatures up to 650 ~ under high vacuum as compared with annealing. Provenzano and Holtz [ 17] at the Naval Research Laboratory used the inert-gas condensation method for the development of metal-based nanocomposites for high-temperature structural applications. The nanocomposite approach is based on a strengthening concept that involved the use of nearly immiscible constituents: a ductile matrix and a particulate reinforcing phase. Based on this approach, copper-niobium, silver-nickel, and copper-aluminum nanocomposites were produced, which displayed some degree of strength enhancement and high-temperature strength retention. However, the results clearly showed certain processing challenges associated with the issues of oxide contamination and consolidation of nanostructured metals and alloys by conventional processing. The highly reactive nature of nanocrystalline metals resulting from their high specific surface areas has led them to consider the potential of nanostructured metals and alloys for gas-reactive applications such as nanocrystalline palladium for hydrogen-sensing applications. Daub and co-workers [18] used a quadruple mass spectrometer (QMS) to control the production of nanocrystalline metals by inert-gas condensation in a flow system. Nanocrystals (~40 nm in size) were produced by the evaporation of zinc in a flow system. The metal atom concentration was monitored in relation to the argon carrier by a QMS. The conventional evaporation process based on the Joule heating method is limited to low-melting-point or high-vapor-pressure materials, such as CaF2 and MgO [19]. The deposition of refractory ceramic and high-temperature materials (e.g., Ti) may require the use of more powerful heating methods such as laser, electron beam, and so forth or other PVD methods like sputtering and ion plating. Furthermore, chemical reactions are likely to occur between most metal evaporants and the refractory metal crucibles, which changes the evaporation conditions. Nonhomogeneous temperature distributions are likely to occur in the molten metal using the Joule heating method, which may lead to unsatisfactory control of the evaporation. Moreover, it is difficult to control the stoichiometry of the deposited materials because the constituents of alloys tend to evaporate at different rates resulting from differences in vapor pressures, which produces films of variable composition. Other PVD methods such as electrical explosion wire, laser ablation, molecular beam expitaxy, and sputtering methods have been employed to enable the deposition of hightemperature and more complex multicompoennt materials.

5.4.2. Electrical Explosion Wire The electrical explosion wire method was first developed by Abrahams [20]. It was subsequently used by several researchers to fabricate metal, alloy, and ceramic powders. Kotov et al. [21, 22] employed the electrical explosion wire method for the synthesis of nanosized ceramic powders in large quantities. The wire explosion is carried out at a discharge voltage of 15 kV and current in the range between 500 and 800 kA through the wire in a few microseconds at a chamber pressure of about 50 bar. The discharge can be repeated with a frequency of 1 Hz. The heating of A1, Ti, or Zr wire, for example, by a high-energy electric pulse to the evaporation point will disintegrate the wire into liquid spheres up to 50/zm in diameter that distribute and evaporate in the oxidizing atmosphere (Ar-O2 mixture) and subsequently undergo combustion to form spherical oxide particles ( 1021 atoms/cm 3) areas of silicon behave as etch stops in the alkaline anisotropic etchants. The etch rate of doped p-type silicon as a function of doping concentration is shown in Figure 18. This agrees well with the electrochemical model of the anisotropic etching

596

APPLICATIONS OF MICROMACHINING TO NANOTECHNOLOGY

Fig. 17. Some techniques used to produce membranes and plates anchored by silicon substrates. (a) Timed etch produces silicon plates or etching to mask film produces thin-film membranes. (b) A selfterminating pyramid from top is used to stop etch when an optic signal is transmitted from the bottom. (c) Etch stops such as p+-doped silicon or electrochemically active layers can be used to stop etch. (d) The grill technique to obtain different-height cavities with one mask.

behavior, in which the access holes in the p++-doped silicon pin the Fermi level much lower than the redox potential in the etching bath, eliminating the charge exchange and the resulting chemical reaction [46]. Cantilevers and beams of p++-doped areas have been readily made using this process. The thickness of the doped region is usually limited to 23/zm because of diffusion-limited growth. As an exception, workers at Michigan [47] have developed an extended-time diffusion doping process that allows for doping to 15-20/zm. They have developed a dissolved wafer process utilizing deep p++ silicon as shown in Figure 19. The p+-doped silicon is at first bonded to a glass substrate using anodic bonding. Then the glass-silicon sandwich is etched in a silicon etchant that leaves the glass unetched. Usually, EDP is used, which leaves the glass substrate undamaged. The entire silicon wafer is dissolved leaving behind the p+-doped areas attached to the glass substrate. This process has been used to make a variety of sensors, including a tunneling pressure sensor [48].

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Boron Concentration [cm-3] Fig. 18. Comparison of silicon etch rate in EDP and KOH solutions as a function of boron doping concentration. Reprinted with permission from C. M. Mastrangelo and W. C. Tang, "Semiconductor Sensor Technologies," in Semiconductor Sensors ( 9 John Wiley & Sons, Inc.).

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c) Shallow Boron Diffusion and Dielectrics deposition

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d) Electrostatic bonding and Final Wafer Dissolution Fig. 19. Dissolved wafer process. Reprinted with permission from K. Suzuki et al., "A 1024-element High Performance Silicon Tactile Imager," IEEE IEDM, p. 674 ( 9 1988 IEEE).

598

APPLICATIONS OF MICROMACHINING TO NANOTECHNOLOGY

+1

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diffusion J

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etching -"1" solution ~

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Fig. 20. Electrochemical etch bath setup, before and after etch. Reprinted with permission from C. M. Mastrangelo and W. C. Tang, "Semiconductor Sensor Technologies," in Semiconductor Sensors ( 9 John Wiley & Sons, Inc.).

4.9. Electrochemical Etch Stops

By electrically biasing the silicon wafer to be etched, one can electrically control the population of charge carriers at the semiconductor-electrolyte interface. The ability to control the carriers can be used to modulate the electrochemical reaction (Fig. 20). Typically, a p-n junction is reverse biased. The voltage drop is largely across the p-n diode leaving the p-type silicon surface at open-circuit potential. The KOH etches the p-type silicon until it encounters the n-type silicon. The p-n junction is destroyed and the n-type silicon gets biased so as to eliminate any carriers on the surface stopping the etch completely [46]. An effective electrochemical reverse-biased diode stops the moving front near the diode depletion region. Such techniques can be used to control diaphragm thicknesses to within nanometers [49]. In addition to electrical biasing, one can bias the silicon by generating electrons and holes via photonic illumination. Hence, one has to take precautions of etching under dark conditions for reproducible membrane thicknesses. 4.10. Other Techniques

Often, it is desirable to etch cavities of two different heights simultaneously onto a silicon wafer. For example, one might want to etch a front that goes through the wafer while another etch front terminates at a desired height. One way to obtain this structure is simply to etch one cavity first and then redeposit and pattem the mask material for the second thickness. However, lithography steps are time consuming and expensive. It is also hard to spin-coat and expose photoresist on a wafer with deep features resulting from the first etching. Figure 17d shows the grill technique that can be used to achieve several different heights using o n e etching mask step. This method utilizes undercutting of the (111) planes, which occurs at a much lower etch rate than the primary etching planes. By using a mask grill that is undercut by two sides, one can slow down the etching front propagation as compared to one with no grill pattems. When the silicon is undercut completely, the sharp intersections with many exposed planes of silicon are etched at a very fast rate. The concave tips are etched away completely until a fiat etch front is formed. By choosing different grillopening-to-width ratios, one can obtain cavities of different heights [50]. In addition to membranes, one can form cantilevers made of silicon or etch stop materials by similar techniques. Figure 21 shows a cantilever of silicon nitride formed by exposing the silicon from the front side of the wafer [51 ]. In the case shown, the silicon nitride film was only 90 nm thick. By using (110) wafers, the cantilevers could be placed into contact with other surfaces and used to make ultrasensitive force measurements. An illustrative example of an early (1979) bulk-micromachined accelerometer is shown in Figure 22 [52]. The p+-doped areas on the front side are piezoresistors that convert the

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Fig. 21. Very thin ('-,900/~ thick) silicon nitride membranes fabricated using the process shown on right. Vertical side walls in (110) silicon wafers can be produced upon anisotropic etching. Reprinted with permission from S. Hoen et al., Fabrication of Ultrasensitive Force Detectors, presented at Solid-State Sensor and Actuator Workshop, Hilton Head, SC ( 9 1994 Transducers Research Foundation). I~E$1STORS

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t'-~ ~('~)uc'r,vE e~,,~,

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Fig. 22. Top view and centerline cross section of bulk-micromachined accelerometer. Reprinted with permission from L. M. Roylance and J. B. Angell, IEEE Trans. Electron Devices ED-26, 1911 ( 9 1979 IEEE).

strain generated by an applied acceleration to the proof mask. Figure 23 shows the bulketched proof mask attached to the silicon frame. Because no comer compensation was used, the comers are etched inward as expected. The ability to attach a large mass to a very thin film strain gauge enables high sensitivities. However, the weak tether holding the mass can lead to the proof mass impacting the package under large accelerations.

5. DRY BULK SILICON CRYSTALLINE MICROMACHINING Dry etching of silicon has several advantages over wet etching. First, dry etching eliminates the process of drying and cleaning wafers exposed to dangerous chemicals. The fluid turbulence associated with drying is particularly dangerous for etched silicon wafers with weakly tethered silicon structures. Second, dry etching tends to be a much more controllable process than wet etching, where most reaction rates are exponentially temperature dependent. By controlling the chemistry and the density, plasma etching can be more insensitive to temperature variations. Furthermore, vertical side walls with wet etching can

600

APPLICATIONS OF MICROMACHINING TO NANOTECHNOLOGY

Fig. 23. Backside of the silicon-etched die with comers etched as expected without comer compensation. Reprinted with permission from L. M. Roylance and J. B. Angell, IEEE Trans. Electron Devices ED-26, 1911 ((g) 1979 IEEE). be obtained with only a few wafer configurations ((110)). Dry plasma etching has the potential of solving most of these problems. Dry plasma etching enables the possibility of vertical etch profiles while requiting no liquid contact. However, a marked disadvantage of dry etching is the complexity and high cost of equipment necessary to sustain wellcontrolled plasmas. Maintaining a uniform plasma density across large wafer areas is also a challenge and usually implies etching rate variations across the wafer.

5.1. Plasma Etching The dry etching discussed in the context of MEMS can be classified into plasma and vapor phase etching. We will first discuss plasma, etching. In a typical etching plasma, the reactive gas is mixed with a dilutant gas and exposed to high-energy radio frequency (rf) electric and magnetic fields (Fig. 24). These fields ionize the gas molecules, creating electronics that further ionize the gas and result in a stable phase of ions and electrons. For plasma etching, the reactive ions have to diffuse toward the surface, diffuse on the surface, react with the surface atoms, and then diffuse away into the plasma. If the ions are very

Fig. 24. Componentsof a typical plasma system.

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Fig. 25. The gas pressure, bias, and chemistriesproducedifferentetch profiles in plasmaetching.

energetic, pure physical etching can occur by ion-surface momentum transfer during impact. If the ions are not very energetic, chemical reactions of charged species take place, which are controlled by the plasma pressure, temperature, and rf power [ 16]. A few of the different kinds of etch profiles obtainable from plasma etching are shown in Figure 25 and described in the following sections.

5.1.1. Isotropic Etching Isotropic plasma etching occurs when the plasma density or pressure is high. The high particle density results in an isotropic velocity distribution and isotropic etching. However, plasma etchants can never really be as isotropic as wet isotropic etchants. Because of the high reactivity of silicon with fluorine, silicon is most commonly etched in fluorinebased plasmas. Typically, SF6 or CF4 gases are mixed with oxygen in plasma. In addition to reacting with the silicon atoms directly, these gases form polymers that are etched by dilutant oxygen radicals. Furthermore, supply-limited reactions result in a loading effect where the more exposed areas of silicon are etched more slowly than the less exposed areas. The loading effect can be reduced by decreasing the reaction rate using a less reactive gas like chlorine, but at the cost of lower etch rates. Chlorine plasmas include gases such as SIC14, CC14, BC13, and C12. To increase the etch rate with chlorine, one has to increase the ion bombardment energy by biasing the substrate, which leads to lower isotropy. The ions bombarding the surface have a higher net velocity perpendicular to the wafer.

5.1.2. Anisotropic Etching One of the key advantages of plasma etching is the possibility of achieving vertical side walls. Momentum from the ions in a low-density plasma is transferred more favorably to the bottom surface of the etch front than to the side walls, because of longer mean-free paths. This phenomenon results in a very low side-wall etch rate and high bottom etch rates. Side-wall passivation can also occur because of organic polymerization on the side walls. Photoresist mask or trace organic gases in the plasma can provide the carbon supply for polymer formation. The plasma etches described previously have low etch rates and low mask/substrate etch-rate ratios (Appendix 2). Maximum depths of 30-40/zm are obtainable using conventional masking films. To increase the etch rates and the etch-rate ratios, while maintaining vertical sidewalls, two new plasma etching techniques have been developed. These etchers are commercially available and they can etch deep trenches in silicon with very vertical side walls with etch rates as high as 1 /zm/min. Both methods utilize very high plasma densities to boost the etching rates and side wall passivation to achieve vertical side walls. Collectively, both methods are referred to as deep reactive ion etching (deep-RIE) techniques [53, 54].

602

APPLICATIONS OF MICROMACHINING TO NANOTECHNOLOGY

In the first method, high-density plasma is operated at cryogenic temperatures, resulting in not only silicon etching, but also the formation of a very thin passivating silicon dioxide film at the side walls. A 1-/zm-thick silicon dioxide mask (Si/SiO2 etch-rate ratio of 300:1) can be used to etch 300-/xm-deep trenches with an aspect ratio of 15:1. This cryogenic chuck etch technology is being offered by Alcatel, Inc. Alternatively, STS Technologies, Inc., has developed a process in which very high density reactive species are created using inductively coupled plasmas. By using photoresist as a mask and source of organic molecules, side walls are passivated by polymerization. The typical etch-rate ratio of silicon to photoresist is 50:1 [53]. Hence, a 6-#m-thick photoresist can be used to etch 300/zm on the photoresist. Both the cryogenic chuck and the high-density plasma suffer from loading effects because of reaction-rate-limited etching. Although the deepRIE methods promise through-wafer etching, they suffer from a large loading effect. Large etching areas etch more slowly than smaller etch areas. The masks have to be designed so that the etching areas do not vary much across the wafer. Deep silicon etching has been used to make high-aspect-ratio structures. One such process flow is used to fabricate single-crystal silicon (SCS) micromachines [55, 56] (Fig. 26). First, silicon wafer is anisotropically etched in a deep RIE, resulting in pillars of silicon. PECVD oxide is then deposited conformably over the pillars. Using a plasma etch that is highly anisotropic, only the oxide on the top and bottom of the trenches is etched. The wafer is then thermally oxidized such that the oxidation fronts at the bottom of the trenches meet and form a sharp tip of single-crystal silicon. Sharp silicon tips are left behind after a hydrofluoric acid etch is used to dissolve the oxide. Because these tips can be formed in large high-density arrays, such devices have been proposed for high-density AFM and/or STM tips for scanning and data storage with nanometer precision [56].

Fig. 26. Single-crystalsilicon micromachining using deep plasma etching. Left shows a nanoprobe created in silicon. Right shows the process flow and cross sections. Reprinted with permission from J. J. Yao et al., J. Microelectromech. Devices 1, 14 (9 1992IEEE).

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5.2. Vapor Phase Etching of Silicon In vapor etching, the etchant is vaporized and the molecules diffuse to the surface of the material to be etched. For example, hydrofluoric acid vapor has been used to underetch silicon dioxide. It has been used to clean surfaces inside LPCVD chambers before epitaxial growth of silicon films [57]. Furthermore, silicon etching using XeF2 vapor has been known since the 1960s [58]. However, it was recently "rediscovered" in the micromachining context [59]. Unlike plasma etching, XeF2 instantaneously decomposes on the silicon surface and the fluorine reacts with the silicon atoms. As in any pure chemical etching, XeF2 silicon etch is isotropic. Most strikingly, XeF2 is highly selective to silicon, not etching photoresist, metals, and silicon dioxide. Residual oxide can act as an etch stop and needs to be removed in a HF etch to obtain smooth XeF2 etches. Polysilicon can be oxidized slightly and, hence, can be made not to etch in XeF2 by simply letting it sit in air for 2 days. A typical XeF2 etch system consists of a pulsed (duty cycle of 50% at a frequency of one per minute) XeF2 vapor exhausted into a chamber nominally held in a dry nitrogen environment. The pulsing reduces the very large loading effect observed in XeF2 etching. Etch rates of 10 #rn/min for small pieces versus 11 nm/min for 4-in. wafers have been observed. Better chamber designs capable of higher XeF2 vapor pressures might reduce this effect. The use of XeF2 etching has been shown to be advantageous for creating microstructures by postprocessing on standard CMOS process wafers. Figure 27 shows a magnetic field sensor integrated in a standard CMOS process. Polysilicon underneath the patterned oxide and metal center plate was underetched using XeF2 etching. Because XeF2 is isotropic, it undercuts not only the desired platform, but also the polysilicon on the outer periphery of the sensor.

6. BONDING The need for bonding silicon structures to other materials or silicon pieces came from packaging requirements. Glass-silicon bonding was developed to seal silicon micromachined devices with a glass cap. For example, an absolute pressure sensor requires a cavity with a well-defined and stable pressure sealed on one side of a micromachined plate. Although there are many kinds of bonding techniques, anodic, fusion, and adhesive bonding play a vital role in micromachined structures.

6.1. Anodic Bonding Glass-to-silicon bonding originated from metal-to-glass (also called Emory) bonding. The glass wafer is placed on top of the silicon wafer in a vacuum environment to eliminate trapped air between the glass-silicon surface. A high electric field (~ 7 • 106 V/m) is placed across the glass-silicon sandwich at elevated temperatures (100-500 ~ The trapped ions, typically sodium and potassium in glass, migrate toward the interface under the influence of the electric field and the increased electronic mobility at high temperatures. Counteracting mirror charges develop in the silicon that form a strong electric field at the interface. When the silicon-glass sandwich is brought back to room temperature and the applied electric field removed, the ions are trapped at the interface. Hence, a permanent electric field holds the glass and the silicon together (Figure 28) [60]. The potential drop across the glass thickness starts out linear but becomes highly localized near the silicon-glass interface (Fig. 29). Because the glass and the silicon have different thermal expansions, the resulting interfacial thermal stresses can cause deformation of the bilayer structure at room

604

APPLICATIONS OF MICROMACHINING TO NANOTECHNOLOGY

Top view photomicrograph of sensor. An oxide plate is suspended over an etched cavity in silicon substrate held by torsional support beams and L-shaped beams. On one side of the plate is a Wheatstone bridge and on the other a current loop comes onto on off from the plate. The dark rim around the structure is the XeF2 etch front.

SEM of a smaller version of the resonant mechanical sensor The oxide plate is seen to have a small stress gradient. The holes on the plate are f o r the purpose of reducing the etch time. This device was released using 50 one minute pulses of XeF2 gas at room temperature. The etch pressure was .- 2 torr. Fig. 27. Top shows the schematic diagram of the standard CMOS magnetic sensor fabricated using XeF2 etching. Bottom shows the hanging oxide structure. Reprinted with permission from E. Hoffman et al., 3D Structures with Piezoresistive Sensors in Standard CMOS, presented at IEEE MEMS 1995, Amsterdam(9 1995 IEEE).

temperature. Hence, much early effort was spent in finding a glass with same net thermal expansion as silicon (2 • 10 -6 ppm/~ at the bonding temperature. One such glass is Coming 7740. The electrostatic field at the interface in anodic bonding is high enough to bond the two materials permanently. Because the field strength is very high, the bonding process is not affected by the presence of surface irregularities and contamination. The glass

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deforms around any contaminant placed at the interface. This fact has been used to seal glass caps around metal interconnects, electrically connecting the inside of the cavity to the outside [60]. However, a disadvantage of anodic bonding is that the high electric field required to seal can damage any underlying electronics.

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APPLICATIONS OF MICROMACHINING TO NANOTECHNOLOGY

6.2. Low-Temperature Glass Bonding In many applications, the high fields and temperatures required in anodic bonding are impractical. In this case, low-temperature glass bonding can be used. Many glasses that have low melting points can be deposited as thin films [61, 62] and then bonded to substrates when heated to the melting point. Thin films of phosphosilicate or borosilicate glass can be sputtered or spun on. The substrate to be bonded is placed under pressure and elevated temperatures on the glass film. Alternatively, relatively thick (greater than 25/zm) glass frit sheets can be purchased commercially. In general, the bond strengths obtained are not as high as those obtained with anodic or fusion bonding. Furthermore, the lack of bonding because of contaminant particles thicker than the glass film make thin-film bonding sometimes impractical.

6.3. Fusion Bonding Fusion bonding is a more recent bonding technique in which surface-treated silicon surfaces are brought into contact with each other to form a medium-strength chemical bond. After high-temperature exposure at 1000 ~ for 1 h, the intermediate chemical layers dissolve and a very strong Si-Si bond layer is formed [63]. Often, the resultant bond interface is indistinguishable from the surrounding crystal structure. Fusion bonding requires extreme cleanliness and wafer flatness to work reliably. Usually, one finds a sequence of steps and a location in a lab that works and rarely to changes anything that might spoil the "black art" nature of this procedure. Furthermore, the high temperatures required eliminate the possibility of bonding wafers with prefabricated circuits. Figure 30 shows an infrared image through a wafer sandwich of the fusion-bonded interface as a function of anneal temperature and duration. In the example, the time- and temperature-dependent nature of gas evolution at the interface is shown. At 600 ~ areas of bond failure appear, which disappear at higher temperatures. This is probably due to gas reactions with the substrate as is the case in gettering gases [64]. Fusion bonding has found a commercial application in silicon-on-insulator (SO1) wafer manufacturing. An oxidized wafer is fusion bonded to a blank wafer. Then one of the

Fig. 30. Infraredimage of intrinsic voids during fusion bonding as a function of anneal temperature. Reprinted with permission from M. A. Schmidt, Silicon Wafer Bonding for Micromechanical Devices, presented at Solid-State Sensor and Actuator Workshop,Hilton Head, SC (9 1994Transducers Research Foundation).

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wafers is chemically and mechanically polished to the desired silicon thickness. Such SOI wafers have found use as starting structures to fabricate silicon microstructures [65].

6.4. Eutectic Bonding In eutectic bonding, one utilizes the positive free energy associated with the chemical reaction of a metal with silicon. When the metal and silicon are put together, the combination melts at a lower temperature than either metal or silicon alone. For example, gold reacts with silicon at low temperatures (363 ~ to form a AuSi eutectic [66]. Typically, gold is either evaporated, sputtered, or electroplated on the surface to be bonded to a silicon surface. When these areas are put in contact under vacuum and at the eutectic temperature, the metal diffuses into the silicon, forming the eutectic melt. When the interface is cooled, the melt solidifies, forming the bond layer. One has to prepare the silicon surface carefully by eliminating any surface contaminants and diffusion barriers such as native silicon dioxide.

6.5. Adhesive Bonding Although technologically less exciting, glues and epoxies have been used to bond silicon parts together. A common problem with adhesives is that they are not easily photopatternable. Ultraviolet (UV) curable epoxies are an exception to this problem. Another issue is that one often needs to bond two parts with microscopic channels. Adhesives tend to flow and fill up these channels. One solution to this problem is to deliver highly viscous microdoses of adhesive through a silk-screening process [67-69]. Silk screening has been used to fabricate silicon needles by bonding silicon pieces with V grooves running along their length (Fig. 31).

7. SURFACE M I C R O M A C H I N I N G As we have seen, bulk micromachining can be used to etch entire wafers. It is, in essence, a subtractive machining technique. In contrast, surface micromachining is an additive machining process. Figure 32 shows the basic procedure for fabricating a surfacemicromachined cantilever. A sacrificial layer material is deposited first on a silicon wafer and coated with a passivation layer such as silicon nitride. Lithography is used to define areas where the sacrificial etch is removed selectively. A conformal thin film of the structural material is deposited over the entire wafer. The structural layer is patterned using lithography and chemical or plasma etch that is terminated on the sacrificial layer using a timed etch or selective etching chemistry. Then the entire wafer is etched in an etch that selectively etches the sacrificial layer but not the structural material. The etch-rate ratio of the sacrificial film to that of the structure has to be very high to maintain controllable structural layer thickness. Furthermore, the interfacial stresses between the sacrificial layer and the structural layer, as well as the internal stresses of the structural layer, have to be very low to avoid curling of the structural material after the release step. The structural material also has to be nearly defect free to reduce the surface roughness that typically results from the sacrificial layer etch. There are very few combinations of sacrificial/structural materials that match all these requirements. The release etch time of a surface micromachine will be linearly dependent on the maximum dimension of the micromachined structure to be underetched. Hence, if one wants to etch very large area solid-plate structures, the etch times would be too long. The long etch times can also lead to a degraded structure, assuming the etch also chemically reacts with the structure. To reduce the etch time of large-area structures, etch holes (Fig. 32) are formed in the structure to give etchant access to the underlying sacrificial layer in a uniform way across the wafer. The etch holes are typically placed a distance d apart, where d

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A P P L I C A T I O N S OF M I C R O M A C H I N I N G TO N A N O T E C H N O L O G Y

Fig. 31. Silicon ultrasonic horns. Top left shows a 4-in. wafer with different-shaped horns. Top right shows the etched horns. Bottom left shows the formation of a needle structure obtained by bonding two horns with V grooves. Reprinted with permission from A. Lal and R. M. White, Ultrasonically Driven Silicon Atomizer and Pump, presented at Solid-State Sensor and Actuator Workshop, Hilton Head, SC ( 9 1996 Transducers Research Foundation).

Fig. 32.

The basic surface micromachining process used to fabricate surface-micromachined structures.

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is twice the product of etch time and etch velocity. Typical etch rates of silicon dioxide can be found in the appendices. Using aluminum as the structural material and silicon dioxide as the sacrificial material, Nathanson [70] fabricated surface micromachines as early as 1967. He was able to connect the resulting cantilevers to feedback amplifiers to create oscillators. The somewhat unpredictable and weak material properties of metals kept this technology in the textbooks for a long time. Work in the 1980s [71-73] led to the development of the LPCVD process that could deposit stress-free polysilicon films on silicon dioxide. Using polysilicon as the structural material, simple bridges and cantilevers could be fabricated. Once stress-free films of polysilicon were obtained, it took little time to realize a whole slew of surfacemicromachined structures. Polysilicon and phosphosilicate glass (PSG)-phosphorus-doped oxide are the most popular choices of structural and sacrificial materials. LPCVD PSG films are chosen for their much higher etch rates in hydrofluoric acid as compared to the undoped thermal or wet oxides. PSGs are patterned using lithography and a dry plasma etch to obtain vertical side walls. Polysilicon is deposited in an LPCVD tube with Sill4 as the source gas and nitrogen and hydrogen as dilutants. The appropriate pressure (300-500 mtorr) and temperature (600-610 ~ result in reasonable deposition rates (,-~10 nm/min) [22]. This process results in slightly amorphous silicon film. A high-temperature anneal step is performed to recrystallize the amorphous silicon and reduce the stress at the same time. The phosphorus dopant in the polysilicon diffuses into the poly and further reduces the stress. The polysilicon is patterned and also etched in a plasma etch. Various wet etches for the sacrificial etch have been tried and produce different final structures. Concentrated HF solutions give very fast etch rates, accompanied by high surface roughness. Dilute HF gives a slower etch rate but does not offer high selectivity between the polysilicon and the PSG. Because the HF PSG etch front moves laterally, very long etch times can result if one wants long structures. To solve this problem, one has to put etch holes in the polysilicon structure that effectively increase the etch front area and keep the etch time manageably small (Fig. 32). A problem that plagued surface micromachines early was that of stiction between the released polysilicon structures and the substrate [74]. After the sacrificial layer has been etched away, the wafers are usually cleaned in water baths. During the wafer drying process, the water-air interface moves and eventually meets the structure. Because the polysilicon is hydrophobic, a surface tension force develops that pulls the released structure to the substrate. The resultant van der Waals or polymer residue-type bonding results in a stuck-on-substrate structure. One usually has to force the release using a probe tip. One technique to reduce stiction is by reducing the contact area between the released structure and the substrate. Dimples can be etched into the sacrificial layer that are reproduced in the structural layer (Fig. 32). These dimples act as contact pins that reduce the contact friction and adhesive forces. Borrowing from the biology-lab technique of triple-point drying, a way to dry the postrelease wafers without stiction was developed [75]. The triple point refers to the simultaneous existence of solid, liquid, and gas phases. By placing the MEMS device in a triple-point material, one can eliminate the liquid-gas interface and the associated surface tension-driven stiction force. In the case of liquid CO2 triple-point drying, the liquid water is replaced first by alcohol and then with liquid CO2. Then the liquid CO2 is driven to its triple point at high pressures (8 bar in a pressure chamber) at an elevated temperature (35 ~ Triple-point drying has virtually eliminated the problem of stiction. An alternative is sublimation drying. The structure is immersed in liquid CO2 and cooled below the CO2 freezing point. Then the dry ice is sublimated at a high temperature in the absence of H20, eliminating the liquid-air interface. Although release stiction problem is solved, in-use stiction due to friction induced changes still remains a major challenge.

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APPLICATIONS OF MICROMACHINING TO NANOTECHNOLOGY

Aluminum Hinge

D Fig. 33. An aluminum-polyimide surface micromachining process. Reprinted with permission from C. W. Storment et al., Dry Released Process of Aluminum Electrostatic Actuators, presented at the Solid-State Sensor and Actuator Workshop, Hilton Head, SC ((g) 1994 Transducers Research Foundation).

Other structural and sacrificial layer combinations can also be used to fabricate surface micromachines [76, 77]. One is the metal-polymer combination [78]. The metal structures are released by simply dissolving the organic layer. The metal layer can be evaporated, sputtered, or electroplated. The organic film can be photoresist or polyimide. The advantage of such materials is the low-temperature processing needed as opposed to the 600700 ~ temperatures needed with polysilicon deposition. An example of such a structure is shown in Figure 33. A recent example of a nanoscale surface-micromachined structure is the bridge of i-GaAs (undoped GaAs) formed by etching away an AlAs sacrificial layer [79, 80]. This bridge, shown in Figure 34, was used to measure the thermal conductance of the nanoscale-thick bridge. 7.1. Stress in Surface-Micromachined Structures

A class of surface-micromachined structures has evolved that measures the mechanical stress in the polysilicon films after release. An example of such a structure is the strain gauge shown in Figure 35. Upon release, any stress results in a net moment that bends the indicator beam. Both compressive stress and tensile stress can be measured using such structures. Another structure is the Guckel ring [81 ] shown in Figure 36. Any tensile stress in the polysilicon results in buckling of the center beam. Similarly, a simple beam anchored on both ends will buckle if compressive stress is present. In addition to internal stresses in the structural material, stress gradients also play a crucial role in surface micromachines. For example, nonuniformity in doping or thickness variations at the anchors of surface micromachines can result in stress gradients at the anchor. These gradients cause the entire structure to bend out, as shown in Figure 36.

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Fig. 34. Nanofabricated GaAs air bridge, suspended 1 /zm over the substrate, was used to measure thermal conductance. Electron beam lithography was used to define 100-nm GaAs lines over intrinsic GaAs bridge. The overall dimension of the device is 1 mm 2. Reprinted with permission from T. S. Tighe et al., Appl. Phys. Lett. 70, 2687 ( 9 1997 American Institute of Physics).

Fig. 35.

A surface-micromachined passive strain gauge. Reprinted with permission from L. Lin et al.,

J. Microelectromech. Systems 6, 313 ( 9 1997 IEEE).

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APPLICATIONS OF MICROMACHINING TO NANOTECHNOLOGY

Fig. 36. Micromechanicalstructures for testing internal stresses in thin films. (a) Compression in beam. (b) Tensile strain creates compression in center beam (Guckel rings). (c) Spiral for measuring strain gradient. Reprinted with permission from G. T. A. Kovacs, "MicromachinedTransducers Sourcebook." (9 1998 McGrawHill).

7.2. Structures Formed from Polysilicon-Phosphosilicate Glass Combination The basic sacrificial layer process has been used to fabricate many kinds of structures. Figure 37 shows the process flow of making an electrostatic motor [73, 82]. Figure 38 shows the resulting micromotor. Time-varying and phased electric fields are established across the rotor and the outer electrodes. The time-varying electrostatic forces resulting from the electric fields force the rotor to rotate. Electrostatic forces have been used quite extensively in micromachined structures. The nonlinear nature of the electrostatic forces can be made linear using the comb structure shown in Figure 39 [83]. Electrostatic forces are generated by the applied electric fields between the combs. However, the force increase is linear because the capacitance increases linearly with electrode overlap increase. When the electric field is driven at the resonant frequency of the mechanical structure, large motions can be achieved. Figure 39 also shows a thermal actuator that works similarly to a bimetallic actuator. Current is passed through the two arms to generate motion. By making one arm of the device thinner and, therefore, having a higher resistance, more heat and, hence, higher thermal expansion occurs in the thinner side. The differential expansion results in the entire structure's bending [84]. Figure 40, shows a pop-up structure that is made possible by a hinge, first created by Pister [85]. The second polysilicon hinge cover is patterned over the first polysilicon beam through etch holes. Such hinged structures have been used to transform surface-micromachined structures into three-dimensional structures. They have been used to

613

Fig. 37. A surface micromachining process for fabricating a rotor on a hub. Reprinted with permission from G. T. A. Kovacs, "Micromachined Transducers Sourcebook." ( 9 1998 McGraw-Hill).

Fig. 38. The surface-micromachined micromotor with electrostatic actuation. Reprinted with permission from G. T. A. Kovacs, "Micromachined Transducers Sourcebook." ( 9 1998 McGraw-Hill).

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APPLICATIONS OF MICROMACHINING TO NANOTECHNOLOGY

Fig. 39. Top shows a common electrostatic comb drive used to linearize the electrostatic force. Bottom shows a thermal actuator that utilizes thermal expansion.

fabricate on-chip hanging rf coils and capacitors [86]. Figure 41, shows structure in which most of the common polysilicon structures are integrated [66]. Electrostatic comb drives are configured as vibromotors to move the beam connected to the hinged structure. A metal coating on the polysilicon hinge reflects light at a controllable angle in this manner.

7.3. Sealed Structures Often, it is necessary to make a sealed resonator structure for either low-pressure operation or isolation from the external environment. Resonant sensors generally require a vacuum atmosphere for high-quality factor operation. Many sealing techniques have been developed to accomplish the sealing of cavities. One way to make a sealed structure is shown in Figure 42. Etch holes are left in the polysilicon through which the PSG is etched away. An LPCVD nitride film is deposited that can seal the etch holes conformably, leaving the pressure of the deposition inside the sealed chamber [87, 88]. This sealing process has also been used to make surface-micromachined needles [ 107]. Instead of silicon nitride as the sealant, another option is to use a thermall oxide, as shown in Figure 42. This method resuits in much lower cavity pressure because the oxygen inside the cavity is consumed in a chemical reaction with the inside wall of the polysilicon [89].

7.4. Polysilicon Structure Direct Transfer It would be desirable to transfer polysilicon microstructures to substrates that are more amenable to surface micromachining processes. For example, one might want to put a surface micromachined on an arbitrary-shaped steel bridge. Another application would be the

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Fig. 40. The out-of-plane hinged structure. (a) The out-of-plane motion. (b) Process flow to fabricate a hinge. (c) Alternative hinge linkages. Reprinted with permission from G. T. A. Kovacs, "Micromachined Transducers Sourcebook." (9 1998 McGraw-Hill).

transfer of polysilicon structures to integrated circuits made on silicon or GaAs. A wafer level transfer of micromachines to another wafer would eliminate the tradeoffs of circuit quality versus micromachine quality in integrated microelectromechanical systems. One way to accomplish this is shown in Figure 43 [90]. A polysilicon cap with a stiffening rib is fabricated and attached to the substrate with thin tethers. Gold contact pads are defined on the cap edges as shown in the figure. The wafer was diced in dies and the poly cap was released in a HF etch and dried in a triple-point CO2 etch. The dried dies were then put in contact with the second blank silicon die (with residual oxide removed). After applying pressure in a vacuum, the temperature was raised to the AuSi eutectic temperature of

616

Fig. 41. A surface-micromachined optical mirror positioner actuated by vibromotors. Top shows the hinged mirror assembly. Bottom shows details of the vibromotor actuator. Reprinted with permission from M. J. Daneman et al., Linear Vibromotor-Actuated Micromachined Microreflector for Integrated Optics, presented at Solid-State Sensor and Actuator Workshop, Hilton Head, SC ( 9 1996 Transducers Research Foundation).

Fig. 42. Sealing techniques for surface microstructures. CVD film or thermal oxides are used to seal structures on the left. Metal is evaporated under vacuum to seal structure on the right. Reprinted with permission from C. M. Mastrangelo and W. C. Tang, "Semiconductor Sensor Technologies," in Semiconductor Sensors ( 9 John Wiley & Sons, Inc.).

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Fig. 43. Direct transfer of surface micromachined cap to silicon wafer via eutectic bonding. Left shows the process flow. Right shows SEM of the top view and section view of the cap. Reprinted with permission from M. B. Cohn et al., Wafer-to-Wafer Transfer of Microstructures for Vacuum Packaging, presented at Solid-State Sensor and Actuator Workshop, Hilton Head, SC ( 9 1996 Transducers Research Foundation).

370 ~ After eutectic bonding, the cap wafer was pulled by applying force normal to the dies and avoiding any shear. The weak tethers were broken and the cap was successfully left behind on the second die.

8. HYBRID BULK AND SURFACE MICROMACHINING In this section, some illustrative examples of hybrid surface and bulk micromachining are presented. As the first example, Figure 44 shows a microgripper [91 ] that was used to pick up an individual bacterium. The process flow is also shown in the figure. The surface micromachines were defined first but not released. A protective nitride film was deposited over the entire wafer and the KOH etch cavity from the back and the front side were defined. The etch fronts from the top and the bottom meet, leaving the surface-micromachined structure intact. An example of a hybrid deep-RIE etch and surface micromachining technique is illustrated by the Hexsil technology developed by Keller [92]. High-aspect-ratio structures are formed using deep-RIE in silicon wafers (Fig. 45). Sacrificial oxide is conformably deposited inside the grooves, followed by a polysilicon trench fill. If the trench width is very wide, open wells are left behind, which can be filled with electroplated nickel. Sacrificial etch in HF solutions results in the entire polysilicon structure being released. These polysilicon structures can be relatively thick (as thick as the silicon wafer) and can span over large areas. By controlling the polysilicon deposition process, proper stress can be designed into the structure such that it "pops out" upon release. Another claim of this technology is the reusability of the silicon mold.

APPLICATIONS OF MICROMACHINING TO NANOTECHNOLOGY

Fig. 44. Top left shows a microgripper holding a protozoan. Top right shows the process flow to fabricate the microgripper. Bottom shows the surface-micromachined comb drives and etch holes to undercut p++cantilever. Reprinted with permission from C. J. Kim et al., J. Microelectromech. Systems 1, 60 (9 1992 IEEE).

8.1. Porous Silicon Micromachines Porous silicon is a term for uniformly etched silicon with pore diameters ranging from nanometer to micrometer dimensions and pore lengths that can be as long as millimeters. This combination of nanoscale and microscale makes porous silicon attractive for nanostructure fabrication [93]. Hence, extremely high aspect ratio devices are possible. Porous silicon can be fabricated by electrochemically etching silicon in a hydrofluoric acid

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Fig. 45. Left shows process flow for fabricating three-dimensional polysilicon structures using the Hexsil process. Bottom shows a milliscale stage that self-assembles as a result of internal stress. Reprinted with permission from C. Keller and M. Ferrari, Milli-Scale Polysilicon Structures, presented at Solid-State Sensor and Actuator Workshop, Hilton Head, SC (9 1994 Transducers Research Foundation).

solution [93, 94]. The silicon oxidizes and then is etched by the HF acid. The pore size can be controlled by HF concentration or exposure to electron-hole-generating photonic sources. The subject of a pore formation mechanism is still unresolved. It is largely believed that electric field concentration resulting from the very small radius of curvature at pore tips results in excessive etching and deep pore formation. The low wall etch rate has been attributed to either chemical passivation or diffusion-limited cartier concentration [94].

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APPLICATIONS OF MICROMACHINING TO NANOTECHNOLOGY

Fig. 46. Bulkporous silicon formation. (A) Randomporous silicon formation. (B) Seeded porous silicon mation. Reprinted with permission from V. Lehmann,J. Electrochem. Soc. 140,2836 (9 1993Electrochemical ziety).

Although pores on a planar surface produce randomly distributed pores, a surface th pore-initiating features can result in highly organized pores [95] (Fig. 46). Surfacecromachined structures using porous silicon have also been fabricated. Figure 47 shows ;urface-micromachined polysilicon film sandwiched between silicon nitride films, with

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Fig. 47. Surface-micromachinedporoussilicon structures. Top showscross section of polysiliconpattern to be anodized. Bottom shows the formationof a porous silicon plug formed during anodization. Reprinted with permission from R. C. Anderson et al., Laterally Grown Porous Polycrystalline Silicon: A New Material for Transducer Applications, presented at Transducers '91, San Francisco (9 1991 IEEE).

an anchor point to the silicon substrate. The silicon substrate is connected to an aluminum film on the back side of the wafer for electrical connection. The anodization circuit is completed by electrical contact to the aluminum film, through the silicon wafer and the poly. By varying the current condition from complete dissolution to porous silicon formation, Anderson et al. [96] were able to fabricate a porous silicon plug, forming a sealed chamber.

8.2. Electroplated Micromachines Micromachining methods enable one to fabricate molds and, hence, provide a way to make micromechanical metallic parts by electroplating in micromachined molds. To fabricate thick micromachined metallic structures with a high aspect ratio, ways of creating deep molds have been invented. One way has been to spin-coat thick polymer coatings that can be exposed through their thickness without diffraction. To achieve this, one can use X-ray lithography to expose thick poly(methyl methacrylate) (PMMA) layers. X-rays are highly directional and do not diffract. The process of using X-rays to expose thick PMMA coatings and filling the resulting cavities with electroplated metal is called LIGA (X-ray Lithographie Galvanoformung Abformtechnik) [97]. The thick PMMA generally require very long exposures and special photoresist spinning apparatus. A LIGA-like process with electroplated aluminum to fabricate a gear is outlined in Figure 48. Figure 49 shows a complete microdynamometer made using LIGA technology [ 104]. Although the original behind LIGA was to make metal molds into which plastic parts could be embossed, most users use LIGA to make metal microelectromechanical parts.

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APPLICATIONS OF MICROMACHINING TO N A N O T E C H N O L O G Y

Fig. 48. Left shows the LIGA-like UV exposure process to make high-aspect-ratio metallic structures. Top shows a 45-/zm-high aluminum gear made using electroplating. Reprinted with permission from A. B. Frazier and M. G. Allen, Uses of Electroplated Aluminum in Micromachining Applications, presented at Solid-State Sensor and Actuator Workshop, Hilton Head, SC ((g) 1994 Transducers Research Foundation).

Fig. 49. A microdynamometer fabricated using LIGA. It contains a 3-phase variable reluctance motor, idling gear, and magnetic break [104].

623

Appendix 1.

Etch-rate data for wet etching (experiments done at UC Berkeley Microlab) ,,,

Material

No.

O~ tO

Etchant:

Material to be

SCSi

Poly

Poly

Wet

Dry

Concentration and conditions

etched

< 100>

n+

undop

ox

OX

23K 18K 23K

LTO

PSG

PSG

Stoic

Lows

A1/

Sput

OCG

Olin

F

> 14K

F

36K

140

52 30 52

42 0 42

n+

undop

ox

ox

SF 6 + He (175:50 sccm) LAM 480 plasma: 150 W, 375 mT gap = 1.35 cm, 13.56 MHz

Thin silicon nitrides

W

6400

7000 2000 7000

300 220 400

W

280

530

540

1300 830 2300

870

-

W

W 30 52

W 0 42

1500 1300 1500

1400

SF 6 + He (175:50 sccm) LAM 480 plasma: 250 W, 375 mT gap = 1.35 cm, 13.56 MHz

Thick silicon nitrides

W

8400

9200

800

W

770

1500

1200

2800 2100 4200

2100

-

W

W

W

3400 3100 3400

3100

CF4 + CHF3 + He (90:30:120 sccm) LAM 590 plasma: 450 W, 2.8 T gap = 0.38 cm, 13.56 MHz

Silicon oxides

W

1900 1400 1900

2100 1500 2100

4700 2400 4800

W

4500

7300 3000 7300

6200 2500 7200

1800

1900

-

W

W

W

2200

2000

CF4 + CHF3 + He (90:30:120 sccm) LAM 590 plasma: 850 W, 2.8 T gap = 0.38 cm, 13.56 MHz

Silicon oxides

W

2200 2200 2700

1700 1700 2100

6000 2500 7600

W

6400 6000 6400

7400 5500 7400

6700 5000 6700

4200 4000 6800

3800

-

W

W

W

2600 2600 6700

2900 2900 7200

Aluminum

W

4500

W

680

670

750

W

740

930

860

6000 1900 6400

W

-

-

6300 3700 6300

6300 3300 6100

C12 + He (180:400 sccm) LAM rainbow 4420:275 W, 425 mT 40~ gap = 0.80 cm, 13.45 MHz

Silicon

W 5000 5000

5700 3400 6300

3200 3200 3700

8 8 380

-

60

230

140

560

530

W

W

350 350 500

300

HBr + C12 (70:70 sccm) LAM rainbow 4420:200 W, 300 mT 40~ gap = 0.80 cm, 13.45 MHz

Silicon

W

4500

W

680

670

750

W

740

930

860

6000 1900 6400

W

3000 2400 3000

2700

0

0

0

0

0

0

0

0

0

0

0

3400

3600

t~

C12 + BC13 + CHC13 + N 2 (30:50:20:50 sccm) LAM 590:850 W, 250 mT 60 o C, 13.56 MHz

02 (50 sccm) Technics PEII-A: 400 W, 300 mT gap = 2.6 cm, 50 kHz sq. wave

Photoresist ashing

undop unanl annld nitride nitride 2% Si tungs

Ti

0

Ti/W 820 PR H N T P R

0

> 9

02(50sccm) Technics PEII-A: 50 W, 300 mT gap = 2.6 cm, 50 kHz sq. wave

Descumming organics removal

10

SF 6 + H e ( 1 3 : 2 1 sccm) Technics PEII-A: 100 W, 300 mT gap = 2.6 cm, 50 kHz sq. wave

Silicon nitrides

11

CF 4 + C H F 3 + H e ( 1 0 : 5 : 1 0 s c c m ) Technics PEII-A: 200 W, 300 mT gap = 2.6 cm, 50 kHz sq. wave

12

13

tO

14

0

0

0

350

300

620 550 800

W

W

W

690 690 830

630

1300

1100

W

1500

2600

2300 1900 2300

1400

2800 2800 2800

2300

760

600

0

0

0

0

0

0

0

0

0

300 300 1000

730 730 800

670 670 760

310

350

370

610

480 230 480

820

Silicon nitrides

1100

1900

W

730

710

730

W

900

SF 6 (80sccm) Tegal Inline 7 0 1 : 2 0 0 W, 150 mT 40 o C, 13.56 MHz

Tungsten

W

5800

5400

1200 2000 2000

W

1200

1800

SF 6 (25 sccm) Tegal Inline 701:125 W, 200 mT 40 o C, 13.56 MHz

Thin silicon nitrides

W

1700

2800

1100 1100 1600

W

1100

1400

Thick silicon-rich nitrides

W

320

W

CF4 + CHF3 4- He (45:15:60 sccm) Tegal Inline 701: 100 W, 300 mT 40 o C, 13.56 MHz

350

360

320

530

450

0

9

W

W

690

600

2800 W 2800 4000

W

2400 2400 4000

2400

W

3400 2900 3400

3100

400

360

W

W

W

W

W

9 Z

Z C~ 9

Note: All etch rates are given in angstroms. The top most etch rate was measured by Kirt Williams, the bottom two (if listed) were measured by others with slightly different conditions. Notation: . . . . = test not performed, W -- test not performed but known to work (etch rates > 100/~,/min), F = test not performed but known to be fast (etch rate > 10 lc~min), P = film peeling observed, A = film was visibly attacked and roughened.

Z

LAL

References 1. 2. 3. 4. 5. 6. 7. 8. .

10. 11. 12.

13. 14. 15. 16.

17. 18. 19. 20. 21. 22. 23.

24. 25. 26. 27. 28. 29. 30.

31. 32. 33. 34. 35. 36. 37. 38. 39.

40.

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APPLICATIONS OF M I C R O M A C H I N I N G TO N A N O T E C H N O L O G Y

41. S. C. Chang and D. B. Hicks, Street Corner Compensation, presented at IEEE Solid-State Sensor and Actuator Workshop, Hilton Head, SC, 1988. 42. H. Sandmaier et al., Comer Compensation Techniques in Anisotropic Etching of (100)-Silicon Using Aqueous KOH, presented at Transducers '91, San Francisco, 1991. 43. R.E. Williams, "Modern GaAs Processing Methods." Artech House, Boston, 1990. 44. Z.L. Zhang et al., Submicron, Movable Gallium Arsenide Mechanical Structures and Actuators, presented at International Workshop on Microelectromechanical Systems, 1992. 45. A. Lal and R. M. White, Micro-Fabricated Acoustic and Ultrasonic Source-Receiver," presented at Transducers '93, Yokohama, Japan, 1993. 46. S.D. Collins, J. Electrochem. Soc. 144, 2242 (1997). 47. Y.B. Gianchandani and K. Najafi, J. Microelectromech. Systems 1, 77 (1992). 48. C. Yeh and K. Najafi, Bulk-Silicon Tunneling-Based Pressure Sensors, presented at Solid-State Sensor and Actuator Workshop, Hilton Head, SC, 1994. 49. B. Koek et al., IEEE Trans. Electron Devices 36, 663 (1989). 50. E.S. Kim, R. S. Muller and R. S. Hijab, J. Microelectromech. Systems 1, 95 (1992). 51. S. Hoen et al., Fabrication of Ultrasensitive Force Detectors, presented at Solid-State Sensor and Actuator Workshop, Hilton Head, SC, 1994. 52. L.M. Roylance and J. B. Angell, IEEE Trans. Electron Devices ED-26, 1911 (1979). 53. C. Linder, T. Tschan, and N. E de Rooij, Deep Dry Etching Techniques as a New IC Compatible Tool for Silicon Micromachining, presented at Transducers '91, San Francisco, 1991. 54. C. Linder, T. Tschan, and N. F. de Rooij, Sens. Mater 3, 311 (1992). 55. Z.L. Zhang and N. C. MacDonald, An RIE Process for Submicron, Silicon Electromechanical Structures, presented at Transducers '91, San Francisco, 1991. 56. J.J. Yao, J. C. Arney, and N. C. MacDonald, J. Microelectromech. Devices 1, 14 (1992). 57. A.E.T. Kuiper and E. G. C. Lathouwers, J. Electrochem. Soc. 139, 2594 (1992). 58. D.W. Oxtoby and N. H. Nachtrieb, "Principles of Chemistry." Saunders, Philadelphia, 1986. 59. E. Hoffman et al., 3D Structures with Piezoresistive Sensors in Standard CMOS, presented at IEEE MEMS 1995, Amsterdam, 1995. 60. W.H. Ko, J. H. Suminto, and G. H. Yeh, in "Microsensors" (R. S. e. a. Muller, ed.), IEEE, New York, 1990. 61. L.A. Field and R. S. Muller, Sens. Actuators, A 21-23, 935 (1990). 62. A. Hanneborg, J. Micromech. Microeng. 1, 139 (1991). 63. M. Shimbo et al., J. Appl. Phys. 60, 2987 (1986). 64. M.A. Schmidt, Silicon Wafer Bonding for Micromechanical Devices, presented at Solid-State Sensor and Actuator Workshop, Hilton Head, SC, 1994. 65. T. Nakamura, SO1 Technologies for Sensors, presented at Transducers, Yokohama, Japan, 1993. 66. M. J. Daneman et al., Linear Vibromotor-Actuated Micromachined Microreflector for Integrated Optics, presented at Solid-State Sensor and Actuator Workshop, Hilton Head, SC, 1996. 67. A. Lal and R. M. White, Ultrasonically Driven Silicon Atomizer and Pump, presented at Solid-State Sensor and Actuator Workshop, Hilton Head, SC, 1996. 68. A. Lal and R. M. White, Sens. Actuators, A 54, 542 (1996). 69. A. Lal and R. M. White, Optimization of the Silicon/PZT Longitudinal Mode Resonant Transducer, presented at ASME World Conference, Dallas, TX, 1997. 70. H.C. Nathanson et al., IEEE Trans. Electron Devices ED-14 (1967). 71. R.T. Howe and R. S. Muller, J. Electrochem. Soc. 130, 1420 (1983). 72. H. Guckel and D. W. Burns, IEEE IEDM 176 (1986). 73. M. Mehregany et al., IEEE Trans. Electron Devices 35,719 (1988). 74. D.J. Monk, D. S. Soane, and R. T. Howe, Sacrificial Layer SiO2 Wet Etching for Micromachining Applications, presented at Transducers '91, San Francisco, 1991. 75. G. T. Mulhern, S. Soane, and R. T. Howe, Supercritical Carbon-Dioxide Drying from Microstructures, presented at Transducers, Yokohama, Japan, 1993. 76. L. Chen and N. C. MacDonald, Surface Micromachined Multiple Level Tungsten Microstructures, presented at Solid-State Sensor and Actuator Workshop, Hilton Head, SC, 1994. 77. C.W. Storment et al., Dry Released Process of Aluminum Electrostatic Actuators, presented at the SolidState Sensor and Actuator Workshop, Hilton Head, SC, 1994. 78. A.B. Frazier and M. G. Allen, Uses of Electroplated Aluminum in Micromachining Applications, presented at Solid-State Sensor and Actuator Workshop, Hilton Head, SC, 1994. 9. T. S. Tighe, J. M. Worlock, and M. L. Roukes, Appl. Phys. Lett. 70, 2687 (1997). 80. K. Hjort, J. Micromech. Microeng. 6, 370 (1996). 81. H. Guckel, Sens. Actuators, A 28, 133 (1991). 82. L. S. Fan Y. C. Tai, and R. S. Muller, IC-Processed Electrostatic Micromotors, presented at IEEE International Electron Device Meeting, San Francisco, 1988. 83. W. C. Tang et al., Sens. Actuators, A 21-23, 328 (1990).

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84. J. H. Comtois and V. M. Bright, Surface Micromachined Polysilicon Thermal Actuators Arrays and Applications, presented at Solid-State Sensor and Actuator Workshop, Hilton Head, SC, 1996. 85. K.S.J. Pister, Sens. Actuators A 33, 249 (1992). 86. L. Fan et al., Universal MEMS Platforms for Passive RF Components: Suspended Inductors and Variable Capacitors, presented at Eleventh International Workshop on Micro Electromechanical Systems, Heidelberg, Germany, 1998. 87. C. Mastrangelo and R. S. Muller, Vacuum-Sealed Silicon Micromachined Incandescent Light Source, presented at IEEE IEDM, 1989. 88. C. Liu and Y. C. Tai, Studies on the Sealing of Surface Micromachined Cavities Using Chemical Vapor Deposition Materials, presented at Solid-State Sensor and Actuator Workshop, Hilton Head, SC, 1994. 89. R. T. Howe, J. Vac. Sci. Technol., B 6, 1809 (1988). 90. M. B. Cohn et al., Wafer-to-Wafer Transfer of Microstructures for Vacuum Packaging, presented at SolidState Sensor and Actuator Workshop, Hilton Head, SC, 1996. 91. C. J. Kim, A. P. Pisano, and R. S. Muller, J. Microelectromech. Systems 1, 60 (1992). 92. C. Keller and M. Ferrari, Milli-Scale Polysilicon Structures, presented at Solid-State Sensor and Actuator Workshop, Hilton Head, SC, 1994. 93. P. Steiner and W. Lang, Thin Solid Films 255, 52 (1995). 94. R. C. Anderson, in "Chemical Engineering." University of California Press, Berkeley, CA, 1991. 95. V. Lehmann, J. Electrochem. Soc. 140, 2836 (1993). 96. R. C. Anderson, R. S. Muller, and C. W. Tobias, Laterally Grown Porous Polycrystalline Silicon: A New Material for Transducer Applications, presented at Transducers '91, San Francisco, 1991. 97. W. Ehrfeld et al., Fabrication of Microstructures Using the LIGA Process, presented at IEEE Microrobots and Teleoperators Workshop, Hyannis, MA, 1987. 98. J. W. Judy, R. S. Muller, and H. H. Zappe, Magnetic Microactuation of Polysilicon Flexure Structures, presented at Solid-State Sensor and Actuator Workshop, Hilton Head, SC, 1994. 99. H. Seidel, The Mechanism of Anisotropic Silicon Etching and Its Relevance for Micromachining, presented at Transducers '87, pp. 120-125. 100. K. Suzuki, K. Najafi, and K. D. Wise, A-1024-element high performance silicon tactile imager, IEEE IEDM, 1988, p. 67. 101. K. Peterson, Proc. IEEE 70, 420 (1982). 102. C. M. Mastrangelo and W. C. Tang, Semiconductor sensor technologies, in "Semiconductor Sensors" (S. M. Sze, ed.). 103. L. Lim, A. P. Pisano, and R. T. Howe, Microelectromech. Systems 6, 313 (1997). 104. H. Guckel et al., Advances in Photoresist Based Processing Tools for 3-Dimensional Precision and Micromechanics, presented at Solid-State Sensor and Actuator Workshop, Hilton Head, SC, 1996. 105. L. Tenerz, Silicon Micromachining with applications in Sensors and Actuators, Ph.D. Thesis, 1989, Uppsala University. ISBN 91-554-2418-X. 106. E. D. Palik et al., J. Appl. Phys. 70, 3291 (1991). 107. K. S. Lebonitz, A. P. Pisano, and R. T. Hour, Permeable polysilicon etch-access windows for microshell fabrication, Transducers '95, Stockholm.

630

Chapter 1 NANODIFFRACTION J. M. Cowley, J. C. H. Spence Department of Physics and Astronomy, Arizona State University, Tempe, Arizona, USA

Contents 1. 2.

4.

5.

6.

7.

Electron Nanodiffraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Interactions of Electrons with Matter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1. The Phase-Object Approximation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2. Kinematical Diffraction and Diffraction from Phase Objects . . . . . . . . . . . . . . . . . . . . 2.3. Dynamical Diffraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Imaging and Diffraction in Transmission Electron Microscopy Instruments . . . . . . . . . . . . . . . 3.1. Transmission Electron Microscopy Instruments . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2. Transmission Electron Microscopy Imaging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3. Selected Area Electron Diffraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4. Fourier Transforms of Transmission Electron Microscopic Images . . . . . . . . . . . . . . . . . 3.5. Diffraction and Imaging from Surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.6. Convergent-Beam Electron Diffraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Imaging and Diffraction in Scanning Transmission Electron Microscopy Instruments . . . . . . . . . . 4.1. Dedicated Scanning Transmission Electron Microscopy Instruments . . . . . . . . . . . . . . . . 4.2. Image Contrast in Scanning Transmission Electron Microscopy . . . . . . . . . . . . . . . . . . 4.3. Nanodiffraction in Scanning Transmission Electron Microscopy Instruments . . . . . . . . . . . 4.4. Combinations of Nanodiffraction and Other Techniques . . . . . . . . . . . . . . . . . . . . . . . Theory of Convergent-Beam Electron Diffraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2. Excitation Errors and Calibration of Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3. Many-Beam Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4. Two- and Three-Beam Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.5. The Relationship between X-ray and Electron Structure Factors . . . . . . . . . . . . . . . . . . Applications of CBED . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1. Space-Group Determination and Phase Identification . . . . . . . . . . . . . . . . . . . . . . . . 6.2. Measurement of Strains and Accelerating Voltage . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3. Measurement of Sample Thickness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.4. Measurement of Debye-Waller Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.5. Determination of Atomic Positions by Convergent-Beam Electron Diffraction . . . . . . . . . . . 6.6. Bond-Charge Measurement by Convergent-Beam Electron Diffraction and Effects of Doping on Bonding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.7. Instrumentation for Quantitative Convergent-Beam Electron Diffraction . . . . . . . . . . . . . . Theory of Nanodiffraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.1. Coherent Nanodiffraction: Overlapping Disks . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2. Symmetry of Coherent Nanodiffraction Patterns . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.3. Shadow Images and Ronchi Fringes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.4. The Incoherent Nanodiffraction Approximation . . . . . . . . . . . . . . . . . . . . . . . . . . .

2 4 4 5 8 9 9 11 13 14 15 17 18 18 20 22 25 26 26 27 29 30 31 32 32 33 34 35 35 37 38 39 39 40 43 45

Handbook of Nanostructured Materials and Nanotechnology, edited by H.S. Nalwa Volume 2: Spectroscopy and Theory ISBN 0-12-513762-1/$30.00

Copyright 9 2000 by Academic Press All rights of reproduction in any form reserved.

COWLEY AND SPENCE

8. Incoherent Nanodiffraction: Nanocrystals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.1. Supported Metal Particles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.2. Light-Atom Particles on Supports . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9. Incoherent Nanodiffraction: Amorphous and Disordered Thin Films . . . . . . . . . . . . . . . . . . . 9.1. Amorphous and Near-Amorphous Films . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.2. Short-Range Ordering in Crystals and Quasi-Crystals . . . . . . . . . . . . . . . . . . . . . . . . 10. Incoherent Nanodiffraction: Carbon Nanotubes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.1. Multiwalled Carbon Nanotubes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.2. Nanotubes with Intercalates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.3. Single-Walled Carbon Nanotubes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11. Coherent Nanodiffraction: Symmetries, Edges, and Faults . . . . . . . . . . . . . . . . . . . . . . . . . 11.1. Diffraction at Edges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2. Domain Boundaries and Faults . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.3. Interfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.4. Individual Defects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.5. Planar Faults with Very Small Beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12. Electron Channeling: Thick Crystals and Surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.1. Axial Channeling in Crystals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.2. Surface Channeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.3. Standing Wave Phenomena . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13. Point-Projection Images, In-Line Holography, and Ptychography . . . . . . . . . . . . . . . . . . . . . 13.1. In-Line Holograms . . . . . . . . . . . . . . . . . .......................... 13.2. Correlated Multiple Nanodiffraction Patterns: Ptychography . . . . . . . . . . . . . . . . . . . . 14. Beam-Specimen Interactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.1. Radiation Damage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.2. Radiation-Induced Chemical Reactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14.3. Hole Drilling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1. E L E C T R O N

46 46 50 52 52 53 55 55 59 60 63 63 65 66 67 67 69 69 70 72 75 75 76 77 77 79 80 81 82 83

NANODIFFRACTION

T h e term nanodiffraction has been coined to reflect the possibility of obtaining diffraction patterns f r o m regions of solids having dimensions on the order of m a g n i t u d e of 1 nm. This is a m u c h m o r e specific t e r m i n o l o g y than microdiffraction, which has b e e n used for m a n y years to refer to diffraction from very small regions of poorly defined size range. Nanodiffraction has b e c o m e feasible because the strong electromagnetic lenses used for i m a g i n g in electron microscopes can also be used to f o r m intense b e a m s of electrons of d i a m e t e r 1 n m or less for electron energies in the range of 5 0 - 1 0 0 0 keV. T h e scattering of electrons of such energies by atoms is so strong that, w h e n a suitably bright source of electrons, such as a field emission gun, is used, solid specimens only about 1 n m thick can give diffraction patterns that are readily observed and can be recorded in a small fraction of a second. H e n c e the m e a n s are available for investigating the structures of nanoparticles or of regions in e x t e n d e d samples, no m o r e than a few n a n o m e t e r s in diameter, which m a y contain only a few h u n d r e d atoms. M a n y such applications have been used in recent years. X-ray diffraction is well established as the major tool for the study of the structures of solids [1, 2], but laboratory diffractometers require samples with d i m e n s i o n s greater than 10 -1 m m . With the advent of very intense synchrotron radiation sources, it has recently b e c o m e possible to obtain diffraction patterns from single crystal specimens with d i m e n s i o n s as small as 1 /zm, but with exposure times of minutes or hours. For n e u t r o n diffraction, the available sources are m u c h less intense, so that the s p e c i m e n v o l u m e s required are m u c h greater. Thus the advantage of electron nanodiffraction m e t h o d s is that the s p e c i m e n v o l u m e required to give diffraction information in a reasonable time is only 10-10 that required for other methods.

NANODIFFRACTION

For polycrystalline specimens containing crystals with sizes down to about 1 nm, X-ray and neutron powder diffraction techniques have been developed rapidly in recent years to provide very powerful methods for the quantitative analysis of the structures of crystals, averaged over samples of many millions of small crystals [3, 4]. For many purposes, such averages are a sufficient and effective means of characterizing a material, but the averaging process inevitably hides many of the features of individual crystallites, which may be of significance for other purposes. It is often important to understand, for example, the relationships of crystal sizes, shapes, and imperfections to local variations in composition, lattice structure, defects, and faulting of the crystalline regions, and such information can be obtained only by the study of individual particles or very small regions of extended specimens. The application of electron nanodiffraction methods is aided enormously by the possibility of imaging the sample with a high-resolution electron microscope, the image resolution of which is currently on the order of 0.2 nm. Nanodiffraction experiments are now invariably conducted either with conventional-type, fixed-beam transmission electron microscopy (TEM) instruments or in scanning transmission electron microscopy (STEM) instruments, with which the transition between imaging and diffraction modes can be made very readily. It is only by use of such instruments that the specimen features to be investigated by nanodiffraction can be seen and selected. The imaging and diffraction data are essentially complementary and must be considered together. Fortunately, the interpretations of imaging and diffraction information rely on the same theory of electron scattering. Hence, in this review, we will be treating these two strongly correlated subjects simultaneously and illustrating many aspects of their combined use and interrelationships. The strong interaction of electrons with matter is important in allowing useful intensities in diffraction patterns to be obtained from very thin (1 nm) specimens in fractions of 1 s. It does introduce considerable complications, however. Because the elastic scattering of electrons may be strong for thicknesses of about 1 nm, particularly when heavy atoms are present, the multiple scattering of electrons may become strong for thicknesses that are not much greater. Hence it is important to take into account the dynamical scattering of electrons, which involves the coherent additions of scattered amplitudes for electron beams scattered one, two, three, and more times within the specimen. Thus the theory of electron scattering can be much more complicated, even for very thin specimens, than the simple single-scattering, 'kinematical' theory, which suffices for most X-ray or neutron diffraction experiments for other than large perfect crystals. Fortunately, for diffraction by nanoparticles or other very thin specimens, convenient simplifying assumptions can be made for the dynamical scattering theory for electrons. These assumptions are usually sufficient for the nanodiffraction experiments on nanoparticles or very thin specimens, usually carried out in STEM instruments, when the object is to obtain diffraction patterns from the smallest possible regions. In the case of thicker, nearly perfect crystals, the effects of dynamical scattering are inescapable, but, rather than being an unwanted complication, they provide significant advantages. They introduce a variety of additional diffraction effects, which form the basis for powerful new methods of analyzing important aspects of crystalline structure, such as absolute lattice symmetry and the detailed distribution of electronic charges or potential within the crystal structure [5]. In experiments of this sort, the emphasis is usually on the precision of the measurement, rather than on minimizing the diffracting area. Regions with a width in the range of 5-100 nm may be selected, and TEM instruments are commonly used. Most of our discussions of nanodiffraction will involve only the elastic scattering of electrons by matter, which is the predominant interaction process. But it is important to also include some discussion of the weaker, inelastic scattering processes that arise because an incident, high-voltage electron may interact inelastically with the specimen electrons, losing energy by creating excited states of the specimen atoms or crystals, with the subsequent

COWLEY AND SPENCE

emission of secondary radiations such as X-rays, low-voltage secondary electrons, Auger electrons, or cathodoluminescence. Observation of small energy losses (a few eV) or of low-energy secondary radiation gives information about excited electronic states of solids and on morphologies, especially of solid surfaces [6, 7]. For the larger energy losses and for the emission of X-rays or Auger electrons, the energies are dependent on the nature of atoms present. Detection of signals from these sources provides the basis for a chemical analysis of the small region irradiated by a nanometer-size incident beam. Alternatively, if the signal from the energy loss or emitted radiation of a particular element is detected as the incident beam is scanned over the specimen, an image showing the distribution of that particular element in the sample may be derived [8, 9]. Thus information on the chemical content of the specimen on a nanometer scale can be added to the information on structure derived from diffraction patterns. In fact, for most of the existing STEM instruments, and for many TEM instruments, the microchemical analysis possibilities are considered to be the most important of the additions to the imaging capabilities. In this review, we first provide overviews of the theory for the scattering and diffraction of electrons by solids and of the experimental arrangements for obtaining nanodiffraction patterns in electron microscope instruments. Then we review applications of the techniques, classified according to the various aspects of the diffraction phenomena. Finally, we treat some of the more obscure aspects of the subject, which seem to us to have great potential for future technique development.

2. THE INTERACTIONS OF ELECTRONS WITH MATTER 2.1. The Phase-Object Approximation For the elastic scattering of electrons by matter, it is sufficient to consider the interaction of electron waves with a medium of variable refractive index for which the deviation from unity depends on the electrostatic potential. For electrons accelarated by a voltage E, the electron wavelength is given approximately (ignoring relativistic effects) as (1.5 / E) 1/2 nm for E in volts. For example, for 100-keV electrons, ~ -- 3.7 pm (or 0.037/~). The wavelengths and other relevant quantities are tabulated, for example, in the International Tables for Crystallography [ 10]. The commonly used electron wavelengths are thus shorter than tne wavelengths of X-rays or neutrons normally used for diffraction experiments by a factor of about 50--100, and the scattering angles are correspondingly smaller, in the range of 10 -2 to 10-1 radians. As a result, electron diffraction experiments are normally made with a forward-scattering geometry, and the scattering theory may often be simplified by the use of small-angle approximations. For scalar waves (electron or electromagnetic), the nonrelativistic, time-independent wave equation can be written as vz~r(r) q- kZ~p(r) = 0

(1)

where k is the wave number, or the magnitude of the wave vector, of magnitude (1/~,), and ~p(r) is the wave function. The Schr6dinger wave equation for electron waves is obtained by putting k 2 --

(2me/h2){Eo + qg(r) }

(2)

Later we will consider the solution of the wave equation for an electron in the electrostatic potential field, qg(r), but for the moment we note only that the refractive index of the medium can be written as

n -- k/ko = {1 + ~o(r)/Eo} 1/2 ,~ 1 + {qg(r)/2Eo}

(3)

NANODIFFRACTION

where the approximation of the last expression is good for solids for which the potential r has values on the order of 10 V, whereas the accelerating voltage E0 is 105 V or more. For an electron wave passing through a solid in the z direction, the change of phase relative to the vacuum is then proportional to the integral of (n - 1) over z, which gives r y) = f r y, z)dz, so that an object may be considered to have a transmission function, which multiplies an incoming wave by

q(x, y) = exp{-ia~o(x, y)}

(4)

where cr = rc/)~E = 27rme~/h 2 is the interaction constant. Expression (4) represents the phase object approximation (POA), which involves two approximations. First it assumes that the only effect of the object on the electron wave is to change its phase; i.e., changes of amplitude due to the absorption effects of inelastic scattering are ignored. This is a reasonable assumption for thin objects. Second, the integration over the potential is made along a straight line, the z axis, which is the incident beam direction. No allowance is made for any change of direction due to scattering, refraction effects, or Fresnel diffraction. Because, for high-voltage electrons, such changes of direction are small (on the order of 10 -2 radians), this approximation is reasonable for object thicknesses of no more than 102 times the width of an atom, or about 2 nm. If the phase change, crop, in (4) is small, it is convenient to make the further approximation of expanding the exponential to the first-order term only:

q(x, y) ,~ 1 - icr~p(x, y)

(5)

which is the weak phase object approximation (WPOA). However, this approximation can be made for light atoms only. Even for single heavy atoms, the product acp may be as great as 1 or 2 near the atom center.

2.2. Kinematical Diffraction and Diffraction from Phase Objects The wave function of the Fraunhofer diffraction pattern of an object is given by the Fourier transform of the exit wave, ~e (x, y), in terms of the angular variables, u = (2 sin Ox)/)~ and v = (2 sin 0y/~., where Ox and Oy are the components of half the angle of scattering:

qJ(u,

U) =

F~e(X, y)= f f

~e(X, y)exp{2Jri(ux + vy)} dxdy.

(6)

Thus for the WPOA (5),

9 (u, v) = Q(u, v) --6(u, v) - ia~p(u, v),

(7)

and ~(u, v) is just the w = 0 section of the reciprocal space distribution, ~(u, v, w), given by Fourier transform of the real-space distribution, ~p(x, y, z), as considered in ordinary kinematical diffraction theory. For a thin crystal, for example, in which the transmission function ~p(x, y) is periodic with periodicities a and b, and expressed as a Fourier series,

~o(x,y):Z~Phkexp{27ri(h~Xa + k ~ ) }

(8)

hk

the diffraction pattern for the WPOA (7) contains ~(u, U) = '~-~hkq~hk~ u -- a--' v -- ~

(9)

which is the set of weighted h, k, 0 reciprocal lattice points in the plane perpendicular to the incident beam. Thus for the WPOA for a thin crystal the diffraction pattern is given by the kinematical theory, with the assumption that the Ewald sphere is a plane perpendicular to the incident beam. It may readily be shown that the assumption of a planar Ewald sphere

COWLEY AND SPENCE

acted beams

1/X

~

phere

Extended hkO reciprocal lattice points Fig. 1. The reciprocal lattice intersected by the Ewald sphere (curvature exaggerated) for the case of electron diffraction from a thin crystalto give a spot pattern such as that in Figure 2a.

is equivalent to the projection approximation, which neglects the spread of the waves in the object due to Fresnel diffraction. We may arrive at the full kinematical theory, as used for X-ray diffraction, if we retain the assumption that the phase changes are very small, introduce the curvature of the Ewald sphere, radius 1/~., and introduce the idea that the reciprocal lattice points are extended into finite regions of scattering power by shape function transforms, so that for a crystal that is thin in the incident beam direction, the reciprocal lattice points become elongated into lines in the beam direction of length proportional to the inverse of the thickness, as suggested in Figure 1. For a parallel-sided thin crystal of uniform thickness, H, the intensity distribution along this line in the w-direction, perpendicular to the crystal plane, is given by

l(h,k, w) = I~hk/I 2. sin2(rcHw)/(:rrw) 2

(10)

The Ewald sphere then may cut through a large number of these lines. Each intersection gives rise to a diffracted beam. For a two-dimensional array of such extended reciprocal lattice points, a pattern of diffraction spots is produced that closely resembles, for the small diffraction angles involved, a section of the reciprocal lattice. In Figure 2a, for example, the diffraction pattern of a crystal, seen in the electron microscope image of Figure 2b, is a pattern of many spots regularly spaced on the points of a lattice with axes reciprocal to the crystal lattice axes, with spacings proportional to 1/a and 1/b. This geometry for electron diffraction contrasts with that for X-ray or neutron diffraction, for which the radius of the Ewald sphere is about 50 times smaller and the shape function extensions of the reciprocal lattice spots, inversely proportional to the crystal dimensions, are about 100 times smaller, so that the Ewald sphere usually cuts only one region of scattering power at a time, producing only one diffracted beam. If, for a sample that is thin enough to allow the projection approximation to be made, the value of the projection, crqg(x, y), is not small, the POA rather than the WPOA is needed, so that, from (4), the diffracted intensity is given by

I(u, v ) = [Fcos{crqg(x, y)}l 2 + IF sin{trqg(x, y)}l 2

(11)

which is clearly much more complicated than for the WPOA. An alternative description may be obtained by expanding the exponential in (4) so that the exit wave function of the

NANODIFFRACTION

Fig. 2. Diffraction pattem (a) and high-resolution TEM image (b) of a thin crystal of Ti2Nb10029 . In (b), the defocus is such that the black spots represent rows of metal atoms in the beam direction. 350 kV, JEOL 4000EX microscope, courtesy of Dr. D. J. Smith.

COWLEY AND SPENCE

object is ~p(x, y) -- exp{-icrqg(x, y)} = 1 - icrqg(x, y) - o'2q92(x, y)/2 + icr3q93(x, y ) / 6 + ...

(12)

and the diffracted amplitude is given by Fourier transform as qJ (u, v) -- ~ (u, v) - itr 9 (u, v) - o "2 { (I) (U, V) * ~ (U, V) } + i~r3{~(u, v) 9 ~(u, v) 9 ~(u, v)} + . . .

(13)

where the 9 symbol represents a convolution integral, defined by

f (x) 9 g(x) = f f (X)g(x

X) dX

(14)

Then the first, second, third, etc. terms of (13) may be interpreted as single, double, triple, etc. scattering components of the total scattered amplitude.

2.3. Dynamical Diffraction For objects that are too thick to allow the application of the simple projection approximation given by (4), it is necessary to take into account the spreading of the scattered radiation by Fresnel diffraction within the object. This, together with the simultaneous multiple scattering, provides the full dynamical scattering picture of the interaction of the electrons with the object. In the "multislice" approach to the dynamical theory of electron scattering [ 1], the object is considered to be divided into a large number of thin, planar slices, perpendicular to the incident beam. For each slice, a phase change of the incident wave, proportional to the projection of the potential within the slice, following (4), is considered to take place on a single plane at the center of the slice. Then the wave exiting that plane is propagated to the central plane of the next slice by Fresnel diffraction, which involves convolution by the "propagation function," which, in the small-angle approximation, is p(x, y) = (i/A~.)l/2exp{rci(x 2 + y2)/A~.}, where A is the slice thickness. Thus the passage of the electron wave through the obiect can be represented in terms of alternate phase changes and propagations between slices, to give the final wave exiting the object. This formulation becomes exact in the limit that the slice thickness tends to zero, but can be made sufficiently accurate, and suitable for computer applications, for a finite number of slices of sufficiently small thickness. It has been widely used for the computerized simulation of electron microscope images and diffraction patterns of thin crystals [11-13]. An alternative approach to the dynamical diffraction theory for electrons, introduced in the classic paper of Bethe [ 14], involves the solution of the wave equation, (1) and (2), for an electron in the periodic potential of a crystal lattice, written in the form [5]

_h 2 ~vZqJ(r) 87rZm

h2K 2 -leIV(r)~P(r)-

2m

~(r)

(15)

where the crystal potential is inserted as U(r) - 2mlelV(r)/h 2 and expressed by the Fourier series U(r) = ~-,h Uh exp{2zrigr}, where K0 is the wave number of the beam in empty space, r is the three-dimensional vector in real space, and g is the vector from the origin to a reciprocal lattice point. The wave function for the electron wave in the crystal must be periodic and so is expressed as a sum of Bloch waves:

ql(t) Z C i exp{2rcik(i)r} ~ Cgi exp{2zrigr} i g

(16)

NANODIFFRACTION

where Ci and k (i) are the amplitude and the incident beam wave vector for the i th Bloch wave that has Fourier coefficients, Cgi Inserting (16) and the Fourier series for U(r) into the wave equation (15) then gives the standard dispersion equation for high-energy electrons [5]: [ K2 - (kj + g)Z]C(gj) + Z

Ug-hc'(j)'~h --0

(17)

h

This equation may then be forced into the form of an eigenvalue problem and solved to yield eigenvalues and eigenvectors. The constants ci are found from the boundary conditions and so depend on the external shape of the crystal. An approximation that is sometimes convenient for thicker crystals is the two-beam approximation, equivalent to that commonly used, and widely applicable, for X-ray diffraction from near-perfect crystals. In this it is assumed that the only waves of appreciable intensity existing in the crystal correspond to the incident beam and only one diffracted beam. This is clearly not appropriate for the situations giving diffraction patterns and images such as those of Figure 2, but may be approximated for particular orientations of crystals with small unit cells such as simple metals. Then only two Bloch waves are assumed to exist in the crystal, each with the component waves qJ0 and qJg. The two Bloch waves travel through a crystal with wave vectors of different magnitudes and gradually become out of phase so that, when they are recombined at the exit face of a crystal, they interfere to give the well-known "pendulum solution" effects, with the intensities of the incident and diffracted beams oscillating sinusoidally with thickness, out of phase [1, 5]. For the many-beam dynamical diffraction theory, a number of alternative formulations have been developed, and these have value for particular types of problems. Following Sturkey [15], the transmission of an electron wave, described as a wave vector with the Fourier coefficients as components, through a thin crystal slab may be expressed as the action of a scattering matrix. Transmission through successive slabs may be represented by multiplication of the associated scattering matrices. In the semireciprocal formulation of Tournarie [ 16], the wave function is considered as periodic and expressed in reciprocal space, in the two dimensions perpendicular to the direction of incidence, but in the direction of incidence, the variation of the wave function as it traverses the crystal is treated in real space. Several treatments have been derived [17], including those dealing with the channelling of electrons along rows of atoms, parallel to the incident beam, relevant to the case of the high-resolution electron microscopy of thin crystals viewed along a principal axis direction [ 18]. The use of coupled differential equations, describing the variations of the diffracted beam amplitudes with depth in a crystal, integrated through the crystal in the incident beam direction, was introduced by Howie and Whelan [ 19] and has been widely used in two-beam or many-beam forms, for the simulation of electron microscope images of defects in crystals [20].

3. IMAGING AND DIFFRACTION IN TRANSMISSION E L E C T R O N MICROSCOPY INSTRUMENTS

3.1. Transmission Electron Microscopy Instruments Figure 3a represents the main components of a conventional transmission electron microscopy system. Electrons from a suitable electron gun are accelerated by a voltage of 100-1250 keV and focused by a condenser lens to illuminate the specimen. The strong electromagnetic objective lens with a focal length of 1-3 mm gives the first stage of magnification and determines the microscope resolution. The image formed on the image plane of the objective is further magnified by an intermediate lens and then by a powerful, shortfocus projector lens before being observed on a fluorescent screen or recorded by the use

COWLEY AND SPENCE

\/

Gun

~/

Condenser lens Specimen

Objective lens Back focal plane

Selected area aperture

Intermediate lens

Projector lens

Final image

Fig. 3. Diagramsof ray paths for electrons in a TEM instrument for (a) image formation and (b) selected area electron diffraction from the specimen regions selected by the aperture in the focal plane of the objective lens.

of a photographic plate or else, as is becoming more common, a CCD camera or an image plate, for quantitative, digitized measurements. The electron source in the electron gun may be a hot filament, a pointed W or LaB6 tip or, more commonly now, a sharp, field-emission metal tip. In modern electron microscopes, there may be two or three condenser lenses that may be coupled to provide a variety of illumination conditions and deflector coils to allow the incident beam on the specimen to be tilted by any required angle. After the main objective lens, the one intermediate lens of Figure 3a may be replaced by two or three lenses to allow the final magnification of the image to be readily varied from zero up to a few million times with a minimum of image distortion and image rotation.

10

NANODIFFRACTION Image Back-focal

ONe

.

p l a ~ I

.4~._-f _ ~ I q(x)

FT.

= Q(u).T(u)

FT.

'~ q(x) ~ t(x)

Fig. 4. Diagramof the image formation by a lens according to the Abbe theory.

3.2. TransmissionElectronMicroscopyImaging The essential imaging properties of the system may be understood by considering the action of the objective lens to provide the first stage of magnification, using the Abbe description of the imaging process, as illustrated in Figure 4 [ 1, 11 ]. Plane parallel radiation is assumed to fall on the specimen so that the wave function after the specimen is given by the transmission function (or scattering matrix) of the specimen as 7t0(x, y). The transmitted, or forward-scattered, electrons are brought to a point focus in the back-focal plane of the lens (a distance f from the lens center). Likewise, all electrons scattered through an angle ~0, components qgx and ~0y, are brought to a focus at a position with coordinates (in a small-angle approximation) ~Pxf, qgyf, in the back-focal plane. Thus the amplitude in the back-focal plane represents the Fraunhofer diffraction pattern of the exit wave from the object and this is given by Fourier transform as qJ0(u, v) = F~(x, y), where u, v are the reciprocal space coordinates given by u = (2/X) sin(~Ox/2) and v = (2/X) sin(~Oy/2). For an ideally perfect lens, the propagation from the back-focal plane to the image plane, effectively at infinity, is given by a further Fourier transform operation so that the image amplitude is 7t(x, y) = FTto(u, v) = ~ ( - x / M , - y / M ) , i.e., a reproduction of the specimen wave function, inverted and magnified by a factor M. Usually the image is referred to the object plane so that the - M factor is ignored. For a real lens, the imaging is affected by the finite aperture of the lens and by the lens aberrations. These effects may be considered to operate in the back-focal plane in which the function qJ0(u, v) is multiplied by the transfer function of the lens, written as T (u, v) = A (u, v)exp{i X (u, v)}, where A (u, v) is the real aperture function, unity inside and zero outside the objective aperture, and X (u, v) represents the phase change due to the aberrations of the lens. For electron microscopy it is usually sufficient to include only the second-order phase change due to defocus, and the fourth-order phase change due to spherical aberration, measured by the spherical aberration coefficient, Cs, so that we write

X.(u, v ) - 7rAX(u 2 -+- v2) q- (Tr/2)CsX3(u 2 q-- v2) 2

(18)

The modified amplitude in the back-focal plane is then qJo(u, v)T(u, v), and because the Fourier transform of a product is a convolution, the image intensity distribution, given by the modulus squared of the image amplitude, becomes

I(x, y ) = ]F{qJ0(u,

v)T(u, v)}[ 2 - I~o(x, Y)* t(x, y)[2

(19)

where t(x, y) is the complex Fourier transform of T(u, v) and is known as the spread function, because the convolution with t (x, y) smears out the image function and so represents the loss of resolution due to the imperfections of the lens. Because both !/*0(x, y) and

11

COWLEY AND SPENCE

t (x, y) are, in general, complex, it is difficult to see immediately how the intensity distribution of the image is related to the structure of the object. It is only for special restricted approximations, such as the WPOA (5), that a simple relationship exists. Using the WPOA and putting t(x, y) - c(x, y) + is(x, y), where c and s are real functions, we obtain, to first order in cr~0, I (x, y) -

I/1 -

icr~o(x, y)} 9 {c(x, y) + is(x, y)}l 2

-- 1 + 2crqg(x, y) 9 s(x, y).

(20)

Thus the image gives a direct representation of the projection of the potential distribution of the object, smeared out by convolution with s(x, y), which is the Fourier transform of A (u, v) sin{x (u, v) }, the imaginary part of T (u, v). The image resolution is as good as possible when s(x, y) is a sharp negative or positive peak of minimum diameter. Scherzer [21 ] showed that this condition occurs for a negative defocus (a weakened objective lens) given by A = - (4C s)~/ 3) 1/2. The criterion for this "Scherzer optimum defocus" is that the function sin X (u, v) should have a value close to unity for as far as possible out into reciprocal space to include in the image the contributions of a maximum amount of the diffraction pattern (see Figure 5a). The "resolution" of the microscope (or, more correctly, the "least resolvable distance") is then taken, by convention, as the inverse of the outermost reach of the region for which sin X (u, v) is close to unity, and then is given as Ax -- 0.66(Cs)~ 3) 1/4

(21)

where the value of the initial constant varies slightly with the criteria used. The outer limit of the diffraction pattern that contributes meaningfully to the image is often taken as the point where the sin X curve cuts the axis. Beyond that, the curve oscillates more and more rapidly, especially as the fourth-order term in (18) dominates. In practice, the sin X curve is usually strongly damped, as in Figure 5b, as a result of so-called incoherent imaging factors: the finite convergence of the incident beam and the "chromatic-aberration" term, arising because the focal length of the objective lens takes a range of values because of the fluctuations of the objective lens current and the variations of the incident beam energy. The outer part of the diffraction pattern, beyond the point where the sin X curve cuts the axis, can contribute to the image detail if it is not excluded by the objective aperture, even though the oscillations of the sin Z function imply that these contributions to the image are not readily interpretable. Then the limitation of the fineness of detail in the image is determined by the damping of the curve by the incoherent factors, as suggested in Figure 5b. The point where the damping function cuts off the information is then often called the "information limit," because information on the corresponding scale is contained in the image, even if it is not readily interpretable. Thus for single-crystal samples with a strong reflection occurring in the region beyond the "resolution limit," interference fringes may still appear in the image. For example, fringes corresponding to a crystal lattice spacing of about 0.1 nm have been observed in a microscope for which the resolution limit, as defined by (21), is about 0.28 nm [22]. When the POA (4) is used in place of the WPOA, it is obvious that the expression for the image intensity is much more complicated and is calculable but not readily interpretable. For crystals and noncrystalline regions that are too thick to allow the POA to be applied, the full three-dimensional dynamical diffraction processes must be included, and the image intensity is calculated by considering the action of the spread function on the wave function at the exit face of the specimen. Clearly, from (21), the resolution for the WPOA may be improved by reducing either Cs or, more effectively, )~. The possible reduction of Cs is limited by the feasible dimensions and properties of the pole pieces of the objective lens. The reduction of )~ with accelerating voltage increased above about 400 keV results in radiation damage of the specimen, which is excessive for many specimens and requires large and expensive instruments. The best

12

NANODIFFRACTION

1-

0.6-

0,2-

-0.2-

-0.6

-1

j

Resolution

limit

(a)

0.6-~

o2t

/ AA

-0.2

-0.6

Resolution

limit

Information

limit

(b) Fig. 5. The function sin X (u), the effective transfer function of an objective lens for the case of weakphase objects, at the optimum "Scherzer" defocus, for the cases (a) an ideally monochromatic plane wave and (b) with a damping function due to incident beam convergence.

resolution available is now around 0.16 nm for 400-keV instruments, decreasing to about 0.12 nm for 1250-keV machines. 3.3. Selected Area Electron Diffraction

The flexibility of the lens systems of TEMs makes it possible to obtain the diffraction pattern rather than the image of the object on the final viewing screen. If the focal length of the intermediate lens of Figure 3a is increased, as in Figure 3b, then it is the back-focal plane of the objective lens that is observed and recorded. Usually it is the diffraction pattern of only a small part of the total image area that is required. This may be arranged by inserting a "selected-area" aperture in the image plane of the objective lens, so that only those electrons that have passed through the selected area contribute to the diffraction pattern. The size of the area of the specimen that can be selected in this way, to give a "selected area electron diffraction" (SAED) pattern, is limited in practice by the spherical aberration of the objective lens (see, e.g., [23]). The minimum diameter of the area may be around 10 nm for 100-keV electrons but decreases to a few times 10 nm for electrons of 1 MeV. The SAED technique is thus valuable and is widely used for finding the average structure and orientation of crystals, or regions of crystals, of this size range, although it is of

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limited value for nanometer-size regions. It is the method used, for example, to produce the diffraction pattern of Figure 2a, which comes from a specimen region comparable with that appearing in Figure 2b. Because the diameters of the specimen regions are relatively large, the diffraction spots can be quite sharp, approximating very well those for plane parallel radiation. The dualism between images and diffraction patterns in the TEM may be extended in various ways. For example, if the beam incident on the specimen is tilted, it may be arranged that any selected part of the diffraction pattern travels down the axis of the microscope and forms the final image. If the central spot of the diffraction pattern is not included, the image is a dark-field image, showing intensity only for those parts of the specimen giving diffracted beams in the chosen directions, within the objective aperture. Although the theory of the imaging process is then not simple, it is a common assumption, often justifiable, that, for a crystalline specimen, the selection of a particular diffraction spot gives an image showing the regions of the crystal that have an orientation such that the Bragg condition is satisfied for the selected reflection. Thus dark-field imaging, in conjunction with SAED, is valuable for the analysis of the distortions and defects of crystalline samples [24, 25]. For noncrystalline specimens, it may sometimes be assumed that the diffraction pattern is a radially symmetric, uniformly decreasing distribution of scattering. Then the selection of any part of the diffraction pattern by the objective aperture gives a image signal that is just proportional to the local strength of the scattering, and so is proportional to the number of atoms present at an image point. This assumption is sometimes useful, but must be made with caution when there is any local ordering present in the sample, as is often the case.

3.4. Fourier Transforms of Transmission Electron Microscopic Images It has been proposed in the past that the limitation on the minimum size of the specimen area giving a SAED pattern could be overcome by taking the diffraction pattern of a smaller region of the high-resolution bright-field image, either by putting the recorded image in an optical diffractometer or by digitizing the image intensity distribution and performing the Fourier transform in a computer. However, in general, the Fourier transform of the image intensity, given by (19), is not the same as the diffraction pattern of the exit wave function of the crystal, ~0(x, y). Even for the very restricted cases for which the WPOA applies, the intensity distribution of the diffraction pattern of the image intensity (20) gives, away from the origin, la~(u, v)l 2 sin2x (u, v), so that the intensity of the diffraction pattern of the specimen area is multiplied by the square of the function shown in Figure 5a or, in practice, Figure 5b. Although the observation of the diffraction pattern of an image area is often useful in that it can reveal the periodicities present and can be used for the exploration of the form of the sin X function, it is of very limited value for simulating the nanodiffraction patterns from small specimen areas. Recently it has been proposed that the limitation on the minimum size of the specimen area that can be used for SAED may be overcome by taking advantage of the reconstruction of exit wave functions made possible by off-axis electron holography [26]. In this form of electron holography, the electron wave that has passed through the specimen near its edge is made to interfere with a reference wave that has passed only through the vacuum, outside the specimen [27]. The interference fringes formed by these two waves in the image plane are deflected by an amount proportional to their relative phases. In this way, both the amplitude and the phase of the exit wave from the crystal can be determined when a correction is made for the phase changes due to the lens aberrations and defocus. Then the diffraction pattern for any chosen portion of the exit wave function, however small, can be derived in principle, subject only to the limitation of the damping functions, such as in the case of Figure 5b. Thus the extent of the diffraction pattern obtainable is given by the

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"information limit" of the image resolution. This limitation may be significant in that the extent of the useful nanodiffraction pattern is often considerably greater than that given by the "information limit" of the image.

3.5. Diffraction and Imaging from Surfaces TEM instruments may be used very effectively for the study of the arrangements of atoms on crystal surfaces. In the usual transmission mode, the scattering of electrons by the surface layers is often obscured by the much stronger scattering by the atoms in the bulk of a crystal. However, there are cases where the surface atoms have periodicities or symmetries different from those in the bulk, so that they give diffraction spots that do not coincide with those from the bulk periodicities and can therefore be used to study the diffraction from the surface layers or to image the surface structures separately [28]. The scattering from the surface layers is so weak, however, that it is not often possible to obtain diffraction patterns from very small regions or to image the surface structure with very high resolution. In an alternative approach, surface layers may be studied in diffraction or imaging modes by using reflection techniques, with the incident beam directed so that it strikes the flat surface of a bulk crystal at a small, grazing angle, equal to the Bragg angle for some prominent lattice planes parallel to the surface, as suggested in Figure 6. The diffraction patterns observed in this mode are the well-known RHEED (reflection high-energy electron diffraction) patterns, such as those in Figure 7a. They show arrays of diffraction spots corresponding to the periodicities of the crystal lattice in directions perpendicular to the surface and at fight angles to the incident beam. They also show extensive patterns of the so-called Kikuchi lines, arising from electrons scattered incoherently (and usually inelastically) within the bulk of the crystal, as seen in the background of Figure 7a. If one of the strong diffraction spots of the RHEED pattern is selected by the objective aperture of the TEM and directed down the objective lens axis, the image that is formed can be described as showing the areas of the crystal surface that give rise to that diffracted beam, as in a normal dark-field TEM image. In the reflection mode, the REM (reflection electron microscopy) image is, severely foreshortened, however, because of the low angles made by the incident and diffracted beams with the surface plane. The image is in focus for only one line across the surface, perpendicular to the incident beam, but may give an interpretable contrast for a large area of the surface, as in Figure 7b. The REM and RHEED techniques are useful for the study of surface structures because, for the small angles of incidence used, the penetration of the electron beam into a smooth surface may be 1 nm or less. It has been shown by computer simulation [29] that, for the particular diffraction geometry that gives rise to the "surface channeling" phenomenon, the

REM

SREM

Objective lens

Surface

Fig. 6. Diagramsuggesting the geometryfor reflection electron diffraction (RHEED) and microscopy (REM) from a crystal surface. The glancing angle of incidence is exaggerated. The objective lens, as in Figure 3, can form the image or diffraction pattern of the surface. For scanningreflection electron microscopy,the electron beam goes from fight to left.

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Fig. 7. RHEEDpattern (a) and REM image (b) of the (111) surface of a Pt single crystal. In (b), singleatom surface growth steps are visible, and at top-center there is a dislocation (black-white streak) at the end of a slip trace left by dislocation movement.

elastically scattered electrons may be confined to the topmost one or two atomic layers on the surface. The resolution of the images in the direction perpendicular to the electron beam may be comparable to that for the transmission images, although in the beam direction the foreshortening limits the effective resolution considerably. Likewise for the diffraction pattern, the width of the region giving a diffraction pattern may be as small as for TEM in the direction perpendicular to the beam, although it is much greater in the incident beam direction. For any small object projecting from the surface, the image resolution and SAED areas are as for the transmission case. Hence R H E E D and REM have been widely used for studies of surfaces, particularly for cases when high spatial resolution, not approachable by many surface study techniques, is needed [30].

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3.6. Convergent-Beam Electron Diffraction So far we have considered the imaging and diffraction in a TEM instrument under the usual conditions of a near-parallel incident beam for which the first approximation is to consider that a coherent plane wave illuminates the specimen. In an alternative approach, a condenser lens is used to focus the incident beam to form a small crossover at the specimen level. The focused beam diameter may be as small as 10-20 nm when a conventional heated tip source is used in the electron gun, or as small as 1 nm when a high-brightness, field emission gun (FEG) is used. Then diffraction patterns may be observed from the small illuminated specimen areas. Under these conditions, as suggested by Figure 8, the incident beam fills a convergent cone, and correspondingly, the incident beam spot of the diffraction pattern, and all other diffraction spots from crystalline specimens, are spread into disks of diameter determined by the condenser aperture size. The diffraction pattern is then a CBED (convergent beam electron diffraction) pattern, like that in Figure 9. Usually the diameters of the diffraction spot disks are made smaller than the separation of the spots, so that the disks do not overlap. Then the coherence of the incident illumination, determined by the source size, does not influence the pattern of a perfect crystal [ 1, 5, 13]. The pattern can be described as the sum of diffraction patterns for a range of incident angles. For crystals which are more than a few nanometers thick, the intensities of the diffraction disks are modulated to reflect the variation of diffraction intensity with angle of incidence. For high-angle reflections, the intensity of diffraction varies very rapidly with angle of incidence, so that the diffraction disks may be reduced to very thin sharp lines. When such sharp reflection lines are generated, the intensity of the incident beam is reduced.

,--4-1/ d.--~

I / (a)

(b)

Fig. 8. Diagrams suggesting the geometry for convergent-beam electron diffraction. For (a), the beam convergence is relatively small, so that the diffraction spots do not overlap. For (b), the spots overlap, and the overlap of the h and h + 1 spots is illustrated.

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Fig. 9. Convergent-beamelectron diffraction pattern from a Si crystal in [111] orientation. The inset is an enlargement of the central beam spot, crossed by HOLZ lines. Courtesy of Dr. R. W. Carpenter.

Consequently there may be sharp dark lines traversing the incident beam disk. Observations with these sharp extinction lines can provide the basis for highly accurate measurements of crystal lattice parameters. When a FEG is used to generate a CBED pattern, the electron beam may usually be considered completely coherent, as if coming from a point source, so that incident electron beams coming from different directions can interfere. Then, when the diffraction disks in the CBED pattern overlap, interference fringes may appear in the overlap regions, with positions depending on the relative phases of the overlapping reflections. These interference effects are the simplest of a range of phenomena that hold great promise for the development of important new "coherent nanodiffraction" techniques that will be discussed in more detail in subsequent sections of this review. The description of the theory and applications of CBED patterns in general will be deferred until Sections 5 and 6.

4. I M A G I N G AND D I F F R A C T I O N IN SCANNING TRANSMISSION ELECTRON MICROSCOPY INSTRUMENTS

4.1. Dedicated Scanning Transmission Electron Microscopy Instruments Although STEM imaging and microdiffraction or nanodiffraction can be performed in modern TEM instruments, the most satisfactory instruments for these techniques are the dedicated STEM instruments that have been built by a few individual research

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Fig. 10. Diagramof a scanning transmission electron microscope with one post-specimen lens, a thin annular detector (inset), a detection systemwith TV and CCD cameras viewinga transmissionfluorescent screen, and an EELS spectrometer.

groups [31, 32] or produced commercially by VG Microscopes. In these, a strong electromagnetic lens, similar to the objective lens of a TEM, is used to form a very fine probe at the specimen by demagnifying the electron source, which is preferrably the very small, bright emission from a FEG. A diagram of a typical STEM instrument is given in Figure 10. The FEG source is preferrably of the cold-field-emission type for minimum size and maximum brightness, operating in a vacuum of better than 10 -1~ torr to avoid the noisy emission associated with transient molecules on the field emission tip. The accelarating voltage is commonly 100 kV, although several 300-kV machines have been produced recently [33]. The vacuum in the column is usually better than 10 -8 but may be 10 -1~ or better in some special instruments designed specifically for surface studies [34]. The strong objective lens may be preceded by one to three condenser lenses and suitable apertures, designed to allow the wide variety of beam-forming configurations that may be required for special purposes. In this region also are included the scanning coils, to allow the fine probe to be scanned over the specimen and stigmators for the objective and condenser lenses. When the fine probe formed by the objective lens passes through the specimen, a convergent-beam diffraction pattern is formed on the distant plane of observation and may be observed or recorded by the use of a suitable phosphor screen, CCD camera, or other twodimensional detector system. The intensity in some part of this pattern is detected to form the STEM signal, which is then displayed on a cathode ray tube with a scan synchronized with that of the probe at the specimen level, to form the magnified image. Detecting any

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portion of the central beam of the CBED pattern gives a bright-field image. Dark-field images may be obtained by detecting individual diffraction spots, or an annular detector may be used to collect all, or some part of, the distribution of electrons scattered outside of the central spot. For high-resolution STEM imaging, the specimen is normally placed within the magnetic field of the objective lens, as in TEM, so that the post-specimen magnetic field of the objective has a focusing effect. In some instruments a series of two or more further post-specimen lenses are added, and these, together with the back field of the objective, may be equivalent to a simple TEM lens system [34]. This combination of lenses, however, is rarely used to form images of the specimen, but serves instead to provide a very flexible system for controlling the dimensions of the diffraction pattern on the final detector plane. One important advantage of the dedicated STEM instrument, as compared with a TEMSTEM system, is the flexibility of the design in allowing a wide variety of detector devices to be inserted to operate separately or simultaneously. In the detector plane, the phosphor or scintillator detectors of various shapes and sizes may be inserted to give various brightfield or dark-field imaging modes, or any part of the CBED pattern may be passed through an aperture into the electron energy-loss spectrometer for the microanalysis of the illuminated specimen area by electron energy-loss spectrometry (EELS) or for the imaging of the specimen with any particular chosen energy loss [9]. Small detector assemblies may be inserted close to the specimen to detect emitted radiations. The detection of characteristic X-ray emissions allows the microanalysis of the specimen or the imaging of the specimen with particular emission energies to map the distributions of particular elements [8]. The detection of low-energy secondary electrons is used to give high-resolution secondary electron microscopy (SEM) images of the surfaces of the specimen [35], and the detection of the higher-energy Auger electrons allows the analysis or selective imaging of the surface layers of the specimen by Auger electron spectrometry (AES) or Auger electron microscopy (AEM) [36].

4.2. Image Contrast in Scanning Transmission Electron Microscopy Although the theory of STEM image contrast is often best derived by tracing of wave functions through the STEM instrument components, it is sometimes convenient to relate the STEM image formation to the well-established theory of TEM imaging by application of the Principle of Reciprocity [37]. This principle may be stated thus: The amplitude of a wave at point B due to a point source at point A is equal to the amplitude of a wave at point A due to a point source at point B. This result applies strictly only in the case of scalar waves interacting with scalar fields, with no changes in energy due to inelastic scattering processes, but may be considered as valid in electron-optical systems, provided that vector field effects, such as image rotations in magnetic lenses, and finite energy losses are ignored. It may be used for cases of finite sources and detectors by considering each point of the source and detector separately. Thus the TEM and STEM imaging conditions are related as suggested by Figure 11, in which the electrons are considered to go from left to right for STEM and from right to left for TEM, with source and detector points interchanged. For a point source and an axial STEM detector, the image contrast is exactly the same as for bright-field imaging in TEM with axial plane.-parallel illumination. The effect of using a detector of finite diameter in STEM is the same as the effect of using a finite source size in TEM. The loss of resolution given by using a source of finite width in STEM is the same as that of using a detector of finite size (or limited resolution) in TEM. The dark-field STEM image given when the detector is displaced is the same as the dark-field TEM image when the incident beam is tilted by an equivalent amount. In the wave theory of STEM imaging, it may be considered that, with a point source, the wave incident on the specimen is given by the Fourier transform, t (x, y), of the transfer

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STEM

9 Source

Objective

-r

Detector i

B

CTEM

Fig. 11. Diagram suggesting the reciprocity relationship of STEM (electrons going from left to right) and conventional TEM (electrons going from right to left) for the essential, objective-lens region of the instruments.

function, T (u, v), of the objective lens, as defined before Eq. (18). Then, for a thin object, the wave leaving the specimen is given by multiplying the input wave by the transmission function, q (x, y), of the specimen. The intensity distribution on the plane of observation is then given by the modulus squared of the Fourier transform of the exit wave at the specimen:

Ix, r(u, v) - [V{q(x, y ) t ( x - X, y - Y)}I 2 - IQ(u, v ) . {T(u, v)exp{Zrci(uX + vY)}}l 2

(22)

when the incident beam center is displaced to the point X, Y. The image signal recorded is then given by multiplying this intensity distribution by a "detector function" D(u, v):

I(X, Y, - f Ix, r(u, v,D(u, v)dudv

(23)

It is readily shown that if the detector function is a delta function at the origin, 6(u, v), Eq. (23) reduces to

I(X, Y) - I / {

Q(u, v)T(u, v)}l 2 - - I q ( X , Y) 9 t(X, y)]2

(24)

which is exactly the same as (19), the image intensity for bright-field TEM. In the dark-field imaging mode introduced by Crewe et al. [38], an annular detector is used to collect all electrons scattered outside the central beam disk of the CBED pattern in the detector plane. Then the detector function D(u, v) is zero within a certain radius in reciprocal space and unity elsewhere. The integral (23) is then, in general, difficult to evaluate. However, if one makes the approximation that the integral of the scattering outside the central spot of the diffraction pattern is proportional to the total scattering, it is possible to make the assumption that D(u, v) = 1, but the transmitted beam is excluded. Then in the weak phase object approximation, q(x, y) - 1 = crqg(x, y), and (23) reduces to

I ( X , Y ) = letup(X,Y) 12 9 It (X, Y) I2

(25)

This is the "incoherent imaging" approximation in which the square of the projected potential function is smeared out by the intensity distribution of the incident beam. Because qg(X, Y) should be interpreted as the deviation from an average potential, it is seen that either positive or negative deviations from the average potential should appear as white spots on a black background. If t (X, Y) is approximated as a Gaussian, the width of It (X, Y)12 is smaller than that of t (X, Y) by a factor of 1.4, so the dark-field STEM resolution is better than for bright-field by this factor. The approximation that the signal is proportional to the total scattering is not usually valid, however. For individual heavy atoms, or for amorphous materials with unresolved atoms, it is possible to assume that the diffracted intensity falls off smoothly with scattering angle, so that this approximation is reasonable, but for pairs or groups of atoms that are only just resolved, the diffracted intensity oscillates on the scale of the dimensions of the

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incident beam spot. Then the fraction of the scattered intensity that is collected by the annular detector may vary strongly with the atom separations and with the beam position [39]. Then the approximation (25) is no longer possible. It was shown originally by Wall et al. [40] that the dark-field image given with an annular detector shows a contrast for single atoms that is strongly dependent on the atomic number and therefore can provide a very effective means for detecting heavy atoms, or clusters of heavy atoms, on thin light-atom supports. This technique seemed ideally suited for the study of, for example, the small metal particles in supported metal catalyst sampies. However, the light-atom supports in such catalyst systems, often consisting of alumina, silica, or other oxides, tend to be microcrystalline rather than amorphous, and the diffraction spots from the crystallites tend to give contrast in the dark-field images, which can mask that from the heavy metal atoms. The solution to this problem, suggested by Howie [41], is to use an annular detector with an inner radius so large that it does not collect the diffraction spots, but only the high-angle scattering beyond the normal range of spot scattering angles. The resulting high-angle annular detector dark-field (HAADF) imaging mode has proved valuable for the imaging of catalyst samples [42] and for the high-resolution imaging of rows of atoms in crystals [43]. For this latter type of application, the HAADF STEM mode has considerable advantages over the more common BF TEM mode in that the image contrast depends on the number and the atomic number of the atoms present, and does not show the same complicated intensity variations with thickness and crystal tilt. Recently it has been demonstrated that if an annular detector with a small width is used, so that the difference between the inner and outer radii is no more than about 10% (see the inset in Fig. 10), several new modes of imaging become possible [44]. If the thin annular detector collects the outer parts of the incident beam disk for WPOA imaging, the bright-field imaging (TADBF) may have a resolution 1.7 times better than normal BF TEM or STEM. If the thin annular detector selects a ring of scattering from the diffraction pattern, the resulting TADDF image may give useful discrimination of particular phases, or regions having particular periodicities [45]. Thus an amorphous or nanocrystalline component can be preferentially imaged in the presence of much larger components with different periodicities.

4.3. Nanodiffraction in Scanning Transmission Electron Microscopy Instruments If the incident beam in a STEM instrument is held stationary on the specimen, the diffraction pattern of the illuminated area of the specimen appears on the plane of observation. For an instrument with a dark-field resolution of 0.2 nm, the region giving the diffraction pattern may have a diameter on the order of 0.2 nm. The diffraction spots have an angular spread of about 10 -2 radians. For most crystalline specimens viewed in a principal-axis direction, the incident beam diameter is then smaller than the dimensions of the projected unit cell, so that the periodicity of the crystal structure is not evident in the diffraction pattern. The pattern is generated by the configuration of atoms in the region within the unit cell that is illuminated by the beam. The individual diffraction spot disks in the pattern may be considered to overlap extensively and interfere to give complicated interference fringe patterns that dominate the intensity distribution. The intensity distribution changes strongly with movements of the beam by 0.05 nm or less as the beam illuminates different sets of atoms within the unit cell. It is only in a few instances that this extreme case of nanodiffraction with extremely small beam diameters has been observed [46], and in even fewer cases have the intensities of such patterns been measured and interpreted [47-49]. The extreme sensitivity of the intensity distribution to beam position and other experimental parameters makes the observation of such patterns a very powerful means of investigating specimen structures

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with ultrahigh resolution, as will be discussed in Sections 11.5 and 13, below, but these same sensitivities introduce considerable complications for applications that do not call for the most detailed examination of specimen structure and so are usually avoided. Most nanodiffraction work has been done with beams of diameter on the order of 1 nm, formed by inserting a relatively small objective aperture and maximizing the beam intensity by a suitable setting of the condenser lenses. Then for most crystals the diffraction spots are well separated, and the diffraction patterns can be interpreted, to a first approximation, as if given by a larger area in SAED. The dimensions of the diffraction pattern on the plane of observation of a dedicated STEM instrument may (preferably) be varied to suit the experiment, by means of the post-specimen lenses. The diffraction intensities are observed and measured by one of two schemes. In one scheme, a set of post-specimen deflection coils, the "Grigson coils" [50], is used to scan the diffraction pattern over the entrance aperture of the EELS spectrometer, and the signal produced by the elastically or inelastically scattered electrons is displayed on the cathode ray tubes used for STEM imaging. This method has the disadvantage that the detection is very inefficient, in that only a small part of the diffraction pattern is detected at any one time, especially if a small detector aperture is used to improve the angular resolution of the pattern. It has the great advantages for some purposes that a quantitative measure of the intensity is given and the elastically or inelastically scattered electrons may be detected separately. The more common, alternative, approach is to allow the diffraction pattern to fall on a transmission phosphor or scintillator screen. The light from the screen is conveyed by means of a mirror and optical lens system to a suitable two-dimensional detector outside of the microscope vacuum [51 ]. The detector may be a film camera or, for more convenient, quantitative recording, a CCD camera coupled to a digital data-handling device, with immediate display of the intensity distributions and the possibility of digital recording for subsequent off-line measurements and analysis. One limitation of such camera systems is that the recording of the pattern may take several seconds. On the other hand, for stable specimens and steady beam conditions, it is possible to accumulate data from weakly scattering specimens for extended periods of time. For real-time observation of the diffraction patterns, and for rapid recording of intensity distributions, it is customary to use a low-light-level television camera with recording on a VCR (video cassette recorder). With standard commercial systems, it is possible to record 30 frames/s, so that rapid surveys can be made of the variation of diffraction patterns with position of the beam, and the time variation of patterns can be recorded. The VCR can be set to record the variations of the diffraction pattern while the incident beam is made to scan along any line or in a two-dimensional pattern over any specimen area. The image of the specimen, obtained with a small bright-field detector or with a HAADF detector, may be recorded simultaneously. The individual frames of the recording may then be played back and studied individually in conjunction with the image contrast data. In one convenient method of operation of the STEM instrument, the image of a specimen is observed using an appropriate imaging mode. One feature of the specimen may be selected by placing a small electronic marker over the image point. The beam scan is stopped at the position of the marker, and the diffraction pattern is recorded. For example, Figure 12a shows a bright-field image of small Au crystals, 1-5 nm in diameter, embedded in a plastic film [52]. Nanodiffraction patterns from individual Au particles, formed by stopping the beam at various particle positions in Figure 12a, are shown in Figure 12b. It could be deduced from such patterns that most of the particles in Figure 12a are not single crystals, but are twinned or multiply twinned. The incident beam diameter in this case was about 1 nm, so that diffraction patterns could be readily obtained from particles as small as 1 nm in diameter, but the images had a resolution no better than 1 nm, so that particles of 1-nm diameter and smaller could be detected but not examined in detail. Higher-resolution imaging of the specimen area could be made by inserting a larger

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Fig. 12. STEMimage (a) of small Au particles embedded in a polyethylene film and nanodiffraction patterns (b) obtained by stopping the scanning beam at the position of the marker (overexposed white spot) placed to overlap the image of a small particle [52].

objective aperture, but this procedure is liable to involve an inconvenient time delay and possible specimen movement. The diffraction patterns of Figure 12b are interpreted as if they are given by a parallel incident beam, but with each diffraction spot enlarged to the size of the incident beam disk. Then the assumption made is that of incoherent diffraction, with an intensity distribution given by convolution of the diffraction pattern with the intensity distribution of the source function. This assumption is useful and is valid for many cases, such as when the diffraction pattern comes from a nearly perfect single crystal region. However, as will be discussed in detail in Sections 7 and 11 and so on, there are important deviations from this incoherent diffraction situation because the incident beam on the specimen produced by a FEG source can be assumed to be almost completely coherent, and interference effects may be produced in the diffraction patterns that are readily observed and may be used to derive important information on the form and nature of the limitations of perfect order in the specimen.

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4.4. Combinations of Nanodiffraction and Other Techniques The flexibility of the detection system of dedicated STEM instruments allows the simultaneous detection of two or more signals, which may be used for imaging or for the analysis of individual specimen areas. For example, the bright-field image obtained with zero-energy-loss electrons or the dark-field image obtained with electrons having lost any particular amount of energy, may be observed by passing the central beam of the diffraction pattern through the aperture into the EELS spectrometer at the same time that the dark-field image is obtained with an annular detector. Or, if the scan rate is sufficiently slow, the image from the EELS detector may be correlated with the variation of the nanodiffraction pattern observed with a two-dimensional detector on the plane of observation. One consequence of this possibility is that pattern recognition techniques may be applied to the diffraction patterns. The positions in the image that give diffraction patterns of a particular form, indicating regions having a particular crystal structure and orientation, may be determined [53]. Correlations in angle may also be made, to allow detection of a particular type of diffraction pattern irrespective of its orientation. This approach can be very effective for the statistical analysis of finely polycrystalline materials or disordered materials. Furthermore, the variation of the nanodiffraction pattern may be observed as the beam is scanned over the specimen while the distribution of particular elements in the specimen is mapped by recording the intensities of characteristic X-ray emission lines or the intensities of the corresponding inner-shell electron energy losses. If the incident beam is held stationary at a chosen image point, the nanodiffraction pattern may be correlated with the EELS spectrum or the X-ray emission specimen, so that the chemical composition as well as the crystal structure of a localized feature may be derived. For studies of the surfaces of thin films in transmission, it is possible to make the correlations of the nanodiffraction pattern with the emission of low-energy secondary electrons or Auger electrons, and images formed by detecting these emissions may be correlated with the bright-field or dark-field transmission images [35, 36]. As in the case of TEM, described in the previous section, the STEM instruments may be used in reflection mode, with the incident beam striking the flat surface of an extended bulk sample at grazing incidence. When the finely focused beam of a STEM instrument illuminates a region of very small width on a crystal surface, the nano-RHEED pattern obtained is much the same as that for the RHEED pattern given in a TEM instrument when a small beam convergence is used but shows large disklike spots, strongly modulated, for larger beam convergences. Detection of individual diffraction spots, or of strong intensity maxima within spots, allows scanning reflection electron microscopy (SREM) images to be formed for which the intensity distributions are much the same as for REM images [54]. The form of SREM imaging that is analogous to the ADF imaging in transmission STEM is given by using an annular detector to detect all, or selected regions of, the convergentbeam nano-RHEED pattern. The image intensity distribution is then considerably different from the usual SREM image, being much more dependent on the surface morphology than on the crystallography of the surface [55]. For the reflection geometry, the SREM images give much the same information on surface structure as REM images but, as in the transmission case, the nano-RHEED and SREM modes allow correlations of the diffraction and microanalytical signals. The EELS spectra and energy-loss imaging, although not so easy to observe as in the transmission case because of high background levels, can be used for the microanalysis of the surface layers on crystals [56, 57]. Similarly, detection of the low-energy secondary electrons and Auger electrons allows the correlation ot their morphological and compositional information on surface layers with that of RHEED and SREM. A particular virtue of the nanodiffraction used in the reflection mode is the ability to give diffraction patterns from very small particles sitting on the flat surfaces of crystals, as a result of nucleation and growth processes, chemical reactions or depositions, as will be described in Section 8.

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One particular advantage of the possibility of obtaining two or more STEM signals simultaneously is that coincidence measurements may be made to relate and compare the generations of the various signals. For example, observations of coincidence have been made between the emission of low-energy secondary electrons and the losses of particular amounts of energy by the transmitted beam for various scattering angles [58]. It had been difficult to understand how secondary electron images could be formed with resolutions of better than 1 nm when simple considerations suggested that the localization of the primary excitations of the crystal electrons could not be better than about 10 nm [59]. The coincidence measurements indicated that the generation of secondary electrons arises preferentially from scattering events for which the incident beam deflection is on the order of 10 -2 radians, rather than from the more common events for which the scattering angle is 10 -3 or less, and hence is more highly localized.

5. THEORY OF CONVERGENT-BEAM ELECTRON DIFFRACTION 5.1. Introduction

In this section we describe in more detail how information may be extracted from the CBED patterns briefly described in Section 3.6 and shown in Figure 9. We have seen that two types of CBED patterns may be distinguished: coherent and incoherent. In Section 7 the relevant theory is given for coherent patterns; here we consider only the incoherent type. The distinction is made according to whether the coherence width of the electron beam in the plane of the illumination aperture is larger than (coherent) or smaller than (incoherent) the illumination aperture. In the former case the probe itself may be considered to be completely coherent. In the later, it is partially coherent. For ideally incoherent patterns, interference between overlapping orders cannot occur, and these are the type of patterns normally obtained on TEM/STEM instruments that do not use a FEG. In general, the incoherent CBED patterns discussed in this section will be obtained from rather thicker crystals than those discussed in Section 3.6. Thicknesses of 100-800 nm are common for incoherent CBED, depending on accelerating voltage. Probe widths are also generally larger for incoherent work (in the range of 10-100 nm), being determined by the product of the total magnification of the probe-forming lens system and the virtual source size, rather than the aberrations of the lenses. Nevertheless, for these thicker crystals, all of the concepts described in this and the following section can also be applied to coherent CBED patterns if the diffraction orders do not overlap. CBED is an extraordinarily efficient technique. The wide range of illumination angles used provides a large amount of information (in the form of rocking curves) from many diffracted orders, presented simultaneously, from the smallest possible region of crystal. Different regions of the pattern are sensitive to different crystal parameters; the following is a summary of all of the information that can be extracted from incoherent CBED patterns. The outer reflections and higher-order Lave zone (HOLZ) line intensities are sensitive to atomic position parameters and temperature factors, the inner reflections to interatomic bonding effects, and the inner HOLZ lines crossing the central disk may be used to determine lattice parameters, to find the Bravais lattice, and to measure local strains. The whole pattern may be used to determine the crystal space group. Two-beam patterns can be used to make quick estimates of crystal thickness in crystals with small primitive unit cells. In this section we discuss the relevant theory for extracting this information; in the next we summarize some recent applications that demonstrate the power of the method. To summarize, CBED patterns are exquisitely sensitive to the details of the Coulomb potential in crystals. By comparing computed and experimental patterns, these details may be extracted. The crystal charge density (as measured by X-ray diffraction) is related to this potential by Poisson's equation, if the nuclear contribution is first removed. If the charge

26

NANODIFFRACTION

density is parameterized in terms of atomic coordinates, multipole expansions, DebyeWaller factors, strains, or bond charges, then a limited number of these parameters may be refined, depending on the size and power of available computers. Because of this limit, no general method for solving unknown crystal structures by electron diffraction has been devised; however, few-parameter structures may now be solved in many cases. In Sections 5 and 6, the term "refinement" means a quantitative comparison of experimental elastic energy-filtered microdiffraction patterns with calculated patterns, using methods closely similar to the Reitvelt method of neutron diffraction, and including all multiple scattering effects. The comparison is based on a goodness-of-fit index, using standard least-squares optimization methods. With a few important exceptions (see Section 5.6), the atomic positions have been known in all previous work, so that refinement consists of adjusting the other parameters listed above for the best fit. Because global minima are most likely to be found if the starting parameters are close to their final values, the crystal structures that have been solved by CBED have so far been simple, few-parameter structures. 5.2. Excitation Errors and Calibration of Data

A quantitative analysis of CBED patterns is only possible if a unique excitation error Sg has been assigned to every point on the experimental pattern. (For two-dimensional patterns it is more convenient to use the value of Kt, the tangential component of the incident electron beam wave vector, as discussed further below.) The excitation error is a measure of departure from the Bragg condition and measures the distance from a reciprocal space point to the Ewald sphere in the direction of the surface normal. Computed intensity distributions can then be compared with the experimental pattern; these are generated as functions of Sg (or Kt). The resulting method has become known as quantitative convergent-beam electron diffraction (QCBED). Figure 13 shows a simplified ray diagram for QCBED. We assume initially that the pattern comes from a known crystal structure and has been indexed. Each point in the pattern (e.g., P') defines a unique plane-wave component of the incident beam (e.g., from direction P) and a family of conjugate points, one in each diffracted disk, to each of which an excitation error Sg can be assigned. Figure 14 shows how this is done, using the relation

S g ,~ 2 0Bot/ ~. ,~ got

(26)

Here the excitation error Sg is defined in terms of the deviation angle c~ from the Bragg angle. The component of the incident wave vector K0 (see Fig. 14) that lies in the plane of the crystal slab is Kt. Figure 15 shows an experimental energy-filtered CBED pattern for the (111) systematics reflections in silicon. The accelerating voltage was measured (as described below) as 196.15 kV, corresponding to a nominal setting of 200 kV. Excitation errors must be assigned along the line shown. For the more general case of a two-dimensional pattern, the excitation errors could be assigned to each point in the experimental pattern using

2K Sg -- - 2 K t . g - g2

(27)

However, it is simplest to start by determining the value of Kt that defines the center of the Laue Circle for the central point of the CBED pattern in the (000) disc, as shown in Figure 16. This circle is formed by the intersection of the Ewald sphere with the zeroorder Laue zone (ZOLZ), or plane of reflections approximately normal to the beam. Kt is a two-dimensional reciprocal-space vector in the ZOLZ that runs from the center of the circle to the origin of reciprocal space. The circle can often be seen as a bright ring of reflections passing through the origin, allowing an approximate assignment of Kt by inspection. Different values of Kt can then be assigned to every pixel of the experimental pattern within the central (000) disk. The Bragg angle and the electron wavelength must be accurately known.

27

COWLEY AND SPENCE

source

Probe-forming lens Jq

~

final condenser lens aperture C2

Electron probe

It Ii '~x ttt

X

\

X=Lg~, Fig. 13. Simplified ray diagram for convergent-beam electron diffraction. If only elastic Bragg scattering is allowed, source point P gives rise to conjugate points pt, one in each disk. Source point Q defines a different incident beam direction and set of diffracted beams Qt. The camera length is L. g is a reciprocal lattice vector; is the electron beam wavelength.

K

\\x x

Off B r a g g

rao

-.,

t

j

g

,~A

|

Fig. 14. Two Ewald sphere orientations differing by c~, just off (continuous lines) and on (dashed lines) the Bragg condition. Note the direction of Kt. The excitation error is Sg.

28

NANODIFFRACTION

Fig. 15. Silicon (111) systematics at 196.15 kV. The bright disc is (000). Fine HOLZ lines can be seen running parallel to the straight line drawn across all of the disks, for which the intensity is shown in Figure 17.

ES

Fig. 16. The Laue circle in the ZOLZ. The definition of Kt is indicated, with the electron beam wave vectors K and K 0.

5.3. Many-Beam Theory M a n y s o f t w a r e p a c k a g e s are n o w available that solve Eq. (17) for the e i g e n v e c t o r s C~j) and e i g e n v a l u e s k (j) - K + y(J)n, w h e r e n is a unit v e c t o r in the direction o f the surface n o r m a l and K 2 _ K~ + U0. It is c o n v e n i e n t to define d y n a m i c a l structure factors as

ug - ~ v~ / ~

29

COWLEY AND SPENCE

_'

-

' ''I

'"'

I''

''i'''

'I

''''I''

''i

""''

I'

~"i

i

' I''

'

i

Fig. 17. A comparison of experimental (dots) and calculated intensity (arbitrary units) along the line drawn in Figure 15 for the elastically filtered Si (111) systematic Bragg reflections. With this agreementbetween theory and experiment it is possible to measure structure factors to an accuracy of 0.1% in the most favorable cases, which is sufficient to directly observethe bonds in the resulting charge density map of a crystal.

In terms of these quantities, the intensity diffracted by a thin slab of crystal traversed by a collimated electron beam in direction g is

Ig(Kx, Ky) --I~g(t)l 2 = ~ Coi-1 Cgi exp(27riyit) n

12

(28)

i=1 The direction of the incident beam is defined by the two components Kx, Ky of Kt, which also defines a family of conjugate points, differing by reciprocal lattice points, one in each CBED disc g. The preceeding equation, for given Kt, therefore gives the intensity for one pixel in every Bragg disc. The variation with Kt gives all of the other pixels. A FORTRAN source-code listing for a computer program to calculate these CBED intensity distributions Ig (Kt) is given by Spence and Zuo [5]. This program includes the effect of HOLZ lines (three-dimensional diffraction) and absorption (depletion of the elastic wave field by inelastic scattering) and may be applied to noncentrosymmetric crystals. A more recent program, in which this many-beam code is combined with a least-squares optimization routine to facilitate matching experimental and computed images, is described in a paper by Zuo [60]; that paper contains references to earlier work. The most recent and most efficient version is described by Zuo [61 ]. Figure 17 shows the result of using this program to fit the experimental data in Figure 15.

5.4. Two- and T h r e e - B e a m Theory

A better understanding of the way in which information can be extracted from CBED patterns can be obtained by considering the case in which the preceding many-beam equation contains only two dominant terms from beams with intensities I0 and Ig. Then expressions for the eigenvalues and eigenvectors are available in closed form, and we obtain the intensity Ig as a function of sample thickness t, structure factor Ug, accelerating voltage, and

30

NANODIFFRACTION

Sg"

excitation error

IUgl2sin2[-~n~K2S2 + lUgl2] Ig

-

KZS2 .+. IUg[2

[Ugl2sin2(ntAy) =

(Kn Ay)2

(29)

with

Io---1- Ig By fitting this curve to the distribution of intensity in a CBED disc around the Bragg condition, both the structure factor Ug and sample thickness t can be found. The usefulness of this two-beam expression is that it allows one to determine the most sensitive conditions of, say, beam energy, thickness, and orientation at which to measure a structure factor Ug. Because the excitation of more than two beams cannot be entirely prevented (e.g., by choice of orientation), it cannot be used for accurate quantitative work. Because the three-beam case can also be solved in closed from, a similar but more complicated expression can be found for that case. A paper by Zuo et al. [62] contains a complete derivation, with full references to important earlier work by Kambe, Gjonnes, Moodie, and others. This result becomes important for the case of noncentrosymmetric crystals, for which the phases of the complex, origin-dependent Ug values must be determined to define the crystal charge density or structure. (The two-beam result is not sensitive to this phase unless absorption is included.) The three-beam result can then also be used to determine the region of a CBED pattern that is most sensitive to a particular phase invariant. These regions, or eigenvalue degeneracies, have been studied in great detail and form the basis of both the critical voltage method and the intersecting Kikuchi line method (see, for example, [63] for an illuminating application to SiC and references to earlier work). A remarkable recent finding is that there are certain lines within three-beam patterns along which the intensity can be described by the two-beam form (Moodie et al. [64]). 5.5. The Relationship between X-ray and Electron Structure Factors

A useful relationship between X-ray scattering factors fi x (s) and electron structure factors Vg was obtained by both N. Mort and H. Bethe as

.el Vg-

z ( (Zi - fiX(s)))

16zr2eof2 .

s~

exp(-Bis2)exp(-2zcigri)

l

h2

:

FB 8rceomelelf2 g

(30)

Bi --87r2(u

where s --sin0B/~. = [g[/2, and the Debye-Waller factor 2) has been introduced for species i, where (u 2) is the mean square vibrational amplitude of the atom. If B, s, and the unit cell volume f2 are given instead in angstrom units, then Vg is given in volts as

Vg =

[Zi --S2fix(s)]exp(-Bis2)exp(-2zrigri)

1.145896f2~

i --

47.878009 F8 ~

(31)

g

This equation allows electron "structure factors" Vg and Fg to be evaluated from tabulations of X-ray atomic scattering factors f/x (s) if Bi is known. Two other quantities commonly used in the literature are Ug and the extinction distance ~g, given by

Ug=

vF~ 2mlelVg = rcf2 h2

31

COWLEY AND SPENCE

and

I)

(32)

where 7 is the relativistic constant.

6. APPLICATIONS OF CBED 6.1. Space-Group Determination and Phase Identification In all but a few cases, the space group of a microcrystal can be determined by study of the symmetry of its CBED patterns. This can be useful for phase identification, by eliminating possibilities when used in conjuction with the X-ray powder diffraction file. The general procedure is as follows. First, the point group is determined. Then the Bravais lattice centering is obtained. Finally, the translational symmetry elements are identified. This information then defines the space group in almost all cases. CBED patterns recorded in the zone-axis orientation (Kt = 0) reveal directly the mirror and rotational symmetry elements present in the two-dimensional crystal structure when projected along particular zone axes, if detail due to HOLZ interactions is ignored. (The HOLZ detail consists of very fine lines, readily distinguished from the slowly varying ZOLZ intensity distribution.) The HOLZ detail reveals similar symmetry elements present in the threedimensional crystal structure. Additional tests can be made for the presence of a center of symmetry, because Friedel's law does not apply to dynamical electron diffraction. The lattice centering is found by projecting the HOLZ spots onto the ZOLZ. Finally, certain remarkable dynamical extinctions can be used in the last step to reveal the presence of glide and screw symmetry elements, thereby determining the entire space group in most cases. Handedness (enantiomorphism) can also be determined [65]. A more systematic procedure based on diffraction tables has been developed by the Bristol group in the England. The approach is summarized with worked examples and full references to earlier work [66] (also [5]). Thus, for example, determining which of the 32 point groups a crystal belongs to might involve the following three steps: 1. Determination of the symmetry of the projection diffraction group, using ZOLZ detail 2. Determination of the diffraction group, using HOLZ detail 3. Determination of the point group from the above information, using tables This determines in turn the crystal class. The next step involves determination of the Bravais lattice, centering, and indexing of the pattern, to determine the crystal system. Methods for doing this are described in two texts [5, 66] and by Ayer [67]. The principle of the method for determining centering is to analyze a zone axis pattern showing both small ZOLZ spots and sharp HOLZ rings. By extending the mesh of HOLZ spots over the ZOLZ spots, it is possible to tell whether the lattice is P, F, or I. The diameter of the firstorder Lave zone (FOLZ) gives the height of the FOLZ, from which the three-dimensional reciprocal lattice vectors can be deduced. A new automated method for obtaining the Niggli cell, based solely on the three-dimensional HOLZ lines in the central disk, is described by Zuo [68]. By using only measurements close to the optic axis (where electron-optical distortions are small), this method is considerably more accurate. Finally, the existence of screw and glide elements allows one to determine which of the 230 space groups the crystal belongs to. These translational symmetry elements are detected by the absence of certain special kinematic reflections (listed in texts on X-ray diffraction) that remain forbidden (despite the effects of multiple electron scattering) for all crystal thicknesses and accelerating voltages. This occurs because of the cancellation of multiple scattering

32

NANODIFFRACTION

on paths symmetrically related by crystal symmetry. The application of this method is described again in the above texts and by Eades [69]. In practice, when confronted with an unknown crystal, one looks initially for mirror lines of symmetry, possibly in the Kikuchi pattern. A double-tilt stage with a large tilt range is essential. A quick look over the full allowable angular excursion of the stage should reveal the main high-symmetry axes. If no mirror lines are seen anywhere, the crystal is likely to be triclinic. Once a mirror line is found, one can tilt along it to find the intersection with other symmetry elements. Rotation axes normal to any mirror line may exist. A condenser aperture should be used that causes the disks to just touch for the largest lattice spacing.

6.2. Measurement of Strains and Accelerating Voltage Using the fine HOLZ lines that cross the central disk of a CBED pattern (see Fig. 15), it is possible to measure lattice strains from regions of crystal whose dimensions are somewhat larger than the probe width and average through the thickness of the sample. (The uncertainty principle relates the width of a HOLZ line to the width of the crystal which contributes to it. Thus, for a HOLZ line one-tenth of the width of the central disk, the contributing width of the crystal is 10 times the width of an ideal diffraction-limited probe. The "width" of the crystal must be measured normal to the HOLZ planes [70].) Strains cause the fine HOLZ lines to shift about laterally relative to the ZOLZ intensity distribution, and this effect can be quantified. Using Vegard's law, these strains may be related to compositional variations. The smallest strain that can be measured is about 0.0001, however, there are a number of complications (see Lin et al. [71] for a summary). (i) The strains measured may have resulted from the thinning process. This problem may be addressed by using thicker samples and higher accelerating voltage, combined with finite-element modeling of the thin-film elastic relaxation [72]. (ii) The HOLZ line positions are about equally sensitive to the accelerating voltage and to strains. The strain Aa/a due to an angular shift A0 in a HOLZ reflection g may be estimated from

Aa a

AO =

AEo

0 = 2E0-

Ag g

2Kov --

g2

(33)

From this we see that the sensitivity of HOLZ line positions to strain increases with accelerating voltage and angle, so that the highest-order HOLZ lines should be used. HOLZ lines become sharper in thicker crystals. If these are faint, a cooling holder and energy filter will increase their contrast. In an instrument fitted with continuous accelerating voltage controls, strain may be measured directly at the microscope in cubic crystals by restoring a HOLZ line pattern to its reference shape for the unstrained crystal and noting the voltage change A E0 needed to do this. Because a fractional change ,5 in lattice spacing produces a fractional change A / 2 in accelerating voltage, it is clear that HOLZ lines may provide a rather accurate method of relative strain mapping; however, the "dynamical shifts" discussed below must be considered. In the general case involving noncubic crystals, it would be necessary to measure all of the independent lattice parameters allowed by the symmetry to fully characterize the strain. (The maximum number is six, three cell constants and three angles, however, a frequently used assumption is that the lattice expansion is isotropic, so that no symmetry change is involved.) (iii) Multiple scattering can shift the positions of HOLZ lines from that predicted by Bragg's law. The simplest demonstration of this effect occurs if Bragg's law is used to determine accelerating voltage, using the HOLZ lines seen at three different major zone axes of the same silicon crystal. The results vary by several kilovolts, because of "dynamical shifts." The effect has been analyzed in detail using three-beam theory and may be avoided to minimize the excitation of strong beams. This suggests the use of orientations near sparse zone axes for greatest accuracy. A detailed analysis is given by Zuo [73]. Here

33

COWLEY AND SPENCE

variations in the a/b cell constant ratio were mapped out for YBa2Cu307-8 to measure the local oxygen deficiency 3. An orientation that minimizes the excitation of strong ZOLZ reflections was used, and the method of Bethe potentials was incorporated to allow for these. Using digitized patterns and a Rietvelt-type analysis, with a goodness of fit index, it was possible to measure the accelerating voltage to an accuracy of 14 V and the cell constants to accuracies of 0.001 and 0.0006 ,~. As an example, the resulting oxygen deficiency responsible for the strain was found to be 0.1 in one local region. The measurement of local lattice spacings, using QCBED, is discussed in detail by Zuo et al. [74]. All of the preceding methods may also be applied to coherent nanoprobe patterns (provided that the orders do not overlap). An example of strain measurement in Si/Si-Ge layers based on coherent microdiffraction patterns can be found in [75]. By using an out-of-focus electron probe, it is possible to superimpose the HOLZ lines on a shadow image of the sample, thus combining, in one image, strain measurement and realspace imaging at limited resolution. The history and applications of this "convergent-beam imaging" (CBIM) approach may be traced through Humphreys et al. [76]. The method is closely related to the formation of ronchigrams and large-angle CBED patterns. The source code for a FORTRAN program that will plot the kinematic positions of HOLZ lines can be found in Spence and Zuo [5]. If a small time-dependent variation in one of the lattice constants (or cell angles) is added before the pattern is displayed, it will immediately become clear from the resulting wobble in some line positions which lines are most sensitive to given cell constants or angles. In this way the best choice of orientation can be made. We may conclude that high accuracy in the measurement of lattice parameters or accelerating voltage can be achieved only at the cost of considerable computational effort. The average composition and structure factors must be known (because changes in composition affect any coupled low-order reflections, and hence the "dynamical shifts"), and thin-film relaxation effects may pose the greatest problem in many materials, depending on elastic constants, specimen geometry, and chemical inhomogeneities. (Spinodal decomposition in a thin film, for example, causes a characteristic elastic relaxation.) Some rather rough conclusions may be drawn, however. At about 100 kV, and ignoring thin-film relaxation and atomic number and density effects, strains and accelerating voltages may be determined to about one part in 100 at best with straightforward application of the Bragg law; they may be determined to about one part in 1000 at best by using the perturbation corrections (Bethe potentials), and they may be determined to perhaps one part in 10,000 at best by using a full dynamical refinement of the type discussed in later sections.

6.3. Measurement of Sample Thickness If the crystalline sample has a small primitive unit cell, it is usually possible to set up strong two-beam conditions. Then the two-beam expression for intensity given above may be used to analyze the intensity distribution across the CBED disk that lies at the Bragg condition. From this two-beam expression, we find that the thickness, extinction distance, and excitation error are related by 1

+

t2

(34)

where Si is the excitation error at the ith minimum, and t is the effective specimen thickness along the beam direction. A plot of (Si/ni) 2 against (1/ni) 2 therefore gives ( l / t ) 2 as the intercept and hence the thickness. The slope gives (1/~g)2, and hence ~g, from which IUgl may be obtained. To obtain the values of Si at the minima, the pattern must be calibrated (i.e., the beam direction must be found at each point), as discussed in Section 5.1. The values of ni are obtained by trial and error~the correct starting value is that which produces a straight-line plot. The method and its history are reviewed, and sources of error analysed, by Ecob [77]. Clearly this method is a more limited form of the general refine-

34

NANODIFFRACTION

ment techniques described below, and the excitation of additional reflections can form a major source of error.

6.4. Measurement of Debye-Waller Factors The Debye-Waller factor enters in two places in the dynamical theory of electron diffraction. By multiplying the electron scattering factors, the temperature factor controls the width of the atomic potential, which becomes wider at high temperatures. Second, a study of few-beam solutions shows that the temperature factor also occurs as an exponential damping on the thickness dependence of the diffracted intensities. We could think of this loosely as an inelastic mean free path. The temperature dependence of electron structure factors for an isotropic, centric crystal containing only one type of atom can be written as Ug(tOt)-

Ug exp(-Bg2/4) + Ug (phonon)

(35)

where B = B(T) is the Debye-Waller factor. By measuring the intensity of several reflections (particularly high orders) as a function of g, it is possible to measure B by using electron diffraction data. Measurements may also be conducted at several temperatures. In centric crystals, the Debye-Waller factor affects the real (elastic) potential, and therefore the ratio of maximum to minimum intensity in a CBED rocking curve, and, most sensitively, the intensity of the high-order reflections. On the other hand, the absorptive effects for beam g are best measured from the asymmetry of the zero-order disk, with beam g at the Bragg condition. The two effects may therefore be separated in centric crystals. The influence of bonding effects may be disentangled from the Debye-Waller effect by matching reflections as a function of g; high-order reflections are more sensitive to the latter and low orders to the former. Both the critical voltage effect and the intersecting HOLZ (or Kikuchi line) methods have also been used to measure Debye-Waller factors. These depend sensitively on temperature, because the intersecting Kikuchi line (IKL) gap and the critical voltage both depend on the real part of the structure factor in centric crystals. Alternatively, temperature may be used to fine-tune patterns near the critical voltage. In recent work, both critical voltages and Kikuchi line splittings for Si, Ge, A1, Cu, and Fe have all been measured as a function of temperature [78]. These workers find that the anharmonic contribution to the temperature factor in the metals is readily detectable above 300 K but is small for the semiconductors. An example of the use of automated refinement of high-order reflections for the purpose of measuring Debye-Waller factors can be found in Holmstad et al. [79]. Here the many-beam pattern-matching method described in the next section is used.

6.5. Determination of Atomic Positions by Convergent-Beam Electron Diffraction Broadly speaking, there have been two different approaches to the problem of solving crystal structures by electron diffraction. First, for organic membranes that form twodimensional crystals whose thickness is a single unit cell, considerable success has been achieved using low-dose techniques and the single scattering or kinematic theory. Both image data (to provide structure factor phases) and selected-area diffraction patterns are used. This method has recently been extended to extremely thin inorganic crystals, in conjuction with both the maximum entropy method, and the "direct methods" of X-ray crystallography for phase determination (for a review, see Dorset [80]). These techniques work best for large unit-cell crystals that form layer compounds, so that extended regions of constant thickness (a few nanometers thick at most) can be found. The aim is to obtain a trial structure for futher refinement, and the variations in thickness under the illuminated region, the perturbing effects of multiple scattering, and curvature of the Ewald sphere are the main difficulties.

35

COWLEY AND SPENCE

A second approach may be based on the microdiffraction patterns described in this chapter. Then, because a subnanometer probe may be used, the variation in thickness under the probe is not a problem, and because multiple scattering calculations are used, neither are perturbations due to multiple scattering. The method can be used to analyze microphases whose volume is too small to produce a useful selected area pattern for the kinematic method. However, the CBED refinement technique depends for its success on the rapid variation of diffracted intensity within each diffracted order, as shown in Figure 15. It follows that the method fails if this intensity varies slowly on the scale of the Bragg angle--in that case there are no subsidiary minima within the rocking curve to be used for matching against calculations. The envelope of all of the intensity oscillations has a width of 1/~g in the two-beam approximation, around the Bragg condition. The ratio of the angular width of the rocking curve to the Bragg angle is thus proportional to the relativistic factor y and so increases with accelerating voltage. In practice this means that refinement is only possible for crystals with rather small primitive unit cells that are insensitive to radiation damage. Thus, most of the work on "solving" crystal structures by CBED has been applied to inorganic structures such as ceramics, new semiconductor phases, or intermetallic compounds that have been found as unknown microphases in a known parent phase. A second limitation concerns the number of parameters that can be refined. In addition to the atomic position parameters (structural parameters), it is always necessary to refine the sample thickness, accelerating voltage, and the four endpoint coordinates of the intensity scan that describe the beam direction (geometric parameters). Thus even for a one-parameter structure, one has a minimum of seven parameters to adjust in each N-beam dynamical computation, with N typically less than 100 in the initial stages. Absorption parameters may also require refinement. Because each N-beam computation takes several minutes, both computing time and the problem of false minima in optimization must be considered. A separate diagonalization of an N • N matrix is required for every incident beam direction if perturbation methods are not used. Details of one computer program that combines an N-beam Bloch-wave program efficiently with an optimization routine are given by Zuo [60], and a FORTRAN listing of the Bloch-wave portion is given in Spence and Zuo [5]. The goodness-of-fit parameter used is

X 2 ._ ~

f / . (r i

_ iexp)2 0"2

(36)

where the experimental CBED intensities are given by i?xP, and the calculated points by

theory . The fi is a weight coefficient, that can be adjusted to increase the importance

Ii

of certain contributions to X2 that are sensitive to particular parameters. Here or/2 is the variance of the ith point, which can be measured from successive experiments or by using ~r2 = lexp "i , assuming Poisson statistics. Furthermore, c is a normalization coefficient, which can be found by either normalizing the theory and experiment at a particular point, or by taking the first-order derivative of X2. In much of our work we have found the Simplex algorithm to be the most robust (if not the fastest) method for finding minima in X2. No algorithm can guarantee finding a global minimum. The entire refinement should be repeated, using different starting parameters to confirm that a minimum is not local. For a completely unknown inorganic structure, much preliminary information can be obtained by CBED, including the space group and the cell dimensions and angles. A rough estimate of the number and type of atoms present can be obtained using energy-dispersive X-ray microanalysis or energy-loss spectroscopy. A vital piece of information for which no method exists at present is the determination of the density of a small microphase. Tables of bond lengths and lattice images can provide additional information. See Eades [81 ] for an example of a structure solved in this way. In favorable cases it can be argued that the weakly excited HOLZ reflections in the outer tings of the diffraction patterns may be kinematic and so give a rough estimate of structure factors directly. (Accurate values of intensities are not

36

NANODIFFRACTION

always needed to solve structures--likely structures can often be distinguished by grouping reflections into classes of strong, medium, and weak.) In general, the refinement for atomic positions concentrates on the medium- and high-order reflections, whereas bonding studies are concemed with the lowest orders. As an example of the CBED approach based on quantitative refinement, we cite the examples of the measurement of the slight rotation of the oxygen octahedra that occur in SrTiO3 [82], and a recent one-parameter refinement of 4H SiC [83]. The silicon carbide analysis is typical of problems in which there are intergrown polytypes that cannot be analyzed by other methods. The 4H variant of SiC is a hexagonal structure with stacking sequence ABACABAC... It may be approximated by a one-parameter structure, the distance z between the Si and C atoms. Simulations were used to determine the reflections most sensitive to this parameter, and elastic energy-filtered CBED pattems were recorded in these reflections for refinement. In such favorable cases, atomic coordinates can be measured to within an accuracy of about 0.0001 ,~ or better, depending on sample quality, accuracy of Debye-Waller factors, and detector characterization (see Note Added in Proof).

6.6. Bond-Charge Measurement by Convergent-Beam Electron Diffraction and Effects of Doping on Bonding In a similar way, low-order crystal structure factors may be treated as refinement parameters rather than atomic positions. This is particularly important for noncentrosymmetric (acentric) crystals, in which structure factor phases are needed to obtain a charge density map of the crystal. For bonding studies, one fixes the atomic coordinates and adjusts only the low-order structure factors (and absorption coefficients) until a minimum is found in X2. For acentric crystals, the structure factor phases and complex absorption coefficients become entangled, but may be disentangled if measurements are made separately for conjugate reflections. An example is found in the measurement of the phase of the (002) and (004) reflections in BeO (wurzite structure) [84]. Here it proved possible to measure phase angles to an accuracy of better than one-tenth of a degree, far better than is possible by any other method. (X-ray many-beam experiments achieve accuracies of about 4-45 degrees in phase measurement.) For certain centric crystals it has also proved possible to improve considerably on the accuracy of X-ray work. A tenfold improvement in the accuracy of structure-factor measurement was recently reported for MgO [85]. This proved sufficiently accurate to distinguish between atomic, ionic, and crystal (band-structure) models of the charge density for the first time and to distinguish (for certain reflections) between the predictions of the local density approximation (LDA) and the more recent generalized gradient approximation (GGA). The resulting charge density map may be used to determine the charge transfer between atoms, to determine the validity of the ionic model, to refine a multipole analysis, and to indicate regions of nonspherical charge density. Figure 18 shows the charge-density difference map for a section on (100). Regions of nonspherical charge density can be seen. In a this way, questions such as How ionic is MgO and What is the hole distribution in YBa2Cu307-8 may be answered. In addition, QCBED provides a test for theories of many-electron effects in crystals, such as the local density approximation. As originally pointed out by H. Bethe, the structure factor most sensitive to bonding effects is the average value of the Coulomb potential, or mean inner potential V0. A full analysis of this effect, including measurements and comparison with calculations, is given by O'Keeffe and Spence [86]. CBED is also sensitive to the effects of dopant atoms. If the approximation is made that low concentrations of doping atoms produce a small average change in all structure factors, it becomes possible to compare charge-density maps for the same crystal, with and without the addition of the dopant atoms. The difference between these may be interpreted as indicating the effect of doping on bonding. This has been done for the case of the

37

COWLEY AND SPENCE

-')t

711) 't~"~m

-_. e~ ,, t ! i l /

~

tt\t

-~

\ \ k \t \

L J ~\\~..~..... j j i t j , k ~1 I" I

0

'

I

25

i

\ \Jl I

50

I'

t\

~

)l

_

;) i f/~._._ I'"

1

75

Fig. 18. Charge density for MgO on (001), as measured by CBED. The increment between contours is 0.03 e-//k 3. Dashed lines indicate less charge than reference atoms, continuous ones excess. Oxygen lies at comers and center, Mg in middle of edges. The cell constant is 0.421 nm.

intermetallic alloy g-TiA1, where it was suspected that the reduction in brittleness due to the addition of 5 at% Mn arose from reduced covalency [87]. CBED refinements for doped and undoped crystals were compared, and a change in covalency was observed in measured charge-densities. Atom location by the channeling-enhanced microanalysis (ALCHEMI) method was used to locate the dopant atoms [88].

6.7. Instrumentation for Quantitative Convergent-Beam Electron Diffraction The accuracies cited above for QCBED work have only become possible within the last decade, since the development of commercial energy filters for electron diffraction. These allow electrons that lose more than a few electron volts when traversing the sample to be excluded from the measurements. A typical modern QCBED system might be based on a field-emission TEM/STEM instrument fitted with either an in-column or post-column imaging energy filter, and a liquid-nitrogen-cooled double-tilt goniometer with large angular range. The cooled holder is essential for reducing contamination. The use of chargecoupled-device (CCD) detectors in conjuction with single-crystal YAG scintillators has also become common: when combined with an imaging filter, this allows rapid parallel detection of the entire filtered CBED pattern in a single exposure. However, the CCD systems introduce many imperfections into the data, and each CCD camera must be individually characterized for QCBED work, and this information is used to correct the detector response by deconvolution. (Deconvolution of the modulation transfer function of the detector system is possible without noise amplification, because it is the low, rather than the high, spatial frequencies that must be corrected.) The modulation transfer function (MTF), detective quantum efficiency (DQE), and sensitivity of the detector must all be carefully measured. Full details of the techniques used to do this are given by Zuo [89]. A comparison with the newer "Image Plate" recording devices is given by Zuo et al. [90]. The accelerating voltage must be measured (e.g., using silicon as a standard sample) by refinement of HOLZ line positions. We have found that this calibration of the microscope must be repeated every few months, and that the MTF functions for similar CCD cameras from the same manufacturer may differ significantly. Incomplete deconvolution of the detector response function has a large effect on the minimum value of X2 obtainable.

38

NANODIFFRACTION

7. THEORY OF NANODIFFRACTION 7.1. Coherent Nanodiffraction: Overlapping Disks

In Section 4.2, it was assumed that, for a sufficiently thin sample, the wave leaving the specimen may be described in terms of a transmission function, q(x, y), multiplying the incident beam wave function, t (x, y), which is the spread function, given by Fourier transform of the transfer function of the objective lens, T (u, v). Then, as in Eq. (22), the intensity distribution of the nanodiffraction pattern seen on the plane of observation is

I(u, v ) = Ia(u, v) 9 T(u, v)exp{27ri(uX + vY)}[ 2

(37)

where Q(u, v) is the Fourier transform of q(x, y), and X, Y is the incident beam position relative to some suitable origin. For the special case of a weak-phase object, for which Q(u, v) = 6(u, v) - icr~(u, v), as in (7), Eq. (37) becomes, I (u, v) - IT(u,

v)12

+ 2RT*(u, v)[exp{-Z.Tri(uX + vY)}] • [ - i o ' ~ ( u , v ) . T(u, v)exp{2rci(uX + vY)}] + ]~r~(u, v) 9 T(u, v)exp{ZTri(uX + vY)}] 2

(38)

where R signifies the real part of the function. The first term of (38) is just the aperture function, A(u, v), which is equal to A2(u, v), and represents the central beam disk of the diffraction pattern. Because the second term is multiplied by T* (u, v), which contains the aperture function A (u, v), this term is zero outside the central beam disk and represents the modulation of the intensity within the central beam disk caused by interference of the zero beam with the diffracted waves. This term is essential for the considerations of bright-field imaging, electron holography, and related affairs, for which the phases of the amplitudes, ~(u, v), relative to that of the incident beam, are significant. The intensity of the diffraction pattern observed outside the central disk is given by the last term of (38). For example, if the specimen is a very thin perfect crystal, qg(x, y) is represented by a Fourier series, as in (8), and the last term of (38) becomes

l(u, v) = Z c r ~ h , ~ 6 h,k

(

u -- --, v -a

9 T(u, v)exp{2rci(uX + vY)}

i

(39)

which gives the intensity within the diffracted beam disks (including the zero beam disk for which h, k = 0). If the diffraction disks do not overlap, the cross-product terms in (47), coming from different h, k pairs, are all zero. Then (47) becomes simply

l(u, V) = Zcr21~h,k123(u -- h/a, v - k/b) 9 A(u, v)

(40)

h,k

that is, the diffraction disks are plane, uniform disks with intensities proportional to the kinematical hkO diffraction intensities. If the diffraction disks overlap, however, the cross-product terms of (39) give interference fringes in the areas of overlap. For example, for the overlap of the h, 0 and h + 1, 0 reflections, ignoring the k index, we may find the intensity relative to the midpoint of the overlap region, so that u = (h + 1/2 + e), as [ , (1 ) (1 ) { ( 1 ) } ] l ( e ) = 2 R ff 2 dph ~ h,k+ l T -~a .-k-e T* -~a - e exp 2rri - + e X a

(41)

Within the area of overlap of the disks,

1

e)T(~--d-e)=exp

[(9+

39

4a3)e+

a

e3]}

(42)

COWLEY AND SPENCE

Then, if the relative phase of the h and h + 1 reflections is given by the angle or, and we consider the case in which e is small and the defocus A is large, the intensity within the area of overlap of the disks is

I(X,e) = 2tr2l~hll~h+llCOS 2rr

+or + --a-e

(43)

Thus the areas of overlap of the disks are crossed by fringes with a periodicity that decreases with the defocus. Such fringes have been shown very clearly in CBED patterns obtained in TEM instruments equipped with FEGs to give the required coherence [91, 92]. It may be noted from (43) that if a small detector is placed anywhere within the area of overlap (for any e value), and the incident beam is scanned over the specimen to vary X, the signal recorded oscillates with X with a periodicity a, so that the STEM image shows lattice fringes [93]. It may readily be seen that this STEM configuration is exactly equivalent, by the reciprocity relationship, to the standard method for generating lattice fringes in TEM images by tilting the incident beam by the Bragg angle with respect to the lattice planes and detecting the beam traveling axially along the objective lens axis. Another point to be made from (43) is that, for any e value, say e = 0, the relative phases of the two reflections, ct, may be deduced for a known beam position, X. Hence, if the variations of the intensities at the midpoints of all regions of beam overlap in the diffraction pattern are observed as a function of X, the relative phases of all reflections may be deduced. In this way the complex amplitudes of all of the coefficients of the Fourier series for the projected potential of the structure may be derived and a complete, unambiguous structure analysis may be performed. The possibility that such a structural analysis could overcome the "phase problem" of normal X-ray or kinematical electron diffraction structure analyses was realized many years ago [94, 95]. However, experimental problems and the limitations of the WPOA have prevented its experimental realization. If the WPOA is not valid, as in the case of most crystalline samples, then the Fourier coefficients, ~Ph,k in (39) become the Fourier coefficients of the periodic wave at the exit face of the crystal. From the observations of the interference fringes in the overlap areas of the CBED disks it may then be possible to deduce the amplitudes and phases of these Fourier coefficients, but the problem then remains of inverting the many-beam dynamical diffraction processes in the crystal to deduce the potential distribution of the crystal [5, 96]. This inversion process is a fundamentally difficult one. Some solutions have been proposed [97, 98], but no convenient practical method has yet been described. From (42) it is seen that, close to focus (A small), the interference fringes in the areas of disk overlap are distorted by the effects of the spherical aberration, as shown in Figure 19. These distortions do not necessarily complicate the deductions of relative phases discussed in the previous paragraph. They are best discussed, however, in relation to the more general observation of "Ronchi fringes" in the next section.

7.2. Symmetry of Coherent Nanodiffraction Patterns When the incident beam diameter is smaller than the repeat distance of the projection of a crystal structure, there is multiple overlapping of diffracted beam disks. The periodicity of the crystal projection may no longer be obvious in the diffraction pattern. The intensity distribution depends on the structure of the region of the crystal illuminated by the beam and so can be seen to change as the beam is translated [46, 47]. In particular, the symmetry of the diffraction pattern may no longer display the symmetry elements of the crystal structure, as in the case of the incoherent CBED patterns discussed in Section 5. The pattern symmetry depends on the symmetry of the region illuminated by the beam and so is independent of periodicity. It is the same whether the group of atoms illuminated is part of a perfect crystal, part of a defect in a crystal, or part of an amorphous material.

40

NANODIFFRACTION

Fig. 19. Interferencefringes in overlapping diffraction disks for MgO (000) and (200) reflections near the in-focus position, showing the deformation of the interference fringes due to spherical aberration for two different values of the defocus. CompareFigure 23a.

A well-known result of kinematical diffraction theory is that the diffraction pattern always has a center of symmetry, whether the sample has a center of symmetry or not. This result applies to nanodiffraction only in the case of the WPOA, and then only in special cases when the only term considered in the intensity expression (38) is the final, secondorder term. The second, first-order, term of (38) represents the interference of the incident beam and the diffracted beams within the central-beam disk to give intensifies depending on the relative phases of these beams and is essentially nonsymmetric. The final, second-order term of (38) can approximate to centro-symmetric only under special circumstances. If, for example, the objective aperture is small so that, for small amounts of defocus, the sin X (u, v) function is negligibly small within the aperture, then the T (u, v) function is real and positive, and if X, Y = 0, the last term has the same symmetry as ~ ( u , v) and this part of the intensity expression is centro-symmetric if qg(x, y) is real, as in kinematical theory. For thin objects for which the POA is valid, it can readily be shown [99] that for a nonsymmetric object projection, the diffraction pattern intensities, as given by the last term of (38), do not have a center of symmetry unless both the incident beam amplitude and the object transmission function have a center of symmetry (or a center of antisymmetry, i.e., are purely odd functions) about the same point. This is rarely the case. For a perfectly aligned microscope and clean apertures it may be assumed that the function T(u, v) is centro-symmetric, although complex, but the center of symmetry has to coincide with a point in the object that is a center of symmetry of the illuminated region. Observations of the lack of a center of symmetry in nanodiffraction patterns are common. Calculations showing this lack of symmetry have been made for models of amorphous objects [100], although the comparison with experiment is limited in this case because the actual structure of an amorphous object is unknown. For this reason the observations made on the walls of multiwalled carbon nanotubes are of interest [99], because these objects are of known structure and, for tubes of circular cross section, the projected structure is largely independent of the incident beam direction. Figure 20a is a diagram of such a multiwalled tube, where each of the concentric cylinders is made up of a graphitic plane of carbon atoms, bent into a cylindrical shape. The projected potential distribution for one side of such a tube is suggested in Figure 20b. This distribution is made up of peaks at intervals of 0.34 nm that are essentially nonsymmettic. Thus, when an incident nanoprobe of diameter ~ 1 nm illuminates such an object, the

41

COWLEY AND SPENCE

3.4A (a)

Projected. potential

/ I

I

I

I

I

I

I

radius

(b) Fig. 20. (a) Diagram of a multiwalled carbon nanotube consisting of concentric cylinders of graphene carbon layers, 0.34 nm apart. (b) Plot of the projected potential distribution for one-half of a multiwalled tube such as that in (a).

nanodiffraction pattern should show an asymmetry that is readily calculable. Calculations show that the two first-order reflections from the 0.34-nm spacing, on either side of the zero beam, should differ by 5-20%, depending on the position of the center of the beam relative to the tube axis. Measurements of such nanodiffraction patterns from tubes of known circular cross section, recorded with a CCD camera for quantitative intensity measurement, show asymmetries within this range of magnitudes. As expected, the direction of the asymmetry is opposite for the two sides of the nanotube. The regions in the walls of carbon nanotubes that give the pronounced asymmetry of the peaks in Figure 20b are sufficiently thin to allow the phase-object approximation to be used. For thicker regions, especially in near-perfect crystals, the diffraction patterns are usually nonsymmetric, even in the kinematical approximation because of the curvature of the Ewald sphere, and the diffraction pattern intensities vary strongly with incident beam orientation. This behavior is observed in the case of carbon nanotubes that have polygonal

42

NANODIFFRACTION

cross sections, so that the beam near the edge of the tube may illuminate a fiat region of the tube wall that is essentially a single-crystal region (see Section 10.1).

7.3. Shadow Images and Ronchi Fringes If the objective aperture size in the STEM instrument is made very large, each diffracted beam disk from a crystalline specimen overlaps all of the other disks. The incident beam is spread out by the spherical aberration effects. It becomes difficult to relate the intensity distribution to that of a normal-type diffraction pattern. The intensity distribution comes to resemble more closely a somewhat distorted image, as can be deduced from the simple geometric-optics picture of Figure 21. When a cross-over formed by an ideally perfect lens is close to a thin specimen, a pointprojection image or "shadow image" appears on a distant screen with a magnification equal to the ratio of the distance of the screen to the distance of the cross-over from the specimen. The magnification becomes infinite as the cross-over approaches the specimen. For a lens with spherical aberration, if the lens is underfocused as in Figure 21, the cross-over for paraxial rays is beyond the specimen. The image is inverted. For rays at an increasing angle to the axis, the cross-over point approaches the specimen. The magnification increases to minus infinity for some particular angle, then becomes plus infinity and decreases for greater angles. For overfocus, the magnification is always positive and decreases with increasing angles. For the three-dimensional case of Figure 21, when cones of radiation with increasing cone angles are considered, there are two cases of infinite magnification to be considered. There is infinite radial magnification when two rays close together in a radial direction cross over at the specimen. This condition is satisfied for points on the caustic of the lens, for an angle with the axis given by (ACs/3) 1/2. However, rays that make the same angle with the axis but are separated in a circumferential direction cross over on the axis, to give infinite circumferential magnification. Thus a circle of infinite circumferential magnification appears on the plane of observation at an angle equal to (ACs) 1/2. This latter circle of infinite magnification is usually more obvious than the smaller circle for infinite radial magnification [ 101 ] and appears prominently, for example, in Figure 22a and b. It can readily be shown that the paraxial region of the shadow image has a resolution for weak-phase objects that is the same as that for bright-field STEM imaging with the same defocus [ 102]. The observation of shadow images serves a very useful purpose in that it may be used conveniently for the alignment, stigmation correction, and focus setting of the STEM instrument [ 103]. The stigmation correction is made by ensuring that the infinite magnification circle is not distorted. Use of a straight edge of a specimen, as in Figure 22b, to give a

I_..

A

.._1 I

I

I_..

w!

Fig. 21. Geometric optics diagram for a lens with spherical aberration, indicating the form of the shadow image for a specimen edge a distance A under focus.

43

COWLEY AND SPENCE

Fig. 22. The shadow images of (a) an amorphous film and (b) a crystal edge, showing the circle of infinite magnification for a negative defocus. Reprinted from Ultramicroscopy, J. M. Cowley,4, 435 (9 1979), with permission from Elsevier Science.

line dividing the infinite magnification circle, is the exact equivalent of the knife-edge test commonly used in light-optics. If the specimen is a thin crystal of known structure, the shadow images may be used to correct the astigmatism with greater accuracy and quantitative measurements of the spherical aberration constant and the defocus become feasible. The parallel, equispaced fringes corresponding to prominent crystal lattice planes become distorted close to focus. If the astigmatism is corrected, these bowed fringes show exact symmetry around the fringe direction but are otherwise distorted into S-shaped curves. The form of such fringes is familiar in light optics, where the almost exact analog is given by the observation of the distortion of the fringes produced by a grating placed near the cross-over formed by an optical lens. These are called "Ronchi fringes", after their discoverer [104], and are commonly used to test the aberrations of large telescope mirrors. Hence we refer to the analogous electron observation as "electron Ronchi fringes" [ 105, 106]. For a crystal with a small unit cell set so that a strong low-index reflection is excited, two sets of bowed fringes are observed, one set centered on the zero beam direction and one set centered on the Bragg reflection direction, as seen in Figure 23a, for the case of the 200 reflection from MgO. These fringes may be compared with the fringes in the areas of overlap for coherent nanodiffraction patterns with a finite objective aperture size, as in Figure 19. For a crystal of larger periodicity, the patterns of Ronchi fringes are seen to have a more complicated form, as in Figure 23b, for fringes given by the lattice planes in a beryl crystal with a lattice spacing of 0.8 nm. Apart from the distortion of the fringes, it is seen in this latter case that there are ellipses in the patterns along which the contrast of the fringes becomes zero and the fringe contrast is inverted. For a one-dimensionally periodic object, in the WPOA, the transmission function of the crystal may be written as q ( r ) = 1 - iG cos(2rc g r + O)

(44)

where G is small, g is the reciprocal lattice vector, and 0 is the phase angle relative to some arbitrary origin. Then the fringe intensity distribution may be written as

I(u)- 1 +2Gsin[E(u,g)]cos[O(u,g)+O]

44

(45)

NANODIFFRACTION

Fig. 23. Electron Ronchi fringes formed by interference effects in shadow images of (a) MgO and (b) beryl. In (b) the observed fringe pattern is compared with a simulated pattern. The ellipses of zero contrast are clearly visible. where E ( u , g) and O(u, g) are the even and odd parts, respectively, of X.(u + g) - X(u) and u is the vector (u, v), so that E ( u , g) = Jr)~gZ[Csk2(3u 2 + v 2 + g2/2) + A] O(u, g) = 2Jrkug[CskZ(u 2 + l)2) -~- A

-+-0]

(46)

The cosine function in (45) then gives the set of bowed fringes as seen in Figure 23a. For large amounts of defocus, A, the periodicity of the fringes is {g~.(A + Csg2~.2)} -1 . The sin term of (45) defines a set of concentric ellipses, with axial ratios equal to 31/2, on which the second term of (45) passes through zero and inverts, as seen in Figure 23b. It can readily be shown [ 106] that, if the spacing of the lattice planes and the wavelength are known, the value of the spherical aberration constant can be derived from the difference in the squares of the major axes of two successive ellipses of zero contrast, irrespective of the defocus value. The absolute value of the defocus can be derived by matching calculated and observed forms of the pattern of fringes, so that the objective lens settings may be calibrated in terms of defocus. Hence the essential parameters needed for the interpretation of STEM images may be obtained from the Ronchi fringes with quite high accuracy. In addition, the astigmatism may be corrected with high accuracy by observation of the symmetry of the Ronchi fringe patterns.

7.4. The Incoherent Nanodiffraction Approximation As stated above, in Section 7.1, for convergent beam diffraction from a perfect crystal, there is no difference in the diffraction pattern intensities for coherent or incoherent illumination,

45

COWLEY AND SPENCE

provided that the diffracted beam disks do not overlap. For coherent illumination, one can assume that the diffraction pattern is the square of the sum of the amplitudes for all different incident beam directions. But for each incident beam direction one can consider an incident plane wave giving a set of delta function diffraction spots, and there is no overlap of the delta function spots for different beam directions. Thus the total intensity distribution is given by adding the intensities for all beam directions separately, as if the radiation for all beam directions were incoherent. From (37), the Fourier transform of the exit wave of the object, Q(u, v), is convoluted with the transfer function, T (u, v), before the squared modulus is taken. For a small objective aperture size, and a sufficiently small defocus value, the sin X (u, v) part of the transfer function is negligibly small and T (u, v) becomes equal to the purely real aperture function, A (u, v). The diffraction pattern with nonoverlapping spots then can be assumed to represent the parallel-beam diffraction pattem with each spot spread into a circular disk of uniform intensity. This assumption cannot be extended to the case of a nonperfect crystal for which the parallel-beam diffraction pattern contains diffuse scattering, such as diffuse streaks due to discontinuities or a diffuse background due to disorder of the atomic positions. But for many cases it can be assumed that the diffuse scattering is so small relative to the sharp Bragg diffraction peaks that the assumption can be made with reasonable confidence that the diffraction pattern can be interpreted as if given by incoherent scattering with enlarged peaks. On this basis, nanodiffraction patterns have often been used to study the structures of very small regions of thin specimens and have been interpreted using the relatively simple assumptions applied to diffraction from larger areas, as in selected-area diffraction. It is important, however, to recognize those cases where these simplifying assumptions are not valid and where coherent diffraction effects modify the intensity distributions appreciably, and to modify the interpretations accordingly.

8. I N C O H E R E N T NANODIFFRACTION: NANOCRYSTALS

8.1. Supported Metal Particles For many years, there has been great interest in the application of various modes of electron microscopy to the examination of small metal particles supported on or in thin layers of light-atom material. Such studies have been basic for research on supported metal catalysts in which the metal particles may have dimensions as small as 1 nm and the supporting material is often a light-metal oxide, such as alumina, silica, or magnesia. The information desired includes the particle size distribution and the crystallinity of the particles, that is, whether the particles are single crystals, whether they are twinned or otherwise faulted, and the nature of the crystallographic planes and edges on the crystal surfaces. Also in cases where it is suspected that the support of the metal particles may influence their catalytic properties, it is desirable to know the orientational relationship of the metal nanocrystals to the support and the presence of any intermediate phase at the interface. With high-resolution bright-field TEM it is sometimes possible to resolve the lattice structure of the small crystals and so derive some of the desired information. However, this is possible only if the supporting film is very thin and amorphous. Amorphous or near-amorphous films can produce phase-contrast noise, which in many cases is sufficient to obscure the details of the images of nanocrystals. An alternative approach is to use dark-field STEM imaging. It was realized in the early days of STEM [31, 40] that the dark-field images may be approximated as incoherent imaging and so are almost free of phase-contrast effects, and the nonlinear variation of scattering with atomic number emphasizes the scattering by heavy atoms in the presence of light atoms, giving the so-called Z-contrast.

46

NANODIFFRACTION

A difficulty that arose in the case of dark-field STEM imaging of metal catalyst particles on oxide supports is that the supports are often nanocrystalline rather than amorphous, giving strong diffraction effects that produce strong dark-field contrast, which can be confused with that from the metal particles. This difficulty was overcome by the introduction of high-angle dark-field (HAADF) imaging ([41, 42] see Section 4), using an annular detector with an inner radius of 80-100 mrads for 100-keV electrons and collecting only those electrons scattered to the angular range beyond the limits of the usual crystal diffraction pattern maxima. HAADF imaging is thus the preferred means for determining size distributions of small metal particles for many types of catalyst. For example, platinum particles embedded in relatively thick films of near-amorphous alumina may be invisible in bright-field TEM or STEM images, but are clearly seen with HAADF imaging [42]. The transmission imaging modes leave some degree of ambiguity in the determination of the distribution of the metal particles in the support, in that the image represents a projection of the structure in the beam direction and it is not possible to deduce the threedimensional distribution. This difficulty may be overcome if the HAADF images are combined with images formed by detecting the low-energy secondary electrons or the Auger electrons given off at the entrance and exit faces of the specimen. In the UHV MIDAS STEM instrument [34], the low-energy electrons emitted by the specimen are first accelerated by biasing the specimen with a few hundred volts negative [35]. These electrons spiral around the magnetic field of the objective lens, but as they drift out of the magnetic field they are "parallelized." Their helical paths increase in pitch until, when they leave the magnetic field and enter field-free space, they are confined to a narrow beam with a divergence of only about 5 ~ and are ideally suited for input into an energy analyzer or energy filter. Hence the secondary electrons or Auger electrons of any selected energy may be detected to form an image. The secondary electrons give an image showing the morphology of the surface and the variations of secondary-emission coefficient, which usually shows strong contrast for metal particles on oxide supports. Detection of the Auger electrons can be used to give a chemical analysis of the surface layers and so can be arranged to give images for a particular type of atom in the surface layers. The resolution attainable with the secondary-electron or Auger-electron imaging modes in the MIDAS instrument has been demonstrated at 1 nm or better. The low-energy electrons can be detected from either side of the specimen. By combining the information from these images with that from a HAADF image, which may be recorded simultaneously, using the fast electrons scattered to high angles, it is then possible to deduce whether individual particles are on one side or the other or are in the interior of the specimen film. Particles of 1 nm diameter or less can thus be imaged using a variety of STEM imaging modes. For any of these imaging modes, a marker may be placed at any point on the display screen, and the beam is stopped at that point to produce the corresponding nanodiffraction pattern. Commonly, for convenience, an electron beam of diameter 0.7-1.0 nm is used. The resolution of the image is then limited to this beam size, but the diffraction pattern coming from such a beam is interpretable in terms of the incoherent approximation of a parallel-beam diffraction pattern with enlarged spots. An example of a straightforward application of this approach is given by the case of small gold particles, 1-10 nm in diameter, incorporated into a film of polyester by cosputtering [52]. A bright-field STEM image of the specimen (Fig. 12a) shows the distribution of gold particle sizes. In Figure 12b are some of the diffraction patterns recorded from individual gold particles. From such patterns it can be deduced that some of the particles are single crystals; some are crystals twinned on one of the close-packed (111) planes, and some are multiply twinned. These results on small gold crystals are of interest in relation to the earlier theoretical and experimental findings on larger gold particles and other particles of face-centered cubic metals. It had been show, by high-resolution TEM, that gold crystals with sizes in

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the range of 10 nm or more are sometimes multiply twinned. Repeated twinning on { 111 } type planes can produce decahedral particles containing 10 twin-related, equal tetrahedralshaped single-crystal regions or dodecahedral particles containing 20 such tetrahedral regions [107, 108]. Consideration of the energy of such configurations [108] led to the suggestion that these multiply twinned forms may be the most stable forms of gold particles for very small particle sizes. The observations of [52] referred to gold particles surrounded by the plastic film, so that the surface energies would not have been the same as for unsupported particles, for which the energy terms were evaluated theoretically. Hence it may not be too surprising that the nanodiffraction results suggested a different behavior for the smallest particle sizes. Whereas the multiply twinned forms occurred reasonably often for particles in the 5-nm range, they became less common for smaller sizes, and particles in the 1-2-nm range were found to be mostly single crystals or to have no more than one twin plane. For the model supported-metal catalyst system of platinum on y-alumina, samples obtained from various sources appear to differ greatly with the source. In particular, the form and degree of crystallinity of the alumina seem to depend strongly on the origin of the material. In each case the Pt particles could be imaged clearly by HAADF STEM imaging, and the nanodiffraction patterns from the Pt particles show them to be untwinned single crystals. For some samples, the alumina-supporting film is seen to be crystalline to the extent that diffraction patterns from crystallites with dimensions of a few nanometers can be recorded and shown to be consistent with the disordered structure proposed for y-alumina [ 109]. Then it is found that the platinum nanocrystals tend to be epitaxially oriented with respect to the alumina crystal lattice. For other samples of Pt on alumina supports, the rather surprising result was found that the oxide ot-PtO2 appears for both the calcined and reduced forms of the catalyst [ 110]. This oxide is present with unit cell dimensions about 6% smaller than for the bulk material, possibly as a result of the small particle size or possibly as a result of nonstoichiometry. Metal catalysts consisting of mixtures of ruthenium and gold on MgO supports were examined by TEM imaging and nanodiffraction in an attempt to find the basis for the surprising result that the catalytic activity of the ruthenium appears to be enhanced by the addition of the nominally inert gold [ 111]. For particles of diameter greater than about 5 nm, the conventional techniques of TEM and microanalysis confirm that, as in bulk samples, no mixing of the Au and Ru occurs. It was envisaged that the enhancement of the catalytic activity by Au could occur because of some interaction of these metals, either chemical or physical, for particle sizes in the 1-3-nm range. Nanodiffraction patterns from particles in this latter size range show single-crystal patterns from the normal cubic Au and hexagonal Ru structures, in each case with the crystals epitaxially oriented on the MgO crystals. However, there are also patterns from a different phase. These patterns cannot be attributed to any mixed Au-Ru phase, but appear to come from a body-centered cubic phase of Ru. Strong diffuse streaks in some of these patterns suggest that this phase is heavily faulted on (110)-type planes. This result is not too surprising in light of other observations that in very small crystals, some metals can form with structures other than those known to occur in bulk. However, this observation of B.C.C. ruthenium does not offer any explanation of the influence of the Au on the catalytic activity of the Ru, in as much as the occurrence of the B.C.C. form of Ru cannot be correlated with the percentage of Au in the sample. For many cases of supported metal particles on oxide supports, and particularly for the commercial catalyst samples, one difficulty of the characterization of the system arises from the lack of knowledge of the nature of the supporting material, which is often partially crystalline or microcrystalline. The extent to which the catalytic or other properties of the system depend on the relationship of the metal crystals to the faces, edges, or defect structures of the underlying crystals is not known. For this reason, it is sometimes of interest to examine metal crystallites on supports of known structure. In the case of MgO, it is possible to use the MgO smoke particles formed by burning magnesium

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in air, which consist mostly of well-formed cubic crystallites with dimensions of about 10 nm up to 1/zm and faces that are atomically fiat or contain only a few atom-high steps. The surfaces of the MgO smoke crystals have been found to be surprisingly reactive when metal particles are formed on them by evaporation, particularly on heating in air or under electron irradiation. Thin films of gold on MgO smoke, for example, can appear to react, giving crystallites shown by nanodiffraction to have relatively large unit cells [ 112]. When silver is evaporated on MgO smoke crystals it forms epitaxial Ag crystals, but under electron irradiation in TEM or STEM instruments the Ag crystals become mobile. The Ag crystallites appear to wet the MgO surface with amorphous-looking intermediate layers, and amorphous-looking filaments may join crystals and allow a flow of matter between them [113] (see Fig. 24a). Nanodiffraction patterns obtained from these thin amorphous-

Fig. 24. High-resolutionSTEM image (a), showing the boundary of an Ag particle wetting the face of a MgO crystal (bottom), and nanodiffraction patterns (b) of the intermediate region, appearing to be liquid, but shown to be single-crystalAg2O.

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looking regions showed them to be single crystalline, with the structure of the oxide Ag20 (Fig. 24b). It seems possible that the formation of this oxide, which is rather unstable in bulk, is induced by a reaction with oxygen and possibly absorbed water vapor under electron irradiation. The deposition of aluminum on the surfaces of MgO smoke crystals results in a complete destabilization of the surface, which becomes highly convoluted, although it is still a single crystal, in a layer 5-10 nm thick. Nanodiffraction shows no sign of the presence of A1 until, with increasing quantities present, it forms the spinel structure, MgA1204, in a thin surface layer [114]. When palladium metal is evaporated on MgO smoke crystals or cleaved bulk MgO, it forms small crystals epitaxed on the { 100 } surfaces. The crystallites on bulk MgO surfaces have been observed using STEM in the reflection mode (SREM) and reflection-mode nanodiffraction. In this way it was observed that under electron irradiation the Pd crystallites, about 10 nm in diameter, become coated with an epitaxial layer of the oxide PdO and gradually transform into PdO single crystals [ 115]. Some attempts have been made to observe the small particles of Pt formed in the channels of the structure of zeolites, because such systems have proved to be very effective for some important catalytic reactions. The main difficulties met in the observations of the zeolite-based catalysts using HREM or nanodiffraction result from the extreme sensitivity of the zeolite structure to electron irradiation [ 116]. By the use of minimum-irradiation techniques, considerable progress has been made in the use of HREM to determine the structures of the various forms of zeolite phases, and STEM techniques have proved effective in revealing the presence of the nanometer-size Pt particles that form within the channels, but the question remains of the structures of the Pt particles and their possible orientational relationships with respect to the zeolite lattice. Nanodiffraction patterns can be recorded readily from the Pt particles, using an electron beam of about 1 nm diameter scanned over the specimen to minimize the exposure of the zeolite matrix to the electron beam. It is seen that the particles give clear single-crystal patterns, but with apparent random orientations for the crystallites [ 117]. The information in the patterns regarding the orientations of the zeolite lattices was minimal, so that no indication of any epitaxial relationship of the Pt and zeolite lattices was found. The orientations of the Pt crystallites were seen to change rapidly with a stationary beam, possibly as a result of the rapid disintegration of the supporting zeolite structure.

8.2. Light-Atom Particles on Supports For the study of light-atom thin films or particles held on a supporting film, the Z-contrast of the normal dark-field STEM and HAADF modes offers no advantage. For the brightfield TEM or STEM modes, the usual phase-contrast noise from the support normally hides any contrast from the specimens. The remaining possibilities for the detection of the light-atom materials include the use of their unique characteristics for the scattering of electrons: differences from the support material in the form of the diffraction pattern or in the inelastic scattering processes. Here we discuss only the former of these two possibilities, namely the use of the fact that the distribution of intensity in the diffraction pattern from the specimen material may differ from that of the support. An interesting example is given by the problem of imaging and nanodiffraction from layers of amorphous, or microcrystalline, carbon about 1-2 nm thick supported on a film of amorphous silica, 5 or 6 nm thick [ 118]. For such a sample, the BF and DF TEM and STEM imaging modes are quite ineffective. For diffraction from regions of amorphous carbon (a-C) and amorphous silica (a-SiO2) containing a very large number of atoms, the diffraction patterns for electrons, as for X-rays, consist in each case of diffuse haloes on a steadily falling background. The strongest haloes are at radii that correspond approximately to the most prominent interatomic bond distances. For a-C, there is a strong halo for a spacing of about 1.2 A. For

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a-SiO2, there is no halo at this radius; the strongest halo corresponds to a spacing of about 4.2/~,. For an electron beam in a STEM instrument, which illuminates a region of diameter 1 nm or less, containing only a few hundred atoms, the diffraction pattern for any beam position does not have continuous haloes but is patchy, with maxima and minima appearing apparently at random (see Section 9). However, the intensity maxima are concentrated at the radii of the haloes given by larger specimens. Hence if, in a STEM instrument, a thin annular detector is used to collect only those electrons that are scattered to an angle corresponding to the spacing of 1.2 A (TADDF imaging), the a-C contributes strongly to the signal intensity used to form the STEM image and the a-SiO2 contributes relatively little. In practice, a thin annular detector with a ratio of the outer and inner diameters of about 1.1 has been used to give reasonable selectivity in the range of diffraction angles detected without reducing the collected signal strength too greatly (see Fig. 10). With such a detector, images can show the distribution of a-C in a film of thickness 1 nm on a 6-nm silica support [45]. The contrast of the a-C film can be seen to show a well-defined maximum as the average detection angle of the thin annular detector is varied through the angle for the 1.2-A spacing by using post-specimen lenses in the STEM instrument to vary the magnification of the diffraction pattern. If the thin films of a-C on silica are heated to about 600~ they are crystallized to form nanocrystals of graphitic structure. The contrast in the TADDF image for the 1.2-A spacing disappears. Instead, strong contrast of the nanocrystals appears for the TAD set to collect diffraction from a spacing of about 3.4 ,~, which is the interlayer spacing for the stacking of the hexagonal layers of carbon atoms in ordered or disordered graphite (Fig. 25). In such images, graphitic nanocrystals appear as bright dots, and the average diameter of the nanocrystals could be determined as 1.1 nm. The form of the nanocrystals could be confirmed by obtaining a nanodiffraction pattern from the positions of the individual bright dots (Fig. 25, inset). These patterns show the strong spots from the interlayer spacing, the 002 graphite reflections, but very little sign of any hkl reflections for non-zero l, suggesting that the individual planes of carbon atoms are stacked randomly within the nanocrystals,

Fig. 25. Dark-fieldSTEM image using a thin annular detector (TADDFSTEM) of nanocrystals of carbon, ~ 1 nm in diameter, supported on a film of amorphous silica --~6nm thick. The detector is set to record, preferentially, the 0.34-nm reflections from the carbon (marker = 10 nm). The inset shows a nanodiffraction pattern from one carbon particle [118].

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with random lateral displacements and rotations about the normals to the planes; that is, the stacking is "turbostratic" [ 119].

9. I N C O H E R E N T N A N O D I F F R A C T I O N : A M O R P H O U S AND D I S O R D E R E D THIN FILMS

9.1. Amorphous and Near-Amorphous Films For a thin film less than 10 nm thick, the volume of the specimen illuminated by a STEM beam 1 nm or less in diameter at any one time may contain only a few hundred atoms. For amorphous films, this small number of atoms is not sufficient to allow for the averaging over the relative orientations of many thousands or millions of interatomic bonds, which is involved in the calculation of the usual diffraction patterns from amorphous materials to give the smooth halo patterns for X-ray diffraction or from electron diffraction in the SAED mode. Instead of a pattern of smooth haloes, a pattern obtained is a random-looking array of diffraction maxima, as in Figure 26e. The maxima may appear to be more pronounced for radii in the diffraction patterns corresponding to the radii of the strong haloes of the big-sample patterns. The average dimensions of the maxima may differ from one sample to another, but may be roughly correlated with the size of the central spot of the pattern, that is, with the beam diameter. The distribution of the maxima may be seen to vary rapidly as the incident beam is moved over the sample, because a movement of the beam by a fraction of a nanometer involves a change in the configuration of the atoms illuminated and hence a change in the diffraction intensities. Frequently it is obvious that the nanodiffraction pattern does not have a center of symmetry [ 100], as is discussed in more detail in Section 7.2. The information that can be derived from the halo diffraction pattern from a large sample of amorphous material under kinematical diffraction conditions is limited to the radial distribution function. This is the orientationally averaged pairwise correlation function of interatomic positions, which gives the lengths and frequencies of occurrence of interatomic distances, weighted by the atomic scattering factors for the various atoms, as in the electron diffraction from gases [ 120]. In electron diffraction from amorphous films that are not very thin, complications in the interpretation may arise from multiple scattering effects [ 121]. The multiple scattering adds no new information, and corrections may be made to the observed intensity data to remove its effects. The radial distribution function gives only a very limited amount of information concerning the structures of amorphous materials. The information that is often desired is the frequency of occurrence of various groupings of atoms, such as might characterize the bonding configurations found in crystals. For this purpose it would be necessary to determine the correlation functions relating to the relative positions of three, four, or more atoms. It is interesting to speculate whether information on such multi-atom correlation functions can be obtained from the nanodiffraction patterns, obtainable from a region of the amorphous film, which obviously contain much more information than the averaged diffraction pattern from the whole area. From a nanodiffraction pattern obtained with a single beam position, some information is obtained about the relative positions of the few hundred atoms in the regions illuminated, but without a recording of the relative phases of the diffracted amplitudes, no actual structural analysis that gives the actual atomic positions is possible. (The case of coherent nanodiffraction for which information on relative phases is present is considered in Section 11.) However, the fact that the most common directions for interatomic bonds are indicated for the illuminated region does allow the derivation of some statistics of the combined occurrence of particular configurations of bonds and therefore of atomic groupings. For the case of amorphous silicon, an exercise was conducted [122] to estimate the amount of data from nanodiffraction patterns that would be required to measure the rela-

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tive frequency of the parallel and antiparallel configurations of two tetrahedral Si groups sharing a common bond, that is, to find the preferred dihedral angle. It was estimated that, under the ideal situation of sufficiently thin films and sufficiently accurate intensity measurements, such information could be derived by correlating the information from 10,000 nanodiffraction patterns. This task has not yet been attempted. There may be more direct methods, requiring fewer data, and the search for such methods seems desirable. Parallel questions arise concerning the information on atomic configurations that can be derived from high-resolution TEM or STEM images of thin films of amorphous or nearamorphous films [ 123]. Such images contain phase information from which the relative positions of atoms may, in principle, be derived. The range of the resolution in reciprocal space is not as great as in nanodiffraction because of the limited microscope resolution. As in the case of nanodiffraction, a serious limitation is that the information accessible refers to only a two-dimensional projection of the structure and not the three-dimensional distribution. However, some progress can be made in that statistical analyses of image intensifies can be used to determine the deviations of the atomic configurations from randomness [ 124], and correlation analyses of local image regions can be used to derive information on the occurrence of local periodicities in the structure [ 125]. In this connection, the recent work of Treacy and Gibson [126] is of interest in that they have shown that dark-field STEM imaging with a variable angle of collection, or the equivalent DF TEM imaging with a variable tilting of a gyrated incident beam, allows a derivation of information on amorphous structures with a variable correlation length in the beam direction, and so provides estimates of the degree of order for the intermediate distances in the range of 1 nm or more. In this way they were able to demonstrate a decrease in the extent of the intermediate-range ordering when thin films of amorphous Ge are annealed [ 127].

9.2. Short-Range Ordering in Crystals and Quasi-Crystals A problem somewhat analogous to that of determining the arrangements of atoms in thin films of amorphous materials is that of determining the structures of thin films of crystals that have a disordered occupancy of the lattice sites by two or more different types of atoms. For many binary alloys, for example, there is a well-defined average lattice. Above a certain critical temperature the occupancy of the sites on this lattice is said to be random in that, for averaging over a sufficiently large crystal volume, all sites are occupied by each of the two types of atom in the ratio indicated by the average composition. However, some degree of short-range order always exists in that an atom of one type tends to surround itself with atoms of the other type. A two-atom correlation function may be defined in terms of short-range order parameters that specify the probabilities for finding either type of atom at any position given by a lattice vector away from any atom of a specified type [ 1]. Below the critical temperature, long-range order develops in that, over distances of many unit cells, the atoms are ordered to occupy specific sites within the average unit cell. However, the long-range ordering is not perfect. For averages over large volumes of the crystal, the long-range order parameter is not unity; that is, for a particular atom at one site within the unit cell, the probability that the same type of atom will occupy the same site within another unit cell decreases with distance to some limiting value specified by the long-range order parameter. The deviation from perfect ordering in this case may be attributed to random errors in the occupancies of the sites or, more commonly, to the occurrence of out-of-phase domain boundaries, where the preferred site for one type of atom within the unit cell switches from one site to a different, symmetrically equivalent site. Such out-of-phase domain boundaries have been observed and studied by TEM, HREM, and SAED, and the forms of such boundaries have been determined in detail for a number of ordering systems [ 128]. The long- and short-range order parameters that characterize the state of order in such a system may by determined by measuring the intensities of the superlattice reflections that

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arise from the deviations from the averaged lattice [ 1]. These reflections are sharp for longrange order but diffuse for short-range order. The shapes of the sharp or diffuse peaks may be interpreted in terms of the order parameters or in terms of models for the configurations of out-of-phase domain boundaries. The short-range ordered state may be described as one in which these domain boundaries occur at intervals of only a few unit cells. It is possible to make models of a region of a short-range ordered alloy with an experimentally observed set of short-range order parameters by using Monte Carlo simulations, and such models may be divided up into domains with the structures of the possible long-range ordered states [129]. For nanodiffraction from a thin film of a binary alloy in a short-range ordered state, with an average microdomain size of 1-2 nm, it is then to be expected that in the individual patterns given when the beam is centered in a microdomain, the superlattice spots of an ordered alloy will appear; this has been verified. Furthermore, it is possible to apply a pattern recognition technique to give a signal whenever particular superlattice spots appear in the pattern and thus form an image showing the distribution of suitably oriented microdomains within a sample [53]. For a number of disordered crystals, however, the form of the diffuse scattering in the diffraction pattern is much more complicated than for the simple binary alloy case, and it is much more difficult to interpret the scattering in terms of local configurations of atoms approximating those of a possible long-range ordered state. For lithium ferrite (LiFeO2), disordered TiO, and a number of other oxide systems [130], continuous wavy lines and loops appear in the SAED patterns. An explanation of the forms of these loops or lines in terms of the relative frequencies of various local configurations of atoms has been offered and is reasonably compelling [131], although it is clear from the patterns that the range of correlations of the atomic positions must be 3-4 nm, which is much greater than the dimensions of the clusters used in the models. An attempt to throw light on the nature of the medium-range ordering for the case of LiFeO2 has been made by using nanodiffraction to investigate the atom configurations in regions with dimensions of 1-2 nm. The individual nanodiffraction patterns often show diffraction spots at positions corresponding to high-intensity regions of the continuous lines in the SAED patterns, but rarely show any evidence of two-dimensional sets of spots such as would arise from local two- or three-dimensional ordering. It is deduced that the local ordering of the Li and Fe atoms giving rise to the diffuse scattering takes the form of one-dimensional correlations, with ordered strings of Li and Fe atoms occurring in a variety of directions. As in other studies of short- or medium-range ordering, dark-field TEM or STEM images of the crystals were obtained. Such images for LiFeO2 showed linear arrays of bright spots, which seemed to confirm the deductions from the nanodiffraction patterns. However, it has been pointed out that deductions of this sort from dark-field images must always be made with a great deal of caution [ 132]. Often it is assumed that a bright spot or patch in a DF image represents a domain of ordered structure giving a diffraction maximum in a direction passing through the objective aperture. However, it must be remembered that for the ideal case of a thin crystal for which all of the diffracted electrons contribute to the image, the dark-field image intensity corresponds to the square of the deviation (positive or negative) of the scattering power from an average value. When different domains overlap in the beam direction there may be an addition or subtraction of these deviations, distorting the imaging of domain sizes and giving a very nonlinear impression of relative domain thicknesses. For the usual situation in which only a small portion of the diffraction pattern contributes to the DF image, the interpretation of the white-spot contrast in terms of domain structure is even less direct or reliable. For the LiFeO2 case, the form of the DFTEM image detail was seen to very highly dependent on the position of the objective aperture in the diffraction pattern.

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An even more complicated but interesting example of the use of nanodiffraction to investigate a disordered system is given by the attempt to determine whether the mode of ordering exhibited by quasi-crystals extends to the near-amorphous state. It is well known that SAED patterns of thin films of quasi-crystals, such as those of some Mn-A1 alloys, in some orientations, show an apparent fivefold symmetry, usually appearing as a 10-fold symmetry by the approximate addition of a center of symmetry. In other orientations, the patterns display three- or twofold symmetries, but in all orientations the diffraction spot spacings are incommensurate [133]. The corresponding HREM images show no translational periodicity, but reveal local regions of fivefold symmetry and uniform orientations of planes of atoms that are not regularly spaced [ 134]. When such alloy films are first formed, they may appear to be amorphous, giving only diffuse tings in SAED patterns. The quasi-crystalline order becomes evident only on annealing, as ordered domains 10-20 nm in diameter are formed. Nanodiffraction patterns from such domains show clear evidence of the five-, three-, and twofold symmetries, as suggested in Figure 26a. The question remains whether such symmetries are also present in the apparently amorphous initial state. Many nanodiffraction patterns were observed with a beam of diameter 1 nm or less, scanned slowly over a film of this sort, and patterns showing some evidence of fivefold and threefold symmetries could be recorded (Fig. 26b-d). However, these patterns were often just partial patterns and very rarely approximated complete patterns showing the full symmetry. For a nanodiffraction pattern to show a clear, complete fivefold symmetry, several conditions must be met. The fivefold symmetry axis must extend through the film and be close to the beam direction. Moreover, the beam axis must coincide with the symmetry axis to within better than about 0.2 nm. The probability ot these conditions being met is obviously quite low for a film consisting of small domains in random orientations. On the other hand, for a completely random arrangement of atoms, there is a finite probability that the group of atom illuminated by a beam of small diameter should give a diffraction pattern that approximates that for a fivefold symmetry (see Fig. 26e). It is not easy to determine whether the frequency with which the nanodiffraction patterns from the Mn-A1 near-amorphous film suggests the presence of fivefold symmetry is significantly greater than for a collection of atoms chosen from an array that is completely random apart from having some prescribed range of interatomic distances. The statistics are complicated by the difficulty of defining when a fivefold symmetry is "suggested." This problem represents a limitation of the nanodiffraction method as presently practiced.

10. INCOHERENT NANODIFFRACTION: CARBON NANOTUBES 10.1. Multiwalled Carbon Nanotubes During an electron microscope study of carbon samples containing fullerenes, formed in an arc struck between carbon electrodes in a relatively high pressure of inert gas, Iijima [ 135] observed long thin objects in the images and interpreted them as coming from carbon nanotubes. These are made up of cylindrical units, each formed by wrapping a hexagonal sheet of carbon atoms, like those in the graphite structure ("graphene" sheet) around an axis. The cylindrical structures may have various helicity values. If the axis of the cylinder coincides with one of the main symmetry axes of the graphene sheet, corresponding to the [100] or [110] directions of the graphite structure, for example, the cylinder may be said to have a helicity of zero. But the graphene sheets may be joined into cylinders by wrapping around other axes to give various helix angles. Similar tubes made by other methods, including chemical reactions, have also been reported [ 136].

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Fig. 26. Nanodiffraction pattems from a thin film of a Mn-A1 alloy that is quasi-crystalline after annealing. (a) From the ordered state showing approximate fivefold (or 10-fold) symmetry. (b) As initially deposited in almost-amorphous state. (c) and (d) After annealing at 230~ For comparison, (e) shows a nanodiffraction pattern from an "amorphous" sodium-aluminum silicate glass showing approximate five-fold symmetry. Courtesy of J. Konnert.

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The nanotubes first observed by Iijima [135] were multiwalled tubes, made up of a number of concentric graphene cylinders, as suggested by Figure 20, with various helix angles. The difference in radii of successive cylinders is about 0.34 nm, a little greater than the interplanar spacing in graphite. The diameter of the innermost cylinder is usually in the range of 1-3 nm, and there may be as many as 20 or more concentric cylinders, giving an outer diameter as large as 16-20 nm. It has been show more recently [ 137] that there may be several different helix angles among the sheets of a single nanotube. If the multiwalled tube can be considered to be built up by the addition of successive layers to the central tube, there is a tendency for the helix angle to change after the addition of every fourth layer, so that the number of helix angles is equal to the number of concentric layers divided by 4. In high-resolution TEM or STEM bright-field images, appreciable contrast is usually seen only where the graphene layers are parallel to the incident beam. Thus images of a multiwalled tube consist of two parallel sets of lines, 0.34 nm apart, corresponding to the two walls of the tube. Occasionally, for a multiwalled tube that has predominantly only one helix angle, some indication of fringes of 0.21-nm spacing, corresponding to the in-layer periodicity of the graphene layers, can be seen in the middle of the tube image, where the incident beam is almost perpendicular to the layers [138]. However, this is uncommon because there is the possibility that several helix angles can exist, and for tubes of circular cross section, the successive tubes are stacked in a disordered manner with lateral displacements and not in a regular array, as in graphite. For graphene sheets wrapped into cylinders of different radius, the successive sheets must be out of step by an amount equal to 2zr times the difference in radii around the circumference of the cylinders. If nanodiffraction patterns are recorded with a beam of diameter 1 nm or less as the incident beam is translated across a multwalled tube, the patterns given from either side of the tube contain the strong row of reflections, corresponding to an interlayer spacing of 0.34 nm, similar to the 00,2 line of reflections from graphite [139] (see Fig. 28a). Parallel to this line of reflections, in the positions of the hkl lines of reflections for graphite, there are only the weak, continuous lines consistent with the disorder in the relative translations and/or rotations of the sheets. For the beam passing through the middle of the tube, the patterns show the hexagonal symmetry corresponding to that of the graphene sheets seen with the beam perpendicular to the layers. For helix angle zero for all cylindrical layers, the pattern shows the hexagonal sets of spots to be expected for one graphene plane. For a single, nonzero helix angle, the top and bottom layers are seen as twisted in opposite directions, so that all of these spots are split into two components. For multiple helix angles, there are two spots for each helix angle, so that the hexagonal sets of spots are spread around the circumference of a ring, with individual spots often unresolved. If, for a multiwalled tube of large diameter, the incident nanoprobe is displaced from the center of the tube toward the walls, the beam passes through graphene layers tilted away from the direction perpendicular to the beam. Then the hexagonal rings of spots are distorted into ellipses, and for disorder of the layers, these ellipses may appear almost continuous. Such ellipses have been observed previously for the case of a disordered stacking of much larger planar graphitic sheets [ 140] and are interpreted as indicating a "turbostratic" disorder in the stacking of the graphitic carbon layers, as derived by B iscoe and Warren [ 119] from X-ray diffraction observations. For some preparations of carbon nanotubes, an appreciable fraction of the multiwalled tubes show evidence that the cross section of the tube is not circular but is polygonal and probably pentagonal, as suggested in Figure 27. The initial evidence for this form came from high-resolution TEM images in that, whereas the spacing in one wall of a tube had the usual value of 0.34 nm, the spacing of the fringes in the image of the other wall was found to be greater, up to 4.1 nm. This is seen to be consistent with the model of Figure 27 if it is remembered that only those portions of the planes parallel to the incident beam give appreciable contrast, and the spacing is greater where the layers are strongly bent at the pentagon comers.

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0.34nm

0.41 nm

Fig. 27. Diagram of the polygonal (pentagonal) cross section of a carbon multiwalled nanotube, to be compared with the more usual circular cross section in Figure 20a.

Fig. 28. Sequenceof nanodiffraction patterns obtained as the incident beam is tranlated across a carbon multiwalled nanotube, showing the diffraction patterns for the beam on one side, the middle, and the other side of the tube. (a) For a tube of circular cross section. (b) For a tube of polygonal cross section, as for Figure 27.

This interpretation of the H R E M images is confirmed by a series of nanodiffraction patterns taken as the b e a m traverses such a tube [ 139] (Fig. 28b). With the b e a m parallel to one fiat face of the tube, the diffraction pattern shows a very strong line of spots from the interlayer spacing plus well-defined spots in the parallel lines, suggesting that in the flat parts of the tube the graphene layers are ordered into a 3D crystalline array, often similar to that in crystalline graphite. On the other side of the tube, where the b e a m passes through

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the corner of the pentagon, the interlayer spacing spots are seen to be weak and have a spacing corresponding to a periodicity of about 0.4 nm, and there are no signs of parallel rows of spots that would indicate interlayer ordering. With the beam passing through the center of the tube, various observed patterns of the hkO and hkl spots are consistent with planar regions of the tube wall, tilted at various angles. It may be concluded that when the multiwalled tube has a polygonal cross section, there may be sufficient flexibility in the configurations in the regions at the sharp bends to allow the graphene sheets to order in the fiat regions. The gain of energy from the ordering may be sufficient to offset the higher energy of bent portions of the layers. 10.2. Nanotubes with Intercalates It is of interest to consider the possibility of inserting various substances into the narrow spaces at the cores of the carbon nanotubes. In this way it may be possible to make small crystals or thin wires with well-defined diameters on the order of 1-2 nm. Such wires should have electrical or optical properties strongly affected by the dimensional limitation of the quantum states of the electrons present. In the first observed case of such an intercalate, Ajayan and Iijima [ 141] reported the imaging of metallic Pb introduced into the core of a multiwalled carbon nanotube by capillary action, after the end cap on the tube had been removed by refluxing in strong acid. In other cases, nanotubes formed in carbon arcs were seen to be filled with intercalate when various metals were introduced into one of the carbon electrodes of the arc [142-144]. In this latter case, the intercalate has usually been identified, by HREM imaging or by nanodiffraction, as consisting of one or more of the metal carbides. Sometimes the intercalates form single crystals, giving clear lattice fringes, and are large enough to give SAED patterns in TEM instruments. In other cases, the intercalates are nanocrystalline and nanodiffraction is required for their characterization. The manner in which the carbides are incorporated into the nanotubes varies greatly for the different metals. For La and Y, for example, the nanotube structure appears to be the same as for unfilled tubes, as shown in Figure 29 [145]. The metal carbide fills the tube in either a nanocrystalline or single-crystal form with no apparent distortion of the tube walls, as if it entered a fully formed tube in a liquid state and crystallized as well as possible subject to the dimensional limitations. In Figure 29, the nanodiffraction patterns of the intercalated YC2 show an alignment of principal planes of the carbide lattice parallel to the layers of graphene structure in the tube walls. This suggests an epitaxial growth process, but it is difficult to imagine how the planes of atoms in the crystalline carbide can be fitted to the strongly curved surface of the innermost graphene sheet. In fact, further observations have suggested that the parallelism of the layers of carbon and carbide, as suggested by the parallelism of the lines of diffraction spots, is a local phenomenon, and a considerable distortion of the carbide lattice may result from the interaction with the nanotube inner walls and the attempt to form the carbide lattice with the spatial restraints [ 145]. The opposite extreme occurs in the case of manganese. Here a variety of carbides of various compositions are formed [ 146]. The carbide particles tend to appear as rather irregular lumps. The walls of the carbon nanotube are heavily distorted and appear to shape themselves to fit around the lumps of carbide, as if the carbide particles formed first and the carbon layers grew around them at a later time. In what seems to be an intermediate case, the carbide particles given by La appear to be shaped by the carbon tubes, in that they are elongated and cylindrical and the carbon nanotubes fit around the particles but are closer to the regular cylindrical form of unfilled tubes [ 147]. This suggests that the carbide particles and nanotubes are formed at the same time but grow in an interactive mode, so that some of the characteristics of both types of individual materials are preserved. In each case, nanodiffraction has helped to determine the carbide structure and its relationship to the graphene sheet orientations of the nanotubes.

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Fig. 29. (a, b) Bright-field and dark-field STEM images ot a multiwalled carbon nanotube partially filled with carbide of yttrium. (c, d) Nanodiffraction patterns from one wall and from the center of the tube, showing that the (110) planes of the YC2 lattice are aligned parallel to the carbon layers of the carbon nanotubed. Reprinted from Micron, J. M. Cowley and M. Liu, 25, 53 (9 1994), with permission from Elsevier Science.

In an interesting example of the use of nanodiffraction in a T E M / S T E M instrument fitted with a FEG [ 148], diffraction patterns were obtained from areas 2-3 nm in diameter, as judged by the diffraction spot sizes, for several tubes filled with intercalated material, and, in addition, the method of energy-dispersive X-ray spectroscopy was applied with the same small probe sizes to determine the composition of the tube-filling material.

10.3. Single-Walled Carbon Nanotubes It was not long after the discovery of the multiwalled tubes by Iijima that Iijima and Ichihashi [149] found that some preparations also contained single-walled nanotubes, made by wrapping a single graphene sheet into a cylinder. They found that for a long straight tube it was possible to record selected-area electron diffraction patterns revealing the helicity of the tube, although because the scattering by the tube was very small and the area of the beam was very much greater than that of the tube, the central beam intensity was overwhelmingly greater than the intensity of the diffraction spots. When nanodiffraction

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Fig. 30. Dark-fieldSTEM image of a short single-walled carbon nanotube that changes its diameter from ~4.5 nm to 6 nm, and a nanodiffraction pattern from part of the broader region, showing a helix angle of ~ 10~

is used with a 1-nm beam diameter, however, this difficulty is avoided, and clear diffraction pattems can be obtained. For example, Figure 30 shows the image of a single-walled nanotube (SWnT) that changes diameter from 4.5 nm to about 6 nm. The corresponding nanodiffraction pattems from the two regions show that the smaller diameter region has a well-defined helix angle of about 10 ~ and the larger-diameter region has a somewhat less perfect structure. Pattems from a large number of SWnT in this sample [ 150] showed a wide range of helix angles, with a preference for a helix angle of about 10 ~ The discovery of the single-walled nanotubes created a great deal of interest, particularly because of unusual mechanical and electrical properties that have been predicted theoretically [151 ]. If such nanotubes could be assembled into bundles with macroscopic dimension, for example, they could provide ropes with a strength-to-weight ratio much greater than any other known material. Considerable progress toward the production of such ropes has been demonstrated, for example, by Thess et al. [152], who have reported the production of ropes of aligned SWnT, 4-30 nm in diameter and up to 100 # m long, by use of a process of double laser irradiation. These authors showed, by use of X-ray diffraction and electron microscopy, that the SWnT within these ropes all have the same diameter of 1.37 nm and are stacked laterally in a near-perfect hexagonal array with a periodicity of 1.69 nm. A theory that has been proposed for the mechanism of formation of the ropes [ 152] suggests that all of the SWnT within a rope should have the same diameter and the same helix angle, and the structure of the SWnT should be that designated as (10,10), which has a symmetry Csv and is predicted to have metallic electrical conductivity. Nanodiffraction and various STEM techniques [153] have been applied to such ropes in an attempt to verify these predictions. Nanodiffraction patterns from a large number of SWnT ropes were obtained with a beam of diameter 0.7 nm, either with the beam held stationary or else with the beam scanned rapidly to give the average pattern for a region of about 10 nm diameter, including the whole width of the rope (see Fig. 31). The conclusion was that a small proportion of the ropes showed just one helix angle. Most of the ropes showed several different helix angles or a range of helix angles, as if the ropes were built of smaller units in which the helix angle was uniform. Overall, the highest proportion of SWnT (about 44%) showed the zero

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Fig. 31. Nanodiffractionpatterns from SWnT ropes. (a) Averaged pattern for a (10,10) rope, helix angle zero, untilted. (b) Pattern from one spot on rope (a). (c) Pattern from a similar rope tilted by 30~ (d) Pattern from one spot on a rope with helix angle 5~ (e) Pattern averaged over a rope with spread of helix angles up to 10~ (f) Pattern from one spot on rope of (e). Reprinted with permission from J. M. Cowley, in "Advances in Metal and Semiconductor Clusters," Vol. 4 (Q 1997 JAI Press).

helix angle corresponding to the (10,10) configuration, a smaller proportion (about 30%) showed a helix angle about 5 ~ away from this, and about 20% showed a helix angle about 10 ~ away, suggesting approximate confirmation of the theory [ 154]. Further information concerning the way in which the SWnT ropes are configured was obtained from series of nanodiffraction patterns obtained as the beam was scanned across nanotube ropes, and the patterns were recorded using a TV, VCR system at a rate of 30 patterns per second [ 155]. Dark-field STEM images of the ropes usually showed a periodicity of about 1.6 nm, corresponding to the lateral stacking of the individual SWnT, and from the strong line of spots on the equatorial line in the diffraction patterns it could be deduced that the SWnT were stacked, as proposed, in a regular hexagonal array with this periodicity. The dark-field images, however, usually showed a very patchy contrast. Series of nanodiffraction patterns taken across and along the ropes could be correlated with the variations of image contrast and showed that the orientation of the hexagoial axes of the SWnT stacking could vary strongly in both directions. These observations were interpreted as indicating that the ropes are both twisted and bent. They appear to be made up of smaller ropes with diameters of up to 10 nm or more within which the hexagonal stacking orientation, as well as the helix angle, tends to be constant, but between such smaller ropes there are discontinuous changes of orientation and helix angle. This suggests that the smaller ropes may have been formed separately and then combined, but because the differences in helix angle produce slight differences in periodicity, and because the fitting together of the smaller ropes may have taken place at several different points along their lengths with no correlation, strains develop in the larger, combined rope that were relieved by the twisting and bending.

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11. COHERENT NANODIFFRACTION: SYMMETRIES, EDGES, AND FAULTS 11.1. Diffraction at Edges The expression for the intensity distribution in the nanodiffraction pattern for a thin object with transmission function q(x, y) (Eq. (22) or (37)) gives a relatively simple result only in the case of a perfectly periodic object for which the Fourier transform of q (x, y) is a set of delta functions, Q(u, v) = Y~h,k Q(h, k)S(u - h/a, v - k/b) for periodicities a and b. Then the intensity distribution in the diffraction pattern, for a probe at the origin so that X, Y - - 0 , is

I (u, v) = Z

Q(h,k)T(u - h/a, v -

k/b>l2

(47)

h,k and, as discussed in Section 7, this gives uniform intensity within disk-shaped spots for no overlap of the disks or interference fringes within regions where spots do overlap. We saw further in Section 7 that the lack of a center of symmetry within the periodically repeated "unit-cell" structure of q(x, y) can lead to the lack of a center of symmetry of the intensities of the diffraction spots, even for the case of nonoverlapping disks, as in the case of the nanodiffraction patterns from the walls of multilayer carbon nanotubes. We now consider the more general case in which the transmission function of the object is not periodic, as in the case of a thin crystal with boundaries, faults, or disorder within the region illuminated by the electron beam, or for a noncrystalline region. Then the diffraction amplitude, Q(u, v), is a continuous, complex function, and the effect of the convolution with the complex function, T (u, v), is not readily envisaged, except for a few idealized cases, which we now explore. A thin crystal terminated by a straight edge perpendicular to the x axis may be represented by multiplying the periodic transmission function of a perfect crystal, qo(x, y), by the step function, h (x), which is zero for x negative and unity for x positive. To separate odd and even parts of h (x), we write 2h(x) = 1 + g(x)

(48)

where g(x) is - 1 for x negative and + 1 for x positive. The Fourier transform of g(x) is - i / u , so the diffraction pattern is written as

l(u, V) --I Q0(u, v) * (1/2){S(u, v) -i/uS(v)} * T(u, V)I2

(49)

The effect of convoluting T (u, v) by 1/u may be approximated by taking the differential of T(u, v) with respect to u. If the objective aperture diameter is relatively small so that T(u, v) can be approximated by the real aperture function, A (u, v), the diffraction spots of Qo(u, v) are each spread out into disks A (u, v) plus squared, differentiated disks (SA(u, v)/Su) 2, which take the form of bright arcs bounding the circular disks, as suggested in Figure 32. Computer simulations of such diffraction patterns [ 156] confirmed this form of the diffraction spots, except that the disks tend to be surrounded by a continuous bright ring. Bright tings around the diffraction spots are readily observed whenever the coherent incident beam forming a nanodiffraction pattem comes close to the edge of a crystal. Figure 33, for example, shows a series diffraction pattems obtained when a beam of diameter --~1 nm is translated across the edge of a small, cube-shaped MgO crystal aligned so that the beam is parallel to one of the faces of the cube [157]. Further investigations of this effect explored possible applications for the determination of the shapes of very small crystals, such as the metal particles of supported catalysts [ 158]. Simulations were made of the diffraction patterns formed for various positions

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Yj

(b)

-"

L

.'~

Fig. 32. Diagram suggesting the formation of hollow arced or circular spots at a straight edge. (a) The convolution of a spot amplitude distribution with a 1/x function. (b) The result in two dimensions.

Fig. 33. Nanodiffraction pattems obtained as the beam is translated across the edge of a MgO crystal in approximate [110] orientation, with the beam (a) just inside the crystal, (b) at the crystal edge, and (c) just outside the crystal.

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of a 1-nm beam relative to the faces and edges of a cuboctahedral FCC gold crystal containing 55 atoms, and it was found that the diffraction spots showed a variety of split and distorted forms, depending on the beam position. A more complete analysis [159] produced the general rule that diffraction spots appear as complete bright rings, with the beam at the edge of a crystal when the edge is long compared with the beam diameter, but for edge lengths comparable to the beam size, the spots appear to be split into two bright spots. A distinction can be made between the forms of the spot splitting for the cases when the crystal edge includes a flat face parallel to the beam and when the crystal edge is a wedge such that the beam strikes the thin edge. Thus, by an examination of the form of the splitting or distortions of the diffraction spots for various beam positions, it may be possible to deduce the three-dimensional shape of the small crystal. 11.2. Domain Boundaries and Faults There are several types of planar discontinuities within crystals for which one component of the crystal structure changes suddenly but another component does not. The splitting of the nanodiffraction spots may be expected for some diffracted beams but not for others. One example is out-of-phase domain boundaries in ordered binary alloys, discussed in Section 9.2. In the case of Cu-Au alloys, the atoms occupy the sites of a face-centered cubic (f.c.c.) lattice, with four sites per unit cell. At high temperatures, the Cu and Au atoms are distributed at random on these lattice sites, when an average is taken over many unit cells, with only a short-range ordering of atoms. Below the critical temperature, however, there is a tendency to form a long-range ordered lattice, with the Cu and Au atoms taking particular sites within the unit cell. For Cu3Au, for example, the gold atom may be assumed to occupy the site at the unit cell origin, with the Cu atoms occupying the three face-center positions. However, because the four sites in the f.c.c, unit cell are equivalent, the Au atom may concentrate on any one of the four sites of the unit cell in various domains of the crystal as the ordering takes place. The domains with Au atoms on different unit cell sites meet on so-called out-of-phase domain boundaries, which are normally planar and may be of two types, "good" boundaries in which there are no nearest-neighbor Au atoms surrounding any given Au atom, and "bad" boundaries for which nearest-neighbor Au atoms occur.

The diffraction spots given by an ordered Cu3Au alloy are of two types: the "fundamental" reflections, coming from the average f.c.c, unit cell, with indices all even or all odd, with intensities independent of the ordering of the two atom types, and the "superlattice" reflections, with mixed indices, which depend on the ordering of the atoms within the unit cell. At an out-of-phase domain boundary, there is no discontinuity in the f.c.c, average structure, so that the f.c.c, diffraction spots in nanodiffraction patterns show no splitting, but for the superlattice spots there is a discontinuity of the structure at the boundary. When the region illuminated by a nanodiffraction incident beam includes an out-of-phase domain boundary, the discontinuity in the structure related to a change of the Au sites in the unit cell results in a splitting of the superlattice diffraction spots. The nature of the splitting depends on the nature of the discontinuity: the shift in the gold atom positions and whether the boundary is a "good" or a "bad" one. The recording of nanodiffraction patterns from the regions of domain boundaries in thin single-crystal films of Cu3Au has shown a variety of patterns, with the superlattice spots split in various ways. Comparison with the predicted splittings has led to the identification of the various types of out-of-phase boundary and a determination of the frequency of occurrence of each [ 160]. Some of the nanodiffraction patterns are shown in Figure 34. The splitting of the superlattice spots is evident. A second example of a boundary within a crystal giving a splitting of some spots but not others is given by the planar stacking faults in f.c.c, metals. It is well known that the

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Fig. 34. Nanodiffractionpatterns from a thin filmof partially ordered Cu3Au. (a) Withthe incident beam within one ordered domain. (b) With the beam on an out-of-phase domain boundary, showing the splitting of the superlattice reflections. (Reprinted from ref. [160].)

f.c.c, structure and the hexagonal close-packed (h.c.p.) structures can be represented in terms of different stacking sequences of hexagonal planar arrays of close-packed atoms. If the (0, 0), (2/3, 1/3), and (1/3, 2/3) sites of the planar hexagonal cell are denoted by A, B, and C, respectively, the f.c.c, structure is represented by a stacking of the hexagonal planes in the ABCABCA sequence, and the h.c.p, structure is given by the ABABA (or BCBCB . . . . etc.) sequence. Other, more complicated, regular stacking sequences exist. The energy term determining the stacking sequence of the hexagonal planes of atoms is relatively small, because it depends on the interactions of second nearest-neighbor atoms, rather than nearest neighbors. Consequently, faults in the stacking sequence occur quite often. One type of fault is a twinning of the f.c.c, structure with the stacking sequence ABCABCBACBA. Or local regions of f.c.c, sequence may occur in a h.c.p, stacking, ABABCBCB, and so on. For all such sequences, the interlayer periodicity of the layer stacking is unaffected, so that the OOl reflections for the basic hexagonal cell, one layer thick, show no effects of the faults and are not split in nanodiffraction patterns. The same applies for hkl reflections for which h -t- k = 3n for any integer n, because the A, B, and C positions all lie on a hexagonal subcell of the basic unit cell. For all of the other hkl reflections, however, a fault in the stacking sequence represents a discontinuity, and if a nanodiffraction beam includes a fault plane, these spots are split. Observations of such splittings have been made for thin crystals of stainless steel containing twin boundaries and other stacking faults [ 161 ].

11.3. Interfaces

The interfaces between two crystals represent regions of great importance for the determination of the physical and electrical properties of materials and have been the subject of intense study by electron microscopy. Nanodiffraction from the interfaces provides a possible means for studying the details of the arrangements of the atoms in the boundary layer, but to date the application of the technique for this purpose has been limited. The interfaces may be between crystals of the same type in different orientations, as in the intergranular boundaries of polycrystalline materials. Or they may be boundaries between crystals of different structure, as in composite materials. Increasing attention has been paid lately to the interfaces of crystal layers grown epitaxially with one or more of the unit cell axes parallel in the two structures, as in the multilayer structures that have interesting electrical and magnetic properties.

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In general it is to expected that, with the incident beam parallel to a planar interface, a splitting of nanodiffraction spots will be seen when the diffraction spots from the two crystals are well separated, but not when their diffraction spots coincide and are of equal amplitude, so that no discontinuity exists in the Fourier coefficient of the scattering potential. Some splitting is present if coincident diffraction spots have different magnitude or phase on the two sides of the interface due to a change in structure or thickness. The central beam of the nanodiffraction pattern may be distorted or split by changes in the thickness or scattering power of the sample. The deflection of the incident nanodiffraction beam to form a streak in the diffraction pattern was observed for the beam tangential to faces of small crystals of MgO [162] and Au [163]. Attempts were made to relate the form of the streaking to the form of the decay of the potential field from the crystal into the vacuum. A simple-minded interpretation of the streaking is that the variation of the potential field acts like a prism to deflect the electrons. A linear variation of potential would give a deflection of the beam. A nonlinear variation gives a streak. On the same basis it is to be expected that at a planar interface between two materials, there will be a deflection of the incident beam into a streak if there is a change of mean inner potential across the boundary. Such a streaking was observed for the interfaces between Mo and Si layers in a multilayer assembly [ 164]. The length of the streak that is formed depends on the gradient of the projected potential and hence on the sharpness of the interface as well as on the sample thickness. It was found that the streaks are consistently longer for the Mo/Si interface than for the Si/Mo interface, suggesting that the interface is more abrupt in the former case. 11.4. Individual Defects As an obvious extension of the application of nanodiffraction for the studies of planar defects, it should be possible to use nanodiffraction for the detailed study of the perturbation of a crystal lattice associated with point defects or linear defects, particularly those extending through a crystal in the incident beam direction. The patterns could be recorded as the incident beam is scanned over an area of the specimen containing the defect and then interpreted individually and correlated. Because the specimen crystals for such experiments are usually of appreciable thickness, the only available means for interpretation of the nanodiffraction patterns is the comparison with patterns calculated from theoretical models of the defect. Some calculations have been made for diffraction patterns expected for a nanobeam of diameter 4 / k at various positions relative to a dislocation dipole in an iron crystal [165], to demonstrate the possibility of determining symmetries of the dislocation cores. However, the prospect of recording a sufficiently large number of nanodiffraction patterns, with sufficiently accurate beam positioning and intensity measurement, and of matching these patterns with many-beam dynamical diffraction calculations, to make a complete analysis of a defect by this method, has so far been considered to represent a project of rather daunting magnitude and so has not yet been attempted. 11.5. Planar Faults with Very Small Beams So far we have considered the diffraction from faulted crystal structures, using electron beams on the order of 1-nm diameter. If a larger objective aperture is used with a sufficiently coherent electron source, the incident beam diameter on the specimen may have a diameter as small as the DF STEM resolution limit, namely as small as 0.2 nm in favorable cases. Then the beam dimensions may be smaller than the dimensions of the projected unit cell of the crystal structure; the individual diffraction spots in the diffraction pattern overlap and interfere to such an extent that outlines of the spots are no longer discernible. As the beam is moved over the specimen, the diffraction intensities fluctuate with the periodicity

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of the projected unit cell. The intensities for any one beam position depend on the arrangements of the atoms within that part of the unit cell illuminated by the beam [46]. Under such circumstances, it may be possible to investigate the way in which the arrangements of the atoms are perturbed at the position of any fault or defect of the structure. An attempt has been made to use such an approach to study the nature of the planar defects that occur on { 100} planes of some diamonds and have been associated with the segregation of nitrogen atom impurities [ 166]. Before the nanodiffraction study, many investigations of these defects were made by X-ray diffraction and by high-resolution electron microscopy, and many possible models of the defect were proposed, but without any clear determination of the defect structure (although more recent work with HREM has been somewhat more successful [167]). Nanodiffraction patterns were obtained from a thin region of a diamond crystal close to [ 110] orientation with an incident beam of nominally 0.3 nm diameter. The diffraction patterns were recorded with a TV-VCR system. In one 10-s scan of the beam across the defect, with a magnification of 22 MX, 300 diffraction patterns were recorded at intervals of 0.021 nm. Some representative patterns chosen from such a series are reproduced as Figure 35. For Figure 35a, the beam is on one side of the defect; for Figure 35b it is centered on the defect, and for Figure 35c it has crossed the defect to the region of perfect crystal. The patterns, even from the perfect crystal regions, do not show evidence of the division into separate diffraction disks. Instead, they show continuous distributions of scattering. The changes in the symmetry and intensity distribution as the beam crosses the defect are obvious.

Fig. 35. Nanodiffractionpatterns recorded, using a TV camera and videotape, as a beam of ~0.3 nm diameter is scanned across a planar defect in diamond, seen edge on. The beam is (a) on one side of the defect, (b) on the defect, (c) on the other side. Reprinted from Ultramicroscopy, J. M. Cowley et al., 15, 311 (9 1984), with kind permission of Elsevier Science-NL, Sara Burgemartstraat25, 1055 KV Amsterdam,The Netherlands.

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Calculations of the intensity distributions to be expected were made using many-beam dynamical diffraction simulations for the various models that had been proposed for the defect structure. The agreement with the observations was poor for all models, except in the case of the model that had been proposed by Humble [ 168]. This model was, significantly, one in which it was proposed that the defect did not contain any nitrogen atoms, but was produced by a rearrangement of the carbon bonding. Some evidence from the variation with time of EELS signals from the defect regions has suggested that, under irradiation by high-energy electrons, the nitrogen content of the defect regions tends to decrease [ 169].

12. E L E C T R O N CHANNELING: T H I C K CRYSTALS

AND SURFACES 12.1. Axial Channeling in Crystals In recent years, evidence has accummulated, from observations and from theoretical simulations, that when either a plane wave or a focused STEM beam is incident on a crystal in the direction of a principal crystal axis, the electrons tend to be "channeled" along the rows of atoms parallel to the beam. Various approximations to the many-beam dynamical diffraction problem have been proposed to take advantage of this special circumstance, which is one of frequent concern in relation to the HREM imaging of crystal structures [170,171]. To present a simplified picture of the effect, we may consider that a single atom, with its central positive charge, partly screened by an electron cloud, presents a peak of positive potential that acts like a lens of focal length 2-3 nm for a high-voltage electron beam [ 172]. A string of such lenses, placed some fraction of a nanometer apart in the beam direction, will have the effect of first focusing the beam down to a small probe of diameter as small as 0.05 nm. Then, when the beam tends to diverge after the focus, the atoms again exert a focusing effect to cause the beam to reconverge. In the region between the rows of atoms, the curvature of the potential field is in the opposite sense, so that electrons entering between the columns of atoms tend to diverge and so are incorporated within the converging regions along the atom rows. Thus all of the electrons entering the crystal tend to become concentrated in beams tightly centered on the atom rows, and the peak intensities around the atoms tend to oscillate in strength and width with some characteristic wavelength along the rows. The inelastic scattering events tend to be enhanced when the electrons are closest to the atomic nuclei and tend to dampen these oscillations with increasing crystal thickness, but the channeling effect can be pronounced for thicknesses on the order of 10-50 nm for most crystals. The formation of fine beams of electrons channeled along rows of atoms in crystals has been treated theoretically and simulated by several authors [172-174] in relation to HAADF imaging and the production of secondary radiation from the atoms in the rows. It has been proposed [ 174, 175] that if the channeled beam is of small diameter at the exit face of a crystal, a means may be provided whereby foreign atoms sitting on the exit face of the crystal may be imaged with very high resolution. It has been pointed out [176] that electron beams may be focused by the channeling effect into probes with diameters of 0.05 nm or less extending into the vacuum beyond the crystal exit face. Such probes may provide the basis for several forms of TEM and STEM with a resolution on the order of 0.05 nm or better. The use of such probes for the production of nanodiffraction pattern presents interesting possibilities, although it must be realized that, for such incident beams, the diameter of the central spot of the diffraction pattern must be much the same as the diameter of the whole parallel-beam diffraction pattern. The region of the specimen illuminated at any one time has a diameter much smaller than the usual atomic radius. Interference effects resulting from the overlapping of atoms

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in projection give intensity modulations in the diffraction pattern that are on much the same scale as the intensity variation of the whole pattern and are sensitive to the separations of the atoms in the beam direction. One consequence of the channeling effect is the formation of clear images of the rows of atoms in a crystal when a high-angle annular dark-field (HAADF) detector is used in a STEM instrument [43]. The HAADF detector collects electrons scattered at angles greater than the range of normal elastic scattering patterns. The signal comes mostly from the thermal diffuse scattering given by the thermal vibration of the atoms about their mean positions. The effective size of the scatterer at an atom site is then the root mean square amplitude of vibration, which is usually much smaller than the atomic radius. Because the thermal diffuse scattering from the various atoms may be considered as incoherent to a good approximation, the HAADF signal is proportional to the integral of the electron beam intensity along an atom row and so, apart from a few minor oscillations for thin crystals, increases smoothly with crystal thickness and depends on the atomic number of the atoms in the row [ 177]. Thus the HAADF signal for a crystal in a principal axial orientation can give an image contrast that may be described, to a reasonable approximation, in terms of an incoherent imaging process, with intensities dependent on the atomic numbers of the atoms and proportional to crystal thickness and with none of the strongly oscillatory and complicated dependencies of the intensities given by coherent elastic scattering in usual bright-field or dark-field TEM or STEM images [178]. A further consequence of the channeling phenomenon is the set of techniques depending on the variation of the channeling properties of crystals as the incident beam direction is scanned through the Bragg angle for one set of lattice planes or through an axial direction [179]. The generation of secondary radiation, such as the characteristic X-ray production from the atoms, depends on the intensity of the incident electron beam at the atom positions and so is highly dependent on the presence of the channeling effect. This forms the basis for the ALCHEMI (atom location by channeling-enhanced microanalysis) technique now widely used for the determination of the positions of minority or impurity atoms within crystals. The variation in the strengths of the characteristic peaks in electron energy-loss (EELS) spectra as a function of the channeling conditions can be used for the same purpose [ 179]. The formation of the characteristic "channeling patterns" produced when beams of electrons pass through thick crystals in axial directions has been observed and discussed in considerable detail, particularly for ultrahigh voltage electrons (in the MEV range) [ 180]. Interesting comparisons can be made with the somewhat similar patterns formed by the channeling of high-energy beams of protons or other particles through crystals [ 181 ] and used in some investigations of crystal defects. Such patterns are necessarily obtained with collimated beams of relatively large diameter. In general, for thick crystals, it is difficult to make meaningful comparisons of observed and theoretical intensity distributions in nanodiffraction patterns obtained from particular sites within the unit cells of crystals. The intensity distributions are strongly affected by the channeling effects for both the elastically and inelastically scattered electrons. It may sometimes be useful, however, to distinguish sites in the projection of a unit cell structure in terms of the symmetries of the patterns, which are, in general, representative of the site symmetries. Thus, for example, it was shown that nanodiffraction patterns obtained with the incident beam placed at the positions of the various types of metal and oxygen atom sites in a high-temperature superconducting oxide crystal could correctly distinguish the sites in terms of their local symmetries [ 182].

12.2. Surface Channeling The observation of reflection high-energy electron diffraction (RHEED) patterns and of reflection electron microscopy (REM) images, formed by detection and imaging with se-

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lected diffracted beams from a RHEED pattern, have provided evidence for the channeling of electrons along the upper one or two planes of atoms on fiat crystal surfaces. In these techniques, the high-energy electron beam is incident on the crystal surface at a grazing angle of incidence, making an angle with the surface comparable to the Bragg angle for a strong surface-plane reflection, in the range of 10 -2 up to 10 -1 radians for 100-keV electrons [30]. Even more direct evidence of the surface channeling effect is given when a STEM instrument is used to produce nanodiffraction patterns and scanning reflection electron microscopy (SREM) images of the surfaces. In a typical RHEED pattern, obtained when the incident beam azimuth is within a few degrees of a principal crystal zone axis lying in the crystal surface, there is a bright ring of diffraction spots corresponding to the zero-layer zone-axis reflections and passing through the incident beam direction, but cut off by the "shadow edge" of the crystal surface plane (see Figure 7a). At higher diffraction angles there may be several more tings of spots corresponding to the intersection of the Ewald sphere with upper layer lines of the reciprocal lattice. A high proportion of the intensity in the RHEED pattern (up to 80%) is usually given by inelastically scattered electrons, because the electrons incident at grazing angles may have path lengths of hundreds of nanometers within, or close to, the crystal surface layers. A strong background to the diffuse scattering produced by the inelastic scattering appears with the diffraction spots, and diffraction of the diffusely scattered electrons within the crystal produces a prominent array of bright and dark Kikuchi lines, parabolas, and circles. Of these, the parabolas with axes parallel to the crystal surface are of particular interest for our present discussions, because it has been shown that these are produced when electrons diffusely scattered into directions almost parallel to the surface are channeled along the surface planes of atoms before being further scattered into the vacuum [ 183]. As the crystal is rotated in azimuth around the normal to the surface, the whole pattern of Kikuchi lines and curves rotates as if fixed to the crystal. At the azimuthal position for which one of the channeling parabolas coincides with a strong Bragg reflection, the condition is established for elastically scattered electrons to be channeled along the surface planes of atoms. The Bragg reflection intensity is then greatly enhanced, and with it, the whole pattern of RHEED spots and lines becomes brighter. A simplified picture of the situation is that a strong diffracted beam is formed which travels in a direction almost parallel to the surface. The electrons in this beam are trapped within the potential well formed by the surface layers of atoms and by the potential barrier at the surface produced by the average "inner potential" of the crystal. The trapped electrons can then travel for considerable distances along the surface before being diffracted out into the vacuum. This behavior of the electrons in the outer layers of atoms of the crystal has been confirmed by computer simulations applying the many-beam dynamical diffraction calculations developed for transmission diffraction by crystals in a form adapted to the surface diffraction situation [ 184]. In this approach, unlike the majority of RHEED theories, which are concerned with the propagation of the incident wave perpendicular to the surface, the incident wave is assumed to propagate almost parallel to the surface. A multislice formulation is used in which successive slices are made perpendicular to the surface, and small-angle approximations may be made for the forward-propagation geometry with no concern for back-scattering. The fact that the scatterer and the wave functions are then nonperiodic in the slices is overcome by the assumption of periodic continuation with a large unit cell in the direction of the surface normal (i.e., it is assumed that there is an array of parallel crystals with surfaces almost parallel to the incident beam). In this way it is possible to model the changes in the wave function as the beam enters the crystal surface at a small angle and is propagated along the surface, through any changes in structure along its path (steps, impurities, surface projections) and out into the vacuum and to the plane of observation.

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Such calculations have shown that, under the conditions of surface resonance, the electrons within the crystal are, in fact, strongly concentrated within the first one or two planes of atoms on the crystal surface [185], and so, by analogy with the transmission case, are said to be channeled along the surface planes. When the incident beam is very narrow, with a width on the order of 1 nm in the direction perpendicular to the surface, it is shown that the beam enters the surface and then travels a considerable distance, on the order of 100 nm, parallel to the surface before it is diffracted out [186]. This is the analogy of the well-known Goos-Hanszen effect for visible light reflected from glass surfaces. When such a surface-channeled beam meets a down step on the surface, it may pass through the step face and continue to propagate parallel to the surface, but outside the crystal [ i 87]. These theoretical predictions have been confirmed experimentally. In a STEM instrument, with an electron probe with a diameter of ~-1 nm, the nanodiffraction pattern in reflection mode shows the appearance of a strong diffracted beam almost parallel to the surface plane, that is, on the shadow edge of the pattern, when surface channeling conditions apply (see Fig. 36a-c) [ 188, 189]. If this surface-channeled beam is collected to form a dark-field SREM image of the crystal surface, as in Figure 36d, bright lines appear in the image corresponding to the down steps on the surface. Images formed with the higherangle diffracted beams show dark-lines for the down steps and bright lines for the up steps, as is normal for SREM. An even more dramatic demonstration of surface-channeling effects may be provided when the crystal surface employed is the perfectly flat surface of a small single crystal, such as that of a cube-shaped magnesium oxide smoke particle. The incident beam may then enter one face of the crystal and pass through the crystal parallel to another face for a distance of, say, 100 nm and then exit through a face parallel to the first, after which either the incident beam or a strong diffracted beam may be detected to form the SREM image. In Figure 37a, for example, the 0.2-nm lattice fringes of the bulk lattice are seen when the incident beam passes within the crystal, but when the beam enters at the surface layer of atoms and is channeled along the surface plane, the image intensity increases greatly, giving a very bright fringe that is often brighter than when the beam does not strike the crystal at all [188]. The intensity profile of such an image is given in Figure 37b.

12.3. Standing Wave Phenomena In images such as that of Figure 37a, it is often discernible that, in the region of the image outside the crystal, there are a few weak fringes that do not have the periodicity of the crystal lattice. These fringes are thought to arise by a mechanism analogous to the formation of standing waves of X-rays, parallel to a crystal surface, which has been explored extensively in recent years. When X-rays are diffracted by lattice planes parallel to a crystal surface, the incident and diffracted waves may interfere to give a standing wave pattern in the vacuum. Because the refractive index of matter for X-rays differs very little from unity and because the Bragg angles are usually large (on the order of 10-1 radians or more), the angles of incidence and scattering outside the crystal are very close to the Bragg angle. The interference gives standing waves with a periodicity very close to that of the lattice planes [190]. Because the intensity of the secondary X-rays or other secondary radiation from any atoms near the crystal surface is proportional to the intensity in the standingwave field, the observation of secondary radiation can allow the positions of absorbed or impurity atoms on the surface to be deduced. Standing waves of much greater periodicity may be produced at crystal surfaces if X-rays are incident on the surface at very small angles such that total external reflection of the waves at the surface, rather than Bragg reflection, takes place and gives the standing wave field. In this case, the investigation of the composition and placement of atoms 10 nm or more from the surface is possible [ 191 ].

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Fig. 36. Reflection nanodiffraction pattems (a-c) with the beam at the Bragg angle for the (004) reflection from a MgO (001) face, showing the intensity enhancement due to channeling of beams exiting the crystal parallel to the surface. (d) The scanning reflection dark-field image of the surface obtained with a channeled beam, showing bright lines at the down steps. Reprinted from Ultramicroscopy, J. M. Cowley, 27, 319 (Q 1989), with kind permission of Elsevier Science-NL, Sara Burgemartstraat 25, 1055 KV Amsterdam, The Netherlands.

For electrons, standing wave fields may be formed in the same way, but with complications arising from the fact that the refraction of electrons at a crystal surface in R H E E D geometry may give changes of direction of the beams that are comparable to the Bragg angles, and for finite crystal geometries such as that of Figure 37, it is possible to get interference between waves passing through a crystal and the waves reflected from, or transmitted through, surfaces nearly parallel to the incident beam [ 193]. Thus a variety of fringe spacings may be observed in TEM or STEM images by appropriately focusing the objective lens, and corresponding reflections may appear in the SAED or nanodiffraction patterns [ 192, 193]. Because these fringe patterns constitute interferences of electron beams that have passed along different paths relative to the crystal, they may be likened to the interference fringes

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Fig. 37. (a) High-resolution bright-field STEM image of the edge of a thin crystal of MgO, showing the 0.2-nm fringes from (200) planes. (b) Intensity profile of (a). The bright fringes are attributed to surface channeling. Reprinted from Ultramicroscopy, J. M. Cowley, 27, 319 (9 1989), with kind permission of Elsevier Science-NL, Sara Burgemartstraat 25, 1055 KV Amsterdam, The Netherlands.

produced in the various forms of off-axis electron holography [ 194] and may be used as a basis for the holographic reconstruction of various features of the structure of crystal surfaces [ 192].

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13. P O I N T - P R O J E C T I O N IMAGES, IN-LINE H O L O G R A P H Y ,

AND PTYCHOGRAPHY 13.1. In-Line Holograms When a thin specimen is placed close to the cross-over formed by the objective lens in a STEM instrument, the cross-over may act, to a first approximation, as a point source of radiation. Such a point source forms a point-projection image or magnified "shadow image" of the specimen on a distant screen. As discussed in Section 7.3, the spherical aberration of the objective lens gives rise to the appearance of circles of infinite magnification and the formation of distorted Ronchi fringes in the shadow images of periodic objects. In the one-dimensional wave optics picture, the intensity distribution on the plane of observation, as given by (37) with X, Y = 0, is (50)

where Q (u) is the Fourier transform of the object transmission function, q (x), and T (u) is the lens transfer function. Putting in that T(u) = exp{ix(u)} with X(u) = rrAZu 2 + :rcCs,k3u4/2, and neglecting high-order terms in Cs and u, which are negligible for paraxial conditions, the wave function can be expressed as

.(., - f

Q(U)T(U)exp{-2zri),.(A + Cs),.2u2)uU} dU

= T(u){q(ou) 9 t(r/u)}

(51)

where 0 = A + Cs~.2u 2. Thus the intensity distribution is Iq (r/u) 9t (r/u) 12, which is just the bright-field STEM or TEM image of the object, except for the distortion of the magnification by an amount depending on the radius. The magnification is seen to become infinite for u = (--A/Cs~.2)1/2. Thus the limiting case of a nanodiffraction pattern for large objective aperture size is a high-resolution image of the object. Close to focus, the distortion of the fringes images given by a periodic object becomes very pronounced, and the form of the resulting Ronchi fringes may be used as a basis for the determination of the defocus and spherical aberration constant of the lens (see (45), (46)). An alternative way of considering the point-projection images arises from the proposal for electron holography made by Gabor [ 195] as a means of overcoming the limitation of electron microscope resolution by correction for the effects of spherical aberration. For a weak-phase object, the intensity distribution on the plane of observation is written as

I(u) --IT(u)[

2-

T*(u)[T(u) 9 i c r , ( u ) ]

+ T(u)[r*(u) 9 icr**(u)] + . . .

(52)

If this expression is multiplied by T(u), and inverse Fourier transformed, because IT(u) 12 = 1 in the absence of an aperture, the first and second terms give t(x){ 1 - icrqg(x)}, which is just the exit wave from the object imaged without any effects of the lens aberrations. The third term gives the "conjugate image" of the object, far out of focus and affected by twice the spherical aberration of the lens. For a small, sharply defined object, the conjugate image may appear as no more than a diffuse background noise. The reconstruction of the object wave in this manner may possibly be carried out by using a light optical system with the same aberrations as the electron optical lens, as suggested by Gabor [195], or may be performed on a digitized image by manipulation in a computer [196, 197]. In either case, the accuracy of the reconstruction depends on a knowledge of T (u) and so of the aberration coefficients and defocus of the STEM objective lens. Methods for the accurate determination of these parameters include the use of information from Ronchi fringes [106] or from iterative calculations of holographic reconstructions [ 198]. The removal of the undesirable effects of the conjugate image may be achieved, in part, by summing the holograms obtained with a series of displacements of the incident beam [197] or, more completely, by use of one or another of the off-axis modes

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of electron holography that have been extensively developed in recent years, as described elsewhere [ 194, 199]. We consider here the in-line, Gabor-type holography only in the context in which it forms the limiting case of nanodiffraction with a very large or no objective aperture. Gabor coined the term hologram to suggest that, in the plane of observation, the whole of the information obtainable from the elastic scattering by the specimen is present in that the transmitted waves and all scattered waves interact coherently to give the observable intensifies. Thus the hologram is a nanodiffraction pattern with complete overlap, and mutual interference, of all diffracted beams. For holography, a defocused beam is normally used to emphasize the relationship to a point-projection image; for nanodiffraction, the in-focus setting is preferred to emphasize the relationship to a diffraction pattern. In practice, the distinction is somewhat artificial. Successful reconstructions have been made, for example, from holograms showing Ronchi fringe patterns for which the curvature of the fringes is such as to suggest a defocus very close to zero [ 197]. For nanodiffraction, it is normally assumed that the objective aperture size and defocus are chosen so that the imaging effects are not important, that is, so that the diffraction pattern intensities are not influenced by variations of specimen structure outside the minimum irradiated area.

13.2. Correlated Multiple Nanodiffraction Patterns: Ptychography An alternative approach to the problem of improving the resolution of STEM images makes more explicit use of the formation of nanodiffraction patterns and represents an extension of the ideas developed in relation to the observation of interference fringes in the areas of overlap of nanodiffraction disks, as discussed in Section 7.1, for which the term "ptychography" was introduced [94]. In general, it may be stated that the normal BF and DF STEM imaging modes are very wasteful of information. For each position of the scanned incident beam on the specimen, only one signal is recorded, given by a single detector. Much more information is available. For each incident beam position, a whole two-dimensional intensity distribution, the nanodiffraction pattern, is produced on the plane of observation, and it should be possible to record and utilize this large amount of available data to extend the amount of information that can be derived concerning the specimen structure. An initial example of such a process has been given in Section 11.5 for the simple case of one-dimensional imaging of an object for the case of the nanodiffraction study of a defect in diamond. In that case, it was necessary to make simulations of the nanodiffraction patterns by means of many-beam dynamical diffraction calculations, because the crystal was ~ 100/k thick. The problem of interpreting the nanodiffraction pattern data is greatly simplified if the weak-phase object approximation is made, as in the usual treatment of high-resolution imaging of thin specimens. A formulation of the problem of interpreting the available data has been made by Rodenburg and associates [200, 201 ] in terms of Wigner distribution deconvolution and in a more straightforward description in which the observable intensity is expressed in terms of a function of four dimensions: the two dimensions, u, of the nanodiffraction pattern and the two dimensions, X, of the STEM image. In the projection-function approximation, the transmission function of the object is written as q ( x ) = 1 - p ( x ) , which has a Fourier transform, Q ( u ) = 3(u) - P ( u ) . For an incident beam centered at the position x = X, the four-dimensional intensity function is I(u, X) -

[T(u)exp{2rciuX} - e(u) 9 T(u)exp{2rciuX}[ 2

IT(u)l 2 - J" T* (U) P (U) T (u - U ) e x p { - Z J r i U X } d U - c . c .

(53)

where c.c. signifies the complex conjugate of the previous term. Because, for no aperture limitation, IT(u)l 2 = 1, the Fourier transform of this function with respect to X gives the

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four-dimensional function

G(u, p) = 8 ( u ) - T*(u)T(u - p)P(,o) - c . c .

(54)

Then the two-dimensional section of this function represented by u = p/2 becomes just

G(p/2, p ) - - 6 ( u ) - P(u) - P*(u)

(55)

and in the weak-phase object approximation this is just the Fourier transform of 1 § 2~r4~(X). The validity of this approach has been confirmed with light-optical analog experiments and with STEM experiments with moderate resolution [49]. Evidence has been presented that this method may produce an improvement of resolution by at least a factor of 2 as compared with normal BF STEM. An alternative approach to the interpretation of the array of nanodiffraction patterns produced as the incident beam scans over a specimen was demonstrated earlier by Konnert et al. [48]. Under the WPOA, the intensity distribution in any nanodiffraction pattern may be Fourier-transformed to give the Patterson or autocorrelation function of the projected potential distribution function of the object. If the projection of the potential distribution takes the form of isolated peaks corresponding to individual atoms, the atom positions can be deduced by the methods derived for the structure analysis of crystals by X-ray diffraction or electron diffraction methods [1, 2]. Without additional information beyond the intensity distribution, the structure analysis is made difficult by the "phase problem," because the diffracted beam phases are lost in recording the intensities. However, by use of methods well known in X-ray crystal structure analysis, the structure can be solved if some part of the structure is known. Hence, if nanodiffraction patterns are obtained from overlapping regions of the specimen, knowledge of the structure of one part makes it possible to deduce the structure of the next part. On this basis, nanodiffraction patterns obtained from overlapping regions in a small area of a thin silicon [ 110] crystal, using a beam of diameter 3 A, were analyzed to give a map showing the atom positions in the projected structure with an effective resolution that was clearly better than 1 ,A,. The extension of this method to deal with defects in crystal structures has been proposed but not yet realized in practice. On the other hand, the set of overlapping nanodiffraction patterns may be considered as a set of in-line holograms. From Eq. (52), if the transfer function of the objective lens is T (u) -- A (u) exp{i X (u) } and a(x) is the Fourier transform of the aperture function, A (u), multiplication by T (u) and Fourier transforming gives

a ( x ) . [ t ( x ) { 1 - i c r q g ( x + X ) } - i t z ( x ) . {~rqg(-x+X)t*(-x)}]

(56)

where tz(x) is the Fourier transform of exp{2ix(u)} and so represents the spread function for twice the defocus and twice the spherical aberration. As the beam position, X, is changed, the inverted, diffused image of the final term of (64) moves in the opposite direction. If the holograms for successive overlapping specimen regions are added, with all of the proper reconstructions referred to the same origin, the conjugate image terms are smeared out into a continuous background [ 197]. The resolution of the reconstructed image is that determined by the objective aperture size.

14. BEAM-SPECIMEN INTERACTIONS

14.1. Radiation Damage It is common experience that most biological and organic materials and many inorganic materials are rapidly degraded when irradiated by electrons in an electron microscope. Structurally ordered substances tend to become amorphous, and there is frequently a weight loss, with material being dispersed into the vacuum. Such radiation damage limits

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the attainable resolution because the radiation dose required to record an image increases roughly with the square of the magnification. The resolution attainable may be limited to 1-10 nm for biological samples in BF TEM and to an even greater figure for DF imaging. For STEM, the efficiency of signal collection is lower than for TEM in BF imaging, although it is greater for DF imaging if an annular detector is used, with corresponding differences in the attainable resolution. For nanodiffraction, radiation damage effects can be extreme, although they can be alleviated if the diffraction patterns are recorded with the first electrons to pass through any particular specimen area and if the exposure time is limited to the minimum required to produce a pattern having sufficient signal to noise to provide the required information. Irradiation with a focused electron beam is by far the most intense possible form of irradiation of solids. With a high-brightness FEG, it is possible to produce a current density of 109 A/m 2 over regions a few square nanometers in area. If it is assumed that for a 100-keV electron beam, inelastic scattering processes involving a transfer of 20 eV of energy to the specimen have a mean free path of 100 nm, it may be deduced that energy is transferred into a volume of a few nm 3 at a rate of 106 MW/c.c. For most nonconducting specimens, the main mechanism of specimen damage is bond breaking and ionization, leading to radiolytic decompositions [202, 203]. For metals, alloys, and semiconductors, this mechanism is not important, but for incident electrons of sufficiently high energy, knock-on damage occurs in which the collision of the incident electron with an atom may displace the atom from its lattice site [203, 204]. This affects most strongly those atoms that are in crystal defects or on crystal surfaces, so that they are more weakly bound to their lattice sites. For inorganic compounds the two damage mechanisms may both be important, resulting in a variety of chemical and physical transformations. In a number of cases, the irradiation effects of small focused beams have provided the basis for technologically significant techniques for forming structures on a nanometer scale, as when irradiation reduces a compound to a metal or a semiconductor to provide components for nanoscale circuit elements, or very sharp metal-insulator or metal-semiconductor boundaries. The nanobeams may also be used for the drilling nanometer-diameter holes in thin films of insulators with potential use for digital data storage. In practice, radiation damage effects are not of great significance for nanodiffraction studies with 100-keV beams for a wide range of specimen materials, including metals and alloys, semiconductors, oxides, and the various forms of carbon, provided that care is taken to prevent the beam from staying for an excessive amount of time in any one position. For a range of other materials, including many minerals and other inorganic compounds, useful nanodiffraction patterns can be obtained by recording the patterns with a TV-VCR system as the beam is scanned slowly over the specimen in a one- or two-dimensional raster. For example, for thin films of crystalline SiO2 and for various clay minerals, the nanodiffraction pattern for a stationary beam of diameter ,~ 1 nm shows the transformation from crystalline to amorphous structure in -~0.5 s or less, but by recording with the TV-VCR system, some 5-10 nanodiffraction patterns can be obtained, showing the original crystal structure for each small feature selected from a STEM image, as in Figure 38. The difference in electron current density by a factor of ~ 104 between TEM and the focused beam of a STEM instrument was not expected to make any fundamental change in the radiation damage processes. The time between the passages of successive electrons (>0.1 ns) is still much greater than the lifetime of the excited states of the primary excitations, so that coherent multiple excitations are relatively rare events. However, investigations suggest that some radiation damage processes are clearly dose rate dependent and that a current density of 107 A/m 2 is required for their initiation [205]. The damage process must involve some stages with relatively large time constants. Various proposals have been made regarding the nature of the processes involved, but the mechanisms are still not well understood.

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Fig. 38. Nanodiffractionpatterns obtained from the clay mineral, kaolinite, using TV-VCR recording. (a) Beam parallel to the silicate layers. (b) Beam perpendicular to the silicate layers. (c) As for (b), but after "-~0.5-sexposure to the electron beam.

The electron beam irradiation may be accompanied by a small increase in temperature, but this is not usually a significant effect, because the cooling of a very small specimen region by conduction or radiation is usually very efficient.

14.2. Radiation-Induced Chemical Reactions Many observations have been made suggesting that electron irradiation of inorganic crystals in electron microscopes may have the effect of changing the composition of the specimen. In HRTEM of oxide crystals, it has been for observed that higher oxides are often reduced to lower oxides; for example, TiO2 is reduced to TiO. In some cases, the oxide may be reduced to the metal [204, 206]. For the small intense beams in a STEM, cases have been reported of the reduction of A1203 or A1F3 to metallic A1 [207]. These latter cases are significant in that they provide a means of forming small metallic particles of known shape and size. Initial experiments with the reduction of A1F3 to A1 produced very sharp boundaries, which allowed the determination of the localization of the

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excitation of plasmons in metal films [196]. More recently, this reduction process and the reduction of CaF2 have featured in efforts to provide small conductors for solidstate device technology. CaF2 in particular has been considered as a possible insulating layer to replace the amorphous SiO2 layer on silicon, and the possibility of reducing very small regions to form metallic conductors offers a range of new device production techniques [208]. In recent years, a great amount of interest has been generated by the observations and theoretical predictions of the properties of nanometer-scale particles of metals and semiconductors, which, in many cases, differ greatly from the properties of bulk materials. In particular, the magnetic properties of clusters, small particles, and thin layers of ferromagnetic and nonmagnetic elements are strongly dependent on the size, configuration, and shape of aggregates in the size range of 1-100 nm. Particles of ferromagnetic metals may become superparamagnetic [209], and clusters of nonmagnetic atoms may be ferromagnetic. The application of the nanometer-size beam of a STEM instrument has provided a very convenient method of formation of shaped conductors on a nanometer scale and means for the study of the structure and composition of the products by nanodiffraction and microanalysis. In a few cases, the irradiation of metallic specimens has been shown to result in oxidation rather than reduction. For small crystals of silver, grown by evaporation on the surfaces of MgO smoke crystals, and for thin self-supporting films of silver, it was observed by TEM, STEM, and nanodiffraction that the oxide Ag20 could be formed by electron irradiation, even for a vacuum level of less than 10 -8 torr. As mentioned in Section 8.1, the Ag particles seemed to wet the MgO surface, and nanodiffraction showed that the liquid-like meniscus at the boundary actually consisted of a single-crystal oxide phase [113]. Furthermore, small single crystals of Pd were shown to change gradually under irradiation to single crystals of PdO. In other observations, the irradiation of Au particles on MgO surfaces with a STEM beam appeared to give rise to several superlattice structures of unknown composition [ 112]. It has been suggested [210] that particular types of chemical reactions may be enhanced under electron beam irradiation by ensuring that particular elements are present either in the residual gas atmosphere of the electron microscope or in the solid state, incorporated as part of the specimen. In some cases the influence of the added material may be catalytic. In the course of nanodiffraction studies of nanometer-size particles of Pt dispersed on a y-A1203 support, we have noted that if the beam is held stationary on the alumina, the alumina is etched away. However, if the illuminated region includes a Pt particle as well as alumina, the alumina may be transformed into a material that gives the sharp energy loss peak in an EELS spectrum at 15 eV, which is characteristic of A1 metal. Sometimes the energy loss peak is shifted to a somewhat lower energy, suggesting the formation of an A1-Pt alloy. The inference is that the reduction of alumina to metal is catalyzed by the presence of Pt.

14.3. Hole Drilling The drilling of small holes in thin films of insulators by the use of STEM beams has been proposed as a means for the storage of digital or analog data with a very high level of information density. It has been shown, for example, that lettering may be produced by the drilling of holes 2 nm in diameter in an A1F3 film on such a scale that the whole of the Encyclopedia Britannica could be written on the head of a pin [211 ]. Figure 39 shows a hole, with a minimum diameter of 0.4 nm, drilled in a thin crystal of/~-alumina using a STEM instrument. STEM images of the crystal were recorded before and after the beam was stopped to drill the hole. The hole dimensions are smaller than the c axis dimension of the crystal unit cell (1.4 nm). Nanodiffraction studies of the dark region of width 1-2 nm surrounding the hole suggest an amorphous structure.

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Fig. 39. STEMimage of a thin/~-alumina crystal after a hole of minimum diameter 0.4 nm has been drilled through the crystal by stopping the beam at one spot for a few seconds. The image shows fringes due to the 1.4-nmlattice spacing of the crystal.

In the case of MgO, holes may be drilled, although at a much slower rate than for alumina or A1F3. The results for MgO crystals are of particular interest, however, because when it is incident in the [001 ] direction, a STEM beam of circular cross section drills a square hole [212]. It is evident that the holes are bounded by the crystallographic { 100 }-type planes of the MgO lattice. It is not clear whether the shape is determined during the actual drilling process or whether the lattice is reconstructed by relaxation after the drilling. Later evidence has suggested that the region of the hole accumulates a strong electrostatic charge during the drilling process, and this may possibly be a factor in the shaping of the hole.

15. CONCLUSIONS In this review we have given some aecount of the theory, practice, and applications of the various means for obtaining electron diffraction patterns from very small regions of thin specimens. Each of the various modes of operation has its own fundamental limitations and special areas of strength and utility. The selected area diffraction mode, available in all transmission electron microscopes, is widely used and is convenient and satisfactory for many purposes, but has the limitation that it cannot conveniently be used for specimen areas less than ~ 100 nm in diameter. For studies of near-perfect single crystal specimens, although a great deal of qualitative and semiquantitative information may be derived, the accuracy with which the intensities of the diffraction patterns can be interpreted is often limited by the knowledge of the values of the parameters describing the selected specimen area. Although much information can be derived from the high-resolution images of the specimen that can be obtained in parallel, it is often difficult to determine the specimen thickness, the variations in thickness, or the bending or local strains or defects of the crystal. The most effective use of single-crystal

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patterns for the derivation of quantitative information on crystal structures has come from the use of relatively large areas of the thin specimens, for which there is sufficient bending or other defects to ensure that there is an averaging over a range of orientations and the specimens are sufficiently thin to ensure that the kinematical approximation is reasonably good [80]. For the convergent beam diffraction mode, the specimen area illuminated is usually on the order of 10 nm in diameter and sufficiently small to ensure that the crystal region being studied is of uniform thickness and orientation. Under these circumstances, as outlined in Sections 5 and 6, the full power of the electron diffraction method to give quantitative results has been demonstrated. The techniques themselves allow the determination of the values of the relative parameters, such as thickness, orientation, and local strain with the accuracy required for the quantitative interpretation of the intensity data, and means for the accurate measurement of intensities are now available. The possibility of obtaining structure factor amplitudes and phases with accuracies beyond those from X-ray diffraction analysis for some materials has opened up an important area of investigation, providing experimental data for comparison with fundamental theoretical studies of the structures ot solids. The fact that these studies can be made using very small volumes of crystal implies that increasing application may be made to the quantitative analysis of crystal phases, crystal defects, and strain fields on a scale far beyond the capabilities of any other technique. For diffraction modes making use of electron beams of diameter 1 nm or less, the potential applications have scarcely been touched. In principle it should be possible to make the same type of quantitative measurements of the intensity distributions of the diffraction patterns as for the convergent beam modes, with the same accuracy of analyses achieved for much smaller regions. However, there is little incentive to do this when the regions of crystal with uniform structure are large enough to allow the CBED methods to be applied. For specimens for which the structure varies more rapidly, there is a fundamental difficulty in the determination of the physical parameters of the illuminated region of the specimen. It is experimentally difficult to correlate the diffraction patterns with high-resolution electron microscope images of exactly the same region, and it is difficult to ensure that extended observations of the diffraction patterns refer to the same groups of atoms when the diffraction pattern intensities can vary with a movement of the electron beam of as little as 0.1 nm. Hence most of the observations of diffraction from subnanometer diameter regions have been of a rather qualitative nature, with no detailed interpretation of the pattern intensifies. Even so, the method has proved useful for many purposes and could obviously be effectively applied in many more cases. The limitation to its broader application comes mainly from the fact that very few instruments appropriately equipped for convenient and efficient recording of the nanodiffracfion patterns are currently in operation, and the sole manufacturer of the most appropriate microscopes, the dedicated STEM instruments, is no longer in business. The possibilities for application of coherent nanodiffraction, including the various modes of holography and ptychography and the studies of crystallite shapes, defects, and discontinuities, have been envisaged and demonstrated in primitive forms, sufficiently to suggest that the development of a wide range of very powerful techniques is possible, extending greatly the range of present microscopy and diffraction methods. The main requirement for progress toward these ends is the provision of instruments designed with these purposes in mind and having the precision and stabilities equal to or beyond those of current or pending TEM instruments. It is hoped that this review may help to stimulate efforts to produce such machines in the future.

Acknowledgment Much of the work reported in this article and the illustrations have depended on support from the ASU Center for High-Resolution Electron Microscopy.

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Note Added in Proof: Very r e c e n t l y a n e w s c h e m e has b e e n d e s c r i b e d that p r o v i d e s an exact inversion o f the m u l t i p l y scattered C B E D pattern intensities to crystal structure factors (J. S p e n c e , A c t a Crystallogr., Sect. A (1998)). Patterns are r e q u i r e d f r o m several different orientations. T h e resulting c h a r g e density m a p gives the a t o m i c positions and can be u s e d to help identify a t o m i c species. T h e Bravais lattice, space group, and lattice constants m u s t be d e t e r m i n e d by other C B E D m e t h o d s d e s c r i b e d here. R e l a t e d p a p e r s on the topic o f d y n a m i c a l inversion can be f o u n d in a f o r t h c o m i n g F e s t s c h r i f t for A. E M o o d i e , to be p u b l i s h e d in A c t a C r y s t a l l o g r a p h i c a , S e c t i o n A, early in 1999.

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M.A. Gribelyuk and J. M. Cowley, Ultramicroscopy 50, 29 (1993). L.F. Allard, D. C. Joy, and E. Voelkl, "Introduction to Electron Holography." Plenum, New York, 1997. J.M. Rodenburg and R. H. T. Bates, Philos. Trans. R. Soc. London, Ser. A 339, 521 (1992). J.M. Rodenburg, B. C. McCallum, and P. D. Nellist, Ultramicroscopy 48, 304 (1993). L. Eyring, in "High Resolution Transmission Electron Microscopy" (P. R. Buseck, J. M. Cowley, and L. Eyring, eds.), Chap. 10. Oxford Univ. Press, Oxford, 1988. L.W. Hobbs, in "Introduction to Analytical Electron Microscopy" (J. J. Hren, J. J. Goldstein, and D. C. Joy, eds.), p. 437. Plenum, New York, 1979. D. J. Smith and J. M. Barry, in "High Resolution Transmission Electron Microscopy" (P. R. Buseck, J. M. Cowley, and L. Eyring, eds.), Chap. 11. Oxford Univ. Press Oxford, 1988. C.J. Humphreys, Ultramicroscopy 28, 357 (1989). M.R. McCartney, P. A. Crozier, J. K. Weiss, and D. J. Smith, Vacuum 42, 301 (1991). M. Scheinfein, A. Muray, and M. Isaacson, Ultramicroscopy 16, 233 (1985). L.J. Schowalter and R. W. Fathauer, CRC Crit. Rev. Solid State Mater Sci. 15, 367 (1989). E. L. Venturini, J. P. Wilcoxon, P P. Newcomer, and G. A. Samaro, Bull. Am. Phys. Soc. Ser. H 39, 223 (1994). T. Sakaguchi, M. Watanabe, and M. Asada, IEICE Trans. E 74, 3326 (1991). C.J. Humphreys, T. J. Bullough, R. W. Devenish, D. M. Maher, and P. S. Turner, in "Proceedings of the 12th International Conference on Electron Microscopy" (L. D. Peachey and L. D. Williams, eds.), Vol. 4, p. 788. San Francisco Press, San Francisco, 1990. P.S. Turner, T. J. Bullough, R. W. Devenish, D. M. Maher, and C. J. Humphreys, Philos. Mag. Lett. 61, 181 (1990).

87

Chapter 2 FOURIER TRANSFORM INFRARED SURFACE SPECTROMETRY OF NANO-SIZED PARTICLES Marie-Isabelle Baraton SPCTS-UMR 6638 CNRS, Faculty of Sciences, F-87060 Limoges, France

Contents 1.

Introduction

2.

Surfaces of Nano-Sized Materials 2.1.

..................................................

Structure of Surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2.2.

Importance of the Surface in Nano-Sized Powders

2.3.

Technological Processes Involving Surface Phenomena . . . . . . . . . . . . . . . . . . . . . . .

Fourier Transform Infrared Surface Spectrometry

4.

5.

6.

7.

8.

90

...................................... .........................

.............................

90 90 92 93 94

3.1.

Basic Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

94

3.2.

Fourier Transform Infrared Spectrometers

96

3.3.

Infrared Spectroscopic Techniques

..............................

..................................

Adsorption Phenomena and Surface Characterization

...........................

................................

97 100

4.1.

Definition of Surface Sites and Probes

4.2.

Physisorption and Chemisorption . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

100 102

4.3.

Criteria for Probe Molecule Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

102

Experimental Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

103

5.1.

Activation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

103

5.2.

Probe Molecules

5.3.

Cell Designs

............................................

104

110

..............................................

Nano-Sized Oxide Powders . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

110

6.1.

111

Silica

..................................................

6.2.

Alumina . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

115

6.3.

Zeolites . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

119

6.4.

Titanium Dioxide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

120

6.5.

Tin Oxide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

122

6.6.

Zirconia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

124

6.7.

Other Oxides

125

..............................................

Nano-Sized Nonoxide Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

125

7.1.

Nano-Sized Nonoxide Powders . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

125

7.2.

Thin Films on Silicon Wafers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

138

7.3.

Carbon-Related Compounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

141

7.4.

Porous Silicon

.............................................

143

Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

147

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

148

Handbook of Nanostructured Materials and Nanotechnology, edited by H.S. Nalwa Volume 2: Spectroscopy and Theory Copyright 9 2000 by Academic Press All rights of reproduction in any form reserved.

ISBN 0-12-513762-1/$30.00

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I. INTRODUCTION Over the last 10 years, the production of nano-sized particles has grown rapidly. The unique size-dependent properties of nanoparticles have aroused the curiosity of scientists worldwide [1-3]. A tremendous number of papers have been published in areas as diverse as synthesis, colloid chemistry, materials engineering, nanotubes, self-assembled systems, biological structures, nanoelectronic devices, modeling, and nanocomposites. Loose or sintered nano-sized powders are used in high-added-value applications in major fields [4] such as metallurgy, catalysis, environment, magnetism, pharmacy, biology, microelectronics, and optoelectronics. Nanoparticles can now be routinely produced if the nanometer size is our only goal. Unfortunately, the control of their properties, reactivity, and long-term stability remains the bottleneck for diversified industrial applications. The quantum confinement effect that appears when the particle size is decreased to a few nanometers still gives rise to fundamental questions. Besides, the very high specific surface area of nano-sized powders implies a key role of the very first atomic layer when the nanopowder is in contact with various gases, liquids, or solids. For example, it is obvious that the atomic composition of the interfaces and grain boundaries in consolidated samples essentially depends on the chemical composition of the first atomic layer of nano-sized particles. Moreover, the chemical composition of the surface controls the degree of particle agglomeration, which is a tremendous problem in nanopowder processing. In all applications involving surfaces and interfaces, the use of nanoparticles will imply a dramatic increase of the role played by the interactions between the two milieus. On the other hand, it must be realized that, in any case, a surface cannot be considered a priori as similar to the bulk with respect to the atomic composition and the crystalline phase. Therefore, the need for a precise surface control and further surface tailoring of nano-sized materials calls for a technique allowing both the characterization of this very first atomic layer and its interactions with surrounding media. Under specific experimental conditions, Fourier transform infrared (FTIR) spectrometry is a relevant tool for the identification of the chemical species constituting the first atomic layer as well as the chemical state of the surface atoms. In this chapter, our approach to the subject begins with the discussion of a fundamental question: Why must the surface of nanopowders be studied independently from the bulk? Then the different methods used in FTIR spectrometry will be described, and a critical assessment will be made of their performances and limitations. The specific experimental conditions suitable for nano-sized particle characterization will be discussed. Because an extensive literature can be found on FTIR surface characterization of nano-sized particles with catalytic properties, we shall discuss only a few striking examples in catalysis and emphasize other applications for which the control of nanoparticle surfaces is also of critical importance.

2. SURFACES OF NANO-SIZED MATERIALS 2.1. Structure of Surfaces

Regardless of the particle size, the surface of any material is expected to have properties that are different from those of the bulk. Ideal surfaces may be obtained by cleaving a single crystal in an ultrahigh vacuum. If the cleavage is perfect, the obtained surface should be a perfect representation of the parallel atomic planes of the bulk. This is called a "bulk exposed plane" Even if no reconstruction has occurred, the loss of periodicity in one dimension would result in changes in the electronic states at the surface, thus implying surface electronic properties different from those of the bulk. The bond breakage resulting in a lack of nearest neighbors of the surface atoms leaves chemical bonds "dangling"

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FTIR SURFACE SPECTROMETRY

outside the solid and thus available for chemical reactions [5]. We shall see how important these dangling bonds are. In the ultrahigh vacuum environment, this bond breakage actually leads to relaxation and/or atomic rearrangements to reach the minimum energy. The relaxation retains the symmetry in the planes parallel to the surface but modifies the separation distance between the atomic planes and can propagate toward deeper layers. By disturbing the symmetry of the solid surface, reconstruction affects all structure-sensitive properties, such as atomic vibrations, and chemical, optical and electronic behaviors of the surface [5]. An alternative method of obtaining a clean surface is to cut the crystal parallel to a crystallographic plane, polish the obtained surface, etch it, and anneal it in an ultrahigh vacuum (or eventually oxygen) to restore the geometric order at the surface [6]. It is obvious that the structure of the surface obtained depends on the cutting direction with respect to the crystallographic planes. But there is no reason to think that the polished and annealed surface will have the same structure as the ideal cleaved one. Other well-defined surfaces can be obtained, in principle, by epitaxial growth of ordered films on top of single crystals or by preparing microcrystals of well-defined morphology [7]. But in these latter techniques, the incomplete control of the processes is responsible for the presence of surface defects. Most scientists working in this area consider the surfaces of the materials obtained by the above methods to be "nearly perfect" surfaces. Obviously, a real surface is nonhomogeneous and presents macroscopic defects such as ledges, kinks, comers, and cracks, as well as point defects such as vacancies or adatoms. Moreover, in the case of complex materials such as alloys or mixed oxides, segregation phenomena must also be taken into account. These may lead to an increase in the concentration of one or several elements in the surface layer. Segregation occurs to minimize the energy at the interface and depends on the pressure and/or the nature of the gaseous environment at the interface. The role of the defects is particularly important in surface chemistry. Indeed, all crystals contain a certain proportion of defects, but their concentration at the surface may be different. These surface defects are often responsible for the catalytic properties and the particular chemical behavior of the surface. The introduction of impurities or dopants should be balanced by vacancies and interstitial atoms, thus resulting in an alteration of the electronic structure. Electrons and holes also may act to change the oxidation state of a transition metal ion [6]. The clean surfaces only survive in an ultravacuum environment. The cleavage of the crystal leaves electrical charges on the surface, that is, coordinatively unsaturated anions and cations [8]. Therefore, when exposed to the atmosphere, all solid surfaces become covered with various adsorbed species. The latter species partly compensate for the surface unsaturation and the dangling bonds due to crystal cleavage. The contamination by any surrounding atmosphere is very fast. Depending on the nature of these adsorbed molecules and the temperature and pressure conditions, chemical reactions can occur. Moreover, the atoms adsorbed on the surface can diffuse and react with the bulk atoms, yielding a surface layer whose chemical composition and morphology may be quite different from those of the bulk. Basic examples are the corrosion and the formation of an oxide layer on metallic surfaces. In the latter case, the surface layers behave as a metal-semiconductor interface. It is obvious that relaxation, reconstruction, structural imperfections, as well as adsorbed molecules and atoms cause drastic changes in the electrical and magnetic properties [9] at the surface by modifying the affinity of the surface for electrons. Moreover, the presence of coordinatively unsaturated anions and cations results in a specific surface chemistry. On the other hand, the nature of the impurities adsorbed on the surface is partly related to the synthesis history of the material. It must also be noted that the molecules, chemical groups or atoms adsorbed on the surface can originate either from the gaseous environment surrounding the sample or from the interior of the sample through diffusion processes. For example, in the case of metal oxides prepared by chemical routes, carbonates, nitrates, and hydrocarbon residues are among the species most likely to be found on the surface. But the most common and abundant component of the surface layer is atmospheric water, whose

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molecules can strongly adsorb and dissociate to form hydroxyl groups. Moisture plays a dominant role in the chemical and electronic surface properties of the materials, and its adsorption on clean elemental solids is the starting point of the formation of the first layer of oxide [10]. This will be discussed later. It must be noted that the definition of a surface is quite subjective. The useful thickness of the surface layer under consideration depends on the studied phenomena and on the experimental technique employed to analyze it. In this chapter, we shall consider as the surface the very first atomic layer, which is usually regarded as being responsible for the chemical interactions. 2.2. I m p o r t a n c e of the Surface in N a n o - S i z e d Powders

Let us consider a cubic stacking of atoms with a density of 1 g/cm 3. The concentration of atoms at this solid surface is ~ 1015 atoms/cm 2 [ 11 ]. Obviously, this concentration varies with the density, but this figure gives an idea of the surface atom number compared to the total atom number. Figure 1 shows the evolution of the number of surface atoms relative to the total number of atoms versus the particle size. It appears that the number of atoms at the surface increases rapidly with increasing specific surface area of the powder. In nano-sized materials, the surface-to-bulk ratio is very high, and the specific surface area can exceed 400 m 2 g-1. The fraction of atoms at the surface [12] is on the order of 10 -7 in single crystals considered as 1-cm-diameter spheres. This fraction may increase up to 0.5 in nanocrystals considered as 1.5-3 nm-diameter spheres. This means that 50% of the atoms are on the surface. In this case, the surface properties compete with those of the bulk. Therefore, when consolidating a nano-sized powder exposed to air, the "foreign" atoms adsorbed on the surface will be trapped in the grain boundaries, and major difficulties may be encountered in the sintering process [13]. If the grain size is on the order of 10 nm or less, the volume occupied by the grain boundary structure can be 30% or more [ 14]. Important efforts have been made to refine powder synthesis techniques and to characterize the mechanical properties of the consolidated materials [ 14-16], yet very few .

0.9 0.8

0.7 0.6 rp~

-9 0.5 o

0.4

.

0.3 0.2 0.1 |

0

10

.

I

20

.

i

.

30

i

40

.

|

.

50

i

60

.

!

70

,

!

80

particle diameter (am)

Fig. 1. Evolutionof the ratio S (number of atoms at the surface/total number of atoms) versus particle diameter (cubic-octahedric stacking).

92

FTIR SURFACE SPECTROMETRY

characterization techniques have been applied to the control of the chemical cleanliness of the surface of the starting nano-sized powders. It should be realized that this must be the very first step in the control of the consolidation process. Besides, because the surface structure depends on the preparation conditions, the reactivity of the nanoparticles is also related to the synthesis method. The usual representation of a surface by the terrace-step model is not really suitable for nano-sized particles. A rigid lattice can hardly be hypothesized, and the model of the surface based on preferentially exposed crystallographic planes becomes of questionable value. The terraces, which are ordered domains, have to be reduced to a very small size, with an increased number of steps and kinks, where the atoms are in low coordination number. This leads to a higher surface reactivity of the nanoparticles compared to their micron-sized counterpart. It is indeed known that an increase in the defect concentration on the surface, by ion bombardment of smooth surfaces, for example, can promote catalytic reactions [ 17]. It must also be noted that, at a high concentration of defects on the surface, defect interactions may occur, causing them to cluster or order in different ways [6].

2.3. Technological Processes Involving Surface Phenomena Many kinds of technological processes involve surface phenomena. For example, we have just mentioned that the quality of consolidated nanostructured materials depends on the surface cleanliness of the starting nano-sized powders. Catalysis also requires clean and controlled surfaces because adsorbates or impurities may have adverse effects (e.g., site poisoning) on the catalytic properties and efficiency. The surface defects and surface rearrangements are of critical importance for the catalytic activity of materials, and therefore detailed surface characterization in relation to the catalytic properties has given rise to thousands of papers for decades. On the other hand, interactions between metal catalysts and supports play an important role in catalysis, especially when the support is a reducible transition-metal oxide. The interactions, which depend on the chemical composition of the support surface, can strongly alter the catalyst behavior [6]. However, studies of this type of catalyst-support interaction are scarce compared to the number of papers published on the surface characterization of the catalyst itself (see [ 18], for example). An important application of metal oxides involving surfaces is gas sensing [6, 19]. These metal oxides are generally n-type semiconductors. In solid state physics, it is known that the adsorption of molecules bends the bands at the surface, thus producing changes in the surface electrical conductivity. The sensing mechanism is based upon these surface interactions leading to electrical conductivity variations. Because impurities adsorbed on the surface also lead to conductivity changes and thus to adverse effects, the control of the chemical composition of the sensor surface is a key issue in the optimization and reproducibility of the sensor response. But conversely, it can be taken advantage of to modify the chemical surface species to improve sensor selectivity and sensitivity. The variety of sensor preparation procedures described by G6pel [ 19] clearly shows that it is of utmost importance to control the sensor surface: 9 to produce well-defined surfaces of ideal bulk materials; 9 to modify these surfaces by thermodynamically controlled surface, subsurface and bulk reactions; 9 to irreversibly modify these surfaces by overlayer formation; 9 to tailor interface properties on the atomic scale. The control of metal oxidation phenomena has a tremendous economic impact. The mechanism of oxidation of metal surfaces in dry and wet environments must be fully understood before the complex action of corrosive atmospheres can be studied. All types of junctions in semiconducting devices involve surface properties. At the interface, it is

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obvious that electronic properties will be affected by the chemistry and structure of both surfaces. As an example, the behavior of electrical contacts between metal and semiconductors is sometimes puzzling because of the lack of control of the surfaces. In microelectronic engineering, crystal growth is largely employed to fabricate semiconducting devices. It is clear that the composition and structure of the very first atomic layer of the substrate are the key points in controlling crystal growth. The dispersion of particles in liquids or polymers is essentially based on surface chemistry. The problem is particularly critical when nano-sized particles must be dispersed. Agglomeration cannot be controlled and the choice of surfactants cannot be made without a good knowledge of the surface chemical species. Once the surface composition is known, predictions can be made about the kind of surfactants that will adsorb and on how ions in solution will affect the surface [20]. The dispersion of particles in matrices finds applications in painting (automotive coatings), compact disks, and polymer coatings [21 ]. As another example, the materials used in biology and medicine must exhibit a specific surface chemical behavior compatible with the surrounding biological milieu [22]. Among many other examples of applications involving surfaces and interfaces, we can name semiconductor passivation, photoluminescence, and wetting and lubricants. Therefore, the nature and properties of the surface itself are key issues in understanding the interactions between various media and solid surfaces. This turns out to be critical when nano-sized materials are involved. A comprehension of the surface structure on the molecular level [21 ] is thus required for a systematic control of technical properties. On the other hand, control of surface properties can be achieved by modifying the surface chemistry with additives. In principle, both reactivity and electronic properties can be tailored. In the following, we shall describe some examples of surface modifications monitored by infrared spectrometry.

3. FOURIER TRANSFORM INFRARED SURFACE SPECTROMETRY Many techniques used to characterize the surface of micron-sized powders have been applied to nano-sized materials without special care. But it appears that these techniques may have a depth resolution larger than the particle size! For example, it is not acceptable to consider as a surface characterization technique one whose depth resolution is on the order of 2-3 nm when the particle size is 5-8 nm. Therefore, the usual surface characterization methods must be reassessed when applied to nano-sized particles. Infrared (IR) spectrometry has been used for decades in organic chemistry as a bulk characterization tool. In the 1940s, the first surface studies using IR spectrometry were published, particularly by Terenin and co-workers [23, 24], who performed measurements on metal oxides in their laboratory in St. Petersburg, Russia. Since then, the technique keeps improving, particularly with Fourier transform spectrometers. Fourier transform infrared spectrometry is currently a very relevant tool for surface analyses because it allows the investigation of the chemical composition and reactivity of the first atomic layer in situ under various environments.

3.1. Basic Concepts The infrared range extends from 12,500 to 10 cm -1 (0.8-1000/zm) and is divided into three parts: the near infrared region from 12,500 to 4,000 cm -1 (0.8-2.5/zm), the medium infrared region from 4,000 to 500 cm -1 (2.5-20/zm), and the far infrared region from 500 to 10 cm -1 (20-1000/zm). The infrared spectrum of a molecule originates from the transition between vibrational and rotational energy levels of this molecule. Detailed descriptions of the theory can be found in references [25] and [26], whereas more applied introductions are discussed in references [23, 27-29]. The rotational fine structure of a

94

FTIR SURFACE SPECTROMETRY

spectrum is only observable when the molecule is in the gas phase. The rotational freedom is lost in the liquid phase. The molecular vibrations can be described as bond stretching, bond bending and eventually torsional modes and concern the medium infrared range. The frequencies of the different types of vibrations are mainly determined by the mechanical motion of the atoms and can be written in the harmonic oscillator model as follows: v (cm-1) - ~ 1

1

1

lz

mx

my

where k is the force constant of the bond linking the X and Y atoms,/z is the reduced mass of the vibrating atoms, and mx and m r are the masses of the X and Y atoms. The intensity of the infrared absorptions is related to electrical factors such as dipole moments and polarizabilities. The ratio of the transmitted radiation energy IT to the incident radiation energy I0 is defined as the transmittance T: T=

IT I0

whereas the absorbance A is given by A--lOgl0 ( 1 ) The integrated absorption intensity corresponding to the area under the absorption band is related to the concentration of the absorbers and to the molar extinction coefficient (e) (liter/centimeter/mole) according to Beer's law: A (v) -- e ( v ) c x

where c is the molar concentration of the absorbing species (moles per liter) and x is the sample path length (centimeters). This equation is the basis of quantitative analyses in nonscattering media. Based on the relationship between absorbance and concentration, difference spectra can be calculated in the case of analyses performed in situ. In this case only, the difference between the spectra recorded at two steps of the experiments allows one to identify the appearing (or increasing) species and the disappearing (or decreasing) species, respectively corresponding to positive and negative bands. These difference spectra are very useful for clarifying the assignments, but one must be cautious when analyzing such spectra, because a frequency shift or a band shape modification may also appear as a positive or a negative band. According to classical theory, the absorption of electromagnetic radiation is possible only when there is a change in the dipole moment of the molecule during the course of the vibration. When there is no change in the molecular dipole moment, the vibration is defined as infrared inactive. However, this "forbidden" vibration may become infrared active if the symmetry of the molecule is modified by an interaction with another molecule or a solid surface, for example. The perturbation of molecular vibrations by interactions with solid surfaces is the fundamental underlying mechanism used in surface analysis by FTIR spectrometry, as will be described later. Modifications in the force constants of the bonds and the geometry of the molecules are related to the vibrational frequency shifts, which, in return, bring information on the nature of the interactions (Section 4.2). On the other hand, certain specific chemical groups (e.g., OH, CH3, C = N . . . . ) have been found to give rise to vibrational bands that are always located in the same IR region, regardless of the complexity of the molecule in which the group is present. This very important observation makes it possible to assign the absorption frequencies of a complex molecule to the characteristic groups constituting this molecule. This reflects the constancy of the bond force constant from molecule to molecule [28]. As a consequence, small

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changes in the environment of a chemical group will lead to small changes in the characteristic frequencies of this group. Another important fact that will be referred to in the following is the effect of the isotopic exchange. For example, by substituting deuterium for hydrogen in a chemical group, theoretically no change in the electronic distribution and thus no change in the force constant will occur. Nevertheless, the vibrational frequencies involving the hydrogen atom will shift toward lower values because of the higher atomic weight of deuterium. Therefore, under specific conditions, the H/D isotopic exchange allows the identification of the vibrations of the hydrogen-containing groups. Similarly, the exchange of oxygen atoms with the 1802 isotope helps the assignments of the absorption bands due to adsorbed oxygen, even though, in this case, the resulting frequency shifts are weak because of the slight weight difference between the two isotopes.

3.2. Fourier Transform Infrared Spectrometers Dispersive spectrometers have been replaced by FTIR spectrometers with a design based on the interferometer originally developed by Michelson. Details on FTIR spectrometers and FTIR spectrometry can be found in several books, particularly in [30]. Let us briefly describe the principle of a FTIR spectrometer. This is a setup that divides a beam of radiation into two paths and recombines the two beams after a path difference has been introduced, so that interferences can occur between the beams. The basic scheme of the Michelson interferometer is given in Figure 2. The infrared radiation emitted by source (1) is split by the beamsplitter (2), which is an essential item of the apparatus. The beams transmitted (IT) and reflected (IR) by the beamsplitter must be equivalent, and theoretically 50% of the incident energy goes in each direction. The IT and IR beams are then reflected by two plane mirrors perpendicular to each other, one fixed (3) and the other movable (4). After the beams return to the beamsplitter, they interfere and recombine. The resulting beam goes through the sample (5) and to the detector (6). The intensity of the beam measured by the detector is a function of the path difference ~ generated by the movable mirror. This function 1(3) is called an interferogram. It is obvious that the intensity of the interferogram depends on the intensity of the

Fig. 2. Schemeof a Michelson interferometer. 1: Source; 2: beam splitter; 3: fixed mirror; 4: movable mirror; 5: sample; 6: detector.

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FTIR SURFACE SPECTROMETRY

source, the beamsplitter efficiency, and the detector response. The I (8) interferogram is mathematically treated by computing its Fourier transform, leading to B ( v ) , which represents the beam intensity as a function of the wavenumbers, that is, the spectrum: I (3) -- f_+oo B ( v ) cos(2yrv~) d v O0

B ( v ) --

A(~)I(~)cos(2Jrv3)d~ L

where A (8) is the apodization function and 2L is the maximum path length of the movable mirror. The advantages of the FTIR spectrometer over the former dispersive ones are described in great detail in [29] and [30]. Let us briefly mention the important Jacquinot's advantage, named after the discovery by Jacquinot that interferometers have a higher optical conductance than dispersive (prism or grating) spectrometers. As for Fellgett's advantage, it results from the fact that all spectral elements are sampled simultaneously, meaning that for the same spectral range and the same resolution, FTIR spectrometers allow a much faster recording with the same signal-to-noise ratio, or that for the same recording time, the signal-to-noise ratio is strongly improved. The Fellgett and Jacquinot advantages are actually at the heart of the performances of FTIR spectrometry. The resolution of interferometers mainly depends on the path difference of the two mirrors. In the most commonly available commercial FTIR spectrometers, the resolution varies from 0.3-0.5 to 16 cm -1. It is worth pointing out that the recent development of new sensitive detectors and sophisticated software for data processing makes FTIR spectrometry an extremely important tool for chemical and structural analyses.

3.3. Infrared Spectroscopic Techniques When radiation reaches a sample, the beam is transmitted, reflected, and diffused while part of the energy is absorbed (Fig. 3). All the resulting beams contain spectral information on the sample. Therefore, according to the selected spectroscopic technique, the analyzed beam is essentially the transmitted beam, the diffused beam, or the reflected beam. The choice of the technique mainly depends on the nature of the sample and on the requested environment in which the sample must be analyzed.

Fig. 3. Infraredspectroscopic techniques for surface analysis. (a) Transmission-absorption. (b) Diffuse reflection. (c) Reflection-absorption. (d) Attenuated total reflection (ATR).

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3.3.1. Transmission-Absorption Spectroscopy For surface analysis, the most popular sampling technique is the convenient absorption measurement (Fig. 3a). Because the analyzed light is the transmitted part of the incident beam, the sample must be transparent to the IR radiation. This excludes very thick samples and highly conducting materials such as bulk metals. For surface analyses, powders must be pressed into thin pellets. When pressing the powders, care must be taken not to modify the crystalline structure, the stoichiometry, and the specific surface area of the original powders. The pressure must be adjusted to the minimum value allowing the reliable fabrication of self-supporting disks. It is worth noting that as a consequence of structural modifications caused by the pressing of the powder, the refractive index of the pellet may become too high to allow the transmission of IR radiation [31 ]. In this case, other techniques should be used. The applied pressure is also an important factor in the reproducibility of the experiments and must be carefully set for each type of material. Because light scattering depends on the particle diameter and on the radiation frequency (Raleigh theory), it is obvious that if the particle size is small enough compared to the wavelength, the scattering component is very weak. Therefore, the transmission mode is particularly well adapted to the study of nano-sized particles. In addition, the smaller the particle, the higher the specific surface area, and the higher the signal is from the surface species. To enhance this latter signal, the amount of powder must be larger than the weight needed for standard bulk analyses. Therefore, pure powders are used to make selfsupporting pellets with no or very rare addition of potassium bromide (KBr) or other salts. Stainless steel grids can be used as a support of the powder to ensure a better temperature distribution in the pellet [32]. The pellets made of pure powder are usually not transparent to the IR radiation in the region where the skeletal absorptions occur. Because most of the materials covered in this chapter are ceramics and related materials, their bulk vibrations fall in the lowest wavenumber region (usually below 1000 c m - 1), which therefore becomes unavailable for surface studies. But we shall see later that surface species are essentially composed of organic groups whose stretching vibrational frequencies fortunately fall in the highest wavenumber range. However, it must be noted that bending and torsional modes of surface species absorb in the low wavenumber region and therefore cannot be studied directly. On the other hand, because of the relatively large amount of powder needed for these surface analyses, overtones and band combinations of the bulk vibrations can be observed in the spectra. Although popular, the use of pressed disks of adsorbents presents some inconvenience. In addition to the above-mentioned pressure effects, the pressing of the powder may slow down both the diffusion of the adsorbates into the pellet and the effusion out of the pellet of the reaction gaseous products [30]. The transmission-absorption technique is quite sensitive to surface species on powders, provided that the specific surface area is high enough. For example, it is possible to detect the absorption related to surface species coveting 1% (and even far less in favorable cases) of the surface [31]. For a typical 1 cm 2 disk of 10 mg made of an alumina powder with a surface area of 200 m 2 g - l , the total developed area of the disk is 2 m 2 [33]. The transmission-absorption technique is therefore particularly suitable for the surface study of nano-sized powders.

3.3.2. Diffuse Reflectance Infrared Fourier Transform Spectroscopy In the diffuse reflectance mode, scattered radiation is the essential effect to be considered (Fig. 3b). The first advantage of this mode over the transmission technique is that loose powders can be analyzed without the need for pressing. As a second advantage, it is possible to study nontransparent samples such as surfaces of bulk materials or thin films deposited on opaque substrates. Another important point is its lower sensitivity to bulk

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FTIR SURFACE SPECTROMETRY

electrical conduction [31 ], making the analysis of conducting samples possible. However, like the transmitted intensity, diffuse reflectance is nearly zero in spectral regions where the absorption of the sample is very high [30]. Another disadvantage is the lack of reproducibility of the band intensities because of variations in the scattering coefficient each time the sample is loaded in the cell [30]. Reproducibility is generally affected by factors such as sample preparation, particle size, particle size distribution, packing density, surface flatness, and sample cup orientation [34]. All of these reasons generally prevent a reliable quantitative analysis. The high sensitivity of diffuse reflectance to surface species is due to the multiple reflection and diffraction of the beam at the surfaces of the particles [29]. To compare the transmitted and diffuse spectra, the latter must be mathematically treated. The model developed by Kubelka and Munk [35a, 35b] is the most widely accepted one. It assumes that the Fresnel reflectance can be neglected when the particle size is much smaller than the wavelength, which is the case for nanoparticles [36].

3.3.3. Infrared Reflection-Absorption Spectrometry In infrared reflection-absorption spectrometry (IRRAS, IRAS, or RAIS), specular reflectance is used in a specific way to analyze thin films or molecules adsorbed onto an absorbing material [30]. The sample to be analyzed is deposited on a mirror so that the absorption of the sample reduces the reflectance. This results in a sort of transmission spectrum of the sample [29] (Fig. 3c). In this case, the angle of incidence is relatively high (greater than 80~ and a single reflection is usually achieved. The absorption of a beam polarized perpendicular to the surface is enhanced, whereas the absorption of a beam polarized parallel to the surface is zero. Under these conditions, only the adsorbate vibrations associated with a change in the dipole moment perpendicular to the surface are detectable [31 ]. Developed by Pritchard et al. [37a, 37b], this method is conveniently used to study organic molecules on the surface of metal substrates and to investigate corrosion, coatings, and metal-solution interfaces [38, 39]. Many studies of CO adsorption and other small molecule adsorption on metallic surfaces can be found [40-42]. For example, the use of IRRAS demonstrates that N2 only adsorbs on a defective Pt(111) surface, thus showing that N2 can be a sensitive probe of monovacancy defect sites [17]. IRRAS is a well-established technique for obtaining bond-specific chemical information with submonolayer sensitivity to adsorbates on metal surfaces [43]. According to Bradshaw and Schweizer [40], it should be possible to detect at least one tenth of a monolayer, corresponding to ~ 1014 atoms or molecules, instead of -~ 1020 atoms in the case of a transmission analysis. However, it is difficult to apply this method to semiconducting or insulating substrates because the IRRAS signal is weak and easily distorted on these surfaces. A way to overcome these difficulties is to deposit a reflective metallic film under the thin layer of interest. Such samples are called "buffed metal layer" substrates and have been found to be effective in the enhancement of the IRRAS signal [43]. A very thin metal oxide layer grown on a metallic substrate also allows the determination of adsorption and reaction studies [44]. In theory at least, it is possible to obtain information on the surface sites and, in the case of molecular adsorption, on orientation as well.

3.3.4. Attenuated Total Reflection Internal reflectance or attenuated multiple total internal reflection (ATR) spectroscopy is a particular case of reflection (Fig. 3d). Because the depth of penetration of the evanescent wave escaping from an internal reflection element (IRE) is relatively small, it is fairly simple to measure the ATR spectrum of a layer deposited on the surface of a prism (IRE) [30]. To a certain extent, ATR can be used as a surface technique to study films. Indeed, the penetration depth dp depends on the wavelength of the radiation ~., the refractive index

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of the IRE, the refractive index of the sample, and the angle of incidence of the beam at the surface of the IRE [30]. For most materials, dp is about one tenth of the wavelength (500 nm at 2000 cm -1), but it is easy to vary dp from ~0.12~. to 0.05~ when the refractive index of the sample is ~ 1.5. When the deposited layer is very thin, the penetration depth can correspond to the entire thickness of the layer, and then ATR spectroscopy becomes a bulk analysis technique. In general, the layer to be investigated is deposited on one or two surfaces of a prism in which the IR beam propagates through several internal reflections. This technique is also used to study directly such surface modifications of the IRE as a silane layer on a germanium element [45]. The ATR geometry has proved its usefulness for the detection of Sill vibrations on the surface of a silicon crystal used as an IRE [46, 47]. When this technique is utilized with a polarized incident beam, the chemisorption sites and the bond configurations of surface Si atoms can be determined. But in this case the frequencies below 1500 cm -1 cannot be analyzed because of the strong absorption of the Si crystal used as an ATR prism. The ATR setup is also very useful for characterizing solutions in water or water films. For example, the silanization of surfaces, which has important applications in chromatography, and self-assembled monolayer formation can be followed in situ with the ATR technique [48, 49]. This spectroscopic method applies to the case of the reaction of trimethylchlorosilane on the surfaces of ZnSe and Si prisms, demonstrating the formation of thin water films [49]. Chemical reactions in slurries can also be monitored in situ with a cylindrical internal reflectance cell [50]. Like the IRRAS technique, ATR can also be applied to the study of metal layers at the interface with a solution. Because the efficiency and area of contact between the sample to be analyzed and the IRE are of critical importance, this technique is not suitable for powders and nanoparticles. It is thus limited to thin films directly deposited on the IRE, to liquids and to soft materials. 3.3.5. Other Techniques Among the other techniques used in IR spectrometry to characterize surfaces, we can mention photoacoustic spectrometry (PAS), photothermal beam deflection spectrometry (PBDS), infrared emission spectrometry (IRES), and surface vibrational sum frequency generation spectroscopy (SFG). We shall not describe these methods here because they are not among the most popular ones. Further details can be found in [30, 31, 33], and limited applications to surface studies are treated in [51-53]. According to [31] and [54], IRES should compete with the other IR techniques for surface analysis, yet very few papers dealing with this subject have appeared. As for SFG, it is a quite recent technique, and, to our knowledge, it has not yet been applied to the surface study of nanoparticles. PAS and PBDS are not suitable for the study of surface species. Indeed, as we shall see later, for surface analyses the samples need to be heated under vacuum, which precludes the use of PAS and PBDS, as these techniques require a gaseous environment. PAS and PBDS compete with the usual techniques only in the case of very absorbent materials, such as carbon and coal [31, 55-57].

4. ADSORPTION PHENOMENA AND SURFACE CHARACTERIZATION 4.1. Definition of Surface Sites and Probes Because relaxation processes (Section 2.1) imply surface reconstruction, differences exist between the bonds at the surface and similar bonds inside the bulk. The surface bonds should lead to particular vibrational frequencies corresponding to the surface modes. These surface modes are due to surface truncation and changes in the surface bond constants [58].

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FTIR SURFACE SPECTROMETRY

Although it is theoretically possible to identify these surface modes in the vibrational spectrum of the sample, it is practically very difficult to do so because these surface modes weakly absorb in the same wavenumber region as the very intense bulk modes. As a consequence, a detailed analysis of the spectra in the bulk absorption regions is usually not possible, except in some favorable cases [58, 59]. However, the surface sites generated by these relaxation and reconstruction processes can be identified. Morrison [ 10] used the term "surface sites" to describe a group of atoms at the surface that are in some way or another reactive. A surface site can be a surface atom of the host lattice with a dangling bond, an unoccupied bonding orbital with an affinity for electrons, or an occupied orbital with a low ionization potential. Because the real surface is heterogeneous (Section 2.1), the surface sites can be associated with defects, and, in this case, their activity is often very high. According to Morrison [10], "the probability of an oxygen molecule sticking after striking a silicon surface is 500 times higher when the surface is covered by steps." According to their affinity for electrons and protons, the surface sites are defined as 9 9 9 9

Lewis acid sites or electron acceptors; Lewis base sites or electron donors; BrCnsted acid sites or proton donors; BrCnsted base sites or proton acceptors.

The presence of these different surface sites determines the reactivity of the surface toward its environment. In addition, it is expected that the concentration of Lewis and BrCnsted acid sites will increase with diminishing particle size (i.e., increasing the powder specific surface area), as a consequence of the corresponding increase in the concentration of surface defects [60]. The defect concentration can even be purposely increased by ion bombardment to modify the surface reactivity. For example, as mentioned in Section 3.3.3, it has been demonstrated by IRRAS that nitrogen does not adsorb on a perfectly clean Pt(111) single crystal, whereas it does adsorb when vacancies are created by Ar + ion bombardment [ 17]. Tanaka et al. [ 10, 61 ] have obtained a relationship between the Lewis acidity (a) on the one hand, and the cation (rc) and anion (ra) radii and the cation oxidation number (Z) on the other: acx

ra)z -rc

2

But the effects of the surface heterogeneity (steps, kinks, etc.) can cause deviations from the Tanaka model, which does not take the coordinatively unsaturated sites into account. Surface heterogeneity must be carefully kept in mind when the experimental results on surface reactivity of nanoparticles are analyzed, because it has a strong influence on both chemical and electrical properties of the surface [60]. As a consequence of the surface reactivity, the interaction of the nanoparticle surface with its environment (atmosphere or gaseous reactants from the synthesis) will yield chemical surface species (Section 2.1). The first use of IR spectrometry in surface studies is precisely the determination of the chemical nature of these species. Let us consider the example of the OH groups, which typically result from the hydrolysis reaction between the surface and atmospheric water. These OH groups are present on almost all surfaces. Such chemical species are called intrinsic probes. The v(OH) stretching frequency of a surface hydroxyl group depends on the chemical nature and on the coordination number of the atom to which it is bonded. If two OH groups are linked to two kinds of atoms (two different atoms, or the same atoms but in two different coordination numbers), two different v(OH) frequencies will appear in the spectrum. They correspond to each type of OH group. Therefore, we can conclude that several v(OH) absorption bands in the spectrum

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will indicate either several types of atoms at the surface or several coordination numbers for this atom if only one kind of atom is possible (Section 6.2). To study surface sites such as Lewis and BrCnsted sites, purposely adsorbed molecules are used as extrinsic probes. These carefully chosen molecules (Sections 4.3 and 5.2) adsorb on the surface and, as a consequence, their IR spectrum will be perturbed with respect to the gas phase. As in the case of intrinsic probes, the vibrational frequencies of an adsorbed molecule depend on the nature of the atom (surface site) to which it is bonded and on the coordination number of the atom within the surface. The magnitude of the modifications in the IR spectrum of the probe molecule caused by the adsorption is related to the strength of the adsorption.

4.2. Physisorption and Chemisorption Two types of adsorption are usually distinguished: physical adsorption (or physisorption) and chemical adsorption (or chemisorption). In the physisorption process, the adsorbentadsorbate interaction is of the van der Waals type. The binding energy for physisorbed molecules is typically 0.25 eV or less [5]. In chemisorption, the interaction is stronger and may be dissociative, nondissociative, or reactive. However, it must be noted that no clear border between physisorption and chemisorption is defined. Ionosorption is a particular case of adsorption occurring on metals or semiconductors in which a free electron from the conduction band or a free hole from the valence band is captured on or injected by surface species [ 10]. The adsorbate species are thus ionized, leading to a variation of the electrical conductivity of the sample. This redox process is the fundamental mechanism taking place in the chemical gas sensors based on semiconducting metal oxides, and it will be discussed in Section 5.2.10 and Sections 6.4 and 6.5. When a molecule is physisorbed or chemisorbed on the surface, the electronic distribution in this molecule is perturbed with respect to the gas phase. Therefore, changes in its vibrational spectrum can be observed according to the nature and strength of the adsorption. If the molecule is slightly physisorbed, the frequency shifts may be less than 1% of the original absorption frequency. The weakly physisorbed species are easily removed by an evacuation at room temperature. In contrast, in the chemisorption process, the molecule adsorbed on an active site may dissociate or react with a neighboring adsorbed species. In this case, tremendous changes are noted in the spectrum of the adsorbed molecule. New compounds may be formed and appear as new adsorbed species. It is also possible that neighboring surface sites such as acid-base pair sites actively participate in a reaction [62]. They are of particular importance in catalytic processes. Physical and chemical adsorptions can occur at the same time on any surface. Moreover, different types of chemical adsorption mechanisms can simultaneously occur. An evacuation at increasing temperature (i.e., a thermal desorption) enables one to discriminate these different chemisorbed species according to their thermal stabilities.

4.3. Criteria for Probe Molecule Selection As just explained, the adsorption mechanism may be very complex. To allow a proper surface characterization, it is obvious that the probe molecules should be chosen to be as simple as possible. Specific probe molecules and their interactions with the surface sites will be presented in Section 5.2. Let us begin with the discussion of some criteria that should be taken into consideration when selecting probe molecules. More details can be found in [60] and [62]: 9 The probe molecule should preferentially interact with only one type of surface site. 9 The concentration and the lifetime of the adsorbed species should be sufficient to allow their detection.

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FTIR SURFACE SPECTROMETRY

9 The adsorption mechanism of the probe molecule should not lead to surface reconstruction. 9 The probe molecule should have a molecular size as low as possible to eventually access the pores. This is also particularly important in the case of coadsorption, where two different probe molecules are simultaneously adsorbed on the surface. Indeed, the steric hindrance of the first adsorbed molecule may prevent the second probe molecule from accessing the still available surface sites. 9 The probe molecule should allow the discrimination between acid or basic sites of different strengths. We shall see later on (Section 5.2) that actually very few probe molecules (if any) simultaneously meet all of these requirements. According to the principle of hard and soft acids and bases (HSAB) [62-65], hard acids are more likely to interact with hard bases and soft acids are more likely to interact with soft bases. In the HSAB concept, hard indicates a low polarizability of the orbital, whereas soft indicates a high polarizability [62, 64]. The hardness of metal oxides, for example, increases with increasing positive oxidation state and with decreasing degree of unsaturation [62]. It is worth noting that in addition to the polarizability of the orbitals, the acid and base strengths depend on the orientation of the orbitals, the electron affinity, and the geometry of the sites. It must be kept in mind that any acid (or base) is defined with respect to a base (or acid). As a consequence, any characterization by a probe molecule only reveals the particular behavior of the particle surface toward this probe molecule [60]. Moreover, the medium in which the interaction is probed may influence the surface. For all of these reasons, 9 The experimental conditions should be clearly defined when the surface composition is given. 9 The scale of acidity/basicity strengths determined by a particular probe molecule for a series of compounds may not be the same as that determined by another probe molecule. 9 To compare the results from different authors, the experimental procedures should be taken into account.

5. EXPERIMENTAL PROCEDURE 5.1. Activation As we have already explained, the contact of a "clean" surface with any type of environment results in adsorbed chemical groups minimizing the energy at the interface. Therefore, the exposure of this surface to regular atmosphere causes a hydrolysis reaction with humidity. Hydroxyl groups are formed, which in turn form hydrogen bonds with surrounding water molecules. The surface thus becomes covered with several layers of hydrogen bonded water molecules. In addition, other contaminants can react with the surface, such as atmospheric carbon dioxide, leading to CO 2- carbonate species. Other gases (such as NH3, CH4, H2, etc.) present in the synthesis chamber may also adsorb or react, thus poisoning surface sites. Under those conditions, only a limited number of surface sites (if any), as defined in Section 4.1, are available for interaction with probe molecules. To identify these adsorbing sites and the surface hydroxyl groups, the surface must be "cleared" of the contaminants. This is partially achieved by a thermal treatment under dynamic vacuum, referred to as the activation process. Some of the contaminating species are removed, but it is possible that some of them remain on the surface, depending on the activation temperature. It is clear that the uppermost layer of adsorbed water is eliminated by a simple evacuation at room temperature and that all hydrogen-bonded species have

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disappeared at 423 K. Depending on the strength of the interactions, other contaminants such as carbonates are released at higher temperatures. The usual activation temperature is around 773-873 K. It is worth mentioning that this activation process triggers the reduction of transition metal oxides. Therefore, the activation temperature must be adjusted to remove most of the contaminating surface species while keeping the original stoichiometry of the sample. However, in some cases, a subsequent oxidizing treatment may be required to restore the original stoichiometry of the compound. The activation temperature also modifies the hydration degree of the surface, which may strongly influence the acido-basicity. A too high activation temperature results in the condensation of neighboring hydroxyl groups to form water, which is eliminated. This also leads to a decrease in the specific surface area. All of these points show the importance of the pretreatment conditions in surface analysis and characterization of the adsorption centers. Because no standard conditions have been established, the pretreatment parameters must be carefully checked before results from different authors and works are compared. Upon removal of the contaminating species, the surface sites become available to selected probe molecules. It should be understood that this activated surface is no longer in equilibrium. Therefore, as soon as any probe molecule comes in contact with the freed surface sites, an adsorption and possibly a reaction will occur to minimize the energy at the interface. Activation, probe molecule addition, and thermal desorption are the essential steps in the surface characterization of nano-sized powders by FTIR spectrometry. 5.2. Probe Molecules

Depending on the compounds and on the surface sites to be probed, several molecules can be used. However, as mentioned in Section 4.3, none of them meet all of the criteria requested for the ideal probe molecule. A thorough description of probe molecules can be found in [60, 62, 66]. In this section, we shall briefly discuss the most commonly used probe molecules; Figure 4 summarizes the main molecules probing the different types of active sites. 5.2.1. Deuterium

Strictly speaking, deuterium (D2) cannot exactly be considered a probe molecule. But it is a marker of hydrogen vibrations. Indeed, as explained in Section 3.1, the exchange of hydrogen for deuterium leads to a shift of the frequencies involving the exchanged hydrogen atoms due to the higher molecular weight of deuterium. Because the exchange can only take place on species accessible to deuterium, that is on surface species, it allows us to discriminate the hydrogen-containing species on the surface from those inside the bulk. However, it may happen that for some surface groups, hydrogen is only partially exchanged. This is due to a low exchange rate and does not necessarily mean that the species that are not exchanged are trapped inside the bulk. Possible interactions with other probe molecules will definitely answer this question. Another advantage of the isotopic exchange particularly concerns the v(OH) stretching absorption bands, which fall in the 4000-3000 cm -1 range. In this region, the signal-tonoise ratio is usually relatively low. By exchanging hydrogen for deuterium, the v(OH) absorption shifts to the v(OD) absorption range at lower wavenumbers in a region where the signal-to-noise ratio is improved. As we shall see later, this is of great interest when a thorough study of the surface hydroxyl groups has to be performed (Sections 6.2 and 7.1.3). However, in the case of semiconductors, caution must be taken when deuterium is used. Like H2, deuterium is a reducing gas and may affect the oxidation state of the surface atoms. Experiments with hydrogen must be performed under the same conditions to discriminate the effect of the isotopic exchange from that of the reducing action.

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FTIR SURFACE SPECTROMETRY

Sample activation I I

Identification of surface groups I

o H, NH,

cH...

773-873 K, 1-2 h dynamicvacuum

[ ....

isotopic exchange H/D internal and external species

I

CH3OHaddition ::> X-OH + CH3OH--~ X-OCH3 + H20 Lewis acid (electron aeceptor): A13+

Acidity of surface sites

Basieity of surface sites

Probe-molecules: CO, CO2, CH3CN,NH3, CsHsN ... Bronsted acidity (proton donor): H+ Probe-molecules: CO, NH3, CsHsN, C6I-I6...

I I

]

Lewis base (electron donor): Oa" Probe-molecules: CO, CO2, CH3CN, C4H5N... Bronsted basicity (proton aceeptor): Off Probe-molecules: CO2, CH3CN, CAIsN ...

Fig. 4. Processfor the characterization of the chemical species and reactive sites on a nano-sized powder surface. Adapted from [32].

5.2.2. Carbon Monoxide Even though carbon monoxide (CO) interacts in a complex way with surfaces, it is one of the most popular probe molecules. The small size of the CO molecule allows its access to all sites. Moreover, the v(CO) stretching frequency is very sensitive to the manner in which the CO molecule is bonded to the adsorbent, thus making this molecule of great relevance in surface studies. Carbon monoxide can actually probe both acid and basic sites. The interaction with acid sites is weak because CO is a weakly basic molecule. Therefore, lowtemperature experiments may be necessary in some cases [60]. Carbon monoxide is the favorite molecule for probing metal surfaces, and the IRRAS technique (Section 3.3.3) has been largely employed to investigate the CO adsorption on single-crystal metal substrates [40, 41]. Carbon monoxide can react with [60, 66] 9 Acidic hydroxyl groups through hydrogen bonds. This causes a shift of the v(OH) frequency. The magnitude of this shift is related to the OH BrCnsted acidity strength. 9 Lewis acid sites. The carbon atom is bonded to acid sites via a a - d o n o r bond, which usually causes a shift of the v(CO) frequency toward the higher wavenumbers with respect to the gas phase. The frequency is related to the acid strength. But in the case of transition metal ions with a sufficiently high density of d states, electrons from the metal can be donated back to an antibonding CO orbital, thus weakening the CO bond and lowering the v(CO) frequency. 9 Basic 0 2- sites leading to CO 2- "carbonite" ions [66] and possibly more complex structures, such as (CO)n2- polymers or carbonate ions [67], depending on the reactivity of these oxygen ions.

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It must also be considered that a shift of the v(CO) stretching frequency toward higher wavenumbers can occur when the CO concentration on the surface is increased (higher surface coverage), because of dipole-dipole interactions. We shall see later on (Sections 6.4 and 6.5) that CO can oxidize into CO2 at relatively low temperatures when adsorbed oxygen species are available on the surface.

5.2.3. Carbon Dioxide Carbon dioxide (CO2) has an acidic character and thus can probe basic sites: 9 It probes the O H - basic groups by forming hydrogenocarbonate (or bicarbonate) species HO-CO 2- (Fig. 5a). 9 It probes the 0 2- basic oxygen ions by forming several kinds of CO 2- carbonate species. These carbonate groups differ in their coordination to the surface, which may involve neighboring metal cations. Monodentate, bidentate, or bridged geometries (Fig. 5c, d, e) are possible and adsorb at different frequencies. Polydentate carbonates may also be formed as a result of the incorporation of the carbonate ions into the oxide bulk [66]. Busca and Lorenzelli [68] extensively described the possible carbonate geometries on oxide surfaces and demonstrated that they could be discriminated by simultaneously observing the thermal stability of the adsorbed species and the A v splitting of the asymmetric Vas(CO) vibration. Indeed, this latter Vas(CO) degenerate vibration in the free carbonate ion splits into two components when the CO 2- symmetry is lost because of the adsorption. A v is about 100, 300, and 400 cm -1 for monodentate, bidentate, and bridged species, respectively. 9 It can also physisorb on Lewis acid sites. In some cases, the linear geometry of the CO2 free molecule is lost and the IR inactive Vl symmetric stretching (1340 c m - 1 in the free molecule) may be observed. Interactions with transition metal atoms may lead to ionized CO 2 carboxylate species (Fig. 5b). It must be noted that, contrary to CO, carbon dioxide can oxidize a partly reduced surface [66].

H

I

o

o C

%C2

I

O

I M

M

(a)

O

O

I~ /c. 0

0

(b)

O

O

--.N.../.-CI

II / C\

0

i

.

M

M

0

!

"'..

II /\ C 0

.

..

M

(C)

O

(d)

O

O

M

M

..'"

(e)

Fig. 5. Possiblespecies formed during CO2 adsorption on an oxide surface. (a) Hydrogenocarbonate. (b) Carboxylate. (c) Monodentate. (d) Bidentate. (e) Bridged. Adapted from [68].

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FTIR SURFACE SPECTROMETRY

5.2.4. Ammonia Ammonia (NH3) is one of the most commonly used probe molecules for surface acidity assessment. Its small size allows one to probe porous materials, such as zeolites. It is a hard base that reacts with the acid OH groups to form the NH 4+ ammonium ion. Ammonia can also coordinate on Lewis acid sites. Both NH 4+ and coordinated ammonia are easily detected in the IR spectra, thanks to their characteristic NH stretching and bending vibrations. The shifts of the vibrational frequencies of coordinated NH3 can be related to the electronegativity of the metal ions. A scale of the surface Lewis acidity of oxides was thus determined by Wilmhurst [69] as follows: A1203 > Ga203 > TiO2, Cr203, ZnO > ZrO2 > MgO > Ni203 > NiO, CuO The first disadvantage is that ammonia dissociates into N2 and H2 at high temperatures and can possibly nitride the surface. The second disadvantage is that the presence of residual water leads to the formation of NH 4+ ions, thus altering the results on the BrCnsted acidity of the surface.

5.2.5. Pyridine Like ammonia, pyridine (CsHsN) is very popular as a probe of surface acidity. This hard base is slightly weaker than ammonia, however. Because of the lone electron pair of the nitrogen atom, pyridine easily interacts with Lewis acid sites. The most sensitive vibrations of the pyridine molecule in the interaction with the surface are two ring vibrations, denoted V8a (1579 cm -1) and Vl9b (1439 cm-1). The shifts of these frequencies with respect to the gas phase are related to the strength of the acid sites to which the pyridine molecule is coordinated. But pyridine can also form hydrogen bonds with surface hydroxyl groups and, like ammonia, react with protonic sites (BrCnsted acids) to yield the [CsHsNH] + pyridinium ion. The characteristic V8a (1640 cm -1) and Vl9b (1540 cm -1) absorption frequencies of the pyridinium ion do not change with the acidity of the BrCnsted sites [8, 60, 62]. However, in the presence of strong O 2- basic sites, a dissociative adsorption can occur. It is characterized by the formation of CsH4N- anions and new O H - groups [66]. Another possibility is the reaction with strongly basic O H - at high temperatures, leading to surface pyridone species characterized by a v(C=O) stretching band around 1634 cm -1 [62].

5.2.6. Pyrrole Pyrrole (C4HsN) is an interesting molecule for probing the basic sites. A hydrogen bond between the NH group of pyrrole and the surface groups can easily be formed. The v(NH) frequency shift is related to the basicity if the surface groups are 0 2- or O H - [66]. However, when the interaction with 0 2- sites is too strong, the NH bonds may be broken, leading to pyrrolate ions (C4H4N-) and OH species [70]. The Jr electrons of the pyrrole ring may participate in the interaction, thus implying distortions of the ring plane. The spectrum of the pyrrole molecule is actually very complex, and analysis of the perturbation caused by the adsorption requires very careful study to determine all of the possible interactions.

5.2. 7. Methanol and Alcohols Alcohols can dissociate on Lewis acid-base pairs or coordinate on strong Lewis acid sites through the electrons of their oxygen atom. Acidic alcohols mainly adsorb on acid-base pairs with a predominantly basic character, whereas less acidic alcohols (such as methanol) can also adsorb on acid-base pairs with a predominant Lewis acid character [66]. The adsorption of alcohols with different acidities has led to a classification of oxides as a function of their surface acido-basicity by correlating the FTIR data and the calorimetric

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adsorption isotherms [66]. For example, the basicity of oxides decreases in the following order: ThO2 > ZnO > MgO > Fe203, TiO2

5.2.8. Nitriles Although some difficulties arise in the interpretation of the IR spectrum of pure acetonitrile (CH3CN) because of the Fermi resonance between the v(C_--N) stretching mode and the 8s (CH3) + v(CC) combination mode [71 ], acetonitrile is used to probe acid and basic sites. It is a weak base and coordinates via the nitrogen atom to the Lewis and BrCnsted acid sites. But another reaction involving acid-base pairs can occur, yielding carbanion CH2CN-. Dimerization of acetonitrile may result. In addition, reaction with strongly basic O H - was proved to transform acetonitrile into acetate groups via acetamide species, depending on the temperature [62, 66].

5.2.9. Other Molecules Other molecules are employed in surface characterization, such as 9 Chloroform, which is a weak acid and probes basic surface sites. It has been used to calibrate the strength of the surface basic sites, the strongest sites being those on the CaO surface [66]. 9 Amines, which, like ammonia, probe the surface acidity. 9 Ketones, which, as soft bases, are expected to be relatively specific toward acid sites because of the electrons of the oxygen atom. But unfortunately, they easily dissociate, thus complicating the spectra interpretation. 9 Ethers, which are reactive on acid sites, but, like ketones, they often dissociate. 9 Benzene, which as a re-donor molecule is specially suited to the characterization of the acid strength of OH groups. Indeed, benzene forms re-bonds with BrCnsted acid sites, and the resulting shift of the v(OH) band is related to the strength of the interaction. A scale of the OH acidity has thus been established for oxides as follows [60, 72]: B-OH < Si-OH < Ge-OH < P-OH 9 Formic and acetic acids, which are not usually considered to be probe molecules in the catalysis field, but may be of interest because they reveal the presence of oxygen vacancies on surfaces [73, 74]. This will be discussed in the case of several examples (Sections 6.5 and 7.1.5).

5.2.10. Oxygen Oxygen is not usually regarded as a probe molecule. However, the oxygen species are of critical importance in oxidation reactions, because oxygen can be adsorbed and/or ionosorbed on the surface of metals or semiconductors. Ionosorption is a complex mechanism involving both chemical reaction and electron transfer. The oxygen ionosorption depends on the material pretreatment temperature, which suggests the influence of impurity movement on the ionosorption process [10]. A simple reaction route for oxygen ionosorption was proposed by Morrison [10] as follows: e- +O2 :

02

O2 = 2 0 e-+O

= O-

108

FTIR SURFACE SPECTROMETRY

An alternative route was proposed by Davydov [75]: e- +02

=

0 2

e- + 0 2 = 2 0 2e- + 2 0 - = 2 0 2 . But additional O 2- species can also exist. Therefore, the possible oxygen species on a surface are O2, O 2, O - , O 2-, and O 2- . Although the reaction route is not considered important, the concentration of the O 2 and O - species at equilibrium has been the subject of several papers [10, 76, and references therein]. The ratio of the O 2 to O - concentrations depends on the temperature. It is expected that the electron affinity of the oxygen atom is higher than that of the oxygen molecule. In general, at intermediate pressures, the concentration of O 2 dominates at low temperatures, whereas that of O - dominates at high temperatures [ 10]. However, in the field of catalysis, it seems that the lattice oxygen (O 2-) is the only recognized active species in both partial and total oxidation over metal oxides [77, 78]. On the other hand, it is known that the most active metal oxides in catalytic oxidation are semiconducting transition metal oxides due to oxygen defects (n-type semiconductors) or oxygen excess (p-type semiconductors). When oxygen is ionosorbed on the surface of n-type semiconductors, a decrease in the electrical conductivity appears due to the removal of defect electrons on the formation of oxygen ions. According to Galwey [73], the total volume of oxygen that may be ionosorbed is much less than a monolayer because of increasing difficulty in the removal of electrons from defect levels at progressively greater depth below the surface. The reverse electrical behavior is observed for p-type semiconductors. Indeed, during oxygen ionosorption, electrons are removed from the conduction band, thus leading to positive hole formation. This is accompanied by an increase in the electrical conductivity. The monolayer or submonolayer of adsorbed oxygen species may considerably modify the properties of the surface toward the adsorption of another species, as observed in the case of catalytic promoters. We shall see in examples later that the variations in the electrical conductivity of nanopowder samples can be followed in situ by FTIR spectrometry under different gaseous environments, including oxygen (Sections 6.4 and 6.5). Although electron spin resonance (ESR) is one of the important methods for demonstrating the presence of O 2- on solid surfaces, it is not convenient for the identification of O - species. Infrared spectrometry can detect not only adsorbed O2, but also O 2 and O zspecies. With regard to O - species, they are identified by M-O- vibrations (where M is the metal atom). Depending on the strength of this interaction, the frequencies may fall too close to the very intense M-O 2- bulk vibrations. The adsorbed oxygen species have been identified by FTIR spectrometry on chromium oxide (Cr203), titania (TiO2), nickel oxide (NiO), tin oxide (SnO2), [75, 79-83] and other oxides [10 and references therein]. It is possible to verify the assignments by adsorbing the 1802 isotope, because a shift of the vibrations involving adsorbed oxygen species is expected. Different geometries in the molecular adsorbed species must also be considered [84]. It is very important to realize that the nature of the adsorbed and ionosorbed oxygen species strongly depends on the oxide pretreatment conditions [79, 81 ]. As mentioned in Section 5.1, the activation treatment is a reducing process, and therefore n-type semiconductors tend to become opaque because of the increase in the electrons in the conduction band. To be conveniently analyzed, the samples must be reoxidized. The p-type semiconductors show the reverse behavior and become opaque under oxidation [77]. Depending on the type of semiconductor, the process of electron (respectively, hole) transfer between the adsorbates and the conduction (respectively, the valence) band is revealed in the infrared spectra by a very broad band, which may even appear as a distortion of the spectrum baseline. This broad band is not associated with vibrational modes but with localized or

109

BARATON

delocalized electronic transitions. It may give information on the reduction state of the metal oxide, which is an important asset for in-depth understanding of the gas adsorption mechanisms in the field of sensor technology [85, 86]. Note that, in some cases, this broad band, appearing as a positive or negative feature in the difference spectra, may perturb the analyses of these difference spectra.

5.3. Cell Designs To perform the activation treatment and probe molecule addition, specially designed setups are used. All of the designs must integrate sample heat treatment, cell evacuation, and gaseous reactant admission under controlled pressure. Therefore, all setups include a furnace, connections to vacuum pumps, gas cylinders, and liquid containers. A large number of cell designs for transmission-absorption measurements can be found in the literature [27, 30, 87-89]. In most of the designs, the sample is moved away from the beam path to be heat-treated in the furnace, which is a part of the cell. This prevents the KBr windows of the cell from being damaged by high temperatures. But the sample must be carefully and precisely moved back and forth to ensure quantitative comparisons between the spectra recorded at different experimental steps. Some more advanced cells, in which the sample remains in the beam path, have been designed to follow the reactions during the thermal treatment [32, 87, and references therein]. In this case, the cell must be air- or water-cooled to protect the KBr windows. In the cell shown in Figure 6, the cooling is done by a water flow, but air is an alternative cooler. The advantage is that the reactions and the possible transformations of the adsorbed species can be followed as a function of the temperature. The disadvantage is that, at high temperature, a ceramic sample may emit an infrared radiation (this effect is usually weak below 873 K). Moreover, because of the temperature effect, the adsorption frequencies may shift, and, therefore, precise frequency measurements must be made after cooling at room temperature. Most of the cells are glass blown, but stainless steel cells are also conveniently used (Fig. 6). The nano-sized powder to be studied is pressed into a thin pellet (Section 3.3.1) and is placed in the sample holder located or placed inside the furnace. The pressures of gases or liquid vapors added to the cell are controlled through precise valve systems. A new generation of commercial cells for diffuse reflectance analysis [30, 78] offers the same capabilities as the transmission cells, that is, a furnace and the connections to a vacuum pump and to gas and liquid containers. The window (or windows) is generally a single zinc selenide crystal. The loose powder is placed in a cup in the furnace so that it can be heated in situ. The DRIFT cell is usually cooled by a water flow. As in the transmissionabsorption setup, controlled pressures of gases are adjusted through a valve system. As for the ATR attachments, they do not usually consist of heatable-evacuable cells. Of interest is the cylindrical internal reflectance (CIR) reaction cell, which allows the in situ monitoring of catalysts synthesis [50 and references therein].

6. NANO-SIZED OXIDE POWDERS Many oxides are used as catalysts. Because for decades it has been known that catalytic reactions take place at the surface of these materials, the increase in their specific surface area was the first concern of the scientists working in catalysis. As a consequence, catalysis is probably the research field in which the surface studies of nano-sized oxide particles were first undertaken, even though nano-sized powders were called "ultrafine" or "ultradispersed" powders. Catalysis still remains the most important area in which the demand for surface analyses is high. The characterization of nanoparticle surface acido-basicity and the assessment of the strength, concentration, and nature of the surface sites are critical points for the further development of catalysts [60]. In addition to surface characterization, FTIR surface spectrometry can provide information on catalytic reactions, because it is possible

110

FTIR SURFACE SPECTROMETRY

electrical feedthrough water cooling . heating element

KBr window o

sample

to the detector

!

IR beam

to pumps and gas inlet water cooling

electrical feedthrough pressure gauge

KBr window furnace_

valve

sample holder ~

sample_ . . pellet/

('X/'] to pumps

\----~----,,.

..Tr

['x~'} valve

gas inlet Fig. 6. Schemeof a heatable vacuumcell to be used in FTIR surface analysis of nano-sized powdersin transmission-absorption mode. Adapted from [32].

to directly monitor the interactions between the catalyst and the adsorbed molecules. In this chapter, we do not intend to review the tremendous number of papers published on the IR surface studies performed on catalytic nano-sized or porous materials. Indeed, for many years, excellent books have been published on this subject [23, 27, 33, 75], and review articles regularly appear, updating the results (see, for example, [8, 31, 60, 66]). We chose to select a few reports that give a good overview of the possibilities offered by the FTIR spectrometry in surface characterization. It is not an objective choice, and we must recognize that many excellent papers have not been discussed here. The transmission-absorption mode is the favorite technique for the acido-basicity characterization of catalytic materials. However, some experiments have been performed in diffuse reflection because of the improved quality of the current setups ([90-92], for example). Although silica and alumina have been extensively studied in the past, new results are still published because of the new generation of high-performance FTIR spectrometers and attached setups, making it possible to record spectra at high resolution and high speed, and thus to identify the transition species. 6.1. Silica

Silica (SiO2) is among the first oxides studied by IR spectrometry, one of the reasons being that ultrafine particles amorphous SiO2 have been produced for decades at high throughput. Even though it is not used as a catalyst but as a catalyst support instead, it is one of the best understood surfaces as far as surface chemistry is concerned. For example, it is known that Lewis acid and base sites are absent unless the sample has been activated

111

BARATON

/H 0

/H 0 I Si

I Si

+

/0\ Si

Si

H:O above 600~

/H 0 I Si

H~O

\/o--H Si

isolated

Hmo

geminal

/H o m H ......... O

I

\/ Si

Si

"'..

/H O

"~176

/

H

O

I

I

Si

Si

associated and adjacent silanols

H

H

I ..... O\ "

/H

. 9

H

/H

0 I Si

0 I Si

i ..0 \

H ....... /H 0 I Si

hydrogen-bonded silanols Fig. 7. Hydroxylgroups on the silica surface and their possible interactions.

at very high temperature, and that Brr acidity is low or nonexistent [93]. The silica surface presents only one type of hydroxyl group that can be involved in mutual interactions or in hydrogen bonds with water molecules, as explained in Section 4.1. Moreover, silica, or more exactly, Si-O bonds are present in several complex compounds such as silicates, alumino-silicates and clays, zeolites, cordierites and mixed oxides, glasses, etc. To understand these complex surfaces, a thorough knowledge of the silica surface is required. Scientists are still working at increasing their knowledge of this silica surface and at modifying it to improve specific properties to be used in chromatography, tribology, dehydration, polymer reinforcement, self-assembled layer fabrication, thermal insulation, etc. [94]. Because the hydroxyl groups are the only reactive sites on the silica surface, all of these surface modifications involve the OH species, whose amount depends on the activation temperature. The hydroxyl groups (silanols) and their mutual interaction, which can possibly exist on a silica surface, are described in Figure 7. On the raw silica surface, hydroxyl groups are hydrogen bonded to molecular water. After activation, that is, after heating under dynamic vacuum, only the isolated groups remain, with some geminal groups, depending on the activation temperature. Depending on the origin of the silica, it is generally admitted that, on nonporous samples, the number of isolated silanols is at maximum at 873 K. Above this temperature, they start to condense, leading to siloxane bridges. Above 1073 K the surface is completely and irreversibly dehydroxylated. The surface becomes hydrophobic, and a decrease in the surface area is observed [23].

112

FTIR SURFACE SPECTROMETRY

3747

H-bonded OH 1630

b 4000

I

I

I

I

I

I

3500

3000

2500

2000

1500

1000

500

Wavenumber(era-1) Fig. 8. FFIR surface spectra of a commercial silica nanopowder (Degussa, Aerosil 130). (a) At room temperature and under vacuum; (b) after activation at 873 K.

The broad absorption band centered at 3500 cm -1 in the IR spectra of a pure silica pellet (Fig. 8a) has been assigned to the v(OH) stretching vibration of surface hydroxyl groups involved in hydrogen bonds with water molecules and/or with adjacent silanols (Fig. 7). The sharp band at 3747 cm -1 is attributed to isolated silanols. The evolution of this band has been studied as a function of the temperature. The desorption of water as well as the condensation of adjacent OH groups lead to a decrease of the 3500 cm -1 band intensity concomitantly with an increase of the 3747 cm -1 band (Fig. 8b). The band at 1630 cm -1 corresponding to the 8(OH) bending vibration of adsorbed water molecules also decreases. Modifications of the spectrum also occur in the 1000-600 cm -1 region, where transparency windows may appear. They are due to the decrease in the following modes: v(Si-O) in Si-OH surface groups, 8(OH) of the Si-O-H angle, and ~(O-Si-OH) of the O-Si-OH angle [58, 93]. Moreover, changes in the frequencies and/or band intensities, caused by thermal desorption, can be related to Si-O surface bonds distorted by surface dehydration. These distortions, which already exist on a surface in equilibrium with its environment (Section 2.1), can increase when the equilibrium is displaced. The H/D isotopic exchange performed by deuterium addition on an activated silica surface shows that the considered sample is not porous, because all of the silanol groups are quickly exchanged (Fig. 9). As a result, the v(OH) band of the isolated silanols at 3747 cm -1 shifts to 2762 cm -1, corresponding to the v(OD) stretching vibration. The surface hydroxyl groups are convenient intrinsic probes (Section 4.1) sensitive to dipole-dipole interactions with each other and with the vibrations of other atoms [95]. An extensive study of different types of silica (pyrogenic silica, precipitated silica at pH < 7 and pH > 7) was published in 1990 [94]. In this study, several analytical methods were used to follow the evolution of the hydroxyl groups under various chemical and heat treatments. Among these characterization methods, FTIR spectrometry was obviously very informative and permitted researchers to distinguish between different types of OH association and to monitor their evolution. The modification of the silica surface by grafting organic molecules such as alcohols, diols, and polyamines on the OH groups was followed and controlled in situ by FTIR spectrometry. Whereas an earlier study showed the replacement of the OH groups by NH2 groups when adsorbing ammonia [96], or more recently by OCH3 groups when adsorbing methanol [97], other modifications by chloromethylsilanes were attempted to increase the hydrophobic character of the surface [98]. The latter study, performed by IR diffuse

113

BARATON

2762

3747

b

OD

OH

4000

I

3800

I

3600

I

I

I

3400 3200 3000 Wavenumber(cm-1)

I

2800

!

2600

Fig. 9. H/D isotopic exchange of the hydroxylgroups on the activated surface of a commercial silica nanopowder (Degussa, Aerosil 130). FTIR spectra were recorded (a) after activation at 873 K; (b) after D2 addition. The spectra have been translated for clarity.

reflection in relation with NMR and XPS measurements, showed that the strong decrease in the IR band associated with isolated OH groups that is observed in the case of trimethylchlorosilane and dichlorodimethylsilane grafting, can be related to the 10% decrease in the O/Si ratio. However, the binding energy differences between oxygen and silicon obtained from the XPS measurements revealed that the Si and O chemical states are not changed. A grafting method was developed by Tripp and Hair [99], in which chlorosilane can be attached to the silica surface at room temperature under mild reaction conditions, avoiding the complex step of polymerization. All of the reaction steps were followed in situ by FTIR spectrometry. In another paper [91 ], the quantification of the silanol groups was based on DRIFT analysis of the v(SiH) absorption bands of Sill groups resulting from the reaction of the surface silanols with chlorodimethylsilane (CDMS). This method makes it possible to ignore hydrogen-bonded or surrounding water, because the latter reacts with CDMS to form volatile products which are subsequently eliminated. The above-mentioned surface modifications of nano-sized silica can lead to a very thin film coating the surface and constitute the starting point of self-assembled monolayers. The processes used to perform such modifications are diverse. Among the various applications, we can name metallization in silicon device technology, sensitive layers in sensor technology, and antireflective coatings in optics. Very often, stringent processing conditions are required, such as low temperature deposition. In many preliminary studies, nano-sized powders are used as a convenient model of adsorbent. We do not intend to review all of the thin films studied by FTIR spectrometry, but rather to give some significant examples that will illustrate the relevance of the technique for the study of the early stages of the deposition process. For instance, it has been demonstrated that the passivation of a silica nanopowder surface with hexamethyldisilazane (HMDS) enhances the selective deposition of two copperbased organic compounds [ 100]. FTIR spectrometry proves the HMDS grafting as well as the selective copper-based compounds deposition. 1,3,5,7-Tetramethyl-cyclotetrasiloxane (TMCTS) was deposited on silicon wafers, which led to a methylsiloxane layer [ 101 ]. The layer formed could have a thickness below 0.5 nm. IRRAS with a polarized incident beam was used to obtain information on the molecular orientation. Depending on the deposition process, well-oriented monolayers or multilayers in rather disordered orientation can be obtained.

114

FTIR SURFACE SPECTROMETRY

To increase the antireflective properties of glass, a coating is needed to obtain a zero reflectance. The low refractive index requirement can be satisfied by using porous materials, in as much as porosity significantly reduces the index [ 102]. To avoid the adhesion of contaminants in the pores, the surface free energy must be decreased by coating with an appropriate material. The IR diffuse reflectance analysis of a SiO2 nanopowder used as a model adsorbent indicates that (heptadecafluorodecyl)trichlorosilane (HFTS) molecules are anchored to the surface via condensation of their terminal functional groups and isolated surface Si-OH groups [ 102]. Moreover, a FTIR analysis of the porous glass by attenuated total reflection (ATR) suggests that the HFTS molecules form a monolayer along the external and internal surface with an orientation nearly normal to the surface, thus mainly exposing the CF3 groups. The surface then becomes highly water and oil repellent. The reaction of ammonia with a methylaluminum adsorbate on the silica surface has been reported by Bartram et al. [103]. A high specific surface area silica was used, thus allowing IR transmission measurements. The formation of A1-N bonds was observed. The thermal desorption of the adsorbed species suggested the formation of A1-NH2-A1 bridging species. The technique can be used as a low-temperature deposition process of A1N thin films on SiO2 substrates. The same method was also applied to coat y-alumina nanoparticles [ 104]. However, because of the higher reactivity of the alumina surface compared to that of silica (Section 6.2), the excess of NH3 is coordinatively bonded to surface aluminum atoms, thus modifying the reaction pathways. 6.2. Alumina Alumina (A1203) is of major interest in the catalytic field, as a pure material, a component in mixed oxides, or a catalyst support. Most of the IR surface studies are devoted to "transition" aluminas, which are actually metastable phases of low crystallinity but can be obtained with a high specific surface area and possibly open porosity [8]. The thermodynamically stable corundum phase (ot-A1203) has no catalytic interest and at this point cannot be properly synthesized as pure alumina nano-sized particles. Most of the articles published on alumina IR surface studies deal with y, 77, and 8-A1203 phases. A recent extensive review of the surface acido-basicity characterization of the transition aluminas has been published by Morterra and Magnacca [8]. But according to Morterra, even though the surface properties of aluminas have been studied for over 30 years, the complexity of the surface and the multiplicity of the transition phases keep the research interest high. Although the reader can refer to several articles dealing with the subject [8, 27, 93, 96, 105], it is useful to present a brief summary of the complexity of the alumina surface and particularly the OH groups. By looking at Figure 10, representing the IR absorption range

OH OD

~a 4000

3800

3600

3400

3200

3000

2800

2600

Wavenumber(cm-1) Fig. 10. FTIRsurface spectra of a commercial F-alumina nanopowder (Degussa, Oxide C). (a) After activation at 873 K; (b) after isotopic exchangeby D2.

115

BARATON

/H O

I

H I

/H O

I

IvAI3+

vial 3+

type Ia

type Ib

v(OH) > 3750 em"1

/ viAl 3+

o

H I

N

/

1vAl3+

type IIa

viA13+

o

\ viA13+

type lib

3720 em"1< v(OH) < 3750 em"1

H I

o

o...- . "..... vial 3+ vial 3+ vial 3+

type III v(OI-I) ~ 3700 em"l

Fig. 11. Possibleconfigurationsof the hydroxylgroupson a y-aluminasurface.

of the hydroxyl groups on a v-alumina surface, we can easily see that the v(OH) band is actually composed of several bands. The isotopic exchange showed that, in this case, all of the OH groups were accessible to deuterium. Note that the higher signal to noise ratio in the OD absorption region allows us to clearly distinguish the component bands (Section 5.2.1). At least five types of hydroxyl groups were identified by Peri [96] on the alumina surface. The precise assignment of their vibrational frequencies is still controversial. Several authors have presented different models by considering some preferentially exposed crystal faces, y-Alumina can be considered as a defect spinel structure that is tetragonally distorted [93]. The model proposed by Knrzinger and Ratnasamy in 1978 [105] is the most frequently used one, even in recent works. Knrzinger and Ratnasamy, showed that on the (111) face of an alumina with a spinel structure, it is possible to discriminate five types of hydroxyl groups, as represented in Figure 11. Only three types are possible on the (110) plane, namely, Ib, Ia, and lib, whereas the type Ib is the only one possible on the (100) face. According to this model, the maximum number of OH types is five, and their relative concentrations will depend on the degree of exposure of the various crystal faces. Indeed, on the (111) face, for example, it is expected that type IIa occurs three times more frequently than type Ia, and that type IIb also occurs three times more frequently than type III. In addition, it is expected that type III should have the greatest BrCnsted acidity, whereas type Ib should have the greatest basicity. Although the Knrzinger model is still under discussion, as it does not take all possible cation vacancies into account and only considers the regular surface terminations, it has the major merit of envisaging several crystal faces and predicting a limited number of possible OH configurations that actually correspond to the number of OH bands observed in the spectrum of all crystalline transition aluminas. Thus we can easily understand that the vibrational frequencies of the surface hydroxyl groups as well as the relative intensities of the corresponding bands will give information on the relative distribution of the aluminum atoms in the tetrahedral and octahedral sites of the first atomic layer. An illustration is given in Figure 12, where the v(OD) absorption ranges are compared for y- and 0-aluminas [ 106]. It is worth noting that the distribution of A1 atoms in the first atomic layer may be different from that determined by a bulk characterization method. The mechanism of the dehydroxylation of the alumina surface is still under investigation. However, at this point it is clear that the creation (if any) of surface defect sites versus the activation temperature is related to the catalytic activity. Moreover, the relative proportions of these defect sites and the other surface sites (Lewis acid and base) also depend on the activation temperature [93]. Aluminas are excellent materials for illustrating the remarkable relevance of the probe molecule addition to characterization of the surface acido-basicity, followed in situ by IR spectrometry. For example, pyridine has been widely used to identify the A13+ Lewis acid sites, either alone [66, 107, 108] or in the presence of other adsorbates [108]. Figure 13 presents the 1700-1400 cm-1 range of the spectra recorded after pyridine addition at room temperature on the activated y-alumina surface and after desorption at increasing temperatures. The spectrum of the activated alumina has been subtracted to emphasize the newly formed species. The V8a frequency of the free pyridine molecule at 1579 cm -1 shifts to 1615 cm- 1. A shoulder appears at 1621 cm- 1 (Fig. 13a). By increasing the desorption

116

FTIR SURFACE SPECTROMETRY

3000

I

I

2900

2800

!

I

I

2700 2600 2500 Wavenumber (cm -1)

I

I

2400

2300

2200

Fig. 12. Comparison of the v(OD) absorption range of two transition alumina nanopowders after activation at 773 K, followed by deuterium addition. (a) y-Alumina (Ba'l~Cowski-Chimie, CR65); (b) 0-alumina (Baikowski-Chimie, T30CR). The spectra have been translated for clarity.

1450 1615

r

O


, lI

u) z 111 lz

(c)

m

(b)

la)

250

300 RAMAN

SHIFT

350 (cm-1)

Fig. 17. Ramanspectra showing the evolution of Ge phonon for different annealing times. Reprinted with permissionfromD. C. Paine et al.,Appl. Phys. Lett. 62, 2842 (1993). 9 1993AmericanInstitute of Physics.

shoulder. The asymmetric peak obtained at 1300 K has been fitted to obtain the average size of the particles. Paine and co-workers performed Raman spectroscopy on S l_xGexalloys oxidized and annealed under various conditions to promote the formation of Ge nanoparticles [51 ]. Raman spectra showing the evolution of the Ge F~5 phonon mode for different annealing times are shown in Figure 17. The FWHM of the Raman line as a function of annealing time at different temperatures is reported in Figure 18. These curves indicate that larger average particle size can be obtained with longer annealing times and higher temperatures. It should be remarked that no frequency shift of the Raman peak is observed, contrary to the prediction of the theory. Samples deposited by rf sputtering in a glassy SiOa matrix and subsequently annealed showed a similar behavior, however, with a shift of the peak position (Fig. 19) [38]. A systematic study of the growth of Ge nanocrystals in SiO2 matrices by Raman spectroscopy and electron microscopy has been performed by Fuji and co-workers [47]. Rf cosputtering and annealing were employed to produce Ge nanoparticles. The dependence of the Raman spectra upon annealing temperature is similar to that of [54], showing a crystallization for temperature higher than 900 K. The size distribution of Ge nanocrystals has been determined by HRTEM analysis and used to calculate the Raman spectra following the phonon confinement relation. They have found a qualitative agreement; however, the peak frequencies of experimental spectra are much lower than the calculated ones, and no shift of the Raman peak is observed (Fig. 20). The discrepancies in the Raman shifts in apparently similar samples are difficult to account. A possible explanation is the deviation of the lattice constant from the bulk value

244

VIBRATIONAL SPECTROSCOPY

14

l

l

-

9 -

9 -

,

9 -

(a) 12

800"C

6 i9

850"C

0

20

"

:E

14

3=

-

9

,D "D Q

~ A 10

i

60

40

80

Ill

100

.i

-

120

J

140

i,

8so'c

(b)

Y

(llv .m, m

Q

.,...

u

I::

6

(I

Q.

40

ZO

40

60

Annealing

Time

80

100

120

140

(minutes)

Fig. 18. (a) FWHMof the Ge Ramanpeak as a function of time at 1050, ll00, and ll50K.(b)Estimated average particle size as a function of time for the temperatures reported in (a). Reprinted with permission from D. C. Paine et al., Appl. Phys. Lett. 62, 2842 (1993). 9 1993 American Institute of Physics.

caused by cluster surface-matrix interaction. Lannin and co-workers have demonstrated the influence of the near-surface dangling bonds and of the bond-angle disorder on the phonon density of states [48]. In addition to the particle-matrix interaction, several other factors can affect Raman response. Fujii and co-workers have suggested that the presence of compressive stress exerted by the matrix on the clusters can compensate for the downward shift of the Raman peak. However, no direct evidence for the existence of the stress has been provided so far. The coexistence of amorphous and crystalline phases in the same particle can also induce a departure of the Raman behavior from that predicted by a too naive theory taking only confinement into account. The effects of size distribution should also be taken into account explicitly. As already discussed, the width of the Raman peak is determined from both homogeneous broadening caused by the phonon confinement and inhomogeneous broadening caused by size distribution. A strong size dependence of the peak frequency should indicate that the inhomogeneous broadening is nonnegligible. To minimize the interaction of particles with host matrices, free particles can be grown from gas phase and in colloidal suspension [44, 59]. In [44] oxidized germanium microcrystals are produced by gas condensation and characterized by TEM and electron diffraction. In Figure 21 the Raman spectra for different average sizes are reported, showing an evolution of the shape similar to the embedded system and a frequency shift of the peak.

245

M I L A N I A N D BOTTANI

'

'

'

'

I

'

;"'

"

I

'

'

"

'

l

'

Si F'2s F2s

Ge

'

'

'

'

'9

(a)

: =

.i

9

it

"'

,,

A

C

~.*a,,.,'..':,::'~'" I tB

o

m C 0 w C m

:: i~

9"~.-'.,t',,i~ 2 T, so that Landau levels evolve with a typical separation in energy of h vc > h r . This reduces the effects of spurious heating by the microwaves,

323

BLICK

because only a limited number of free carriers can be excited out of the source contact. A somewhat more explanatory picture is found in the VG-VDs characteristics shown in Figure 15b. Regions of Coulomb blockade form the common diamond-shaped structure, flanked by the regions of single electron tunneling. Excitations can occur via ground states, for example, of the N to the N + 1 electron system or via the excited states of the (N - 1)* and N* systems. We focus on the absorption of photons for simplification, but in principle the emission processes have to be considered as well (+h v). The scaling of the center gate voltage to the appropriate energy is given by the dependence of the resonance pattern on the drain source bias voltage. In this case, the scaling factor is c~ = (0.311 -t- 0.023) meV/mV, resulting in a total charging energy of Ec = e2/C~ ~ (1.24 4-0.088) meV (C~ is the total capacitance). To obtain good coupling of the applied microwave field at the quantum dot, we used an integrated broadband antenna, as described before. This method of coupling is useful at high frequencies, because the quasi-optical waveguide allows transmission of frequencies larger than 30 GHz, in contrast to coaxial transmission lines. Coupling and polarization depend on the antenna structure chosen. The antenna was designed with principles known from microwave technology. We chose a modified broadband "bow-tie" antenna structure with an impedance fairly well matched to that of free space, Z = 377 ~. The antenna itself is defined by optical lithography, then a contact sheet of Ni/Ge with a thickness of 10 nm is evaporated, followed by 150-nm-thick Au metallization. To verify the properties of the antenna we performed numerical simulations of the high-frequency current distribution at different frequencies (Fig. 16a-c). Using a commercially available program [ 15], we were able to simulate the coupling of the radiation, taking into account the 2DEG, the heterostructure itself, and the metallic back-short. A slight offset from beam center is taken into account, but does not qualitatively change the current distribution on the antenna tips near the microstructure. As seen from Figure 16, a clear maximum in the high-frequency current density is obtained in the tips of the bow-fie arms for all frequencies (calculations are shown for v = 100 GHz, 150 GHz, and 200 GHz), confirming the broadband characteristics of the antenna. The dark regions represent the maximum current density (16 A/m) and the minimum density is in white (0 A/m). In Figure 17a, the conductance through our quantum dot without microwave radiation is shown at VDS = 0; the CB oscillations can be seen clearly and are well separated. A magnetic field of B = 1.5 T was applied perpendicular to the plane of the 2DEG. Obviously a rectified current is obtained even without the application of microwaves due to EMF noise, as the dashed curve in Figure 17a indicates. This rectification at low frequencies in the adiabatic limit is discussed elsewhere [24] in detail. In Figure 17b the conductivity is shown under the influence of microwave radiation of v = 155 GHz at different intensifies. This frequency corresponds to an energy of Erad = 0.64 meV. As seen, additional conduction peaks evolve between the SET resonances as the intensity of the radiation is further increased. The peaks at A and B are somewhat less pronounced, but peaks D and E can be identified clearly. These additional peaks are induced by the photon absorption process discussed above. The energy position coincides with the additional peaks. The effect of the excitation of electrons in the leads is shown in Figure 15: the quantum dot is filled with N - 1 electrons in the ground state (solid line). The next higher Coulomb ground state with N electrons in the dot is empty (dashed line). If the dot is turned into the CB regime, no conductance is found. In this case, the absorption of a photon in the leads by an electron with the appropriate energy would allow the electron to tunnel through the N electron ground state, thus overcoming the CB gap with e2/(2C~:). It should be noted that this mechanism only leads to a net current when the barriers of the quantum dot are asymmetric or if a small bias is applied. In our case, we used barriers with slightly different transparencies and, in addition, the leads to the tunneling barriers are asymmetric because of other split gates nearby. It is important to note that the main SET resonances (e.g., the peaks marked by C) are not shifted by increasing intensity of the radiation. Furthermore,

324

MICROWAVE SPECTROSCOPY ON QUANTUM DOTS

Fig. 16. Simulationsof the high-frequencycurrent distributionon the antennaused. Blackregions correspond to high current density; low density regions are white. The frequencies are (a) v = 100 GHz, (b) 150 GHz, and (c) 200 GHz. (Source: Reprinted with permission from [16]. 9 1995 American Institute of Physics.)

the additional peaks in the resonance pattern are not shifted. Thus, there is no DC voltage drop at the different gate contacts or at the leads, which could influence the tunneling through the barriers. Obviously the peaks are surrounded by a region of finite conductivity, which is probably due to induced transport through excited states in the dot and to nonresonant heating of the reservoirs. With very low radiation power, the Coulomb blockade and the SET resonances are well defined (solid curve), and only the maximum conductance of the peaks is decreased by A a ~ 1 /zS (see peak C). With increasing intensity of the microwaves, the conductance resonances are broadened and the Coulomb blockade is weakened. In Figure 18 measurements of the DC current through the device under microwave irradiation are shown. As in Figure 17a peaks B, D, and E show the induced peak structure. At very high intensifies another fine structure is seen (marked by X), which cannot be explained by simple PAT. Most likely this peak results from excitation of electrons in the dot, which then tunnel out of the dot, leaving a vacancy to be filled by an electron out of the source contact. Varying the frequency of the microwaves slightly in the range of 4-2 GHz around 155 GHz, we found peaks similar to those in Figure 17. At larger variations, we found a strong increase in the background conductance (145 GHz) and asymmetric peak shapes (162 GHz), which incorporate the additional peak structure found at 155 GHz and are probably a result of exited states opening additional channels for transport through the quantum dot (see Fig. 18b). The strong response at 155 GHz can be explained as a

325

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,

(a)

(b)

12

0.2

C-.~

~

,_

9

hv b

0.0

I~ 6 A

-0.2

0

B !

L~.

6

0

0.36

0.37

i , i , i 0.355 0.360 0.365

-VG(V)

i 0.370

"VG(V)

Fig. 17. (a) Resonance pattern without radiation applied. The dotted line shows the rectified current due to low-frequency EMF noise. (b) Pattern identical to that in (a) under irradiation of microwaves with increasing power level at v = 155 GHz. The radiation induces peaks A,B,D, and E, at half of the Coulomb gap. (Source: Reprinted with permission from [ 16]. 9 1995 American Institute of Physics.)

0.3

9

145 GHz

0.2

A

'< c

=L6

0.1

b

~ m

'

:

v

i

,,

0.0

3

I -0.1 ( I

0.355

.

I

i

0.360

I

0.365

,

I

I

0.370

-v G (v)

l

0.360

,

I

,

0.365

I

0.370

-VG(V)

Fig. 18. (a) Rectified current due to 155-GHz millimeter wave radiation: Induced resonances are found at B, D, and Emin addition we observe a feature X, indicating a different absorption mechanism at a lower energy. (b) Differential conductance through the dot under different millimeter-wave freqUencies applied, as indicated. Dotted curve, without radiation applied. The strong increase in background conductance covers distinct excitation peaks. (Source: Reprinted with permission from [16]. 9 1995 American Institute of Physics.)

326

MICROWAVE SPECTROSCOPY ON QUANTUM DOTS

superposition of two replicas of conductance peaks corresponding to an absorption and an emission process [22]. In these first experiments on a single quantum dot, we have seen that it is possible to couple microwave radiation in the high-frequency regime via an integrated antenna structure into quantum dot microstructures. When the quantum dot is irradiated with microwaves at v = 155 GHz, we find additional resonances, which are attributed to photon-assisted tunneling through the quantum dot. Hence, photon-assisted transport can be employed for spectroscopy of quantum dots, Furthermore, it demonstrates the feasibility of using quantum dots as sensitive and frequency-selective detectors in the microwave frequency range.

5. ELECTRON SPIN RESONANCE IN QUANTUM DOTS Let us now focus on electron spin resonance (ESR) in a single quantum dot at filling factor v ~< 2 as an example for applications of microwave spectroscopy on single dots. ESR is a well-known experimental technique. One of the most intriguing applications was the observation of the Lamb shift in hydrogen [25]. In 2DEGs, ESR was first found in transport experiments by Stein et al. [26]. The optical detection of single spin resonance in a molecule has recently been reported [27]. We will first give a brief summary and will then present a theoretical explanation for the strong enhancement of the effective ge*ff factor, which causes spin splitting in a few electron system. We will focus on magnetic fields corresponding to a filling factor v ~< 2, where v is defined as v = hns/eB (where ns denotes the sheet electron density). Thereafter I will discuss the experimental approach and give the first results. There are only a few publications in which the effect of the electron spin on electron transport through a quantum dot is considered. Some authors have explained the variation of the Coulomb blockade (CB) oscillations at moderate magnetic fields (perpendicular to the plane of the dot), where in many cases the quantum dots are analyzed at v > 4 and with a comparatively large number of electrons within the edge-channel model [28a-c, 29a, b]. Although up to now several studies on transport through quantum dots at finite magnetic fields exist [30-32] it is not understood in detail how the few-electron system behaves at magnetic fields corresponding to filling factors close to and below unity, where spin effects become important. So far, the internal spin density structure of single quantum dots was suggested [33], and recently the detection of compressible and incompressible states in quantum dot lattices in far-infrared spectroscopy was reported [34]. Here we will combine these two ideas of transport and optical spectroscopy by presenting the ESR in a single quantum dot. The typical implementation of a single quantum dot for our transport measurements is shown in the SEM micrograph in Figure 19. Applying a negative bias voltage to these gates, a well-defined quantum dot is formed, connected to the 2DEG reservoirs by tunable tunneling barriers. Transport through such a single quantum dot is only possible when, for example, the two gate voltages G1, G2 vary the electrostatic potentials in such a way that electrons from the lead can overcome the Coulomb blockade of transport (see Fig. 19). At B = 0 the density of electrons is smooth, whereas at finite magnetic fields discrete Landau levels (LLs) in the dots are formed. For example, for v ~< 2, two compressible LLs are separated by an incompressible region, defining a dot structure, which consists of an outer ring and a core. The CB oscillations of this ring/core dot are best analyzed in a charging diagram, as was shown in measurements on a double quantum dot [35]. This model is visualized in Figure 19, where the smooth spin density in the quantum dot is deformed to such a ring/core dot structure; the compressible tings are shown. We have to emphasize the" in our case at v ~< 2, the ring and the core dot represent different orientations of the electron spins. The question arising is how such a strong spin-split state can be explained and if the transition from the spin-up ring to the spin-down core is induced by microwave radiation.

327

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Fig. 19. Image of the quantum dot structure in a perpendicular applied magnetic field. Plotted are the compressible stripes in the quantum dot at v = 1. The dot is split into a core and a ring state in the lowest Landau level; the arrows depict the spin-up and -down states. The inset shows a SEM micrograph of the split-gate structure. In the center of the left dot the spin distribution in the lowest Landau level is depicted. The width of one gate finger is 80 nm.

* factor, well known in 2DEGs [36], is found in sysTheoretically the enhanced gefl~ tems of reduced dimensionality such as quantum dots [37]. The effects of the exchange interaction lead to an enormous spin splitting in these dots, which strongly influences electronic transport. In our model, we consider Ns strictly two-dimensional electrons to model qualitatively a real heterostructure in which the 2DEG is confined to the lowest electrical subband. It is confined to a disk of radius R in the 2D plane by a potential step Vconf(r) -- U0 exp

4Ar

+ 1

(1)

where zXr = 22 ~ . To ensure charge neutrality of the system, a positive background charge nb resides on the disk: nb(r)

= hs[exp( r - R

+ 1] -1

(2)

with the average electron density of the system given by hs = Nb/(ztR2). In the H a r t r e e - F o c k approximation, the state of each electron is described by a single-electron Schr/Sdinger equation:

{/10 +

VH(r)+

Vconf(r)}~r

fd2r'A(~,;')~rr162

(3)

nb(r r I F - F']

(4)

for an electron moving in a Hartree potential, VH(r) - - tc

d2r 'ns(r')

and a nonlocal Fock potential with e2

~r~ (~')r

;3 = 7

- ")

328

j ; - ;'l

(~)

(s)

MICROWAVE SPECTROSCOPY ON QUANTUM DOTS

(a)

30 ~ / ~ 20

~-~

~ ~,, /

~ ;

~

~.

25

. . . . . . .

~'

!,

~

(b)

~ 20

~" Io

( ,

0

15

o

_1ol +-+~../~ v = l

~=

~" ~o o

0

'

2 -lo

o

~o

20

M

3'o

Filling factor

Fig. 20. (a) Hartree-Fock Landau bands in a quantum dot at different numbers of electrons. Upper graph shows filling factor v = 1 (Ns = 22) and lower graph v = 2 (Ns = 42). Crosses mark the spin-up s = +1/2 state, and the diamonds mark spin-down s = -1/2 states. (b) Calculated r . m . s , g e*f f factor for all states in the lowest three Landau bands in the quantum dot at different filling factors (parameters: m* = O.067me, r -- 12.4, geff = -0.44).

where f(e~ - lz) is the Fermi distribution at the finite temperature T. The electron density is ns(r) = ~~___, " [#C (F)12f(e( ' -/ZDot) C with the chemical potential//,Dot

(6)

label ( represents the radial quantum number nr, the angular quantum number M, and the spin quantum number s = 4-89 H ~ is the single particle Hamiltonian for one electron with spin in a constant perpendicular external magnetic field [38, 39a, b]. A Landau band index n can be constructed from the quantum numbers nr and M as n = (IM! - M ) / 2 + nr. The Landau levels of H 0 with energy En, M,s = ha)c(n Jr 1) -Jr"sg* (/ZB/h) B are degenerate with respect to M with the degeneracy --

t ~ S / D 9 The

no = (2rr12) -1 per spin orientation./za is the Bohr magneton and (Oc denotes the cyclotron frequency. The Hartree-Fock energy spectrum e~ and the corresponding wave functions are now found by solving (3)-(6) iteratively on the basis of H ~ [39a, b]. The chemical potential/z is recalculated in each iteration to preserve the total number of electrons Ns. The number of basis functions used in the diagonalization is chosen such that a further increase of the subset results in an unchanged density ns(r). The specific confinement potential (Eq. (1)) and the positive background charge (Eq. (2)) are used here to induce a region inside a small quantum dot with fiat Landau bands, thus enhancing the exchange effects. Similar effects can be found in parabolically confined quantum dots with many electrons. In assuming a quantum dot with a total number of electrons Ns = 22 (v ,~ 1), we obtain at a magnetic field B = 3 T a large spin splitting, which is shown in the upper graph of Figure 20a. The crosses mark the spin-up s -- + 1/2 state, and the diamonds mark the spin-down s = - 1/2 state. In the lower graph we consider 42 electrons (v ~ 2) and obtain a large separation of LLs, but no spin splitting, that is, the qualitative spin structure in quantum dots strongly depends on the even/odd number of electrons in the dot and the filling o f the Landau bands. In Figure 20b the large root mean square (r.m.s.) geff factor of the lowest three Landau bands is plotted vs. the filling factor v ,-~ Ns/23. It is clearly seen that the enhancement is at its maximum whenever the filling factor is odd. Close to odd integer u the effective geff factor within a quantum dot reaches a value at which the clear separation into a spin-up and a spin-down state (ring/core) in the quantum dot is possible. Considering the existing experimental work [33], it is reasonable also to

329

BLICK

(a)

hv

NR

K

(b) NK+I

~

E

(c) VGI~,

NR ) B

s s

S

"'

,.,.

, s~-sJ ,I s s~-si.,~ s "' " Y

,'f,>,.,y;,

Fig. 21. (a) Energy level diagrams of the ring/core dot. With varying gate voltages G1 and G2, the numbers of electrons in ring and core dot are changed (NR,NK).(b) Microwaveradiation of energy/1o9induces spin transitions between ring and core dot at different magnetic fields. (c) A honeycomb pattern of lines of conductance is obtained in the case of the ring/core dot with variation of two electrostatic potentials VG1, VG2. The solid lines give the ground-state resonances, and the dashed lines indicate conductance resonances induced by microwaveradiation.

adopt the edge-channel picture in the integer quantum Hall regime for filling factors v < 2 for quantum dots. Hence, we can assume a self-consistent arrangement of the charge due to the exchange interaction, which leads to the formation of a compressible ring and core dot with different spin orientation and an incompressible quantum Hall liquid, separating the two dots. To transfer an electron from the ring with spin-up orientation to the core with spindown orientation, a spin-flip is necessary. The energy required can be supplied by a variation in the electrostatic potentials by a charge in the number of flux quanta connected to the ring/core dot or by millimeter wave radiation. It has been shown that photon-assisted tunneling can be used for millimeter-wave spectroscopy of single quantum dots [ 16]. In Figure 2 l a a spin-flip resonance is depicted in the simplest case: the photonic mode transfers energy to an electron in the ring R, which then tunnels into the core dot (K' spindown). This is more clearly seen in Figure 21b, which shows for clarity the common E vs. B representation of spin-up and -down states and the condition for ESR. Because of the large value of ge*ff around v - 1, we find a spin-split LL in the quantum dot, which evolves into the ring/core structure, sketched in Figure 19 (number of NR electrons in the ring and NK in the core). Keeping the magnetic field fixed, this structure can be analyzed within the typical charging diagram shown in Figure 2 lc. Here the solid lines mark finite conductance through the system, because the two dots are effectively connected in parallel. Obviously the resonances in the VG1-Vc2 plane form a honeycomb pattern, typical for a double quantum dot [35]. Considering for simplicity only absorption processes in the ring

330

MICROWAVE SPECTROSCOPY ON QUANTUM DOTS

dot with an energy of the radiation corresponding to ~ 1/5 of the charging energy of the ring, additional lines of conductance resonance in the charging diagram will be found. These are marked as dashed lines in Figure 2 l c, crossing each hexagon. The thin dashed lines cannot be found in such a parallel geometry and are only shown as a guide to the eye. The energetic conditions for resonance are extracted by referring to the level diagram in Figure 2 lb. The states of the ring with NR electrons and the core with NK electrons can be tuned by the gate voltages VG1, VG2 or the magnetic field B and are given by the different charging energies. The spin orientation representing the influence of the ge*ff factor in the dot is then easily obtained. In the current experiment we applied circularly polarized microwave radiation from a background wave oscillator of o9 = 2zr x 73 GHz corresponding to an energy Ev -ho9 = 300/zeV to the ring/core dot structure. This additionally supplied energy results in the spin-flip transition of an electron from the ring to the core dot. Our split-gate device, on top of an AlxGal_xAs/GaAs heterostructure (x = 0.33, # -- 80 m2/V s and ns = 2 • 1015 m -2) is biased, and the quantum dot formed contains roughly Ns ~ 50 electrons (see inset, Fig. 19). A magnetic field of B = 8.47 T is applied corresponding to a filling factor v < 2. The charging energy of the quantum dot is obtained by the relation Ec = e 2 / C z (Cz: total capacitance of the system). The quantum dot in our experiments has a diameter of d = 350 nm and a total charging energy of Ec ~ 1.4 meV at B = 0. At a finite magnetic field, where the ring/core dot is formed, we determined the individual charging energies to be E~ ~ 1.10 meV of the ring and Ec~ ~ 0.29 meV of the core. The calibration is obtained using the drain source dependence [8]. In the following we will refer to the charging energies and the resulting gate voltage periodicities as or,/3, and y. The energy E~ for the ring is surprisingly larger than that for the core Ec~. This can readily be explained by the fact that the effective area and hence the "charging capacity" of the ring are smaller compared to those of the larger core dot. The schematic ring/core structure in Figure 19 is not to scale; more likely the ring itself is very thin, resulting in a larger charging energy. As seen in Figure 22 we determined charging diagrams of the ring/core dot structure depending on one gate voltage (Vg = VG1) and the magnetic field. The step size of the magnetic field variation of the different traces is 6B = 15 mT. The two diagrams show the same part of the charging diagram and differ only in that (a) is measured without radiation applied and (b) is taken under irradiation at co = 2zr x 73 GHz. In (a) the two characteristic resonance periodicities ot and/3 refer to the charging energies of the dots from Figure 21 c. Adding those two charging energies, one obtains y, the charging energy for the whole quantum dot at B -- 0. The variation in conductance amplitude is due to the different strengths of coupling to the leads. The application of radiation in (b) leads to a new structure of the conductance resonances in the charging diagram: the left peak shows an additional resonance, and the fight peak structure of (a) is replaced under irradiation by a single peak. This redistribution of resonances is a clear sign of the photon-assisted spin-flip transition, because the radiation energy and the charging energy match Ev -- Ec~. Hence, electrons are pumped from the ring into the core dot. In the case of the left peak this means a new transport channel is opened by pumping electrons through the ring and core structure. In the case of the right peak the electrons are pumped out of the core dot, that is, there is one transport channel missing. Computing from the microwave energy and the magnetic field the effective geff* factor (ho9 -- ge*ff#BB), we obtain a value of geff -- 0.61 which is considerably larger than the geff factor for electrons in a 2DEG of A1GaAs/GaAs heterostructures (geff-- -0.44). We have given an explanation of the enhancement of the g*eft factor and have shown that it has considerable influence on the transport properties of a quantum dot, because it reflects a certain spin orientation in the dot. The enhanced ge*fffactor leads to the formation of Landau levels at v ~< 2 in the dot, which evolve as a ring/core dot similar to a double-dot geometry measured in a charging diagram. This ring/core dot consists of regions with different spin orientations, which show a spin-flip under irradiation with circularly polarized

331

BLICK

8

6

::

.,._.

A

:::L

4

>

"O

~

"O

.....

"0

2

...

_ j \

0.02

....... 0.()3

0

0.()4

0.02

"

0.03

0.04

-v (v)

-v (v) g

g

(a)

(b)

Fig. 22. Measuredcharging diagrams of a single quantum dot at a magnetic field of B = 8.47 T. The conductance is shown, depending on one gate voltage Vg. The magnetic field is varied in steps of gB = 15 mT. (a) Resonances of the ring/core dot with the characteristic periodicities ot and fl without microwave radiation. (b) The same part of the charging diagram, with microwave radiation of 73 GHz. The periodicity y represents the total dot charging energy, y = ot +/3.

microwaves of 73 GHz. From these measurements we determined the enhanced effective * factor is smaller than the g*eft factor to be 0.61 That the measured value of the effective geff value predicted by the Hartree-Fock approximation has two explanations: the exchange is too strong in the approximation, and a model including correlations would produce a more appropriate value. Second, it is still an open question that might be answered by further experiments what g factor, the bare or the enhanced, is actually measured in experiments on microwave-induced tunneling in few-electron systems. The determination of the complete frequency dependence will give further insight into the complex spin structure within quantum dots.

6. S P E C T R O S C O P Y O N A D O U B L E Q U A N T U M D O T We have demonstrated the combination of SET and PAT through single quantum dots as suggested [22] and then reported by Blick et al. and Kouwenhoven et al. [16, 23]. We will now apply this as a tool for millimeter wave spectroscopy to two coupled quantum dots [40]. The aim is to study the different possible excitation mechanisms and especially the influence of coherence on electronic transport. The energy scales dominating the transport properties of quantum dots are the thermal energy ks T and the Coulomb energy Ec, competing with the radiation energy hr. The frequencies corresponding to the charging energies of the individual quantum dots A and B are on the order of E A/2 ,~ 390 GHz and E~/2 ~ 150 GHz. In the measurements presented here we will concentrate on the excitation range of quantum dot B. The ratio Y = hv/kBT gives an estimate of how far from thermal equilibrium electrons are excited. Applying the experimental parameters, v = 150 GHz and T -- 200 mK, we obtain a value of y = 36, that is, excitation creates a prominent nonequilibrium electron distribution.

332

MICROWAVE SPECTROSCOPY ON QUANTUM DOTS

Fig. 23. Excitation spectrum of the conductance through a double quantum dot in a gray-scale plot (trmax) 3/zS, black; Crmin ~

. v

.."''""

E

u.I c~ II

>

0.5

,

0"00

I

50

i

I

,

100

I

150

,

I

200

v (GHz) Fig. 26. Frequency dependence of the induced peak positions 6 VG with respect to the ground state. A linear dependence is observed, as expected. The solid line shows an extrapolation of the data points, and the dotted line represents the slope h = 6.62 x 10-34 J s. (Source: Reprinted from [40], with permission of Elsevier Science.)

As w e have seen in F i g u r e 26, the i n d u c e d r e s o n a n c e s o b e y the linear relation E =

hv = otrVG. Interestingly, we o b s e r v e d that at certain f r e q u e n c y bands we hardly f o u n d r e s o n a n c e s , for e x a m p l e , in the large gap f r o m 100 to 130 GHz. This b e h a v i o r is c o m prehensive, c o n s i d e r i n g the discrete excitation spectra f o u n d for such artificial atoms or m o l e c u l e s [8, 41 ]. T h e r e are only a finite n u m b e r of excited states that can be p o p u l a t e d by m i l l i m e t e r w a v e radiation. This is an indication that the a b s o r p t i o n of the radiation occurs within the q u a n t u m dots.

335

BLICK

100

g -

75

50

-0.1

0.0

0.1

v G IV) Fig. 27. Charging diagram of the current through the double quantum dot under irradiation at v = 151 GHz. The back-gate voltage is varied in steps of 8VBG ---0.5 V from VBG = --30 V. The solid line indicates the ground state (GS) resonance of the large quantum dot B, and the dashed line shows the ground state of the small dot A. The induced (ind.) resonance (dashed-dotted) obviously follows the slope of the resonances of dot B. (Source: Reprinted from [40], with permission of Elsevier Science.)

We have to point out that in addition to PAT, a strong electron pump effect is observed, which was explained as electron pumping by spatial Rabi oscillations [44]. This is best seen in Figure 25, where a large backward current, ~ - 10 pA, even under forward bias, is induced. Such a coherent electron pumping mechanism might overcome the limitations of metrological devices that are based on sequential tunneling. We also performed millimeter wave spectroscopy on the double dot by determining the charging diagram under radiation of v = 151 GHz, as seen in Figure 27. This approach differs from the method applied before--where the frequency is varied--because it allows us to distinguish between absorption in the leads and that in the dots. With varying backgate voltage, the induced resonance line of the large dot can be tuned into resonance with the other dot, thus allowing spectroscopy of one dot by the other, as shown in Figure 25b. Here we measured the current under a small forward bias of VDS = 20/zV, depending on the top-gate voltage VTG, as in Figure 27. In addition, we changed the back gate in steps of VBG = 0.5 V from VBG = 30 V, thus shifting both quantum dot potentials. The different shifting of the CB resonances is caused by the different capacitive coupling CBG-A and CBG-8. This is seen in the slopes of the solid and dashed lines in Figure 27. These lines represent the ground states of the two dots. In the measurements shown, the resonance line (dashed-dotted) shifts parallel to the ground-state resonance of the large dot. This parallel shifting shows that the photon is absorbed in the large quantum dot. By varying the two potentials, it is now possible to match any specific resonance condition of the double dot. Regarding the possible application as a single electron/photon detector, it is obvious that such a quantum dot offers a very sensitive device for detection of millimeter- and submillimeter-wave radiation, which might even reach the quantum limit of detection [21].

7. T H E MICROWAVE I N T E R F E R o M E T E R PAT [ 16, 23, 45] through single quantum dots has been demonstrated and is now applied as a tool for millimeter-wave spectroscopy on these devices. Measurements with microwave radiation performed so far give evidence that the well-known effect of Coulomb blockade

336

MICROWAVE SPECTROSCOPY ON QUANTUM DOTS

Fig. 28. Schematicenergy diagram of the double quantum dot, showing the tunnel splitting of the discrete levels el, 82 and the resulting Rabi oscillations (hv = 3e). The millimeter-wave radiation at frequency v interacts with the oscillating electron. (Source: Reprinted with permission from [42]. 9 1998 American Physical Society.)

(CB) [ 1] can be overcome with this continuous-wave (cw) radiation. Time-dependent measurements reveal more detailed information about coherent electronic modes in quantum dots. Initial experiments were undertaken by Karadi et al. [46] to investigate the dynamic response of a quantum point contact and by Dahl et al. [47] in measurements on large metallic discs. Other measurements on superconductor tunnel junctions have shown the importance of electronic phase effects (also termed quantum susceptance) on electronic transport [48]. Recently measurements of the electron's phase were reported with quasiDC measurements of a single quantum dot [49]. In quantum dot systems to date, only cw frequency sources have been applied for spectroscopy in the range from some MHz up to 200 GHz [ 16, 50]. Moreover, the common method of detection gives only scalar information; that is, it shows signals in the magnitude of the induced current without information on the phase. Recent work demonstrated the ability of integrated broad-band antennas to couple cw millimeter- and submillimeterwave radiation to nanostructures, such as quantum dots and double quantum dots, showing the expected PAT resonances in transconductance [ 16]. The energy acquired by the electrons through the absorption of the photons allows them to tunnel through states of higher energy above the Fermi energy, which are otherwise not accessible. We now present transport experiments, performed on a coupled quantum dot structure under irradiation with a new type of broad-band millimeter-wave interferometer. This is of major interest, because the double quantum dot we investigate contains only a few electrons and should thus evolve molecular modes; that is, an electron's wave function can be spread out across the whole double dot. This is schematically illustrated by the level diagram in Figure 28. The discrete states El, ee in the two dots split due to the tunnel coupling, and coherent Rabi oscillations result. An externally applied frequency h v --- 6e on the order of the Rabi frequency then suppresses the coherent modes in the quantum dots. The new source we apply generates picosecond pulses of radiation, corresponding to harmonics in a frequency range of 2--400 GHz. Because these pulses are coherent, we can obtain the magnitude and phase of the induced signal. In Figure 29a such a source, consisting of nonlinear transmission lines in series, is shown: the transmission line is intersected by Schottky diodes, which cause a steepening of the sinusoidal input signal, leading to the generation of harmonics. The lower part of Figure 29a depicts the magnified center of the bow-tie antenna at the termination of the transmission line. The double quantum dot system used in these experiments is seen in the SEM micrograph in the fight part of Figure 29b. In the measurements we found CB energies of E A = e e / c ~ z ,~ 3.0 meV for the small dot A and for the large dot B E~ ~ (1.17 4-0.1) meV (C~" total capacitance of the dot). The complete characterization of such a double quantum dot is performed within the so-called charging diagram, discussed in detail elsewhere [35]. The

337

BLICK

Fig. 29. (a) Nonlinear transmission line used to generate the millimeter wave radiation. The upper part shows the whole circuit (4 x 5 mm); in the lower part the antenna apex is magnified. (b) The broad-band antenna of the double dot. The antenna arms serve as gate contacts for the quantum point contacts defining two quantum dots of different sizes (see right side). (c) Setup of the millimeter-wave interferometer: the radiation of two nonlinear transmission lines (A and B) is superimposed, radiating onto the sample and inducing a drain source photoconductance. The transmission lines are driven by two phase-locked frequency generators in the lower K band (v0: offset frequency). Current through the sample is amplified, which allows analysis of the amplitude and phase of the high-frequency signal. (Source: Reprinted with permission from [42]. @ 1998 American Physical Society.)

m e a s u r e m e n t s w e r e p e r f o r m e d in a t o p - l o a d i n g 3He/4He dilution refrigerator with a sample holder, a l l o w i n g quasi-optical t r a n s m i s s i o n [16]. T h e t e m p e r a t u r e in the m e a s u r e m e n t s p r e s e n t e d is a r o u n d 250 mK. T h e p e r f o r m a n c e of the a n t e n n a was verified with a detailed n u m e r i c a l analysis, using a c o m m e r c i a l l y available p r o g r a m [ 15].

338

MICROWAVE SPECTROSCOPY ON QUANTUM DOTS

,oJ

"y .... JlAA ....................

"~ ol

0 0 . . . .

VTgV)

/ H/-Vt .. iT

g CH3/CH3 (1.0 40.4 n N ) > COOH/CH3 (0.3 q-0.2 nN). This is consistent with their expectation that the hydrophilic COOH groups, which can form hydrogen bonds, interact more strongly than the hydrophobic CH3 groups. Taking into account the tip radius (determined from SEM measurements) of 55 nm in combination with the JKR model, the pull-off force can be used to estimate the work of adhesion WSMT to separate the sample (S) and tip (T) in medium (M) (liquid, vapor, or vacuum): 3 F a d h - - - ~ 7 r . R . WSMT

(29)

(Remarkably, the authors have calculated the effective tip radius, including the roughness of the sample surface with an effective curvature of the gold islands of Rs = 500 nm, and the tip radius, determined with SEM of Rt ----60 nm. Then, the effective tip radius is given by Reff "- RtRs/(Rt 't" Rs) = 55 nm.) The work of adhesion is given by the surface free energies of the sample and the tip FSM, )'*I'M in contact with the medium, and the interfacial free energy }'ST: WSMT - - YSM -+ ~*I'M -- )"ST

(30)

If sample and tip have identical surfaces (e.g., CH3/CH3), then FST = 0 and YSM = ~*I'M, and the work of adhesion is equal to twice the surface free energy in the medium WSMT - - 2 y . Experimentally, a surface free energy of y(CH3/ethanol)= 1.9 mJ/m 2 is found in ethanol, which is consistent with contact angle measurement of ethanol on CH3terminated SAMs. The contact angle of ethanol on CH3-terminated SAMs is about 0 = 40 ~ the surface tension of ethanol is Flv(ethanol) = 22.5 mJ/m 2, and the surface free energy of CH3-SAMs in vacuum is approximately 19.5 mJ/m 2 [79, 80]. According to Young's equation, Ysl -" Ysv -- }'Ivcos 0

(31)

the surface free energy of CH3 in ethanol is given by Ysl = 2.3 mJ/m 2, which is in reasonable agreement with the adhesive force measurements.

374

TRIBOLOGICAL EXPERIMENTS WITH FRICTION FORCE MICROSCOPY

In addition, the surface free energy of the COOH-terminated surface could be determined [77]: ysl(COOH/ethanol)=4.5 mJ/m 2 with force measurements. Remarkably, contact angle measurements cannot be used in the case of COOH, because this high free energy surface is readily wetted by ethanol. In addition, the interfacial free energy YCH3/COOH - - 5.8 mJ/m 2 could be calculated, which explains the strong reduction of adhesive forces in the mixed case. The contact area at the pull-off point was estimated to be about 3.1 nm 2, which corresponds to about 15 functional groups on the sample and the tip. For tip radii of about 10 nm, even single molecular contacts are predicted. Adhesion measurements in water showed the strong influence of electrostatic interactions. NH3- and COOH-terminated tips and/or sample surfaces were found to be charged, which made a large contribution to the adhesive force [77]. A trend similar to that in the adhesion measurements was observed for the friction measurements: greater friction for COOH-terminated tips on COOH-terminated regions than on CH3-terminated regions, whereas CH3-terminated tips gave large friction on CH3terminated sample regions and lower friction on COOH-terminated regions. Frisbie et al. mentioned that the friction contrast appeared only above a threshold of 3 nN. Otherwise, a rather linear loading dependence was observed, where friction coefficients # were determined from the slopes of the frictional force vs. normal force curves: # = 2.5, 0.8, and 0.4 for COOH/COOH, CH3/CH3, and COOH/CH3. In one case (CH3 on CH3), a nonlinear analysis has been used by Noy et al. [78]. Based on these measurements, Frisbie et al. suggest that adhesion is directly correlated with friction, at least when systems in the same aggregate state are compared with each other (e.g., solid films with different functional groups). Previously, SFA measurements were discussed (see Ref. [58]), where friction is related to adhesion hysteresis. However, in this case different phases (solid-like and liquid-like) were compared with each other.

11.4. Chemical Force Microscopy The term "chemical force microscopy" was introduced by Frisbie et al. to emphasize that the functionalized FFM tips give more chemical specificity: depending on the functional group of the probing tip, different contrasts were observed. In analogy to the molecular recognition experiments of Florin et al. [81], Lee et al. [82], or Dammer et al. [83], they envision attaching a specific oligonucleotide or receptor to the probe tip and then mapping friction forces on a surface that contains an array of different nucleotide sequences or ligands to find those with the strongest interaction, corresponding to the complementary ligand-receptor pairs. An early example of an application of FFM to biological materials has been given by Marti et al. [84]. There are some limitations to the chemical specificity of force microscopy with functionalized tips: 9 Capillary forces: Measurements in air are dominated by capillary forces [85], which are one to two orders of magnitude larger than more specific chemical interactions. These capillary forces will thus obscure small differences in molecular forces. Mainly, hydrophilic surfaces will give increased contrast due to the condensation of water on these areas [86]. Although capillary forces can be avoided in most cases, moderately hydrophobic tips are suitable for distinguishing hydrophilic from hydrophobic areas on heterogeneous surfaces in air. This mode is also called acid imaging, because the acid-terminated surfaces are covered by water and cause the strongest capillary forces: respectively, adhesion or friction forces. Measurements performed in dry inert gases [87, 88] may reduce the thickness of adsorbate films, but it is difficult to exclude them completely. Measurements in ultrahigh vacuum may be ideal but are often not compatible with the

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chosen organic systems (high vapor pressures). The capillary effect can be eliminated in liquids; however, the influence of solvent exclusion has to be taken into account. 9 Solvent exclusion: Adhesive forces are not only given by the bondings between tip and sample, but are also influenced by the presence of the fluid. A systematic study of adhesive forces with different functionalized tip/sample combinations in different liquids (water, ethanol, n-hexadecane) by Sinniah et al. has shown that adhesive forces are strongly influenced by solvent exclusion. Adhesive forces in water with hydrophobic surfaces are larger than with hydrophilic surfaces. In ethanol and n-hexadecane, adhesive forces are reduced. In water, these adhesive forces are dominated by the work required to exclude the solvent from the tip-sample interface. In ethanol this macroscopic solvent exclusion is not sufficient to explain the data. Microscopic concepts, like the increased fluidity at the chain endings, leading to fewer interdigitations between these monolayers, are proposed by Sinniah. Although the influence of solvent exclusion may appear as an additional complication for the interpretation of the data, it has been shown by Sinniah et al. that optimum contrast on heterogeneous copolymers can be achieved by an appropriate choice of the functional group of the tip to distinguish between hydrophobic and hydrophilic blocks [79]. 9 pH dependence: Adhesive force and friction measurements in aqueous solutions depend on the pH [89, 90]. Depending on the degree of ionization, electrostatic forces arise between the charged surfaces, which are measurable with force vs. distance curves. These experiments are in close analogy to the contact angle measurements vs. pH [91 ]. If the experimentalist is aware of this effect, it can be a useful tool: at the isoelectric point charge compensation is observable, corresponding to minimum pull-off forces. Thus, adhesive force vs. pH measurement gives the opportunity to measure local isoelectric points or pK values. This type of experiment has been called force titration. So as not to influence the Debye length by the change in pH (inlet of acid or base), it is favorable to measure in electrolytes (buffered solution), where the Debye length is approximately constant for an appropriate range of pHs. 9 Elasticity: Contrasts in friction force microscopy are influenced by the surface compliances of sample and tip. It has been shown by Koleske et al. [92] that Langmuir-Blodgett films with identical end groups but with different chain lengths (CH3(CH2)22COOH vs. CH3(CH2)14COOH) have different adhesion values. Therefore, in addition to the short-range chemical force, a longer range phenomenon, such as elastic deformation due to the repulsive forces, must be effective. Comparing the compressional modulus derived from film pressure vs. area isotherms of the pure components, the adhesion difference can be qualitatively understood. Furthermore, Koleske et al. observed reduced step heights in topography, which is in agreement with the elastic deformation of the films due to the presence of the probing tip. They find that the shorter chain length films deform more than the longer chain length. A quantitative analysis was difficult because of unknown plastic or viscoelastic deformations. 12. TRADITIONAL AND NEW CONCEPTS FOR UNDERSTANDING THE MATERIAL-SPECIFIC CONTRASTS OF FRICTION F O R C E MICROSCOPY A fundamental understanding of contrast mechanisms not only depends on experimental work, but also requires theoretical models. Most of the present ideas are based on empirical models:

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TRIBOLOGICAL EXPERIMENTS WITH FRICTION FORCE MICROSCOPY

1. Adhesion traditionally plays an important role in the understanding of friction and wear. Adhesive forces include van der Waals forces, capillary forces, electrostatic forces, and short-range chemical forces (including metallic adhesion and polarization forces). An increase in adhesive forces leads to an increase in contact area, which also increases friction. Apart from this rather trivial effect, there is some hope that adhesion due to short-range chemical forces might be more intimately related to friction. In some cases [78] a rather good correlation between adhesion and friction was found. However, examples were found in which high adhesion is accompanied by low friction [58]. Alternatively, adhesion hysteresis was proposed from SFA experiments to be the relevant parameter to be compared with friction. There is some experimental evidence [57, 90] that adhesion hysteresis might be a relevant process in FFM. 2. Elasticity plays a role similar to that of adhesion. Local variations in sample elasticity cause changes in the contact area and thus changes in friction as well. Local elasticity is measurable by force microscopy. A systematic study of mixtures of fluorocarbons and hydrocarbons has shown that there are similarities between the friction force map and the elasticity map. However, the correlation is not always fulfilled [51 ]. Similar discrepancies were observed by Garcia et al. [57] on semiconductors. 3. The plucking mechanism, originally proposed by Tomlinson [93] predicts that friction depends on the potential TV]at(X, y) (Flat ~-~ 0 TC]at/0x) and on the weakest lateral spring constant [94]. Mate et al. [11, 95] have already observed that a slip occurs at ~ 10 -6 N for a 155 N/m spring, which is substantially lower than the ~5 • 10 -5 N onset observed for a 2500 N/m spring. If the lateral spring constant of the cantilever is larger than the effective sample spring, instabilities occur in the sample and can be characterized by measuring the slope during the stick period [96]. Lateral stiffness measurements give the opportunity to calculate the contact diameter. 4. Adsorbed molecules (e.g., lubricants) or surface atoms are presumably first excited by the action of the tip. The amount of energy that can be transferred to such a molecule depends on the degrees of freedom, such as bond stretching, rotation, bond bending. In a second stage, the vibrational motion is transferred to the substrate, for example, in the form of phonons or electronic excitations. Local inhomogeneities of the substrate can lead to a different coupling of the adsorbed molecules, which is also observed in the friction force map [42]. 5. The structure of the surface influences the measurements as well. Overney et al. [64] observed that the tilt angle of molecules changes the friction forces significantly. Different faces of a crystal can have different surface phonons or plasmons, which can affect the dissipation process. 6. As discussed above, the chemical nature of the tip can play an important role and has always to be taken into account.

In summary, there are many contrast mechanisms that can influence friction. There is a strong need for fundamental models from which predictions are made that can be confirmed or denied by FFM. MD simulations play a central role and are discussed in this book. Other models relate the concepts of commensurability to friction [62, 72, 97]. Ultimately, a theory would be desirable that makes predictions for friction similar to the predictions of the BCS theory for superconductivity, incorporating parameters such as the coupling of phonons or the density of states at the Fermi edge.

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13. OUTLOOK Friction force microscopy is a valuable tool for the characterization of heterogeneous surfaces. Material-specific contrast allows the identification of different components. The contrast mechanisms are still not well understood. However, it is possible to get more quantitative information about friction and wear. Calibration procedures are described where the normal and lateral spring constants are determined accurately. Even the contact areas can be well estimated from stiffness measurements and continuum elasticity theory. It turns out that long-range attractive forces are important because they have to be compensated for by short-range repulsive forces. Thus, these long-range forces determine the contact area and, consequently, the resolution. In ambient conditions, capillary forces are dominant and limit the resolution to about 5-10 nm. In a liquid environment, capillary forces are eliminated and van der Waals forces can become repulsive: true atomic resolution is achievable. In an ultrahigh vacuum, where van der Waals forces are always present, the resolution in contact mode is about 1 nm. In noncontact mode, true atomic resolution can be achieved. The loading dependence of friction is investigated with the 2D histogram technique, where excellent statistics are achieved. In addition, comparison with the original images gives the opportunity to distinguish between wearless friction and wear processes. Another type of experiment that was performed with FFM is the nanometer-sled experiment. Small islands are moved by the action of the probing tip. Lateral forces are measured during the manipulation. Then, the shear strength at the interface between island and substrate is measurable. The following open questions might be of interest for future experiments: Is there a dependence on the mismatch between island lattice and substrate lattice? Are there angles where friction disappears (incommensurate case), or does the finite size of these objects make concepts of commensurability obsolete? What happens when the size of the islands is below 10 nm (single-atom limit)? FFM is still a young technique. Many questions about the contrast mechanisms are unanswered. However, it opens a path to the fascinating world of atoms and molecules. Today, microfabricated machines are already facing severe problems of high power dissipation. Adhesive forces become dominant at those small scales. Boundary lubricants or novel materials remain to be found that can be combined with microfabrication processes. FFM might be one of the instruments that yields information about the fundamentals of dissipation mechanisms in micromechanical systems and therefore can help to solve those problems in technology.

14. APPENDIX: CALIBRATION PROCEDURE OF FRICTION FORCE MICROSCOPY

The calibration procedure is one of the essential parts of FFM experiments. Each cantilever should be characterized accurately. Manufacturers' data are usually not sufficient and can lead to errors of up to a factor of 10. Thus, each cantilever has to be characterized. One way is to use an electron microscope and to determine all of the relevant parameters, such as tip radius R; height of tip h; width, thickness, and length of cantilever (w, t,/); and position of the tip on the cantilever (Fig. 30). In addition, elastic constants are needed: Young's modulus E and shear modulus G. With all of these parameters determined, the normal spring constant Cn and the torsion spring constant ct for a rectangular cantilever are given by E.w.t

Cn =

ct =

3

(32)

4.13 G.w.t

3.h 2

378

3

(33)

TRIBOLOGICAL EXPERIMENTS WITH FRICTION FORCE MICROSCOPY

Fig. 30. Schematic diagram of the beam-deflection AFM. The relevant dimensions of the rectangular cantilever are indicated: length (I), width (w), thickness (t), and height (h) of the tip (note: h = h e ft -Jr-t/2). Normal and lateral forces are measured with normal and torsional motions of the cantilever. A laser beam is reflected off the rear side of the cantilever. Angular deflections of the laser beam are measured with a positionsensitive detector (four-quadrant photo diode). The A-B signal is proportional to the normal force, and the C-D signal is proportional to the torsional force.

For commercially available silicon cantilevers [73, 74], the elastic properties are well defined, and the first resonance frequency in the normal direction f l can be used to determine the thickness of the cantilever more accurately [98]:

t=

2. v / ~ z r ~

i7~7--~1--~2

fl"

12

0- 4 12 --7.23 x 1 s/m 9 f l "

(34)

where p is the density of the cantilever (p = 2.33 x 103 kg/m 3, E = 1.69 x 1011 N/m2). Thus, the procedure is more simplified. The lateral dimensions of width and length (w, 1) can be determined with an optical microscope. Usually, these dimensions are quite reproducible by current microfabrication procedures. The height of the tip h can vary by a few microns and should be checked with an optical or electron microscope. It has been pointed out by Lantz et al. that the lateral stiffness of the tip can be rather low and should be taken into consideration [37]. For the beam-deflection-type AFM, the sensitivity of the photodetector S (nm/V) has to be determined by measuring force vs. distance curves on hard surfaces (e.g., A1203), where elastic deformations can be neglected and the movement of the z-piezo Zs equals the deflection of the cantilever zt. It is found that the laser focus should be well defined to position the laser beam above the probing tip and to achieve accurate calibrations. Furthermore, force-distance curves should be plotted before and after spectroscopy measurements to exclude changes in the sensitivity S, for example, those caused by variations in laser

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intensity or laser b e a m position. Following this procedure, the forces in normal and lateral directions are given by the difference signals of the four-quadrant detector in the normal direction ( U A - 8 ) and the lateral direction ( U c - o ) : Fn = Cn" S . U A - B

(35)

3 h F1 -- -~ "ct-{ " S" U C - D

(36)

Triangular cantilevers are more difficult to accurately calibrate; the thickness of the cantilever, the length of the tip, and the position of the tip on the cantilever can lead to large deviations in the spring constants from manufacturer data. Thus, it b e c o m e s necessary to characterize each cantilever with electron microscopy. Using this procedure and the formulae given by N e u m e i s t e r et al., we could achieve a reasonable accuracy of 10% [99]. The radius of curvature of the tip can be determined by scanning electron microscopy. Otherwise, well-defined structures, such as step sites [26, 100] or whiskers [101], can be imaged. The image of those high-aspect ratio structures is a convolution with the tip structure. A simple deconvolution algorithm allows extraction of the radius of curvature of the probing tip. Ogletree et al. proposed the use of stepped surfaces of A1203 for calibration, where lateral forces due to geometrical effects (topography effect) on the inclined terraces can be m e a s u r e d [102].

References 1. G. Binnig, C. E Quate, and Ch. Gerber, Phys. Rev. Lett. 56, 930 (1986). 2. H.-J. Gtintherodt, D. Anselmetti, and E. Meyer, eds., "Forces in Scanning Probe Methods" NATO ASI Series E: Applied Sciences, Vol. 286. Kluwer Academic, Dordrecht, the Netherlands, 1995. 3. (a) R. Overney and E. Meyer, MRS Bull 18, 26 (1993). (b) I. L. Singer, "Dissipative process in tribology" (D. Dowson, C. M. Taylor, T. H. C. Childs, M. Gopdet, and G. Dalmaz, eds.), in "Proceedings of the 20th Leed-Lyon Symposium on Tribology," Villeurbanne, September 7-10, 1993. (c) E. Meyer, R. Overney, and J. Frommer, in "Handbook of Micro/Nanotribology" (B. Bhushan, ed.). CRC Press, Boca Raton, FL, 1994. (d) O. Marti, Physica Scripta T49, 599 (1993). (e) E. Meyer, R. Ltithi, L. Howald, and H.-J. Gtintherodt, in "Forces in Scanning Probe Methods" (H.-J. Giintherodt, D. Anselmetti, and E. Meyer, eds.), NATO ASI Series E: Applied Sciences, Vol. 286, p. 285. Kluwer Academic, Dordrecht, the Netherlands, 1995. (f) J. Krim, Comm. Condens. Mater. Phys. 17, 263 (1995). (g) B. Bhushan, J. N. Israelachvili, and U. Landman, Nature 374, 607 (1995). (h) R. W. Carpick and M. Salmeron, Chem. Rev. 97, 1163 (1997). 4. (a) O. Marti, J. Colchero, and J. Mlynek, Nanotechnology 1,141 (1990). (b) G. Meyer and N. Amer, Appl. Phys. Lett. 57, 2089 (1990). (c) L. Howald, E. Meyer, R. Ltithi, H. Haefke, R. Overney, H. Rudin, and H.-J. Giintherodt, AppL Phys. Lett. 63, 117 (1993). 5. G. Neubauer, S. R. Cohen, G. M. McClelland, D. E. Horn, and C. M. Mate, Rev. Sci. Instrum. 61, 2296 (1990). 6. O. Marti, J. Colchero, and J. Mlynek, Nanotechnology 1, 141 (1990). 7. G. Meyer and N. Amer, Appl. Phys. Lett. 57, 2089 (1990). 8. G.M. McClelland and J. N. Glosli, in "Fundamentals of Friction: Macroscopic and Microscopic Processes" (I. L. Singer and H. M. Pollock, eds.), NATO ASI Series E: Applied Sciences, Vol. 220, pp. 405-425. Kluwer Academic, Dordrecht, the Netherlands, 1992. 9. D. Rugar, H. J. Mamin, and P. Gtithner,Appl. Phys. Lett. 55, 2588 (1989). 10. R. Kassing and E. Oesterschulze, in "Micro/Nanotribology and Its Applications" (B. Bhushan, ed.), pp. 3554. Kluwer Academic, Dordrecht, the Netherlands, 1997. 11. C.M. Mate, G. M. McClelland, R. Erlandsson, and S. Chiang, Phys. Rev. Lett. 59, 1942 (1987). 12. G.M. McClelland, R. Erlandsson, and S. Chiang, in "Review of Progress in Quantitative Non-Destructive Evaluation" (D. O. Thompson and D. E. Chimenti, eds.), Vol. 6B, pp. 1307-1314. Plenum, New York, 1987. 13. J.B. Pethica, Phys. Rev. Lett. 57, 3235 (1986). 14. R. Ltithi, E. Meyer, M. Bammerlin, L. Howald, H. Haefke, T. Lehmann, C. Loppacher, H.-J. Giintherodt, T. Gyalog, and H. Thomas, J. Vac. Sci. Technol. B 14, 1280 (1996).

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3. 94. 95. 96.

97. 98. 99. 100. 101. 102. 103.

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383

Chapter 8 ELECTRON MICROSCOPY STUDY OF NANOSTRUCTURED AND ANCIENT MATERIALS Miguel Jos6-Yacamfin, Jorge A. Ascencio Instituto Nacional de Investigaciones Nucleares, Amsterdam No. 46-202, Hip6dromo Condesa, 06100 M~xico, D. F., Mdxico

Contents 1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2. High-Resolution Electron Microscopy of Nanostructured Materials . . . . . . . . . . . . . . . . . . . . 2.1. Image Formation Theory and Weak-Phase Object Approximation in Electron Microscopy . . . . 2.2. Effect of Lenses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3. Experimental HREM of Nanoparticles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3. Image Processing and its Application to Nanoparticles . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1. General Principles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2. The Study of Nanoparticles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3. Image Processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4. Energy Loss Analysis of Nanoparticles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5. Nanodiffraction of Particles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6. Examples of Studies of Ancient Nanostructured Materials . . . . . . . . . . . . . . . . . . . . . . . . . 6.1. Maya Blue Colorant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2. Pre-Hispanic Metallurgical Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

385 386 386 390 393 402 402 406 406 408 410 413 413 423 426 426 427

1. INTRODUCTION N a n o s t r u c t u r e d materials c o m p r i s e one o f the m o s t m o d e r n areas in m a t e r i a l s science, and m a n y future t e c h n o l o g i c a l applications will be b a s e d on such materials. H o w e v e r , it is n o w w e l l d o c u m e n t e d that m a n y materials u s e d in antiquity w e r e b a s e d on n a n o s t r u c t u r e d m a terials. S t u n n i n g e x a m p l e s o f these are the colloidal g o l d p r e p a r e d b y the early C h i n e s e ; the M a y a b l u e c o l o r a n t u s e d t h r o u g h o u t M e s o a m e r i c a f r o m a r o u n d 700 A D up to the nineteen century, w h i c h w a s u s e d to paint m a g n i f i c e n t m u r a l s that stood for m a n y centuries in the m o s t c o r r o s i v e conditions; and finally, the m e t a l l u r g i c a l t e c h n i q u e s o f the M o c h e civilization that flourished in n o r t h e r n Peru, w h i c h a l l o w e d t h e m to p r o d u c e c o p p e r objects c o v e r e d with a thin l a y e r o f silver a few n a n o m e t e r s thick. R e p r o d u c t i o n o f these artifacts

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385

JOSI~-YACAMAN AND ASCENCIO

by modern technology would require a high vacuum evaporator or advanced electrochemical methods. Of course, none of those civilizations had any knowledge of the structure of matter or knew the concept of the atomic cluster. Nevertheless, just as Faraday discovered the optical properties of colloidal particles, they knew that finely divided matter has properties that are different from those of bulk matter. This knowledge came from many generations of trial-and-error empirical experience. There are many techniques that can be used to study ancient materials. However, highresolution transmission electron microscopy (HREM) is one of the key techniques. We divide the present work into two parts. First we discuss the particulars of HREM and their application to nanostructured materials. In the second part, we will discuss applications of HREM and related techniques to the study of ancient nanostructured materials.

2. HIGH-RESOLUTION ELECTRON MICROSCOPY OF

NANOSTRUCTURED MATERIALS 2.1. Image Formation Theory and Weak-Phase Object Approximation in Electron Microscopy To understand image formation and its application to the study of nanostructured materials, it is important to consider some theoretical aspects of image formation theory. The theory of scattering of electrons in the TEM has been fully discussed in the literature [ 1-6]. The key problem is to correlate a high-resolution image with the structure, that is, with the projected potential. In the case of a thick crystal, multiple scattering and nonlinear effects make the relation between the Fourier transform of the image and crystal structure very complex; the image is not related to the projected potential in a simple way. There are several methods of explaining the image formation theory in electron microscopy; however, it is important to deduce the electron diffraction theory first by understanding electron beam behavior clearly, supported by the straightforward development of quantum equations. For the case of elastic scattering, the time-independent Schr6dinger equation for scalar waves can be used. It must be written as V2~(Y) + k2~(7) - 0

(1)

where k is the magnitude of the wave vector k. When the spin is not considered, we have to use k 2 = (2me/he)[E + V(?)] where eE corresponds to the kinetic energy of the incident electron in free space and V is the distribution of electrostatic potential. The corresponding equation is

V2~(~)-I'-[k 2 -+-qg(~)]l/t(~)- 0

(2)

where

2meE k2

=

and

tt 2

2me

The solution to the wave equation can be obtained as a sum of plane wave functions as

1~(~) -- ~

~(J) (~)e -2Jri[c(oj)'~

(3)

J When the initial beam conditions are used, the wave vector k0 is parallel to the z axis, and then for every j component there is an expression of the form

(J) -- ~ (J) e -2rcik(oj)z

386

(4)

EM OF NANOSTRUCTURED AND ANCIENT MATERIALS

only in the z direction, where the j index is omitted by the monochromatic approximation. From the wave equation (2) for a vacuum and an initial solution to 7t = 7t (z = z0), we can obtain the wave function ~p and its corresponding derivative 07t/Oz values for every position over the z axis, using an operator h: 0z

(Tt(x y, z))

grip(x, y zo)

(5)

where fi only operates over perpendicular coordinates. To fulfill the monochromatic conditions, k0 is considered constant in electron microscopy; to find an expression easier then Eq. (5), a solution for h in the angular domain is calculated, in which the wave function is transformed to

(p(u, v, z) - f f ~ r

y, z)e-i(ux+~ dx dy

(6)

Then the relation between ~ and its first derivative over z will be 0 ^ ~zTt(u, v,z)--i

v2)l/2~r(u, v,z)

(4:r2k 2 - u 2 -

(7)

Where the fi operator appears directly and in the spatial domain, this is equivalent to 0z 7t(x, y, z) -- riTz(x, y, z0) --

1 V2~p(x,y, zo)

(8)

4zrk0

but this solution is obtained just for the wave in free space without any perturbation influence. Therefore a more general solution, where matter characteristics affect the wave function, is required. When the potential contribution is considered, the wave beam can be regarded as being generated by two different sources; one of these is established before and inside the sample, and the other is considered to generate the beam after it leaves the specimen (also called the Born approximation). This is mathematically expressed as -- ~1 -~- 1/r2 -- ~ e l ( ~ l ~ t) -~- 7tez(U I ~')

(9)

which separates the wave equation into two parts, defined by el(;I;')--

Z

.................

.>

.................

>9

OQooo~O W0(xy) = 1

Qo

/ """

\ /

Z

=ram=O,,

'-"

oQeo

\

O-OO- O O ~ O O L

~ic~ess:

J

t = c Nz

Fig. 1. Representationof the phase object approximation for electrons moving in a crystal.

The ~ex can be expanded on a Taylor series as 2 2 ~ex(X, y) -- 1 -- icrNz(p(x, y) - o" 2Nz [~o(x, y)]2-t-i

3 3 6 [~o(x, y)]3 -t-""

(36)

If we neglect the nonlinear terms in Eq. (36), we have the weak-phase object approximation (WPOA), which basically ignores higher order terms due to multiple scattering. This approximation is only valid for very thin crystals. In the case of metal nanoparticles, strong scattering is produced, and the WPOA will be valid for H

0.8 -Or~

o

D

M2 o

0.6

+ o~ 0.4

50-

1 o ~

_

Io 0

.#

0.2

.~3-

:

_

_

-

-

-

J

I -tO0

""--'

"1%.0

'

~

0-1 0.2

'

"

0.3

9

0.4

0.0 0.0

0.1

0.2

0.3

0.4

Magnetic Field H (kOe) Fig. 11. Orientationof magnetization in each Fe film of a Fe/Cr/Fe sandwich. Biquadratic exchange coupling is evidenced by the existence of a 90~ angle between magnetizations for a limited range of applied fields. Reprinted with permission from A. Azevedo et al., Phys. Rev. Lett. 76, 4837 (9 1996 by the American Physical Society).

442

MESOSCOPIC MAGNETISM IN METALS

tive anisotropy field did not alter the magnetic order. At a critical field determined by anisotropies and exchange, the magnetization of the Fe films nearest to an edge of the multilayer canted around the direction of the applied field and was observed by measuring the field dependent susceptibility. The canting nucleates at the surface, indicating a surface spin flop transition.

3. MAGNETIZATION, DYNAMICS, AND M E A S U R E M E N T TECHNIQUES Many magnetic materials have been studied as archetypal examples for a wide variety of behaviors. Examples include dimensionality and phase transitions, soliton formation and dynamics, and high-frequency linear and nonlinear response. Much of this work has been inspired by technological device application potentials and examined in the context of domain wall formation and magnetization processes, magnetic ordering and temperature dependences, and optical microwave properties. These topics have been widely discussed in the literature in many contexts. The discussion here concentrates on special features associated with magnetization processes and dynamics in mesoscopic systems. The first subsection deals with the formation of domains and dynamics of the boundary regions (domain walls). The next subsection contains a brief description of a new, extremely useful tool for observing domain nanostructures: magnetic force microscopy. The final subsection is an overview of dynamic spin wave excitations associated with the magnetic system and how these can provide a wealth of surface and interface specific information.

3.1. Domains, Magnetization Processes, and Domain Walls To study static and dynamic magnetism of very small particles, say a few tens to a few hundreds of nanometers, two approaches are possible. The first one consists of studying a single particle at a time with a very local technique, like a SQUID loop surrounding the particle to be studied [59]. The second technique consists of performing an ensemble average measurement on an assembly of many identical (monodisperse, likely shaped) particles [60]. Whereas the first approach is mainly limited by technological and sensitivity considerations, the second one is hampered by the difficulty of synthesizing a huge number of perfectly identical particles. With modem X-ray [61] and e-beam [62] techniques, however, this limitation is largely overcome. An additional advantage of working with arrays is that by varying the period of the array, the magnitude of the interaction between the particles can be tuned. It was shown that the switching field is reduced for interacting permalloy particles formed by nanolithography techniques [63]. Magnetic order and reversal processes, which have been studied extensively since the turn of the century, have now to be reexamined for nanostructured materials. The results on domain structure in submicron magnetic patches presented here exemplify current state-of-the-art growth and imaging technologies. Equally important, these were the first reported results of periodic domains in submicron magnetic patches, and they demonstrate the potential for precise control of micromagnetic behavior in patterned materials. A large number of groups have recently contributed to the new field of mesoscopic systems. This combination of individual experiences has facilitated and increased the possibility of creating a knowledge base for these novel magnetic structures that never have been studied before. Emphasis was put on the creation of nanostructures of magnetic materials and the analysis of the respective magnetic and electrical properties. New preparation techniques have been developed, and magnetic characterization techniques have been

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OUNADJELA AND STAMPS

refined. The various types of systems, such as granular "bulk-like" structures, submicroscopic patterned arrays, and self-organized cluster assemblies have been investigated in terms of their potential for controllable nanoscale design. This has involved developing a better understanding of magnetic properties like anisotropy, exchange interaction, and magnetotransport in systems with reduced dimensions. As the effects of nanostructuring on the key properties of magnetic domain formation, anisotropy, and spin dependent transport in magnetic films and multilayers were to be studied, the evolution of these properties in the continuous films was established first. Domain evolution was studied by magnetic force microscopy (MFM) in single films of Co, Ni, and NiFe. The perpendicular anisotropy achieved in thin Co films made possible a detailed study of the magnetoresistance and spin precession attributed to domain walls, excluding the effects of anisotropic magnetoresistance. As a result, a recent observation of giant magnetoresistance in a homogeneous thin film was made. The magnetic anisotropy in Ni/Cu multilayers was studied in situ as a function of temperature and their Curie temperature studied as a function of anisotropy. Interactions and coupling affects were also studied in Co/Ag and Fe/V multilayers. The origin of the perpendicular anisotropy in Co/Pt and Ni/Pt multilayers was directly probed, using magnetic circular X-ray dichroism to measure directly both the enhanced orbital moment Lz and the ratio of the orbital to spin moment.

3.1.1. Construction of Mesomagnetic Systems The formation of mesomagnetic systems was achieved by the development of techniques that fall into two distinct categories: self-organizing systems and post-deposition patterning.

3.1.1.1. Self-Organized Systems Regular five-monolayer-deep nanoscale pits were successfully created by ion bombardment of Cu(001) and preliminarily on W(110) surfaces. These pits can be filled with magnetic materials by evaporation to form magnetic nanostructures. Ten-nanometer Co clusters have been formed on W(110) surfaces by heating of a 1-3 monolayer film of Co under UHV conditions. Co clusters down to a few nanometers in a Ag matrix have been formed by coevaporation in an MBE system, cosputtering, and mechanical alloying. Their structural, magnetothermal and magnetoelectrical transport properties have been extensively studied and modeled by consideration of a new spin precession mechanism within the Co clusters. The direction of the shape anisotropy of the Co clusters was found to vary as a function of Co composition, and at the cross-over region between in-plane and out-of-plane anisotropy the two components were found to coexist.

3.1.1.2. Post-Deposition Patterning of Films This has been carried out by UV, X-ray, and e-beam lithography. The smallest structures are dot arrays fabricated by direct write e-beam lithography. The highlight is a complete study of the magnetization process and domain evolution in NiFe dot arrays as a function of dot diameter (80 nm to 1/zm) and thickness. A comparative study of Co dots, in which there is a magnetocrystalline anisotropy, is in competition with the shape anisotropy, was conducted on dot arrays formed using X-ray lithography. The change in the domain pattems within the dots was studied as a function of dot separation and the effects of interdot interactions observed.

3.1.2. Self Organized Nanostructures The formation of nanostructured particles and structures was investigated by looking into the possibilities of exploiting the intrinsic balances of attractive and repulsive forces in

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MESOSCOPIC MAGNETISM IN METALS

surfaces and thin film systems. Although these inherent forces are theoretically difficult to predict on a quantitative level, experimental results for two complementary approaches have been obtained: (a) the formation of rectangular, five-monolayer-deep pits on a copper 001 surface under bombardment with Ar + ions of well-defined ion beam parameters. Theoretically this observation of nanoscale pits forming a regular pattern on the copper 001 surface is not fully understood. This work has been extended to the tungsten 110 surface, where preliminary results indicate that pits are also formed, but no regular pattern is found. (b) The formation of cobalt clusters with a lateral dimension that depends on the thermal treatment of a continuous two-monolayer film initially deposited on a tungsten 110 surface. For these films, the Curie temperature and the ac susceptibility have been investigated as a function of thermal treatment.The results can be interpreted in terms of a crossover from ferromagnetic long-range order to superparamagnetic behavior of an assembly of Co clusters. The cross-over region provides the opportunity to study the magnetism of clusters of different sizes and separation. Valuable insights into the coupling behavior of patterned arrays can be obtained from these results.

3.1.3. Domain Formation in Thin Films Exchange due to Pauli exclusion tends to align magnetic moments in a ferromagnet, whereas interaction with crystalline fields via spin orbit coupling can lead to a preference for orientation along particular directions. This behavior is often described in terms of effective exchange and anisotropy fields acting on a position-dependent magnetization vector. The concept of domains was originally introduced by Weiss [64] to explain why ferromagnetic materials can have zero average magnetization while still having a nonzero local magnetization. The essential idea is that the energy in the static magnetic fields associated with the magnetization in a finite material can be minimized by alternating the direction of the magnetization with respect to a surface. The transition from one direction of magnetization to another between adjacent domains involves a rotation of the magnetization vector. The rotation occurs over a finite distance whose width is determined by a competition between exchange and anisotropy. The resulting magnetic structure is called a domain wall. When a magnetic field is applied, domains with the magnetization oriented along the applied field direction grow by displacement of the walls at the expense of domains with the magnetization oriented opposite to the field direction. In three-dimensional reality, numerous possibilities exist. Under suitable conditions, magnetic domains in thin plates of some ferromagnetic magnetic oxides have a circular cylinder (bubble domains) or serpentine (stripe domains) shape, with the magnetization perpendicular to the surface of the plate. A large amount of work performed in the 1970s on bubble and strip domains, observed mainly in single crystals of orthoferrites, hexagonal ferrites, and magnetic garnets, was performed with the idea of using these surprisingly stable structures for storing and processing binary data in magnetic recording devices [65, 66]. Typical bubble diameters were on the order of 10 # m and do not allow for sufficiently dense packing of information to be competitive.

3.1.4. Domains in Mesoscopic Ferromagnets The high quality epitaxially grown metallic ferromagnetic films now available have large saturation magnetizations and controllable anisotropies. This means that a thin Co film, for example, can be manufactured to support useful domain structures such as bubbles with dimensions 100-1000 times smaller than possible with the garnets. This is obviously exciting from the point of view of possible applications. Recently [ 19], thin hcp (0001) Co films grown on Ru buffers were studied for orientational switching behavior. Strong perpendicular magnetocrystalline anisotropy K has been

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OUNADJELA AND STAMPS

Fig. 12. Switchingof magnetization from in-plane (a) to out-of-plane (c) as the filmthickness increases. The film is hcp (0001) Co grown on a Ru buffer. Reprinted with permission from K. Ounadjela et al., "Domain Confinement in Mesoscopic Epitaxial Cobalt Patches,"475 (9 1997 Kluwer Academic Publishers).

measured, which causes the magnetization to switch from in plane to out of plane as the film thickness increases. This was predicted by Kittel [67] on energetic arguments (competition between wall and magnetostatic energy), and the predicted value of the film thickness d for which the magnetization turns from in plane to out of plane was calculated to be dl ~ 6.8~rw ( ~-~s )

(8)

where Ms is the saturation magnetization and crw is the wall energy density. When this condition is applied to hcp cobalt films, the crossover is predicted to occur at --,30 nm [68]. The only way for a thicker film with out-of-plane magnetization to lower its energy is then to split up into small domains with up and down magnetization, as shown in Figure 12c. We have also identified a continuous reorientation of the magnetization in thin epitaxial cobalt films from fully in plane (Fig. 12a) to fully out of plane (Fig. 12c) for thicknesses between 10 and 50 nm, as in previous works [69]. This occurs through a magnetization configuration with in-plane and out-of-plane components (Fig. 12b) [68, 69]. The observed domain patterns arise from the up and down components of the perpendicular magnetization. In all of these cases, the patterns are stabilized by competing interactions, leading to periodic variations of the order parameter [70]. The opportunity for new physical studies appears when domain patterns are induced in magnetic structures constructed with dimensions on the order of a few thousand of angstroms or less. In Co, the width of a domain wall is around 200 ~ (~/A/K -- 140 ,~ for a Bloch wall, where A is the exchange stiffness), so that wall widths, domain size on the order of 100 nm, and sample dimensions are comparable.

3.1.5. Observing Domains on Nanometer Length Scales Interesting properties are expected when the geometrical dimensions become comparable to characteristic nanoscopic length scales as exchange length on the order of 10 nm ((A/M2) 1/2) and mesoscopic dimensions as domain width. The lateral dimension of each patch is 5000 A, and the thickness varies from 250/k to 1500 ~. Up to ten domains were

446

MESOSCOPIC MAGNETISM IN METALS

Fig. 13. An array of square magnetic dots. The material is Co grown on a Ru/A1203 substrate and patterned using X-ray lithography and ion beam etching. Note the quality of the edges with a nearly vertical profile. Reprinted with permission from K. Ounadjela et al., "Domain Confinement in Mesoscopic Epitaxial Cobalt Patches," 475 (9 1997 KluwerAcademic Publishers).

counted from one side of the patch to the other, implying that the domain walls are therefore separated by a distance involving around 250 atoms. Effects of the boundaries then become apparent, and the domain geometry is strongly dependent on the aspect ratio of the magnetic patches. The samples were 5 x 5 mm 2 square arrays of square dots with a 0.5-/zm lateral dimension and 1-/zm array periodicity, as shown in Figure 13. They were fabricated on Ru(5 nm)/Co(tco)/Ru(20 nm)/A1203(1,1,2,0) films, with tco varying from 10 to 150 nm, and developed using X-ray lithography and ion beam etching. The films were prepared by electron beam evaporation. The crystallographic structure of the films was studied using different in situ and ex situ techniques reported elsewhere [71 ], which reflect the high crystallinity of the film and revealed a very good hcp (0001) phase for the cobalt films grown at 400 ~ Cobalt films were patterned using a soft technique developed earlier to avoid deterioration of fragile multilayered samples. The patterning process begins with the creation of holes in a high-sensitivity resist, using X-ray lithography, followed by an aluminum liftoff process. The edges are straight with a nearly vertical profile, and the dot surface retains the smoothness already observed on the as-grown films. This quality of patterning is kept up in cobalt films up to 150 nm thick.

3.1.6. Effects of Microscopic Structure on Domain Formation Similar to what has been observed in the cobalt films (Fig. 14a), bubble and stripe formation is possible in the magnetic patch array, but in a manner very sensitive to the direction of the applied demagnetizing field. This is indeed indicated by our results on the 50-nm (Fig. 14b) and 150-nm (Fig. 14c) Co patches, where stripe patterns in magnetic patches appear after an external parallel demagnetization. A straight stripe domain pattern is observed. In the case of the 50-nm-thick sample, the stripe direction is given by the magnetic field component in plane prior to relaxation. The tendency of the domains to avoid the edges of the dot and to increase the surface of the domain wall is pronounced in the case of the 50-nm-thick dot (Fig. 14b). These peculiarities clearly appear to be results of the geometrical constraint and will be analyzed in the next section. Bubble domains appear in the remanent state after perpendicular saturation, as shown in Figure 14. The domain structure observed in a 50-nm-thick cobalt dot array consists of a metastable network of bubbles that is very similar to the domain array found in the thick continuous film (Fig. 14a). At 150 nm, however, circular bubbles are nucleated at the center of the dot, where the effective field is lowest, and do not grow larger because of the repulsive interactions with the edges. In comparison with Figure 14b, now the available

447

OUNADJELA AND STAMPS

Fig. 14. Stripe domains in films (a) and domain confinement effects in square magnetic elements (b and c). Reprinted with permission from K. Ounadjela et al., "Domain Confinement in Mesoscopic Epitaxial Cobalt Patches," 475 (@ 1997 KluwerAcademic Publishers).

space within each patch is just sufficient to accommodate a single bubble, as shown in Figure 14c.

3.1.7. Shape Effects: Geometrical Control of Domain Patterns Two effects of patterning on domain formation can be distinguished: the effect of patch height and the effect of patch shape. Patch height determines domain size in much the same way as film thickness does. If the domain size is much smaller than the lateral dimension of the patch, one expects identical behavior for a continuous film and a magnetic patch array, because the average stray demagnetizing fields outside a multidomain patch are very small. This means that the magnetostatic energy at any point inside a patch is primarily determined by nearby domains within the patch. This can be verified by comparing domain size as a function of patch height to domain size as a function of film thickness. Measured values for the diameter and stripe period show a functional power law behavior with exponent 0.5, as expected from theoretical predictions for magnetic films [68, 72]. The dependences on patch height and film thickness are the same, although the stripe data appear to deviate from the film behavior for the thickest patch investigated. At this thickness, the domain size is close to the lateral dot size, and dipolar stray fields from the edges may significantly affect the domain pattern and size. A simple argument can be given for the relation between film thickness and stripe domain period. The formation of a stripe pattern depends on reducing the magnetostatic energy at a cost of creating domain walls across the thickness of the film. Defining the lateral

448

MESOSCOPIC MAGNETISM IN METALS

size of a domain in a periodic stripe structure as d and the film thickness as t, the magnetostatic energy is proportional to MZd. If the energy per unit area of a domain wall is g, and with 1/d domain walls per length along the film, then the energy cost of creating a domain in the film is gt/d. The value of d that minimizes the sum of these two energies depends on t 1/2. One can also argue for a similar dependence of bubble domain diameter on film thickness. Shape effects in the patch array dominate the orientation of domains in the patches and distinguish patterned array behavior from continuous film behavior. Finite size effects on the domain formation appear at all thicknesses and are particularly interesting when the domain width is comparable to the lateral extension of the dot. Figure 14c shows the domain configuration in dots patterned from a 150-nm-thick cobalt layer. For this thickness the expected stripe width in a continuous film is about 120 nm [69]. The remanent state after perpendicular magnetization in the dots is a predominantly single bubble configuration (Fig. 14c), although the precision of the MFM experiment cannot exclude the presence of domains or "flower" states at the dot borders. The bubble is located in the center of the dot, where the demagnetizing field is the smallest and did not grow larger because of the repulsion of the edges. Simple arguments can be given to explain the formation of domains during in-plane demagnetization. In the range of thicknesses above 50 nm, the magnetization curves are characteristic of perpendicularly oriented magnetic domains. As the dot is exposed to a large enough in-plane magnetic field, one expects all magnetic moments to align along the field direction. When the field is decreased, and while the main component of the magnetization remains in plane, vortices start to form at the corners of the dots to reduce the in-plane demagnetizing field. The mechanism is similar to the one described for permalloy particles with in-plane magnetization [73, 74], where the vortices are shown to move toward the center of the dot as the field is further decreased. To minimize the exchange energy, the magnetization at the center of the vortex is perpendicular to the surface. During the field decrease the magnetization rotates coherently out of plane, resulting in a magnetization perpendicular to the film with regions (where vortices were created, that is, mostly at the comers) with opposite magnetization. When the bubble diameter is comparable to the lateral dimensions of the dot (as for a 150-nm-thick dot array), only two bubbles nucleate at opposite comers to minimize their repulsive interactions, which coalesce to form dumbbell domains (Fig. 14c). For symmetry reasons, when the field is applied along the side of a dot, the dumbbells will be aligned along one diagonal or the other, as can be seen from Figure 14c. When the bubble diameter is small compared to the lateral dimensions of the dot (as for the 50-nm-thick dot array), the bubble nucleated at the edge remains pinned on it but can run out into stripes (Fig. 14b) if there is enough space to accommodate more than one domain. What distinguishes the 25-nm-thick dots from the thicker ones is the magnetization curves, characteristic of mostly in-plane magnetization with small alternately up and down perpendicular components, as reported in [75] and shown in Figure 12b for hcp cobalt films. The nucleation process remains similar to the one explained previously, but the main component of the magnetization is now in plane. The particular domain structure must be analyzed in terms of in-plane and out-of-plane components of magnetization. First, the in-plane magnetostatic energy is reduced for inplane magnetic moments parallel to the edges of the dots, which results in a circular domain structure, as shown in Figure 15a. This implies that a singularity occurs at the center of the dot, where the in-plane magnetization reorients fully perpendicular to form a so-called vortex structure. Second, to reduce the perpendicular magnetostatic energy, the small perpendicular component of magnetization adopts a concentric magnetic domain pattern, in agreement with the weak contrast observed by MFM (Fig. 15a). How domain confinement proceeds is particularly interesting to investigate in the 25nm-thick Co dot array. The curve of the first perpendicular magnetization (Fig. 15b), taken

449

OUNADJELA AND STAMPS

Fig. 15. A circular domain structure in magnetic dots is responsible for in-plane and out-of-plane components. The domain configuration is shown in (a), and magnetization curves are shown in (b). Reprinted with permission from K. Ounadjela et al., "Domain Confinement in Mesoscopic Epitaxial Cobalt Patches," 475 (9 1997 KluwerAcademic Publishers).

after the sample has undergone in-plane demagnetization, displays one pronounced jump of the magnetization, which occurs within a field interval of 20 e. Because the dipolar interaction between dots is so weak that no collective behavior can be invoked to explain this phenomenon, the observation of the simultaneous switching of millions of dots necessarily implies that the collapse field is mostly sensitive to local parameters like thickness and quality of the material, which is, in principle, identical over the whole sample surface. We attribute this singularity, which corresponds to about 6% of the magnetization at saturation, to the collapse of central domains. It is less sensitive to dot shape, and the edges of about half the dots are oriented antiparallel to the field direction. Close examination of the magnetization curve (Fig. 15b) reveals at least two more, though weaker jumps at lower field (reproducible under identical conditions) that can be attributed to the initial collapse of part of the outer tings. Such a distribution of jumps may result because the height of one jump is proportional to both the size of the domain to be reversed and to the number of dots with the same configuration. Not surprisingly, after the dots have become single domain, a further increase of the field is necessary to overcome the strong demagnetizing field near the bottom and the top of the dots and completely align the moments along the field direction. To further improve the interpretation of these experimental results, we have undertaken 3D micromagnetic calculations of domain configurations in submicronic cobalt dots. Details of the technique are given in [66]. Good agreement is shown between the calculated and measured hysteresis loops, as well as between the calculated and experimental domain patterns discussed in this paper. To show the excellent agreement between experiments and theory, two examples are shown in Figure 16 for the 25-nm and 50-nm-thick cobalt dots in the case of in-plane demagnetization. For the 25-nm-thick cobalt dot, the appearance of a radially modulated vortex structure at zero field has been found theoretically (Fig. 16b) and can be well compared to the experimental data (Fig. 16a). The domain wall configuration obtained for this system presents a Nrel-type wall at both surfaces of the dot, whereas the inner part of the wall is of Bloch type [76]. The mean size of the wall is found to be 230 ,~, on the order of the Bloch wall size. For the 50-nm-thick cobalt dot, the serpentine stripe domain structure observed experimentally (Fig. 16c) is found on the calculated magnetic patterned structure (Fig. 16d) and is attributed to the fact that at nucleation, oscillations in perpendicular magnetization are of

450

MESOSCOPIC MAGNETISM IN METALS

Fig. 16. Experimentallyobserved (a and c) and theoretically calculated (b and d) structures confined to a magnetic dot. The height is 25 nm in (a) and (b) and 50 nm in (c) and (d), leading to very different walllike configurations. Reprinted with permission from K. Ounadjela et al., "Domain Confinement in Mesoscopic Epitaxial Cobalt Patches," 475 (9 1997 KluwerAcademic Publishers).

opposite sign at the two borders, and the only way for the system to overcome this "frustrating" situation is to form "serpentine" perpendicular domains. All of these results have been discussed in detail by Ferr6 et al. [76].

3.1.8. Domain Wall Resonance in Multilayers As described earlier, exchange coupling across interfaces in magnetic multilayers can exist and have large effects on the overall magnetic properties of a structure. The presence of domains in a multilayer suggests an additional interesting effect: coupling of domain wall configuration and oscillations via interlayer exchange [77]. The coupled wall oscillations are analogous to breathing wall vibrations in isolated films [78, 79]. The essential idea is indicated schematically in Figure 17. The spin configuration of two antiparallel coupled films is shown in this figure for (a) an equilibrium case and (b) a nonequilibrium case. A single domain wall exists in each film, separating regions of uniform magnetization. At equilibrium, the energy of the configuration is least when the two walls are positioned directly above one another, because this allows exact antiparallel alignment between spins from separate films. A slight displacement of the walls from this equilibrium configuration results in effective restoring forces due ultimately to the interlayer exchange that opposes the displacement. The resulting dynamics is that of a simple coupled oscillator wherein the walls can oscillate in phase and out of phase with one another. A quantitative description of the dynamics can be made in a straightforward manner. Neel walls are assumed, and the films are supposed to be thin enough that there is no curling of the magnetization near the surfaces. The films lie in x y planes, and the magnetization

451

OUNADJELA AND STAMPS

Y

(a

', I t t . , , " j

'

(b)~..~

,~ ,, /'Sft't'j

Fig. 17. Schematicillustration of relative motion and orientation of magnetizations for Neel walls in two antiparallel coupled films. The walls are in equilibrium in (a) and slightly displaced relative to one another in (b). Reprinted with permission from R. L. Stamps et al., 55, 6473 (9 1997 American Physical Society).

Phys.Rev.B

far from the walls is aligned along the z axis. A free energy of the coupled film system is given by

E_f{A[(d01~ d022 --~x,]2+ (-~x ) ] 4-K[siniO14-sin202]}dx 4- 2yr M 2 f [sin 2 01 sin 2 q~l 4- sin 2 02 sin 2 ~b2] J

+j f{

dx }dx

sin 01 cos q~l sin 02 cos ~b2 + sin 01 sin q~l sin 02 sin q~2 + cos 01 cos 02

f

- Mh J [ c o s 0 1

+

cosO2]dx

(9)

The subscripts indicate which film the magnetization belongs to, and 0 and 4~ are angles describing the orientation of the magnetization at a position x along the film. The intrafilm exchange is A, J is the interfilm exchange, and K is a uniaxial anisotropy with easy axis in the z direction. Solutions describing domain walls are assumed in each film. The strategy is to assume trial solutions corresponding to the uncoupled film case and use the wall width as a variational parameter to find the minimum energy of the coupled wall system under the assumption that J h/2). In general, uncertainty relationships can be derived for operators (belonging to physical quantities) that are not commutative. Such operators follow from the existence of wave functions and average values defined by them. Furthermore, they are independent of the special form of the Hamiltonian operator (see [53]). So, strictly speaking, nothing about tunneling time can be determined from Heisenberg's uncertainty relationship, because one can consider only relationships like Eq. (2), but without time. Instead we can discuss the relationship with average kinetic energy and the square of the locus. The latter results from a preliminary stage that one gets for the average kinetic energy Ekin when deriving Heisenberg's relationship: h2 Ekin ~>

8m(Ay) 2

(3)

One may use this equation to explain the stability of the hydrogen atom, which follows the differential equation of the harmonic oscillator. Whereas in nanoelectronics, single electrons mostly are starting out of quantum wells (e.g., when they are localized in microclusters), similar explanations as for the hydrogen atom may become important as well for the pure tunneling problem and for the tunneling of electrons from (out of) clusters. The only difference with respect to an atom is that now the electrons are not located in atomic orbitals, but in cluster orbitals [33], and we now have the problem of harmonic oscillators without a central force. We will briefly sketch the line of thought: The greater the average kinetic energy, the smaller the average square of variation Ay, which refers to the scope of motion of the electron. If D is the diameter of the nanoparticle (smaller than 2 nm for Au55 clusters), then Ay is on the same order of magnitude and so Ekin ~' D - 2 and the average potential energy E--pot ~ D-1. For small D, the kinetic energy outweighs the potential energy, thus resulting in a "repulsion" from potential force: the confinement, for example, in a microcluster core will loosen, and the electron knocks at the walls of the quantum well, which may represent a tunnel barrier to a neighboring cluster (see Fig. 12 of the two-cluster switch). In other words, the nearer an electron approaches the barrier, the higher the kinetic energy and thus the greater the chance to pass.

2. L A R M O R C L O C K APPROACH In 1967, Baz' [43, 44] proposed the use of Larmor precession as a clock ticking off the time spent by a spin 1/2 particle inside a sphere of radius r -- a. His idea was to consider the effect of a weak homogeneous magnetic field B on an incident beam of particles. Following the idea of Baz', let us suppose that inside the sphere r = a there is a weak homogeneous magnetic field B directed along the z axis and which is zero for r > a. The incoming particles have a mass m and a kinetic energy E - h2k2/2m, and they move along the y axis with their spin polarized along the x axis (so that their magnetic moments/z are aligned along the x axis). As long as a particle stays outside the sphere, there are no forces

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TUNNELING TIME IN NANOSTRUCTURES

acting on the magnetic moment and its direction remains unchanged. However, as soon as the particle enters the sphere, where a magnetic field is present, its magnetic moment will start precessing about the field vector with the well-known Larmor frequency O)L - - 2 1 z B / h

(4)

The precession will go on as long as the particle remains inside the sphere. The polarization of the transmitted (and reflected) particles is compared with the polarization of the incident particles. The angle 0_L in the plane xy, perpendicular to the magnetic field, between the initial and final polarizations is assumed to be given, in the lowest order in the field, by the Larmor frequency ~OLmultiplied by the time ry spent by the particle in the sphere: /9_1_• 99LTy

(5)

The change in polarization thus constitutes a Larmor clock to measure the interaction time of the particles with the region of interest. Rybachenko [22], following the method of Baz', considered the simpler problem of the interaction time of particles with a one-dimensional (1D) rectangular barrier of height V0 and width L, for which everything can be calculated analytically. For energies smaller than the height of the barrier, E < V0, and for the important case of an opaque barrier, where there is a strong exponential decay of the wave function, Rybachenko found for the expectation value of the spin components of transmitted particles, to lowest order in the field B, the result h (Sx) -~ 2

(6) h 2 WLry

(Sy) ~

(7)

where ry is a characteristic interaction time given by

hk Z'y--- Vo~

(8)

and ~ is the inverse decay length in the rectangular barrier __ (k 2 _ k2 ) 1/2

(9)

with k0 = (2m Vo)l/2/h. Here we have assumed that the directions of the field and of propagation of the particles are the same as defined at the beginning of the section. Rybachenko thought that the spin, in first order in the field, remained in the xy plane and so (Sz) = O. Note that the characteristic time Z'y is independent of the barrier thickness L. Instead of being proportional to the length, L is proportional to the decay length. For an opaque barrier this decay length can become very short and so "t'ycan be very small; in fact, smaller than the time that would be required for the incident particle to travel a distance L in the absence of the barrier. A similar result was found by Hartman [21 ], analyzing the tunneling of a wavepacket through a rectangular potential barrier, which is known as Hartman's effect. Hagmann [54] also arrived at the previous result, Eq. (8), by a curious argument related to the uncertainty principle. He assumed that the particles cross the barrier by borrowing certain energy AE during a time interval r. Equation (8) precisely corresponds to the time that minimizes the product r A E. In the method proposed by Baz' [43, 44] and in the one worked out by Rybachenko [22], the change in energy of the particle, due to the interaction - # B , is assumed negligible for a small magnetic field B and there is no induced spin component parallel to the field. However, as we will see, the particles also acquire a spin component parallel to the field, even to first order in the field, due to the fact that particles with spin parallel to the field have a higher transmission probability than particles with spin antiparallel to the field.

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GASPARIAN ET AL.

2.1. Biittiker Analysis

Btittiker [45] presented a detailed analysis of the Larmor clock for the case of a 1D rectangular barrier. He concluded that the main effect of the magnetic field is to tend to align the spin parallel to the magnetic field to minimize its energy (Zeeman effect). This means that a particle tunneling through a barrier in a magnetic field does not only perform a Larmor precession, but also a spin rotation produced by the Zeeman effect, which necessarily has to be included in the formalism. The idea behind this Zeeman rotation is the following. A beam of particles polarized in the x direction can be represented as a mixture of particles with their z component equal to h/2 with probability 1/2 and equal to - h / 2 with probability 1/2. Outside the barrier the particles have a kinetic energy E independent of the spin, but in the barrier the kinetic energy differs by the Zeeman contribution +hWL/2, giving rise to a different exponential decay of the wave function that depends on its spin component along the direction of the magnetic field. In the limit of small fields we have mogL) 1/2 ~+ --

k2 - k2 =t= - - ~

mogL ~ ~ m 2h~

(10)

where the sign indicates whether the z component of the spin is parallel (+) or antiparallel ( - ) to the field. Whereas ~+ < ~_, the particles with spin h/2 will penetrate the barrier more easily than the particles with spin -h/2, and so the transmitted particles will have a net z component of the spin. This net component of the spin along the direction of the field defines a second characteristic time rz of the particle in the barrier. Btittiker assumed that the relevant interaction time depends on the times associated to both effects, the Larmor precession and the Zeeman splitting, and is given by

~/ BLx2 1/2 {02+012} 1/2 17BL --/[Ty ) -+- (TBL) 2} = COL

(ll)

Here 011 is the angle through which the expectation value of the spin in the transmitted beam is turned toward the magnetic field direction because of the difference in transmission probabilities for spin up (Sz = + h / 2 ) and spin down (Sz = -h/2) particles. The traversal time defined by the previous equation is the so called Biittiker-Landauer (BL) time for transmitted particles. Although it was obtained in the context of tunneling, it is a general definition that applies for the traversal time of a particle or an electromagnetic wave through any given region of space. The mathematical analysis of the problem is based on the standard expressions for the spin expectation values (Sx), (Sy), and (Sz) of a transmitted particle for arbitrary field strength B and potential barrier V (y) confined to a finite segment 0 < y < L [45]:

hI

(Sx)

~-~qJlo'x I~!=

(Sy) --

h t+t* +t~_t_ ~ It+l2 + it_l 2

(12)

h ~ h t+t*_ - t~_t_ ~(~lCryl~)--i~ it+12+ it_l 2

(13)

h (~lcrzl~)--- h It+l2 - I t _ l 2 -~ It+l2 + It-I 2

(14)

(Sz) - -~

where crx, Cry, and Crz are the Pauli spin matrices, and the spinor qJ corresponds to (see the next section)

~ -- (,t+12 -+-lt_12)-l/2 ( t+ t_ )

(15)

t+ =- x / ~ e i~~

(16)

where

524

TUNNELING TIME IN NANOSTRUCTURES

is the transmission amplitude for particles with Sz = + h / 2 , and T+ and qg• are the corresponding transmission coefficient and phase, respectively. For each of the spin components Btittiker defined a characteristic time describing the interaction of the tunneling particle with the barrier for an infinitesimal magnetic field:

r

lim ( S x ) 0

lim ~L"--~0

(Sy)-

lim ( S z ) -

WL----~0

1-

"2 h

2

(17)

2

COLTB yL

(18)

h . _BL ~WLL z

(19)

Only two of these characteristic times are independent, rxBL, for example, can be obtained B L 2 § "C BL2 which can be deduced from "t'yBL and "t"BL through the expression Z"BL2 - - - ~y from the relationship between the spin components: h2

(Sx) 2 § (Sy) 2 § (Sz) 2 = - -

4

(20)

In the next subsection we calculate ZyBL and rzBL for a rectangular barrier, and in Section 3 we obtain their general expressions with the formalism of Green's functions.

2.1.1. Rectangular Barrier For the special case of a 1D rectangular barrier, given by V ( y ) = VoO(y)O(L - y), it is possible to find exact analytical expressions for the time. For energies smaller than the height of the barrier, E < V0, Btittiker [45] obtained an expression for the characteristic time associated with the direction parallel to the field: rzBL _ --

m 0 In T 1/2 h~

0~

m k 2 (~2 _ k 2) sinh2(~L) + (~Lk~)/2) sinh(2~L)

4k2~ 2 + k4 sinhZ(~L )

-- h~ 2

(21)

For the time ryBL associated with the direction of propagation, perpendicular to the field, he found BL "gY :

m Oq9

m k 2~L(~ 2 - k 2) § k2 sinh(2~L)

4k2~2 § k4sinh2(~L )

h~ 0~ --" ] ~

(22)

Here T and ~o are, respectively, the transmission coefficient (probability) and the phase accumulated by transmitted particles due to the rectangular barrier in the absence of the magnetic field. These magnitudes are given by { T--

1§

(k2 + e2)2 sinh2(~L) } -1 4k2~ 2

(23)

and k 2 _ ~2 tan ~p = ~ tanh ( ~ L ) 2~k

(24)

The total BL time, defined by Eq. (11), which corresponds to the characteristic time for the spin component along the direction of the original polarization, is then given by

rBL-- m { (OlnT1/2)2 -- h~

0~

( 0 ~ ) 2 } 1/2 +

This is the BL traversal time for a rectangular barrier.

525

(25)

GASPARIAN ET AL.

It is not difficult to check that when the energy E of an incident particle is well below the barrier height V0 of an opaque rectangular barrier, 01~ >> 02, and Btittiker's result (25) is approximately equal to z.BL ~, m L

h~:

(26)

which is very different from the result of Rybachenko, Eq. (8). It is, however, in exact agreement with the traversal time obtained by Btittiker and Landauer [55] based on the transition from adiabatic to sudden limits for a time-modulated rectangular opaque barrier (see Section 4.2).

3. F O R M A L I S M IN TERMS OF G R E E N ' S FUNCTIONS Let us now derive a general expression for the Btittiker-Landauer traversal (and reflection) time using the Green's function (GF) method [56, 57]. We will consider a 1D system with an arbitrary potential V (y) confined to a finite segment 0 < y < L, as represented in Figure 3. We will call this region the barrier, and we will assume that scattering in it is purely elastic. As in the case of a rectangular barrier, we apply a weak magnetic field B in the z direction and confined to the barrier:

B = BO(y)O(L - y)~

(27)

Here O(y) is the step function (later theta will refer to a completely different function). If we concentrate on the motion of an electron, with spin S - 1/2, we have to consider its two wave functions ~1 and qJ2, corresponding to the two spin projections of + 1/2 and - 1 / 2 along the z axis. The column wave function qJ(y) represents both spin states compactly: qJ(Y) --

~IJ2

Our electron is incident on the barrier from the left with an energy E and with its spin polarized along the x direction, so its wave function before entering the barrier is given by

A

~(Y)--

(1)exp(iky)

(29)

1

where k0 - (2mE)l/2/h. We are considering a plane wave for the wave function, but our results are valid for any wavepacket provided it is much longer than the size of the barrier L.

B V(y) e iky ,

te iky ,

re-iky

..-y v

L

X

Fig. 3. Generalpotential barrier restricted to the interval 0 < y < L with a magnetic field applied.

526

TUNNELING TIME IN NANOSTRUCTURES

In the presence of a magnetic field, the Schr6dinger equation takes the form (

h2 d 2

)A

~

2m dy 2 t- V(y) - E qJ(y) = - g B ~ ( y ) -- - / z B

(1 0

0)~(y) -1

(30)

The term on the fight-hand side describes the interaction - # B ; whereas by assumption the vector B is directed along the z axis and the magnetic moment/z is of the form/z - 2#S, where S is the particle spin vector, we have

IzB-21zSzB--lzcrzB = / z B

(1 0) 0

-1

(31)

where crz is a Pauli matrix. The problem is solved by perturbation theory. In the lowest order in B, the spinor qJ (L) of the electron on the right end of the barrier is given by [56]

A (1) e b B ( 1)foL qJ(L) -- 1 ~t(L) + ~mc -1 r

(32)

Here ~p(y) is the solution of the spatial part of the Schr6dinger equation in the absence of a magnetic field. This spatial part of the wave function can be written in terms of the GF of the system as

f0 L a(y,

~(y) =exp(iky) -

y')V(y ') exp(iky')dy'

(33)

where G(y, y') is the retarded GF, whose energy dependence is not written explicitly. It should satisfy Dyson's equation,

a(y, y') - Go(y, y') +

Go(y, y")V(y")G(y", y')dy"

(34)

where Go(y, y') -- i(m/kh 2) exp(ikly - y'l) is the free-electron GE We can obtain all the relevant properties of the problem in terms of the GF solution of the previous equation. 3.1. Traversal Time

We will first concentrate on the calculation of the traversal time. The expectation value of the component of the spin along the direction of the magnetic field of the transmitted electron, up to second order in B, is (Sz>

-

(L)l,,z

. -

m

~

[

eh2BRe ~*(L) mc

f0L~(y)G(L, y) dy ]

(35)

We want to express the wave function 7t(y) that appears inside the integral in the previous equation in terms of the GF. To do so, we take into account the relationship between the wave function and the GF of a 1D system"

ih2k ~(y)---~G(O,

y)

(36)

m

For one-dimensional systems also, we can further simplify the problem by writing the general expression of the GF, G (y, yt), in terms of its own expression at coincident coordinates y -- y' [58],

G(y, y') - [G(y, y)G(y', y,)]l/2

expl-r'y'm Jmin(y,y')

---~ h

a(~l~Yl)

= [G(y, y)G(y', y,)]l/2 exp[ilO(y) - 0(y')[]

(37)

where the phase factor 0(y), which implicitly depends on energy, is defined as 0(y)=

foy im dy' h 2 G(y~ y')

527

(38)

GASPARIAN ET AL.

In Appendix B we will use the relationship (37) to calculate the transmission coefficient of an electron through a layered system. Substituting expression (37) for the GF into Eq. (35) and making use of the relationship between the wave function and the GF [Eq. (36)], we find the spin component along the direction of the magnetic field:

eh2B

fo L G(y, y)dy

(Sz)- ~I~(L)12Re

mc

(39)

A similar procedure for the spin component along the y and x directions leads to

(Sy}

:

e h2B

2 Im fo L G(y, y)dy

mc

(40)

and 21 2ehBfoLmc G(y,y)dy [2)

= hl l 2 ( 1 -

(41)

Btittiker-Landauer characteristic traversal times for the z and y directions are proportional to the corresponding spin components [Eqs. (19) and (18)] and we finally arrive at r BE = h Re fo L G(y, y) dy

G(y, y) dy

ZyBL _ h Im

(42)

So, the BtRtiker-Landauer traversal time [Eq. (11)] is given by r BE

-

-

h

G(y, y) dy

(43)

J Instead of defining the modulus of rzBL and rzBE as the central magnitude of the problem, we prefer to define a complex traversal time r as

"C-- "CBL + i ryBL _ h

L

G(y y) dy

(44)

As we will see, other approaches also get a complex time. All we are saying is that the two characteristic times of the problem can be written in a compact form as the real and imaginary parts of a single well-defined magnitude. In addition, these two time components may be separately relevant to different experimental results, and do not necessarily have to enter into the problem through the modulus [Eq. (43)]. We will come back to this question in the next section.

3.1.1. Expression in Terms of Transmission and Reflection Amplitudes The final result [Eq. (43) or (44)] only depends on the integral of the GF at coincident coordinates. For practical purposes and to compare this result with those of other approaches, it is interesting to rewrite it in terms of the transmission t and reflection r amplitudes or, alternatively, in terms of the transmission T and reflection R = 1 - T probabilities and the phases ~0 and q) 4- q9a of the scattering-matrix elements s ~ :

s(E)_(rt)_(-i~/-Rexp(iq)-t-i~oa) t

r'

~/Texp(i~o)

x/~exp(iq)) ) -i~/Rexp(i~o - iqga)

(45)

This scattering matrix is assumed to be symmetric, which holds in the absence of a magnetic field. ~0a is an extra phase accumulated by reflected particles incident from the left with respect to transmitted particles. Reflected particles incident from the right accumulate

528

TUNNELING TIME IN NANOSTRUCTURES

in the opposite phase. For a spatially symmetric barrier V((L/2) + y) = V((L/2) - y), the phase asymmetry ~Oavanishes and additionally r = r'. The integral of the GF at coincident coordinates can be calculated quite generally in a finite region in terms of t and r [57, 58]. In Appendix C we show how to perform this calculation. Making use of Eqs. (C4), (C7), and (C8), it is straightforward to show that the spatial integral of the GF over the length of the barrier at coincident coordinates can be expressed in terms of partial derivatives with respect to energy E:

r -- h

f0

a(y, y)dy - h

/ OE ln' + - ~1( r

+ r')

/

(46)

This is a general expression, independent of the model considered. For an arbitrary 1D potential profile, the two components of the tunneling time, rz and ry, can be written in general as the real and imaginary parts of Eq. (46). Using the explicit expression of the matrix element of the scattering matrix [Eq. (45)], we find

- ~ sin(~o)cos(~oa)) l n T + -~/-R rzBL -- h Re f0 L G(y, y)dy - h \( d 2dE ryBL --= h Im

f0

G(y, y) dy - h ~

)

2E cos(q)) cos(~pa)

(47) (48)

The term proportional to 0 In t/0 E in Eq. (46), or equivalently the first term on the RHS of Eqs. (47) and (48), mainly contains information about the region of the barrier. Most of the information about the boundary is provided by the reflection amplitudes r and r', and is on the order of the wavelength )~ over the length of the system L; that is, O0~/L). Thus, it becomes important for low energies and/or short systems. This term can be neglected in the semiclassical Wentzel-Kramers-Brillouin (WKB) case and, of course, when r (and so r') is negligible; for example, in the resonant case when the influence of the boundaries is negligible. Certain approaches share this feature of obtaining only the contribution to the time proportional to an energy derivative, missing the terms proportional to the reflection amplitudes. We will discuss this point in more detail later on. The same type of problem arises when calculating densities of states or partial densities of states [59].

3.1.2. Properties of the Traversal Time The integral of the GF at coincident coordinates, and so the components of the traversal time, can be related to the density of states and the resistance. It is well known that the imaginary part of G (y, y) is proportional to the local density of states at the corresponding energy. So, ryBL can also be written in terms of the average density of states of the electron in the system per unit energy and per unit length VL (E):

ryBL -- JrhLvL (E)

(49)

Landauer's conductance for a 1D structure coupled to two perfect leads G(E) is related to the transmission coefficient T by the expression [60] 2e 2

G(E) = ~ T

(50)

h

Substituting this result into Eq. (47), we obtain the expression for the characteristic time:

rBL--h(dlnG(E)+v/1-h/2e2G(E) 2dE 2E

) sin(~p) cos(~pa)

(51)

Thouless [61] has shown the existence of a dispersion relationship between the localization length and the density of states. This relationship can be expressed [62] in the form of a linear dispersion relationship between the real part, Re ln t, and the imaginary part,

529

GASPARIAN ET AL. Imlnt, of the transmission amplitude. The self-averaging property of r BL and of ZyBL is therefore an immediate consequence of self-averaging of the localization length and of the density of states [62]. If we calculate the transmission time through a barrier by dividing the barrier arbitrarily into two parts, the total tunneling time r BL, given by Eq. (43), is not the sum of the individual transmission times, as would be expected. On the contrary, we can easily deduce from Eqs. (47) and (48) that rz and ry are additive, in the sense that rBL(0, L) -- h Re f0 L G(y, y) dy - hRe

If0y G(y, y) dy -4-fyL G(y, y) dy 1

= rBL(0, y) + rBL(y, L)

(52)

ryBL(0, L) -- h Im f0 L G(y, y) dy = h Im

"-- "t'BL(0, y y) + rBL(y

[f0y G(y, y) dy + fyL G(y, y) dy 1

L)

(53)

This property was also pointed out by Leavens and Aers [63] when they discussed the local version of the Larmor clock with an arbitrary barrier potential and a localized magnetic field inside the barrier. It is a consequence of the fact that for an infinitesimal B, the interference between the effects of the magnetic field in the separate regions [0; y] and [y; L] is of higher order than linear and does not contribute to the local times [63]. Mathematically speaking, we say that the BL time [Eq. (43)] adds as the absolute value of complex additive numbers, and so it is not additive.

3.2. Reflection Time

For reflected particles we can proceed in the same way as for transmitted particles. The change in orientation of the spin of reflected waves and so the reflection time rR from an arbitrary 1D barrier can be calculated in the same way as we have done for transmitted waves. We will use the subindex R to indicate that the magnitude corresponds to reflection, and we understand that similar magnitudes related to transmission will have no subindex. Proceeding as before, for the expectation values of the spin components of the reflected wave, we find h

(Sz)R -- ~ ( ( ~ ( 0 ) - 1)l~zl(~(O)- 1)) = ~ehZB 10"(0) - llZRe

O(y)G(O, y)dy

(54)

mc (Sy)R

eh2B -- --~1 mc

~,

(0) -

h ap. (o)-1 L

541

y L differs from zero, and so we will assume that the potential is zero outside the barrier. We evaluate Eq. (116) in three steps, following the procedure of [86]. First, we incorporate the fact that the wave function appearing in this equation is a solution of the Schrfdinger equation. Second, we rewrite the wave functions in terms of Green's functions. Finally, we express the Green's functions in terms of the density of states and the reflection coefficients. First of all, we take explicitly into account that the wave function appearing in Eq. (116) is a solution of the Schrfdinger equation in the way we show in Appendix C. Substituting Eq. (C 10) for the integral over the barrier of the modulus square of the wave function in Eq. (116), we arrive at

.g(D) =

O (~'(y)~z(y)) ~2 O (O*'(Y)C~i(Y))]L I~(y)l.2 + . (y) ~__~ I~P(y) 0

hi . . 4k ~p.2(y) ~__~.

(117)

This expression is formally the same for particles incident from the left or from the fight, but we have to remember that the corresponding wave functions will not be the same. Garcfa-Calder6n and Rubio [87] arrived at the same result by a completely different method. Our second step is to rewrite Eq. (117) in terms of the retarded GF of the system, as we have done for the other times. Taking into account expressions (C7) for the GF in terms of wave functions and (C8) for the derivative of the GF, we can write the first factor on the RHS of Eq. (117), containing the partial derivative with respect to the energy,

G(y, y~)

as

0 (~r'(y)ap(y)) 0E

lap(y)l 2

0 ((3(y+O,y) ~(y)) = ~

G-(yl y-)

ap(y)*

-- OEO(-2m/h2 + G'(y' y) y)

(118)

O(y)

is the phase function previously defined [Eq. (38)] and which implicitly dewhere pends on energy. A similar expression is valid for the other factor in Eq. (117), which contains the partial derivative with respect to the energy. Thus, using the previous expression and Eq. (C 11) for the integral of the GF at coincident coordinates, the dwell time can be written in terms of the GF as

(G'(y'Y))] L ~.(D) = [ O---~-O(y) - G(y, )7-=_0 i OE

Y-OE G(y,y)

o

(119)

Whereas it occurs for the wave function, the GF G (y, y') depends on whether the particle arrives to the barrier from the left or from the fight. This technique was already applied to obtain the traversal time [57] and the dwell time [86] of an arbitrary barrier. After some cumbersome algebra, using Eqs. (C12)-(C15)

542

TUNNELING TIME IN NANOSTRUCTURES

and (C 17), we arrive at the following result for the dwell time in terms of the transmission and reflection amplitudes: .g(D) = h Im

/Fk In, 1 OE + -~(r

]

lnr--7r -f- ~-~(r 1 -

+ r') + -~ ~

OE

r')

]/

(120)

The subindex minus indicates that the particle is coming from the left. r and r' are the reflection amplitudes from the left and from the fight, respectively, R is the modulus square of these amplitudes R = [rl 2 --= Ir'[ 2, and t is the transmission amplitude, which is independent of the incident direction as can be deduced from the time-reversal and current conservation requirements [88]. When the particle is coming from the right, the dwell time is given by an expression similar to Eq. (120), but interchanging r and r'. We will refer to this case with the subindex plus. Gasparian et al. [57] showed that the first term on the RHS of Eq. (120) is proportional to the density of states. Then, we finally arrive at the expression for the dwell time:

h [ O r l ~/-R~oE 2 - ~E l +n

r(,D ) - r c h L v ( E ) 4 - ~ I m

(r-r')

]

(121)

For a symmetric potential we have that the reflection coefficients from the fight and from the left are equal, r = r t, and we obtain r(D) _ - r+(D) - rchLv(E), which is in agreement with the result of Gasparian and Pollak [56]. For an asymmetric barrier, it is easy to check that the contribution from the asymmetry is the opposite for particles coming from the left and from the fight. Then we find that 1

v(E) = 2zchL (v(-D) + v(+D))

(122)

This result was obtained in a much wider context by Iannaccone [89], who considered the relationship between the dwell time and the density of states for a three-dimensional region f2 of arbitrary shape with an arbitrary number of incoming channels. He arrived at N

1

vf~(E) -- 2Jrh E

(123)

"t'(D)

n=l

where v~(E) is the density of states per unit volume and t (D) is the dwell time for particles coming from the n channel. This result shows that the density of states in ~ is proportional to the sum of the dwell times in ~ for all incoming channels. A controversial question concerning the dwell time is whether or not it satisfies the relationship (see [63, 66, 90]) t (D) -- RryB~ +

T'cBL

(124)

This result is trivial for classical particles, for which the traversal time coincides with the y component of our complex traversal time and for which there is no interference between the reflected and the transmitted particles. For the quantum coherent case, this result is not as clear. We can prove this relationship, which we believe must hold, because a particle incident on the barrier is either transmitted or reflected. Reflection and transmission of a particle are mutually exclusive events in the sense of Feynman and Hibbs [77]; that is, without interfering with the scattering event, a measurement can determine whether a particle has been transmitted or reflected. Our results for the y component of the transmission and reflection times, [Eqs. (48) and (62), respectively] and for the dwell time [Eq. (120)] allow us to prove exactly the previous relationship between these times: r(D)_ _ T r B L

+ RryB,L

4/zl + r') ] + R [ 00_EIn-tr = Im {[01nt0E + -7=(r

543

4/~rl ( l + r r ' - ' 2 ) ] }

(125)

GASPARIAN ET AL.

On the other hand, our results also prove that the relationship involving the full BL times, .g (D) __ R r BL + T .yBL

(126)

does not hold. This relationship has been claimed very often in the literature and also has been strongly criticized by other authors [ 11 ]. To close this section, we briefly sketch a derivation of the initial expression of the dwell time [Eq. (116)] deduced by Btittiker. We will follow the papers by Hauge, Falck, and Fjeldly [91] and by Leavens and Aers [92]. Let us assume once more a one-dimensional region of interest with a potential V(y) in an interval [0, L]. The quantum mechanical probability for finding the particle on an arbitrary fixed interval [0, L] at time t is (see, e.g., [72]) e ( 0 , L; t) --

/0'lO(y, t)l 2

dy

(127)

Let us define the average time spent on [0, L] by the particles described by the wavepacket ~(y, t) as ('~(D) (0, t ) ) --

fo

P(O, L; t) dt =_

dt

fo

IO(y,t)12dy

(128)

We can expand the wavepacket ~(y, t) over the scattering states given by Eq. (115) as ap(y; t) --

fdk (ihk2,) ~-~o(k)~(y; k)exp - 2m

(129)

where the coefficients ~0(k) determine the initial form of the wavepacket. Substituting this expression for the wavepacket into Eq. (128), we have [92]

L)>- f_"dk

]2mfoLI~:(y)lady- f_~dk l 0, the integration over t gives us a delta function and the subsequent calculations can be performed readily. Thus (r (D) (0, L)) is an average time spent in the barrier region, 0 ~< y >kT. Thus usual lithographic SET circuits with capacitances between 10 -15 and 10 -16 F must be cooled down far below 1 K. SET at ambient temperature can be achieved only with capacitances between 10 -18 and 10 -19 F, which are typical for sub-10-nm microclusters (see Section 6.2). If the foregoing conditions are met, charge transport through this structure can be controlled by external voltage and current: Transfer of single electrons can be realized by means of QM tunneling if the probability of such tunneling depends on current biasing and driving voltages applied to the circuit.

6.1. Transit Time and Recharging Time in SET Junctions In ME there is general agreement about the notion "transit time," which is independent of the mechanisms through which conduction takes place [19]. If we consider a region of a conductor in space with length y2 - yl - L, between one point left and the other right, with electrons constantly being supplied from the left-hand side and taken out on the right-hand side, then the magnitude of the total electron charge within this length is fixed by Q. Then current jy can be defined by

dQ JY-- dt

(131)

Here only the convenient assumption is made that each electron spends the same amount of time dt -- A r traveling from left to right, where the time r is called transit time. In the present design of semiconductor devices and integrated circuits, transit times have been greatly reduced. Performance and limitations of operation speed as well as overall time constants of nanostructured switch elements depend on transit times. As for SET devices, a single tunnel junction with length L, capacitance C ~ L -1 , and tunneling resistance RT is the simplest system (Fig. 6a). Then charging effects will appear if a current source supplies this junction with a charge independently of tunneling events by jy. Starting outside the Coulomb blockade region, time-dependent recharging of the junction occurs with

o = f j dt - Or where the first term is the charge supplied by the source and the second term is the charge transferred through the barrier junction by tunneling, which is regulated by the tunneling rate. Here we recall the tunneling times that were discussed in Sections 1.3 and 2.2.1. Note,

545

GASPARIAN ET AL.

island

Metal/insulator/Metal

jy v k

~2nm

(a)

(b)

Fig. 6. (a) Simplest system of a single metal/insulator/metal tunnel junction with length L. Charging effects will occur if a current source supplies this junction by jy. (b) Simplestequivalent tunnel junction with a ligand-stabilized cluster (see Fig. 9) between the metaljunction.

that in this section we have already introduced transit time r. Furthermore, we will discuss SET period Z'SET, then recharging time rR, uncertainty time Z'q, and tunneling time "Yt;the latter are three types of times that have different origins. Whereas in metallic tunnel junctions tunneling time rt - 10 -15 s is very short [55, 68], external recharging of the junction in time-correlated SET will be periodic with the socalled SET tunneling frequency

Jy

VSET = - e

(132)

Generally, the smaller the current, the more regular are the SET oscillations, but they have an inherent noise component due to the stochastic nature of the tunneling process. Note that transit time r (131) refers to the "external" system around the single tunnel junction, supplying its current bias jy. The tunnel junction system itself is characterized by "recharging time"

rR = RTC

(133)

Depending on the approach to recharging time, it may be defined in either of two ways: 1. As a "decay time" of an excess charge that appears, say, on the right side of the barrier after a fast tunneling step (with finite but ultrashort traversal time on the order of 10 -15 s), forming a polaron-like state together with the "hole" it left on the left side. 2. As a "relaxation time," which the junction system needs to return to equilibrium, ready for a new cycle of external recharging. Thus recharging time and much faster tunneling time add in SET systems. Furthermore, transit time r, which is produced by the current bias system connected by jy with relation-1T defines ship (132), starting with Q - 0 at t - 0, adds to them also. Note, that rSET -- vSE (in oscillating case) SET period and thus a time depending on jy (see Fig. 7). Typically, in nanostructured materials with the smallest possible conventional chip architecture ("classic" structuring techniques by shadow evaporation reveal a present day limit for SET junctions of 30 • 30 nm) the single tunnel junction comes up to a tunneling resistance RT ,~ 105 f2 and, with L ~ 1-2 nm, a capacitance C ~> 10 -16 F is feasible. Thus recharging time with rR ~ 10 -11 s is still much larger than the tunneling time rt that an electron spends under the barrier. An intermediate time scale is the "uncertainty time" rq = RqC, where Rq is the resistance quantum. The theory of SET assumes a clear separation of time scales rt 10rR, the situation of a very high-frequency SET turnstile device is given, where the Coulomb barrier has to be overcome only once. Second, interesting questions arise with the case RT --+ Rq, because quantum wires surely can be chemically tailored by suitable ligand shells and spacers (see Section 6.2.1). Now the time-dependent play between slowly refilling a reservoir (a SET island), fast tunneling, and recharging of the junction is definitively over because one of the prerequisites of SET is no longer satisfied. Then the electron tends to go into a delocalized state and rR is no longer a relevant quantity. To handle this problem, we start with the question, which collective total resistance can be attributed to the foregoing chain? To answer this question we have to visualize that, even in arrays, which are fabricated by lithographic techniques in the submicrometer range, the device dimensions are smaller than the inelastic scattering length of the conductor materials of which they are composed. Thus, charge transport is govemed by coherent wave propagation, whereby elastic scattering leads to (macroscopically observable) quantum interference effects. With respect to a 1D array, the resistance will fluctuate with portions on the order of quantum resistance Rq, depending on the position and distribution of elastic scattering centers. In an array of ligand-stabilized clusters these may be, for example, packing defects; that is, fluctuations in capacitance Cmicro [94]. Some scientists believe that the length-independent resistance quantum Rq -- h/e 2 is connected with the electron motion in the ground state of the most elementary anharmonic electron resonator: the s orbital of the hydrogen atom [104]. Similar to Bohr's model of the hydrogen atom with the first K shell, we can speak of s electrons in "cluster" cr orbitals [33]. This concept means that wave functions exist, which are in turn tailored by the size and shape of the cluster [ 105, 106]. Consequently, the resistance quantum Rq may be attributed [33] to such an elementary harmonic electron resonator, as well as to the propagation of single electrons in an ideal array with interparticle resistance Rq. On the other hand, it has been shown [60] that the resistance Ra of a 1D array in the case of a defined potential difference on its edges is expressed by h Ra = 2e 2 T

(137)

where T is the energy-averaged transmission probability. This also implies, in the absence of disorder, that the total resistance of a size-tailored periodic 1D cluster array at low temperature may be h/2e 2. A combination of low resistance and low temperature variation of the resistance is expected to be of enormous importance in ME device design [107]. If we again look at the concept of recharging time after tunneling, we have to realize that it is now failing in its strict sense: The former recharging times rR of single cluster sections of the array are now converted into uncertainty time rq, if we disregard recharging time of the electrodes that serve as reservoirs to supply and equilibrate the charges resulting from the potential difference applied to the array. However, in real systems the macroscopic recharging time may still roughly be expressed by n Rq Cmicro.

6.2.2.3. Measuring Ultrashort Recharging Times With regard to Eq. (136), one might have the idea to measure ultrashort recharging times by macroscopic relaxation time, similar to the IS measurements described in Section 6.2.2.1 with high interparticle resistance RT-. With RT- --+ Rq, relaxation frequencies would be expected in the 1-GHz region. Experiments could be done at on adequate array (or a bundle

551

GASPARIAN ET AL.

Fig. 12. Two neighboring clusters idealized as two quantum wells with a tunneling barrier in between. Single electrons near Fermi level EF may tunnel, depending on biasing.

of chains) of Q dots of ligand-stabilized clusters (say arranged in a crystal or in channels of a host structure) by dividing macroscopic relaxation time by the number of chain members n. However, we must be aware that then, because of rt ~ rR ,~ rq, we always measure a sum of times, but it would provide access to the order of tunneling time. Currently, there exist no tunneling time experiments at such arrays, but the preceding suggestions may lead to qualitative approximation. We emphasize that the foregoing simple considerations only make sense for approaching (to make transparent) this new field of chemical quantum dot arrangements figuratively speaking. Of course, they are not adequate to replace still missing analytical calculations of fast tunneling problems with possible superluminal speed in periodic chemical nanostructures, as we indicated in Section 1.5.

6.2.3. The Cluster-Pair Switch The simplest and smallest hypothetical one-dimensional SET device with an area of 2 x 4 nm that has been discussed [33] is the two-cluster switch, consisting of a pair of small ligand-stabilized metal clusters separated by their own ligand shells. It corresponds, for example, to one pair section of Figure 11, say clusters 3 and 4. The principle is sketched in Figure 12. The probability of one electron tunneling out of the left-side quantum well into the fight-side well depends on biasing and on the distribution of excess electrons over sites. Again, with microclusters there are only a few "conducting" electrons available at Fermi level EF in both reservoirs. For current switching, one excess electron must pass the tunnel barrier. With respect to Section 4.2, it is interesting to see that discrete energy modulation of the barrier can be used to create a discrete spectrum of particle energies in the next quantum well.

7. N U M E R I C A L RESULTS We have divided this section into two parts. The first corresponds to the long wavepacket limit, when the spread of the wave function is longer than the size of the system and then expressions (46) and (64) for the traversal and reflection times, respectively, are valid. In this case, the numerical problem reduces to evaluation of the transmission and reflection amplitudes and their energy derivatives, which can be conveniently achieved through the use of the characteristic determinant method introduced by Aronov and Gasparian [58] and explained in Appendix A. Different similar mathematical methods, which allow us to take into account multiple interfaces consistently and exactly without the use of perturbation theory, have been proposed. For example, Garc/a-Moliner and Rubio [108] and Velicky and Barto~ [ 109] introduced a method, based on the surface Green's functions, to study the energy spectra of electrons in systems containing interfaces between different crystals. This method has been applied previously to various problems in solid state physics [ 110-113].

552

TUNNELING TIME IN NANOSTRUCTURES

The second part of this section concentrates on finite size effects, and in this case we have to consider a specific wavepacket and evaluate its probability amplitude at different values of the time so as to calculate the amount of time taken to cross the system.

7.1. Long Wavepackets The evaluation of Eqs. (46) and (64) for the traversal and reflection times can be performed directly for simple systems or with the help of the characteristic determinant for more complex systems. Here we review the results for a rectangular barrier, for a finite periodic system, and for two barriers, that is, for resonant tunneling.

7.1.1. Results for a Rectangular Barrier In the section on the Larmor clock, we gave the explicit expressions for the y and z components of the traversal time that correspond to a rectangular potential barrier, Eqs. (22) and (21). In Figure 4 we showed the variation of these times as a function of energy. These expressions refer to under-barrier transmission. For energies above the potential of the bartier, the analytical continuation of these expressions applies. In this case, the traversal times oscillate with energy. We can calculate the average of rl exactly and check that it is equal to the classical crossing time without including reflections; that is, equal to the time taken by the first pulse to cross the barrier in the limit of very short pulses.

7.1.2. Periodic Structure We now consider a periodic arrangement of layers. Layers with potential V1 and thickness dl alternate with layers with potential V2 and thickness d2. We assume that the energy is higher than max{V1, V2}, and so the wave number in the layers of the first and second type is ki --- [2m(E - V/)]l/2/h (i -- 1,2). In this case, the results for long wavepackets apply equally well to electromagnetic waves, considering ki -- wni/c, where ni is the index of refraction of the two types of layers. Let us call a to the spatial period, so a = d l + d2. The periodicity of the system allows us to obtain analytically the transmission amplitude using the characteristic determinant method [49],

t -- exp(-ikldl) x

{

cos

sin 2 fla +

( Nfla ) _ i sin (Nfla /2) 2

sinfla

kl - k2 sinkzd2 2klka

(138)

where fl plays the role of quasimomentum of the system and is defined by cos fla = coskldl cosk2d2 - k~ + k~ sinkldl sink2d2 -2kit2

(139)

When the modulus of the RHS of Eq. (139) is greater than 1, fl has to be taken as imaginary. This situation corresponds to a forbidden energy band. The term within brackets in Eq. (138) depends only on the properties of one barrier, whereas the quotient of the sine functions contains information about interference between different barriers. The transmission coefficient is equal to 1 when sin(N~a/2) = 0 and fl is different from 0. This condition occurs for 2Jrn

fla = ~

(n = 1 . . . . . N / 2 - 1)

N and we say that it corresponds to a resonant frequency. For the reflection amplitude we have 2 _ k22

r - t exp(-ikldl) kl

2k 1k2

553

sin kzd2

sin(Nfla/2) sin fl a

(140)

(141)

GASPARIAN ET AL.

150 m

-

1:1

lOO

i

=o -

A/ A

- ~ A A

."

I

i

,

,

I l

-5o_ - -

!/ ',I

-100 3.0

I

,

,

I

I

,

,~

3.5

I

4.0

kl

,

,

,

!

4.5

,

,

I

5.0

Fig. 13. Traversaltimes versus the size of the wavepacket for a periodic system. The solid line corresponds to rl, and the dashed line to z2. The values of the parameters are N = 20, n 1 -----2, n 2 = 1, d 1 = 0 . 6 , and d2 = 1.2.

With these expressions for the transmission amplitude [Eq. (138)] and for the reflection amplitude [Eq. (141)], we can calculate the traversal time via Eq. (46) and the reflection time via Eq. (64). We concentrate on the simplest periodic case, which corresponds to the choice kldl -k2d2. This case contains most of the physics of the problem and is also used in most experimental setups [9]. From Eqs. (138) and (141), Ruiz et al. [15] calculated numerically the traversal time for electromagnetic waves by considering a system of 19 layers (N -- 20) with alternating indices of refraction of 2 and 1, and widths of 0.6 and 1.2, respectively. Their main conclusions are also applicable to the problem of an electron in a periodic potential. In Figure 13, rl and r2 represent electromagnetic waves in a periodic system as a function of kl. In the energy gaps, the traversal times are significantly smaller than the crossing time at the vacuum speed of light (horizontal line). The average of rl with respect to wave number is equal to 22.8 and coincides with the classical crossing time (i.e., for very short wavepackets, without including multiple reflections); it corresponds to the horizontal straight line in Figure 13.

7.1.3. Resonant

Tunneling

Double-barrier potential structures present resonant tunneling, which has been studied for electrons since the early days of quantum mechanics [90, 114, 115]. Resonant tunneling for electromagnetic waves is easier to carry out than corresponding experiments on electrons [26]. A double-barrier structure is a special case of a periodic system that consists of N = 4 interfaces with two evanescent regions separated by a propagating region. In the evanescent layers, the potential energy V2 is larger than the energy of the electron E. The results of the previous section part also apply to this case where one type of layer is evanescent. We merely have to replace k2 by - i x , where x - [2m(V2 - E)]l/2/h (correspondingly, sink2d2 becomes sinhxd2). Cuevas et al. [49] calculated the traversal time r for electromagnetic waves through a double-barrier structure using the previous equations for the transmission and reflection amplitudes [Eqs. (138) and (141) with N = 4] and convoluted with a Gaussian distribution

554

TUNNELING TIME IN NANOSTRUCTURES

function with a standard deviation of 6 MHz, which reproduces the same average height of the peak as the corresponding experiments [26]. The behavior of the traversal time at a resonance is fairly universal. The phase of the transmission amplitude changes by an angle of :r at each resonance, as predicted by Friedel's sum rule. Its frequency dependence can be fitted quite accurately by an arc tangent function. The time, which is proportional to the derivative of this phase, is a Lorentzian with the same central frequency and width as the Lorentzian corresponding to the transmission coefficient. Whereas the lifetime rl of the resonant state is the inverse of the width of the transmission coefficient at half-maximum, we conclude that it must be equal to half the traversal time at the maximum of the resonant peak: Z'I - -

(142)

1 Z'res

This result was obtained by Gasparian and Pollak [56] by considering the traversal time for an electron tunneling through a barrier with losses; that is, with a decay time.

7.2.

Finite Size Effects

The kinetic approach is suitable for studying numerically the evolution of wavepackets with sizes on the order of the width of the region of interest. Up to now this has been done only by neglecting dispersion [15]. This is not very adequate for electrons, although the results shed some light on a very interesting aspect of the problem, so we include them here. We will describe the numerical simulations of the time evolution of finite size wavepackets that cross the region of interest and we will measure the delay of the peak of the transmitted wave as a function of the size of the original packet. The simulations also can be used to calculate the change in size of the packets. Whereas we are not including dispersion effects, the results are directly applicable to electromagnetic waves, so we will use a nomenclature appropriate for them, although the results are equally valid for electrons, in the absence of dispersion, provided that we translate the indices of refraction into their corresponding potentials. Let us consider a three-dimensional layered system with translational symmetry in the Y-Z plane, and consisting of N layers labeled i - 1. . . . . N between two equal semiinfinite media with a uniform dielectric constant no. The boundaries of the ith layer are given by yi and yi+l, with yl - 0 and YN+I -- L, so that the region of interest corresponds to the interval 0 ~< y ~< L. Each layer is characterized by an index of refraction ni. In the case of electrons, we assume that the energy E of the electron is higher than the potentials of the different layers and that the wave numbers are inversely proportional to the indices of refraction; so the potential V/in layer y is equal to Vi = E(1 - (no/ni)2). We calculates the position of the packet at different times, and from this information we extract the time taken by the packet to cross the region of interest. In particular, neglecting dispersion, we can measure the average positions Yl and Y2 of the square of the modulus of the wavepacket at two values of t, tl and t2, such that the packet is very far to the right of the structure at tl and very far to the left at t2. These average positions are defined as

yl~,(y, t)[ 2 dy

y(t) --

(143)

oo

The traversal time of the wavepacket through the region of interest is given by r = t2 -- tl --

(Y2 -

Yl -

c

L)no

(144)

Although we refer to this time as a traversal time, we have learned that, strictly speaking, it is a delay time. Part of the interest in this type of simulation is to study how delay times relate to the previously obtained expressions for the traversal time.

555

GASPARIAN ET AL.

25

. . ~ 1 7 6 1 7 6 1 7.6. . . . . . . . . . . . . . . . . . .~176176

23

20

9, . , . . , . .

,..,

,,,,.

_,,

18 15 1

10

100

1000

Fig. 14. Traversal time versus the size of the wavepacket for a rectangular barrier. The dashed line corresponds to a central wave number k = 81~r/80, the solid line to 41Jr/40, and the dotted line to 21zr/20. The values of the parameters are L = 10, n = 2, and no -- 1.

7.2.1. Rectangular Barrier Let us first consider finite size effects for a rectangular barrier or slab confined to the segment 0 ~< y ~< L and characterized by an index of refraction n. In Figure 14 we plot the traversal time versus the size of the wavepacket for three different values of the central wave number: k = 8 1 n / 8 0 (dashed line), 41Jr/40 (solid line), and 21Jr/20 (dotted line). The values of the parameters are L = 10, n = 2, and no = 1, and the velocity is taken as equal to 1. The values of the wave numbers are chosen so that sin 2u -- 1, sin u = 1, and sin u -- 0, and so that the characteristic time rl is a central value, a minimum, and a maximum, respectively. We can check that the long wavepacket limit of these results corresponds to the value of rl, given by Eq. (21). The traversal times of very short pulses are all equal to 20.8, independently of the central wave number considered. This value is the classical crossing time, taking into account multiple reflection, which for the slab is given by

Ln 1 + Irl 4 r --

c 1-lr

14

(145)

The transition between the long and short wavepacket limits takes place for wavepacket sizes on the order of 20; that is, on the order of the width of the slab. The transmission coefficient presents a similar behavior to the traversal time [ 15]. In the regions with destructive interference, so that the transmission coefficient is very small, the crossing times are also very small.

7.2.2. Periodic Structure We now consider finite size effects in the periodic arrangement of layers previously study in Section 7.1. Layers with index of refraction n 1 = 1 and thickness dl alternate with layers of index of refraction ne = 2 and thickness de. In Figure 15 we show the delay time versus the size of the wavepacket for two values of the central wave number, k0 = 3.927 and k0 = 4.306, which correspond to the center of the gap and to a resonance, respectively. There is again a strong similarity in the behavior of the traversal time and of the transmission coefficient [ 15]. The long wavepacket limit of the traversal time coincides with the characteristic time rl, whereas the short wavepacket limit is independent of wavenumber and equal to 29. The speed of the wave is greater than in vacuum for a wide range of sizes9 The minimum size of the packets that travel faster than in vacuum is about 9, so that the corresponding

556

TUNNELING TIME IN NANOSTRUCTURES

100

m

m

. . . . . . . . . .

D

~ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

n

B

10

m

D m

D

, I llllll

1 o.1

I

, ,ll,lll

1.0

I

10.0

I ,l,Jlll

I

100.0

I I Ill,I

1000.0

Fig. 15. Traversaltime versus the size of the wavepacket for a periodic system. The solid line corresponds to a central wave number k = 3.927 and the dashed line to k = 4.3. The values of the parameters are the same as in Figure 12.

width 2o-i is very much the same as the size of the system. Velocities larger than in vacuum occur when the transmission coefficient is very small. In regions with a very small density of states, the traversal time is very short and, at the same time, transmission is very difficult due to the lack of states at the corresponding energies. The width of the transmitted packet O-T is slightly smaller than the width of the incident packet o-I. According to the results in Section 4.4, we obtain that, in the absence of dispersion and up to second order in perturbation theory, this change in width depends on the derivatives with respect to the frequency of rl and r2. Whereas the first of these derivatives is equal to zero in the center of the gap, we arrives at o.2_o. 2

2 l)g dr2 2 dw

(146)

To check the upper limit to which second-order perturbation theory is valid, Ruiz et al. [ 15] plotted o.2 _ o.2 as a function of the size of the packet and compared it with the value of (1/2)(dr2/dog) obtained from the characteristic determinant. Second-order perturbation theory works adequately for a wide range of sizes and, in particular, for the sizes for which we obtain velocities larger than in vacuum. The error in the measurement of the traversal time of a single wavepacket is its width divided by its velocity. All the packets that travel faster than in vacuum are so wide that their uncertainty in the traversal time is larger than the traversal time itself and even larger than the time it would take a wave to cross the structure traveling at the same speed as in the vacuum.

8. C O N C L U S I O N S A N D O U T L O O K In this review we have discussed the topic of tunneling time in mesoscopic systems, including nanostructures, particularly in 1D systems with arbitrarily shaped potential. However, the treatment of tunneling time in "nanostructured materials" approaching the molecular and atomic scales is still open.

557

GASPARIAN ET AL.

In the field of tunneling time there are problems in all of the existing approaches, and we do not have a clear answer for the general question, "How much time does tunneling take?" Unfortunately not one of these approaches is completely adequate for the definition of time in QM. Nevertheless, we note that all these different approaches can be consistently formulated in terms of Green's functions and their main differences can be fairly well understood. As we pointed out in Sections 1.2 and 6, great progress in the application of ligandstabilized microcluster quantum dots in SE has been made. Therefore, it seems that the race between "physical" and "chemical" nanostructured materials is running decidedly in favor of chemistry: At present, the physical requirements for further investigation of nanostructured tunneling devices can be satisfied by chemically size-tailoring zero-, one-, two-, or higher dimensional cluster materials in molecular scale, although fabrication techniques for hybrid or pure cluster nanodevices are still lacking.

8.1. Complex Nature of Time For 1D systems, we obtained closed expressions for the traversal and reflection times [Eqs. (46) and (64)] in terms of partial derivatives of the transmission and reflection amplitudes with respect to energy. Results of other approaches can be related to these expressions, and the main differences can be grouped into two categories: the complex nature of time and finite size effects. Our conclusion about the complex nature of time is that it is clear that there are two characteristic times to describe the tunneling of particles through barriers. (Similar conclusions can be reached for reflecting particles.) These two times correspond to the real and imaginary components of an entity, which we can choose as the central object of the theory. Different experiments or simulations will correspond to one of these components or to a mixture of both. Biittiker and Landauer argued that these two times always enter into any physically meaningful experiment through the square root of the sum of their squares, and so they claimed that the relevant quantity is the modulus of the complex time.

8.2. Finite Size Effects in Mesoscopic Systems With regard to finite size effects, we believe that Eqs. (46) and (64) are exact and adequately incorporate finite size effects. These effects correspond to the terms that are not proportional to derivatives with respect to energy. They are important at low energies and whenever reflection is important (as compared to changes in the transmission amplitude). Several approaches do not include finite size terms, because they implicitly consider very large wave functions. The WKB approximation, the oscillatory incident amplitude approach, and the wavepacket analysis, for example, do not properly obtain finite size effects. On the other hand, our GF treatment, based on the Larmor clock, the generalization of the time-modulated barrier approach, and the Feynman path-integral treatments arrived at exact expressions. To see that these expressions are all equivalent, we have to transform the derivative with respect to the average barrier potential, appearing in the time-modulated barrier approach, into an energy derivative plus finite size terms. The same has to be done with the functional derivative with respect to the potential appearing in the Feynman pathintegral technique. Finite size effects can be very important in mesoscopic systems with real leads with several transmitting modes per current path. The energy appearing in the denominator of the finite size terms [Eqs. (46) and (64)] corresponds, in this case, to the "longitudinal" energy of each mode, and so there is a divergence whenever a new channel is opened. In the exact expressions there are no divergences; the problematic contributions of the finite size terms is cancelled out by the terms with energy derivatives.

558

TUNNELING TIME IN NANOSTRUCTURES

8.3. Bopp's Approach 2 Finally, one of us (G.S.) wants to give some hints about a new altemative QM approach: Bopp's approach seems us to be not too well known in a broader circle of physicists, but we hope that readers will find it as interesting as we do, because within its framework there still is some freedom for the definition of time. Furthermore, some critical problems with the wavepacket approach in mesoscopic systems and nanostructured materials hopefully can be avoided. Bopp's QM [116] gives up the meaning of waves as some real dualistic appearance of quanta, and operates with manifest annihilation and creation processes instead. Wave functions are only the expressions of the stochastic process and of our often incomplete knowledge of the events. Until now, Bopp's QM seems to have been ignored in the theoretical treatment of tunnel processes. Bopp's derivation, which he completed 10 years ago on the basis of von Neumann's equation of the alternative, starts with the undeniable (experimental) fact that in quantum physics, particles can be created and annihilated. Therefore, creation and annihilation must be considered as basic processes. Philosophically speaking, motion is not the fundamental driving force, but only occurs when a particle (a quantum) is annihilated at a certain point (of space) and an equal quantum is created at an infinitesimal neighboring point, and this process is continuously going on during a certain time. Motions of this kind are compatible with the existence of some manifest creation and annihilation processes. Based on this idea, quantum physics can be derived from the above-mentioned first principles. According to this scenario, the nature of tunneling may be annihilation in front of a tunneling barrier and immediate creation (only with different probabilities) either in front or behind the barrier (reflected or transmitted). Thus we cannot exclude the possibility that the time for creation on the right side (after tunneling) can be infinitesimally small, perhaps even zero (and the same for creation on the left side in the reflected case), pretty much independently of the barrier height and shape. Note that some problems, like deformation, size of the wavepacket during such a process, or the location of the center of gravity, then have no further meaning, a fact which possibly simplifies analytic treatment of tunneling problems. Unfortunately, two other difficulties with the tunneling problem arise. First, when approximating "classical" QM, Bopp's framework of QM claims that motion is creation in an infinitesimally neighboring point. The main question is how to operationalize analytically the creation of a transmitted particle far away beyond a tunnel barrier; the secondary problem is the introduction of a tunneling time.

APPENDIX A: G R E E N ' S FUNCTIONS OF A LAYERED SYSTEM We have been able to obtained the characteristic barrier interaction times in terms of the GF of the system and, more specifically, as spatial integrals of the GF at coincident coordinates; see, for example, Eq. (43). In the Appendices we present a convenient model for calculating these GF integrals. We will closely follow Aronov et al. [58], and introduce a general model for GF calculations of complex systems. Let us consider that our system can be divided into (N - 1) layers, labeled n = 1 . . . . . N - 1, which are placed between two semiinfinite media. The positions of the boundaries of the nth layer are given by Yn and Yn+l. We allow a possible discontinuity in the potential Vn (y) at each boundary between two layers. This assumption does not imply a loss of generality, because we can reproduce any reasonable potential shape in the limit of an infinitely large number of layers, each of them of an infinitesimally small width. 2

Introducedand discussed by G. Schrn.

559

GASPARIAN ET AL.

We consider a plane wave incident from the left onto the boundary y = yl and we want to evaluate the amplitude of both the reflected wave and the transmitted wave, propagating in the semiinfinite media for y >~ YN. In this method, the GF is evaluated first for the case of a single boundary between two media. Then, the case of two boundaries is solved using the GF for one boundary. The problem is solved iteratively for n + 1 boundaries, considering that the solution for n boundaries is known. A.I. One

Boundary

Let us first discuss the contact of two semiinfinite media, which will clearly show the spirit of the method. Assume that on the left of the boundary at yl (y < yl) the potential energy of the electron is Vo(y), while on the right of the boundary (y > yl) the potential is V1(y). We suppose that the one-dimensional electron GF G~n~ (y, y'; E) (n --0, 1) for each medium is known when the media are infinite. In the following discussion, the energy parameter E will be omitted from the arguments of the GF. The GF is the solution of the equation [

(A1)

E)' h2 02 ]G(n~ 2m Oy 2 + gn (y) - E (y, y'; -- (y - y')

The upper index (1) will indicate the number of boundaries considered in the calculation of a given GE In Eq. (A1), for example, the index is I = 0. The lower index of the GF labels (1) the interval for which the GF is valid. The GF G o for the case when one interface is taken into account in the first medium can be expressed in the form G(1) G(o~ (Y, yl)G(0~ (yl, y') 0 (Y, yl) _ G(00)(y, yf) + r01 G(0~ (Yl, Yl)

Y,

y,

~< Yl

(a2)

The first term on the RHS corresponds to direct propagation between the two arguments of the GF, y and y~, while the second term corresponds to propagation from y to the surface, reflection on the surface, and propagation back to the point y~. rol is the reflection amplitude of the electron propagating from region 0 into region 1, and we will calculate it subsequently. A similar expression holds for the GF G~1) in the region on the fight of the boundary (y, y' ~> yl):

(1)

G 1 (y, y') -- G

~0)

(y, y') + rl0

G~0) (Y, yl)G~ 0) (Yl, Y')

(A3)

G~~ (yl, yl) rl0 is the reflection amplitude of the electron propagating from region 1 into region 0. To calculate the quantities r01 and rio, we have to enforce the condition of continuity (1) for G(01)(yl, yl) and G 1 (yl, yl), (1) G O (yl, Yl) - G~1)(yl, Yl)

(A4)

and the conservation of current at the boundary y = yl, 0 [G(01)(yl, yl) - G~1) (yl, yl)] "- 0 Oy

(A5)

where the derivative is taken simultaneously over the two variables in the argument of the GF. This condition may also be written in terms of derivatives with respect to the first argument of the GF only in the form 9 .(1) 2m G(01)(yl - 0 , Yl) - G 1 (yl + 0 , yl) = h2

560

(A6)

TUNNELING TIME IN NANOSTRUCTURES

Here the dot signifies the derivative with respect to the first argument, and it is necessary to distinguish between left-side and right-side derivatives of the GF due its discontinuity:

m 1 0 G(y T O, y)--t---~-i + -~~y G(y, y)

(A7)

Solving Eqs. (A4) and (A6), we obtain the expressions for the amplitudes of reflection r01 and rl0,

G~0) G(00)(Yl -I- 0, Yl) -- G(00)(~0)(Yl + 0, Yl) r01 -- G~o)r

- 0, Yl) -- G(00)(~0)(Yl + 0, Yl)

GI 0) G; 0) (yl - 0, Yl) - G(o0) 010) (yl - 0, yl) rio -

(A8)

(A9)

G~o)G(oO) (yl - 0, Yl) - G(o0) a~ 0) (Yl + 0, Yl)

where we have used the notation G(n~ - Gn(~ (Yl, Yl), for n - 0, 1. We shall usually consider homogeneous media with constant potentials Vn of arbitrary strength. In this case, we have

0 ~(o)

ay "-"0,1 (Y, Y) -- 0

(AIO)

and the final expressions for r01 and rl0 [Eqs. (A8) and (A9)] become G~~ _G(o~ rol = - r i o = G~o) + G(oO)

(A11)

A.2. Many Boundaries We can generalize the previous procedure by adding new boundaries and each time using the previously obtained GF as the starting point. In this way, we derive the new amplitudes of reflection of the electron on subsystems composed of many layers. Finally, the GF for the complete system at coincident coordinates in the nth layer [the left block containing n boundaries and the right block consisting of (N - n) boundaries] is given by

[ R-(n)-D(--n+N)~nn+l'-~-R(n) n,n_l,,n,n+ 1 , n,n-1 exp(2i[On(y)--On(Yn)])

G(nN)(y, y) -- G(nO)(y,y) 1 +

+ " l~(-n+N) n , n + l exp (2i[On(Yn+l ) -- On(y)]) ] DN 1

(A12)

where the R are reflection amplitudes that we will define subsequently and DN is a very important magnitude, containing all the information about the self-consistent problem of multiple reflections in the boundaries. This magnitude is called the characteristic determinant and can be expressed as a product:

DN -- D ~ U Xn-l,n(1 -+- rn,n-1)(1 -k- rn-l,n)

(113)

n=l

We now define the different symbols that appear in this expression. The quantity rn-l,n (rn,n-1) is the amplitude of reflection of the electron propagating from the region n - 1 into n (n into n - 1). In general the values of rn,n-1 are model dependent and, for a piecewise constant potential, are given by Eq. (A11) by replacing 0 by n - 1 and 1 by n in the lower indices: G(nO) - G (nO-)1

rn-l,n

(A14)

a(O) "+"a(nO)__l

The GF are the unperturbed GF evaluated with their two arguments at coincident coordinates in Yn, G~n~ = G~n~ (Yn, Yn). The amplitude of reflection in the opposite direction

561

GASPARIAN ET AL.

satisfies rn-l,n = --rn,n--1. For a tight-binding model and for a set of delta functions, we have

Vn a(O) rn,n-1 -- -- l + VnG(n~

(A15)

and rn-l,n = rn,n-1, where Vn is the nth diagonal energy in the fight-binding case and the strength of the nth delta function in the other case. The factors ~.n-1,n are defined, in general, as

(fy ~.n-l,n--exp

yn2mdy

--

n-1 ~

)

G(n0)l(y, y)

(A16)

and the factor )~0,1 is defined as equal to 1. For a piecewise constant potential, the previous expression reduces to

~.n-l,n -- exp

(2myn--Yn-1) h2

~0-S"-"n-1

(A17)

D ~ is the determinant of a tridiagonal matrix and satisfies the recurrence relationship

o O - - a n D O _ 1 - n n O n _0 2

(A18)

where A1 - 1

D O- 1

DO1 - 0

(A19)

and we have for n > 1,

rn-l,n An -- 1 + ~.n-l,n ~ ( 1 rn-2,n-1

+ rn-2,n-1 + rn-l,n-2)

(A20)

+ rn-2,n-1)(1 + rn-l,n-2)

(A21)

and

rn-l,n Bn -- )~n-l,n ~ ( 1 rn-2,n-1

The generalized quantity/?(n) "~n,n-1 is the amplitude of reflection from the left block, containing n boundaries (when the electron is incident on this block from the right), and R(-n+N) n,n+l is the amplitude of reflection from the fight block, containing N - n boundaries (when the electron is incident on this block from the left). On(y) is the phase factor defined in Eq. (38). The reflection amplitude Kn,n_ l'~(n) also may be written in the form "~0

(n) __ Dn+l n,n-1 -- D O

(A22)

"~0+ 1 is given by where Dn "0

Dn+ 1 --

(1 -k- rn,n-1)(1 -+-rn-l,n)

rn-l,n

0 (1 + rn,n-1 + rn-l,n) 0 Dn_ 1 Dn rn-l,n

(A23)

R(-n+N) n,n+l also can be written in a similar way to R(,n~_l In the case of a symmetric barrier, o(-n+N) (n) we have l~n,n+1 = gn,n_ 1. To conclude this appendix, let us note that the GF on the right side of the Nth boundary

(y, yl >~ YN) has the form l?(N) G(N) (y, yt) _ ~(0) "-"N (Y, yt) _.1..*"N,N-1

G(0) N (Y, yN)G(ON) (YN, Y')

(A24)

G(oO)(YN, YN) Here/?(N) "'N,N-1 is the reflection amplitude of the whole system from the Nth boundary when the electron falls in from the right.

562

TUNNELING TIME IN NANOSTRUCTURES

In a similar way, the GF on the left of the system (y, y, ~< yl) can be written as

G(N)

1)

R(N) G(OO)(Y, yl)G;0:_(Y1' yl)

0 (Y' y l ) = G(0o)(y, y +

0,1

G(0bS(yl, Yl)

(A25)

where R o,1 (N) is the reflection amplitude of the system from the first boundary when the wave falls in from the left.

APPENDIX B: TRANSMISSION COEFFICIENT OF A LAYERED STRUCTURE The method described in the previous appendix allows us to calculate any electronic property of a layered structure. In this appendix, we show how to obtain the transmission coefficient of such a system from the characteristic determinant defined in Appendix A. By definition, the transmission coefficient is equal to the modulus square of the amplitude of the wave function at the fight of the system when the electron is incident on it from the left. Using the Fisher-Lee relationship between the scattering matrix and the GF, the transmission coefficient may be written as

y,)lla(ON~(YN,yN)l]-llaN(yl, yN)l 2

T - [Ia(o~

(B1)

where GN (Yl, YN) is the GF of the electron in the layered structure with N boundaries. To simplify the previous equation, we rewrite the general expression for the GF G (y, yl) in terms of GF at coincident coordinates y - yt, which can be done using Eq. (37),

G(N)(yl, YN) -

[IG(N)(yl,Yl)IIG(N)(yN,YN)I]I/2expi[O(yN)

- 0(yl)]

(B2)

where O(y) is again the phase function defined by Eq. (38), so that

O(yN) -- 0(yl) -- --

fyYN m dy it--~ G(N)(y y) 1

N-1

f y~+lm

n=l a Yn

dy

h2 G(N) (Y' Y)

(B3)

(.:(N) (y, y,) that appear in these We remember that the GF G(nN) (y, y'), G(NN) (y, yl) ' and "~0 two expressions are defined by Eqs. (A12), (A24), and (A25), respectively. To calculate the integral appearing in Eq. (B3), we use the final expression Eq. (A12) for the GF obtained in the previous appendix. The spatial integral corresponding to layer n is equal to

m

f Yn+l m dy _ m yn h2 G(N) (Y, Y) h2 In

l~(n) ~n,n+l(1 +..n,n+l)(1 + R(-n+N) n,n+l ) , R(n) , l~(_n+U) (1 -+-~n n+l--n,n+l)(1 -k- ~.n n+l..n,n+ 1 )

(B4)

Taking into account the previous expression, the definition of the determinant D O [Eq. (A18)], and the values of the generalized reflection amplitudes [Eq. (A22)], we arrive at the expression for the GF:

G(N)(yl, YN) --

/?(N)

G(oN)(yl, yl)G(ff)(YN, yN)(1 + Ro(N))(1 + "'N,N-1) ,

R(n)

o(-n+N),~

" X I-I , R(n) i~(-n+N) n=l (1 + ~n n+l-.,n,n+l)( 1 + ~n,n+l..n,n+ 1 ) N-1

~.n n+l(1 +-.n,n+l)(1 + "'n,n+l

[ 1/2

I

N-1 = (DO) -1 G(oN)(yl, yl)G(N)(yN, YN) U (1 + rn,n-1)(1 + rn-l,n) n=l

563

(B5) ) 1/2

GASPARIAN ET AL.

Substituting this final expression for the GF G (N)(yl, YN) [Eq. (B5)] and the analogous expression for the complex conjugate of the GF [G(N)(yl, YN)]* into the expression for the transmission coefficient [Eq. (B 1)], we finally arrive at T = IDN1-2

(B6)

where DN is the characteristic determinant, given by Eq. (A13). This is a general expression that is valid for any model and that tells us that the transmission coefficient T of a system is inversely proportional to the characteristic determinant DN.

APPENDIX C: INTEGRAL OF THE GREEN'S FUNCTIONS We showed that the traversal time is proportional to the spatial integral of the GF at coincident coordinates, which can be calculated exactly using the method developed in the previous appendices. Here we first prove the relationships used in this chapter that involve integrals of the GF, and, second, we obtain the exact expression of the integral of the GF at coincident coordinates in terms of the transmission and reflection coefficients. Let us derive the equations that appear in Section 5. Our first aim is to obtain the spatial integral of the modulus square of the wave function. To do so, we start by trivially rewriting the wave function ~p(y) in terms of derivatives with respect to energy:

0 ~ ( y ) - (V(y)- E)-~/(y) - -~0 (V(y)- E)O(y)

(C1)

From here, and taking into account that the wave function is a solution of the Schr6dinger equation, we can express the square of the wave function in the form

h2 (~ptt 8 (y)-~gt(y)- r

r

0

_ ~m

r (y)

)

])20(0 O ) : 2m Oy ~r'(y)-~~(y)- ~p(y)-~~'(y)

(C2)

By integrating both parts of this expression over y, we get 7t(y) 2 dy

-

- ~mmr (y)2 ~--~

- - ~mmap(y)2 ~

(C3)

We now express this equation in terms of the GF, taking into account that the wave function is of the form

r = [r iO where

O(y) is the phase function

f G(y, y)e2i~

(C4)

[Eq. (38)]. Equation (C3) becomes

[(2m)

dy -- 4m G(y, Y)ezi~ OEO G'(y, y) - ~

G-1 (y, y)

]

(C5)

In a similar way, we have

f G(y, y)e -2i~

dy

= - ~ G ( y , y)e -2i~ 4m

8E

G'(y y) + '

~

G-1

(Y' y)

(C6)

We derived Eqs. (C5) and (C6) by making use of the fact that the wave function O(y) at energy E is related to the retarded Green's function G(y, y~) of the system through the expression

G(y, y')-

{ iyrv(E)~p(y)ap*(y') iyrv(E)~r*(y)~/(y')

564

i f y > y' i f y ~< y'

(C7)

TUNNELING TIME IN NANOSTRUCTURES

where v(E) is the density of states per unit energy and per unit length. Note that at coincident coordinates, this expression reduces to the well-known result G(y, y) = iv(E)l~(Y)l 2. From Eq. (C7) we can obtain the left-side and fight-side derivatives of the GF with respect to coordinates, which have to be distinguished due to discontinuity:

G(y TO, y ) - •

m h"

1

+ -~G'(y, y)

(C8)

Z

Here the dot signifies the derivative with respect to the first argument, keeping the second argument and the energy fixed. Using the expressions for the wave function [Eq. (C1)] and for its square [Eq. (C2)], we can represent I~(y)l 2 in the form I

y)l 2 = 4m Oy

~'(Y)-~P

-

7r(y)~-~

(y) + ~P*'(Y)-~~(Y)

(y) +

(y)~-~

(y)

(C9)

0 + ~2 (y) ~__~( ~*'i~ (-~/:~(y)~*(y)) }

(ClO)

Integrating both parts of this expression over y, we get f

I7~(y)l e d y

=

{

h2 _ _4m _ ~.2 (y) ~__~

I~P(Y)I2

A straightforward calculation, using Eqs. (C4), (C7), and (C8), leads to

f G(y' y) dy - i o8-~---0 h2 O(Gt(y'y)) E (Y) - -~m G(y' Y)-ff-E G(y, y)

(CI,)

This completes the deduction of the set of useful integrals that were used in this chapter. Now we can go a step further and calculate the spatial integral of the GF at coincident coordinates, given by Eq. (C 11), over the region [0, L], which appears in the calculation of the traversal time [Eq. (43)]. Without loss of generality, we will discuss the case when the potential V(y) is zero outside the interval [0, L]. In this case the GFs outside the barrier are G(o~ 0 ) = G(N~ 0 ) - im/kh 2. The expression for the GF on the left of the barrier, given by Eq. (A25), when evaluated at y -- y~ --- 0 reduces to G(0, 0) = G0(0, 0)(1 + r)

(C12)

where we have relabeled the total reflection amplitude from the left as r = o(N) n0,1 9 Analogously, the expression for the GF on the right of the barrier [Eq. (A24)], when evaluated at y = y~ -- L, becomes

G(L, L) -- Go(L, L)(1 + r t)

(C13)

is the total reflection amplitude from the right. The derivative of the where r ~ =_ "p(N) 'N,N-1 GF G ~(y, y) at the origin is equal to

2mr

G'(0, 0) = h----Y-

(C14)

whereas its derivative at y = yt = L is G'(L L) --

,

2mF !

h2

(C15)

Making use of the expressions of the GF at 0 and at L [Eqs. (C12) and (C13)] and of the derivative of the GF at 0 and at L [Eqs. (C14) and (C15)], we can rewrite the integral of

565

GASPARIAN ET AL.

the GF [Eq. (C11)] as

G(y, y; E) dy - i - ~ [0(L) - 0(0)] +

ln(1 + r)(1 +

r') + -4-~(r + r') (C16)

The next step to get the final answer is to calculate the first bracket in Eq. (C16). It is straightforward to show, using Eqs. (B4) and (B5), that the bracket can be represented in the form

t

i[O(L) - 0(0)] -- In (1 + r)(1 + r')

(C17)

Substituting this expression into Eq. (C 16), we finally obtain, for the spatial integral of the GF, and so for the traversal time [Eq. (43)], the expression

fo L G(y, y; E)dy-- 0OE lnt 1 + -~(r + r')

(C18)

In the rest of this appendix, starting from the explicit expression for the integral of

G (N) (y, y) in each layer, given by Eq. (A12), we show that the sum of the contributions of all the layers also yields the result previously obtained [Eq. (C18)]. For a piecewise constant potential, the integral over a layer of the GF, as was first done by Aronov et al. [58] is lnt fyYn+l G(nN) (Y, Y) dy -- 0

(C19)

OVn

n

where Vn is the potential energy of the electron in the nth subsystem and t is the transmission amplitude of the whole system. We could write the total integral of the GF as a sum of terms of the form given by Eq. (C19)"

fo L

N-1

a (N) (y, y) dy -- Z

f y.+,G(N) (y' y) dy -- N-1 0 lnt Z 0 Vn

n=l ayn

(C20)

n=l

An expression similar to Eq. (C20) was found, in a different context, by Garcfa-Moliner and Flores [ 117] in terms of surface GF. In the N ~ c~ limit (keeping L fixed) and converting the summation into an integral, Eq. (C20) becomes

fo L G (u) (y, y) dy - foL (~•lnt g (y-----~dy

(C21)

where ~/3 V (y) is a functional derivative. This is the result of Sokolovski and Baskin [66]. As was shown by Leavens and Aers [65], the functional derivative with respect to the potential can be replaced by the derivative with respect to the average height of the potential V, keeping the spatial variation of the potential fixed. We thus obtain f0 L 6 ln___~tdy _ 6 In t

6V(y)

(C22)

6V

Remember that we have shown that the integral of the GF at coincident coordinates, equal to Eq. (C22), also can be written exactly in terms of derivatives with respect to energy plus a correction term; see expression (C18). Acknowledgments

V.G. and M.O. would like to acknowledge the Spanish Directi6n General de Investigati6n Cientifica y T6cnica for financial support in the form of sabbatical grant SAB95-0349 (V.G.) and project number PB96/1118 (M.O.). G.S., U.S. and V.G. would like to acknowledge financial support from the Bundesminister ftir Bildung, Wissenschaft und Forschung (BMBF) of the Federal Republic of Germany, contract number 03N1012A7, and thank A. Th6neb6hn for technical assistance. All authors thank J. Jockel for preparing the illustrations in this manuscript.

566

T U N N E L I N G TIME IN NANOSTRUCTURES

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50. R. Landauer and Th. Martin, Solid State Commun. 84, 115 (1992). 51. V. Gasparian, G. Sch6n, J. Ruiz, and M. Ortufio, EPJ B7, 756 (1998). 52. M. Born, in "Werner Heisenberg und die Physic Seiner Zeit" (E Bopp, ed.), p. 103, Vieweg Verlag, Braunscheig, 1961. 53. E Bopp and O. Riedel, "Die Physikalische Entwicklung der Quantentheorie," Verlag der Bayer, Schwab, Stuttgart, 1950. 54. M.J. Hagmann, Solid State Commun. 82, 867 (1992). 55. M. Btittiker and R. Landauer, Phys. Rev. Lett. 49, 1739 (1982). 56. V. Gasparian and M. Pollak, Phys. Rev. B 47, 2038 (1993). 57. V. Gasparian, M. Ortufio, J. Ruiz, E. Cuevas, and M. Pollak, Phys. Rev. B 51, 6743 (1995). 58. A.G. Aronov, V. Gasparian, and U. Gummich, J. Phys.: Condens. Matter 3, 3023 (1991). 59. V. Gasparian, T. Christen, and M. Btittiker, Phys. Rev. A 54, 4022 (1996). 60. R. Landauer, Philos. Mag. 21,863 (1970). 61. D.J. Thouless, Phys. Rep. 136, 94 (1974). 62. V. Gasparian, B. L. Altshuler, A. G. Aronov, and Z. H. Kasamanian, Phys. Lett. A 132, 201 (1988). 63. C.R. Leavens and G. C. Aers, Solid State Commun. 67, 1135 (1988). 64. V. Gasparian, Superlattices and Microstructures: Special issue in honor of Rolf Landauer on the occassion of his 70th birthday 27, 809 (1998). 65. C.R. Leavens and G. C. Aers, Solid State Commun. 63, 1101 (1987). 66. D. Sokolovski and L. M. Baskin, Phys. Rev. A 36, 4604 (1987). 67. M. Biittiker and R. Landauer, Phys. Scr. 32, 429 (1985). 68. M. Biittiker and R. Landauer, IBM J. Res. Dev. 30, 451 (1986). 69. Th. Martin and R. Landauer, Phys. Rev. B 47, 2023 (1993). 70. M. Biittiker, in "Electronic Properties of Multilayers and Low Dimensional Semiconductors" (L. E. J. M. Chamberlain and J. C. Portal, eds.), p. 297, Plenum, New York, 1990. 71. M. Jonson, in "Quantum Transport in Semiconductors" (D. K. Ferry and C. Jacoboni, eds.), p. 203, Plenum, New York, 1991. 72. L.D. Landau and E. M. Lifshitz, "Quantum Mechanics" Pergamon, New York, 1979. 73. A.P. Jauho and M. Jonson, J. Phys.: Condens. Matter 1, 9027 (1989). 74. Th. Martin, Int. J. Mod. Phys. B 10, 3747 (1996). 75. E. Pollak and W. H. Miller, Phys. Rev. Lett. 53, 115 (1984). 76. E. Pollak, J. Phys. Chem. 83, 1111 (1985). 77. R.P. Feynman and A. R. Hibbs, "Quantum Mechanics and Path Integrals" McGraw-Hill, New York, 1965. 78. R. Landauer, Ber. Bunsen-Ges. Phys. Chem. 95,404 (1991). 79. A. P. Jauho, in "Hot Carriers in Semiconductor Nanostructures: Physics and Applications" (J. Shah, ed.), p. 121, Academic, Boston, 1992. 80. D. Sokolovski and J. N. L. Connor, Phys. Rev. A 42, 6512 (1990). 81. H.A. Fertig, Phys. Rev. Lett. 65, 2321 (1990). 82. H.A. Fertig, Phys. Rev. B 47, 1346 (1993). 83. K.L. Jensen and E Buot, Appl. Phys. Lett. 55, 669 (1989). 84. J. G. Muga, S. Brouard, and R. Sala, Phys. Lett. A 167, 24 (1992); S. Brouard, R. Sala, and J. G. Muga, Europhys. Lett. 22, 159 (1993); S. Brouard, R. Sala, and J. G. Muga, Phys. Rev. A 49, 4312 (1994). 85. C. R. Leavens, Phys. Lett. A 197, 88 (1995); C. R. Leavens and G. C. Aers, in "Scanning Tunneling Microscopy and Related Methods" (R. J. Behm, N. Garcia, and H. Rohrer, eds.), p. 59, Kluwer, Dordreht, 1990; C. R. Leavens and W. R. McKinnon, Phys. Lett. A 194, 12 (1994). 86. V. Gasparian, M. Ortufio, J. Ruiz, and E. Cuevas, Solid State Commun. 97, 791 (1996). 87. G. Garcia-Calder6n and A. Rubio, Solid State Commun. 71,237 (1989). 88. P.W. Anderson, D. J. Thouless, E. Abrahams, and D. S. Fisher, Phys. Rev. B 22, 3519 (1980). 89. G. Iannaccone, Phys. Rev. B 51, 4727 (1995). 90. J.A. StCvneng and E. H. Hauge, Phys. Rev. B 44, 1358 (1991). 91. E.H. Hauge, J. P. Falck, and T. A. Fjeldly, Phys. Rev. B 36, 4203 (1987). 92. C.R. Leavens and G. C. Aers, Phys. Rev. B 39, 1202 (1989). 93. K.K. Likharev, IBM J. Res. Dev. 32, 144 (1988). 94. V. Gasparian and U. Simon, Physica B 240, 289 (1997). 95. D.V. Averin and A. N. Korotkov, J. Low Temp. Phys. 3/4, 173 (1990). 96. U. Simon, R. Flesch, H. Wiggers, G. Sch6n, and G. Schmid, J. Mater. Chem. 8, 517 (1998). 97. U. Simon, G. Sch6n, and G. Schmid, Angew. Chem., Int. Ed. Engl. 32, 250 (1993). 98. R. Horbertz, T. Feigenspan, E Mielke, U. Memmert, U. Hartmann, U. Simon, G. Sch6n, and G. Schmid, Europhys. Lett. 28, 641 (1994). 99. L. E Chi, S. Rakers, T. Drechsler, M. Hertig, H. Fuchs, and G. Schmid, Langmuir (in press). 100. L. E Chi, M. Hartig, T. Drechsler, Th. Schaak, C. Seidel, H. Fuchs, and G. Schmid, Appl. Phys. A 66, 187 (1998). 101. G. Schmid, G. Sch6n, and U. Simon, U.S. Patent 08/041,239, 1992. 102. G. Schmid, G. Sch6n, and U. Simon, German Patent 402-12220, 1992.

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103. C. Hamman, H. Bughardt, and T. Frauenheim, "Electrical Conduction Mechanism in Solids," VEB, Berlin, 1988. 104. P. Marquardt and G. Nimtz, Festk6rperprobleme 29, 317 (1989). 105. G. A. Ozin, Adv. Mater. 4, 612 (1992). 106. M.T. Reetz, Spekt. Wiss. 3, 52 (1993). 107. M.J. Kelly, J. Phys.: Condens. Matter 7, 5507 (1995). 108. E Garcia-Moliner and J. Rubio, J. Phys. C: Solid State Phys. 2, 1789 (1969). 109. B. Velicky and I. Barto~, J. Phys. C: Solid State Phys. 4, L 104 (1971). 110. E Garcia-Moliner, Ann. Phys. 2, 179 (1977). 111. H. Ueba and S. G. Davison, J. Phys. C: Solid State Phys. 13, 1175 (1980). 112. E. Louis and M. Elices, Phys. Rev. B 12, 618 (1975). 113. V.M. Gasparian, B. L. Altshuler, and A. G. Aronov, Phys. Tverd. Tela 29, 2671 (1975). 114. T . C . L . G . Sollner, W. D. Goodhue, P. E. Tannenwald, C. D. Parker, and D. D. Peck, Appl. Phys. Lett. 43, 568 (1983). 115. Y. Zohta, Solid State Commun. 73, 845 (1990). 116. E Bopp, Z. Naturforsch. 29a, 113 (1984). 117. E Garcfa-Moliner and Flores, "Introduction to the Theory of Solid Surfaces," CUP, Cambridge, 1979.

569

Chapter 12 THEORY OF ATOMIC-SCALE FRICTION Susan B. Sinnott Department of Chemical and Materials Engineering, The University of Kentucky, Lexington, Kentucky, USA

Contents 1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2. Methods Used to Study Atomic-Scale Friction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1. Experimental Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2. Continuum Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3. Atomistic Theories . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3. Atomic-Scale Friction between Bare Sliding Surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1. On Metals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2. On Layered Ceramics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3. On Crystalline Ceramics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4. On Polymers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4. Effects of Lubrication on Atomic-Scale Friction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1. Background Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2. Small Molecules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3. Liquid Films . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4. Self-Assembled Thin Films . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5. Solid Thin Films . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5. Atomic-Scale Friction at Surface Debris . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6. Summary and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

571 573 573 574 575 575 577 581 587 590 593 593 596 599 606 607 613 613 614 615

1. I N T R O D U C T I O N U n d e r s t a n d i n g the interactions b e t w e e n t w o surfaces in sliding c o n t a c t is crucial to control friction in m a n y t e c h n o l o g i c a l l y i m p o r t a n t fields, such as w e a r o f m o v i n g m e c h a n i c a l parts and m a c h i n i n g . In an effort to achieve this u n d e r s t a n d i n g , researchers have studied friction on e v e r - s m a l l e r scales in a search for its f u n d a m e n t a l cause. Today, it is possible to e x a m i n e sliding surfaces on the atomic scale and relate the findings to m a c r o s c o p i c a l l y o b s e r v e d p h e n o m e n a . T h e study o f a t o m i c - s c a l e friction has the additional benefit o f p a v i n g the w a y for n e w innovations, such as the d e v e l o p m e n t o f self-lubricating surfaces and wearresistant materials. As w e shall see, the m e c h a n i s m s r e s p o n s i b l e for friction at the atomic scale can s o m e t i m e s be quite different f r o m those that d o m i n a t e at the m a c r o s c a l e . This has i m p l i c a t i o n s for devices such as m a g n e t i c storage disks, that have b e e n shrinking in size

Handbook of NanostructuredMaterials and Nanotechnology, edited by H.S. Nalwa Volume2: Spectroscopyand Theory Copyright 9 2000 by Academic Press All rights of reproduction in any form reserved.

ISBN 0-12-513762-1/$30.00

571

SINNOTT

steadily over the last few years and are approaching the nanometer regime where atomicscale friction, adhesion, and wear will be the dominant processes. Interest in atomic-scale friction has been on the rise since the late 1980s [1-11]. This is due to the concurrent development of sophisticated new experimental tools to measure friction over very small distances at low loads and the rapid advances in both computer power and the theoretical methods needed to study material processes in a realistic manner. Theoretical models and simulations assist in the interpretation of experimental data and provide predictions of phenomena that the experiments can subsequently confirm or refute. Hence, the field of atomic-scale friction uses analytical models, large-scale atomistic simulations and detailed experiments. On a very basic level, friction can be thought of as a force that opposes the motion between two surfaces in contact. The primary origin of this force [ 11, 12] is the adhesion between the two surfaces. A force is needed to start the surfaces moving relative to each other (static friction) and also to sustain this motion (kinetic friction). Traditionally, the way that friction has been determined quantitatively has been through the coefficient of friction,/z, defined by Amonton's law as FF = IZ FN

(1)

Hence # is the ratio of the frictional force FF to the normal force FN, and it goes up as the amount of friction increases. This relationship between the normal and frictional forces is quite different from the case of single asperity contacts in classical mechanics. If the single asperity can be considered to be a single perfect sphere, then when it is pressed onto an atomically flat surface with a load FN, elastic Hertzian contact mechanics give the relationship r'2/3

FF--C, N

(2)

between the frictional force and the applied load, where c depends on the shear force per unit area of contact, the radius of the asperity, and the Young's modulus of both the asperity and the surface. Amonton's law works for most types of materials because macroscale material surfaces have significant surface roughness and sliding between them occurs mostly at the tips of numerous, small surface asperities. As the normal force pushing the surfaces together (FN) increases, more asperities come into contact. Therefore, even though the contact area at each asperity is relatively independent of FN, the overall contact area grows as FN increases, thus increasing the resistance to sliding, FF. However, there are several issues that are not addressed by Eq. (1). For instance, friction coefficients of many solids decrease with increasing temperatures [14]. This is thought to be due to increased softening of the surfaces at high temperatures or even a change from solid to liquid lubrication. In other cases, sudden increases in friction are observed that are due to coating failure from decomposition or delamination. As the sliding speed between the surfaces increases, the friction goes up because of the increased heating at the interface. Finally, it has been shown [15] that for simple lubricants between smooth (mica) surfaces, the friction per unit area is independent of external load which indicates that elastic deformation is the cause of the relationship between FF and FN. However, for metals, the cause of this relationship is usually due to plastic deformation. Amonton's law has, therefore, be rewritten in terms of contact area, A, and shear stress as FF = A Fs = IZ FN

(3)

where Fs is the shear force per unit area needed to shear the connective bonds formed between the sliding surfaces. It is through A and Fs that it is possible to relate the mechanisms of macroscale friction to those of atomic-scale friction [ 1].

572

THEORY OF ATOMIC-SCALE FRICTION

2. M E T H O D S USED TO STUDY ATOMIC-SCALE F R I C T I O N

2.1. Experimental Methods 2.1.1. Quartz-Crystal Microbalance The quartz-crystal microbalance (QCM) is an apparatus that has, only recently, been modified to study friction [ 16, 17], although it has been in use for some time for other applications. It works by oscillating a single crystal of quartz. Materials are chemisorbed onto metal electrodes that are grown in ultrahigh vacuum (UHV) conditions onto the microbalance. Changes in the vibrational properties of the quartz indicate how much the deposited layer slips over the substrate. The QCM can, therefore, measure friction between the electrode and a few layers of the chemisorbed material, and provide slip times and interfacial friction coefficients [ 1].

2.1.2. Surface Force Apparatus The surface force apparatus (SFA) was first adapted over two decades ago for use in atomicscale friction measurements [18], and it works by trapping lubricant molecules in a small volume. Usually, liquid films are sheared between two parallel, molecularly smooth mica surfaces (contact zone ~ 100/zm) that can be moved relative to each other in the normal or lateral directions [1 ]. The deflection of a force mapping spring is used to measure all the forces between the two surfaces. For films with a thickness of less than about 50/k, this trapping of the molecules results in an increase in the collective movement of the molecules as the film thickness decreases, which subsequently increases the viscosity of the films [19, 20].

2.1.3. Frictional Force Microscope The frictional force microscope (FFM) is a modified version of the atomic force microscope (AFM) that was invented quite recently [21 ] and was soon used to measure atomicscale friction [22]. The AFM has a rigid cantilever with a sharp tip on the end that is pressed against the sample surface. The FFM is similar to an AFM except that it applies lateral and normal forces to the surface [23, 24], as shown in Figure 1. As the tip is indented or dragged across the surface, the cantilever is deflected and the forces acting upon it are determined down to very fine scales (about 10-11 N) [1 ]. In addition, methods exist

ction

friction

Fig. 1. An illustration of a frictional force microscope measuring friction on a corrugated surface. Reprinted with permission from T. Gyalog, M. Bammerlin, R. Luthi, E. Meyer, and H. Thomas, Europhys.Lett. 31,269-274 (1995). 9 1995 Societh Italiana di Fisica.

573

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Load (nN) Fig. 2. Data from a frictional force microscope using a Si3N4 tip on a mica sample. Top: Lateral force versus lateral displacement felt by the microscope. The solid line shows the relationship for a stiff contact; the dashed line is for a soft contact. Middle: Plot of the lateral stiffness (crosses) and friction (triangles) versus load for the same system. The solid line is a fit of the Hertz model. Bottom: Plot of the total stiffness, indicated by r, versus load. The data are the same as in the middle figure. Reprinted with permission from R. W. Carpick, D. E Ogletree, and M. Salmeron, Appl. Phys. Lett. 70, 1548-1550 (1997). 9 1997 American Institute of Physics.

to d e t e r m i n e the relationships b e t w e e n friction, load, and contact area, as illustrated in F i g u r e 2 [25].

2.2. Continuum Theory F r o m classical c o n t i n u u m m e c h a n i c s , m u c h p r o g r e s s has b e e n m a d e in u n d e r s t a n d i n g the a t o m i c - s c a l e b e h a v i o r of sliding surfaces. O n e of the m o s t w i d e l y used m e t h o d s d e v e l o p e d in this w a y to study friction is the J o h n s o n - K e n d a l l - R o b e r t s (JKR) theory [26], w h i c h d e t e r m i n e s the characteristics of surfaces in sliding elastic contact t h r o u g h a calculation

574

THEORY OF ATOMIC-SCALE FRICTION

of surface and interface energies. Specifically, the surface and interfacial energies are used to determine the forces needed to separate surfaces when they are in sliding contact. JKR theory has provided insight into friction in many instances. However, it does not allow for atomic motion or individual bond formation and breakingmfactors that, as we shall see, are very important for atomic-scale adhesion and friction. 2.3. Atomistic Theories Simulation techniques exist to model the evolution of an atomistic systems in time. The most common is molecular dynamics (MD), where Newton's equations of motion are integrated to observe the motion of atoms in response to applied forces, F = ma -VE

-- m ( O 2 r / O t 2)

(4a) (4b)

where F is the force on each atom, m is the atomic mass, a is the acceleration of each atom, E is the potential energy felt by each atom, r is the position of each atom, and t is time. The forces are calculated for a given geometry of atoms. The atoms move a short increment Ot (called a time step) forward in time and their geometric configuration changes in response to the applied forces. Then the energy of the new arrangement of atoms is calculated, the forces are derived, the atoms move again, and so on. The advantage of this method is that it is possible to observe the individual motions of all the atoms in real time. The disadvantage is that the time scales are very limited (picoseconds to nanoseconds). In addition, the size of the system that can be considered is presently limited to about a million atoms, which, while impressive, is still far removed from real systems that contain 1023 atoms or more. Hence, although MD has been used to model atomic-scale friction and does a reasonably good job of providing insight into the atomic-scale mechanisms of friction, it is still limited to an unrealistically small number of atoms and short time scales. To model a material atomistically, mathematical expressions are needed to characterize the potential energy of the material (VE in Eq. (4b)), and there are several methods available to do this. The first principles methods include all quantum and electronic effects and have been used to map out the potential energy surface for the sliding of molecules over a surface [10]. However, it is only in the last few years that it has been possible to perform MD simulation with first principles techniques [27], and such simulations are still extremely time intensive and typically limited to systems of a few hundred atoms. Therefore, most simulations use approximate chemical potentials that are mathematical functions fitted to experimental or first principles data. The function is then used to reproduce the data from the system quickly enough to be used efficiently in the simulations. The best potentials do a good job of capturing the chemistry and physics of a particular material or series of materials, and are, therefore, predictive for phases not included in the original fitting data base. However, the most popular methods do not allow for changes in the electronic structure of the atoms as the simulation develops. For a thorough discussion of MD simulations and potentials the reader is referred to [7].

3. ATOMIC-SCALE FRICTION BETWEEN BARE SLIDING SURFACES As stated earlier, friction at macroscopic surfaces involves the pressing and sliding of many atomic-scale asperities against each other, leading to complex mechanisms for the process as a whole. Partially in an effort to better understand this process, model systems of single atomic-scale asperities pressing or sliding over atomically smooth surfaces have been considered with the AFM/FFM. In these experiments, the tip has a radius in the range of 1-100 nm that is pressed against the surface under UHV, in air (ambient conditions), or in

575

SINNOTT

a liquid. The tip moves normal to the surface to indent (AFM) and/or across the surface (FFM) at sliding speeds of 1 nm/s to 1/z/s [6]. In contrast, atomistic simulations of this process have much higher sliding speeds of 1-100 m/s due to the time constraints mentioned previously [6]. Simulations have shown that on an atomic scale, FF depends on the sliding speed if the heat is efficiently dissipated and the sliding speed is less than the speed of sound [28]. However, the sliding speed is not included in Eq. (1) because the value for a single asperity at any instant of time is not the same as the sum of the sliding speeds of all the asperities in a normal, macroscopic system. At the macroscale, each asperity might have a nonuniform atomic-scale motion, but the whole system will appear to slide with no discontinuities [ 1]. Experimental wear tests have investigated the effects of loading force, number of scan cycles, scan speed, scan pitch, and tip type on friction [29] and they confirm this hypothesis. Theoretically [30], it has been shown that if the sliding speed decreases to such an extent that it is close to zero, the release of strain during the "slip" part of the atomic-scale "stickslip" that takes place at the surface can cause the kinetic friction to fall below the value for the static friction. When a tip touches a sample, the first interaction between the two is usually attractive. As the tip presses closer, the tip and the surface will usually experience a repulsive interaction. However, if the tip continues to press against the sample, the two might adhere to each other. This can occur through the formation of covalent or metallic bonds between the tip and the substrate or the entanglement of chains if the tip and the substrate are coated with polymers [1]. If the experiment is taking place in ambient conditions, the surface will not be perfectly clean, but will be coated with a small number of hydrocarbon and water molecules. In this case, adhesion might occur by capillary formation between these molecules and the tip. Any adhesion between the tip and the surface is measured through hysteresis (anisotropy) in the resulting curve of FN versus penetration depth (the force curve) [7]. It is not easy to extract quantitative numbers for tip-surface adhesion strengths or contact areas due to experimental error, so the force curve is usually taken several times at various places on the sample surface and then averaged. Simple models can then be used to calculate the effects of the stiffness of the cantilever, the scan direction, and the preparation of the surface on the force curves measured with an AFM [31 ]. The forces working against the relative motion of the two surfaces in sliding contact contain a ploughing term, when one surface removes small amounts of the other (softer) surface with its asperities, and a shearing force to break connecting bonds that form between the asperities on the two surfaces when they are in contact. On the macroscale, the energy generated during friction can be dissipated by elastic contacts between the two surfaces, dislocation motion in one or both surfaces, and plastic deformation of the softer material. On the atomic scale, mechanisms for dissipation of friction energy include lattice vibrations (phonon excitation) and electronic excitation in conducting systems [1]. The electronic mechanisms are due to the electrical resistance felt by valence electrons in a metal as they move in response to the forces caused by the surfaces sliding against one another. When the phonons and/or electrons in one surface are excited by atoms in the opposite surface, the energy generated during the sliding is converted into phonon or electron excitation. Hence, for the surfaces to continue to slide, more mechanical energy must be added so friction increases [ 1]. When no lubricant has been intentionally applied between two surfaces in sliding contact, the friction is labeled "dry" even if it is taking place in air where we know the surface is covered by a thin film of impurities. Dry sliding friction can be modeled very simply by considering the motion of a single atom over a monatomic chain (see Fig. 3) [32]. This model provides insight into the effect on energy dissipation of elastic deformation of the substrate due to the sliding atom (see Fig. 4a). It also shows how the average frictional force varies with the changes in the force constant of the substrate normal to the scan direction

576

THEORY OF ATOMIC-SCALE F R I C T I O N

Z

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2.0

Fs[nN] Fig. 4. (a) Results for the model shown in Figure 3 for the change in the average frictional force as a function of the perpendicular force constant, kz. The normal force applied was 0.2 nN. (b) The average frictional force versus normal force for various values of kz. Symbols: filled squares, kz = 5 eV/A,2, triangles, kz = cx~; stars, k z = 15 eV//~2; filled circles, k z = 10 eV/A 2, empty squares, an anharmonic potential of substrate atoms in the perpendicular direction. Reprinted with permission from A. Buldum and S. Ciraci, Phys. Rev. B 55, 26062611 (1997). 9 1997 American Physical Society.

(see Fig. 4b). It is i n t e r e s t i n g to n o t e that m u c h o f the c o r r e c t b e h a v i o r is c a p t u r e d by s i m p l e m o d e l s such as this. H o w e v e r , m o s t t r e a t m e n t s are m o r e c o m p l e x as s u b s e q u e n t l y discussed.

3.1. O n M e t a l s

N u m e r o u s M D s i m u l a t i o n s o f d e f o r m a b l e m e t a l tips i n d e n t i n g m e t a l s u r f a c e s [ 3 3 - 3 7 ] have e l u c i d a t e d the n a t u r e o f the a d h e s i v e i n t e r a c t i o n s b e t w e e n m e t a l surfaces and single m e t a l

577

SINNOTT

.......

i

"

-50

'

i'

!

|

''

'

[

f

Z v

Q) 0

-100

o

J -150 i 0.0

! TM

I

, I

I

0.4

I

,,,

1.2

0.8

displacement (nm) ,!

(.9

,

,

] ....

I"

I

o,

4

edb

9

v

0 ~O Q} t._

-4

Q. I

500

E Z v

. . . .

I

i

300

'

I

O0

9

-~ 200

I 2

0

,

I 4

contact radius (nm) Fig. 5. Top: The experimental values for the force between a tip and a surface that have a connective neck between them. The neck contracts and extends without breaking on the scales shown. Bottom: The effective spring constant, keff, determined experimentally for the connective necks and corresponding maximum pressures, versus contact radius of the tip. The triangles indicate measurements taken at room temperature; the circles are the measurements taken at liquid He temperatures. Reprinted with permission from N. Agrait, G. Rubio, and S. Vieria, Langmuir 12, 4505-4509 (1996). 9 1996 American Chemical Society.

asperities. Clean metal surfaces have very high surface energies and will, therefore, be strongly attracted to each other. In fact, the attraction can be so strong that when the tip gets close enough to the surface to interact with it, surface atoms "jump" upward to wet the tip. This phenomenon has been termed jump-to-contact (JC) and has been confirmed experimentally by extensive studies [38-41] using the AFM (see Fig. 5). If the temperature of the system is increased enough to melt the topmost surface layers [37], the JC phenomenon is enhanced and occurs at larger tip-surface separations. As the tip continues to be pressed against the surface, the simulations show that strong adhesion develops between the two, and the tip is flattened, which increases the contact area. Therefore, when the tip is withdrawn, it resists pull-back and a "neck" forms between the tip and the surface, as illustrated in Figure 6.

578

Fig. 6. Snapshots from a molecular dynamics simulation of a Ni tip being pulled back after indenting a Au(001) surface. Reprinted from U. Landman, W. D. Luedtke, and E. M. Ringer, Wear 153(1), 3-30 (1992), with kind permission from Elsevier Science S. A., P.O. Box 564, 1001 Lausanne, Switzerland.

SINNOTT

Before

After

/\

E

Z I loonm

/

11

z IlOOnm F-~

i

Fig. 7. Imagesof a Au surface before and after being indented with a pyramidal shaped diamondtip in air. The indentation created a surface crater. Note the pileup around the crater edges. Reprinted fromT. Yokohata and K. Kato, Wear 168(1), 109-114 (1993), with kind permission from Elsevier Science S. A., P.O. Box 564, 1001 Lausanne, Switzerland. When the tip is significantly stiffer than the surface, the indentation will cause pileup of surface atoms around the tip to relieve the stresses caused by the indentation [34, 36]. Simulations using perfectly rigid tips [28, 42] show how, after its elastic threshold is exceeded, the surface yields plastically by "popping" atoms out onto the surface under the tip, which leads to the pileup of atoms (because the indenter was rigid, no bonding was permitted between the tip and the surface). Variations in the speed of indent from 1 to 100 m/s [28] showed that point defects created as a result of the indentation relax by moving through the surface at the slower speed. At the higher indentation speed, however, there is no time for the point defects to relax and move away from the indentation area. It is possible to model the indentation of a surface with a hard-sphere indenter in a manner that is independent of the indentation speed. In one such study on Au(111) [43], rather than use MD, the indenter was pushed against the substrate and then the system was allowed to relax using standard energy minimization methods. When the system had fully relaxed, the tip was moved closer and the process was repeated. The indentation created several dislocations in the surface. If the tip was pulled back after indenting less than a critical value, the atoms in the dislocations were able to slide back to their original positions and the surface was healed. However, if the tip was indented past the critical depth, more dislocations were created that interfered with the healing process. As a result, a crater was left behind. Rigid indenter simulations are analogous to experiments that use surface passivation to prevent JC between the tip and the surface [44, 45]. These experiments also show the predicted results of pileup and crater formation, as shown in Figure 7 [46]. The sliding of metal tips across clean metal surfaces has also been studied extensively [47-52]. An illustrative case is shown in Figures 8 and 9 for a Cu tip indenting Cu(111) and Cu(100), respectively. Adhesive wear is found to occur when the attractive force between the asperity atoms and the surface becomes greater than the attractive forces within the asperity itself. Kinetic friction is observed, caused by the atomic-scale stick and slip that occurs through nucleation and subsequent motion of dislocations between the close-packed (111) surfaces. Wear is also seen as part of the tip gets left behind on the surface in Figure 9. Atomistic simulations [52] have provided data on how the characteristic "stick-slip" friction motion can depend on the area of contact, the sliding speed, and the direction of sliding (see Fig. 10). They show that during the "slip" state, the friction energy is dissipated by the system through an increase in temperature at the interface between the sliding surfaces.

580

THEORY OF ATOMIC-SCALE FRICTION

9~,,';.,'::., . . . . . . .

(-)

"'s..',++~,

9,::~,. . . . . . . .

9 . . . .

":,:~i.

9

9 9 9

i...........

(

" "'~J""

+:!i-i:+

"" " " "

X

.... (d)

,:: , . , ~

. ,o

(e)~'"

9 9

..

9.'." / . ' ~

9 9 o

"'" "

9 0.

z

i . .

/

,[1111

{11Xl

[01i]

x [~Oil -~p.-

Fig. 8. Contourplots of the stresses at the interface between a Cu tip and a Cu(111) surface as the tip slides across the surface. The dashed lines indicate negative stresses; the solid lines are positive stresses. Reprinted with permission from M. R. Sorensen, K. W. Jacobsen, and E Stoltze, Phys. Rev. B 53, 2101-2113 (1996). 9 1996 American Physical Society.

All of the foregoing simulations assumed that the electronic contributions to friction on metals are negligible. However, recent experiments have been done to directly measure the contribution of conduction electrons to friction [53]. In these experiments, a QCM was used to measure the friction associated with sliding solid nitrogen along a Pb surface above and below the Pb's superconducting transition temperature. The friction force that was measured when the sliding took place while Pb was in the superconducting state was about half the value measured when the Pb was at normal temperatures. This was explained [53] by assuming an abrupt decrease in the contributions of the conduction electrons to the friction process while Pb was superconducting. This work, therefore, shows that the electronic contributions to friction can be very significant and, for the best results, should be included in the models.

3.2.

On

Layered

Ceramics

Layered ceramics have long been known to have important lubricating properties because of the weak van der Waals bonds between the layers that are easily broken to allow the layers to slide over one another. Hence, some of the earliest experimental friction

581

SINNOTT

(.)

(b)

(c)

d)

(e)

(z

[loo]

[oi l

x [0It] Fig. 9. Snapshotsfrom a molecular dynamics simulation of a Cu tip sliding across a Cu(100) surface. Note the connective neck between the two that is sheared during the sliding, leading to wear of the tip. The simulation was performed at a temperature of 0 K. Reprinted with permission from M. R. Sorensen, K. W. Jacobsen, and P. Stoltze, Phys. Rev. B 53, 2101-2113 (1996). 9 1996 American Physical Society.

studies [54, 55] were on layered compounds such as mica, graphite, and MoS2. The experiments showed astonishing detail, such as atomic-scale stick-slips measured with a W tip on graphite, for relatively high loads (10 -4 N) and large contact areas (106 A2) [1 ]. This was not expected because the forces between the W and graphite should have been out of phase with one another due to the disorder at the surface of the W tip [ 1]. It has been hypothesized that at high loads and for large contact areas, measured friction forces on layered ceramics could be related to "incipient sliding" [56, 57] caused by a small flake from the surface becoming attached to the end of the tip. Therefore, the measured interactions are proposed to be between the flake and the surface, and so will have a larger contact area than that determined for the clean tip and the surface. However, standard molecular mechanics simulations of constant force AFM images of graphite [58] show that there is no need to assume a graphite flake under the tip to reproduce the experimental images of a graphite surface. Instead, the simulations suggest that a proper orientation of the tip and choice of applied forces is sufficient to model the changes seen experimentally [58].

582

THEORY OF ATOMIC-SCALE FRICTION

-!

LL

0

.... g

,,

i,

~

.2

ZE

-

9

'"1"

ii

,,

,,

s

-

iF.

8 6 4

,,

,

lit

,

.

9

"

.f,... ,

'. WIF'

'',r

I

"

9

f

0

-2

e-

A

z v

~

,

IIr',

,

64 ~.....~. ,

,

.if,

,

.'/, , ,#. (~)i, -12K,10m/s, 9

2

0 -2

.....

0

2

;iPi

,

4 6 Distance (A)

'.""w'r', 8

.

"v. ~ 10

Fig. 10. Plotsof the lateral force versus distance from a simulation similar to that shown in Figure 8. The plots illustrate the dependence of the force on temperature and sliding velocity. Reprinted with permission from M. R. Sorensen, K. W. Jacobsen, and P. Stoltze, Phys. Rev. B 53, 2101-2113 (1996). 9 1996 American Physical Society. Layered materials have also shown surprisingly strong localized fluctuations in atomicscale friction [59-62]. Square-well frictional signals with subangstrom lateral width were obtained across the FFM scan direction on MoS2(001), while sawtooth signals that were in synch with the square-well values were detected along the scan direction (see Fig. 11). The measurements were explained by a stick-slip model where the tip does a zigzag walk along the scan. Variations in the frictional force with the periodicity of cleavage planes also have been observed, as shown in Figures 12 and 13 [63]. However, additional experiments indicate a more complex tip-surface interaction. It has been shown that in some cases, the observed displacements in frictional force and the corresponding topography may not be due to atomic-scale stick-slip, but instead are caused by changes in the intrinsic lateral force between the sample and the AFM tip (see Fig. 14) [64]. In addition, studies have shown [65] that tip shape and composition are critical in determining the frictional behavior in AFM experiments, thus opening up the possibility of variations in the results from one experiment to the next due to differences in the experimental setup. Finally, sliding-induced chemistry at the tip or the surface could affect the results. For example, a scanning-induced decrease of the adhesion and friction between a tip and a surface was observed [66] that was thought to be due to the changes in the chemical or structural composition of the surface of the Pt-coated Si3N4 tip. Furthermore, layer-by-layer wear of mica has been observed by scratching the surface repeatedly in the same location despite the use of relatively low loads [67]. The effect of contaminants on the friction and indentation results has been deduced through several measurements [68, 69], leading to the development of the "composite-tip" model. A Si3N4 tip was used to scratch mica and glass at low loads under ambient, nitrogen gas, and argon gas conditions. In ambient conditions, the friction versus load curve showed nonlinear behavior (FF c = ta n-] ( k y / k x ) . The unitary transformation makes the ordering of the transformed basis symmetric, that is, HH, LH, SO, SO, LH, and HH. Under the unitary transformation, the upper and lower block Hamiltonians H U and H L are decoupled. Let us denote the upper and lower block envelope functions by r

(r) - y ~ O~)(kll, z) exp(ikll, rll)lV)

(17)

!)

where g(mU)(kll,z) are the envelope functions, {Iv)} denotes the transformed Bloch basis (Appendix D) at the zone center, m is the quantum-well subband index, kll - kx.~ + ky~, rll - x~ + y~, and a - U (or L) refers to the upper (or lower) blocks, respectively. We note that the summation is for v = 1, 2, 3 for a -- U and v - 4, 5, 6 for a = L. We consider a quantum well of width Lz, grown along the z axis with a biaxial strain. Biaxial strain is assumed to be adjustable by changing alloy compositions (or lattice constants) in the active layer and the barrier regions. The block-diagonalized envelope functions {9(mY)},satisfy Z [ H ~ v' ( k l l,- i - ~ )

a v,]o(v') ~m (kll, z) + Vv(z)6vv, + Hey

p/

= E~ (k,)g~)Ck,, z)

(18)

Here Vv(z) - Vh(z) for v -- 1, 2 or 5, 6, V,~(z) -- Vso(Z) for v -- 3, 4, and H~ is the blockdiagonalized Hamiltonian for the strain (shear) potential. The strain potential H~ is given by

[~

0

0 ] (19a)

0 ,/5~

0

and HeL -

,r

0 ,/~ 01 -~" 0 0

0

(19b)

~"

The hole confining potentials Vh (z) and Vso(z) are obtained from the calculated valenceband offsets at both lattice-matched and strained-layer quantum wells from the modelsolid theory [42] of Van de Walle and Martin. The major idea is to set up an absolute energy scale. Such an absolute reference can be present only when the energies in the bulk semiconductor can be referred to the vacuum level. The principal feature of the model-solid theory involves a particular way of relating all calculated energies on an absolute energy scale, allowing us to derive band lineups. In the model-solid theory, the average energy over the three uppermost valence bands (heavy-hole, light-hole, and the spin-orbit splitoff bands) Ev,av is obtained from theory and is referred to as the absolute zero energy level.

625

AHN

This theory provides a simple method for estimating the band offsets. The differences in the Luttinger parameters for the well and the barrier are taken care of following the approach of [41]. 2.1.3. Dipole Moments of the Quantum Well

In the density matrix formalism, the evaluations of the second- and fourth-order dipole matrix elements are needed to calculate the optical susceptibility. In the multiband effective mass approximation, the optical dipole matrix element is given by (g~)lq~/)(vl~-er[S, O) for a -- U )7o. 8" Mlm (kll) --

v=l,2 ~

(g(m~)14>t)(vl~.erlS, n)

(20) for cr -- L

v=3,4 where cr denotes the upper and lower blocks of the Hamiltonian, r/is the electron spin state, 1 and m are the subband indices for the conduction band and valence band, respectively, )7ois a unit vector along the polarization direction of the optical field, Mlm (kll) is the dipole matrix element between the/th subband in the conduction band with a spin state )7 and the mth subband in the valence band of the 2 • 2 block Hamiltonian Ho., and g(mv) and (~l are envelope functions. )7o. 2 for the TM polarizaAfter some mathematical manipulation, we can obtain 1~ 9Mlml tion (the optical electric field is polarized in the z direction) and the TE polarization (the optical electric field is polarized in the x-y plane) [15]:

(i) For TM polarization, )7U 2

I~ Mlm I =

1

(SlezlZ

)2{

1

(qbllg(m 2)} -- -~/~(4,11g~ ) )

}2

(21)

I

)7L 2 1 { ~ { ~ 1 ' (4)'} 2 Igm, I~" Mlm I = -3(SlezlZ)2 (q~/lg(m5)) - -

(22)

I

(ii) For TE polarization, )7U 2 2 Mlm I - -~l (SlexlX)2 { (~/Ig~)}2 + ~(~/Ig(m2))2 + 5(~/Ig(m 3))2 -1- T((~I lYm ' -(2) )(t~lIg(m3)) -{-

(t~l Ig(ml))(t~/IgmtCOS24)

2 _(1)]t(Ig(m2)) (~l } + ~(~bl [Ym cOS 24>_ )7LI2

le" Mlm

1

{

}2

1

(23) )2

2

-- -4{SlexlX} 2 (~/Ig(m6) + 5(~/Ig(m5) + 5(~/Ig(m4)}2 i

+7- (~l I g(mS))(~/Jg(m4)} + ~-(q~l Jg(m6))(4>/[g(m4)) COS24) +

IgOr/cos

(24)

where 4~ is related to kx and ky by kx = Nil cos ~, ky = ell sin 4~, and ~ = 1" and ,1, for both electron spins. In our calculation, we use the bulk value of (SlezlZ), which is given by

(SlezlZ) = (SlexlX) =

eh [ EG + A ]1/2 . ~ EG(EG + 2A /3)m*

where me* is the effective mass of an electron in the conduction band.

626

(25)

THEORETICAL ASPECTS OF STRAINED-LAYER QUANTUM-WELL LASERS

Once the subband structure and the dipole matrix element are known, the linear and nonlinear optical gains can be derived using the density matrix formalism. The linear gain is the result of kll-space integration of the product of the absolute square of the dipole matrix element, the Fermi function difference between electrons and hole (and is related to the density of state), and the line-shape function.

2.2. Reduced Description of a Density Operator in Semiconductors Conventional theoretical calculations of the optical gain of the quantum-well laser are usually based on the density matrix formalism with a phenomenological damping term which gives the Lorentzian line-shape function for the optical gain [16-18]. However, it was shown that the optical gain spectra calculated with the Lorentzian line-shape function are not quite correct when they are compared with the experimental results [19, 20, 43]. Especially, an incorrect absorption region appears at photon energies below the band gap in the gain spectra as long as the Lorentzian line shape is used. Moreover, the detailed balance between absorption and emission of photons requires that the transparency point in the gain spectra coincide with the Fermi- (or quasi-Fermi) level energy [21]. In general, the gain spectra with the Lorentzian do not satisfy the detailed balance condition either. In addition, most of the previous work on many-body effects on the optical gain also assumed Markovian (or Lorentzian) line-shape functions to describe the intraband relaxation processes [22-25]. However, recent study showed that the decay dynamics of the polarization in semiconductors indicates strongly nonexponential decay that can be satisfactorily described only if the processes are non-Markovian [27, 28]. The physical nature of the dephasing is due to the interactions of the interband polarization with its surroundings. These relaxation kinetics in nonequilibrium cases are often characterized by the presence of memory effects and are also important in related areas such as nonlinear optical gain in semiconductors in which the competition between the stimulated emission and the intraband relaxation contribute to the spectral hole burning. In those nonequilibrium kinetics, the system has the memory effects on a very short time scale and the equations of the motion for the system have time-convolution forms of the integral kernels that are responsible for the memory effects [44-51]. These quantum-kinetic equations can be obtained with reduced-density matrices and with nonequilibrium Green's function theory. To obtain stable kinetic equations numerically, it was pointed out that a consistent treatment of the memory kernels of the equations and the Green's functions or the density matrices for the scattering processes is necessary [51 ]. In general, however, it is very difficult to solve for the memory kernels of the time-convolution forms of the equation self-consistently and, in almost all ways, one must be content with the narrowing limit or the fast modulation limit to obtain the non-Markovian relaxation. Some time ago, Tokuyama and Mori [52] suggested the time-convolutionless equations of motion in the Heisenberg picture for problems in nonequilibrium statistical mechanics. These formulations were then developed in the Schrrdinger picture by Shibata and his co-workers [53-55] by using the projection operator technique. They obtained equations of motion for a reduced-density operator of a system interacting with the surroundings. Saeki [56-59] generalized these equations by considering the response of the system to an external driving field. He derived generalized master equations for an arbitrary driven system interacting with the heat bath [60] and for a weakly driven system interacting with the stochastic reservoir [57, 58]. It was shown that the time-convolutionless equations of motion incorporate both non-Markovian relaxation and renormalization of the memory effects. Tomita and Suzuki [60] used the time-convolutionless equations in the lowest Born approximation to obtain the density matrix theory of nonlinear gain for noninteracting electron-hole pairs in semiconductors and showed that the non-Markovian relaxation enhances both linear and nonlinear optical gains. A detailed band structure of the quantum well and many-body effects were not considered in their work.

627

AHN

In this section, we first derive a time-convolutionless equation for a reduced density operator of an arbitrary driven system coupled to the stochastic reservoir by extending the work of Saeki [57] on the stochastic Liouville equation for a weakly driven system. The density operator method is found to be convenient for us to transform the memory kernel into a time-convolutionless form that is suitable for the perturbation expansions in the system-reservoir interaction and the driving field. Second, we apply the formulation to obtain time-convolutionless quantum-kinetic equations for the system of interacting electronhole pairs an under an arbitrary external optical field. These equations are generalizations of the semiconductor Bloch equations [33-37, 61] by incorporating the non-Markovian relaxation and the renormalization of the memory effects through the interference between the external driving field and the stochastic reservoir.

2.2.1. Time-Convolutionless Equation for a Reduced-Density Operator of a n Arbitrary Driven System In this section, we derive an equation for a reduced-density operator of an arbitrary driven system coupled to the stochastic reservoir [33, 61]. We consider an arbitrary driven system interacting with the stochastic reservoir and assume that the interaction of the system with its surroundings can be represented by the stochastic Hamiltonian. The Hamiltonian of the total system is assumed to be

HT(t) -- Ho(t) + Hi(t) + Hext(t) = H(t) + Hext(t) - Hs (t) + Hi (t)

(26)

where Ho(t) is the Hamiltonian of the system, Hext(t) is the interaction of the system with the external driving field, and Hi (t) is the Hamiltonian for the interaction of the system with its stochastic reservoir. Every physical quantity we observe is accompanied by fluctuations due to the thermal motion of microscopic degrees of freedom in the motion. Whenever a system is coupled to a heat bath or reservoir, its evolution has a stochastic element, which is absent from the Hamiltonian evolution of a closed quantum mechanical system. At present, we do not have the first principle theory of how to separate the interaction into stationary and stochastic parts. As a result, our approach includes a phenomenology, and we assume that the stationary part of the interaction can be put into an effective Hamiltonian Ho(t) in the time-dependent Hartree-Fock approximation. The equation of motion for the density operator PT (t) of the total system is given by the stochastic Liouville equation

dpr(t) = --i[HT(t), pT(t)] dt = --iLT(t)pT(t)

(27)

LT(t) -- Lo(t) + Li(t) --I-Lext(t) -- L(t) + Lext(t) -- Ls(t) + Li(t)

(28)

where

is the Liouville superoperator in one-to-one correspondence with the Hamiltonian. In this chapter, we use a unit where h = 1. The stochastic Hamiltonian Hi (t) may include the electron-electron interaction and electron-LO phonon interaction for both conduction and valence electrons, which would be responsible for the intraband relaxation or optical dephasing that appears as correlation functions of Hi (t). Our approach resembles the wellknown method of the stochastic Liouville equation formulated and applied by Kubo [62] to the stochastic theory of the spectral line shape. Many-body effects such as band-gap renormalization and phase-space filling are included by taking into account the Coulomb interaction in the Hartree-Fock approximation. Plasma screening can be taken into account by using an effective Hamiltonian in the time-dependent Hartree-Fock approximation. The

628

THEORETICAL ASPECTS OF STRAINED-LAYER QUANTUM-WELL LASERS

information of the system is then contained in the reduced-density operator obtained by eliminating the dynamic variables of the reservoir from the total density operator using a projection operator [34-36]. It is convenient to introduce the projection operators [63-65] that decompose the total system by eliminating the dynamic variables of the stochastic reservoir. We define timeindependent projection operators P and Q as [57] and

PX - po(R)(X)i

O - 1- P

(29)

for any dynamical variable X. Here P0 (R) is the initial distribution function of the random variable R and (.. ")i is the average over the stochastic process Hi (t). Projection operators P and Q satisfy the operator identity p2 _ p , Q2 _ Q, and P Q Q P = 0. The information of the system is then contained in the reduced-density operator p(t), which is defined by p(t) - ( P p T ( t ) ) i

(30)

To derive time-convolutionless equation, we first multiply Eq. (26) by P and Q to obtain coupled equations for P p r ( t ) and Q p r ( t ) , d P pT(t) -- --i P L T ( t ) P pT(t) -- i P L T ( t ) Q pT(t) dt . . . . m

(31)

d d----;Qp r ( t ) - - i Q__LT(t)Q pT(t) - i Q _ _ L r ( t ) P p r ( t )

(32)

and

where we use the identity P + Q - 1. We assume that the external driving field is turned on at t - 0 and the total system is in an arbitrary initial condition PT (0). It can be shown that the formal solution of (32) is given by

__Qpr(t)

-

-i

L'

dttI(t,

r)__QLT( r ) P p r (r) + H(t, 0)__Qpr (0)

(33)

where the projected propagator H(t, r) of the total system is defined as __H(t, r) -- __Texp - i

ds __QLT(s)__Q

(34)

Here T denotes the time-ordering operator. Next, we transform the memory kernel in (33) into the time-convolutionless form by substituting the formal solution of (27),

pT(r) = G(t, r)pr (t)

(35)

into Eq. (33). Here the evolution operator G(t, r) of the total system is given by G(t, r) -- T c exp i

ds L r ( s )

(36)

where __Tc is the anti-time-ordering operator. Evolution operators G(t, r) and H(t, r) satisfy the relationships G(t, r)G(s, t) - G(s, r)

(37)

n ( t , r ) n ( r , s) = n ( t , s)

(38)

and

From Eqs. (23) and (25), we obtain Q p T ( t ) -- {0(t) - 1 } P p T ( t ) + O(t)H(t, O)QpT(O)

629

(39)

AHN

where 0(t) -1 -- g(t) = 1 + i

f0'dr H(t, r)Q__Lr(r)P_GG(t, r)

The time-convolutionless equation of motion for P p r ( t ) and (39) as

(40)

can be obtained from (31)

d - - P p r ( t ) -- - i P L T ( t ) P p r ( t ) - - i P L r ( t ) { O ( t ) dt . . . . - i P L r ( t ) O ( t ) H ( t , O)Q PT(O)

- 1}Ppr(t) (41)

It is now straightforward to obtain the time-convolutionless equation of motion for a reduced-density operator p(t). By taking the average of (41) over the stochastic process Hi (t), we get d dtP(t)---i(Ls(t)+(Li(t))i)P(t)+C(t)p(t)

(42)

where the generalized collision operator C (t) is defined by

C(t) -- - i ( L i ( t ) { O ( t ) - 1})i = -i(Li(t)~(t){1-

~-~(t)}-l)i

(43)

in which ~(t)

-- 1 -- 0(t) -1

= -i

I0t d r I t ( t ,

= -i

f0 d r U(t)S_(t, r ) U -1 (r)__QLr (r)PU(r)R__(t, r ) U -1 (t)

r)Q_Lr(t)PG__(t, r) (44)

Here we define

{ f tds Ls (s) /

(45)

{ f r t dsQ__u-l(s)Li(s)U(s)Q__ }

(46)

U(t) -- T e x p - i

__S(t, r) - T e x p - i and

{it

R(t, r) - - T c exp i

dsU-l(s)Li(s)U(s)

}

(47)

where U(t) is the evolution operator of the system with driving field, and R(t, r) and S(t, r) are the evolution operator and the projected propagator of the total system in the interaction picture, respectively. In (16), we assumed that the initial condition pr(0) is given by

pT(O) -- p(O)po(R)

(48)

which means that the system and the reservoir were uncoupled before the external driving field was turned on and that the system was in an arbitrary state p(0) at t = 0. Then it is obvious that Qpr(O) = O. We now consider the case when the system is interacting weakly with the stochastic reservoir and we expand (42) up to the second order in powers of the stochastic Hamiltonian Hi (t). We assume that the random force vanishes on the average over the stochastic process, that is,

PLi(t)P--0

630

(49)

THEORETICAL ASPECTS OF STRAINED-LAYER QUANTUM-WELL LASERS

We further assume that the stochastic process is stationary. The equation of motion for p(t) up to the second-order expansion in Hi (t) becomes d

d t P ( t ) = - i Ls(t)p(t) + C (2) (t)p(t)

(50)

where C(2)(t) - - i ( L i ( t ) Z ( 1 ) ( t ) ) i

= -

/0'

dr(Li(t)U(t, v)Li(r)u-l(t,

v))i

(51)

with y~(1) (t) = - i

f0 t d r

U(t, v)Li (v)U -1 (t, r)

(52)

and U(t, r) = U ( t ) U -1 (r). Some important mathematical properties of the evolution operators are summarized in Appendix D. Using Eq. (D.6) from Appendix D, we transform C (2) (t) to be more suitable for the perturbation expansions with respect to Hext(t)"

C(2)(t)---

dr(Li(t)Uo(t)Uext(t, r)U__o-l(r)Li(r)Uo(r)Uelxt(t, v)u_.u_o-l(t))i (53)

We can expand C (2) (t) in powers of the driving field as C (2) (t) -- y ~ C(m2) (t)

(54)

m--O where

--,(2) Cm (t)

is the mth order term given by

m

C(m2) (t) = - ~ ( - i )

k (i) m-k

/0, dr

drl

dr2""

drk f t d r k + l ' "

k=O

frm-1 drm dZ

• (Li(V)~k(t, Vl ..... rk, r)Li(r)~m-k(t, rk+l ..... rm, r))i

(55)

with r

(56)

r) = u 0 ( t - r)

9 k(t, rl . . . . . rk, r) = Uo(t - rl)Lext(Vl)_U_Uo(rl - r2)Lext(r2)_U_Uo(r2- r 3 ) . . . • __Uo(rk_l -- rk)Lext(rk)Uo(r k -- r) qJ0(t, r) -- U 0 ( r - t)

(57) (58)

and

~k(t, rl . . . . . Tk, V) = _U_U0(r- Tk)Lext(rk)Uo(r k -- rk_l)Lext(rk_l)Uo(rk_ 2 -- rk-3) 999 x U 0 ( r 2 - Vl)Lext(Vl)U0(v 1 - t)

(59)

The time-convolutionless equation of motion for a reduced-density operator given in (50) with (54)-(59) can be used in any time scale such as the femtosecond regime and is valid up to second-order power in the interaction between the system and the stochastic reservoir. In the next section, a time-convolutionless equation for a reduced density operator is used to obtain quantum-kinetic equations for the system of interacting electron-hole pairs near the band edge in semiconductors under an arbitrary optical field.

2.2.2. Time-Convolutionless Quantum.Kinetic Equations for Interacting Electron-Hole Pairs in Semiconductors In this section, we apply the time-convolutionless Eq. (50) to the system of interacting electron-hole pairs in semiconductors with an external driving field. We assume that

631

AHN

the system is weakly interacting with its stochastic reservoir. Many-body effects such as band-gap renormalization and phase-space filling are included by taking into account the Coulomb interaction in the Hartree-Fock approximation. The stochastic Hamiltonian Hi (t) may include electron-electron interaction and electron-LO phonon interaction for both conduction and valence electrons. We will not specify the explicit forms of Hi in this work and we leave the detailed calculations of correlation functions involving Hi to future work. Instead, we obtain the intraband relaxation and the dephasing as correlation functions of Hi (t). We employ the two-band model for the semiconductor and introduce two shorthand notations [ck) and Irk) such that

[ck) = Ic, k)

Irk) = Iv, k)

and

(60)

where c and v denote conduction and valence bands, respectively, and k is the electron wave vector. In the following discussion, we suppress the vector notation for simplicity. In the time-dependent Hartree-Fock approximation, the unperturbed Hamiltonian Ho(t) is given by [33]

(, kl no(t

E~

-

k'

v(a: -

Ip(t) I a:' )

(61)

where c~,/~ = c or v and V (k - k t) is the Coulomb interaction. The interaction of the system with an extemal driving field gives the interaction Hamiltonian Hext which is given by Hext(t) -- - M E p ( t )

(62)

where M is the dipole operator and Ep is the electric field strength of the optical radiation. The equation of motion for the reduced-density operator becomes d --(2) -dT P(t) -" - i (Lo(t) -k- Lext(t))p(t) -k- C(02)(t)p(t) -+- D 1

(63)

where

C(o2)(t)p(t) = -

f0 t d z ( L i ( t ) U o ( r ) L i ( t -

(64)

r)Uol(r))iP(t)

and DI 2) = C~2) (t)Uo(t)p(O)

(65)

C~e) (t) is responsible for the intracollisional field effects and can be derived from (55): C~2)(t) = i

dr

d s { ( L i ( t ) U o ( t - s)Lext(s)Uo(s - r ) L i ( r ) U o ( r

- (Li(t)Uo(t - r)Li ( r ) U 0 ( r - s)Lext(s)Uo(s - t))i }

- t))i (66)

It can be shown that DI 2) contains information on the effects of the interference of the extemal driving field with the stochastic reservoir of the system and is the renormalization of the memory effects. The nonequilibrium distributions nck(t) and nvk(t) for electrons in the conduction band and in the valence band, respectively, and the nondiagonal interband matrix element p~ (t), which describes the interband polarization induced by the optical field, are the matrix elements of the reduced-density operator and are given by

nc~(t) = Pcck(t) = (c lp(t lc )

nvk(t) = Pvvk(t) = (vklP(t)lvk)

632

(67) (68)

I

4~

--..l

~ - " ,x.

I

-L"d

II

I

+

~

t

~'*

+

I

~

~

. II

~

.

~

.I .

I

'

+

o

~

~

I

~

~

~

~

~l ~

l::r

o

~.

~o ~ ~

~o~

~.,~0

.

IX.)

~

v

I........J

~

I~

~

~

v

~

~

~

~

II

~

v v ,.,,.

~

~

9

~

~

II

0

~.,o

.~

II

~

o~ ~

II

~

-...I

~

v

"*

~

~

~

,.,o

II

v

~

oi

~ o ~ . , ~ o ~ o ~ ' ~

~

~

_

~

o~ ~

~

.-..I

~

X

~

~

L--....J

~

~

~ ~

~

~-I

9

~

II

~

v

ol

~.,o

II

~

~

~

~

~

~

o

0

g~ 9

~

~


.

x=0.53 -15

- - x=0.4

"

"i J

-20

--

!

I

_m

m

_m

!

_m

_m I_

_m

_9

_i

-2 cm

10

11

1012

Surface

Carrier

Density

Fig. 8. Plot of the screened band-gap renormalization (BGR) as a function of the carrier density for a 60-/~ InxGal_x As quantum well surrounded by InP outer barriers shown for x = 0.65 (compressive),x = 0.53 (no strain), and x = 0.4 (tensile) versus the carrier density.

Whereas the typical energy transfer for the intraband process is on the order of k8 T, we get a correlation time of approximately 20 fs from the uncertainty relationship. We do not specify the explicit form of the intraband relaxation in this chapter; previous calculations [7, 8] of the intraband relaxation can be used. In Figure 8, we plot the screened band-gap renormalization (BGR) as a function of the carrier density for a 60-,~ InxGal_xAs quantum well surrounded by InP outer barriers for x = 0.65 (compressive), x = 0.53 (no strain), and x = 0.4 (tensile) versus the carrier density. Biaxial strains for x - 0.65 and x = 0.4 correspond to - 0 . 8 1 and 0.92%, respectively. From this figure, we predict that the BGR strongly depends on the magnitude and sign of strain applied to the quantum well. The reason for the increase (or decrease) of the BGR (in magnitude) with the compressive (or tensile) strain is due the reduction (or the increase) of the density of states (DOS) for holes in the valence band with the change of the valence-band structure by the built-in strain potential. In Figure 9, the inverse screening length x [ 15] for the two-dimensional electron-hole system is plotted for x - 0 . 6 5 (compressive), x - 0 . 5 3 (no strain), and x = 0.4 (tensile) versus the carrier density. For the large carrier density, the strain effects on x can be explained by the change of the density of states (DOS) with strain potential applied to the quantum-well region. On the other hand, for the relatively small carrier density, the nonparabolic nature of the valence-band structure can be accounted for. In Figure 10a-c, we plot the Reqll (solid line) and the I m q l l (dashed line), which are defined by Eqs. (126) and (127), respectively, for x = 0.65 (compressive), x -- 0.53 (no strain), and x = 0.4 (tensile), respectively, versus the in-plane wave vector (in units of 2Jr/ao). A cartier density of 3 x 1018 cm -3, intraband relaxation time of 0.1 ps, and correlation time of 20 fs are assumed in throughout the calculation. In all three cases, the Re qll is larger than the Im q ll in magnitude when compared as functions of the inplane wave vector. However, they both vanish when the in-plane wave vector is far from the zone center. In other words, the Coulomb enhancement of gain is only appreciable near the zone center. This makes sense because slower electron-hole pairs can feel the attractive Coulomb force more strongly than faster electron-hole pairs. If we ignore the Imq11, then the Coulomb enhancement factor is inversely proportional to 1 - Reqll. From this figure, we expect that the Coulomb enhancement of optical gain would be appreciable

653

AHN

x 108 2

-,

i

i

i

i

i

i

i

i

i

i

i

i

i

i

i

i

i

i

i

l

i

i

i i

A

"7,

E 1.5

9 -

- x = 0 . 6 5

"

-

/

x=0.53 X = 0.4

-

I

.--1 ~

.'-

O}

I

J /

T = 300 K

O 1===

.

~~

."''"

tt ===

//i

e,

J

I

/

. J

J

I

q) l_

o w

////

0.5

J

.

0 _ ,

0

,

,

,

_

1

,

;

,

,

!

,

/

/ 1

9

2

,

;

"

!

;

3

Carrier

Density

;

,

;

!

4

,

;

,

;~

5 x 1018 cm 3

Fig. 9. The inverse screening length Kfor the two-dimensionalelectron-holesystemplotted for x = 0.65 (compressive), x = 0.53 (no strain), and x = 0.4 (tensile) versus the cartier density.

for both compressive strained and unstrained quantum wells and would be negligible for the tensile strained quantum well. It is predicted that the enhancement of an optical gain would be most pronounced in the case of compressive strained quantum wells. In the case of a tensile strained quantum well, we consider the Coulomb enhancement for the TM polarization because the TM mode gain is dominant over the TE case for tensile strained quantum wells. in Figure 1 l a-c, we plot the renormalized (or Coulomb-enhanced) line-shape func0or tion Clm (kll) (solid line) and the original line-shape function Re ~o~r ~a (kll)) (dashed ""lm (0, Aim line), which are defined by Eqs. (29) and (26), respectively, for x = 0.65 (compressive), x = 0.53 (no strain), and x = 0.4 (tensile), respectively, versus the in-plane wave vector (in units of 2Jr/a0) for I = 1 and m = 1. Calculations were carried out for photon energies at respective gain peak positions for all three cases. In the case of a tensile strained quantum well, we considered the line-shape functions for the TM polarization. Again, it is expected that the enhancement is most pronounced in the case of a compressive strained quantum well and is negligible in the case of a tensile strained quantum well. In Figure 12a-c, non-Markovian optical gain spectra with (solid lines) and without (dashed lines) Coulomb enhancement are plotted for x = 0.65 (compressive), x = 0.53 (no strain), and x = 0.4 (tensile), respectively, versus the photon energy for carrier densities of 3 • 1018 and 5 • 1018 cm -3. Band-gap renormalizations are taken into account in all cases. From these figures, we expect that the many-body effects become more important in cases of compressive strained quantum wells and large carrier densities in the well. In previous papers [26, 29], the author showed that the optical gain model with the non-Markovian line-shape function removes two anomalies that occur when the Lorentzian line-shape functions are used in the gain calculation. These anomalies are the unnatural absorption region below the band-gap energy and the mismatch of the transparency point in the gain spectra with the Fermi-level separation; the latter suggests that the carriers and the photons are not in thermal (or quasi) equilibrium. In the absence of spectral broadening the optical gain spectra are related to the spontaneous emission spectra by the detailed balance between absorption and emission of photons [17-19]. One can easily see from this relationship that there is a transparency point in the gain spectra that coincides with the

654

THEORETICAL

ASPECTS

0.5 F ;

;

;

OF STRAINED-LAYER

;

i

!

i

i

i

i

!

QUANTUM-WELL

i

i

i

,

i

i

LASERS

i

i

,

;

x = 0.65

0.4

Re qll

Im qll

0.3 i

0.2

' T = 300K

I

N=3x101a cm3

0.1

o -0.1

/ L

,

_,

,

,

0

I

!

;

!

!

0.05

(a) --

i

i

i

i

l

:

,

,

!

0.1 In-Plane

0.5

I

i

i

i

i

;

,

0.15

Wave

i

I

0.2

Vector

i

i

i

i

i

i

i

i

i

-

x=0.53 0.4

Re qll Im

0.3

qll

-

0.2 T = 300K N=3x101a cm-3

0.1

-0.1

~

,

,

,

,

0

I

,

,

,

,

0.05

(b)

In-Plane

0.5

-

,

i

i

i

i

I

,

,

,

,

0.1

i

i

Wave

i

i

i

I

=

~

~

~

0.15

_ 0.2-

Vector

i

;

;

;

i

i

i

i

i

-

x-O.4 (TM polarization)

0.4

Re qll

.

0.3

.

Im qll 0.2

"

T

=

300K

"

N=3 xl 01 e cm-a 0.1

.

-o .1 0

(c)

,

,

,

,

m

,m

9

_m

0.05

m

m

.

.

.

0.1

In-Plane

Wave

.

m 0.15

9

!

m

n 0.2

Vector

Fig. 10. Plot of R e q l l (solid line) and Imq11 (dashed line) for (a) x = 0 . 6 5 (compressive), (b) x = 0 . 5 3 (no strain), and (c) x = 0.4 (tensile) versus the in-plane wave vector (in units of 2rr/a0). A cartier density of 3 x 1018 c m - 3 , intraband relaxation time of 0.1 ps, and correlation time of 20 fs are a s s u m e d throughout the calculation.

655

AHN

1020 15

-.

(joule "1) ,

i

i

i

i

i

,

i

I

i

i

i

,

I

i

i

I

i

i

;

i

i

;~-

x = 0.65 /

__ ....

/ 10 -

/

Coulomb enhanced lineshape function Original lineshape function (both calculated at gain peak position)

~

.

/ \ / -/ 5

N=3x101s cm-3

0

__~-~.-r-----t[~i'~ _l' , , , , a "~...~ , , a . . . . 0.01

0

0.02

(a)

In-Plane

1020 10

~-,

a , , ,

0.03 Wave

0.04

0.05

Vector

(joule "1) ,

i

i

I

'

i

i

i

I

'

i

;

;

i

i

i

i

;

i

i

i

i

i.

x = 0.53 ~. 8 |

//~ / \

6t ~, ~_~ 4 I-

I ,'

_ _ Coulomb enhanced lineshape function .... Original lineshape function (bothcalculatedatgainpeakposition)

\

T OOK =

N=3x101s cm-S 2

o L . .

9

.

0

i

;

9

9

9

!

0.01

."~_

=i

I

,

9

.

.

I

0.03

In-Plane

1020

,

0.02

(b) 15

9

Wave

.

9

,

0.04

_ 0.05

Vector

(joule "1) i

i

;

I

'

i

i

i

!

i

i

.

.

!

.

.

,

9

i

'

9

'

'~

X = 0.4 (TM polarization) Coulomb 10

----

"

enhanced

lineshape

function

Original lineshape function (both calculated at gain peak position)

"

T = 300K N=3x1018 cm-Z

-

0

(c)

0.01

0.02

In-Plane

0.03

Wave

0.04

.

0.05

vector

Fig. 11. Plot of the renormalized (or Coulomb-enhanced) line-shape function (solid line) and the original non-Markovian line-shape function (dashed line) for (a) x = 0.65 (compressive), (b) x = 0.53 (no strain), and (c) x = 0.4 (tensile) versus the in-plane wave vector (in units of 2zr/a 0) for I = 1 and m = 1. Calculations were carried out for photon energies at respective gain peak positions for all three cases.

656

THEORETICAL ASPECTS OF STRAINED-LAYER QUANTUM-WELL LASERS

" i 8000

i i

i i

i

i

i

T = 300 K

i i i

i i

/

i i

i i

i i

"~

i

i

i

i

i i

i

i

i

-

with Coulomb effects

/

-

6000

i

x = 0.65

==

~ - - -

without

Coulomb

effect

-

A

"7,

E o

4000

........

c

-

. . . .

"

2000

. . . .

~iI

0.7

.

,

,

,

0.75

I

i

i

i

i

i

-

8000

i

i~.

- .

0.8

0.85

Photon

energy

(a) -i

. . . .

i

i,

,

i

i

i

" I

9 .'-

- I

0.9

i

i

0.95

1

(eV) i

i

i

i

i

i

i

i

i

i

i

i

-

x = 0.53 with C o u l o m b effects w i t h o u t C o u l o m b effect

....

6000 A

"7,

E o

4000

-

T = 300 K

N = 5x1018 cm ~'

,=!,,

t~

N = 3x1018

r

2000

.i . . . .

I,

0.7

0.75

(b) " i

i

i

i

i

i..

,-~-~-,,

i

,, i

8000

i

. . . .

0.8

0.85

Photon

energy

i

i

X = 0.4

6000

I...'i't

i

i

i

i

, ,~,,

0.9

i

i

,-

0.95

1

(eV) i

i

i

i

i

i

i

i

i

i

i

i

(TM polarization) ....

-

with C o u l o m b effects w i t h o u t C o u l o m b effect

A

T = 300 K

"7,

E o

4000

-

2000

-

N = 5x1018 crn 3

m

Ir .=...

0

N = 3x1018 c m "3

.

0.7

(c)

, . , , . ,

0.75

,.

,,

. , . ,

, , , , ,

0.8

0.85

Photon

energy

0.9

0.95

1

(eV)

Fig. 12. Non-Markovian optical gain spectra with (solid lines) and without (dashed lines) Coulomb e n h a n c e m e n t plotted for (a) x = 0.65 (compressive), (b) x = 0.53 (no strain), and (c) x = 0.4 (tensile) versus photon energy for carrier densities of 3 x 1018 and 5 x 1018 c m - 3 .

657

AHN

Fermi- (or quasi-Fermi) level separation and that suggests the carriers and the photons are in thermal (or quasi) equilibrium [17]. The result is, in fact, a general one, as discussed in [44]. In Figure 12, it can be seen that the transparency points for a given carrier density converge regardless of the inclusion of the Coulomb enhancement effects, which results in a consistent picture with the thermodynamic relationships. The reason why the use of the non-Markovian line-shape function suggested in Eqs. (131) and (132) shows better agreement on a transparency point with the quasi-Fermi-level separation is the faster convergence of the Gaussian-like nature of the non-Markovian line-shape function as compared with the Lorentzian line-shape function in the spectral integration for the gain.

4. CONCLUSIONS In this chapter, we have presented the theory of strained-layer quantum-well lasers with the nonparabolic valence-band mixing and the many-body effects taken into account. Our theoretical approach for the electronic properties is based on the Luttinger-Kohn Hamiltonian, taking into account the strains and the cartier-induced band-gap shifts using the Hartree-Fock approximation. The effects of the biaxial compressive and tensile strains on the gain, the output characteristics, the band-gap renormalization, and the modulation response of strained-layer quantum-well lasers were studied. We also calculated the effects of the spin-orbit (SO) split-off band coupling on the valence-band structure, density of states (DOS), dipole moment, and the linear and nonlinear optical gains of the strainedlayer quantum wells and compared them with the results obtained without accounting for the SO coupling (the 4 x 4 Luttinger-Kohn model). Unlike previous theoretical work on band-gap renormalization that assumes a parabolic band model, we calculated the bandgap shrinkage, including the valence-band mixing and the multisubband effects. We found that the band-gap renormalization depends strongly on the nature of strain in the quantum well. The linear and the nonlinear optical gains of a quantum well were then calculated from the complex optical susceptibility derived from the density-matrix method. The gain spectra calculated with the Lorentzian line-shape function show two anomalous phenomena: an unnatural absorption region below the band-gap energy and a mismatch of the transparency point in the gain spectra with the Fermi-level separation, the latter suggesting that the carriers and the photons are not in thermal (or quasi) equilibrium. We also presented a more rigorous theoretical model of the optical gain of a quantumwell laser, taking into account the non-Markovian relaxation, many-body effects, and the valence-band mixing within the 6 x 6 Luttinger-Kohn model. The optical gain and the line-shape function of the quantum well under an external optical field were derived from recently developed time-convolutionless quantum-kinetic equations for electron-hole pairs near the band edge. Many-body effects, such as band-gap renormalization and excitonic enhancement, were included by taking into account the Coulomb interaction in the HartreeFock approximation. It is shown that the non-Markovian gain model with many-body effects removes the two anomalies associated with the Lorentzian line-shape function. It is also found that the optical gain spectra depend strongly on the correlation time of the system, which can be determined by the intraband frequency fluctuations. As a numerical example, an InxGal_x As-InP quantum well was chosen for its wide application in optical communication systems. The Coulomb enhancement of gain is predicted to be pronounced in the cases of compressive and unstrained quantum wells, whereas it is negligible in the case of tensile strained quantum wells.

APPENDIX A

3 The basis set for the matrix, Eq. (3), is the lJ, m j) for J - ~" ~,

=

~/_~ [(X +

658

ir)~)

THEORETICAL ASPECTS OF STRAINED-LAYER QUANTUM-WELL LASERS

~,-

= ~I(X-iV)'~)+

~,

--

i-5'-

IZ$)

iY)$)+

v/_~ I(X +

(A.1)

IZ$)

- - ~ 1 I(x - iY)4")

The unitary transformation U is defined by U

where

ot* 0 0 /~* o ~* o~* 0

-r0 r 0

-cr 0 1 o c~

exp i

4

2

I

ot -- ~

(A.2)

(A.3)

' exp[/( and 4, is the angle defined by The new basis is given by

kx =

kll cos r and

I~/-,~, 12)

ky =

-~

,8 ~ , - -

kll sin 4,.

~,-~

-,8" ~, (A.4)

13)

/~ ~ , -

+1~* ~,

3 3)

141-~,~

+,~

,3 3) ~,-~

APPENDIX B

We describe the finite difference method for the upper block Hamiltonian H U.Formulation for the lower block Hamiltonian is straightforward following the same procedure. We have two coupled differential equations for 9(m1)(kll, z) and 9(m2) (kll, z)"

IP+QWV(z) R*

/~

] [ g(ml)(kl', z) ] [ 9(ml)(kl,, z) 1 9(m2)(kll,Z) = EU(kll) gm(2)(kll, z )

P + O + V(z)

(B.1)

From now on we suppress the subscript m and define ~bh (z) and ~bI (Z) by ch (Z) -- g(m1)(kll, z)

and

~bl (z) -- 9(m2) (kl], z)

(B.2)

for each kll. Then the coupled differential equations for 4,h (z) and ~l (Z) are (Y1 -I- y2)kff - ~(Y1 - 2}"2)~Z 2 Jr- ~ V(z)

(z)

{ ~/c~-'2 d }qbl(z)--h-2 mEdph(z) -+" --~ YKII -- ~/3y3kll dzz

(•

(B.3)

- n ) ~ - ~(• + 2n))-~z2 + f f V(z) ~l(z)

+ [,v/-3 - T ; ~ +,/5•

m ~(z) ~d}dph (z) - ~EO

659

(B.4)

AHN It is convenient to normalize Eqs. (B.3) and (B.4) by defining

Z

mL 2

=-{

~ 22 C = ~ - y L kll

1

A2 = ~(gl -21/2) 1

B1 = ~(Y1 -

mL 2

1

A1 = ~(Y1 -]- n)Z2k~

h~-E f=--rv-V(~) w"

~=

D = V/-3y3Lkll

1

y2)L2k~I

B2 = ~(Y1 + Y2)

Then Eqs. (B.3) and (B.4) become

I A1 - A2~--~ -d2 . + f(~) 1 ~bh(~) + I C - D d~l ~l (~) _ ).q~h(~)

(B.5)

[ B 1 - B 2 - ~d2 +

(B.6)

f(~)]dpl(~)+[C J L + D d~]~h (~) -- ~,~l (~)

Then the rest of the procedures follows the standard finite difference method. One need to discretize kll, evaluate the coefficients in (B.5) and (B.6) for each kll, and solve for the eigenvalue ~. numerically. APPENDIX C

The basis set for the matrix is the IJ, m j) basis for J = 3 and J = 89 3 3)

~,~ --

1

-

,/~l(x+iY)t) Iz;)

- ~[(x-iv)t)+

-

I-

,/_g[(x+iY)$)+

IZl")

1

-~[(X-iY)$) 1 1)

1

= -~[(x -iY)t)-

IZ4,)

(C.1)

The new bases are given by

,1/o,133) ~,~ -,~ 13 ~,-~3) ~,13)=y,

-~,

1 1 ) I+v~,~ 1 1) ~,-~

~,15) = r , ~,-~ 3 1)

-• + , ~3, ~1)

~,g +'~ ~,-~

660

(C.2)

THEORETICAL ASPECTS OF STRAINED-LAYERQUANTUM-WELL LASERS

APPENDIX D" OPERATOR ALGEBRA

In this section, we prove some useful functional relationships among evolution operators (or propagators) defined in Section 4. Theorem 1. Let V(t) be the projected evolution operator of the system defined as

{fot

V(t) -- T__exp - i

dr Q__Ls(r)Q

}

(D.1)

Then

(D.2)

V(t) - P + QU(t) Q Proof By expanding V(t) in Taylor series, we obtain V(t) - 1 - i

-- I + Q

f0'

dr Q__Ls(r)Q__+ (_i)2

1-i {fot

f0' f0 dr

d r L s ( r ) q-(-i)2

ds Q__Ls(r)Q QLs(s)Q__ + . . .

dr r d s L s ( r ) L s ( s ) + . . . I Q - Q fotfo

= P + QU(t) Q

We use the commutativity of Q and Ls (t) and the idempotent property Q2 = Q. Theorem 2. Projected propagators H(t, r) and S(t, r) satisfy

H(t, r) = V(t)S(t, r ) V - l ( r )

(D.3)

Proof We differentiate Eq. (D.3) with respect to obtain

d --H(t, r)--i dt m

Q L T ( t ) Q H ( t , r) -_

with the initial condition H ( r , r) -- 1. On the other hand, ~ V ( t ) S ( t , r)__V-1(r) = - i QLs(t)QV(t)S_(t, r ) V - l ( r ) q- V_(t){-i Q_U -1 (t)Li (t)U(t)Q}S_(t, r)__V-1 (r) = - i QLs(t)QV__(t)s_(t, r)__v-1 (r) + {P + Q U ( t ) Q } { - i Q__U- l ( t ) L i (t)u(t)Q}S_(t, r)

v-l(r)

-- --i QLs(t)QV__(t)S(t,17)V-1('~) -iOLi(t)O

au(t)as(t,

r)v-l(r)

= -i QLs(t)OV(t)s(t, r)v -l(r) -iQLi(t)Q{P__ + Q_=_u(t)Q}S(t, r ) v - 1 (z) = - i Q L T ( t ) Q V ( t ) S ( t , r ) V -1 (r)

with

V(t)S(r, "t')_VV-1 ('t') = 1 Whereas any two functions that satisfy the identical differential equation and initial condition must be identical to each other, it is obvious that H(t, r) - V__(t)S(t, r)__V-1 (r). Lemma. It can be shown that

H(t, r) Q -- U(t)S(t, "t')U -1 (l") Q

661

(D.4)

AHN

T h e o r e m 3. Evolution operators G(t, r) and R(t, r) satisfy

G ( t , r) - U ( r ) R ( t , r ) U -1 (t)

(D.5)

Proof of this theorem is similar to that of T h e o r e m 2. T h e o r e m 4. Let Uext(t ) be the evolution operator of the system in the interaction picture

such that U(t) = U0(t)Uext(t )

(D.6)

where Uo(t) -- T e x p { - i

f o t d s Lo(s) }

is the unperturbed evolution operator of the system. Then Uext(t ) -- T e x p

lyo -i

ds U o 1(s)Lext(s)Uo(s)

(D.7)

Proof. We differentiate U ( t ) with respect to t to obtain d

--d~U(t) - - i Ls (t)U(t) -

~U0(t)

Uext(t) - t - U 0 ( t ) ~ U e x t ( t )

Then we have d ~-~Uext(t) -- _ i U o 1(t)Lext(t)Uo(t)Uext(t)

(D.8)

The formal solution of (D.8) is T e x p { - i fo ds U__Uo1(s)Lext(s)U_U_o(S)}.

Acknowledgments

This work was partially supported by the Institute of Information Technology Assessment (IITA), the Ministry of Information and Communications, through the research grant AB97-G-164, and by the Ministry of Science and Technology through the Creative Research Initiatives.

References

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18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43. 44. 45. 46. 47. 48. 49. 50. 51. 52. 53. 54. 55. 56. 57. 58. 59. 60. 61. 62. 63. 64. 65. 66. 67. 68. 69. 70. 71.

663

Chapter 14 CARBON-NANOTUBE-BASED NANOTECHNOLOGY IN AN INTEGRATED MODELING AND SIMULATION ENVIRONMENT Deepak Srivastava, Fedor Dzegilenko, Stephen Bamard, Subhash Saini NASA Ames Research Center, Moffett Field, California, USA

Madhu Menon Department of Physics and Astronomy, University of Kentucky, Lexington, Kentucky, USA

Sisira Weeratunga Lawrence Livermore National Laboratory, Livermore, California, USA

Contents 1. 2.

3. 4.

5. 6.

7.

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 665 Computational Nanotechnology: Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 668 2.1. Scaling in Physical Models and Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 668 2.2. Scaling in Device Technologies--Hardware . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 670 2.3. Architectures, Operating Systems, and Software . . . . . . . . . . . . . . . . . . . . . . . . . . . 675 Integrated Problem-Solving Environment for Nanotechnology . . . . . . . . . . . . . . . . . . . . . . 678 Prerequisites for a Successful Simulation Environment . . . . . . . . . . . . . . . . . . . . . . . . . . . 678 4.1. Information System-Based Problem-Solving Environment for Nanotechnology Developments . 679 4.2. Functional Requirements of a TCAD Problem-Solving Environment . . . . . . . . . . . . . . . 680 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 681 Carbon-Nanotube-Based Nanotechnology: Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . 682 6.1. Mechanical Properties and Strength Characterization of Carbon Nanotubes . . . . . . . . . . . . 683 6.2. Carbon-Based Molecular Electronics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 690 6.3. Nanoscale Electromechanical Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 696 6.4. Nanotube Nanolithography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 699 Comments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 702 Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 703 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 703

1. I N T R O D U C T I O N N a n o t e c h n o l o g y is t h e s c i e n c e a n d t e c h n o l o g y o f a t o m i c a l l y p r e c i s e ( n a n o s t r u c t u r e d ) m a terials, d e v i c e s , a n d a p p l i c a t i o n s ; s u c h d e v i c e s i n c l u d e s e n s o r s , a c t u a t o r s , m a c h i n e s , a n d c o m p u t e r s . T h e b a s i c a p p r o a c h o f this e m e r g i n g t e c h n o l o g y is d r i v e n b y t h e i n c r e a s i n g

Handbook of NanostructuredMaterials and Nanotechnology, edited by H.S. Nalwa Volume2: Spectroscopyand Theory Copyright 9 2000 by Academic Press ' All rights of reproduction in any form reserved.

ISBN 0-12-513762-1/$30.00

665

SRIVASTAVA ET AL.

ability to control, manipulate, and construct macroscopic materials systems at the atomic or molecular level. Its principles were first stated in 1959 by Richard Feynman, who said, "The principles of physics, as far as I can see, do not speak against the possibility of maneuvering things atom by atom" [1, 2]. The invention of scanning probe microscopy in 1980s and subsequent rapid advances in the sophistication and control of these techniques within the last few years, has made it possible not only to image atomic nanostructures on solid surfaces, but also to manipulate them to desirable configurations. In 1990, IBM scientists used a scanning tunneling microscope (STM) tip to write the letters "IBM" by moving inert xenon atoms to the appropriate places on a nickel surface [3]. Significant progress has also occurred in developing many other physical, chemical, optical, and biological techniques as well. The basic aim of this research has been to achieve still better control over the ability to position atoms or molecules in the fight place in any materials system. The development of nanotechnology is important for the exploration and future settlement of space. Current manufacturing technologies limit the reliability, performance, and affordability of aerospace materials, systems, and avionics. Nanotechnology has an enormous potential to improve the reliability and performance of aerospace hardware while lowering manufacturing cost. For example, nanostructured materials that are perhaps 100 times lighter than conventional materials of equivalent strength are possible. Embedding nanoscale electromechanical system components into earth-orbiting satellites, planetary probes, and piloted vehicles potentially could reduce the cost of future space programs. The miniaturized sensing and robotic systems would enhance exploration capabilities at significantly reduced cost. Thousands to millions of such miniaturized devices could help map a planet in a single launch. Each launch cost could be drastically reduced as well. In the ultimate realization of nanotechnologymmolecular nanotechnology--there could be self-replicating or self-reproducing nanorobots [4] that would search for extraterrestrial life or make an environmentally hostile planet hospitable for human exploration and settlement. Many of the nanotechnology applications of relevance to the National Aeronautics and Space Administration (NASA) have been summarized in a recent review article [5]. The design and simulation of realistic nanotechnology systems presents formidable computational challenges. Future nanotechnology systems simulation may need to be performed for 100 million atoms. The most accurate methods available may remain limited in scope to smaller molecular systems. As an example, for an n basis function representation of an N electron system, the ab initio Hartree-Fock (HF) procedure results in a computational complexity that is proportional to the fourth power of the number of basis functions. This would exhaust the computing capabilities of even the most advanced current generation of highly parallel supercomputers, such as IBM SP2 and Cray T3D and Origin 2000 [6]. The highly accurate ab initio calculations for large systems may remain beyond the capabilities of current and foreseeable supercomputers. For design work to be feasible at all, less accurate but faster methods must be used. The data points from ab initio methods and experimental observations are used to compute simple two-body or complex many-body reactive potential energy surfaces (for a recent review on reactive potential energy surfaces, see, for example, [7]), which are then used in molecular dynamics (MD) computations [8, 9]. Classical MD methods involve solving Hamilton's equations of motion for each atom in the system with respect to every other atom, where the forces acting on an atom are a combination of forces due to bonding, van der Waals, and charge multipole interactions. The long-range nonbonding van der Waals and charge multipole interactions require special treatment for implementation on parallel supercomputers [ 10]. Good quality classical molecular dynamics simulations involving reactive potentials and possibly long-range interactions have been implemented typically for a few hundred thousand to a few million atom simulations [ 11-14]. For simplified potential energy surfaces and for specific problems, the simulations have started to include up to a billion atoms. If the electronic effects are important during the dynamics, the quantum potential energy surfaces

666

CARBON-NANOTUBE-BASED NANOTECHNOLOGY

or interactions are used in the ab initio (based on local density approximation (LDA) to the density functional theory [ 15]) or tight-binding [ 16, 17] molecular dynamics methods, with a few hundred atoms in the former and a few thousand atoms in the latter. The structural, mechanical, and chemical characteristics are simulated from the foregoing methods, whereas electronic transport for device applications is calculated from the solution of transport equations with drift-diffusion, hydrodynamic, and Monte Carlo methods [ 18, 19]. The quantum effects in electronic transport are important in the nanoelectronic regime and are incorporated through Green's functions, the Wigner function, or density-matrix-based approaches to solution of the time-dependent Schrodinger equation [20]. The design and simulation of nanotechnology systems, materials, and applications starts with the implementation on parallel supercomputers of algorithms and codes derived from the laws of physics and chemistry. Microscopic and mesoscopic properties of the individual components and full systems are investigated. The data are analyzed through numerical methods, graphic representation, or full three-dimensional visualization and animation techniques. The application of virtual reality (for example, the ability to manipulate physical models in a virtual world with haptic interfaces) is also the subject of experiments. A successful environment for overall development of the computational nanotechnology therefore requires integration of the physical and materials sciences applications and analysis tools with computer-systems technologies (such as parallel programming and advanced graphics) in the overall simulation and modeling environment. Specific examples of the usefulness of simulation are that over the last decade highfidelity process and device simulation capability has led to rapid developments in the design and development of complex integrated circuits (IC), optoelectronics devices, and microelectromechanical (MEMS) systems. Computer simulations have reduced the time and costs associated with the component and system design and development, thereby playing a significant role in shrinking device dimensions to ever lower values, while managing the growing complexity of the processes involved in the final fabrication. From the application point of view, NASA's interest in nanotechnology can be broadly categorized into three classes: 9 Lightweight, very strong, and elastic materials for fabrication of aerospace systems components capable of operating under harsh environmental conditions for long periods of time; 9 Nanominiaturized electronic, computing, sensing, and actuating device systems, leading to the reduction of the cost-to-weight ratio, while maintaining similar or enhanced operational capabilities; 9 Lightweight and low cost materials and devices for the storage of fuel and energy that can be carried aboard a space mission. Modeling and computer simulation has not only contributed significantly to progress in these areas, but has also provided radically new ideas for enabling technologies for the 21st century. The requirements for computational nanotechnology in a 21st century integrated simulation and modeling environment will be discussed, as well as the recent results of computer simulation in carbon-nanotube nanotechnology. In Section 2 we analyze computational resource requirements and the scaling of physical models, hardware, and software needed for large-scale nanotechnology simulations. Section 3 presents requirements for an information-technology-based integrated modeling and simulation environment (ISTCAD) nanotechnology. Section 4 discusses nanotechnology applications in relation to NASA's aerospace and avionics materials and device systems requirements. Finally, in Section 5 we describe modeling and simulations of carbon-nanotube-based nanotechnology applications performed recently at NASA Ames Research Center.

667

SRIVASTAVA ET AL.

2. COMPUTATIONAL NANOTECHNOLOGY: REQUIREMENTS Many experts agree that information technology is one of the premier enabling technologies for the next century. The future of U.S. leadership in advanced computing, communication, and information technology will be determined by long-term research and development in the electronics and computer industry. In the short run, ultrasmall and ultra-powerful computers, long-distance broad bandwidth communications systems, and energy-efficient fiat panel displays are needed. In the long run, however, intertwined with these developments will be the advances in nanotechnology that could provide smaller, faster, and cheaper engines for the growth of information technology itself. It is not surprising, therefore, that the requirements for the growth of nanotechnology, in general, and computational nanotechnology, in particular, may parallel the requirements for the growth of information technology. Information technology needs devices that are faster, cheaper, more robust, and more reliable, with higher gigaflops per watt and higher gigaflops per second per square foot than current technology can offer. This sounds familiar as a goal of nanotechnology, as well, suggesting a cross-coupling between nanotechnology and information technology. The attraction of computer simulation and modeling is that, on one hand, they can accelerate the development of the underlying field and, on the other hand, they can be the testbed for new devices and technologies. In the following text, we discuss algorithmic, hardware, and software requirements for practicing computational nanotechnology in the next century.

2.1. Scaling in Physical Models and Algorithms The design and simulation of nanotechnology systems present a formidable computational challenge. Atomistic simulations of molecular nanotechnology components need to be performed for anywhere between a few thousand to a few million atoms. As the components are put together into functional units, system size could easily reach hundreds of million of atoms. As previously mentioned, the most accurate quantum mechanical methods available are necessarily limited in scope to smaller molecules containing only up to few hundred atoms. The scaling in complexity with the size of the system can be explained as follows. For an n basis function representation of an N electron system, the Hartree-Fock (HF) procedure results in a total of (n 2 + n)/2 kinetic energy, (n 2 + n)/2 nuclear attraction, and (n 4 + 2n 3 + 3n 2 + 2n)/8 electron repulsion integrals. Thus, in such methods, the computational complexity is proportional to the fourth power of the number of basis functions. The scaling of several available computational ab initio methods is shown in Figure 1. The full configuration interaction method (FCI) is the most accurate method. In any practical simulation, the set of possible configurations becomes so large that the complexity of the FCI is on the order of (1 ON)!, where N is the number of atoms and where we have assumed that there are 10 basis functions for each atom. The FCI computations converge slowly and are very expensive. Therefore, this method can be used only for systems with one or two atoms. The coupled-cluster singles and doubles (CCSD) method, with a perturbational estimate of the connected triply excited CCSD(T) method, is probably the most accurate and practical approach in use today. The computational complexity of CCSD(T) is proportional to (10N) 7. This method can be used only for systems with up to about 20 atoms. The CCSD method ignores the triplet excited states, leading to a computational complexity proportional to (10N) 6. This method can be used only for systems with up to about 30 atoms. The density functional (DFT) method has complexity (10N) 4 and can be used for systems containing up to about 50-100 atoms. Figure 1 underlines the limitations of quantum-chemical methods and their inability to compute the potential-energy surfaces (PES) of nanoscale systems with millions of atoms. One alternative is to use a combined quantum-classical approach [21-24]. In this method, the system is subdivided into two nonequal parts. The first small part, which

668

CARBON-NANOTUBE-BASED NANOTECHNOLOGY

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669

SRIVASTAVA ET AL.

space. The energies of formation, sublimation, and dissociation also can be calculated, as well as the vibrational and Raman spectra. The energy minimization problem in MM methods has computational complexity that scales as N 3 and memory requirements that scale as N 2, where N is the number of atoms. Recently, new algorithms have been developed with less computational complexity and memory requirements. The main conceptual deficiency of MM methods is that they are nonreactive in nature. The bonding of the constituents is predetermined and cannot change during the simulation. Simulations of this type are thus nonpredictive in the sense that no new product is formed and no existing reactants are consumed. For gas-phase reactants or products this is not much of a problem because system sizes are small enough to be dealt with entirely by quantum chemical methods. For liquid simulations of biological and biochemical systems, the molecular mechanics simulations are limited to predicting mostly the conformational and vibrational properties as previously mentioned. Their application to nanotechnology also will be limited to modeling in cases where, based on chemical rules and physical principles, one could predict or guess a structure in advance. Beginning in the 1980s, significant progress has been made in reactive many-body atomic interaction potentials for condensed-phase metals and semiconductors. The word "reactive" means that bond breaking and bond making are allowed during the dynamics. Physical and chemical structural transformations are possible, and new structures may be predicted that were not constructed a priori. Starting from the London-Eyring-PolanyiSato (LEPS) approach (see [7] for definition) for reactive gas-phase interactions, which was first generalized to gas-metal surface dynamics [30], many-body potentials for fcc, bcc, and hcp metals have been formulated [31-34]. Atomic potentials for semiconductor materials (which are commonly known as diamondoid in the nanotechnology community) also have been formulated for reactive many-body interactions that can be used in MD simulations [35-37]. The many-body potentials have two-body stretching, three-body bending, and four- and higher-body torsional, dihedral, and bending-bending interaction terms. The main cost involved is in computing the atomic forces for these systems. However, due to the short-range nature of these potentials, the algorithms are amenable to parallelization. The local nature of the forces means that the computational efforts scale linearly with the number of atoms. Parallelization is implemented through atomic or spatial decomposition schemes, and it is not necessary to utilize the same scheme for parallelization of the neighbor-list formation and for computation of the forces [11]. The long-range (global) nonbonding interactions are dealt separately with fast multipole expansion and cell multipole methods [38, 39]. The complexity of MD methods involving long-range forces is on the order of N 2, whereas the complexity of MD using fast multipole expansion methods scales down to N log N. A comparison of the scaling of the complexity of MD methods with short- and long-range interactions is shown in Figure 2. Assuming the preceding general strategy outlined (ab initio § CASSCF § MD), we have estimated the computing power and disk space needed to perform long-range MD simulations for systems of interest to nanotechnologists. The results are shown in Figure 3 [40]. It is clear that petaflop computing capabilities might be needed for full-scale nanotechnology system simulations. Nanotechnology component simulations, on the other hand, could well proceed with the current computing capabilities.

2.2. Scaling in Device Technologies---Hardware Considering the high demand on the computational power that will be needed for full-scale nanotechnology system simulations, we briefly review the status and scaling in the current silicon-based complementary metal-oxide-semiconductor (CMOS) technology. The issues involve the limitations of the conventional silicon-based technologies due to physical limits, lithography, heat dissipation, and quantum and statistical effects. Central processing unit (CPU) clock cycle time is ultimately limited by the physical speed of electrons in a conductor, which at most can be equal to the speed of light. Figure 4

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etc. The outstanding success of CMOS technology is due to the "scaling" of the process technology. By scaling we mean that the performance of the semiconductor device can be increased simply by reducing the dimensions of the device by a constant factor. It is widely believed that below 0.07/zm, several factors may inhibit the demonstrated progress in the semiconductor technology. These factors include the sky-rocketing cost of manufacturing plants, the 0.1-p~m foreseeable limit of the photolithography process, quantum effects, data communication bandwidth limitations, heat dissipation, and others.

2.2.1. Lithography Miniaturization of semiconductor devices is driven by lithography techniques that determine the gate length and source-drain spacing. A road map for process technology is shown in Figure 7. In the semiconductor technology, for example, the Intel Pentium Pro (which is used in the DoE ASCI "red" parallel supercomputer system) and the DEC Alpha 21164 (which is used in the Cray T3E) both are fabricated using 0.35-/xm process technology; 0.25-/zm technology chips are available and 0.18-/zm feature size chips are knocking at the door. Beyond 0.18/zm, X-ray lithography may be the only means to manufacture circuits with hundreds of millions of transistors. In 1994, IBM, Motorola, and AT&T initiated a collaborative effort to share the development costs needed to make X-ray lithography commercially successful. However, there are two major problems with this approach: first, the synchrotron source of X-rays is expensive; second, focusing X-rays is not commercially feasible. Most of the X-ray lithography work is still at the research and development level. Logic gates as small as 0.07/zm, using X-ray lithography, have been fabricated. "They work, they switchmbut there are still manufacturing challenges to be addressed." At present there are no well understood manufacturing techniques for process technologies at or below 0.07 /zm. It is commonly believed that beyond 0.07-/zm process technology, quantum wave function engineering will play an important role. Recently,

Fig. 7. Nationalroad map for process technology. (AdaptedfromRef. [40].)

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atomic force microscope (AFM) tips have been proposed as "unique lithographic tools," with which one can draw a pattern on a silicon surface by using a nanoscale probe tip (discussed later). The marked pattern serves as a mask for a subsequent etching process, and a corrosive liquid dissolves away silicon around the mask. Arrays of multiple parallel probe tips, which may be able to write in parallel are fabricated. Independent control and operation of each tip in the array, however, may be desired, and this aspect needs to be investigated. Nanolithography is a top-down approach, but it shows tremendous potential to become a viable technology beyond 0.07-#m process technology.

2.2.2. Heat Dissipation Heat dissipation is a major problem in n- or p-type metal-oxide-semiconductor fieldeffect transistor (MOSFET) semiconductor devices. However, heat dissipation is drastically reduced when n- and p-channel devices are used in series. Current flows, and power is consumed only when the switch is on. The low power consumption of CMOS technology makes CMOS very attractive for very high-density applications such as Intel Pentium Pro and differential random access memories (DRAMs). The number of transistors that can be put on a chip depends on the amount of heat they dissipate. The heat-dissipation problem can be overcome to a great extent by placing the chip on a diamondlike substrate with high heat conductivity or by developing new nanoscale, high thermal conductivity, materials that can be used as heat-dissipation carriers and sinks on the chip.

2.2.3. Quantum Effects As the thickness of the insulating material (silicon dioxide) between the gate and channel is decreased, electrons have a significant probability of tunneling across this area, even when the energy of the electron is less than the energy of the potential barrier. This quantum tunneling increases exponentially as the thickness of the insulating material is decreased. Therefore, quantum effects such as tunneling have to be taken into account when solving the transport equations that govern the motion of electrons and holes through a device. In molecular or nanoelectronics approaches such as the one based on carbon nanotubes (discussed later), the quantum effects will be significant, but can be utilized for efficient operation of the devices.

2.2.4. Statistical Effects The total number of impurities in the depletion region has decreased gradually as the minimum feature size has decreased. It is about 3000-4000 at 0.35 /zm. At and below 0.1 #m, the active region will have impurities in the range from a few tens to a few hundreds, and even small fluctuations will affect the performance of the device. Also, at and around 0.1 #m, bulk properties would reduce to quantum mechanical properties of ten or a few hundred impurities. In molecular or nanoelectronics, however, as previously mentioned, the carriers may not be statistically controlled and the concepts also might change entirely. The nanotechnology-based solutions in nanoelectronics thus could be the enabling technology for future computers with capabilities that are not bounded by most of the limitations discussed herein.

2.3. Architectures, Operating Systems, and Software As shown already, the full-scale nanotechnology system simulations with complex design of national computer aided design (NCAD) may require petaflop computing capabilities, which in turn depend on advances in many disciplines and technologies. A possible road map of the intertwined developments in nanoelectronics, nanoscale aerospace systems,

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Fig. 8. Roadmap for future molecularnanocomputersand molecularnanosystems.(AdaptedfromRef. [40].) and petaflop computing is shown in Figure 8. The architectural requirements of computer systems capable of doing full-scale nanotechnology system simulations are similar to the requirements for a petaflop computer in general [40]. Figure 9a shows the architecture of a globally shared, cacheless multiprocessor composed of 1000 processors, each consisting of 1 Tflop. The major cost of this machine will be for the memory of 1 Pbyte. The crossbar network has to be very fast, with latency of 1 ps (10 -9 s) and bandwidth of 16 Gbytes per second per CPU, and should be able to keep 1000 data streams active from main memory to the individual CPUs. Figure 9b shows a network of high-performance workstations with local memory, L1 data cache, and L2 data cache on each processor. This architecture, which follows the current trend of highly parallel systems such as the IBM SP2, will have 10,000 workstations, each composed of 100 Gflops. It is more likely that in this architecture each node will be a symmetric multiprocessor (SMP) of 10 processors, each rated at 100 Gflop. Thus, each node is rated at 1 Tflop and we have 1000 such nodes. Figure 9c shows a new architecture, where the processor and the memory are on the same chip. Here we will have 100,000 processors, each rated at 10 Gflops. A global shared-memory architecture with 1000 processors will be easiest to program. A network-of-workstations architecture will be hard to program, because the application scientist must perform data partitioning to take advantage of the local memory. This problem may be overcome by efficient high performance Fortran (HPF) compilers [44, 45]. However, if this architecture is a cluster of SMPs, a new programming model needs to be developed that can make use of a global shared-memory model within a node and message-passing paradigm between the SMP nodes. For applications requiting global communication, scalability will be an issue, especially where communication is all to all. Petaflop computers will require operating systems radically different from those currently in use. Typical functions of operating system are to allocate processes and to create, destroy, and manage subprocesses; to handle communication between processes, both locally and on other computers; to ensure that each process can access only the memory it is entitled to access; and to allocate and manage memory. Currently, there are two approaches for designing operating systems: (1) a host computer as a front end and (2) a symmetric systemma complete operating system on each node. Both of these approaches, however, have major problems, and few solutions have been analyzed [46-49].

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(c) Fig. 9. (a) Globalsharedmemoryarchitecture. (b) Network-of-workstationsarchitecture. (c) Processors in memoryarchitecture. Dramatic improvements in software technology and numerical algorithms are essential to achieve sustained high performance on petaflop computer systems. Improvements in innovative hardware must be matched by new software and by algorithms to enable computational scientists to expand the boundaries of computational capabilities. System software is a vital link between the hardware and the applications running on it. It includes tools for developing applications, such as compilers, performance analyzers, and debuggers. It also includes operating systems, parallel input-output (I/O), communication, file systems, parallel batch systems, and security. The big challenge of system software development is to extract maximum performance for the end users, and that is already a challenging problem for highly parallel systems. For example, in the IBM SP2 the sustained floating point operations rate is only about 20% of the advertised peak. Research in computational techniques thus will include improvements in numerical analysis, parallel and scalable algorithms, and computational models.

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In the following section, we discuss the requirements and structure of an integrated modeling and simulation environment for nanotechnology simulations.

3. INTEGRATED PROBLEM-SOLVING ENVIRONMENT FOR NANOTECHNOLOGY The present level of understanding within the physics and chemistry community of the fundamental microscopic processes involved in nanoscale phenomena is generally considered to be accurate. As summarized in the preceding text, a quantum mechanical description of nanoscale phenomena can be obtained via an appropriate many-body Hamiltonian. Along with prescribed initial conditions, this Hamiltonian contains all the required information for describing the correlated motion of the electrons and nuclei in the material, when subjected to either external electromagnetic fields or thermal, mechanical, or chemical energy sources. Consequently, this mathematical model is adequate for a sufficiently accurate description of all the physical phenomena associated with the modeling, simulation, fabrication, and operation of nanotechnology components and devices. Significant limitations exist when attempting to use this microscopic physics knowledge to predict more macroscopic physical behavior required for the full system development. To realize technologically relevant quantitative description, a large number of simplifying approximations need to be introduced as described previously. In these physical models, most nanoscale-related processes are viewed as consisting of the structural, mechanical, chemical, and transport behavior of the system. As a result, apparently diverse phenomena may not be grouped together and provided with a unified characterization. The physical model-building activities in nanotechnology and the simulations that are carried out fall into two broad categories: quantum mechanical computations and classical and semiclassical approaches. The range of approaches already described do not all yield the same information for the process or system under investigation. In fact, the investigation of how the different simulation approaches properly relate to each other could constitute a major thrust for improving the state-of-the-art simulation of nanotechnologyrelated phenomena. In this context, two issues of importance are (a) under what conditions does one approach becomes invalid or requires modification and (b) when do the extra details provided by a computation incorporating only a modest number of phenomenological models become largely unnecessary. Irrespective of the level of physical model sophistication that is used for a simulation, there is a wide range of sophistication in the underlying numerical methods by which a computational model can be constructed. Indeed, enormous effort is also required to create computational models that are as computationally robust and efficient as possible, so as to produce results that are numerically convergent over a wide range of conditions and yield sufficiently accurate answers in a reasonable amount of time. The complexity of underlying numerical algorithms, as well as the ever present limitations imposed by computer resources, constitute two of the major constraints for realizing accurate physical descriptions in advanced nanotechnology modeling and simulations. Introduction of scalable parallel computing systems, on one hand, tends to alleviate the situation, but at the same time introduces an additional dimension of complexity to the design and implementation of the numerical algorithms involved.

4. PREREQUISITES FOR A SUCCESSFUL SIMULATION ENVIRONMENT For a robust technology-development environment there are three main areas that need to be addressed: (1) physical model development; (2) algorithm/software development; (3) applications and experimental verification.

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Advanced simulations call for models that are comprehensive and well grounded in laws of physics and chemistry. However, this task is rather difficult to achieve, because many of the pertinent processes involved in model development are quite complex. When confronted with such circumstances, a viable alternative is to use empirical microscopic or mesoscopic models (as discussed) and compare the results to the values obtained either from experiment or from microscopic models calculated from first principle approaches. Such models, while limited in scope, are attractive in technology development because they help to minimize the structural and operational parameter space that needs to be explored for the final device fabrication, operation, and application. A strong experimentation and characterization program thus is vital for a successful integrated environment. In reality, although preliminary efforts to perform specific carbon-nanotube-based nanotechnology experiments are underway, the computational nanotechnology at NASA Ames is not in a position to generate all such data on its own. The integrated environment, however, can contribute to the ready availability of large amounts of data to all the concerned parties through the creation of an electronic data repository where a variety of publicly available nanotechnology-related data and information can be collected and stored in a systematic fashion. Provided with an intelligent user interface, such a data base will enable the ready retrieval and analysis of pertinent information for use in aiding both technology and process model development and verification efforts. The degree of physical model complexity causes the simulation algorithms and associated software to be highly complex. Coincidently, advanced software development practices call for programs that are numerically robust, modular in nature, optimized in their execution, portable among a variety of computing systems, and easy to learn and use. Particularly from the end user's point of view, this latter criterion is one of the most desirable features that can greatly influence the extent to which a program is used for various applications. Consequently, considerable attention must be given to intelligent preand postprocessors, data storage and retrieval, and other components that are needed for a comprehensive, state-of-the-art simulation system. From the foregoing description of the essential ingredients for success, it is clear that the NASA Ames Research Center possesses the technical expertise to make significant contributions in all three critical technology areas. This is evidenced by the long-standing, internationally recognized and pioneering contributions the center has made in the areas of large-scale simulations in computational aerosciences, high-performance computing, scientific visualization, and knowledge-based expert systems. The computational nanotechnology effort at NASA Ames has also been recognized for being the first program to be established and gain credit in just a couple of years. The integrated software environment for future developments is designed to facilitate contributions in the following areas: 9 9 9 9 9 9

new physical models advanced algorithm development state-of-the-art information systems engineering scalable, high-performance computing modern data visualization and data management systems distributed computing environments

4.1. Information System-Based Problem-Solving Environment for Nanotechnology Developments A problem-solving environment (PSE) is defined as an integrated software environment that supports the complete process required to solve a problem in computational science or engineering in a user-oriented way. The PSEs can be classified into two broad categories. First are the application-domain-specific PSEs for fields such as computational fluid dynamics, semiconductor process/device modeling, and nanotechnology. The second

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are cross-disciplinary or core-problem PSEs that support more generic activities such as scientific visualization and computing tools development. A number of PSEs belonging to both categories already exist. However, these are mostly in an embryonic stage. Development of application-domain-specific PSEs is motivated by several emerging realities. First, the rapidly growing complexity of modeling and simulation software calls for more discipline and organization in the software development process. This complexity is brought about by the increasing need for high-fidelity, multidisciplinary simulations, as well as the need to develop efficient applications on a variety of state-of-the-art computer systems. Second, as the use of computer simulations in engineering design and analysis processes becomes more widespread, users spanning a broad spectrum of computational science skills need to be supported in the application-development process. In addition, the complexity of such multidisciplinary simulations demands collaborative development efforts among experts spanning highly specialized fields of computational and computer sciences. This requires a software-development environment capable of supporting effective collaboration among practitioners of diverse disciplines, some of whom may be geographically dispersed. Finally, the increasingly heterogeneous, multisite distributed computing environments that will be deployed to provide computational resources for these simulations necessitate the use of transparent resource management tools at the user level. The required technology by computer aided design (TCAD)-PSE environment should be the one in which the different component, process, and device simulators and their preand postprocessing programs interact with each other and use a common data repository. For example, the most important requirement for advanced IC or MEMS designs is that the simulation system be able to analyze realistic three-dimensional structures whose geometry either is provided directly by the designer or is derived from simulation of the fabrication process using a process flow and mask description. In a virtual design environment, a designer should be able to verify descriptions and specifications before beginning fabrication; to insure a robust design by examining device performance sensitivities to process variations, to include the dependence of material properties on process conditions; and to isolate experimental artifacts from real phenomena by correlating measured data with simulated results. The ultimate objective of such an integrated environment is to accelerate the technology development, while reducing the product-development and manufacturing costs as well. This is to be achieved by enabling the use of large-scale, multidisciplinary computer simulations in all phases of technology development. Such a computer simulation environment will allow for inexpensive and rapid experimentation with new and innovative ideas and designs without ever fabricating a prototype in the initial stages. In the past, there were several technological impediments that prevented the full realization of this vision. However, enormous progress over the last decade in information-related technologies, such as software engineering, artificial intelligence, high-performance computing, mass storage devices, networking, distributed computing, and powerful workstations capable of supporting immersive visualization environments, has now placed such virtual design environments well within reach.

4.2. Functional Requirements of a TCAD Problem-Solving Environment A TCAD-PSE is required to cater to the needs of two broad categories of customers. The first category is an individual or team of designers engaged in the concurrent and collaborative design of the nanotechnology systems. Their primary requirement is to have access to a user-friendly simulation environment to define a design problem, to represent the results in the most understandable form, and to control the execution of the program in a transparent way. The major interest will be to generate reliable results as quickly as possible and to be able to change the problem definition easily. The second category is composed primarily of researchers engaged in either advanced physical model development or the design

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and development of a myriad of simulation software and algorithms. They need an environment that is conducive to rapid experimentation and validation of either mathematical models that incorporate new physical effects or novel algorithmic ideas and computational methods that provide enhanced robustness or efficiency. In both these categories, the potential users are likely to span a continuous and a rather wide spectrum of skill levels in semiconductor and computing technologies. The two extremes of the spectrum are delineated by the so-called novice users and the expert users. A novice user is a highly skilled expert in one or more areas associated with nanotechnology with little knowledge about complex software systems, computer architectures, or programming. In contrast, an expert user has detailed knowledge in one or more areas of algorithms, physical models, software engineering, computer systems, and programming, but, in general, a relatively moderate level of expertise in nanotechnology systems or products. Based on these observations, the functional requirements of a TCAD-PSE can be summarized as follows: 9 Support a user-oriented terminology, which is highly aligned with the conceptual models, knowledge structures, and working processes commonly deployed by practitioners in nanotechnology development. 9 Permit a high degree of automation and abstraction in all phases of the simulation. 9 Allow all users to easily adapt the environment to their changing needs. 9 Provide mechanisms for expert users to easily enhance the functionality of the environment through expanded coverage of their particular area of interest. 9 Allow the expert users, if desired, to get successively more involved in the problem-solving processes at decreasing levels of abstraction. 9 Allow for rapid and flexible execution of large-scale, multidisciplinary simulations. 9 Allow users to choose among many different approaches to solve one specific problem in the most efficient way. 9 Protect software development costs by promoting reuse. 9 Enable the possibility of realizing near-optimum levels of application performance, portability, and scalability on a variety of high-performance computer systems. 9 Support the transparent use of a multisite, multimachine distributed computing environment. 9 Promote increased collaboration among members of interdisciplinary project teams. 9 Enable the rapid introduction of advanced information technologies. To realize a PSE with all these characteristics, close collaboration between computer and computational scientists with physical scientists is mandatory because the expertise of both groups is necessary for a successful implementation of the environment. Also, due to the enormous complexity of the task, a step-by-step development process that is usercentered and a p p l i c a t i o n - d r i v e n is the only viable option available.

5. APPLICATIONS The potential applications of nanotechnology, in general, and molecular nanotechnology, in particular (i.e., atomically precise control and production of materials and devices), are manifold [4, 5]. They can be broadly categorized into two classes: nanostructured materials and nanoscale devices. The nanostructured materials' refer to atomically or molecularly precise materials in which the materials' properties can be controlled by manipulating the structure of the material itself. In the ideal case there are proposals, in considerable technical detail, in which the key to the development of nanotechnology is the development

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of programmable molecular assemblers and replicators [4, 50]. The molecular assemblers are atomically precise programmable machines that can make a wide variety of materials and devices, including copies of themselves. Interestingly, living cells exhibit many properties of assemblers, because cells make a wide variety of products, including copies of themselves, and are programmed with DNA. A considerable debate exists about whether and when synthetic molecular assemblers can be made [50]. Nevertheless, the concept is simple. If such hypothetical machines are possible, then all materials could be made to atomic or molecular specification [4]. There has been considerable experimental progress in the underlying concepts as well, such as scanning-probe microscopy (SPM) tip-assisted manipulation of single atoms and molecules on solid surfaces, mechanochemical reactions, supramolecular chemistry, self-assembly of large aggregates, and synthesis of molecularly precise shapes and materials. Concurrently, there also have been recent discoveries by traditional experimental techniques in which molecularly precise extended synthetic materials (such as fullerenes and carbon nanotubes) are regularly made and manipulated. Other exotic shapes such as cones, rectangular boxes, toroids, and helical coils also have been observed. It has been proposed that these shapes could form the building blocks of shapes and structures that would go into making molecular assemblers in the future. In the second category of nanotechnology device applications, a wide variety of nanoelectronic devices, computers, sensors, and actuators should be possible. In the long term, these devices will provide system components for making miniaturized programmable machines capable of performing predetermined tasks. As previously mentioned, NASA's primary interest in nanotechnology-based materials and devices is threefold: (1) lightweight ultra-strong materials or composites for making aerospace system components; (2) nanoscale or molecular electronics, computers, sensors, and actuators; (3) low-density, high-absorption, and packing material for gas-fuel storage and carrier devices for future space missions. The integrated environment for computational nanotechnology at NASA Ames is in a nebulous stage in the sense that many of the requirements for such an environment (as already discussed) are satisfied by the existing technical expertise and computing environment. Large-scale simulations in computational aerosciences, high-performance computing and tools, scientific visualization, and knowledge-based expert systems are internationally recognized. The technical expertise in large-scale classical and quantum atomistic simulations for structural, mechanical, and transport characteristics of nanostructured materials and devices has been established. The physical models are coded and component systems are simulated. As an example, in the following section, we will discuss carbon-nanotube-based nanotechnology materials and devices.

6. CARBON-NANOTUBE-BASED NANOTECHNOLOGY: EXAMPLES Nanotubes are large linear fullerenes--close-caged molecules containing only hexagonal and pentagonal faces [51-54]. Since their discovery about seven years ago [55], carbon nanotubes (and many derivatives of fullerenes, such as nanocones, nanotips, and nanotoruses) have been investigated by both experimental and theoretical means. Many of the nanoscale fullerene materials (which are made entirely of carbon) are observed regularly in experiments, although their controlled production in large quantities and with well-defined characteristics has not been completely understood and worked out. A single-wall carbon nanotube is a rolled-up sheet of graphene made of six folded benzene-type tings. The ends of the nanotubes are capped by half-fullerenes that contain a combination of hexagons and pentagons that satisfy Euler's rule for the number of pentagons in any closed structure [51 ]. Multiwall nanotubes are more common and can be produced in bulk with current experimental techniques. Multiwall nanotubes can be thought of as a stack of graphene

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CARBON-NANOTUBE-BASED NANOTECHNOLOGY

sheets rolled up into concentric cylindrical structures, with the ends again capped by halffullerenes. A bundle or rope of single-wall nanotubes held together only by weak van der Waals forces is also possible and is regularly produced in experiments. In fact, single-wall nanotubes are produced mostly in bundles of nanotubes, which are then separated into single tubes through chemical and physical means. Figure 10 shows single- and multiwall nanotubes as well as a rope (bundle) of single-wall nanotubes held together with van der Waals forces. The single- and multiwall nanotubes are interesting nanoscale materials for three reasons: 1. A single-wall nanotube can be either metallic or semiconducting, depending on its chiral vector (n, m), where n and m are two integers. The rule is that when the difference n - m is either 0 or a multiple of 3, a metallic nanotube is obtained, whereas when the difference is not a multiple of 3, a semiconducting nanotube is obtained [51]. In addition, it is also possible to connect two nanotubes with different chiralities by introducing pentagonal and/or heptagonal defects in an otherwise all-hexagonal graphene sheet. Quasi-one-dimensional heterojunctions, including metal-metal and metal-semiconductor, can thus be expected, resulting in nanoscale electronic components [56]. 2. Single- and multiwall nanotubes have very good elastomechanical properties because the two-dimensional arrangement of C atoms in a graphene wall allows large out-of-plane distortion, while the strength of carbon in-plane bonds keeps the graphene sheet exceptionally strong against any in-plane fracture or distortion. When compressed with axial force, the single-wall nanotubules are found to buckle sideways, with a corresponding jump in the elastic energy versus applied strain curve [57]. All distortions induced in a simulation or observed in a static snapshot of experiments appear to indicate high elasticity of the nanotubes and point toward their possible use as a lightweight, highly elastic, and very strong fibrous material. 3. Whereas nanotubes are hollow, tubular, caged molecules they have been proposed as lightweight packing material for hydrocarbon fuels, as nanoscale containers for molecular drug delivery, and as casting structures for making metallic nanowires and nanocapsulates [58]. NASA's interest in single-wall and multiwall nanotubes derives from all three of the foregoing technologically interesting properties of the nanotubes and nanotube-based materials. Nanotube heterojunctions with electronic switching properties can be used to develop the next generation of computer components. Nanotubes with exceptionally strong elastomechanical properties can be used to make future generation lightweight spacecraft components as well as nanoscale probes for nanolithography in the semiconductor industry. Nanotubes as capsulates can be used to store and carry hydrogen and other hydrocarbon fuel aboarcl a spacecraft as well nanoscale target-oriented delivery of chemicals and medicine in biological systems. In the following section, we describe mechanical and material properties of nanotubes, nanotube-based electronic devices, nanotube-nanomotor, and nanotube lithography simulations performed in the NAS computing environment at NASA Ames Research Center.

6.1. Mechanical Properties and Strength Characterization of Carbon Nanotubes Molecularly perfect elongated fullerenes--carbon nanotubes--are the dream fibers for future generations of materials and mechanical engineers wishing to apply their skills in the "nano" world. Single-wall carbon nanotubes are the strongest and longest molecules realized so far. For materials characterization, however, there are multiwall nanotubes as

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Fig. 10. (a) A (10, 10) single-wall carbon nanotube. (b) A multiwall nanotube made of four concentric nanotubes. (c) A nanotube rope or a bundle.

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well as ropes of nanotubes, where 100-1000 nanotubes are produced in aligned bundles, which could have very different material and mechanical properties than either the single- or multiwall nanotubes. Dynamic simulations of the mechanical properties thus could involve anywhere from a few ten thousand atoms for single-wall nanotubes to a few hundred thousand atoms for moderate-size multiwall nanotubes and nanotube bundles. Simulations of composites or polymeric materials made of nanotubes could easily involve a few million atoms. The molecular dynamics (MD) simulations of the mechanical properties employ Brenner's many-body reactive potential [37, 60] for carbon-carbon bonding interactions and Lennard-Jones (LJ) (6-12)-type long-range potentials for nonbonding interactions [59, 60]. As the system size increases to include hundreds of thousand atoms, it is imperative that the originally written code be parallelized and implemented on NAS high-performance supercomputers.

6.1.1. Parallelization of the Molecular Dynamics Code The serial Fortran 77 code that implements Brenner's potential was originally developed by Brenner in 1990 [37, 60]. Since then it has been modified by a number of researchers. In its global structure, the code implements a more or less conventional moleculardynamics algorithm. A set of coupled, first-order ordinary differential equations, given by the Hamiltonian formulation of Newton's second law applied to a collection of atoms with well-defined potential-energy functions, is integrated forward in time using a predictorcorrector method. The major distinguishing feature of Brenner's potential is that the shortrange bonded interactions are reactive, meaning that bonds can form and break during the course of the simulation. Therefore, unlike some other molecular-dynamics codes, the neighbor lists that describe the environment of each atom must be updated frequently. The cost of the computation of the many-body bonded interactions is relatively high compared to the cost of similar methods in nonreactive algorithms with simpler functional forms. As a result, the costs of computing both the short-range interactions and the long-range, nonbonding (van der Waals) interactions are roughly comparable. Our one goal was to create a code capable of simulating large numbers of atoms, on the order of hundreds of thousands or more, on a parallel shared-memory supercomputer. This required some modifications to the serial code. The major modification is that the computation of neighbor lists, for both the short- and long-range interactions, has been implemented with a cell method instead of with the O (n 2) method of the serial code (where n is the number of atoms) [ 11]. To compute neighbor lists, a three-dimensional bounding box enclosing all atoms is determined. This volume is divided into cells of 2.5 ~ size on each side. Each cell contains a list of pointers of all the atoms that fall within its volume. A size of 2.5 ,~ ensures that the immediate neighbors of a particular atom can be found in the cells immediately adjacent to the cell of that atom. The neighboring atoms participating in the short-range interactions can be found within a distance of one cell length. The long-range interaction potential has a cutoff of 9.58 ,~, so the long-range neighbors can be found within a distance of four cell lengths. Computation of the neighbor list is parallelized through a spatial decomposition as shown in Figure 11. The spatial decomposition for force calculations, however, leads to concurrency and load-balancing problems. The force calculations, therefore, are performed through a lexical decomposition in which the computation of forces on all atoms is parallelized in a block fashion [ 11 ]. If a processor modifies the short-range force on a neighboring atom not within its lexical domain, then the incremental modification to that force is saved in a list. After all short-range force computations are done, the processors collect the force terms that modify the forces on "their" atoms. The long-range interaction function is computed such that the forces on atoms are modified independently, without affecting their neighbors, so it is not necessary to record the incremental long-range force changes of the neighbors. The parallel implementation of Brenner's potential MD code is designed to run on Silicon Graphics Inc. (SGI) SMPs (symmetric multiprocessors) and on the SGI Origin 2000

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(a distributed s h a r e d - m e m o r y system). The scaling of the code for a system containing 84,480 atoms on the SGI Origin 2000 c o m p u t e r for using up to 32 processors is shown in Figure 12. The scaling is good up to 16 processors and then starts to level off for this system. The systems including more atoms show better scaling for an even greater n u m b e r of processors.

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6.1.2. Dynamic Deformation of Single- and MultiwaU Nanotubes The static elastic properties are strongly determined by the nanotube radii and weakly by the helicity. Simulations of single-wall nanotubes undergoing dynamic deformation have been performed, and results have been compared with the continuum theory shell-model description [57]. Three types of dynamic deformation--axial compression, bending, and torsion--of the single- and multiwall nanotubes were performed. The results of single-wall nanotube deformations are similar to those reported earlier by Bernholc and co-workers at North Carolina State University [54, 57, 61]. Comparisons of the single- and multiwall nanotube compression, bending, and torsion are shown in Figures 13, 14, and 15, respectively. The general observation is that for axial compression, the single-wall nanotube is stiffer than the multiwall nanotubes. The single-wall tube goes through sudden instabilities, within elastic limits, during which symmetric pinching modes are observed as shown in

Fig. 13. (a-c) Single- and (d-f) multiwall nanotubes under axial compression. The arrows indicate localized deformationmodesand are explained in the text.

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Fig. 14. (a-c) Single- and (d-f) multiwall nanotubes under symmetric bend. Details of the bending deformations are explained in the text.

Figure 13a. The symmetric pinching modes mean that the tube is symmetrically pinched at a series of locations such that successive pinches are orthogonal to each other. For example, two successive orthogonal pinches in Figure 13a are marked in the figure. The randomly distributed pinching modes start to coalesce at a few points where sideways buckling occurs (shown by arrows in Fig. 13b). On further compression, all the strain gets redistributed and accumulated at the extreme points of the sideways buckled structure (shown by arrows in Fig. 13c). When the tube is compressed further, all the strain gets accommodated at the sites shown in Figure 13c. As the tube was allowed to relax by the removal of the strain, it was found to have gone through plastic deformation at the spots shown by the arrows in Figure 13c. The magnitude of the sideways buckling of the multiwall tube is less than the corresponding values for the single-wall tube (Fig. 13d-f). The inner walls of the multiwall tube tend to support each other against the external deformation. Characteristic

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Fig. 15. (a-c) Single- and (d-f) multiwall nanotubes under torsional twist. Details of the torsional deformations are explained in the text.

surface modes exhibiting diamond patterns during the deformation of the multiwall tube are also observed, indicating that the middle layers are constrained by the outer and inner surface layers (Fig. 13d). The localized plastic failure of the multiwall tubes occurred at the spots shown by the arrow in Figure 13f. Even though the multiwall nanotube deforms less than the single-wall nanotube for the same amount of strain, we found that the multiwall nanotube breaks (plastically deforms) under less strain, too. The bending deformation of the tube shows a single symmetrically kinked structure at a gradual bending angle (Fig. 14a) that undergoes further changes as the tube is bent more. The single symmetric kinked structure is similar to that observed earlier in experiments and computer simulations [61 ]. Striking differences occur on further bending of the tube. One to three spherical nodal structures are observed in the bending kink as the tube is

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almost doubled onto itself. For example, Figure 14b shows a single spherical node in the center of the kink and Figure 14c shows a three node structures at the kink. The nodal structures in the kink are due to elongated nature of the kink in our simulation as compared to earlier work [61], where a shorter tube was used in simulations. The nodal structures are due to the instabilities in the elongated kink because the outer wall of the tube with positive curvature is stretched and the inner wall of the tube with negative curvature is compressed. Compression of the inner wall in the extended kink leads to instabilities in the compressed section, as discussed before. The half-spherical nodal structures are the resultant configurations that would occur only when one side of the tube is compressed and the other is not. The multiwall tube bending is more gradual, and a multikink structure is observed at low bending angle. The multikinks coalesce into two kinks and one nodal structure as observed before [61 ]. The size of the node and location of the two kinks is determined by the tube diameters and the number of tubes used in the simulations. The nodal structure, on detailed examination, reveals a symmetric pinch in the center, indicating that the tube wall with negative curvature is locally compressed at the position of the bend. The torsional deformation of the single-wall tube resulted in flattening of the tube in a ribbonlike structure (Fig. 15b) with all the strain located at the edges of the ribbon (Fig. 15c) [57]. On further twisting, the flattened tube starts to wrap onto itself. The multiwall tube twists or undergoes torsional deformation without much flattening because the inner walls resist flattening of the outer walls (Fig. 15e). Traveling surface wave modes are observed in the simulation. The surface modes are initiated at the ends and travel toward the center as the multiwall tube is gradually twisted. A characteristic stationary interference (of the traveling surface modes) pattern is observed in the center of the tube (Fig. 15a). The velocities of the traveling mode can be measured and used to estimate the Young's modulus of the multiwall tube. The estimated Young's modulus, 0.61 TPa, is comparable with the Young's modulus calculated by other techniques [62]. A correlation between the electronic properties of the single and multiwall nanotubes and the demonstrated mechanical deformation is under investigation for their use as nanoscale electromechanical sensors. A correlation between the accumulated strain energy at a mechanically deformed location and the chemical reactivity of the location is also currently under investigation and will be published elsewhere [63]. 6.2. Carbon-Based Molecular Electronics At the present pace of miniaturization in the current silicon-based microelectronics technology, the size of a typical electronic device is halved every three years. How far can one go along this road? Although devices contain small material domains and their junctions, each domain and junction basically reflects the electronic properties governed by mesoscopic or macroscopic counterparts. The traditional route to miniaturization, therefore, should reach a limit when the device and feature sizes start to reach 10-50-nm scale, because quantum effects become dominant and materials behave differently. Quantum effects, however, can be specifically made use of in devices based on exotic computing architectures and algorithms. Nanotubes are metallic or semiconducting, depending on their underlying network topology [51, 64-70, 72]. Recent experimental measurements on conductivity and density of states in single-wall nanotubes (SWNTs) have confirmed the initial theoretical predictions. The conductivity measurements of micrometer-long nanotubes show their behavior to be like quantum wires, indicating that the electronic transport through SWNTs is ballistic in nature. The possibility of connecting nanotubes of different diameter and chirality has generated considerable interest recently [56, 71-74], because of the possibility of using the junctions as building blocks for nanoscale electronic devices. The simplest way to connect two dissimilar nanotubes is via the introduction of a pentagon-heptagon pair in an otherwise perfect hexagonal graphene sheet. The resulting structure still contains threefold coordination for all carbon atoms forming the junction.

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In reality, nanotubes have finite lengths and, in most cases, tend to be closed with fullerene caps. The closure introduces a small gap in the electronic structures of these tubes. Also, formation of tube junctions results inconsiderable local strain, which is relieved by the relaxation of the atoms. The relaxation is also expected to alter the electronic structure and local density of states (LDOS) of the atoms that form the junction and their neighbors. Although several theoretical models have been used to study nanotube heterojunctions, most of them tend to ignore the effects of relaxation altogether. We have investigated the effect of symmetry-unconstrained relaxation of the nanotube heterojunctions on the structural and electronic properties using the generalized tight-binding molecular dynamics (GTBMD) scheme of Menon et al. [75]. The GTBMD makes explicit use of the nonorthogonality of the orbitals to treat interactions in covalent systems. The method has been found to be very reliable in obtaining good agreement with experimental and local density approximation (LDA) results for the structural and vibrational properties of fullerenes and nanotubes [75, 76]. Additionally, GTBMD was applied earlier to obtain equilibrium geometries for small carbon clusters [77], in good agreement with ab initio [78] results for the lowest energy structures of carbon clusters of sizes up to N = 10 (for which ab initio results are available).

6.2.1. Two-Half Nanotube Junctions We first consider simple two-point junctions of dissimilar tubes. All the tubes have been capped with fullerenes of suitable sizes. We begin with an approximate structure and relax it using the GTBMD scheme. This ensures that the geometry obtained is at least a local minimum of the total energy. In all cases, the relaxed structures had threefold coordination for all carbon atoms. Connecting nanotubes with different chiralities gives rise to the formation of stable quasi-one-dimensional heterojunctions. For example, both (9, 0) and (5, 5) tubes are semimetals. The (9, 0) tube has a zig-zag configuration, whereas the (5, 5) tube has an armchair configuration. The tube junction shown in Figure 16a is made up of a (9, 0) tube at the top and a (5, 5) at the bottom. The connecting angle is rather large (35~ owing to the change in chirality in crossing the junction. This is achieved by placing a pentagon-heptagon pair symmetrically on opposite sides of the knees (behind and in front, respectively). The carbon atoms that form the pentagon and the heptagon are shown as filled balls in in the figure. Earlier work on this junction using a simplified molecular mechanics model yielded a bending angle of 40 ~ [71 ]. The average bond length in the pentagons that form the junction is 1.438 A and the average bond length in the heptagon is found to be 1.436 A. The (10, 0) tube is semiconducting, whereas the (6, 6) tube is a semimetal. Again, because the junction connects a zig-zag tube with an armchair tube, the bending angle is expected to be relatively large. As in the (9, 0)-(5, 5) case, the pentagons and the heptagon are at the opposite sides of the knee. Optimization using a simplified molecular mechanics model gives an angle of 37 ~ [71 ]. The GTBMD relaxed junction is shown in Figure 16b. The (10, 0) tube is at the top. The bending angle obtained is 34.8 ~ The average bond length in the pentagons that form the junction is 1.436 A and the average bond length in the heptagon is 1.439 A. In Figure 16c we show electronic energy levels for the capped (10, 0), (6, 6), and (10, 0) + (6, 6) junction. As can be seen in the figure, the introduction of the states in the gap for the combination is due to the defects at the junction. The small gap seen for the metallic (6, 6) tube is due to the capping. Nanotubes can also be connected through quasistraight or straight junctions. The (8, 0)(7, 1) tube junction illustrates the joining of a semiconducting zig-zag tube with a metallic chiral tube. Here the bending angle is small because the C-C bonds do not undergo any major change in orientation in crossing the junction. The small bending angle is realized by placing a pentagon and heptagon adjacent to each other. This heterostructure was first investigated by Chico et al. [56]. The GTBMD relaxed junction is shown in Figure 17a. The

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(b)

(a)

.~

(9,0)

O)

(6,6)

(c)

-6.0

-8.0

-i0.0 (i0,0)

(i0,0)+(6,6)

(6,6)

Fig. 16. Two terminal bent nanombe heterojunctions. (a) Metal-metal nanotube heterojunctions for (9, 0) and (5, 5) tubes. (b) Semiconductor-metalnanotubejunction between (10, 0) and (6, 6) nanotubes. (c) Energy levels for isolated (10, 0) and (6, 6) nanotubes in comparisonwith the energy levels of the (10, 0)-(6, 6) bent heterojunction.

bending angle obtained is 3.8 ~. The bending angle, however, can be changed by changing the relative orientation of the pentagon and heptagon with respect to the tube axis. The angle is at a minimum when both the pentagon and the heptagon are aligned parallel to the tube axis. Chico et al. [56] found the value of the bending angle to lie between 0 and 15 ~ depending on the particular case. The average bond length in the pentagons that form the junction is 1.441 ~ and the average bond length in the heptagon in found to be 1.426 A. Finally a straight (12, 0)-(11, 0)junction is shown in Figure 17b. The (12, 0) tube is semimetal and the (11,0) tube is a semiconductor. Additionally, both tubes are zig-zag. Whereas the C-C bonds along the tube axis do not undergo any change in orientation in

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Fig. 17. Examples of two terminal quasistraight nanotube heterojunctions: (a) (8, 0)-(7, 1) junction; (b) (12, 0)-(11, 0) junction.

crossing the junction, the connection is straight. The diameter-changing bend can be realized by placing the pentagon-heptagon pair along the tube axis with a shared edge, as shown in Figure 17b. This structure was first proposed in [71], where a conventional orthogonal tight-binding molecular dynamics method was used to relax the structure. The average bond length in the pentagons that form the junction was 1.439 ]k, whereas the average for the heptagons was found to be 1.433 ~. The GTBMD relaxed junction is shown in the figure. The average bond length in the pentagons that form the bend is 1.436 A and the average bond length in the heptagons is 1.434 ~. Charlier et al. [71] used periodic boundary conditions to repeat the structure, whereas isolated capped tubes were used in the present work. We chose to work with capped tubes because tubules observed in experiments tend to be closed with fullerene caps. Additionally, caps can be used to functionalize the junction and achieve interconnectivity if these devices are ever realized in experiments. Collins et al. [79] reported an experimental, functioning carbon-nanotube device based on nanotube heterojunctions in a rope. Rectifying characteristics of a functioning device were demonstrated, but the structure of the device (in a sample of nanotube ropes) was not clear.

6.2.2. Three-Half Nanotube Junctions In general, there are two kinds of elemental device structures: two terminal and three terminal. The diodes and rectifying switches are two-terminal devices. The transistor is a threeterminal device with a variety of structures, materials, and basic functional materials [80]. The nanotube-nanodiode reported by Collins et al. is a kind of two-terminal rectifying device [79]. The three-terminal (three-half nanotube) junctions of single-walled carbon nanotubes could be used as building blocks of nanoscale tunnel junctions in a twodimensional network of nanoelectronic devices. As a prototype of such junctions, we study

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the "T-junction" formed by fusing two nanotubes of different diameter and chirality perpendicular to each other [81-83]. The T-junctions provide a challenge to the conventional rules applicable to tube bends. This is because, unlike the knee joint, where one can clearly define the opposite sides of the joint as either the front or the back, both sides of a T-junction are topologically equivalent. As a result, we can expect a net excess of heptagons over the pentagons at the junction. Furthermore, whereas the bending angles at a two-point tube junction depend on the tube parameters (diameter and chirality) of both the component tubes, no such dependence exists for the T-junction, where the angle remains fixed at 90 ~. We explore an alternative route to the formation of T-junctions that is not constrained by the usual heptagon-pentagon defect pair considerations [81]. In particular, we examine a metal-semiconductor-metal T-junction, namely, the (5, 5)-(10, 0)-(5, 5)junction shown in Figure 18a. The structure is composed of 314 atoms. The numbers chosen are sufficiently large to avoid the effects of the dangling re bonds at the edges on the junction. The (10, 0) tube is semiconducting and the (5, 5) tube is a semimetal. The (5, 5) and (10, 0) tubes have armchair and zig-zag configurations, respectively. As seen in Figure 18a, in going across the junction from the (10, 0) side to the (5, 5) side, the orientation of the C-C bonds remains unchanged. Interestingly, the junction thus formed contains six heptagons and no pentagons at the junction. As in the simple junction case, the T-junction shown in the figure was also fully optimized without any symmetry constraints using the generalized tight-binding molecular dynamics (GTBMD) scheme [75]. The starting configuration has twofold coordinated atoms at the open ends of the armchair and zig-zag tubules. The twofold coordinated atoms in the armchair configuration are within strong bonding interaction range of each other. The GTBMD relaxation results in the closure of the tube at the armchair ends. No such closure results at the zig-zag end because the twofold coordinated atoms are sufficiently far from one another. The average bond lengths in the heptagons and hexagons at the junction are found to be 1.427 and 1.419 ,~, respectively. The room-temperature stability of this junction was also tested in a classical MD simulation employing Brenner's reactive hydrocarbon potential [37]. The junction was found to be quite stable for the entire duration of the simulation. Additional investigations regarding its stability against externally applied strains are currently being pursued. The Fermi levels of the (5, 5) nanotube lie within the gap of the (10, 0) semiconducting tube. The T-junction forms a microscopic tunnel junction, made up entirely of carbon atoms, through which electrons can cross by quantum mechanical tunneling. The tunneling current can be controlled by application of a potential difference that raises the chemical potential of one side with respect to the other. Whereas the tunneling currents have been observed to obey Ohm's law, the T-junctions can thus form one of the smallest microscopic Ohmic resistors. Furthermore, either n- or p-type doping of the semiconducting portion of the T-junction should yield Schottky-barrier-type devices. We investigated the local density of states (LDOS) using the tight-binding 7rband approximation. Only nearest-neighbor interactions were considered, with Vppzr = 2.66 eV [67]. Figure 18b shows the LDOS for the relaxed (5, 5)-(10, 0)-(5, 5) structure at various cross sections indicated in Figure 18a. The LDOS for the panel labeled stem, for example, is for the cross section containing 20 atoms zig-zagging along the circumference of the semiconducting (10, 0) portion. As can be seen in the figure, in going from the semiconducting side into the junction, localized states begin to appear in the gap. Detailed study indicates their origin to be the heptagonal defects present in the neck region. These defect states may pin the Fermi level of the system. The implications of these findings are intriguing. The T-junctions defy the conventional arguments made in favor of equal number of heptagon-pentagon defect pairs for the stability of dissimilar tube joints. As shown here, T-junction joints can be made without the incorporation of pentagons. The presence of large localized states in the gap that can pin the Fermi level has interesting implications for complex device modeling. Furthermore, the T-junctions can be used as "universal

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Fig. 18. (a) The (5,5)-(10,0)-(5,5) "T-junction?' Carbon atoms forming the heptagons are shown as light grey balls. (b) Local density of states (LDOS) for the relaxed (5, 5)-(10, 0)-(5, 5) structure at various cross sections indicated in (a) showing the increase in the defect-induced localized states in the gap as the junction is approached.

joints" for forming a two-dimensional network of tubes in which conduction pathways can be controlled. Other complex three- ("T" and "Y") and four-point "X" junctions have also been created and studied with the G T B M D method [81-83]. Controlled realization of the previously discussed "T, Y, X junctions" could move us into an era of truly molecular electronics devices. A room-temperature transistor [84] made from a single carbon nanotube, lying on metal electrodes for source and drain terminals, and gate voltage supplied by the back silicon gate insulated by SiO2 layers, has been demonstrated recently as proof of principle for carbon- or hybrid carbon/siliconbased molecular electronics technology. The uncertainty about nanotube/metal contacts and the limitations of lithographic techniques to fabricate such contacts still remain. Three-

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terminal fully carbon junctions with controlled doping in between would be the model for the next generation of carbon-based nanoelectronics.

6.3. Nanoscale Electromechanical Systems A correlation between the electronic properties of single- and multiwall nanotubes and the mechanical deformation shown herein is under investigation, and could easily form the basis for their use as nanoscale electromechanical sensors as shown schematically in Figure 19. Preliminary results for this correlation and characterization seem promising [85, 86]. More work, however, is needed to study the effects of mechanical deformation on the conductance characteristics of the nanotubes, especially with more accurate methods and better characterization of deformation-induced defects. Additionally, pure nanotubes could be doped substitutionally or with chemical functionalization to tailor the electronic properties in the first step and their correlation with the mechanical properties in the second [85, 87]. The device phase space of the schematics shown in Figure 19 is quite large, and work to search it with computer simulations has just begun. Other types of nanoscale electromechanical systems (NEMS) are molecular machines that would be nanoscale molecular bearings, shaft-and-gear systems, and multiple-gear systems. Such a machine would operate by powering the input component from an external source, with the resulting rotational or translational motion used to do mechanical work by the output component. In the initial stages, a few examples of molecular gears, such as diamondoid molecular planetary gears [4], fullerene gears [88], and carbon-nanotube gears [89], have been designed and simulated. In the carbon-nanotube gears, as shown

Fig. 19. Schematicsof the correlation between the mechanical deformation of a nanotube with the changes in the electronic properties at the resultant kink sites. A positive correlation could be used in the application of nanotubes as nanoscale electromechanical system(NEMS) components.

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Fig. 20. A carbon-nanotube-based gear with positive and negative point charges in the powered (left) gear. in Figure 20, benzyne molecules bonded to a carbon nanotube form teeth, whereas the nanotube forms the body about which the gear rotates. Through structural and dynamical calculations using the ab initio electronic structure and analytic Brenner [37] reactive hydrocarbon potential methods, respectively, Jaffe et al. [90] showed that carbon-nanotube gears are simple in structure and could be synthetically accessible as well. Moreover, using molecular dynamics simulations with the Brenner potential, Han et al. [89] have shown that stable rotations of the driven gear are possible with forced rotations of the powered gear. The benzyne molecular teeth do not break and suitable operating conditions for uniform rotations of the powered and driven gears can be identified. The powering of such molecular gears or other motors can be accomplished with an external electric field or lasers, which can supply a local electric field to the system. The first simulations of the laser-driven molecular motor, such as graphitic molecular bearings, were reported by Tuzun et al. [91]. The molecular bearings were formed by rolling two graphite sheets into two concentric cylindrical tubes. This structure is not a multiwalled carbon nanotube because the spacing between the tubes is much larger than the experimentally observed value for carbon nanotubes. The external tube was held fixed, while the internal tube was allowed to move under the forces of interaction between the applied laser electric field and two unit charges, one positive and the other negative, fixed on the circumference of the inner tube. A wide range of operating parameters, such as laser frequency and power, molecular bearing sizes, and the positions of the charges within the molecular bearing, were investigated for stable unidirectional rotations of the inner bearing tube. For a single applied laser field under all investigated operating conditions the bearing oscillated with positive and negative angular velocities; that is, for some time it would rotate in one direction and then would rotate in the opposite direction. Under two applied laser fields, the duration of unidirectional rotation was increased and an attempt was made to find the optimal set of operating parameters with a neural net simulator. A simplified heuristic model for the laser-induced rotational dynamics of the gear system shown in Figure 20 has been proposed and verified through MD simulations [92]. The

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rotation of a carbon nanotube or a nanotube gear due to interaction with a laser electric field is accomplished through the forces of interactions between free charges in the body of the tube and the applied laser electric field. An "intrinsic" frequency of the gear/laser interaction dynamics has been derived in terms of mass, radius, moment of inertia, and laser field strength. It tums out that if the frequency of the laser power source is in quasiresonance with the intrinsic frequency of the motor system, it is possible to rotate the motor unidirectionally with the laser electric fields, as shown in Figure 21a. If the laser field frequency is much less than the intrinsic frequency of the nanotube or the gear, the motor shows rotational oscillations with positive and negative angular velocities. When the laser field frequency is on the same order of magnitude as the intrinsic frequency, however, a quasiresonance between the nanotube oscillations and the laser field oscillations is established. If the phases of the two oscillations are also properly matched, a unidirectional rotation of the nanotube (though with accelerating and deaccelerating angular velocities) is possible as shown in Figure 21 a. The inertial damping effects of the driven-gear rotations on the powered-gear rotations can be used to reduce the fluctuations in the magnitude of the

Fig. 21. Unidirectionalrotations of the nanotube gear with a 140-GHz laser field. The angular velocities are plotted in number of rotations per picosecond, and angular rotation between 0 and 1 has been shifted to be between 0.5 and 1.5 for clarity. (a) Rotational dynamics with a CW laser field and (b) with a pulsed laser field.

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rotational angular velocity of the entire system. The laser power needed to turn these motors on is in the gigawatt to terrawatt range. The power delivered to a target, however, can be boosted by using pulsed laser beams. The effect of pulsing the laser field has also been investigated. As long as the phase coherency is maintained between the external laser field and the motor rotations, the pulsed laser field also can be used to power the motor as shown in Figure 2 lb. The details of the dynamics essentially remain same. In fact, it was noticed that pulsing of the field can be used to drive the same motor at a lower temperature than possible with a continuous wave (CW) laser field [93]. A word of caution, however, is in order. The reliability of classical potentials for applications in environments very different from the ones used in fitting their parameters is generally not established. The simulations for nanoscale electromechanical systems, therefore, should also be compared with those based on quantum mechanical methods. Using a quantum GTBMD method, other carbon-based clusters--gearoids--have been proposed [94], which probably could also be powered in a similar way. With the synthesis and production of new nanoscale materials, such as fullerenes and carbon nanotubes, it is possible to think of other ways in which electronic, mechanical, and chemical properties can be coupled in clever ways to come up with other designs of nanoscale electromechanical, and chemical sensors and actuators. The field is just beginning, and simulations have a major role to play in the developments.

6.4. Nanotube Nanolithography Lithography plays a key role in semiconductor manufacturing. Currently, surface patterning is achieved by means of optical lithographic techniques. However, with the industry moving toward the fabrication of semiconductor devices with feature sizes of 100 nm and less [95], the ability of even deep ultraviolet (193-rim) light sources will be exhausted due to the absence of optically transparent materials at wavelengths significantly shorter than 193 rim. The technological community is, therefore, actively searching for alternative approaches to materials fabrication at nanoscales. Future quantum and molecular electronics, compatible with the current Si-based technology, will be realized only with the development of controlled nanolithography and nanodeposition techniques. Among several alternatives to optical lithography are the use of high-resolution-laser direct writing to structure silicon on the nanometer scale [96], electron-beam lithography [97], and scanning-probe microscopy (SPM) tip-based lithographic methods [98]. SPM has been shown to be a powerful tool for the manipulation of individual atoms and molecules at the nanometer scale. Using SPM, researchers have demonstrated controlled manipulation of atoms for creation of quantum corrals and quantum dots [99-102]. Individual atoms have been removed from surfaces [ 103], and one-dimensional metal wires have been assembled [98]. The main difficulty faced in these studies is that the SPM metallic tips often break following direct collision with the solid surface. Therefore, alternatives to the metallic tips need to be explored. A recent experimental advance is the use of carbon nanotubes as nanotip probes by mounting them on top of the silicon cantilever of an SPM [ 104]. The nanotubes are both of single- and multiwall types, and have unique elastomechanical properties. These are the strongest material known along the axial direction and yet are highly elastic and flexible along the radial direction [7]. The carbon-nanotube tips--sharp to within few nanometer scale--may be ideally suited for nanolithography on soft semiconductor surfaces such as silicon and germanium. Nanotube nanolithography, however, may have a long way to go before an acceptable technique emerges because of low throughput expected in singleprobe tip-based lithography. Concurrent advances made in the ability to put multiple, parallel (up to few hundred) tips on a probing or lithographing arm may enable nanotube nanolithography as a viable technology. On the theoretical side, several groups have undertaken atomistic simulations of tip-surface interactions using models of metallic or diamond tips [37, 105-109]. Not much work has been done to simulate the dynamics of

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Fig. 22. Nanoscale etching of a diamond surface by a chemically modified carbon-nanotube tip: (a) chemically modified tip approaching the surface; (b, c) the transition state for the etching reaction; (d) a carbon dimer from the surface etched awayby the tip.

nanotube tip-surface interactions for nanodeposition and nanolithographic applications. As shown in Figure 22, we have simulated the possibility of selective etching of a diamond surface using a carbon-nanotube tip chemically modified with a C2 species attached to the end cap of the tip [ 110]. A single dimer of carbon atoms is etched out of the surface by the tip, and the main result is that the strongly bonded C2 chemical species is able to etch a weakly bonded C2 dimer from the surface. This raises the possibility that one can perhaps use a bare nanotube, made of strong C-C covalent bonds, for nanolithography on comparatively weakly bonded soft semiconductor surfaces such as silicon and germanium. Apparently, the production of bare-nanotube tips should be significantly simpler than production of chemically modified tips. The bare-nanotube nanolithography is also expected to be simpler than the cases where additional voltage is supplied to assist in lithography [104, 111, 112]. The nanolithography parameters are entirely determined by the mechanical properties of the tips, and many of the complications involved in controlling the electronic behavior of the tip can be overcome.

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Two types of simulations are performed [113]. In the first scenario, chemical reactions between the nanotube and the silicon surfaces are induced with minimum possible disturbance of the bulk of the surfaces. To accomplish this, the nanotube is moved toward the surface at a fixed rate until it barely (chemically) touches the surface, and then it is pulled back with the same or slower rate. In the second scenario, the nanotube tip is lowered and pushed down so as to penetrate the surface like a knife and then pulled back to create a nanohole in the surface (nanoindentation). The results also are separated into two classes. In the first case of surface-selective etching (Fig. 23), the simulation results in the removal of one of the silicon dimers from the surface, while the remaining surface is disturbed minimally. In the second case of surface penetration or indentation, Figure 24 shows the moment when the nanotube has penetrated inside the silicon surface. The nanotube more or less preserves its original shape. The retraction of the nanotube causes

Fig. 23. Nanoscaleetching of a Si(001) (2 • 1) surface by a carbon-nanotube tip: (a, b) side views of a carbon nanotube first touching the surface and then removing Si dimers from the surface; (c, d) the residual Si surface after removal of one dimer and the removed dimer on top of the tip, respectively.

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Fig. 24. Nanoindentationofa Si(001) (2x 1) surfaceby a carbon-nanotube tip: (a) side view ofa carbonnanotube tip indenting the silicon surfaces where the tip has penetrated the surface by up to 6/~, while completely preserving the shape of the tip; (b) view of the tip pulled back from the surface; (c) a nanoscale hole with minimal disturbance to the rest of the surface; (d) silicon atoms from the top and inner layers removedby the tip.

absorption of both the surface and bulk silicon atoms at the nanotube tip. At the end of simulations, the internal structure of the silicon surface is strongly altered in the interaction region, although no apparent "hole" is observed due to the "healing" thermal motion of bulk surface atoms (Fig. 24c). We believe that this situation might change for surface penetration with either larger diameter or multiwall nanotubes, or with a bundle of parallel nanotubes. The effects of larger surface/substrate size with multiwall nanotubes, ropes, and arrays of nanotubes are also being explored and will be needed before this technique is fully developed and useful for practical cases.

7. C O M M E N T S Nanotechnology is poised to move beyond a mere dream of the 1990s, to become an enabling technology of the 21st century. Once derided by some as a buzzword or an overhyped passing fad, nanotechnology is attracting increasing interest. Universities are

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establishing interdisciplinary programs. The governments of some technologically advanced countries, such as the United States and Japan, are funding research in nanotechnology. There are even a few start-up companies pursuing speculative ventures. Most importantly, there have been some impressive scientific discoveries and engineering developments, many of which have been described in this review. New technologies typically follow paths unanticipated by the visonaries who first conceive them, and nanotechnology is probably no exception. However, while we cannot be certain what nanotechnology will look like in the 21 st century, we can make plans to foster its development. This chapter is intended to define the requirements of a TCAD-based environment in which the basic concepts behind nanotechnology can be investigated. This involves developing physical models of nanoscale objects and conducting large-scale simulations to test the validity of these models under realistic physical and chemical conditions. The nanoscale objects then can be investigated for structural, mechanical, electronic, and transport behavior, and their integration into larger systems can be studied. Simulations of larger systems of many nanoscale devices working together could easily involve 10-100 million atoms. The NAS Systems Division at NASA Ames Research Center has provided some of the key features of an integrated modeling and simulation environment for nanotechnology. In its relatively short existence (about two years), the Computational Nanotechnology Group at NAS has achieved significant results and has been awarded the 1998 Feynman Prize in nanotechnology (theory) by the Foresight Institute. We have presented as examples of this work the results of carbon-nanotube simulations. The application simulations have been divided into four categories: mechanical and materials properties of nanotubes; nanotube heterojunctions as molecular electronic device components; nanoscale electromechanical systems and a laser-driven molecular motor; and nanotube-based nanolithography on silicon surfaces. The possible applications of nanotechnology are many and are not limited to those discussed herein. The applications of nanostructured materials and device components are just starting to be conceived and simulated. The applications of molecular nanotechnology via molecular assemblers or replicators have not been addressed because these concepts are at more rudimentary stages.

Acknowledgments This work was supported by MRJ Inc. under NASA contract NAS2-14303. MM acknowledges support from the National Science Foundation grant OSR 94-52895 and the University of Kentucky Center for Computational Sciences.

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Chapter 15 WAVE-FUNCTION ENGINEERING: A NEW PARADIGM IN QUANTUM NANOSTRUCTURE MODELING L. R. Ram-Mohan Worcester Polytechnic Institute, Worcester, Massachusetts, USA

I. Vurgaflman, J. R. Meyer Naval Research Laboratory, Washington, DC, USA

D. Dossa Lawrence Livermore Laboratory, Livermore, California, USA

Contents 1. 2. 3.

4.

5.

6.

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Novel Localization in Layered Heterostructures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1. Quasibound States . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2. Surface Quantum-Well Confinement and Above-Barrier Localization . . . . . . . . . . . . . . . Design of Layered Heterostructure Optoelectronic Devices . . . . . . . . . . . . . . . . . . . . . . . . 4.1. Type-II W Laser . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2. Interband Cascade Laser . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3. Second-Harmonic Generation with Phase-Matching Regions . . . . . . . . . . . . . . . . . . . . Quantum Wires and Two-Dimensional Superlattices . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1. Bound States in a Rectangular Quantum Wire . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2. Finite-Element Analysis of the Quantum Wire . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3. Symmetry Properties of the Square Quantum Wire . . . . . . . . . . . . . . . . . . . . . . . . . 5.4. The Checkerboard Quantum Wire Superlattice . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.5. Quantum Wires of Arbitrary Cross Section . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

707 710 712 712 713 716 717 720 724 728 728 728 729 731 733 735 736 736

1. I N T R O D U C T I O N In t h e s t e a d y m a t u r i n g o f t h e n a n o t e c h n o l o g y f o r q u a n t u m s e m i c o n d u c t o r h e t e r o s t r u c t u r e s , t h e r e a r e r e c o g n i z a b l e m i l e s t o n e s in t h e c o n c e p t u a l d e v e l o p m e n t s a n d t e c h n i c a l a c h i e v e m e n t s t h a t h a v e b e e n r e p o r t e d in the l i t e r a t u r e . T h e E s a k i - T s u p r o p o s a l [ 1 ], t h a t o n e c a n

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impose a superperiodicity in the crystalline growth of layered semiconductors clearly represents such a milestone: It demonstrated that one can modify, at a very fundamental level, most of the electronic and optical properties of semiconductors through heterostructure layering. Using molecular beam epitaxy (MBE) and metallorganic chemical vapor deposition (MOCVD) [2, 3], artificially grown layered semiconductor structures, such as superlattices and quantum wells, may be obtained through a modulation of the material composition along the growth axis. When ~ 100-,~ layers of different materials, for example GaAs and A1GaAs, are juxtaposed one on top of another, the natural or bulk band gaps of the individual layers will generally not align with the adjacent ones. An electron in the conduction band of the GaAs layer will then confront a barrier in the adjacent A1GaAs layer. Such confinement, through the Heisenberg uncertainty principle, leads to a raising of the conduction band edge of the heterostructure. A similar effect occurs for the carriers in the valence bands, leading to an overall change in the band gap of the heterostructure. Commercially significant examples of the wide array of optical and electronic devices that are based on quantum mechanical phenomena in semiconductors include the double-barrier resonant tunneling diode [4], the quantum-well diode laser [5, 6], and the high-electronmobility transistor (HEMT) [7]. Whereas the degrees of freedom in forming heterostructures include material composition, layer thicknesses, strain, growth direction, and so on, it is clear that these properties can be manipulated within a range of possibilities. This notion led Capasso and coworkers [8, 9] to propose the concept of "band-gap engineering," which has provided the modus operandi in designing and growing multiple quantum wells, superlattices, graded energy gap materials, and the like, and in envisioning novel applications for such structures. The manipulation of the subband edges through the appropriate selection of layer thickness and material parameters, and the control this provides in altering the optical properties of the heterostructure have been a central focus of research in semiconductor heterostructures over the past two decades. This was made feasible because of remarkable advances in the technology of molecular beam epitaxy. The implementation of this control over the conduction and valence band edges and hence the energy band gap in the composite semiconductor may be considered a second milestone in the nanotechnology of semiconductor heterostructures. Over the past decade, ongoing improvements in growth that allow control down to the atomic scale, coupled with rapid advances in device fabrication technologies, have encouraged a trend toward increasingly complex structural configurations. Fortunately, recently developed modeling techniques provide the flexibility to explore such complexities through numerical simulations. This has led to the crystallization of the concepts that may be referred to as "wave-function engineering" [10]. This third milestone, in terms of fundamental shifts in paradigms, is providing a lodestone for directing efforts toward formulating new electronic mechanisms and concepts, exploring basic physics, and designing new optoelectronic devices. The aim of this chapter is to describe the computational aspects, present the basic physics of heterostructures derived from the application of this paradigm, and display results from recent research. We should note that for over a decade there have been sporadic references to the idea and potential of wave-function engineering [11-16]. However, a full realization of the concept required an implementation of advanced software tools that allow one to explore issues associated with optimizing heterostructure design for specific applications [ 17-27]. This advance has not been merely in modeling; in fact, heterostructures grown to specifications for individual applications have performed as promised. We provide examples of this remarkable synergism between modeling, growth, and experimental characterization, which are the three facets of the efforts toward bringing new devices from conceptual development to the feasibility stage and toward commercialization. The interpretation of the experimentally observed optical properties of heterostructures requires that we understand the effects of layer thicknesses and material properties of the

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layers. The analysis of the data is usually done by modeling the structure using computer calculations for the actual energy levels and energy bands in the system. This intertwining of modeling and simulation with experimental characterization is a feature that has become vital as the structures being studied have increased in complexity. Having adequate computational resources has thus become imperative for progressing on both the experimental and the theoretical fronts. Accurate theoretical modeling of the electronic dispersion relations and optical properties of the new multilayered quantum heterostructures entails a serious computational investment. Whereas standard multiband k . P model calculations are adequate for treating simple, two-constituent quantum wells and superlattices, the boundary conditions become intractable whenever there is either a larger multiplicity of constituents or a substructure within each period. Here we discuss a multiband finite-element implementation of the k. P model, which is particularly well suited for taking into account the details of the geometry and the complex boundary conditions imposed on the wave functions of the carriers. This computational package permits a straightforward and flexible construction of the geometrical model for the heterostructure. The energy levels and wave functions of the carriers can then be obtained in a routine manner. Excellent precision is achieved by improving on the typical engineering finite-element methods for application to quantum heterostructures. The finite-element method (FEM) has long been a standard computational tool in such engineering and scientific fields as structural mechanics, fluid dynamics, and atmospheric modeling [28, 29], but until recently has only rarely been applied to quantum mechanics except in crude one-band approximations. This is probably due in large part to the unfortunate perception that the FEM is a clumsy method of last resort, which should be avoided whenever more elegant techniques are available. However, it will become apparent in the following sections that the FEM is, in fact, ideally suited to the types of computation required here; that is, finding solutions to complex systems of coupled nonlinear and partial differential equations with complicated boundary conditions. The algorithm derives much of its power from a particularly effective manner of treating the boundary conditions, as well as from an optimization of the nonuniform interelement boundary placements. This separates it from more elementary FEM calculations carried out previously for quantum systems, even in the limit where only one band is considered. Thus, besides enabling one to accurately calculate the electronic structure and optical properties of complex structures that would otherwise be intractable without severe approximations, our FEM algorithm is also remarkably efficient. We find that the computer time required to treat simple two-constituent quantum wells or superlattices is only marginally greater than that needed for a conventional eight-band k . P calculation. It should be noted that the tight-binding approach [30, 31] may be viewed as a limiting form of the FEM, in which each atom or plane of atoms functions as a separate element. However, while tight-binding calculations can, in principle, treat many of the same problems, excessive matrix sizes and computation times limit their practicality when applied to complex systems of the type that are quite tractable within the FEM. Furthermore, the tight-binding parameters are not directly related to experimentally observable quantities, as in k . P, which adds another layer of uncertainty to the input parameters. The implementation of this high-precision FEM model has several useful aspects. These include the ability to incorporate any III-V or II-VI direct gap semiconducting material in any geometry and to include the effects of built-in strain and external perturbations such as electric or magnetic fields or hydrostatic pressure. One of the most valuable features is the ability to generate the carrier wave functions and then display them on the computer screen. This visualization should be viewed as an integral component of wave function engineering as it is ideally practiced, because, in effect it allows one to manipulate the electron and hole spatial distributions dynamically to achieve a desired set of properties. The tailoring may be accomplished, for example, by changing the geometrical placement

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of different materials in the heterostructure so as to maximize the desired localization or shape of the wave functions. This has profound implications for both optoelectronics device design and the exploration of fundamental physical issues. By tailoring the wave functions, we can control optical selection rules, optical matrix elements, carrier lifetimes, overlap integrals, tunneling currents, electrooptical and nonlinear optical coefficients, and so on. The discovery that carriers with energies above the barrier height in supeflattices are localized in the barrier layers and have quantum-well-like spectra is leading to a new spectroscopy of abovebarrier states. Other quantum phenomena that are currently being explored with the finiteelement method with very interesting results include surface quantum wells and their role in defining heterostructure optical properties, bound states and their symmetry properties in laterally confined systems, control over optical nonlinearities in checkerboard superlattices of quantum wires, modification of the density of states in type-II laser diodes, and the suppression of phase incoherence in intersubband second-harmonic generation devices. Also developed have been type-II and type-I interband cascade lasers based on a mulfilayered InAs/GaInSb/A1Sb structure in which the radiative recombination of carriers is followed by tunneling and recycling of electrons into the next stage of the multistage device. This is a natural extension of the AllnAs/GalnAs intersubband quantum cascade laser demonstrated by Faist et al. [32]. In the following sections, we elaborate on the implications of wave-function engineering and describe the integration of the eight-band k . P model for calculating band structures of composite quantum heterostructures into the finite-element method. Following a summary of mulfiband FEM theory in Section 2, we consider several examples illustrating the application of FEM modeling and wave function engineering to quantum systems of practical and fundamental interest. Calculated wave functions, interband and intersubband optical matrix elements, and energy levels and dispersion relations will be discussed for both complex multilayer two-dimensional quantum wells (Sections 3 and 4) and lateral superlattices of one-dimensional quantum wires (Section 5).

2. THEORY

We first consider planar layered semiconductor heterostructures with the planes perpendicular to the growth direction z. The layers are taken to be composed of compound III-V or II-VI semiconductors with their conduction- and valence-band edges located at the 1` point in the Brillouin zone (BZ). The periodic components of the Bloch functions, Uj,k=0(r), with j being the band index, at the band edges are assumed not to differ much as we traverse the layer interfaces [33-35]. We assume that the original bulk crystal translational symmetry is maintained in the transverse direction. We consider the zone-center bulk band structure of the constituent semiconductors, within the spirit of the k . P model. While additional bands (such as a 14-band model) may be treated analogously by our formalism, we find the 8-band k- P model to have sufficient sophistication for most applications. The usual eight-band model consists of the 1`6 conduction band (c), the I'8 heavy-hole (hh) and light-hole (lh) bands, and the 1'7 spinorbit split-off band (s.o.), with their spin degeneracies. The complete 8 x 8 Hamiltonian is displayed in [36]. However, for the sake of clarity in the presentation, we will consider here the simplified example of a layered system with no external electric or magnetic fields or built-in strain, and the limit of vanishing in-plane wave vector [kll _= (k2 + k2) 1/2 --+ 0]. We note that the following considerations also hold for the more general case, except that the dimensions of the matrices correspond to the full eight-band model, and with external perturbations or finite kll, the Kramers degeneracy of the bands is lifted. With these simplifications, the problem reduces to a three-band model, with the hh band factoring out. Within the envelope function approximation, the problem then reduces to the

710

WAVE-FUNCTION ENGINEERING

solution of a set of three simultaneous second-order differential equations for the envelope functions fi (z) of the constituent layers. The three coupled second-order differential equations can be written as

--Aab-~z 2 --i~ab-~z +Cab fb(Z) -- E fa(Z)

(1)

Although the matrix coefficients .A,/3, C in Eq. (1) are usually assumed to be constant in each layer, there are cases for which each material parameter should more generally be considered as a function of the coordinate; for example, in a graded band-gap system or a structure for which the strain is a function of position within a given layer. In a heterostructure, the differences in the band edge energies give rise to the confining potentials experienced by the carriers. In the full eight-band formalism, Eq. (1) consists of eight coupled Schrrdinger equations as discussed in [36]. The finite element method [28, 29, 37, 38] may be used to solve the coupled Schrrdinger equations for symmetric as well as asymmetric quantum wells, for superlattices with two or more than two constituents in each period, for resonant tunneling structures, etc. In fact, this method can accommodate the possibility of every material parameter being a function of the coordinate. It has been demonstrated that the present FEM can be adapted to yield very accurate eigenvalues for bound state problems [39, 40] and for obtaining solutions in quantum semiconductor heterostructures with complex geometries [41, 42]. One begins by writing the appropriate symmetrized (Hermitian) Lagrangian that would generate the foregoing coupled equations through a variational procedure. The integral over the physical region of the Lagrangian density, the action integral, is then split up into a number of "cells" or elements, in each of which the physical considerations of the problem hold. The wave functions are assumed to be given locally in each element by fifth-order Hermite interpolation polynomials, which have the property that the expansion coefficients correspond to the values of the wave function and its derivatives at select points, called nodes, in the element. The global wave functions ft (z) are constructed by joining the locally defined interpolation functions and matching the function and its derivative across the element boundary for each of the bands included in the analysis. The heterointerface boundary conditions consisting of continuity of the envelope functions and of the probability current, and the boundary conditions for the bound states as well as for scattering states [43] at z = +CxD are readily incorporated into the FEM. It is useful to derive the probability current density that is conserved across the interfaces by employing a gaugevariational approach for the multicomponent wave functions using an extension of the gauge-variational method of Gell-Mann and Levy [44]. The spatial dependence of the wave functions, manifested through the interpolation polynomials, is next integrated out, leaving the action integral dependent on the unknown nodal values of the wave function. The usual variational principle is then implemented as a variation of the nodal values of f* (z) under which the action integral is a minimum. This nodal variational principle leads to a "Schr0dinger equation" for the nodal values. The integration of the action integral is performed element by element, giving rise to element matrices, which are then overlaid into a global matrix in a manner consistent with the interelement boundary conditions. This results, finally, in a generalized eigenvalue problem [28, 45], which may be solved for the eigenenergies and wave functions with a standard diagonalizer on a computer workstation. Use of the FEM with three elements per layer leads to very accurate quantum-well and superlattice energies and eigenfunctions. In the limit of simple geometries, the eigenvalues agree with those obtained from the eight-band transfer-matrix method [36, 46-48] to within 10 -6 eV, and double-precision accuracy can be obtained by employing more elements in the computation. Section 5 will discuss the extension of these methods to the case of carrier confinement in two dimensions (quantum wires and other structures).

711

RAM-MOHAN ET AL.

3. NOVEL LOCALIZATION IN LAYERED

HETEROSTRUCTURES Recent investigations employing FEM-based computational methods have helped to clarify the concept of wave function localization and have provided a visualization of that localization. Here we discuss several novel and perhaps counterintuitive findings from those studies: that quasibound states in compositionally asymmetric quantum wells strongly participate in optical transitions, which may be exploited in nonlinear mechanisms [49], that the asymmetric vacuum confinement in a heterostructure cap layer leads to surface-bound states [50], and that states with energies above the barrier in a quantum well or superlattice localize in the barrier layers.

3.1. Quasibound States In quantum wells constructed using semiconductor heterostructures, well-defined localization of the wave functions below a barrier leads to increased excitonic binding, which has been exploited in electrooptic devices based on the electric field modulation of the excitonic transition. While it is well known that symmetric quantum wells (QWs) must have at least one bound state, this theorem does not hold in asymmetric QWs. In fact, the asymmetric well can "push out" the wave functions such that there are no bound states at all in the well. In compositionally asymmetric wells, the confined ground states, when they exist, in the conduction and the valence bands, are very close in energy to the corresponding ground state energies in compositionally symmetric quantum wells. Thus, there is not much difference between them insofar as band-gap engineering is concerned. However, the wave functions of the higher bound/quasibound states are substantially different in the two cases. This is an example of wave-function engineering in which the carrier localizations are altered to induce asymmetry. The feature that asymmetric wells need not have bound states has been verified experimentally [51]. Single asymmetric QWs made of GaAs were grown with unequal A1 content in the AlxGal_xAs barrier layers. This compositional asymmetry, shown in Figure 1, yields barriers on the two sides with different heights V1 and V3, say, and leads to a continuum of energy levels with half-confined states in the energy range V1 ~< E ~< V3. In

Fig. 1. The band edge profile for a compositionallyasymmetricquantumwell.

712

WAVE-FUNCTION ENGINEERING

3

''1

....

I ....

I ....

20A Symmetric Quantum Well T=6K

I ....

AIGaAs x=0.27

11H ".~

2 1L

Eo+Ao

%

1

X

o , , I , , , , 1 ~ , , , 1 ~ , , , I

1.75

....

1.80 1.85 1.90 Energy (eV)

1.95

Fig. 2. Piezomodulated-reflectivity spectrum of a 20-/~-wide A10.27Ga0.73As/GaAs/A10.27Ga0.73As symmetric quantum well at T = 6 K. The GaAs buffer layer signature has been omitted for clarity. Reprinted with permission from C. Parks et al., Phys. Rev. B 24, 14215 (1992). 9 1992 American Physical Society.

this continuum, there exist special states that are "quasibound" in the sense that they have increased, or resonant, occupancy in the well layer. Such states are remnants of the bound states that would be present in the symmetric well if both barriers had height V3, and they closely correspond to such states in energy because the boundary condition on one side of the well is still the same as in the symmetric well: they occur at energies where an integral multiple of half the particle wavelength nearly fits within the well layer, and are associated with a maximum in the occupancy of the QW layer as defined by the probability density of the carrier. These quasibound states are found to participate strongly in optical transitions [49]. Estimates for the second-order nonlinearity using virtual transitions involving such states are comparable to those with fully bound states in asymmetric four-layer QW structures with a step potential within the well region. Interband transitions in a series of asymmetric wells of different widths were observed experimentally in piezomodulated reflectivity and fitted theoretically using the FEM. As an illustration of wave-function engineering, calculations were performed to predict the well width for which no bound states should be present in the asymmetric quantum well. Samples were MBE-grown to specifications, and experiments indeed verified the absence of a bound lh state in a 20-A. asymmetric well. The corresponding differences in the observed spectra for the symmetric and asymmetric wells are shown in Figures 2 and 3, respectively [51 ].

3.2. Surface Quantum-Well Confinement and Above-Barrier Localization Here we consider the confinement of electronic states in the simplest of semiconductor heterostructures; namely, a quantum well (QW) bounded by vacuum on one side and a quantum barrier on the other [50]. Figure 4 illustrates the conduction-band profile for vacuum/

713

RAM-MOHAN ET AL.

) 1] ~

t

t

t

r

AIGaAs

, ]1 x:O,4 II

r--I

-I

It

Eo+Ao II J

ia s' o

x

-a

20,~ Asymmetric

Quantum W e l l

AIGaAs x-0.29

T=6K

-10 _ _ . . _ t ~ l ~ l ~ l i ._1_ 1.65 1.70 1.75 1.80 1.85 1.90 1.95 Energy (eV) Fig. 3. Piezomodulated-reflectivity spectrum of a 20-A-wide A10.14Ga0.86As/GaAs/A10.29Ga0.71As asymmetric quantum well at T = 6 K. The GaAs buffer layer signature has been omitted for clarity. Reprinted with permission from C. Parks et al., Phys. Rev. B 24, 14215 (1992). @ 1992 American Physical Society.

[ > v

/

CJ) (1) cuJ

/ / / / v

AIo.3Gao.7As

GaAs I~

1S

GaAs

/b

"1"

Z

"1 9

Fig. 4. Potential energy diagram for a surface quantum well (QW) and single quantum barrier (SQB). The surface QW states are localized within the GaAs cap layer, while the above-barrier resonant states are localized within the A10.3Ga0.TAs layers. The probability density of the wave functions for the first surface QW and SQB energy levels are also shown. Reprinted from C. Parks et al., Solid State Commun. 92, 563 ( 9 1994), with permission from Elsevier Science.

G a A s / A l x G a l _ x A s Q W s that w e r e fabricated by M B E . T h e piezo- and e l e c t r o m o d u l a t e d reflectivity spectra for these surface q u a n t u m wells w e r e f o u n d to exhibit an e x t r a o r d i n a r y n u m b e r (as m a n y as 69 in one sample) of clear signatures for optical transitions b e t w e e n the q u a n t u m - c o n f i n e d states in the v a l e n c e b a n d to those in the c o n d u c t i o n b a n d [50].

714

WAVE-FUNCTION ENGINEERING

Although the concept of the surface QWs and the occurrence of states confined in them had been contemplated in earlier reports [52-55], the sensitivity and power of modulation spectroscopy [56, 57], as exploited in [50], displayed their electronic structure with unprecedented clarity and richness. By comparison, photoluminescence experiments allow one to observe only optical transitions between the lowest quantum-confined states in the conduction and valence bands. Another unique property of a structure such as the one illustrated in Figure 4 is the presence of states localized above the single quantum barrier (SQB) in the AlxGal-x As layer. These states are actually part of the continuum and not bound states as in a single QW. However, their dependence on the barrier thickness and their wave functions is remarkably similar to their bound counterparts in single quantum wells. The FEM calculations are carried out with a very high confining barrier to the right of the structure so as to generate real wave functions. The barrier-localized states are found to occur at energies where an integral multiple of half the particle wavelength nearly fits within the barrier layer [49, 51 ]. In the modulated-reflectivity spectra of SQBs, a large number of above-barrier states are observed in these structures. Although there is little difference in the main energy gaps between the ground state band edges in surface quantum wells and regular quantum wells (band-gap engineering), the above-barrier-confined states participate strongly in optical transitions and present possibilities for a new "above-barrier" spectroscopy. By controlling the thickness of the barrier layer, we can adjust the spectrum of the above-barrier states. This example is an outcome of wave-function engineering. To establish the origin of the optical transitions as originating from electronic states confined in the surface QW as opposed to those localized above the SQB, we applied the finite-element method to solve Schr6dinger's equation for the envelope functions in the heterostructure with a one-band model as well as with an empirical two-band model [47]. The continuity of the envelope function and its "mass derivative" was applied at the layer interfaces. The confining surface potential was taken to be much larger than the E0 of GaAs, whereas the material parameters in the layers were taken from [58]. For each state, a calculation was made to determine where the wave function was localized. The overlap integral was calculated between conduction and valence states for all possible transitions; those with the largest overlap values were selected as the theoretical transition energies. After applying a correction for the excitonic binding energy as estimated by Nelson, et al. [59], the derived theoretical values were found to be in agreement with those obtained from the experiment. The strong localization of SQB states in the barrier layer was verified to be essentially insensitive to the thickness of the GaAs cap layer. The density of states (DOS) was also calculated for the conduction and valence bands [60]. The peaks in the DOS were used to reconfirm the preceding transition energies. Consistent with the experiment, the envelope of the peaks in the DOS showed a falloff with energy, as well as oscillations whose maxima corresponded well with the observed transitions at high energies above 2 eV. In Figure 5, we display the optical transition energies between the surface QW states and the above-barrier SQB states as a function of transition index n for three different samples. The data points obtained from the electromodulation spectra are fitted with curves from the theoretical calculation, with lw and lb as the only adjustable parameters. The E0 gap of the barriers was determined from experiments to be 1.943 eV in all samples. The departure of the theoretical calculation and experiment at higher energies is due to the neglect of nonparabolicity in the DOS calculation. Again, the data points for the SQB states from Figure 5 virtually overlap because both samples have identical barrier heights and widths. We have plotted the lw - 400-* surface QW states in Figure 5 above 2.1 eV as a continuation of the surface QW states from below the barrier energy. Strictly speaking, the DOS was calculated for the combined surface QW and SQB structure. However, the quantum numbers in Figure 5 were still assigned above 2.1 eV as though the states in the lw - 4 0 0 - A sample are a continuation of the surface QW states. Between the E0 of

715

RAM-MOHAN ET AL. u u n n l l u u u u | n u u l u u u n u u n n n l u u u u n u n n u O

2,5 0

O0

0

2.3

OO

0

9

0

9 OO

X

>

X

2.1 >,, 03 I.... (D c

uJ

O~

oOO

~

gig O~ OO

~176176176 o O~

Al0.3Ga0.7As

1.9 E0+A0 GaAs X

0

x ~

1,7 0

1.5

o9 ~o~

e~176176 oo~176

o

~176 o OOO0

20

/s=150 A lb=800 A

o

ls=400 A lb=800 A

9

.o~ ooooOo~176176 j, ,ooooO . . . . . . . . . .

10

x

1~,= 1650 A lb= 120 A , . . . . . . . . . . . . . . , ....

30 40 50 Transition number

60

70

Fig. 5. Transition energies versus transition number for three surface QWs. The index n corresponds to a transition between the nth heavy-hole level and the nth conduction-band level. All three samples have GaAs cap layers grown on top of a A10.3 Ga0.7As SQB. Reprinted from C. Parks et al., Solid State Commun. 92, 563

((g) 1994), with permission from Elsevier Science. A10.3Ga0.7As and 2.1 eV, the theory correctly predicts the SQB states to be highly localized in the barrier layer, the corresponding transitions being more intense than the surface QW transitions below 2.1 eV. The structure in Figure 4 is not the only type of structure that should exhibit surface QW states. Virtually any structure with a GaAs cap layer of 200 A or more can, in principle, exhibit observable surface QW states, which may coexist with features associated with the underlying heterostructure. As we might by now expect, superlattice structures also display above-barrier localized states [61-64]. In other words, wave-function localization in the barrier layers above the barrier energy is a fairly universal property. Effects of external perturbations on the surface QW states, SQB states, and abovebarrier states are clearly of interest with regard to novel physical issues as well as for their promise in optoelectronics. In conclusion, the theoretical analysis using FEM has provided a clear and unambiguous interpretation of the transitions observed in modulatedreflectivity spectra for SQW structures; in fact, feasibility studies using the FEM were performed before the structures were grown. The preceding examples clearly illustrate the basic shift in the way we envisage quantum heterostructures, in having progressed from band-gap engineering to wave-function engineering. Furthermore, on the practical side, wave-function engineering has allowed us to explore issues associated with above-barrier localization, and also has opened up this new area of "above-barrier spectroscopy."

4. DESIGN OF LAYERED HETEROSTRUCTURE O P T O E L E C T R O N I C DEVICES

In this section, we illustrate the application of the FEM to optoelectronic device design. It will be used to determine energy levels, dispersion relationships, wave functions, and optical properties for specific wave-function-engineered materials that, following fabrication and testing, have shown promising performance in the laboratory.

716

WAVE-FUNCTION ENGINEERING

4.1. Type-ll W Laser Until 1994, all interband quantum well (QW) lasers employed well and barrier constituents having a type-I band alignment, because the achievement of gain requires strong optical coupling between the conduction- and valence-band states. However, recent work has demonstrated that type-II InAs-Gal_xlnxSb structures produce substantial gain as long as the layers are thin enough to allow significant interpenetration of the electron and hole wave functions [65, 66]. In fact, mid-wave infrared (mid-IR) lasers based on the InAsGaSb-A1Sb family of type-II heterostructures are not only feasible, but exhibit some significant advantages [67, 68] over the type-I systems that have been investigated for this application [69]. Fundamental limitations of many of the type-I structures include inadequate electrical confinement due to the small conduction- and/or valence-band offsets (which lead to escape from the active region at higher temperatures) and the increasing predominance of Auger recombination when the energy gap is lowered and the temperatures raised. The nonradiative decay in narrow-gap III-V systems currently under investigation is often dominated by the so-called conduction-to-heavy-hole-heavy-to-split-off-hole (CHHS) Auger process, in which the conduction-to-heavy-hole (CH) recombination is accompanied by a heavy-to-split-off-hole (HS) transition. In InAs-rich alloys such as InAsSb, InAsSbP, and InGaAsSb, this process easily conserves both momentum and energy because the energy gap is nearly equal to the split-off gap A0 [70, 71 ]. Grein et al. [67] theoretically discussed the minimization of Auger rates in type-II InAs-Gal_xlnx Sb superlattices for mid-IR laser applications. The simplest type-II structure is a two-constituent type-II superlattice, such as that whose conduction, valence, and split-off band profiles are illustrated in Figure 6. Also shown are the corresponding energy levels and wave functions calculated using the eightband FEM algorithm. Note first that even though the electron wave functions (solid curves) have their maxima in the InAs layers and the hole wave functions (dashed curves) are centered on the Gal_xlnxSb layers, there is significant overlap because each penetrates into the adjacent layers. Hence, the optical matrix element is nearly as large as values typically obtained for type-I QWs. We also find that the resonance between Eg (the separation of E1 and H1) and A0 (the difference between H1 and S1) is completely removed by the type-II band alignment, even though it is present in bulk InAs and GaSb, and is potentially an issue in Gal_xlnxSb. Furthermore, Grein et al. [67] pointed out that for these particular layer thicknesses, the energy gap does not resonate with any intervalence transitions involving HI near its maximum (it falls approximately halfway between H1-H2 and

Fig. 6. Conduction-,valence- (heavy-hole),and split-offbandprofilesfor a type-IIInAs-Ga0.75In0.25Sb superlattice clad by Ga0.88A10.12Sb.Also shown are eight-band FEM results for the electron (solid) and hole (dashed) wavefunctions, along with energyminimafor the various conduction and valence subbands.

717

RAM-MOHAN ET AL.

H1-H3). Hence all multihole Auger processes are energetically unfavorable. Moreover, the rate for CCCH events [in which the CH recombination is accompanied by an electron transition to a higher-energy conduction-band state (CC)] is suppressed by the small in-plane effective mass for holes near the band extremum (~0.047m0). It has been demonstrated experimentally that type-II quantum heterostructures can have significantly smaller Auger coefficients than analogous type-I structures with the same energy gap [72, 73]. However, the structure shown in Figure 6 is nonoptimal in that the electron dispersion is effectively three dimensional. It is well known that QW lasers (two-dimensional) usually significantly outperform [3, 6] double heterostructure lasers (three dimensional) once a given fabrication technology has matured, primarily because the more concentrated twodimensional density of states yields much higher gain per injected carrier at threshold. Although the holes in the type-II superlattice shown in Figure 6 have minimal dispersion along the growth axis (i.e., they are quasi-two-dimensional), the strong penetration of the electron wave functions into the thin Gal_xlnxSb barriers leads to a nearly isotropic electron mass (mnz/mnll ~ 1.2). The most straightforward approach to reducing the electron dimensionality is to convert the superlattice into a multiple quantum well. Figure 7 illustrates the incorporation of additional A1Sb layers, which serve as barriers for both electrons and holes, into each period of the structure. The FEM calculation for the structure in Figure 7 yields two-dimensional electron and hole dispersion relationships (the electron miniband width is 0.2) and provide a nearly exact lattice match to the active quantum-well region. Note also that we still expect intervalence Auger processes to be weak because the energy gap between E1S and HI again falls halfway between the gaps for H1-L1 and H1-H3 (and is of course far out of resonance with the split-off gap). We finally point out that electrical confinement ceases to be an issue in type-II W structures because the A1Sb cladding layers provide large offsets for both the conduction and valence bands. The quantum structural design considered here has quite literally taken the form of wave-function engineering. Optically pumped type-II W structures were the first interband

Fig. 8. Band profiles, wave functions, and energy levels for a type-II "W" structure (InAsGa0.70In0.30Sb-InAs-Ga0.1A10.9Sbfour-constituent multiple quantum well). This structure combines both the two-dimensional electron dispersion of Figure 7 and the large wave function overlapof Figure 6.

719

RAM-MOHAN ET AL.

lasers emitting beyond 3/xm to operate at room temperature [75] (up to 360 K) and they also hold the record for maximum CW operating temperature (220 K) [76] for all III-V semiconductor lasers in that wavelength range.

4.2. Interband Cascade Laser In the quantum cascade laser (QCL) [32], unipolar electron injection into a series of coupled QWs produces a subband population inversion and lasing owing to stimulated intersubband transitions. A key feature is that in contrast to conventional diode lasers, in which a maximum of one photon is emitted for every injected electron and hole, in the QCL each injected electron can, in principle, produce an additional photon for each period of the structure. High threshold current densities are required to obtain population inversion, however, because the nonradiative lifetime of electrons in the upper lasing subband is only 1 ps due to intersubband relaxation via optical phonon emission. It was recently pointed out that this shortcoming can be overcome if type-II interband rather than intersubband transitions are used in conjunction with a cascade geometry [77]. In the interband cascade laser (ICL), the phonon relaxation path is eliminated, while the advantages of electron recycling are retained. Detailed simulations of optimized designs generated using wavefunction engineering are predicted to yield high CW output powers for high-temperature operation [19, 78, 79]. Conduction- and valence-band profiles along with quantized energy levels for one period of a type-II ICL designed to emit at 3.15/zm are shown in Figure 9. Electrons are injected into the InAs electron quantum well from an adjacent period on the left side and emit mid-IR photons by making type-II radiative transitions to the valence band of the GalnSb hole quantum well. This hole well is optimized so as to avoid possible resonances between the energy gap and any of the valence intersubband splittings, which is again necessary to minimize losses due to Auger recombination and free-carrier absorption. Holes

Fig. 9. Band profiles and energy levels for an ICL structure under external (75-kV/cm) and chargetransfer fields corresponding to the laser threshold at room temperature.

720

WAVE-FUNCTION ENGINEERING

tunnel into the active GalnSb well from the adjacent GaSb well. The second hole well provides a substantial barrier to electron leakage from the active InAs well (i.e., negligible wave-function overlap between the active region and the electrons in the first quantum well of the injection region), while assuring a large indirect optical matrix element (i.e., large overlap of the active electron and hole wave functions). The GaSb well is populated through the establishment of a semimetallic thermal equilibrium with the 120-* InAs well via simple phonon and carrier-carrier scattering processes. The 120-,~ InAs well is followed by an n-doped InAs/Al(In)Sb superlattice, whose well thicknesses are graded such that under the appropriate bias the bottom subbands merge into a miniband of width ~65 meV to insure a rapid transfer of electrons across the injection region and into the active InAs quantum well of the next period. Resonances between the lasing photon energy and the intersubband transition energies have been avoided in all electron wells to prevent absorption, although even near resonance the intersubband absorption processes are strongly suppressed for the TE polarization of the lasing mode. The lattice constant for the entire period can be matched to that of the cladding layers by using A10.gzIn0.18Sb rather than A1Sb for some of the barriers. All layers are lattice matched to the GaSb substrate. The internal electric fields generated by the hole populations in the undoped GaInSb and GaSb wells are gradually compensated by the excess electron concentrations near the left end of the n-doped injection region. Under the biasing conditions required for nearthreshold operation at room temperature, the steady-state field is ~70 kV/cm toward the middle of the injection region, while that value is substantially reduced in most of the active region. In fact, the internal field across the GaSb well is so strong that the net field is in the opposite direction from the applied bias. We have simulated the operation of a 15-period ICL structure surrounded by 1.5-#mthick optical cladding layers consisting of n-doped InAs/A1Sb superlattices. The optical confinement factor for the active region is ~78%, and we estimate a net loss of ~52 cm -1 . Energy dispersion relations and optical matrix elements for this complex structure were derived from the eight-band FEM algorithm. Fermi levels and electronic heat capacities were then calculated as a function of the carrier concentration for each well of a given period, and the corresponding optical gain was determined as a function of electron and hole densities in the active wells. These dependences were then inputted to the time-dependent equations for interwell carrier transfer, which are coupled to the photon-propagation equation and the heat balance equation for the carrier temperature in the active wells. As the calculation progresses, the internal electric fields were self-consistently adjusted according to the spatial buildup of excess charge in the various quantum wells. Electron-hole recombination is taken to result from spontaneous and stimulated radiative emission, as well as Shockley-Read (assuming rSR = 10 ns) and Auger nonradiative processes. The Auger coefficient was estimated from experimental results for optically pumped type-II W lasers [80]. Carrier heating due to Auger recombination, free-carrier absorption in the active, injection, and cladding regions, and hot-carrier injection from one well to the next have been calculated using electronic heat capacities derived from the electron and hole dispersion relationships for each well. We take the energy relaxation time to be 1 ps and assume that frequent interwell carrier-carrier scattering events lead to a common carrier temperature throughout the structure. For operation at room temperature, the calculations yield that the carrier heating does not exceed ~ 4 K near threshold and increases to -~65 K at a current density of 4 kA/cm 2. If the ICL is mounted junction side down on a heat sink, we calculate a CW lattice heating of ~8 K at threshold and increasing to ~33 K at j -- 4 kA/cm 2 for a thermal conductivity of the top cladding equal to 0.2 W/cm K. The simulation yields that at 300 K, a threshold current of 1.1 kA/cm 2 (due almost entirely to Auger recombination) induces lasing when a net bias of 6.6 V is applied across the 15-period structure. The solid curves of Figure 10 illustrate the predicted ICL output

721

RAM-MOHAN ET AL.

Current Density (kA/cm 2) 1.0

0

1 A~3.t5#ml

2

3

i

l/

4

o.s

9~:

0.6

_

1oo;/

IL_

z~ 0.4 9 0.2

_

/ /

-/ _ ~ - - . r - - Z - C ] - -

0.0 / 0.0

,

0.2

W-Ls?r

/

/

0.4

__

200 K

1

J _~--*-T- I 0.6 0.8 1.0

Current (A) Fig. 10. Output power per facet versus injected current density for the ICL structure of Figure 9 at 100 and 300 K (solid curves) and for a type-II "W" laser structure emitting at the same wavelength (3.1/zm) at 100 and 200 K (dashed curves). In both cases, the cavity length is 500/zm and the stripe width is 50/zm.

powers as a function of injection current at 100 and 300 K, which are compared with analogous 100 and 200 K results from the modeling of a uniformly injected 15-period W laser with the same Auger coefficient (dashed curves). The ICL threshold currents are seen to be much lower, because for a cascade geometry the contacts only need to supply enough carriers to establish a population inversion in the first period, from which the carriers are then injected into the next period, etc. Furthermore, the differential slope efficiency (with a maximum of 0.9 W/A per facet) is much higher due to the generation of 15 photons for every electron injected. Especially encouraging is the prediction that output powers exceeding 1 W may be feasible, although the maximum is limited by the carrier and lattice heating at high injection currents. When the temperature is decreased from 300 to 100 K, the threshold current density falls by more than an order of magnitude, to 80 A/cm 2, if the same Auger coefficient is used. The theoretical predictions for the threshold current density of the quantum cascade laser are ~3 and 1 kA/cm 2 at 300 and 100 K, respectively [81]. Further wave-function engineering of the structure of Figure 9 can be introduced to improve the laser performance [79]. Conduction- and valence-band profiles, quantized energy levels, and n-type doping densities for the active region of a W-ICL structure, in which the introduction of a second active InAs QW produces a larger matrix element and, hence, considerably higher gain per period, are shown in Figure 11. The square of the momentum matrix element for this structure is increased by a factor of ~2 compared with the structure of Figure 9. Another difference from Figure 9 is the addition of a thin A1Sb barrier between the GaSb hole well and the first InAs electron well of the injection region. This barrier suppresses interband absorption at the GaSb/InAs interface by reducing the H2/E 1I wave-function overlap while maintaining enough overlap to assure adequate transport. Interband cascade lasers with designs similar to those illustrated in Figures 9-11 have been demonstrated experimentally [73, 82-84]. Even at this preliminary stage of development, external quantum efficiencies greater than one photon per injected electron have been confirmed [73, 82, 83]. This implies that true cascading has been successfully realized. A W ICL has generated up to 170-mW peak power at 180 K [84], which is the highest for any electrically pumped interband mid-IR semiconductor laser at that temperature. The

722

WAVE-FUNCTION ENGINEERING

Fig. 11. Bandprofiles, wave functions, and energy levels for the active region of the W-ICL structure under extemal bias and including charge-transfer fields. 10

'

I

I

'

'

I

'

~-3.6gm T0=53 K

~

./'

t"q

< ~

I

50

100

,

I

,

150

I

200

,

I

250

,

300

Temperature (K) Fig. 12. Thresholdcurrent density versus temperature for a gain-guided W ICL with three hole wells. same device operated up to 225 K, and at that temperature had a slightly lower threshold than any previous mid-IR result. That threshold was nonetheless more than an order of magnitude higher than the theoretical prediction. A refined W-ICL design was therefore developed [84] with a third GalnSb hole QW added to the design of Figure 11 to minimize the wave-function overlap and, hence, leakage from the two InAs active electron wells to the InAs-A1Sb superlattice injection region. The experimental [84] peak wavelength was 3.53 # m at 210 K, with a temperature coefficient dl./dT = 1.8 nlrdK in the range 100-210 K. The threshold current density (jth) as a function of temperature in Figure 12 shows a characteristic temperature To of 160 K for T ~ 235 K, while To = 57 K for 235 < T < 276 K. The maximum lasing temperature of 286 K is more than 60 K higher than the best previous result for any electrically pumped interband semiconductor laser emitting at ~. > 3 . 3 / z m [85]. Even this Tmax was limited by the onset of permanent damage at high injection levels rather than by any intrinsic limitation.

723

RAM-MOHAN ET AL.

Wave-function engineering also has been used to design active regions [79] for the first III-V vertical-cavity surface-emitting lasers to emit beyond 2.2/xm. The optically pumped devices emitting at 2.9-3.0/zm have been operated up to 280 K pulsed [86] and 160 K CW [87]. Intersubband quantum cascade lasers based on antimonide QWs have been designed as well and are predicted to have lower thresholds than InGaAs-InA1As Q f L s [81 ].

4.3. Second-Harmonic Generation with Phase-Matching Regions Our final example of the application of wave-function engineering to the design of actual layered heterostructure devices is an efficient intersubband frequency mixer. Intersubband processes for the second-harmonic generation (SHG) of high-intensity IR radiation [88-91] have such advantages as large oscillator strengths and narrow linewidths, as well as considerable flexibility in designing the resonance wavelengths, transition matrix elements, conversion efficiencies, and other properties by varying the layer thicknesses and material system constituents. Although second-order nonlinear susceptibilities X (2) exceeding the bulk values by 3 orders of magnitude [91 ] have been reported, high intersubband absorption coefficients that accompany the large X (2) tend to severely reduce the conversion efficiency at double resonance; that is, when the pump and second-harmonic photon energies match the 1 --+ 2 and 1 --+ 3 intersubband transition energies. Although it has been suggested that detuning of the intersubband transitions from double resonance can increase the net conversion efficiency [90, 92], another critical requirement is to maintain phase coherence of the pump and second-harmonic beams over relatively long interaction paths (on the order of 100/zm) [93]. It has been shown that if control over the three levels in the active QWs is the sole degree of freedom, high conversion efficiencies are probably not feasible in realistic devices [94]. However, the inherent difficulties of combining high X (2), weak absorption, and phase matching can be overcome by incorporating a novel phase-matching scheme for intersubband SHG [94, 95]. This is accomplished by introducing a physically distinct region into the waveguide core, whose sole purpose is to compensate for the phase mismatch that would ordinarily result due to contributions from the bulk dispersion, waveguide dispersion, and active region transitions. To avoid disturbing the balance between absorption and nonlinearity, such a region must be (nearly) transparent at both the fundamental and second-harmonic frequencies. The simplest configuration meeting both objectives is a quantum-well structure, whose intersubband transition energy is tuned midway between the first and second harmonic. An applied electric field can add further flexibility and allow dynamic tuning of the SHG device [95]. For a three-level system, the second-harmonic generation coefficient for TM-mode interactions in a waveguide is given (in centimeter-gram-second units) by n 2e 3 S2Nz12z13z23 (2) X(2) ~,~ 2w /r E12 -- i h r ' l z ) ( 2 h w - El3 - ihF13) where $2 ,~ (N1 - 2N2 -t- N 3 ) / N is a saturation factor, N is the three-dimensional electron density averaged over the period, Ni is the intensity-dependent density populating subband i, Eij and r'ij are the energy and linewidth for transitions between the subbands i and j, n is the refractive index, and x is the dielectric constant. The absorption coefficient is given by [96] . .

4:rrne2S~J N h w z 2. sin 2 0 Otij =

KhC

hF (ha)-

E i j ) 2 nt- (hi') 2

(3)

. .

where S~1 - otij ~Or0 = ( g i - N j ) / N is the saturation factor for absorption, t'~o is the confinement factor for the optical mode at the first-harmonic frequency, and r12 is the intersubband relaxation time.

724

WAVE-FUNCTION ENGINEERING

The intersubband contribution to the refractive index reduces in the near-resonance limit to

ij nisb(o9)

hCOtoJ (])09-- Eij ) I" 2Eij (t)o9- Eij) 2 + 1-'2

(4)

The mismatch between the refractive indices in the pump and second-harmonic beams is An -- neoJ -- n~o, where the net refractive index at a given frequency is n~o = nb(og) + nisb(og) + nwg(og), nb is the bulk index, nisb is the Kramers-Kronig contribution due to intersubband transitions, and nwg(og) is the contribution due to waveguide dispersion [94]. The conversion efficiency as a function of position may be found by solving the coupled differential equations for propagation of the pump and second-harmonic beams, where the saturation of the absorption coefficient and the resonant contribution to the refractive index are determined by the relative populations of the various subbands at each step along the propagation path of the pump and second-harmonic beams [94]. Optical heating is included by equating the energy loss and gain rates to yield an electron temperature. The lattice temperature is taken to be 300 K. Here we will consider SHG in In0.saGa0.47As/In0.seA10.48As asymmetric double QWs (ADQWs). The eight-band FEM formalism was used to calculate the subband energy levels, wave fuctions, and optical matrix elements. Figure 13a shows that the ADQW active region has a 65-/k InGaAs well separated from a 37-~ InGaAs well by a 17-,~ InA1As barrier. The wells are doped to 5 • 1011 cm -2, and a 100-,~ InA1As barrier separates adjacent periods. The 5-/zm-thick active region is combined with two identical 2-/zmthick phase-matching regions, each consisting of a 17-13-38-/k InGaAs-InA1As ADQW as shown in Figure 13b, with an intersubband transition energy of El2 -- 175.5 meV midway between the fundamental and second-harmonic frequencies. The relatively high doping of 1 • 1012 cm -2 is necessary to provide full compensation for An. A 1-/zm-thick top cladding of InA1As is added to complete the waveguide (the InP susbtrate acts as the bottom cladding layer, because its refractive index is lower than that of the active region at o9 and 2o9). A relatively thick waveguide is necessary to assure that most of the optical mode is confined to the waveguide core. Competition between closely spaced modes at 2o9 is not expected to be a significant factor because the overlap integral is much larger for the fundamental mode. The compensating refractive index difference due to the phase-match regions is predicted to reduce the original An of 0.06 to ~0.01, and a smaller Anisb from the active region reduces the mismatch virtually to zero. For the proposed structure at zero field, the pump and second-harmonic beams are predicted to maintain phase coherence up to path lengths extending beyond 100/zm, implying that relatively long waveguides may be used. An optimized structure without a phase-matching region can maintain relatively good phase coherence owing to the mismatch compensation in the active region, but is not nearly as successful as the structure that includes a phase-match region. Conversion efficiencies as a function of propagation distance are shown in Figure 14 for the optimized structures with and without a phase-matching region. The maximum conversion efficiency in the phase-matched structure is predicted to be 16.5% at L = 72 # m and a pump-beam intensity of 40 MW/cm e. The relatively modest improvement over the result of 14.3 % for the structure without a phase-match region is primarily a consequence of the smaller confinement factors for the active region. However, the conversion efficiency at L = 100/zm is > 14% and remains above 10% over the entire range from 35 to 130/xm, whereas highly efficient SHG is obtained only for a much narrower range of short device lengths in the structure without a phase-matching region. Longer devices will be easier to fabricate, and a broader peak in the conversion efficiency relaxes the tolerances on the optimum waveguide length. Furthermore, the phase-matched structure is not particularly sensitive to the assumed value of An. Calculations indicate that a +0.01 variation in the absolute value of An results in only a q:2% change in the maximum conversion efficiency.

725

RAM-MOHAN ET AL.

Ino.53Gao.47As 1.3

1

Ino.52Alo.48As

In0.52A10.48As

1.2 1.1

>

9

1.0

o

0.9

/

f

~

2 J 0.8

E1

3"7~

65A

0.7

17A

(a)

Ino.52Alo.48As 0.6

I

,

I

I

I

100

150

,

50

-50

!

I

200

Distance (A) Ino.53Gao.47As

Ino.2Alo.4AsI

1.3

[

Ino.52A10.48As

1.2 1.1

>

1.0

_J

o/) o 0.9

___EL___

0.8

38A

~

13A

0.7

I

ino.52Alo.48As 0.6

I

-50

,

I

,

0

I

50

(b) ,

I

100

,

I

150

Distance (/k) Fig. 13. Band profiles, wave functions, and energy levels for (a) the active region and (b) the phasematching region of the ADQW intersubband SHG structure.

Also, ADQW structures with an even higher degree of detuning are predicted to maintain adequate phase coherence up to 300/xm with a peak conversion efficiency exceeding 6%. Although the structure with a phase-matching region exhibits nearly perfect phase coherence at zero field, the c o h e r e n c e length Lc can be drastically r e d u c e d by a p p l y i n g a

726

WAVE-FUNCTION ENGINEERING

20

L,~,x(no PM) t

Lmax(PM) t

f

lnGaAs/InA1As A=10.6#m

15 r

~

noPM,F

=

PM, F = 0 0

~

~

10 9

o~..~ q)

>

5

9 c~

- / p M , F = -32 kV/cm 0

0

20

40

60

80

100

Propagation Distance (#m) Fig. 14. Predictedconversionefficiency as a function of propagation distance at applied fields of 0 and Fmin = -32 kV/cm for the optimized structure with a phase-matching region and at zero field for the structure without a phase-matchingregion.

negative field. Figure 14 illustrates that for the same device length and excitation intensity for which the conversion efficiency had a maximum at F = 0, the application of Fmin ~ - 3 2 kV/cm causes the second-harmonic signal to vanish; that is, the SHG output can be modulated electrically. Preliminary calculations of the device capacitance indicate that modulation frequencies of 10 MHz should be readily attainable. Electrical tuning can also be used to extend the spectral bandwidth. For example, conversion efficiencies exceeding 1% should be achievable for pump wavelengths between 9 and 20/zm. The concept of intersubband SHG with a separate phase-matching region was demonstrated experimentally in a structure designed for a 8.5-ttm pump beam [97]. A semiconductor waveguide grown by MBE consisted of a 3.5-ttm-thick ADQW active region sandwiched between two 2.2 # m single quantum-well phase-match regions and two InA1As optical claddings. The designed transition energies of the ADQW with three confined subbands were strongly detuned from the first and second harmonic so as to minimize the intersubband absorption coefficient while maintaining a relatively high value of the nonlinear susceptibility, and the positions of the intersubband resonances were confirmed by measuring the linear absorption spectrum. The sample was cleaved to cavity lengths between 100 and 440 ttm. Single 90-ps pulses from a tunable traveling-wave optical parametric generator (OPG) were focused onto the sample with a spot size of ~100 ttm, giving a peak radiation intensity of up to 100 MW/cm 2. Results for the SHG conversion efficiency (77) in the 200-ttm-long waveguide (Fig. 15) show a nearly linear increase for pump intensities below 20 MW/cm 2 and a plateau at higher pump intensities. The maximum conversion efficiency was ~0.9%, which is at least a factor of 3 higher than any previously reported results for intersubband SHG [98]. It should also be noted that waveguides as long as 440 ttm yielded r / ~ 0.2%. Because the conversion efficiency for a 200-ttm cavity was higher than for the 100-ttm cavity, we can conclude that phase matching was successful. Analogous structures with a smaller Lorentzian linewidth of 5 meV are predicted to exhibit r/of up to 8%. Greatly improved flexibility is also expected by tuning with an applied voltage.

727

RAM-MOHAN ET AL.

SHG EFFICIENCY VS INTENSITY

o~ r

1.0lll

Ai I

iI

o

&

~E LLI

&

tO .m > tO . .o.

0.5"

e'0

iI

E t._

"1"0 tO o (!) 09

i 0.0

9 z-scan data 9 filterdata I

10

i

i

i

i

20

30

40

50

60

Pump Intensity (MW/cm2 ) Fig. 15. Experimenalresults for the SHG conversionefficiency (points) as a function of input intensity for the ADQWSHG structure.

5. QUANTUM WIRES AND TWO-DIMENSIONAL SUPERLATTICES 5.1. Bound States in a Rectangular Quantum Wire In 1980, Sakaki [99] considered theoretically the consequences of growing heterostructures that would confine electrons in two dimensions, the so-called quantum wire (which we will denote by "quantum well wire" or QWW) or the two-dimensional quantum well. Since then, it has increasingly become possible to fabricate such heterostructures [ 100, 101 ]. As in one-dimensional confinement, the principal effect is to profoundly change the energy spectra of electrons, which in turn influences the optical and transport properties of the composite material [ 102-107]. We consider the calculation of electron and hole energy levels in a GaAs quantum wire with a finite confining potential arising from the band offset of the surrounding A1GaAs medium. Our results show that the energy levels for the finite potential are significantly lower than those obtained with the infinite barrier, which suggests that the infinite-barrier approximation is not valid for quantum wires. More striking, however, is that when a finitebarrier potential is used to calculate the energy spectrum for a quantum wire with a square cross section, there is a lifting of the degeneracies of only certain of the energy levels.

5.2. Finite-Element Analysis of the Quantum Wire In the envelope function approximation [33, 34], the most general form of the differential equation for the electron's QWW envelope function f (x, y) contains a nonseparable potential V (x, y) corresponding to a finite-barrier height,

-(h2/2m*)(O2/Ox 2 + 02/Oy2)f(x, y) -Jr-V(x, y)f(x, y)= Ef(x, y)

728

(5)

WAVE-FUNCTION ENGINEERING

* or m b * in the well or barrier, respectively. Aswhere the carder effective mass m* is m w suming a rectangular-well wire of dimension a x b centered at the origin, the "kitchen sink" potential is V(x, y) = 0 for Ixl ~< a/2 and lyl ~< b/2, and V = V0 outside the well. The input parameters for the band offsets and conduction-electron, light-hole, and heavyhole effective masses in GaAs and in A1GaAs are obtained in the same way as in earlier investigations using the Bastard model [47]. The FEM procedure employed to solve the two-dimensional Schrtdinger equation for the energy levels as well as the eigenfunctions f (x, y) is an extension of the approach discussed in Section 2 for the case of confinement along only one axis. The region of interest is partitioned into small elements, in each of which the physical conditions of the problem hold. The as yet unknown function f (x, y) in each element is approximated by local Hermite interpolation functions, which have the property that the expansion coefficients correspond to the values of the function and its derivatives at select points, called nodes, in the element. The global function f (x, y) is constructed by joining the locally defined interpolation functions and requiting that f (x, y) and its derivatives are continuous across the element boundaries. As mentioned earlier, in the FEM it is quite easy to implement the boundary condition at the well-barrier interface, which requires the continuity of both f ( x , y) and the effective mass derivative. The resultant eigenvalue problem is solved for the energy spectra and for the values of f , Of/Ox, Of/Oy, and O2f/Ox Oy at the nodes. Details of the two-dimensional FEM are given in [39]. In Table I, we reproduce the FEM values [41 ] for some of the energy levels (accurate to within 0.1 meV) of heavy holes in a GaAs/Ga0.63A10.37As wire of dimension 100 x 100/~. A conduction band offset of 0.6 AEg at the heterointerface was used in the calculations. As in the case of one-dimensional quantum-well confinement, it is convenient to label the energy levels using the quantum numbers (nx, ny) associated with the infinite well, where nx and ny are the quantum numbers for the one-dimensional infinite square well in the x and y directions. The energy levels obtained using the infinite-barrier approximation are also included in Table I for comparison.

5.3. Symmetry Properties of the Square Quantum Wire The symmetry properties of the envelope functions for the square quantum wire are governed by the symmetry of the potential, C4v. The character table for C4v is given in [ 108].

Table I. Heavy-HoleEnergy Levels in GaAs/A10.37Ga0.63AsQWs, with * = 0.3774m0 and m~ = 0.3865m0a mto Energy (meV) V0= 184

(nx,ny)

Energy (meV) V0=c~

(nx,ny)

74.0

(1, 3) + (3, 1)

99.6

(1, 3)

74.2

(1, 3) - (3, 1)

99.6

(3, 1)

144.2

(2, 4) + (4, 2)

199.3

(2, 4)

145.9

(2, 4) - (4, 2)

199.3

(4, 2)

178.32

(1,5) + (5, 1)

259.1

(1,5)

179.70

(1, 5) - (5, 1)

259.1

(5, 1)

(Source: J. Shertzer and L. R. Ram-Mohan, AmericanPhysical Society, 1990). Energy levels with odd-odd and even-even quantum numbers have their degeneracy lifted, and only the corresponding energies are reported for a 100 x 100-/~2 wire.

a

729

RAM-MOHAN ET AL.

For this group, the effects of the operators {E, C2, 2C4, 2av, 2ad} on the function

f(x, y)

are

E f (x, y)= f (x, y)

C2 f (x, y)-- f (-x, - y)

C4f (x, y)= f (y, - x )

C41f (x, y) = f ( - y , x )

av f (x, y) = f (--x, y)

av 1f (x, y)= f (x, - y )

o'df (x, y) = f (y, x)

o'dl f (x, y) = f (--y, --x)

It is straightforward to determine the representation corresponding to the infinite well eigenfunctions (nx, ny). The (odd, odd) singlet states with nx = ny belong to the A 1 representation and the (even, even) singlet states belong to B2. The degenerate states with nx 5/: ny can be classified as follows: (even, odd) and (odd, even)

E

(even, even)

A2 + B2

(odd, odd)

A1 + B1

Because the (even, even) and (odd, odd) degenerate states are combinations of two distinct irreducible representations, the degeneracy of these levels is not a consequence of the symmetry group of the square, but rather is due to the separability of the infinite square well potential. Using linear combinations of the standard (nx, ny) eigenfunctions, it is possible to construct eigenfunctions that correspond to one of the one-dimensional irreducible representations A 1, A2, B1, or B2. For example, (1, 3)+(3, 1) transforms as A 1 and (1, 3)-(3, 1) transforms as B1. As we shall see, these are a more natural choice for the basis functions of this two-dimensional subspace in that they are the V0 ---> c~ limit of the finite-barrier eigenfunctions. For finite barriers, the potential is nonseparable and the accidental degeneracy that was present in the infinite-barrier case for the (even, even) and (odd, odd) levels is lifted (see Table I). The state that is antisymmetric about the diagonal of the square (B1 or A2) is less bound than its symmetric counterpart (A 1 or B2). As expected, the splitting of these particular energy levels decreases as the barrier height increases, and in the limit V0 --+ oo, the states are truly degenerate. The FEM wave functions for the square well with finite barrier are similar to their infinite-barrier analogs except that there is penetration of f (x, y) into the barrier region. For the degenerate states of the E representation, any two orthogonal states that span the subspace are acceptable eigenstates. In the cases where the degeneracy is removed, the wave functions for the finite barrier must correspond to a single representation as required by the group properties; the wave functions are either even or odd with respect to reflection through the diagonals. By studying the symmetry properties of the confining potential, it is straightforward to predict which of the degeneracies present in the infinite-barrier approximation are due to the separability of the potential and, hence, are accidental and will be removed in the presence of a finite barrier. Examples are given in Table I. The FEM provides realistic numbers for the energy spectra in rectangular quantum wires. Such accuracy is crucial in the study of linear and nonlinear optical properties of semiconductor heterostructures. In particular, the infinite-barrier approximation is invalid and leads to serious errors in both the qualitative and quantitative aspects of the energy spectra. The FEM can readily be applied to two-dimensional confinement problems where the effective mass and the potential are more complicated functions of the coordinates. As we shall see subsequently, it is also possible to accommodate any cross-sectional configuration, including QWWs grown on grooves.

730

WAVE-FUNCTION ENGINEERING

5.4. The C h e c k e r b o a r d Q u a n t u m Wire Superlattice

Recent progress in the fabrication of QWWs with electronic confinement in two dimensions suggests that the growth of periodic structures of quantum wires will eventually become feasible. The microfabrication advances already achieved and the novel optoelectronic properties expected from such structures have motivated us to study a quantum structure consisting of rectangular semiconductor wires (of GaAs and A1GaAs, for example), stacked alternately and having two-dimensional periodicity. In the following discussion, we refer to this as a checkerboard superlattice (CBSL) [42]. Here we will consider the effects of carrier wave-function overlap across the barriers in the directions parallel to the CBSL axes, and the free-carrier-induced nonlinear optical properties of such a structure with carriers in the lowest conduction miniband. We first obtain the energy minibands for conduction electrons moving in the periodic CBSL confining potential, arising from the (finite) conduction-band offset of A1GaAs with respect to GaAs. These results are then used to obtain the optical nonlinearity for radiation propagating along the longitudinal (z) axis of the wires, with electric fields being either along the x or the y directions. It has been demonstrated that band nonparabolicity induces a nonvanishing third-order nonlinear optical susceptibility, X (3), in bulk semiconductors [ 109, 110] and in superlattices [ 111-115]. We evaluate the free-carrier-induced optical nonlinearity due to the band nonparabolicity generated by the Brillouin zone folding of the CBSL conduction band in two directions. The analysis [ 114] of the optical nonlinearity in planar superlattices has revealed, contrary to expectations, that superlattices with wider wells and/or barriers have larger values of X (3). This is reconfirmed here for the particular case investigated. In the envelope function approximation, we again solve the two-dimensional Schr6dinger equation for the energy E, using m* - 0 . 0 6 6 5 m 0 in the GaAs wells and/or m b*= 0.0858m0 in the Ga0.7A10.3As barriers. The nonseparable potential V(x, y) corresponds to a finite barrier height (V0 - 0.274 eV) in the A1GaAs region. The well and barrier thicknesses along the x and y directions are taken to be (alia2) and (bl/b2), respectively, with periodicities of lengths a - al +a2 and b - bl + b2 expressed in units of d = 5.642 (the lattice parameter of GaAs). Again, the boundary conditions imposed on the solutions are the continuity of the envelope functions f(x, y) and the continuity of (1/m*)f'(x, y) across all interfaces. In addition, Bloch's conditions, f(a, y ) - exp(ikxa)f(O, y) and f(x, b) = exp(ikyb)f(x, 0), are imposed to account for the supertranslational symmetry of the CBSL. Schr6dinger's equation for the CBSL has been solved subject to these two-dimensional boundary conditions using the FEM as discussed herein. Here the basic "unit cell" of the CBSL of dimension a x b is split up into a number of elements, where the heterointerface boundary conditions and Bloch's periodicity conditions mentioned previously are easily incorporated into the FEM. The resultant global eigenvalue problem is solved for the eigenenergies for each value of (kx, ky) ~ [(rc/a)qx, (rc/b)qy] to obtain the energy bands. Results for the energy dispersion in a CBSL can be compared with SLs of dimensions (6/4) along x and (8/5) along y. The band edges at q -- 0 are lower in the planar structures because there the carriers are confined only in one direction. It may be noted that the bands in the CBSL do not arise from a simple additive effect from the planar superlattice bands. We now evaluate [42] the optical nonlinearity X (3) due to the carrier band nonparabolicity [109, 110]. The nonlinear susceptibility X{3) (i - x, y) is given by g~3) -- --

e4n(O4E/Ok4)

(6)

24h40)lW2093(Wl q- 092 -- 093) where o91 and co2 correspond to incoming CO2 laser beams in a four-wave mixing experiment with photon wavelengths of )~ = 10.6 /xm, w3 corresponds to photons with ~. - 9.2/zm, and the outgoing photon has energy h(Wl + 092 - co3). The index i refers to the electric field polarizations in the x or the y direction.

731

RAM-MOHAN ET AL.

The nonlinearity X{3) is proportional to the fourth derivative 04E/Ok4 averaged over the Fermi distribution of the carriers:

n(O4E/Ok4)_ [2/(27r)3]

f.3,

04E/Ok4 f (EF, E, T)

(7)

At T = 0 K, the Fermi function f(EF, E, T) reduces to a step function O(EF -- E(qx, qy) - Ez). The nonseparability of the potential does not allow the energy to be represented by a sum of terms dependent on qx or qy alone, so the the integrals are performed numerically by evaluating E(qx, qy) over a grid of values. The fourth derivatives are obtained using a nine-point difference formula on the energy dispersion. Figure 16 displays X{3) as a function of the number density n of carriers. The optical nonlinearity Xy(3) is larger than Xx(3), even though 04E/Oq4 happens to be larger than 04E/Oq 4. A systematic investigation of GaAs/A1GaAs superlattices [114] over a wide range of well and barrier thicknesses has shown that this can be understood in terms of the scale factors (a/zr) 4 and (b/zr) 4, the effects of band-filling, and the details of the phase-space integrations. The downtum in Xy(3) for number densities above ~1018/cc is due to a broad minimum in 0 4 E/Oq 4 at q y "~ 0.9, which becomes positive near the zone edge. This leads to a partial cancellation in the contribution over the Brillouin zone as the number density pushes the Fermi level to the band edge near the Brillouin zone boundary. The fact that X (3) can be lower than in bulk GaAs for certain layer-thickness values has been noted previously by Chang [113] 9 This is, in fact, the case for X- x(3) , y (see Fig. 16) in our particular calculation with the specific choice of layer thicknesses for cartier concentrations below 5 x 1017/cc, whereas Xy(3) is about 1-2 orders of magnitude larger than XGaAs" (3) for larger carrier concentrations. The envelope function approximation has been used extensively to solve for the energy levels and bands in quantum semiconductor heterostructures involving one-dimensional confinement. The FEM permits the use of this approximation to study structures with twodimensional electronic confinement; an extension to periodic structures with nonrectangular geometry is particularly straightforward in the FEM. We note from Figure 16 that control over the well and barrier thicknesses (al, a2) and (b], b2) in the two directions can allow for a much broader range of choices for the layer thicknesses so as to increase X (3). This is of importance in applications such as intensity-dependent optical switching and optical signal processing. Further investigations of the optical and transport properties of

1 0-6

10 e

10 "1

! [-

- - = - - bulk GaAs

"[ [-

= -- = 6/4 SL "-*-*" 8/5 SL

/ .~,'

-.

2 [ ..

ll x

~.~

II y

1

i ...

l o ~8

l o ~7

l o ~8

n (cm -3) Fig. 16. The free-carrier optical nonlinear susceptibility X (3) for the electric vector parallel to J (full curve) and ~ (dashed curve). For reference, the values of X (3) for bulk GaAs (long-dashed curve with open squares), for a (6/4) planar supedattice (full curve with filled circles), and for an (8/5) superlattice (dashed curve with open diamonds) are also shown as functions of cartier density. Reprinted with permission from L. R. Ram-Mohan and J. Shertzer, Appl. Phys. Lett. 57, 282 (1990). (g) 1990 American Physical Society.

732

WAVE-FUNCTION ENGINEERING

CBSLs would be of great theoretical as well as practical interest, especially for Q W W of more general shapes for cross sections. In conclusion, in the proposed new CBSL structure there is an enhancement of X (3) over the bulk nonlinearity by about 1-2 orders of magnitude, with the freedom to tailor X (3) for each field polarization. The FEM clearly provides the means for doing realistic computations on such complex structures.

5.5. Quantum Wires of Arbitrary Cross Section In the foregoing examples, for illustrative purposes, we used quantum wires of square or rectangular geometry. However, the finite-element method comes into its own when we start considering the physics of quantum wires of arbitrary cross section. We limit ourselves to just one example here and discuss how an FEM calculation for the energy eigenvalues can be performed for a quantum wire with a "bread-box" cross section. Such a cross section can arise for wires grown by the process of ion-etching a substrate (denoted by region I with material labeled I in Figure 17a), followed by filling the "notch" on the surface with

300 ~

'r III

\\

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I, . . . . .

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/

/

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300 9

,,,

-

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\,

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,~

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I /'\ /", F,~",,&/",/x/x/v..xA./"-.7,,xT/W,Z,-(G~,,../vvx,i~fx/\/\/x/', A ,/\ / \ ~ \ , ,"N,,,"\/",,/N/N/\J",I",L"',/"\,/\,/~/",/x/XZV~/~/x/'\,/,,jm i ../I I', I ,, / \ t.,J\,/',/,,/\/',,/\/',/x/',,/\/\l\.~/~'v~\/\/\/\~,~/\/\ ", ,

\ / '\/ ~2~jx)\./\/,,/\/\.,,\/\s\/\l\/~/,v,,/\l,~ '\ ,"?\\/ "/-i' "&"/'\l\'/\/",,, ., \ \/\// \" C' /

, /

,\ / ' \

.

/

i

/',

0

450 (b)

Fig. 17. (a) The boundary of the physical region and material boundaries are delineated with line elements (dashed lines) connecting boundary nodes. (b) The region is meshed adaptively with higher mesh density in and around region II. Regions I, II, and III refer to the substrate, the wire, and the cap materials, respectively.

733

RAM-MOHAN ET AL.

another material (material II occupying region II) and overlaying with a capping layer of material III. The most time-consuming part of the finite-element programming used to be the generation of a physically desirable mesh, with higher mesh density in regions of interest where the solution may be expected to vary rapidly. With the advent of automatic adaptive meshing, this issue has now been resolved for over a decade. We begin the FEM calculation by delineating the three regions using boundary nodes, as in Figure 17a. The boundary is constructed using linear elements, which separate the regions. Every boundary line is assigned a material on either side. The region outside the box is labeled as material 0. We considered triangular meshes for our calculations. The triangular elements are easier to break up for adaptive meshing and can be made to conform to the physical boundary as closely as desired. There are several approaches to triangulating the physical region for further finiteelement computations. In the Delauney triangulation, a number of internal node points are supplied, which then form the vertices of the triangles. We have used the "algebraic integer method," developed by Sullivan [ 116], which is faster than Delauney meshing and requires only the outline boundary elements to be specified. The physical region is discretized by assigning a uniform grid of interior points that are used for triangulation of the entire region. Now the grid points near the boundary are adjusted to conform to the boundaries of the materials. Every linear boundary element is also assigned a radius of refinement around it so that the mesh generated by the interconnecting lines can be refined in specific regions of interest where we might expect to see a rapidly varying solution. The result of this adaptive meshing is shown in Figure 17b. The boundary elements of the wire itself were assigned two levels of refinement; in each level of refinement, the radii of refinement were chosen such that the regions associated with the boundary elements overlapped to provide a finer mesh over the entire cross section of the wire. Once the mesh is created, it is checked automatically for the shape of each triangle to ensure that the mesh is compatible with the FEM calculations and that it will represent faithfully the physical region. Each triangular element is tagged for its material properties. The nodes of the elements are now renumbered so that the global matrices generated in the finite-element procedure are highly banded. This bandwidth reduction is essential because our adaptive procedure introduces additional nodes for more triangles in regions of higher mesh density. We employ the reverse Cuthill-McGee bandwidth reduction algorithm. This node renumbering precedes any actual FEM calculation. In the present calculation, we chose materials I and III to be A1GaAs with 30% A1 concentration, and material II to be GaAs. We employed linear triangular interpolation functions in the application of the FEM. There were 117 nodes at the initial phase of triangulation. With the first refinement this number increased to 277, and with the second level of refinement there were 515 nodes and 982 elements generated. After verification of the acceptance level of the triangles, we had 501 nodes and 958 elements. The halfbandwidth prior to bandwidth reduction was 459; after the band reduction this was reduced to 34. The global matrices depend on the model employed. For each energy band we expect to have a matrix dimension of about 501. The discretized action integral associated with the Schr6dinger equation was evaluated over each element. An empirical two-band model [47] was used to represent the conduction band states. The variation of the nodal wave-function parameters in the action integral leads, as usual, to a generalized eigenvalue problem. The global matrix is stored in a sparse-matrix format, which retains in computer memory only those elements that are not zero. The diagonalization itself is carried out using either the Lanczos, the subspace, or the Davidson algorithms modified to account for the complex-number arithmetic required in the multiband calculations, and for the sparsematrix format. These sparse-matrix considerations permit the direct in-core solution of the eigenvalue problem for fairly large matrix sizes. In this calculation the matrix dimension was 1002. The six eigenvalues for the bound states in the conduction band were determined for the present complex-matrix generalized eigenvalue problem using the method of sub-

734

WAVE-FUNCTION ENGINEERING

0.015 F

0.01 -

0.005

0 300

-0.005 0

!

-""

450

0

Fig. 18. The wavefunction of the lowestbound state in the conduction band of the "bread-box" quantum wire. The calculations were performed in a two-band model. space iteration. Figure 18 shows the conduction-band component of the electron's wave function. The resulting wave functions are then used to compute optical matrix elements, overlap integrals, etc. The methodology outlined here is still in its infancy. The FEM can be extended to triangular Hermite interpolation functions for much higher accuracy at the cost of having to work with larger matrices. We can clearly anticipate immediate extensions of the preceding considerations to the eight-band model and to much more complex two-dimensional heterostructure geometries, with profound consequences for wave-function engineering. We can expect the interplay between the geometry of the heterostructure and the optical and electronic properties of the system to lead to the discovery of new electronic processes and mechanisms that will be amenable to the design of new devices.

6. C O N C L U D I N G R E M A R K S Recent developments in what we call wave-function engineering of the electronic and optical properties of quantum heterostructures have been reviewed in this work. We have emphasized, in particular, the evolution of the field beyond the more restrictive concept of band-gap engineering, in which the confinement of carriers over the physical dimensions of the layers controls the energy gap as a manifestation of Heisenberg's uncertainty relationship. Technological advances in the crystal growth of semiconductor heterostructures of III-V and II-VI materials as well as masking and pattern etching, now allow us to much more directly alter the shape of the carrier wave functions to suit specific applications. Thus, to a remarkable degree we can control the probability density, or occupancy, of the carriers in any region of the heterostructure. Through the appropriate insertion of thin (even atomic) layers of a different material, by employing asymmetric wells, through the use of type-II interfaces, through localization in the barrier layers for carriers with above-barrier energy, through control over the dynamics of intervalley transfer via externally applied fields and optical phonon emission, through the use of strain to tailor the band mixing and valence-band properties, through the use of diluted magnetic semiconductor layers, and so on, we can significantly alter the carrier wave functions. Wave-function engineering provides a greater appreciation of the mechanisms governing carrier dynamics, because overlap integrals, optical matrix elements, density of states, tunneling times, lifetimes for carrier recombination, optical detection efficiencies, nonlinear

735

RAM-MOHAN ET AL.

optical properties, etc., can now all be altered through a judicious use of "heterostructure architecture." In creating the new generation of advanced devices based on detailed control over the electronic and optical properties of quantum heterostructures with novel geometries, the designer must necessarily rely, to a considerable extent, on computer modeling of the energy bands and wave functions. In the present work, we have demonstrated that the FEM is well suited to the task of efficiently calculating the required properties for structures of arbitrary complexity. Although our emphasis has been on integration of the FEM into the k - P framework, it should be mentioned again that tight-binding models may also be viewed in the same context, with individual atoms functioning as the "finite elements." FEM computations have allowed us to explore some fundamental aspects of the band structure of quantum semiconductor systems. The investigations of quasibound states and above-barrier states in III-V heterostructures were driven by modeling and feasibility studies performed with the FEM. The level degeneracy issues in square and rectangular quantum wires with finite-barrier height were also revealed through finite-element calculations. That we can compute in detail the optical properties of the checkerboard superlattices is based on the ability of the FEM to model complex geometries. By extrapolation, exciting new results revealing new physics can clearly be anticipated with explorations into the properties of systems with three-dimensional confinement. Wave-function engineering, made feasible by finite-element modeling, will play a vital role in the exploration of new physical concepts and in the development of new devices based on quantum heterostructures.

Acknowledgments We wish to thank E. H. Aifer, E J. Bartoli, W. W. Bewley, C. L. Felix, J. K. Furdyna, C. A. Hoffman, Lok C. Lew Yan Voon, C.-H. Lin, H. Luo, L. J. Olafsen, A. K. Ramdas, J. Shertzer, and J. Sullivan for collaboration on a number of topics presented here. We wish to thank Quantum Semiconductor Algorithms (QSA) for the use of their finite element and fight-binding algorithms.

References 1. 2. 3. 4. 5. 6.

7. 8. 9. 10. 11.

12.

13. 14.

15. 16.

17.

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Sakald, Jpn. J. Appl. Phys. 19, L735 (1980). 100. P. M. Petroff, A. C. Gossard, R. A. Logan, and W. Wiegmann, Appl. Phys. Lett. 41,635 (1982). 101. J. Cibert, E M. Petroff, G. J. Dolan, S. J. Pearton, A. C. Gossard, and J. H. English, Appl. Phys. Lett. 49, 1275 (1986). 102. H. Temkin, G. J. Dolan, M. B. Panish, and S. N. G. Chu, Appl. Phys. Lett. 50, 413 (1987). 103. E. Kapon, D. M. Hwang, and R. Bhat, Phys. Rev. Lett. 63, 430 (1989). 104. J. Lee, J. Appl. Phys. 54, 5482 (1983). 105. H. H. Hassan and H. N. Spector, J. Vac. Sci. Technol., A 3, 22 (1985). 106. H. S. Cho and E R. Prucnal, Phys. Rev. B 39, 11150 (1989). 107. D. A. B. Miller, D. S. Chemla, and S. Schmitt-Rink, Appl. Phys. Lett. 52, 2154 (1988). 108. M. Tinkham, "Group Theory and Quantum Mechanics" pp. 325-329. McGraw-Hill, New York, 1964. 109. C. K. N. Patel, R. E. Slusher, and E A. Fleury, Phys. Rev. Lett. 17, 1011 (1966). 110. E A. Wolff and G. A. Pearson, Phys. Rev. Lett. 17, 1015 (1966). 111. W. L. Bloss and L. Friedman, Appl. Phys. Lett. 41, 1023 (1982).

738

WAVE-FUNCTION E N G I N E E R I N G

112. 113. 114. 115. 116.

G. Cooperman, L. Friedman, and W. L. Bloss, AppL Phys. Lett. 44, 977 (1984). Y.-C. Chang, J. Appl. Phys. 58, 499 (1985). H. Xie, L. R. Ram-Mohan, and L. R. Friedman, Phys. Rev. B 42, 7124 (1990). J.R. Meyer, E J. Bartoli, E. R. Youngdale, and C. A. Hoffman, J. Appl. Phys. 70, 4317 (1991). J. Sullivan, in "CAD/CAM Robotics and Factories of the Future" (B. Prasad, ed.), Vol. 1, pp. 60-64. Springer-Verlag, Berlin, 1989.

739

Chapter 1 ELECTRON TRANSPORT AND CONFINING POTENTIALS IN SEMICONDUCTOR NANOSTRUCTURES J. Smoliner, G. Ploner Institut fiir FestkOrperelektronik und Mikrostukturzentrum der TU- Wien, Floragasse 7, A-1040 Vienna, Austria

Contents 1.

4.

5. 6.

7.

1.

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1. Aim of This Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Quantized States in Low-Dimensional Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1. Electrons in One-Dimensional Potentials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2. Parabolic Confinement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Basic Methods for Self-Consistent Calculations in One and Two Dimensions . . . . . . . . . . . . . . 3.1. Self-Consistent Treatment of One-Dimensional Problems . . . . . . . . . . . . . . . . . . . . . . 3.2. Self-Consistent Calculations in Two Dimensions . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3. Three-Dimensional Modeling of Quantum Dots . . . . . . . . . . . . . . . . . . . . . . . . . . . Transport Spectroscopy of Quantum Wires . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1. Magnetic Depopulation Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2. Magnetosize Effects and Weak Localization in Quantum Wires . . . . . . . . . . . . . . . . . . 4.3. Magnetophonon Resonances in Quantum Wires . . . . . . . . . . . . . . . . . . . . . . . . . . . Weakly and Strongly Modulated Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Vertical Tunneling through Quantum Wires . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1. Experimental . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2. Transfer Hamiltonian Formalism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3. Influence of the Potential Profile on 2D-1D Tunneling Processes . . . . . . . . . . . . . . . . . Vertical Transport Through Quantum Dots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.1. First Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2. Lateral and Vertical Transport through Quantum Dots: Coulomb Blockade Effects . . . . . . . . 7.3. Tunneling via Zero-Dimensional Donor States . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.4. 0D-2D Tunneling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1 2 4 5 6 8 9 13 19 20 21 25 31 41 48 48 53 56 68 68 71 77 82 86 86

INTRODUCTION

Before nanofabrication of semiconductor

processes became

available, the fundamental

devices were independent

of their geometrical

electronic properties

size. Through

nanofab-

Handbook of Nanostructured Materials and Nanotechnology, edited by H.S. Nalwa Volume 3: Electrical Properties ISBN 0-12-513763-X/$30.00

Copyright 9 2000 by Academic Press All rights of reproduction in any form reserved.

SMOLINER AND PLONER

rication, however, the geometrical dimensions of a semiconductor device can be made smaller than any of the other characteristic lengths of the electron system, such as the mean free path or the Fermi wavelength. Consequently, the device geometry is expected to influence the fundamental device and transport properties, which has made the investigation of the electronic properties of nanostructured systems a continuously growing field of solidstate research. Together with advances in molecular beam epitaxy (MBE) growth, nanofabrication allows for so-called "band structure engineering" in the vertical and lateral directions suitable for the design of semiconductor devices of almost any desired properties. In the very beginning of nanofabrication, quantum wire structures were suggested to provide efficient semiconductor lasers, because the artificial confinement of carriers in the active region of a nanolaser was expected to give a better performance [ 1, 2] than a bulk system. After that, the electronic properties of the wires themselves and their possible use for device applications became the center of worldwide activities [3]. In 1985, Luryi and co-workers [4] were the first to report a quantum wire device with negative transconductance, and it was demonstrated that this kind of quantum device is interesting for practical applications, for example, as field effect transistors [5]. With forthcoming advances in nanotechnology, the idea of an "artificial atom" or quantum dot became realizable and a topic of great interest. As ohmic contacts to quantum dots are difficult to establish, the first investigations of quantum dots concentrated on optical properties such as size effects in the absorption spectra [6] and the exciton dynamics [7]. Later tunneling spectroscopy [8, 9] was established as the genuine method for the investigation of the electronic transport properties of quantum dot structures [ 10]. After the presence of size quantization effects and quantum interference phenomena in wires and dots was demonstrated in the early experiments, further investigations revealed numerous other features that were partially not predicted by theoretical considerations, such as the quantized conductance in ballistic quantum wires [ 11, 12] or the quenching of the quantum Hall effect in strong magnetic fields [ 13, 14]. An artificially imposed lateral potential modulation is expected to induce a miniband structure similar to that obtained by MBE-grown perpendicular superlattices. Lateral surface superlattices (LSSLs) provide the possibility of creating artificial crystals made of quantum dot "atoms." Because the electron mean free path in these LSSLs extends over many periods, they are expected to reveal interesting quantum or band structure effects that are not accessible in conventional crystal lattices [ 15]. In particular, the evolution of the band structure in magnetic fields is expected to display several interesting features [ 16]. Indeed, the experiments performed on one-dimensional (1D) and two-dimensional (2D) LSSLs in a perpendicular magnetic field revealed a wealth of additional structure in the magnetoresistance, which has been shown, however, to be due to a geometrical commensurability between the electron's cyclotron orbit and the periodic potential landscape [ 17-21 ]. For details on these so-called (magnetic) commensurability oscillations, see Section 5. LSSLs were also investigated by tunneling experiments using a coupled quantum well system and equilibrium tunneling spectroscopy [22] (see Section 6). Tunneling spectroscopy principally offers the interesting possibility of studying electron transfer between systems of different dimensionality, for example, using a 2D gas as the emitter and a system of quantum wires [23] or dots [24] as the collector electrode. The tunneling characteristics give rather direct information on the Fourier transforms of the low-dimensional electron wave functions. Moreover, it turns out that the results obtained in the simulation of tunneling spectra are very sensitive to the actual shape of the potential, which brings us to the main motivation for writing this review. 1.1. Aim of This Review

While writing this chapter, it became clear that the lack of space and time as well as the huge amount of material published in the field of nanostructured systems makes it necessary to restrict the material presented here to several characteristic topics, selected with

ELECTRON TRANSPORT AND CONFINING POTENTIALS

regard to a few guiding aspects. The main emphasis in this chapter will be put on the role of the confining potential in low-dimensional systems. We will discuss the extent to which the confinement potential has a direct influence on the obtained results of lateral and vertical transport experiments, which serve as standard characterization methods for nanostructures. It will be shown how the different transport methods can be used to obtain a consistent picture of the shape and magnitude of confinement potentials and related parameters. Furthermore, in writing this review, we wanted to give the beginning experimentalist in the field some basic idea of the phenomena typically encountered in a transport investigation of low-dimensional systems and how the observed features will allow him or her to estimate the various sample parameters necessary for a detailed knowledge of the systems under investigation. From the preceding discussion, it is clear that the present review will be far from giving a complete overview on all the transport investigations performed on nanostructured systems in the past decade. As a major omission, we only mention the transport experiments in the ballistic regime. One reason for this is the fact that the topics of interest in the ballistic regime have only marginally to do with the major guiding aspect of this review, that is, the confinement potential and its direct influence on various transport properties. Another reason is, of course, that this transport regime has been extensively reviewed previously (see, e.g., the excellent review articles by Beenakker and van Houten [25, 26], covering the developments up to the year 1991) and that an in-depth account of the recent progress in this field deserves a review of its own. We would just like to mention some of the outstanding experimental achievements in this field, such as the study of the phase correlation behavior of electronic matter waves in semiconductor devices by ballistic transport experiments [27, 28]. Some other highlights include a modification of Young's double-slit experiment for ballistic electrons [29], as well as the experimental proof that lateral tunneling through a quantum dot is at least a partially coherent process [30], which was achieved with an extremely sophisticated device structure. Until very recently, the observation of ballistic transport phenomena was possible only in very short and narrow constrictions, the so-called quantum point contacts. Recent progress in the fabrication techniques of quantum wires and dots such as, for example, cleaved edge overgrowth [31, 32], however, has made it possible to create long conducting channels exhibiting the phenomena characteristic of ballistic transport [33, 34]. This allows an experimental test of several theoretical predictions on the behavior of onedimensional systems of interacting electrons (Luttinger liquid state) [35, 36]. Considerable progress has also been made in adapting suitable fabrication processes for narrow channels on very high mobility 2D electron gases at relatively large distances below the sample surface [34, 37]. This led to the first experimental evidence of specifically one-dimensional electron-electron interaction effects such as a theoretically predicted [38] zero-field spin polarization in short and narrow constrictions [39]. We also do not discuss fabrication techniques in great detail. This is partly due to the fact that the complexity of the transport investigations makes highly specialized solutions necessary. Almost any new fundamental experiment uses innovations and improvements especially conceived for its special purposes. The very fundamental fabrication principles in the nanotechnology of low-dimensional systems, however, were already reviewed earlier. Some basic references on these topics can be found in [25, 40, 72] and, of course, the literature cited therein. This chapter is divided into three main parts. In the first part (Sections 2 and 3), a survey of the basic electronic properties of low-dimensional systems is given, including the discussion of some simple numerical methods for self-consistent calculations in one and two dimensions. The second part (Sections 4 and 5) mainly deals with magnetotransport in quantum wires and lateral surface superlattices with an emphasis on the experimental determination of fundamental wire parameters and on methods to gain information on the actual shape of the confining potential. The third part (Sections 6 and 7) is dedicated to

SMOLINER AND PLONER

tunneling phenomena in low-dimensional systems. The systems and experiments reviewed in this last part are also selected under the aspect to which extent they allow access to potential parameters and/or the shape of the corresponding wave functions. Because in the theoretical apparatus underlying the analysis of tunneling phenomena the notation is not as unified in the literature as in the conventional magnetotransport sector, we decided to use the same notation as in the original articles in all cases where model calculations are discussed. This makes the description of the formalism somewhat incoherent but facilitates the direct reference to the cited articles.

2. QUANTIZED STATES IN L O W - D I M E N S I O N A L SYSTEMS Low-dimensional electron systems are commonly defined by lateral potentials artificially imposed on the two-dimensional electron gas (2DEG) situated at the interface of a modulation-doped semiconductor heterostructure. Throughout this chapter, we shall focus on results obtained using the GaAs-A1GaAs system. Several methods exist to create a lateral modulation of the effective potential at the heterointerface, which all use advanced lithographic or crystal growingtechniques. For details of nanostructure fabrication and nanolithographic techniques, see [25, 40, 41 ] and the references cited therein. The common starting point in the study of the electronic properties of low-dimensional systems is provided by confining the electrons of a 2DEG into narrow electron lines through an additional nanofabrication process. In case the lines are sufficiently narrow, lateral size quantization effects will occur and quasi one-dimensional electron systems, socalled quantum wires, are established. A typical quantum wire sample, fabricated by laser holography and subsequent wet chemical etching, is shown in Figure 1. To analyze the electronic properties of a quantum wire, we consider the electrons as independent particles moving in a confining potential V (x, z). Here V (x, z) describes the joint influence of the confinement in the growth (z) direction and the lateral confinement in the x direction induced by nanolithographic patterning. The latter is thought to leave only the y direction for free motion of the electrons. This one-particle point of view ignores the presence of correlations resulting from the Coulomb interaction between different electrons and summarizes the effects of electron-electron interactions by an average global contribution to the potential. The problem is often simplified further by assuming that the confining potential V (x, z) can be decomposed into a sum of two independent contributions V(x, z) = V(z) + V(x), where the first term is due to the confinement at the heterointerface and the second term accounts for the lateral potential modulation. It will be shown later that this treatment is not quite correct but it can be used in many situations as a good approximation to understand the results obtained in various experimental situations. This approximation also allows the separation of the motion in the growth (z) direction

Fig. 1. Schematicalview of a typical multiple quantum wire sample, which was fabricated by laser holography and subsequent wet chemical etching.

ELECTRON TRANSPORT AND CONFINING POTENTIALS

from the one-particle Schr6dinger equation describing the confined electrons by a separation ansatz ~ ( x , y, z) = ~(x, y)~o(z), where ~o(z) corresponds to the ground state of the underlying 2DEG with energy E z2D. Higher subbands in the z direction are not considered here, because commonly only the lowest subband is occupied in typical high-mobility GaAs-A1GaAs heterostructures. Within the effective mass approximation, this leaves us with the equation H d~ =

( p2 py2 ) E1D+ ~m, + ~m, + V (x) dp =

(1)

which gives the quantized states in the quantum wire and also the corresponding energy levels. The bottom of the 2D subband E 2D is commonly taken as the zero point of the energy scale and all quantization energies are given relative to this origin. In general, the confining potential V(x, z), or V(x) if the x and z dependence have been separated, has to be determined from a self-consistent solution of the Schr6dinger and Poisson equations. In the following sections, we will summarize the simplest methods for such self-consistent calculations, which can be used to analyze the electronic properties of quantum wires and quantum dots. To give some insight into the physics of quantumconfined motion and to introduce several notions used in nanostructure physics, we also show how the actual confining potential can be approximated by simple and analytically tractable functions. From the self-consistent calculations, it will become evident that these approximations are often sufficient to describe the experimental data, but not always and not under all conditions.

2.1. Electrons in One-Dimensional Potentials As stated before, we describe a one-dimensional electron system by a Schrtdinger equation of the form

#

H~=\2m,

+ ~

+V(x)

)~=E~

(2)

Because the motion along the wire axis in the y direction is assumed to be free, one can use the following factorized form of the wave function: r

1 y) = - - ~ exp(ikyy) ~(x)

(3)

where L is the wire length. Inserting this wave function into the Schr6dinger equation shows that the energy eigenvalues of the laterally confined electrons are quantized into subbands according to h 2 ky2 En (ky) = En + 2m*

(4)

To determine the 1D subband energies En, it is necessary to know the shape of the lateral confining potential V (x). There are several ways to model V (x) in a more or less realistic way. The two most familiar examples for analytical model potentials are the square-well potential V(x)

[0 / o~

i f - W / 2 l"t/3 Z IdJ D Z

V

400 nm SLIT z=5.6 nm

__

o

I-LtJ ....J ILl ._1 I.t.I Z Z .< "-r" (.9

1 -

0 -120

.__

-80

-40

0

40

80

120

LATERAL DISTANCE (nm) Fig. 9. Self-consistently calculated electron density for a quantum wire in split-gate geometry. The electron density is plotted for different gate voltages. (Source: Reprinted from [44], with permission of Elsevier Science.)

18

ELECTRON TRANSPORT AND CONFINING POTENTIALS

1.005

~"

,

'

i

. . . .

'l

. . . .

~

. . . .

i

,1

,

~-~., ./1

lO K ~

-248




"0

rr

"O

,I

0

2

4

6

8

10

B (T) Fig. 13. Derivativeof the magnetoresistance with respect to the modulated gate voltage Vg, measured for an array of quantum wires. The sample layoutis shown in Figure 12a. The period of the shallowetched grating was 450 nm. The inset shows the same data plotted as a function of the inverse magnetic field together with a Landau plot of the corresponding magnetoresistancemaxima.

shown in Figure 12a, where the confinement is achieved by shallow etching, the purpose of the gate in this configuration scheme is twofold. First, it produces the 1D confinement and, second, it serves as a modulating gate for contact resistance elimination. For the purpose of spectroscopic investigations, it furthermore provides an effective grating coupler for far-infrared radiation (see [79]). This sample configuration has the advantage of supplying quantum wires with a tunable confinement strength. Figure 13 shows a typical magnetoresistance trace obtained for a sample structure as depicted in Figure 12a, using a modulated gate voltage to eliminate the contact resistance [78]. A minimum occurs whenever the Fermi level is shifted across the bottom of the highest occupied magnetoelectric subband, where a sharp maximum in the density of states is followed by a region of minimal density of states (DOS). If a running subband index nose is assigned to each minimum and the index nosc is plotted against the inverse magnetic field position of the corresponding minimum in Rxx, a fan chart or so-called Landau plot is obtained (cf. the inset of Fig. 13). The characteristic feature in this plot, which demonstrates the presence of a 1D confinement, is the deviation from linearity at low magnetic fields. This behavior can be understood from Eq. (42), which describes the subband energies in a parabolic confinement potential. For the subband edge (ky ---0) of the nth subband, Eq. (42) yields

En(B) - h/o92 + o~(n + 89

For large magnetic fields, o~0 may

be neglected and the resulting dependence of nose on B -1 is linear. This is the well-known behavior of the Shubnikov-de Haas oscillations observed in the magnetoresistance of unstructured 2DEGs. The presence of the lateral confinement characterized by the additional frequency coo becomes visible only when it is at least of the same order of magnitude as the cyclotron frequency. For those magnetic fields where this is the case, the relation between nose and 1/B is no longer linear. This is the general signature of lateral confinement in narrow channels, no matter what the actual shape of the confining potential is [74, 81 ]. It is instructive to analyze the nosc(B -1) dependence in terms of a parabolic confinement potential [75] because this allows the analytical treatment of the magnetic depopulation effect and provides a particularly simple way to determine wire parameters from an actual measurement. The situation encountered in a magnetic depopulation experiment is depicted in Figure 14, which shows the energy of the magnetoelectric subband edges as a function of B. Whenever the Fermi level crosses the edge of the highest occupied magnetoelectric hybrid subband, that is, whenever EF -- Nhco(B), a minimum in the magnetoresistance is observed. Because the 1D electron density in the channel is constant, the

23

SMOLINER AND PLONER

/./ /

20

/i" 16

.,.

9

,:,

7 :

./" ,-

J

..

9........

..-r /':,...... .'............................ ~ ................. EF ,.. ......................

E lO

F~'-/-"- ~ 'i'"

~ 0

,

"

"'

a

~

=

300n m

v~-1oo

mV

~....~

o

;

2

8

B (T) Fig. 14. Dependenceof the magnetoelectric subband energy on magnetic field strength, calculated for a parabolic confinement with ho)0 = 1.57 meV.The dashed-dotted lines show the corresponding behavior of the Landau levels in an unstructured 2DEG. Also shown is the oscillating Fermi energy, calculated for a 1D carrier density of n 1 D = 5.68 x 106 cm-1. n is the subband index.

Fermi level oscillates with increasing magnetic field. From the 1D carrier density at zero temperature EF

nlD =

L

glD(E,

one obtains, together with Eq. (44) and EF = nlD .

B) dE

(46)

EN,

2. / 2 h. * . ~ k n 1/2 7t" o)0 n=0

(47)

This finally leads to the following relation between the index N of the highest occupied subband and the magnetic field position of the corresponding magnetic depopulation minimum in Rxx:

m IIn.o v .o.,2

4/3

O N - - -~e

/8m*

-- (hO)0) 2

N

(48)

Zn=0 n

If this relation is fitted to the experimentally determined Landau plot, N plays the role of the previously introduced nosc. As fit parameters, one obtains the subband spacing E0 = boo0 and the 1D carrier density n lD. The latter is related to the approximately linear behavior of the nosc(1/B) plot for high-magnetic-field values [75], which is obtained by replacing in Eq. (47) o) by a~c:

m*/e ( 3 7 r ) 2 / 3 N ~ (2m,h)l/3 -~-nlDE0

1 BN

(49)

In the preceding section, we have seen that in the case of quantum channels defined by a split-gate geometry the confining potentials as obtained from self-consistent calculations have the shape of a Woods-Saxon potential with a flat bottom. Only for very narrow channels or at quite low electron densities does the potential assume an approximately parabolic form [44]. In the case of quantum wires defined by the shallow etching method, the self-consistent calculations showed that the effective potential felt by the electrons is of a sinusoidal shape [61 ]. It is again for relatively low electron densities that the electronic wave functions are concentrated near the bottom of the sinusoidal potential where it is well described by a parabola. Only in these cases will the parabolic model and the described fitting procedure be able to reproduce the experimental depopulation data and give results

24

ELECTRON TRANSPORT AND CONFINING POTENTIALS

(a)

12 _a 8

C

./ §247

4 0 0

4-

r

4- calc. 4.- exp.

1

2

3

(b)

6

~ 4

(-

4- calc. 4- exp.

2 0

0.5

1.0

1.5

g-1 (T-l) Fig. 15. Experimental and calculated sublevel index nL versus the inverse magnetic field positions of the resistance minima for two different samples. The theoretical values are calculated under the assumption of a square-well potential and fitted to the experimental points with the channel width and the 1D carrier density as fit parameters. (a) Wide channel (estimated width and carrier density are 378 nm and 1.16 nm-1, respectively). (b) Narrow channel (162 nm, 0.38 n m - 1). The wide-channel sample is well described by a square-well potential. The parabolic approximation is found to give better results for the narrow channel (cf. [75]), but turned out not to be suitable for a description of the wide-channel experiment. (Source: Reprinted with permission from [81].)

for channel width and electron density that are in good agreement with independently estimated values. The second strongly simplified model potential, the square well, does not lend itself to as simple an analytical treatment as the parabolic potential. Rundquist [81] applied a numerical fitting procedure to describe wide and narrow channels defined by the split-gate geometry using a square-well confinement potential. As expected, the square-well model is able to describe wide channel experiments where the parabolic model does not give convincing results and vice versa (cf. Fig. 15, where the experimental results are plotted together with a numerical fit of the results with a square-well model). However, even in the simple case of a square well, the fitting procedure becomes numerically very expensive and is not easily implemented in routine investigations. Another model potential used to approximate the flat bottom potential of split-gate wires at high electron densities (or, alternatively, low gate voltages) is given by V (x) = (m*wZ/2)([xl- t/2) 2 for lxl >/t/2 and zero otherwise. It has been investigated in Wentzel, Kramers, Brillouin (WKB) approximation by Berggren and Newson [76]. The use of this potential in the numerical analysis of an experimental situation requires one additional fit parameter, namely the width t of the flat potential section. If, in addition, a modulating gate configuration is used for the magnetoresistance measurement, a phase shift in the d Rxx/dVc traces has also to be taken into account, which requires adding a further unknown parameter Boffset to the positions of the magnetic depopulation minima. Altogether, one thus needs four fit parameters for the analysis of the Landau plot. The so obtained values of E0 and no are questionable in particular when the Landau plot consists of only a few data points.

4.2. Magnetosize Effects and Weak Localization in Quantum Wires

4.2.1. Magnetosize Effects A useful quantity for the characterization of quantum channels is the electrical width W, which can be estimated from several independent effects in the magnetic field and temperature dependence of the sample resistance. The values extracted for W allow us to

25

SMOLINER AND PLONER

(b)

(a) 25 2O

200 150

15 X

n'-"x

~ 100

10

n-'

5O

5 0

/

J

.,,,-.-'~#BG=0V 0

0

1

2 B (T)

3

'--

o

4

W

1

,

|

2 a (m)

|

|

3

|

4

Fig. 16. Low-temperature (T = 2 K) magnetoresistance of an array of shallow etched quantum wires, measured with different back-gate voltages applied to the substrate. At low back-gate voltages, the behavior of the system corresponds to a modulated 2D gas. At higher gate voltages, the Fermi level is reduced below the modulation potential amplitude and typical 1D features are observed, such as the large magnetosize peak at B = 0.27 T and the negative differential magnetoresistance caused by a suppression of 1D weak localization at B ~< 0.1 T. The pronounced negative differential magnetoresistance superimposed on the depopulation oscillations at VG >/-- 100 V is due to the suppression of backscattering by a magnetic field (cf. Fig. 17). The - 173-V trace has been drawn separately for clarity (b). The squeezed traces at the bottom of part b are the same curves as in part a.

cross-check whether a model potential used in the analysis of magnetic depopulation experiments is well suited to describe the experimental situation. Figure 16 shows two-terminal magnetoresistance traces for an array of quantum wires fabricated by laser holography and shallow etching. The etching is very shallow in this case such that without additional measures only a periodic potential modulation is superimposed on the 2DEG. The results of Figure 16 were obtained without application of a modulating front-gate voltage and, therefore, contain the contribution of the contact resistance which, however, is small in this case. The electron density was reduced by applying a negative back-gate voltage on the substrate side of the sample. In this way, the Fermi energy becomes gradually smaller than the amplitude of the potential modulation, eventually leading to a system of well-separated quantum wires. The magnetoresistance traces depicted in the figure clearly show the evolution of two magnetoresistance phenomena typical for narrow electron channels in the diffusive transport regime: magnetosize effects and weak localization. We first consider magnetosize effects. With increasing back-gate voltage, that is, increasing confinement of the electrons to 1D channels, a magnetoresistance peak evolves at about 0.3 T. This so-called magnetosizepeak has been shown by Thornton et al. [82, 83] to be due to diffuse scattering from the channel walls of electrons moving on cyclotron orbits. It can be shown that this effect can be explained by purely classical arguments and that the presence of diffuse boundary scattering is an essential prerequisite for the observation of a magnetosize peak. Note that the mean free path of the electrons has to be large enough that boundary scattering contributes appreciably to the total wire resistance. The situation is depicted schematically in Figure 17, which shows two classical electron trajectories at two different field strengths [25]. For field strengths where the cyclotron radius is of the order of Rc ~ W/2 (Fig. 17a, W is an effective wire width), the probability for electron backscattering is considerably larger than in the case of Rc > W > > l

(56)

Here, W is the width of the channel, l is the mean free path, lm = ~/h/e B is the magnetic length, and l0 - v/Dr0, where D denotes the diffusion constant, is the phase coherence length. A first-principles justification of Eq. (56) can be found in the review article of Beenakker and van Houten [25]. The preceding relation is derived under two assumptions. First, the magnetic length lm has to be larger than the effective width of the channel; otherwise, the localization is of a 2D nature. This requirement is usually well established at the low magnetic fields for which the suppression of weak localization is observed. The second condition requires that the width W be larger than the electronic mean free path l, which is usually not the case for the conventional high-mobility GaAs-A1GaAs samples used to study the effect. It has been shown by Beenakker and van Houten [90] that in the opposite regime 1 >> W one has to take into account the effects of boundary scattering on the phase accumulated along a closed trajectory enclosing a magnetic flux (flux cancellation effect). Equation (56) has then to be replaced by

(57> The weak localization correction tums out to be much weaker in the case of an un9 ID so that structured 2DEG (which also finds its expression in the W dependence of 3gloc), the negative magnetoresistance at low field becomes more and more pronounced as the 1D confinement becomes stronger. This is what is observed in parts a and b of Figure 16, where a pronounced negative differential magnetoresistance is observed only for the highest back-gate voltages and, hence, the narrowest channels. The magnetic field dependence of the weak localization correction can be exploited to obtain wire parameters such as the width W and the phase coherence length l o. One simply fits one of the expressions Eq. (56) or Eq. (57), chosen appropriately to the sample geometry, to a plot of G ( B ) - G(O) = I / R x x ( B ) - I / R x x ( O ) versus magnetic field, using W and 1o as adjustable parameters. This is done in a field range where Im > W and the suppression of weak localization is clearly observed in the magnetoresistance. This method was applied for the first time by Thornton et al. [91] for a 15-#m-long channel defined by a split gate on top of a GaAs-AIGaAs heterojunction. We reproduce their results, obtained for various temperatures below 1 K, in Figure 18. The solid curves are fitted according to Eq. (56). It has been discussed if the "dirty metal" expression Eq. (56) for 6gllDc is suitable in this case, because the estimated mean free path is larger than the channel width. However, the extracted values for the different characteristic lengths give a more or less consistent picture, if one assumes that the damage induced by the electron beam lithography [74] has led to a

29

SMOLINER AND PLONER

0.41 K 0.46 K

4.0 10-7

0.56 K 3.0

m

0.6 K 1.0 K

o - - 2.0 rn n

1.0 -

0.0 . . . . 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14

Magnetic Field (TESLA) Fig. 18. Differenceof magnetoconductance and zero-field conductance for a split-gate wire, measured at different temperatures. The sample geometryis shownin the inset. The solid fines stem from a two-parameter fit according to Eq. (56). (Source: Reprinted with permission from [91]. 9 1986 AmericanPhysical Society.)

drastic reduction of the mean free path in the wire, compared to the value of the unstructured 2DEG. The values for the phase coherence length l0 (200 nm or below) found from the fits shown in Figure 18 together with the condition l0 >> l underlying Eq. (56) would be consistent with a mean free path that certainly is not reduced below the estimated width of 50 nm, but could have reached the same order of magnitude. An example of the application of the correct expression Eq. (57) to the low-field magnetoresistance in short and narrow channels defined by the shallow etching technique can be found, for example, in [92]. For the sake of completeness, it should be mentioned that there is another correction to the Boltzmann-Drude conductivity go that is due to electron-electron interactions. Because both the weak localization and the interaction effects are relatively weak, they may to first order be taken into account as additive corrections to go: o loc (58) glD -- go + OglD -Jr-8ge---e The interaction correction has been estimated to be [93]"

e 2 ~ hD 8 g e-e -" -otto----~ 2 k B T

(59)

which is valid if the thermal length ~/h D/kB T < W. ot is a coupling constant that depends on the electron density and on the screening length in the system under consideration. Its magnitude is usually of order unity and in the commonly encountered experimental situations its sign is positive [25]. Electron-electron interactions thus reduce the conductivity of a narrow channel. The localization correction can be easily distinguished from the interaction correction in a magnetic field. As is obvious from Eq. (56) or Eq. (57), the former is completely suppressed already at very weak fields, whereas the latter is almost unaffected in this field regime. Theoretical considerations indicate that there is a small contribution to 8ge---e which is also sensitive to weak magnetic fields. But the main contribution to the conductivity correction reveals its magnetic field dependence only in strong fields. Usually, the weak-field-dependent part of 8ge--e is neglected, which makes the distinction between

30

ELECTRON TRANSPORT AND CONFINING POTENTIALS

the two corrections feasible [94]. If one wishes, one may use the T dependence of the interaction correction, determined from the magnetoconductance after subtraction of the weak localization correction, to estimate the diffusion constant D of the narrow channel [74, 91 ].

4.3. Magnetophonon Resonances in Quantum Wires In 1961, Gurevich and Firsov [95] discovered that the quantization into Landau levels at high magnetic fields should lead to resonant longitudinal-optical (LO) phonon scattering of electrons between these equidistant Landau levels. As the LO phonons are assumed to be dispersionless in the interesting k-space region, resonant scattering between Landau levels is expected whenever the phonon energy equals an integer number of Landau levels:

hwLo = Nhcoc

(60)

This so-called magnetophonon effect has been shown to result in an oscillatory behavior of the magnetoresistance at temperatures high enough to ensure a sufficient population of the phonon states (usually at T >t 100 K). Since then, magnetophonon resonances (MPRs) have been observed in a variety of semiconductor systems (for a review of the work until 1975, see [96]). In the bulk, MPRs have become a standard method for the determination of effective masses [97, 98] and proved to be a useful tool for the investigation of the conduction band nonparabolicity in ternary compounds for temperatures up to 400 K [99, 100]. After the first detection of MPRs in 2D systems [101], a wealth of phenomena was investigated also in 2D electron gases using the magnetophonon effect. Besides the determination of effective masses, an important subject that could be investigated using the magnetophonon effect in 2DEGs was the influence of the reduced dimensionality on the electron-phonon interaction [ 102-104]. As discussed previously, in quantum wires the energy spacing of magnetoelectric hybrid levels does not only depend on the magnetic field strength, but also on the 1D subband spacing induced by the lateral confinement. If, for example, parabolic confinement is assumed, the energy levels are calculated according to En(B) -- hw(n -+- 89 --

hv/co2 + wZ(n + 1). This leads to a modification of the magnetophonon resonance condition Eq. (60) where now hw has to be used instead of hwc. As a consequence, the magnetic field positions of the magnetophonon resonances should be shifted to slightly lower fields compared to the 2D case. Because this shift depends on the subband energy hwo, it is expected that MPRs can be used for subband spectroscopy of 1D quantum channels. After a brief r6sum6 of the relevant theoretical work on MPRs in quantum wires, it will be shown in the following that MPRs are indeed useful for the experimental determination of 1D subband energies. The obtained results for the sublevel spacings turn out to be different from the values extracted from low-temperature magnetic depopulation investigations. We discuss the reasons for this difference and show that it gives direct qualitative information on the shape of the wire potential.

4.3.1. Magnetophonon Resonances in Quantum Wires: Theory The first theoretical investigation of MPRs in quasi one-dimensional electron systems was performed by Vasilopoulos et al. [105]. To determine the contribution to the magnetoconductivity due to electron-LO phonon scattering, they started from a quantum transport equation of the form e2

trxx = 2kBTVo Z ( n r ~,~'

-(nr162162

(('lYlY(')) 2

(61)

which follows from a modification of the formalism developed to describe the magnetophonon effect in 2D systems [106]. Here, (n~) denotes the Fermi-Dirac distribution

31

SMOLINER AND PLONER

function, y is the coordinate along the wire axis, and Wr162is the usual Fr6hlich-type transition probability between the two states ~ and ~I. The I~) denote the one-particle states of the 1D confined electrons. For their calculation, it is assumed that the confinement in the growth direction can be separated from the lateral confinement and that the latter is well described by the usual harmonic oscillator potential. The z component tp0(z) of the wave function is approximated by the well-known Fang-Howard trial functions ,3/2 qgo(z) = o o z e x p ( - b o z / 2 ) . Thus,

(r[~ ) = On (v/md)/h(x - 2)) 1//,~/-Lexp(ikyy)q)o(z) where the harmonic oscillator functions, given in the paragraph following Eq. (11), have been used. It turns out that in the case of relatively weak confinement (o90 < Wc) Crxx may be calculated analytically. The LO phonon-mediated magnetoconductivity consists of a contribution falling off monotonically with increasing B and an additional oscillatory part tr~ which is given by [105]: crosc X

O(

(wc ) NlsD12 cos(2yrWLO/W) -- exp(--2yrI"N/hw) w kBThw cosh(2yrI"N/hW) - cos(2yrwLO/W)

(62)

A plot of this relation is shown in Figure 19. The total magnetoconductivity, including the monotonic part, is obtained from Eq. (62) by replacing the numerator cos(2zrWLO/W) -exp(--2Jr FN/hw) by sinh(2~r FN/hw). w is again the combined "renormalized" frequency w = V/W2 + COc 2, F N is the magnetic field-dependent width of the Nth magnetoelectric hybrid level, l-2B-- h / m * w is a modified magnetic length and, finally, WLO is the frequency of the LO phonons, which is assumed to be given by its bulk value. In the case of weak confinement the oscillatory part of the magnetoconductivity is thus described by a series of exponentially damped cosine oscillations just as it is well known from the magnetophonon theory in the bulk and in 2D systems [107, 108]. Whenever the resonance condition hwLo = vhw with integer v is satisfied, a maximum in the magnetoconductivity is observed (cf. Fig. 19). The main effect of a weak 1D confinement on the magnetoconductance is thus simply a shift of the resonant maxima in Crxx to smaller magnetic fields as compared to the resonance condition [Eq. (60)], valid for bulk and 2D systems. This first investigation of the 1D magnetophonon effect has been followed by several improvements of the theory, mainly concerning the extension to the case of arbitrary confinement strength. Mori et al. [109] pointed out that, in the case of strong confinement, the influence of the confining potential on the electron motion may not be neglected. Employing a Green's function approach to the general Kubo formula and using the same parametrization of the confinement as before, they were able to show that, in addition to the weak confinement expression already given by Vasilopoulos et al. [105], there is a second, qualitatively different contribution to the 1D magnetoconductance. To understand the difference between the two contributions, one may resort to a simple classical picture. Consider a wide, weakly confined quantum wire. In sufficiently strong magnetic fields, a considerable part of the electrons will be in Landau level-like states. Classically, they are localized on circular cyclotron orbits. LO phonon scattering will lead to hopping motion between these localized orbits and, therefore, to an enhancement of the electron mobility. This is why maxima occur at resonance in the magnetoconductance as indicated in Figure 19. On the other hand, if the confinement is strong and the wire narrow, a considerable fraction of electrons will be in edge states corresponding to skipping orbits propagating along the wire. The LO phonons will scatter electrons off their propagating modes, thereby reducing their mobility. This is expected to lead to resonant minima in the magnetoconductance. In Figure 20, the second derivative of trxx, calculated according to the model of Mori et al. [ 109], is plotted for the two cases of low and high confinement energy.

32

ELECTRON TRANSPORT AND CONFINING POTENTIALS

o -~ x x

0

T=140 K ~/~LO=0.039 (W=100nm)

90.0 80.0 70.0 60.0 50.0 40.0

NIl D=105cm-1

Ns2D=5x1011cm-2

30.0 20.0 10.0 0.0

I

i

t

I

I

,

~--

~

I

i

, - ~

i

2.0 1.0 0.0

o ~ -1.0 -2.0 -3.0 -4.0 0.2

I

0.4

0.6

f

,p

0.8

i

t

i

1.0

1.2

0)/0,) LO Fig. 19. Top: Magnetoconductivity in units of tr0 = e2/hkLo as a function of the combined frequency ~o (= ~ in the figure). The parameters used in the calculation are also shown, g2 is the confining frequency of the parabolic potential; N 2D is the depletion charge density, needed for the calculation of 1"N. Bottom: Oscillatory part Oxx _osc according to Eq. (62). (Source: Reprinted with permission from [105]. 9 1989 American Physical Society.)

~c/~oO

~c/~O0 0.2 0.4 0.6 0.8 1.0 1.2

0.2 0.4 0.6 0.8 1.0 1.2

rn x

% I

o

i .....

e

"~

%

i;0

o2 . . . . .

I

0.0 0.2 0.4 0.6 0.8 1.0 1

0.0 0.2 0.4 0.6 0.8 1.0 1.2

~c/O~0

~c/O~0

Fig. 20. Calculated second derivative of the two contributions to the magnetoconductivity for weak (left) and strong (right) confinement, trpo denotes the contribution corresponding to the skipping motion of electrons along the wire boundaries, cre_ph is due to electrons without interaction with the channel boundaries. The traces are calculated for T = 100 K, a level broadening F of 1 meV, and a confining frequency of the parabolic potential of 1 meV (left) and 5 meV (right). The insets show the corresponding underived quantities in units of cr0 = ne 2/otogOm*, ot being the Frtihlich coupling constant. In the figure, 090 is the LO phonon frequency, O9c is the cyclotron frequency, and ~c is again the combined frequency of the magnetoelectric hybrid levels. (Source: Reprinted with permission from [109]. 9 1992 American Physical Society.)

These results have been confirmed theoretically by Ryu and O'Connell [ 110, 111 ], who used a different quantum transport approach [ 112] to describe the influence of resonant LO phonon scattering on the magnetoconductance. Their model calculations also assume a parabolic confinement potential and again give two contributions to the magnetoconduc-

33

SMOLINER AND PLONER

tivity, the first being almost identical to the result of Vasilopoulos et al. [ 105]. The second term was attributed to a "nonhopping" contribution to the electron conduction, which is qualitatively reminiscent of Mori's skipping orbit motion term.

4.3.2. Magnetophonon Resonances in Quantum Wires: Experimental Results Regarding the nature of the magnetic depopulation experiments discussed previously and the methods of calculating the subband spacing from the resulting Landau plots, it is clear that it is necessary to have a sufficient number of occupied subbands in order to obtain reliable results for E0 and n 1D. It is the main advantage of the magnetophonon method of subband spectroscopy that the number of occupied subbands is largely irrelevant for its application. It is, therefore, a transport characterization technique for quantum wires with low carrier densities or relatively large subband spacing. It could even be used to characterize quantum channels in or at least very near to the quantum limit where only one 1D subband is occupied (provided, of course, the subband spacing is substantially smaller than hWLO). However, it has been shown experimentally [ 103] and theoretically [ 108] in the case of MPRs in 2D systems that the oscillation amplitude of the magnetoresistance strongly depends on various scattering mechanisms such as scattering from charged donor impurities. These scattering mechanisms influence the broadening of the Landau levels or magnetoelectric hybrid levels in 2D and 1D, respectively. The experimental results [113, 114] indicate that if the influence of charged donors is reduced by low total doping and large spacer layers of the underlying heterostructures, a much more pronounced magnetoresistance oscillation is obtained at high temperatures. Consequently, the low-density regime is the natural field of application of the magnetophonon effect for the characterization of quantum wires both because this regime is not readily accessible to magnetic depopulation measurements and because the magnetophonon effect is more easily resolved. On the other hand, one has to be aware of the considerable amount of unwanted scattering sources that are introduced by any nanofabrication process. The shallow etching method, in particular, introduces considerable side-wall roughness in the narrow channels. This, in turn, will reduce the amplitude of the high-temperature magnetoresistance oscillations and be disadvantageous for their resolution. For this reason the following experiments discussed briefly were conducted on a set of quantum wires obtained by very shallow etching on a low density, high mobility heterostructure. The most prominent features of the sample material used in the experiments are the low integral doping and the relatively wide spacer layer. Due to these features very shallow etching is sufficient to obtain appreciable 1D confinement, keeping the amount of sidewall roughness within tolerable limits. Some details of the sample structure are given in the caption of the following Figure 21. This figure shows a set of typical magnetoresistance traces, recorded at T --- 100 K and revealing pronounced oscillatory structure due to the magnetophonon effect. Figure 22 shows two examples of the oscillatory part of the magnetoresistance ARose, which were obtained from similar data as those shown in Figure 22 after subtraction of a monotonous background resistance. The lower trace corresponds to a sample (labeled "1" in the following), where slightly deeper etching is done in comparison to sample "2". The two samples are otherwise identical. The R (B) traces shown in Figure 21 were obtained for sample "2". Note that for the more shallow wires of sample "2" the oscillation amplitude is almost an order of magnitude greater than for sample "1". On the other hand, the oscillation of sample "1" does not seem considerably broadened as compared to the ARose of the other sample. The most interesting feature of the traces of Figure 22 is that they seem to be "phase-shifted" with respect to each other. This phase shift together with the large reduction of the oscillation amplitude observed for sample "1" indicates that for the more strongly confined wires of this sample one en-

34

ELECTRON TRANSPORT AND CONFINING POTENTIALS

8OO

~.

600

n"

400

20O

0

o

~;

,:

~

8

~o

B (T)

Fig. 21. Typicalmagnetoresistance data measured on an array of shallow etched quantum wires at T = 100 K. The various traces correspond to sample "2" for different electron densities (see text). The underlying heterojunction consists of 100 ,~ GaAs cap undoped, followed by 300/~ A10.4Ga0.6As, doped to 2 x 1018 cm -3, and 600/~ undoped A10.4Ga0.6As spacer.

'

'

' sample 2'

. '

20

A

~"

0

0.5

-20

0

ft.

-40

sample 1 3

4

5

6

~/ 7

8

9

10

B (T)

Fig. 22. Oscillatory part of the magnetoresistance A Rosc plotted for two different samples. The curves are obtained after subtraction of the monotonic background from the R (B) traces, some examples of which are shown in Figure 21. Sample "1" (bottom curve) was slightly deeper etched than sample "2" (top curve). This slight increase of the etching depth leads to a reduction of the oscillation amplitude by almost an order of magnitude as well as to a drastic "phase shift" of the oscillation. Note the different y-axis scales valid for the two traces.

counters a situation where there is a crossover b e t w e e n the two transport regimes discussed in the previous section. For sample "1" scattering off skipping orbits seems to be the dominant source that influences the magnetoresistance. Therefore one observes resistance maxima at resonance whereas the other sample "2" displays m i n i m a at resonance. It turns out that this assumption leads to a consistent explanation of the features of A Rosc observed in Figure 22. To analyze the experimental data quantitatively, one assumes a parabolic confinement 2 V (x) = ~1 m , 2o90x for the q u a n t u m wire. Again, x is the direction perpendicular to the wire and m* is the electron effective mass (frequently called the polaron mass in the context of MPR). In a perpendicular magnetic field, the bottoms of the magnetoelectric hybrid levels are quantized according to E ( B ) = hCOeff(n + 1) with ~O,)eff-- W/(hO)c)2 '[- E~ and Eo = hcoo being the 1D subband spacing. As discussed before, one assumes that the weak confinement case is valid for sample "2". The resonance condition Nhcoeff --- hmLO

35

(63)

SMOLINER AND PLONER

60

(a)

a'

(b)

50 ~ 16_. 0.3 r n e U [ I"- 40 ~" 30

/ a=6 f

l

"

/

//

z 4 T X I..U 3 z

N=3

/

,~ 2 z

4

,,:I: 1 ._J

f /

0

0

I

I

I

0.04

I

0.08

EO=1.1___0.2 meV n1D=1.9.108m-1

I

0

0.12

1/N 2

0'.5

i

1'.5

1/B (T-l)

Fig. 23. (a) Plot of the squared magnetic field position of the resonance minima in ARosc versus 1/N 2, obtained from the data shown in Figure 22 for sample "2". The corresponding value of the subband spacing obtained from the intersection of the resulting straight line with the B2-axis is 1.6 meV. (b) Landau Plot obtained from magnetic depopulation data for the same sample and electron density as in (a). The solid line represents a fit using a harmonic oscillator model, which gives a subband spacing of 1.1 meV.

thus applies to the minima in the magnetoresistance oscillation ARosc [109]. For sample "1" this condition is related to the resonant maxima in A Rosc. Using ELO = hOgLO, this resonance condition may be rewritten as follows: B2

=

( m * ) 2 E20 (m*) 2 -~- - ~ - - - -~- E 2.

(64)

According to this equation, the B 2 values, corresponding to the resonant extrema in A Rosc, plotted versus 1/N 2 should lie on a sfl'aight line. Its slope is a measure of the effective mass of the confined electrons, whereas its intersection with the B2-axis is proportional to the squared subband spacing E0. It should be emphasized that this simple relationship is only valid if the confining potential can be approximated by the harmonic oscillator form given above. Figure 23a shows the positions of the resonant minima in ARosc taken from the upper curve in Figure 22 (corresponding to sample "2"). The solid straight line stems from a fit of the data according to Eq. (64), using the LO phonon energy for bulk GaAs, ELO = 36.6 meV. The simple parabolic model potential is seen to describe the experimental data quite well. As parameters of the fit one obtains a magnetophonon effective mass of (0.069 4- 0.007)me and a subband spacing E0 of (1.6 4- 0.3) meV. The value for E0 can now be compared to the corresponding low temperature value, obtained from a magnetic depopulation measurement on the same sample at T = 2 K. The resulting Landau plot is shown in Figure 23b. The deviation of the plot from a straight line clearly shows the 1D behavior of the laterally confined electrons. The solid line interpolates between calculated points fitted to the data according to the model of Berggren et al. [75] (see Section 4.1.1), which also assumes a parabolic confinement potential. The resulting subband spacing is E0 = (1.1 -4- 0.2) meV, which is somewhat smaller than the corresponding high temperature subband energy. When one changes the carrier density of the quantum wires, for example by illuminating the samples with a red light emitting diode, one obtains the subband spacing as a function of the 1D carder density as shown in Figure 24. Solid circles correspond to data obtained from an analysis of the MPR signal of sample "1". Open diamonds represent the same data for sample "2". The open circles were obtained from magnetic depopulation experiments on sample "2". Figure 21 shows a set of typical magnetoresistance traces measured for varying carder density of sample "2". To arrive at the plot of Figure 24 the electron density

36

ELECTRON TRANSPORT AND CONFINING POTENTIALS

3.5

2.5 ,.-..,

> E o ILl

2 1.5

0.5 0

1

1

15

I

2 nl0

2'5

t

s

315

(x 10 8 rn-1)

Fig. 24. Subband spacing as a function of the 1D electron density for the two samples considered in the text. Solid circles: Magnetophonon results for sample "1". Open diamonds: Magnetophonon results for sample "2". Open circles: Subband energies obtained by magnetic depopulation from sample "2". The increase of E0 with decreasing nlD is attributed to screening effects, as discussed in [115].

was determined from the linear part of the low temperature Landau plots according to Eq. (49). Details of the experimental procedure can be found in [114] and [115]. Note that in order to determine the low temperature subband spacing from the magnetic depopulation data it is necessary that the number of occupied subbands in the wires is large enough for the usual evaluation methods to be applicable. This is the case only for sample "2" at relatively high carrier densities. In all cases where a direct comparison was possible, the low temperature subband spacing turned out to be systematically smaller than the high temperature value by 30-50%. Before giving an explanation of this apparent difference, it is worth mentioning that both in the theoretical and the experimental analysis the LO photon energy of 36.6 meV of bulk GaAs is assumed. Note that there is experimental evidence that the presence of the GaAs-A1GaAs interface leads to a modification of the photon energies. From a combination of cyclotron resonance and magnetophonon resonance experiments on various GaAs-A1GaAs heterojunctions, Brummell et al. [ 102] found that the LO phonon energy appears to be reduced by approximately 5% to 34.8 meV. However, this possible slight modification of the LO phonon energy has no influence on the above analysis. The reason for this insensitivity is that the statistical error of the fit in Figure 23a is, in spite of the excellent correlation to the data, not very much smaller than approximately 10%. This experimental error far exceeds that introduced by any uncertainty in the phonon energies. To explain the difference in the E0 values obtained at low and high temperatures, respectively, we first note that the thermal rearrangement of the electrons among the 1D sublevels at elevated temperatures cannot account for the observed difference. If this rearrangement is considered in a self consistent calculation, it can be shown [ 116] that it will indeed lead to a slight enhancement of the subband spacing. However, these changes in E0 are small (less than 10%) unless one assumes considerable recharging and reordering of the electrically active impurities, which is not a very realistic assumption. It rather turns out that the observed difference can be consistently explained if one takes into account that the actual confinement potential for shallow etched quantum wires is not exactly parabolic but sinusoidal. To demonstrate this, we model the experimental situation by choosing a one-dimensional potential of the form V ( y ) = Vmod(COS(2Jry/w) + 1)/2 that best approximates the self-consistently calculated potential for a shallow etched wire (cf. Fig. 6). Using this model potential, we calculate both the magnetoelectric confinement and the corresponding energy states as a function of magnetic field, simply using the onedimensional Schrrdinger equation and the discretization schemes described in Section 2.

37

SMOLINER AND PLONER

30 ~" 25 0 v

E 20

~15 c 10 UJ

50 100 150 200 250 300 350 400 X (nm) Fig. 25. Cosine-shaped model potential with a period of 400 nm and a modulation amplitude of 25 meV. The energy levels are calculated for zero magnetic field. Because of the shape of the potential the subband spacing decreases with increasing energy.

,-, >

80 70 60 5o

N 4o ~ 3o c

w

20 10 0 0

0.5

1

1.5

2

2.5

3

B (T) Fig. 26. Magnetoelectric subband edges as a function of magnetic field calculated for the cosine potential shown in Figure 25.

Figure 25 shows the energy levels for a cosine potential with V m o d -'- 25 meV and a period of 400 nm for zero magnetic field. To calculate their magnetic field dependence, one adds the magnetic confinement according to V(y) = Ve(y)+ Vm(y)-

Vmod[

2

cos

(~)

] 1 , 2

+ 1 + ~m COc(X- x0) 2

(65)

To cover the essential features of a magnetophonon or magnetic depopulation experiment, it is sufficient to consider the positions of the sublevel bottoms, that is, to calculate the magnetic field dependence of the 1D subbands setting the center coordinate x0 = 0. The resulting B dependence of the hybrid level energies is shown in Figure 26. Two main features are interesting. First, the subband spacing of the high-lying subbands is obviously smaller than that of the low-lying levels of the cosine potential. This is important when considering the information on the subband spacing E0 obtained from the magnetic depopulation method. E0 is found from that part of the Landau plot where it deviates from a straight line. That is, the main information is obtained from those high-lying subbands that are depopulated at low magnetic fields. If the Landau plot is fitted with a model curve calculated from a simple parabolic potential (Section 4.1.1), one has to be aware that this will only reproduce the subband spacings for the high-lying levels. Numerically, one can simulate this situation by determining the magnetic field positions, where the magnetoelectric subbands cross the Fermi level. The resulting Landau plot is then evaluated using the simple harmonic oscillator model. In fact, performing this procedure for the model potential of Figure 25, we obtain an energy spacing of 1.35 meV, which excellently reproduces the subband spacing of the high-lying subbands (1.3 meV)

38

ELECTRON TRANSPORT AND CONFINING POTENTIALS

0

,

|

i

i

,

,

,

70 8o

g

5o

~, 4o ~

30

~ eo 10 0 0

50 100 150 200 250 300 350 400 x (nm)

Fig. 27. Sum of the electrostatic and magnetic confinementpotentials in the range between B = 0 T and B = 1 T, plotted in steps of 0.25 T. The parameters of the cosine potential are the same as in Figure 25.

in the cosine-shaped potential. Note that, in the numerical simulation of the magnetic depopulation experiment, the Fermi level has to be calculated as a function of magnetic field, taking into account the one-dimensional density of states. Because this is easily achieved only for the harmonic oscillator potential but computationally very expensive for an arbitrarily shaped electrostatic potential, one may assume an approximately constant Fermi level at low magnetic fields. As can be seen from Figure 14, this assumption is justified at low magnetic fields. The oscillations of the Fermi level are relatively small there and the error introduced by assuming a constant EF will be negligible. We now consider the situation encountered in a magnetophonon resonance experiment. Because of the strong damping of the magnetophonon (MP) magnetoresistance oscillations with decreasing magnetic field, it is clear that, in contrast to the magnetic depopulation experiment, the relevant information is drawn from the structure in Rxx(B) observed at high magnetic fields (B > 4 T). As can be seen from Figure 27, the magnetic confinement strongly dominates over the electrostatic one already at fields of 2 T. The resulting total potential is parabolic to a good approximation with the nonparabolic parts of the superposed electrostatic potential entering only as a weak perturbation. At the high magnetic fields at which MP resonances are observed (cf. Fig. 22), only the lowest subbands are occupied. Because the transition probability between the subbands at elevated temperatures is weighted by a Boltzmann factor, resonant LO phonon scattering mainly occurs between the lowest subbands. Hence, what is probed by the magnetophonon effect is the subband spacing of those levels lying near the bottom of the cosine confinement potential, which is larger than that of the high-lying levels. Quantitatively, we demonstrate this by the following considerations. In analogy to the previous simulation of the magnetic depopulation experiment, we calculate those magnetic field positions where an integer number (N) of subbands equals the LO phonon energy (36.6 meV) and plot their squared values against the inverse-squared N (see Fig. 28). The solid straight line in the figure is a fit according to Eq. (64), ignoring all nonparabolic contributions to the electrostatic confinement. As can be seen from Figure 28, the parabolic model fits perfectly with the simulated data points. The values for the effective mass and the subband spacing obtained from the fit are m* -- 0.070 and AE = 2.0 meV, respectively. The latter reproduces almost exactly the subband spacing at the bottom of the underlying cosine potential. To summarize these considerations, one may state that magnetic depopulation experiments always probe the subband energies at the Fermi energy, whereas magnetophonon resonance experiments are sensitive to the sublevels near the bottom of the confinement potential. This not only explains the experimentally observed difference between the energy values determined by the two methods. It also shows that the combination of the two methods provides in a simple manner direct information on the actual shape of the underlying confinement potential, in that it allows us to decide immediately if the potential is

39

SMOLINER AND PLONER

60

m=O.070 m0

5O

. ~

,

4O 3O m

20 10 0 -10

i

i

!

!

I

0.02 0.04 0.06 0.08 0.1 0.12

1/N2 Fig. 28. Simulated magnetophonon resonance experiment for a wire with cosine-shaped confinement. The squares correspond to those magnetic fields, where an integer number of the low-lying subbands fits the LO phonon energy. The straight line stems from a fit using a simple harmonic oscillator potential. The subband spacing extracted from the intersection of the straight line with the B 2 axis is AE = 2.0 meV. This value reproduces the subband spacing at the bottom of the cosine potential almost exactly. The mass value obtained from the slope of the line is m* = 0.070me.

25 20 > E

15

10 w

5

50 100 150 200 250 300 350 400 X (nm) Fig. 29. Confinement potential according to Eq. (66) plotted together with the calculated energy levels at zero magnetic field.

cosine or square well like. Consider as an example a potential calculated according to V(y) --

Wmod(

2

cos

( ~ ) ) 4

+ 1

(66)

which is shown in Figure 29 together with the corresponding subbands. This model potential exhibits a fiat bottom and has relatively steep side walls as is typical for a split-gate wire at high carder densities. Inversely to the previous case of a simple cosine potential, the upper subbands now have a higher spacing than the low-lying ones. Again, the simulation of the magnetic depopulation and the magnetophonon resonance experiment shows that the former will give the higher subband spacing of the top levels, the latter that of the bottom levels. Finally, it is worth noting that the estimate of the 1D carder density from a magnetic depopulation experiment should be interpreted with some care. The application of the standard parabolic model to the interpretation of a Landau plot also yields the 1D cartier density of the wire [cf. Eq. (49)]. If the "true" confinement is sinusoidal, however, the so-obtained n 1D slightly underestimates the actual value, because the procedure leading to Eq. (49) presupposes that the subband spacing appropriate for the high-lying levels is valid for all occupied subbands.

40

ELECTRON TRANSPORT AND CONFINING POTENTIALS

5. W E A K L Y AND STRONGLY M O D U L A T E D SYSTEMS A practical problem that sometimes arises when one fabricates an array of shallow etched quantum wires is that one needs to know whether one has really achieved a system of separated quantum wires or only imposed a periodic potential modulation on the underlying 2D electron gas. Also, the variation of the potential amplitude with varying etching depth or gate voltage is sometimes of interest for theoretical or technological reasons. As will be shown in the following, the magnetoresistance measured perpendicular to the equipotential lines of a lateral potential modulation contains a wealth of information on the relevant potential parameters. Depending on whether the modulation is only weak, that is, the potential amplitude V0 is much smaller than the Fermi energy, or whether V0 is no longer negligible in comparison to EF, different characteristic features of the magnetoresistance can be used for the characterization of the potential. This will be the topic of the present section. Because modulated systems are of great interest not only from the point of view of potential properties, they have been extensively investigated and reviewed in the past (see, e.g., [84]). We will consider these systems only under the aspect of obtaining insight into the shape and magnitude of the periodic potential. In order to do this, we restrict our discussion to the very simplest (semiclassical) model considerations commonly employed for the explanation of the observed effects. We start with the case of a weakly modulated system. A weak potential modulation can be realized by different techniques such as very shallow etching, by application of small voltages to a grating gate, or even by brief illumination with two interfering laser beams [19]. The magnetoresistance p• measured perpendicular to the equipotentials of the so-introduced modulation exhibits a number of characteristic low-field oscillations (see Fig. 30). The oscillations are periodic in 1/B, just as the Shubnikov-de Haas oscillations of the unstructured 2DEG, but, as the different field scale indicates, of an obviously different origin. After the first observation of these oscillations [19], which have later on been termed commensurability oscillations, several equivalent models were developed to explain their origin [117-120]. In the following, we give a very brief account of the semiclassical model of Beenakker [ 117], because it facilitates an intuitive understanding of the underlying physics. Its basic ideas can also be used to explain the special features occurring if the modulation height is gradually increased.

32 28

~" 24 20 16

12

0.0

0.1

0.2

0.3

0.4

0.5

B (T) Fig. 30. Longitudinalmagnetoresistance of a weakly modulated 2DEG with current flowingperpendicular to the equipotential lines (see inset). The thick solid line represents data from Weiss et al. [19], showing commensurability oscillations below B = 0.4 T and the onset of Shubnikov-de Haas oscillations for B ~>0.4 T. The thin solid line is calculated from the semiclassical guiding center drift resonance model of Beenakker [117]. The vertical arrows indicate those magnetic field values where the cyclotron diameter matches the period of the grating. The commensurability oscillations are phase shifted relative to these values by zr/4. Bcrit is the critical field for magnetic breakdown and will be discussed later in this section. (Source: Reprinted with permission from [25].)

41

SMOLINER AND PLONER

(a)

a

Y x

(b)

Y+R

Y

Y-R

Fig. 31. Illustration of the electron motion in a weakly modulated 2DEG with a magnetic field applied perpendicular to the electron gas. (a) Potential landscape with cyclotron orbit. (X, Y) are the coordinates of the orbit center (guiding center); Y 4- R are the extremal points, where the orbit center acquires a net E • B drift. (b) Numerically calculated cyclotron orbits in a sinusoidal potential. Horizontal lines indicate the equipotential lines of the periodic modulation. The figure shows a resonant orbit at 2R/a = 6.25 and a nonresonant one at 2R/a = 5.75 with negligible drift. (Source: Reprinted with permission from [25].)

Figure 31 shows the classical cyclotron trajectory of an electron moving in a weak periodic potential modulation with a magnetic field applied perpendicular to the plane of the 2DEG. (X, Y) denotes the center of the cyclotron orbit and R - hkr/eB is the cyclotron radius. Because the modulating potential is assumed to be very weak, it can be considered as a small perturbation that leaves the cyclotron orbits essentially undistorted. The simultaneously present electric ( E - -VVmod(y)) and magnetic fields classically give rise to an E • B drift of the center of the otherwise unaffected cyclotron orbit. Because at low magnetic fields the electronic orbit extends over many periods of the potential modulation, only the drift acquired at its extremal points Y 4- R will be essential. This is depicted in Figure 3 lb. If the position and radius of the orbit are such that the drift acquired at opposite extremal points adds up constructively, one speaks of a guiding center drift resonance. Off resonance, the drift acquired at one extremal of the orbit will cancel that at the other extremal, leading to zero net drift. At resonance, the electron drift, which is directed parallel to the equipotential lines, will lead to a maximum in p• An off-resonant, stationary orbit accordingly corresponds to a resistance minimum. This qualitatively accounts for the oscillatory behavior shown in Figure 30. The preceding ideas can be integrated into a rigorous solution of the semiclassical Boltzmann equation. If the strength of the potential modulation is characterized by the parameter e = e V / E F , the magnetoresistance is then obtained to second order in e" PYY

PO

--

1 + l (2:rr ~ e l )2 Jg(2JrRc/a) -2 a 1 - JZ(2rcRc/a)

(67)

Here, P0 is the usual semiclassical expression for the longitudinal magnetoresistivity, a is the period of the potential modulation, and 1 = vFr is the mean free path. J0 is a Bessel function. The exact analysis gives the condition 2Rc/a = n - 1/4 for a resistance minimum and 2Rc/a = n + 1/4 - o r d e r ( l / n ) for a maximum. In the limit 27r(Rc/a) >> 1, Eq. (67) can be shown to reduce to the following frequently quoted expression for p• [ 117]: P• -- P0 ( 1( + l 2e~ 2 c )

7r)) cos 2 ( R2 c7 r ~ - -a 4

(68)

Basically, the same result can also be derived directly from the simple classical picture outlined previously [ 117]. Note that the V entering the definition of e is a root mean square

42

ELECTRON TRANSPORT AND CONFINING POTENTIALS

average of the modulation potential amplitude. If, for example, a sinusoidal modulation Vmod(Y) -- Vocos(27ry/a) is considered, one has V0 - 2x/~. The guiding center drift oscillations have also been explained on purely quantum mechanical grounds [118, 119]. If the weak periodic modulation V(x) is treated by simple first-order perturbation theory, it is easily shown that this leads to a widening of the Landau levels to Landau bands according to EN(ky) = (N + 1/2)hCOc + (NkylV(x)lNky). The kets in the matrix element denote the Nth Landau state with center coordinate x0 = hky/eB of the unperturbed system. If the matrix element is replaced by the classical expectation value, which can be done because high numbers of Landau levels are occupied at low fields, an expression very similar to Eq. (68) can be derived for P_L. The result of the semiclassical calculation is shown in Figure 30 (thin solid line). A parameter value e --0.015 is assumed to reproduce best the corresponding experimental trace. The most interesting feature of Eq. (68) is the phase shift of zr/4 appearing in the argument of the cosine term. The value of this phase shifts depends on the shape of the modulating potential and equals zr/4 only if a simple sinusoidal potential is assumed. The perfect agreement with the phase shift of the experimental trace indicates that this assumption describes the actual shape of the potential very well. Another important source of information on the potential parameters is the positive magnetoresistance at very low magnetic fields (denoted by the arrow labeled Bcrit in Fig. 30). This property of P_L is clearly not accounted for by the strongly simplified classical picture of undistorted cyclotron orbits undergoing a resonant drift. Beton et al. [ 121] investigated this positive magnetoresistance systematically by using a grating gate geometry similar to that used by Brinkop et al. [79] (cf. Fig. 12), which allowed them to vary the height of the modulating potential. We reproduce their results in Figure 32, where several magnetoresistance traces are shown for different voltages applied to the modulating gate. As shown in the figure, with increasing gate voltage and thus increasing potential amplitude, the positive magnetoresistance is significantly enhanced and extends over a larger field range. Simultaneously, the number and peak-to-valley ratio of the commensurability oscillations are reduced. This behavior is easily explained by a modification of the simple

4400 l ~

~

/ /

3500

5 o'J -~ rr

/

800 /

400, 40O .00

:,,~,.'V "0' ,

0

~ h

-

~,

0.5

I

1

1.5

B (T) Fig. 32. Magnetoresistancetraces measured at 2 K for different top-gate voltages. From top to bottom, VG = - 1.0, -0.8, -0.6, -0.5, -0.3, -0.2, and 0 V. The curves are displaced for clarity. The period of the modulation potential was a = 300 nm. Bcritis the critical field for magneticbreakdown(see also Fig. 30). For B ~>0.5 T the usual Shubnikov-deHaas oscillations are observed. (Source: Reprinted with permission from [121]. 9 1990 American Physical Society.)

43

SMOLINER AND PLONER

'a'l I ~ ,c,i I

(b)

(d)

(f)

(h)

Fig. 33. Numerically calculated classical electron orbits in a periodic potential with a magnetic field applied perpendicular to the 2DEG. The straight lines symbolize the equipotential lines of the periodic potential. The orbits (a), (c), (e), and (g) correspond to 2Rc/a = 6.25; the orbits (b), (d), (f), and (h) correspond to 2Rc/a = 5.75. The left-hand orbit of each partial figure is symmetric with respect to the periodic potential; the right-hand one is positioned asymmetrically with respect to the equipotential lines. The values of the parameter e -- e V0/EF are (a), (b) 0.01; (c), (d) 0.05; (e), (f) 0.09; and (g), (h) 0.15. (Source: Adapted from [121].)

classical picture outlined previously. The main ideas become clear from Figure 33, which shows numerically calculated classical trajectories for different potential heights (characterized by the parameter e defined previously). The left-hand set of orbits is calculated for 2Rc/a = 6.25, which, in the case of a weak modulation, would correspond to a maximum of P_L; the fight-hand orbits were obtained for 2Rc/a = 5.75, corresponding to a resistance minimum. If the potential amplitude is increased, the corresponding electric field consequently enhances the E x B drift. On the other hand, this also leads to an increasing distortion of the cyclotron orbits. As a consequence those trajectories begin to drift (fight-hand trajectories of parts b, d, f, and h of Figure 33), which are stationary in the weak potential case and lead to a distinct minimum in p• This fact explains the reduction of contrast of the commensurability oscillations with increasing potential amplitude. As shown in parts g and h of Figure 33, there is also a possibility of open orbits traversing parallel to the equipotential lines. Beton et al. [ 121 ] conclude from their classical model that a certain fraction of open orbits is present even for the smallest magnetic field values. Because the open orbits are traversed with the Fermi velocity VF rather than with the slower E x B drift velocity, they dominate the resistivity at very low magnetic fields and lead to the observed positive magnetoresistance. As shown in Figure 32, the magnetoresistance (caused by open orbits) remains positive up to a certain magnetic field Befit where it has a maximum, followed by commensurability oscillations resulting from closed and drifting orbits. It was shown by Beton et al. [121] that the maximum in p• occurs when the Lorentz force equals the electric force caused by the potential gradient:

v0

2re m = e Bcrit VF a

44

(69)

ELECTRON TRANSPORT AND CONFINING POTENTIALS

Magnetic fields weaker than Bcrit are unable to force an electron on a closed cyclotron orbit against the action of the potential wells, which leads to a dominant fraction of open orbits. When the magnetic field exceeds the critical value determined by Eq. (69), the number of open orbits is drastically reduced ("magnetic breakdown"). It can be easily shown [ 121 ] that the magnetoresistance can be approximated by

APxx No ,~ 2w 2r ~ (70) /90 NT where No/NT denotes the fraction of open orbits relative to the total number of trajectories and po is the resistivity at zero magnetic field. In Eq. (70), the magnetic field dependence contained in wc together with the drastic reduction of N0/NT at B/> Bcrit =

2JrV0

(71) ea VF leads to the observed peak in P_L at low magnetic fields. Beton et al. also gave a semiqualitative quantum mechanical explanation of the observed low-field behavior [122]. A rigorous analysis of the semiclassical dynamics in lateral superlattices was given by Streda and Kucera [ 123, 124], who analyzed the detailed features of the electronic energy spectrum and obtained the characteristic low-field magnetic breakdown peak from the Chambers solution of the semiclassical Boltzmann equation. A similar magnetic breakdown concept had been used earlier by Streda and MacDonald [ 125] for an investigation of the weak modulation limit. In principle, the classical considerations made responsible for the magnetoresistance peak remain a valid picture also in the more detailed study of Streda and Kucera. In contrast to the classical model of Beton et al. [ 121 ], however, the latter does not predict a magnetoresistance that falls off abruptly for fields B ~> Bcrit, but behaves smoothly in this field regime. Also the relation for the expected peak position is slightly modified to Bcrit = 4Vo/eavF. According to Eq. (69), the determination of ncrit allows the characterization of the amplitude V0 of the periodic potential, if the Fermi velocity VF is known. An example of the application of Eqs. (68) and (69) to the systematic study of V0 and its dependence on various sample parameters is given in Figure 34 [ 126]. The shown data were obtained from the magnetoresistance of an inverted, back-gated heterostructure. The lateral superlattice is induced by a grating metal gate, fabricated on top of the heterostructure. The gate fingers had a width of only 25 nm and formed a grating with period a = 200 nm. The height of the potential modulation was tuned by a voltage VG applied to the top Schottky gates, whereas the electron density could be independently varied by a back-gate voltage. The different symbols in Figure 34 indicate different methods used to extract the value of V0. The squares are obtained from an analysis of the magnetic breakdown peak discussed previously. The circles and triangles stem from a comparison of the n = 1 and n = 2 commensurability oscillations (labeled i = 1, 2 in the figure) to the theoretical expression Eq. (68), where this was possible. As shown in Figure 30, this approximate relation not only reproduces the correct period and phase of these oscillations, but also gives a fair approximation of their amplitude for low values of n. For higher n, the calculated amplitude generally overestimates the measured one, which is due to the previously discussed reduction of the oscillation "contrast" by distorted orbits not accounted for by the simple classical picture of [ 117]. Figure 34a shows the dependence of the potential amplitude on the gate voltage for a certain fixed back-gate voltage, that is, for fixed electron density. The two different evaluation methods approximately give the same results when the modulation is very weak. This is the regime for which Eq. (68) is conceived and where it gives a fair representation of the actual situation. For higher VG, Eq. (68) yields smaller values than Eq. (71). It is expected that in the case of stronger modulation Eq. (68) overestimates the oscillation amplitude, particularly at higher indices n and, consequently, underestimates V0. In part b of the figure, the same analysis is performed for fixed VG but at different electron densities, varied by a back-gate voltage. Again, the two evaluation methods give different results for the

45

SMOLINER AND PLONER

(a)

3.0

i 9

' .

E

2.5

"

2.0

9

= 9

I

=

9

1.5 1.0

= =

9 AAA 9

0.5 0.0

m

9

A

. . . . . . . . . . -0.6 -0.5 -0.4-0.3-0.2 -0.1 0.0 0.1 Vg (V)

(b) 2.5 2.0 >

9

9

I

9

1.5

E "-" > 1.0 0.5 .0

- Bc 9 i=1 9 i=2

"':.It

r

|

i

l

,

1

2

3

4

5

6

n (1015 m "2)

Fig. 34. Amplitude V of the periodic potential modulation for a back-gated inverted heterostructure, plotted as a function of the voltage applied to a grating gate, fabricated on top of the sample. Squares are obtained from an analysis of the magnetic breakdown peak at Bcrit; circles and triangles are obtained from the application of Eq. (68) to the i -- 1 and i = 2 commensurability oscillation. (Source: Adapted from [126].)

same reasons as before. However, all values confirm the observed trend of an increasing modulation amplitude (at fixed top gate voltage) with decreasing carrier density ns. This carrier density dependence is a signature of screening effects that should be independent of ns in a purely 2D electron system. The results of Figure 34b, therefore, nicely illustrate the reduction of screening when the potential amplitude increases and an increasing number of electrons become bound in one dimension. A similar analysis has been applied to the characterization of short-period (a = 100 nm) lateral surface superlattices, fabricated by a plasma etching process [127]. An additional blanket gate on top of the etched superlattice has been used to improve the properties of the potential modulation. Indeed, the analysis of the phase of the commensurability oscillations shows that the blanket gate smooths the periodic potential and suppresses most of its higher harmonics; that is, the potential is sinusoidal to a very good approximation and, consequently, yields a phase shift of the commensurability oscillations equal to rr/4. According to Davies and Larkin [128], a potential that is not perfectly sinusoidal creates higher harmonics in the magnetoresistance commensurability oscillations. Thus, an additional possibility to obtain information on the shape of Vmod(Y) is to analyze the Fourier transform of the low-field oscillatory magnetoresistance, taken as a function of 1/B. This method was also applied in [ 127] and was found to confirm the results obtained from the phase analysis. When the lateral superlattice potential becomes still stronger, the magnetoresistance anomalies change their character. This is illustrated in Figure 35 [129]. In this example, the periodic potential is created by shallow etching on a GaAs-A1GaAs heterostructure. The potential amplitude relative to the Fermi level is tuned by brief illumination from a red LED. In part a of the figure, V0 and EF, measured relative to the subband bottom in the wells of the lateral potential, are nearly equal. In this case, there is no trace of

46

ELECTRON TRANSPORT AND CONFINING POTENTIALS

(a)

80

9

A

T:0.5 K

~. 60 X X

40

Q 20 /

0 12

(b)

i

!

t

i

,!

,

.

,

9

.

,,,

.

J

O] 9 x6 X

3

(c)

\

\

0.0

0.4

|

10

2 0 -2.0

-1.0

1.0

0.0 B(T)

2.0-0.4

B (T)

Fig. 35. The left-hand curves show experimental magnetoresistance traces for different amplitudes of the modulating potential. The top curve corresponds to the strongest modulation, the bottom curve to the weakest one. The inset in part b shows the experimental setup. The fight-hand figures display the calculated magnetoresistance (thick solid lines; see text). The dashed curves correspond to the isotropic contribution to Pxx, thin solid lines to the anisotropic part, which dominates for very strong modulation. The Fermi level (measured from the bottom of the potential wells) and the potential amplitudes used in the calculation are: (a) E~ eiI = 8.1 meV, V0 = 7.8 meV; (b) 8.6 meV, 7.0 meV; (c) 9.0 meV, 6.7 meV. (Source: Adapted from [ 129].)

a positive magnetoresistance, which, on the contrary, becomes negative. With increasing difference between V0 and EF, that is, decreasing e, a positive contribution to the low-field magnetoresistance becomes visible, which dominates for the lowest value of e (part c of the figure). This behavior can be explained semiclassically if one assumes different scattering times for electrons bound in the wells and for those having sufficient energy to overcome the barriers and to move freely [ 129]. In the following outline of the underlying semiclassical model, we suppose that the potential modulation is in the x direction. One assigns a scattering time rob to those electrons bound in the well and r f to those electrons whose energy is high enough to overcome the barriers, both defined for zero magnetic field. With an applied magnetic field, the number of free electrons is not constant, because due to the Lorentz force electrons can acquire an additional momentum component in the x direction, which transforms previously bound electrons into free ones. Thus, for B r 0, one can define an average, magnetic field-dependent scattering time for free electrons 1

;f=0

Oo 1

Oa--O0 1

f+

0.

which is equivalent to the assumption that the phase space average of the scattering probability is not changed by a weak magnetic field. The angles 00 and 0B delimit those regions in k space (at zero and nonzero magnetic field, respectively) that correspond to a free-electron

47

SMOLINER AND PLONER

dispersion, that is, where the electrons have sufficient kinetic energy in the x direction to overcome the barriers. One finds from a semiclassical treatment [129] that the resistivity in the x direction may be split up into two components: _iso

,Oxx -- Pxx ('YY) -Jr- A,oxx

(73)

The first term follows from the Chambers solution of the Boltzmann equation (74)

m* 1 + r Pxx (r) = eZnsr 1 -- C(0B) iso

if for r an isotropic scattering time is used, which is given by "ry -- "t"f -~-

Jr + 0B + sin OB

('t"b -- "rf)

(75)

7/"

The effect of anisotropy, induced by the presence of two different scattering times, is subsumed in the second term of Eq. (73):

Apxx =

m* e2ns'r:y

yr--0B+sin0B r b - - r f 013 + sin0s

Z"f

(76)

In Figure 35, the magnetoresistance traces calculated according to Eqs. (74) and (76) are J s o which, in analogy to shown on the right-hand side. The dashed lines correspond to Pxx the strongly modulated case discussed previously, exhibits a positive magnetoresistance followed by a breakdown peak. The solid lines correspond to the anisotropic contribution A,oxx. It can be seen that at large values of e the anisotropic part strongly dominates the low-field magnetoresistance, leading to the characteristic spiked helmet form. The model calculations also allow one to estimate the amplitude of the periodic potential. However, the involved formalism is much more intricate than the methods described previously and does not lend itself to systematic routine investigations. The V0 values corresponding to the different experimental situations shown in Figure 35 are given in the caption. In conclusion, it is worth mentioning that the semiclassical modeling of magnetotransport in a periodic potential gives in a way complementary information on the underlying potential for weak and strong modulation. In the first case, the commensurability oscillations provide phase information that allows one to draw conclusions on the shape of the potential. However, because the semiclassical model treats the potential modulation as vanishingly small, the potential amplitude is not well reproduced by the semiclassical expressions (see [126]). In contrast to that, the magnetic breakdown picture yields a particularly simple tool for the determination of potential amplitudes but it is basically insensitive to the exact shape of the modulating potential. Sinusoidal or Kronig-Penney-like model potentials give essentially the same results [123, 129].

6. VERTICAL TUNNELING T H R O U G H QUANTUM WIRES

6.1. Experimental In this section, we discuss the use of tunneling spectroscopy as a tool for the investigation of confining potentials and wave functions of 1D systems. Experimentally, tunneling via 1D states can be realized in various ways. Lateral tunneling between a quantum wire and 2D systems, for example, can be implemented on modulation-doped heterostructures using a split-gate geometry with a "leaky" channel. In this geometry, electrons are allowed to tunnel out of a 1DEG through a thin side-wall barrier into an adjacent 2D electron bath [130, 131]. A pronounced oscillatory structure can be observed in the 1D-2D tunneling current when the carrier concentration in the 1D channel is modulated through the split gates. These features reflect the modulation of the 1D density of states as the 1D subbands are successively depopulated with increasing split-gate bias.

48

ELECTRON TRANSPORT AND CONFINING POTENTIALS

However, tunneling between electron systems of different dimensionality in the vertical (growth) direction turned out to be the more interesting situation. In vertical geometry, epitaxial regrowth techniques either on V-groove etched substrates, as proposed by Luryi and Capasso [132], or on the edge of in situ cleaved substrates [133] can be used for devices, where electrons tunnel resonantly from a 2D emitter state into the 1D subbands of a quantum wire [134]. In such a sample, tunneling proceeds from the edge of a twodimensional electron source through a bound state in a quantum wire into the edge of another 2D electron system and the combined effects of the longitudinal and perpendicular motion of electrons allows a detection of the excited wire states. On double-barrier resonant tunneling diodes, the lateral dimension can be restricted by use of focused Ga ion beam implantation [ 135]. In this case, the mixing of 2D emitter subbands and 1D subbands in the double-barrier region can be observed [ 136]. In theoretical models, these subband mixing and coupling effects turned out to be important and have, therefore, to be taken into account [137, 138]. The most instructive way to investigate tunneling processes through quantum wires, however, is to use a nanostructured double-layer electron system consisting of two coupled two-dimensional electron gas (2DEG) systems separated by a thin tunnel barrier. Three types of such bilayer structures have been extensively investigated: the double heterostructure with a two-dimensional electron gas on both sides of an A1GaAs barrier, the doublebarrier resonant tunneling diode with two-dimensional emitter, and the coupled quantum well system. On all types of samples, either the upper 2D-channel, lying closer to the sample surface, or both channels can be patterned into quantum wires. In this way, tunneling processes from a 2D emitter into a system of one or more quantum wires and also vertical tunneling between insulated quantum wires can be investigated. In all these cases, the fundamental technological problem, which makes the construction of a vertical tunneling device a challenging task, is the formation of independent ohmic contacts to each of the barrier-separated low-dimensional systems. In the following, we discuss three representative experiments, each performed on one of the three mentioned systems of coupled electron channels. We describe briefly the sample geometry used and show some typical data obtained for each of these devices. In a subsequent section, we shall discuss briefly the theoretical models underlying the interpretation of these data. In the discussion, the emphasis will be put on the influence of the confining potential on the resonant tunneling characteristics or, vice versa, on the question to which extent the latter can provide substantial information on the former. The double GaAs-A1GaAs-GaAs heterostructure, used in [23, 139-142], is shown in Figure 36a. The sample structure is made up of a nominally undoped GaAs layer

Fig. 36. (a) Schematic cross section of a processed single-barrierresonanttunneling device and resulting surface potential in the y direction (top). (b) Corresponding conduction band profile in the z direction. Em and En denotethe energy levels on the 2D and 1D side, respectively. EF is the Fermi energy; Vbis the applied sample bias.

49

SMOLINER AND PLONER

(NA ~< 1 x 1014 cm -3) grown on a semiinsulating substrate, followed by an undoped A1GaAs spacer (d = 50 ,~), doped AlxGal_xAs (d - 50 ,~, ND ~< 3 x 1018 cm -3, x = 0.36), another spacer (d = 100 ,~), and n--doped GaAs (d - 800 ,~, ND V0), resonant tunneling is forbidden because the total energy cannot be conserved in such a process. If the bias voltage reaches Vb = V0, the subband edges of the 2D subband

56

ELECTRON TRANSPORT AND CONFINING POTENTIALS

cq

,.b e~

v

Ie4

.~

A

vIyk /

V' 1

>uJn" IeV-~l ~ = l / I n O 7 _1/ I/v1 o o22) t.t_ i.u >

e

v_12 Fn=2

,v 2 1

~ --I Izzzn=3 ~,V"3y 3

,,, IV31 F (5 _z

-15 -10 -5 0 5 10 15 BIAS VOLTAGE Vb (mV) Fig. 43. Plot of the overlap integrals for the lowest four 1D subbands (n = 0 . . . . . 3) in a cosine-shaped potential [Eq. (89)], with a single 2D subband; Vn is the resonance position of the subband edges (ky --0), whereas A Vn denotes the deviation between the first overlap maximum and the position of the subband edge resonance Vn (only present for even n). The parameters for the 1D potential were Vmod = 60 mV, w = 350 nm. The lowest curve represents the sum of the upper four. (Source: Reprinted with permission from [23]. 9 1993 American Physical Society.)

and of the lowest 1D subband (n = 0) are in resonance, and the overlap integral of the lowest 1D subband, I0, reaches its maximum value. As Vb is decreased further, I0 drops gradually toward zero. Note that I0 indirectly reflects the spatial extent of the wave function, because it is nothing else than its Fourier transform. For the first excited 1D subband (n = 1), the tunneling probability, moreover, reflects the parity of this state. If the subband edges of both the 2D and the n = 1 subband coincide at Vb -- V1, 11 is still zero because the corresponding 1D state has odd parity, 11 (ky = 0) -- 0. The tunneling probability then increases with decreasing bias voltage and reaches its maximum, which is slightly shifted by A V1 from the subband edge resonance. With further decreasing bias voltage, 11 drops toward zero. The behavior of the tunneling probabilities for the higher 1D subbands can, in principle, be understood in an analogous way. It is obvious from Figure 43 that the maxima of In at the positions of the subband edge resonances (even 1D subband index, V2n) or most close to them (odd 1D subband index, g2n+l -~- A V2n+l) are much more pronounced than all the other structures caused by the nodes of the 1D wave functions. In addition, the values of A V2n+l become smaller and smaller with increasing n (e.g., A V1 > A V3 etc.). Therefore, resonances caused by an energetic alignment between the subband edges of the 1D and 2D states can be expected to be dominant in the 1D-2D tunneling experiments, but are by no means the only reason for structures in the tunneling characteristics. As has been shown previously, the confining potential in split-gate structures is rather "boxlike" than cosine shaped. Therefore, it is necessary to study also the influence of the steepness of the confinement walls. For this purpose, we choose an analytical expression

57

SMOLINER AND PLONER

Fig. 44. Potentialprofiles for a series of a values, tuning the shape of V(y) from smooth parabolic like (or = 8) to almost rectangular box like (or = 192).

for the potential, which allows us to control the steepness by a single parameter or. To obtain a potential profile that is smooth within one period of the multiple quantum wire system under consideration, we use the one-dimensional Woods-Saxon potential [42], which was already introduced in Section 2: V (y) -- Vmod 1 +exp('~(w/2-y)) w

- gmin

+ 1 + exp(~

(90)

to

The last term Vmin = Vmod{2/[1 + exp(ot/2)]} sets the potential minimum to zero. The parameter c~ allows a continuous variation of the potential shape from an approximately parabolic to a nearly rectangular form. Figure 44 shows the potential profiles for a series of ot values, starting at ot = 8 (nearly parabolic) and ending at ot -- 192 (nearly rectangular box). The other parameters used in the calculation are Vmod -- 50 meV and w = 250 nm. In analogy to the case depicted in Figure 43, the overlap integral for the 1D ground state n = 0 and the third excited 1D subband n = 3 as well as their sum ( ~ n = 0 . . . . . 3) is calculated for various values of a. The results are plotted in parts a-c of Figure 45. Because of the variation of the potential profile, the energies of all 1D subband edges are shifted to lower values with increasing parameter or. The change in shape of the wave functions has a pronounced effect on the corresponding overlap integrals. This is illustrated for the 1D ground state in Figure 45a. With rising or, the spatial extent of the wave function is increased. As a result, the overlap integral of the single 1D wave function is squeezed on the wavevector scale ky and, consequently, on the bias voltage scale Vb, too. In addition, the m a x i m u m tunneling probability is increased by more than 50%, whereas the integral tunneling probability, which is represented by the area enclosed by the curve, decreases simultaneously by a factor of 2. This behavior is even more pronounced for the overlap integrals of the higher quantum wire states, as shown in Figure 45b for the subband index n = 3. While a increases, the resonance structure close to the position of the subband

58

ELECTRON TRANSPORT AND CONFINING POTENTIALS

Fig. 45. Plot of the overlap integrals for the 1D subbands n = 1 (a) and n = 3 (b) with a single 2D subband as a function of the parameter c~. (c) Sum of the overlap integrals of the lowest four subbands. (Source: Reprinted with permission from [23]. 9 1993 American Physical Society.)

edge resonance (labeled V~ in Fig. 43) is systematically degraded. In contrast to that, the tunneling probability at the bias voltage position of the second maximum (labeled V~~ in Fig. 43) is drastically increased and becomes the by far most dominant structure for high values of or. Comparing the amplitudes of the overlap integral at the voltage positions V~ and V~~, their ratio increases from 1.4 for ot = 8 to above 8 for c~ = 192. For the rectangular potential profile, the maximum in the tunneling probability at V~I coincides with the subband resonance position of the lowest 1D subband, that is, Vb = V0. To illustrate this remarkable behavior more clearly, we have recalculated the results shown in Figure 43 for a box potential with infinitely high walls and a width of w--100 nm. For this potential profile, the values of In (n -- 0 . . . . . 3) as well as their sum are plotted in Figure 46. Although the shapes of the curves are qualitatively identical with the corresponding curves of Figure 43, the intensity ratios of the structures within a curve show a completely different behavior. As pointed out previously, only the structures in the vicinity of the resonance of the lowest 1D subband (labeled V0, V[, V~', and V~I) remain important. The width of these resonance structures, however, increases as the 1D quantum number increases. All other peaks of In for the higher 1D subbands at voltage positions Vb > V0 are of minor importance, because their intensity can be neglected. All these features are also present in the sum of all overlap integrals, which determines the total tunneling probability (lowest curve of Fig. 46). There is only one broad maximum dominant, peaking at a bias voltage of V0. This result is valid for all quantum wire subbands, but particularly pronounced for higher subband indices. The total tunneling probability exhibits less and less structures as the potential profile is tuned from a smooth parabolic shape to a rectangular shape, as shown in Figure 45c. In the latter case, just one broadened maximum, located at Vb -- V0, characterizes the tunneling probability for all 1D subbands. Therefore, a single, but broad resonance structure

59

SMOLINER AND PLONER

I'v' % v

13..


o Z

o

'

I--

/ V"

o z

!.1_ u..I > ,
O n+

V=O

(a) i " 6'*'r'=,.!

(b)

n+

I.-"..

GA'rE 1 I

edge

V 0, and (c) V < 0. In (a), the cross-hatched area represents the region that is depleted by the gate. In (b), the conduction band profile indicates how the device can be on resonance at the edge, but not at the center. (Source: Reprinted with permission from [202].)

300

40 mV

0

150

-150

-300 -50

-25

0

a 25

50

VSD (mV) Fig. 66. I - V curve close to threshold for Vg = 0 V measured at T = 39 mK. The inset shows I - V in reverse bias for temperatures of T = 2, 4.2, 10, and 20 K. (Source: Reprinted with permission from [202].)

o b s e r v e d for b o t h bias directions a l t h o u g h for reverse bias the peaks are better resolved. T h e s e peaks are a universal feature and also occur for different s a m p l e s at similar voltage positions, but always b e l o w the onset of the m a i n resonance. T h e y are attributed to e n e r g y levels lying b e l o w the first confined state in the well. T h e striking f e a t u r e of these peaks is, however, that their position is i n d e p e n d e n t of the side-gate voltage and, as can be seen in the inset o f F i g u r e 66, they are also relatively insensitive to t e m p e r a t u r e . Thus, q u a n t u m

80

ELECTRON TRANSPORT AND CONFINING POTENTIALS

//

(a)

200

,f - - 7 - - _ / i

0

30

40

I

5o 30 VSD (rnV)

40

50 60

Fig. 67. Dependenceof I (V) on the applied side-gate voltage in reverse bias (a) and forward bias (b) for voltages of Vg = 0, 1, 1.5, 2.25, and 3 V from top to bottom. (Source: Reprinted with permission from [202].)

confined states or Coulomb blockade effects cannot be made responsible for the structures in the low-bias range; otherwise, they would occur at a position above the main resonance and show a distinct voltage dependence. Tunneling via a local inhomogeneity, such as a donor impurity unintentionally incorporated in the well between the AlAs barriers, provides a possible explanation for the observed behavior. In contrast to the large-area DBRTDs considered previously, the gated structures now offer the possibility of probing the spatial extent of these donor states using the following considerations. A peak in the I - V curves will be unaffected until the depletion edge impinges on the region of the corresponding localized state, through which the electrons tunnel. If the depletion zone moves across the active area of the localized state, the amplitude of the corresponding resonance peak will decrease, because electrons are prohibited from entering the depletion zone. Thus, the current path for electrons flowing through this impurity state becomes smaller. If the side-gate voltage becomes large enough, the localized states will lie totally within the depletion region and the corresponding resonance will be quenched. This is shown in Figure 67, where the near-threshold I - V curves are given for various side-gate voltages. If the effective diameter d of the resonant tunneling device as a function of the side-gate voltage is known, the spatial extent Ax of such an impurity-related level can be determined. If Vgl is the highest voltage for which the resonance peak is still unaffected and Vg2 is the lowest voltage, where the peak is totally suppressed, one estimates Ax = l[d(Vgl) - d(Vg2)]. For the lowest peak in the I - V curves of Figure 67, one obtains, for example, a spatial extension of approximately 30 nm, which is close to the value for a single-donor bound state, expected from a simple first-principles calculation. In the preceding experiment, donor-related tunneling was investigated using squeezable quantum dot devices, which, however, showed no sign of resonant tunneling via 0D states. It was shown by Blanc et al. [205], however, that the inverse situation can be achieved by some modifications of the device design. By growing a larger spacer layer in front of the double barrier (7 nm instead of 3.4 nm in the case of Eaves and co-workers [202]), the unintentional incorporation of shallow donors in the quantum well region is largely suppressed. A reduction of the mesa size down to 0.1 /zm leads to relatively high 0D quantization energies, which facilitates the observation of resonant tunneling via quantized states. With increasing side-gate voltage, the main resonance peak current is reduced in analogy to the previously discussed experiment, but no asymmetry is observed for forward and reverse bias. In contrast to the previous experiment, no evidence of donor-related tunneling processes is found. The low-temperature conductance exhibits a series of well-resolved

81

SMOLINER AND PLONER

25

(a)

20

1.5 0c.-

E

:::L

(b)

~ E ~10 (.9 5 0

1

v

(.9 0.5 0.04

0.06 0.08 V (Volt)

0.1

0.04

0.06

0.08

0.1

v (VoLt)

Fig. 68. Conductancemeasured at 40 mK for a device with a diameter of 0.2/zm (Vg = -0.2 V) (a) and a device with a nominal diameter of 0.8/~m and Vg = 0 V (b). The resonance structures are due to resonant tunneling via 0D states. For the smallerdevice (curve a), the energy spacing of the quantized states is considerably enhanced compared to the larger device (curve b). (Source: Reprinted from [205], with permission of Elsevier Science.)

peaks (Fig. 68), which are attributed to resonant tunneling via 0D states. This is confirmed by the observed dependence of the I-V characteristics on gate voltage as well as magnetic field.

7.4. 0D-2D Tunneling So far, the presented experiments on quantum dot tunneling were not or only superficially analyzed in terms of the properties of the confinement potential defining the dot. Whenever an attempt of a quantitative comparison between experiment and calculation was made, the confinement was assumed to be parabolic and subband energies or the spatial extent of electronic wave functions were calculated within this assumption. The transfer Hamiltonian formalism, which was introduced in Section 6.2, can also be employed to gain more detailed information on the shape of the quantum dot potential from 0D-2D tunneling processes. This will be discussed in the following for tunneling experiments performed using the double-heterostructure layout already treated in Sections 6.1 and 6.3 in the context of 1D-2D tunneling. The same sample structure turned out to be also suitable for the fabrication of a 0D-2D tunneling device [206]. For this purpose, the upper (emitter) channel is nanostructured into quantum dots as schematically depicted in Figure 69. The dot array can be fabricated by laser holography using a double-exposure technique. In order to deplete the accumulation layer between the dots, the structures were wet chemically etched 300 deep into the GaAs cap layer. An ohmic contact to the dots is obtained by evaporating a Au/Ge electrode coveting the dot array. The experimental data shown in Figure 70 were obtained for a period of the dot array of a = 350 nm. The corresponding dot diameter was estimated to be approximately a/2. As discussed in Section 6.1, the applied bias voltage can be assumed to drop exclusively across the potential barrier separating the 2D collector from the 0D islands. A bias voltage A Vb is, thus, equivalent to a relative energetic shift of the 0D states by A E -- e A Vb. A negative bias voltage Vb < 0 corresponds to tunneling processes from a 0D state into a 2D subband of the inversion channel. The band structure of the biased sample is shown in Figure 69b for both the etched and the nonetched regions (upper and lower parts, respectively). Some experimental results are plotted in Figure 70. Part a of this figure shows the dI/dVb characteristics of the nanostructured (0D-2D) sample for various temperatures in the range between T = 1.7 K (curve 1) and T = 40 K (curve 12). For reference purposes, the dI/dVb characteristics of an unstructured sample are plotted in part b of the figure for two temperature values T = 1.7 K (curve 1) and T = 40 K (curve 2). All resonance peaks of the (0D-2D) dI/dVb characteristics show a strong dependence on temperature.

82

ELECTRON TRANSPORT AND CONFINING POTENTIALS

Fig. 69. (a) Schematic view of a 0D-2D sample. (b) The corresponding conductionband profile for the etched and nonetched areas of the sample. (Source: Reprinted with permission from [24].)

Above T = 4.2 K (part a, curve 2), the number of resolved resonance structures is already considerably reduced. A further increase in temperature results in a monotonic broadening of the resonance structures, accompanied by a decrease in the peak amplitudes. Generally, the resonance positions observed for Vb < 0 are slightly shifted toward more negative bias voltages. This behavior, which also occurs for the subband resonances of the (2D-2D) tunneling characteristics, is due to the thermally activated occupation of the first excited subband in the inversion channel causing a modification of the self-consistent potential profile. In both parts a and b of Figure 70, the positions of the (2D-2D) subband resonances are denoted by arrows. Similar to the 1D-2D tunneling processes discussed in Section 6.3 it can be shown that the structures in the measured tunneling characteristics can be traced back to the form of the overlap integral formed by the initial and final states. To see this, we introduce cylinder coordinates and write the wave functions for the collector and the emitter system in the form 2DEG"

~I2'~ -

1 1 ~~p~0 ~PI,v(z) ~

ODEG"

tpOD -

X/A1__ P/-% 7" ~A(Z)

exp(imlqg)Jmi(kllP) (106)

1 ~/~

exp(imAqg)~OnA,mA(P)

In the expression for qjlD, n A represents the radial and m A the azimuthal quantum number. Because prior to the nanofabrication process the upper 2DEG (accumulation layer, index A) contains only one occupied subband in the z direction, these two quantum numbers are sufficient to describe the 0D states of the quantum dot system. The wave functions of the subbands in the lower 2DEG (inversion layer, index I) are given by qJi2,D (/9, qg, Z; mI). Here, v is the 2D subband index and mi takes the degeneracy of Ell (energy of the motion parallel to the interface) into account. Apcprepresents the normalization area in both systems.

83

SMOLINER AND PLONER

~

~-

& TM

T-40K

,

T=40K E3 O4 !

C) o t__._l

d3 > 13 13

-40 -30

-20

-10

0

10

20

BIAS- VOLTAGE Vb (mV) Fig. 70. (a) Measured dI/dVb curves in the temperature range between 1.7 and 40 K. (b) For comparison, dI/dVb curves of an unstructured sample are also shown. The corresponding temperatures are 1.7 K (curve 1), 4.2 K (2), 6.5 K (3), 9.5 K (4), 11.7 K (5), 13.9 K (6), 15.7 K (7), 18.5 K (8), 22.7 K (9), 29.0 K (10), 35.5 K (11), and 40 K (12). (Source: Reprinted with permission from [24].)

The matrix element MAI [Eq. (81)], which is governed by the overlap of the single wave functions, now has the following form:

o.t] MAI--

2m*

h2 [ 2m* 0I*v

dxdy qJ~ Oz

OOa az

AaVs OZ

igz ] X t~mi,mA X Z=Zb

9

tB

fdppJmi(kllP)qgnA,mA(P)(107) 9

-v.( Jm (kll P)[~nA,m (P) )

9

The first term in this equation, tB, represents the transmission coefficient of the barrier. The Kronecker symbol guarantees the conservation of the angular momentum (quantum number m) during the tunneling process. The matrix element is nonzero only if mI = mA=_m. The value of the corresponding matrix element is a function of the radial quantum number n A, the (common) azimuthal quantum number m, and the wavevector kll which depends on the applied bias voltage. Its value, however, is completely determined by the

84

ELECTRON TRANSPORT AND CONFINING POTENTIALS

requirement of total energy conservation: kll(Vb) -- V j~2

[EnA,m

-

Evi

--

(108)

eVb]

As in the case of 1D-2D tunneling, the (0D-2D) matrix element MAI not only depends on the quantum numbers nA and m and on the bias voltage Vb, but also on the particularities of the potential profile. Considering the multitude of resonant structures in the tunneling differential conductance, a strictly rectangular potential profile can be excluded, because just as in the 1D-2D case it would lead only to weak fine structure (cf. Section 6.3). As in the case of shallow etched quantum wires, one obtains a relatively realistic description of the situation by assuming a cosine-shaped radial part of the quantum dot potential profile: Vdot(P) = Vmod

q- ~ COS

with p ~< Rdot

( P - Rdot)

(109)

In Figure 71, the tunneling probability, calculated from this potential profile, is compared to the measured dI/dVb at T = 1.7 K. The parameters of the model potential were adjusted to obtain the best possible agreement with the experimental results. Again, an energy (i.e., bias voltage) independent transmission coefficient of the tunnel barrier was assumed for this calculation. Hence, the model is, just as in the 1D-2D case, unable to reproduce the monotonic background in the experimental tunneling characteristics. It should be noted that the tunneling probability is proportional to the tunneling current, so that, to be rigorous, one has to compare the calculated curve directly with the measured tunneling current. Because the resonant structure is too weak to be observed in I (Vb) directly and because a numerical derivative of the calculated results would somewhat obscure their structure, a direct comparison is not feasible in this case. Nevertheless, good agreement between the experimental results and the calculated peak positions is immediately obvious. The parameter values used in the calculation are Rdot -- 62.5 nm and Vmod = 38 meV.

>p.. _.J rn < rn

nA=l

o

I

rr" o_ (5

nA=2

z

...3 UJ z z p..

-30

-25

-20

-15

-10

BIAS- VOLTAGE

Vb

-5

0

(mY)

Fig. 71. Comparison between the calculated tunneling probability and the measured dI/dVb curve at 1.7 K. The downward arrows denote the n = 0 . . . . . 3 resonance peaks. The upward arrows denote the peak positions where individual 0D and 2D subbands are exactly aligned. As for 1D-2D tunneling, A Vn denotes the distance between the resonance maximum and those positions. (Source: Reprinted with permission from [24].)

85

SMOLINER AND PLONER

The sharp structures in the total tunneling probability are due to sharp peaks in the wave function overlap integrals for nA = 0, 1, 2, 3 and can, therefore, be assigned to single peaks in the measured tunneling characteristics (denoted by downward arrows). In this way, the energy spacings of the lowest three 0D subbands in the quantum dot can be determined. If one takes into account that the relative energy shift of the 2D and 0D states is approximately equal to eA Vb, these subband spacings are given by AE01 ~ 7 meV, AE12 ~ 6 meV, and AE23 ~ 5 meV. A E i j is, thus, found to decrease with increasing subband index, which is consistent with the assumption of a cosine-shaped dot potential. Finally, it is worth noting that Coulomb charging effects will play no significant role in the discussed experiment. This is mainly due to the particular sample layout. As discussed earlier in the context of an asymmetric double-barrier tunneling device (cf. Fig. 61), Coulomb blockade effects are not observed, if the emitter barrier is less transmissive than the collector barrier. This picture is valid for f o r w a r d bias also in the present situation, if one identifies the emitter barrier with the A1GaAs layer separating the two electron systems and the collector barrier with the broad but low barrier between the dot and the alloyed AuGe contact. Because the collector barrier is then clearly much more transmissive than the emitter barrier, Coulomb blockade is not expected for positive sample bias. For negative bias, Coulomb charging effects could, in principle, play a role. In practice, however, the sample design leads to a large capacitance between the dot and its surroundings: Each dot is capacitively coupled vertically to two large electrodes coveting the whole area of the quantum dot array, namely, the underlying 2DEG and the top electrode. A rough estimate shows that this leads to an effective "capacitive" radius of the dot on the order of 150 nm. The corresponding Coulomb charging energy is far below 1 meV and, therefore, an order of magnitude smaller than the average subband spacing of the dot. This means that in the temperature range of the preceding experiments quantization effects are dominant.

Acknowledgments The authors are grateful to G. Berthold, W. Demmerle, and E Hitler for their substantial contribution to the scientific part of this work and N. Reinacher for solving the numerical problems. The excellent samples used in our experiments were grown by G. Brhm, W. Schlapp, G. Strasser, and G. Weimann. Valuable technical help during the sample preparation process was provided by C. Eder, C. Gmachl, M. Hauser, R. Maschek, and V. Rosskopf. The authors also acknowledge numerous fruitful discussions with W. Boxleitner, C. Hamaguchi, M. Heiblum, Y. Levinson, U. Meirav, J. C. Portal, D. Schneider, F. Stem, P. Streda, and P. Vogl. Financial support was obtained through the Gesellschaft fiir Mikroelektronik (GMe) and the Jubil~iumsfonds der Oesterreichischen Nationalbank (OENB). Finally, we wish to thank E. Gomik for his help and continuous support during the past years.

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Gouldner, Solid State Commun. 87, 513 (1993). 187. M. Tewordt, L. Martin-Moreno, T. J. Nicholls, M. Pepper, M. J. Kelly, V. J. Law, D. A. Ritchie, J. E. E Frost, and G. A. C. Jones, Phys. Rev. B 46, 3948 (1992). 188. J.W. Sleight, E. S. Hornbeck, M. R. Desphande, R. G. Wheeler, M. A. Reed, R. C. Bowen, W. R. Frensley, J. N. Randall, and R. J. Matyi, Phys. Rev. B 53, 15727 (1996). 189. Z.-L. Ji, Phys. Rev. B 50, 4658 (1994). 190. H.C. Liu and G. C. Aers, Solid State Commun. 67, 1131 (1988). 191. S.Y. Chou, E. Wolak, and J. S. Harris, Appl. Phys. Lett. 52, 657 (1988). 192. B. Su, V. J. Goldmann, and J. E. Cunningham, Phys. Rev. B 46, 7644 (1992). 193. T. Schmidt, M. Tewordt, R. H. Blick, R. J. Haug, D. Pfannkuche, K. von Klitzing, A. Foster, and A. Luth, Phys. Rev. B 51, 5570 (1995). 194. M. Tewordt, L. M. Moreno, J. T. Nicholls, M. Pepper, M. J. Kelly, V. Law, D. A. Ritchie, J. E. E Frost, and G. A. C. Jones, Phys. Rev. B 45, 14407 (1992); M. J. Kelly, V. Law, D. A. Ritchie, J. E. F. Frost, and G. A. C. Jones, Phys. Rev. B 45, 14407 (1992). 195. T. Schmidt, R. J. Haug, K. von Klitzing, A. F6ster, and H. Ltith, Phys. Rev. B 55, 2230 (1997). 196. K. Nomoto, T. Suzuki, K. Taira, and K.~Hase, Phys. Rev. B 55, 2523 (1997). 197. M. Tewordt, R. J. E Hughes, L. Martin-Moreno, T. J. Nicholls, H. Asahi, M. J. Kelly, V. J. Law, D. A. Ritchie, J. E. E Frost, G. A. C. Jones, and M. Pepper, Phys. Rev. B 49, 8071 (1994). 198. A.K. Geim, T. J. Foster, A. Nogaret, N. Mori, P. J. McDonnel, N. La Scala, P. C. Main, and L. Eaves, Phys. Rev. B 50, 8074 (1994). 199. J.W. Sakai, P. C. Main, P. H. Beton, N. La Scala Jr., A. K. Geim, L. Eaves, and H. Henini, Appl. Phys. Lett. 64, 2563 (1994). 200. P. H. Beton, H. Buhmann, L. Eaves, T. J. Foster, A. K. Geim, N. La Scala Jr., P. C. Main, L. Mansouri, N. Mori, J. W. Sakai, and J. Wang, Semicond. Sci. Technol. 9, 1912 (1994). 201. W.B. Kinard, M. H. Weichold, G. E Spencer, and W. P. Kirk, J. Vac. Sci. Technol. B 8, 393 (1991). 202. L. Eaves, in "Physics of Nanostructures" (J. H. Davies and A. R. Long, eds.), p. 149. IOP Publishing, 1992.

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ELECTRON TRANSPORT AND CONFINING POTENTIALS

203. E C. Main, E H. Beton, M. W. Dellow, L. Eaves, T. J. Foster C. J. G. M. Langerak, M. Henini, and J. W. SakaJ, Physica B 189, 125 (1993). 204. M. W. Dellow, P. H. Beton, M. Henini, P. C. Main, L. Eaves, S. P. Beaumont, and C. D. W. Wilkinson, Electron. Lett. 27, 134 (1991). 205. N. Blanc, P. Gueret, R. Germann, and H. Rothuizen, Physica B 189, 135 (1993). 206. J. Smoliner, Semicond. Sci. Technol. 11, 1 (1996).

91

Chapter 2 ELECTRONIC

TRANSPORT PROPERTIES OF

QUANTUM DOTS M. A. Reed, J. W. Sleight*, M. R. Deshpande t Departments of Physics, Applied Physics, and Electrical Engineering, Yale University, New Haven, Connecticut, USA

Contents 1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2.

3. 4.

5.

1.1. Fabricated Quantum Dots: Vertical and Horizontal Systems . . . . . . . . . . . . . . . . . . . . 1.2. Impurity Dot System: Coulomb Potential Confinement . . . . . . . . . . . . . . . . . . . . . . . Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1. Energy States of a Fabricated Quantum Dot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2. Energy States of the Impurity Dot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3. Current-Voltage Characteristics of Vertical Dot: Fabricated and Impurity Systems . . . . . . . . Sample Growth and Fabrication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1. Current-Voltage Characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2. Variable-Temperature Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3. Magnetotunneling Measurements: Diamagnetic Shifts and Current Suppression . . . . . . . . . 4.4. Magnetotunneling Measurements: Fine Structure . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5. Magnetotunneling Measurements: Spin Splitting and g* Factor . . . . . . . . . . . . . . . . . . 4.6. Magnetotunneling Measurements: Electron Tunneling Rates . . . . . . . . . . . . . . . . . . . . Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

93 93 95 96 96 97 100 101

101 101 103 106 113 117 121 128 129 129

1. I N T R O D U C T I O N

1.1. Fabricated Quantum Dots: Vertical and Horizontal Systems T u n n e l i n g in l o w - d i m e n s i o n a l s e m i c o n d u c t o r s t r u c t u r e s has b e e n a v e r y active r e s e a r c h field, b o t h e x p e r i m e n t a l l y [ 1 - 1 0 ] a n d t h e o r e t i c a l l y [ 1 1 - 1 9 ] . T r a d i t i o n a l l y , t h e r e h a v e b e e n t w o d i f f e r e n t a p p r o a c h e s to a c h i e v i n g a t h r e e - d i m e n s i o n a l l y c o n f i n e d s y s t e m (Fig. 1). In o n e a p p r o a c h , h o r i z o n t a l d o t s [ 7 - 1 0 ] , e l e c t r o n s are first c o n f i n e d to a t w o - d i m e n s i o n a l ( 2 D ) e l e c t r o n l a y e r f o r m e d at the i n t e r f a c e o f

GaAs/AlxGal_xAs. B a n d b e n d i n g

*Present address: IBM Semiconductor Research & Development Center, New York. tCurrent affiliation: Motorola Corporate Research Laboratories, 2100 East Elliot Road, Tempe, AZ 85284.

Handbook of Nanostructured Materials and Nanotechnology, edited by H.S. Nalwa Volume3: ElectricalProperties Copyright 9 2000 by Academic Press All rights of reproduction in any form reserved.

ISBN 0-12-513763-X/$30.00

93

REED, SLEIGHT, AND DESHPANDE

Fig. 1. (a) Comparison of the starting epitaxially grown material for a horizontal quantum dot structure (left) to a vertical structure (right). (b) Same structures after the fabrication that forms the quantum dot showing the top view of the horizontal dot and the side view of the vertical dot.

at the interface results in the formation of a triangular potential well in the GaAs region. Electrons are confined in this well and their motion in the direction perpendicular to the interface (z direction) is restricted. The number of electrons in the well can be controlled by suitably doping the barrier AlxGal_xAs material sufficiently far from the interface. The electrons released by these donors accumulate in the well formed in the GaAs. These electrons are free to move in the lateral 2D plane and, therefore, this system is called a 2D electron gas. One can also control the density of the electrons by putting a gate electrode on top of the Alx Gal-x As barrier and applying a suitable bias to it. A negative voltage applied to the gate repels electrons from underneath it. A suitable pattern of gate electrodes will electrostatically confine the electrons in a small area of the 2D layer. A full three-dimensional confinement is achieved as a result of the interface band bending and electrostatics. The electronic states of this confined dot can be probed by the tunneling of electrons into and out of the dot from the 2D electron gas surrounding the dot. The barrier between the dot and the 2D electron gas is due to the electrostatic potential of the fringing electric field of the patterned gate electrodes. The transport in this system is thus within the interface plane and, hence, this system is known as a horizontal quantum dot. Another approach, vertical dots [1-6], starts with a double-barrier resonant tunneling structure consisting of heterostructure layers such as, GaAs/AlxGal_xAs/GaAs/ AlxGal_xAs/GaAs. In this system, electrons are confined along one direction, the z direction, in the quantum well region (GaAs) in between the two barriers (AlxGal_xAs).

94

ELECTRONIC TRANSPORT PROPERTIES OF QUANTUM DOTS

Reactive ion etching is used to physically reduce the lateral size of the device (Fig. 1), thus confining electrons along the remaining two (x and y) dimensions. The electronic states of this confined dot can be probed by tunneling of electrons into and out of the dot from the GaAs electrodes on either side of the device. The barrier between the dot and the GaAs electrodes is composed of the AlxGal-xAs layers. The transport in this system is thus perpendicular to the interface and, therefore, this system is known as the vertical quantum dot. In both techniques, the confinement potential spatially localizes electrons in a region, and quantizes the allowed energy levels in this region. However, there are major differences between the two systems. The barriers in the vertical dot system are well defined, atomically precise, and rigidly formed during growth of the layers. In contrast, the barriers in the horizontal dot are electrostatically defined and are soft barriers as they are ill defined, smooth, and flexible. The vertical dot is essentially a two-terminal system, whereas in the horizontal dot system it is easily possible to incorporate a gate electrode that makes it a three-terminal system. Usually, the total number of electrons residing in a vertical dot is very small (from 0 up to approximately 10), while that number is typically much larger in the horizontal dot system. In the case of horizontal dots, the single-electron charging energy, Uc, is usually much greater than 6E, the spacing between single-particle states in the dot. In the case of vertical dots, 3 E and Uc are of the same order [2], or Uc can be less than BE. In the regime where they are on the same order, it is difficult to distinguish between the transport phenomena caused by each of these effects [2, 17] and proper modeling [15] is required to appropriately assign the observed structure to either spatial quantization or single-electron charging. In this chapter, we restrict ourselves to the discussion of vertical quantum dots only. The vertical quantum dots described previously were the first structures where the effects of fully three-dimensionally confined electron states were observed [3]. These devices are small in size and, hence, have potential for high-density device applications. It is thus important to fully understand and characterize this and similar systems.

1.2. Impurity Dot System: Coulomb Potential Confinement There is another way in which one can create a three-dimensionally confined experimental system consisting of discrete, single-electron states. This is by having a small number of donor impurities in the quantum well regions of large-area resonant tunneling diodes [2023, 38]. The Coulomb potential of the ionized donor atoms gives rise to shallow, hydrogenic bound states (Fig. 2). These localized states are physically similar to discrete quantum dot states. The I(V) characteristics of this system are similar to those of a quantum dot system. The impurity system has certain advantages over the quantum dot system. It is a truly 3D-0D-3D

Fig. 2. Schematicof an impurity systemshowingan impuritystate in the quantumwell.

95

REED, SLEIGHT, AND DESHPANDE

tunneling system unlike a 1D-0D-1D system of the fabricated quantum dot. There is no fabrication-imposed unknown potential in the emitter and collector regions. The Coulomb potential experienced by the electron resulting from the impurity is a known potential and the impurity states and energies are better characterized. It is possible to get devices with only a few isolated impurities and thus investigate the basic properties of a single, discrete state without having to worry about other states and their occupancy. The physical extent of the impurity state in a GaAs quantum well is on the order of 10 nm, which is smaller than the lateral extents of fabricated quantum dot eigenstates. An understanding of the basic physics of this impurity system is thus valuable for the understanding of the fabricated quantum dot system. In Section 2, we first discuss the theory of the quantum dot eigenstates, the charging energy, and the effect of a magnetic field. We then discuss the eigenstates of the impurity potential. In Section 3, we discuss growth and fabrication details and, in Section 4, we present experimental results and, finally, conclude in Section 5.

2. THEORY 2.1. Energy States of a Fabricated Quantum Dot

2.1.1. Quantum Size Confinement Effects In a fabricated quantum dot as described previously, the potential an electron experiences along the z direction is due to the semiconductor heterostructure band alignments and is modeled as a finite square well potential as in a quantum well. The potential the electron experiences along the lateral (x-y) directions depends critically on the highly anisotropic reactive ion etching process. This confinement potential, which is enhanced because of Fermi-level pinning on the side walls [2, 3], may be modeled in a few different ways. If the lateral shape of the dot is asymmetric, then each eigenstate of the system is, in general, nondegenerate (except for the spin degeneracy). If the dot has cylindrical symmetry, then the various eigenstates reflect that symmetry. An additional effect to be considered is the Fermi-level pinning of the exposed side walls of the device. The Fermi level in the exposed semiconductor material gets pinned at a fixed value near the midgap. This induces bending of the bands and depletion of carriers from the region near the surface. The effective lateral size of the electrically active device is thus smaller than its physical dimensions. The potential an electron experiences along the lateral directions because of band bending and depletion is often modeled as a cylindrically symmetric parabolic potential [2, 3] as 9 (r) = ~T

[1-(R-r)]

2

(1)

W

where OT is the Fermi-level pinning energy at the side walls, R is the lateral physical dimension, r is the radial coordinate, and W is the depletion depth. Schr6dinger's equation for such a structure is best expressed in cylindrical coordinates. There is no 0 dependence, and, because the potential is separable along the radial and the z directions, O(r, z) = O(r) + O(z), separation of variables is possible. The single-electron eigenenergies are given by EN = Ez + En,l. Ez comes from the vertical quantization, and this will almost always be E0, the quantum well ground state in the vertical direction. En,t are the eigenenergies that result from the parabolic potential. En,l (2n + Ill + 1)h~o0 where the radial quantum numbers n = 0, 1,2 . . . . and the azimuthal quantum numbers l -- 0, 4-1, 4-2 . . . . . If we assume that we are in the first vertical subband, E0, and that the lateral dimension is reduced to 2 W or less, then the energy spacing between states is =

Ae-h

o-

( 2*T ] 1/2h

96

]

(2)

ELECTRONIC TRANSPORT PROPERTIES OF QUANTUM DOTS

For a GaAs well, with A1GaAs barriers, typical values for energy state separation are on the order of 25 meV, for ~T -- 0.8 eV and R ~ 500/k.

2.1.2. Magnetic Field Effects The dependence of electronic transport on magnetic field is a valuable tool in understanding the nature of localized states in semiconductor nanostructures. If a magnetic field oriented parallel to the current direction (perpendicular to the heterointerfaces) is applied, according to first-order perturbation theory, the shift of the energy levels is given by

3EBIII--

(eh ) ~

e2B2{r 2) g.B+

8m*

(3)

Note that spin is neglected in Eq. (3), as the spin splitting energy, gehB/2m, is only 0.25 meV at 10 T. The shift for a localized level with g- = 0 is entirely due to the diamagnetic term, •Ediamagnetic- eZB 2 (r2)/8m *, where (%2) is the spatial extent of the localized wave function. Therefore, the observation of an experimental diamagnetic shift is a direct measure of (r2). For a magnetic field oriented perpendicular to the current, the first-order perturbation term is more difficult to evaluate, and numerical methods are required [24, 25]. Numerical results indicate an increase in dot energy states by a diamagnetic shift term, which is predicted to be less than 0.5 meV at 10 T for a GaAs/A1GaAs quantum dot system with the same well width (50 A) as in this study. The small value for the state energy shift in this field orientation is due to the interaction of a relatively weak magnetic potential with the much stronger confinement potential in the epitaxial confinement (z) direction.

2.1.3. Charging Effects Charging effects become important as the lateral device area is scaled down. Charging can be introduced into the usual single-electron model by modeling the Coulomb charging energy of the quantum dot as arising from a single effective capacitance C [ 1]. This approach uses the semiclassical geometric capacitance (the sum of an emitter capacitance Ce and a collector capacitance Cc): C - Ce + Cc ~

8eozga 2 4

(de 1 + d c 1)

(4)

where de and dc are the thicknesses of the emitter and collector barriers, respectively, and a is the dot effective electrical diameter. For the structures in this paper, C ~ 2.6 x 10 -16 F using 8A1GaAs ~ 11.6, and a ~ 800 A. The value a is the electrical diameter, which is the extrapolated value determined from current density measurements on large-area samples. In this case, the estimated charging energy, Ec -- e2/2C, is approximately 0.31 meV. 1 More generally, EC,N -- e2/C(N - 89 is the Coulomb charging energy for N electrons residing on the dot [ 1, 26].

2.2. Energy States of the Impurity Dot 2.2.1. Energy of a Donor Impurity in Bulk GaAs In GaAs, a group IV atom (such as Si) at the Ga site acts as an electron donor. Upon ionization, the impurity site has an unbalanced positive charge, which introduces a Coulomb potential that is screened by the available free carriers in the semiconductor. The attractive Coulomb potential gives rise to hydrogen-like energy states that can bind free carriers.

1 In [1], the expression for capacitance incorrectly includes a factor of 4rr in the denominator. EC is given as e2/C, whereas it should be e2/2C.

97

REED, SLEIGHT, AND DESHPANDE

To determine the energy states of such a semiconductor hydrogenic atom, we follow the treatment of Bastard [28]. The wave function of a donor state in a semiconductor can be expressed in the form (from Kohn [29]) N (r) -- Z Oli Fi (r)qbi (r) i=1

(5)

where N is the number of equivalent conduction band minima, q~i (r) are the Bloch wave functions, and Fi (r) are the envelope functions. In GaAs for the conduction band that is nondegenerate and isotropic with parabolic dispersion relations (N = 1 and single effective mass m*), the envelope functions, F(r), of the impurity states fulfill the equation [p2 2m*

e2

1

4zr eokr

F (r) = E F (r)

(6)

where p is the momentum, m* is the carrier effective mass, k is the dielectric constant of the semiconductor, e is the electronic charge, e0 is the permittivity of space, and E is the energy of the impurity state. The ground bound state of this system is the 1S hydrogenic wave function:

1

(r)

Fls(r) = (b ) .aa.1/2 exp - - - ab

(7)

where ab is the effective three-dimensional Bohr radius of the semiconductor hydrogenic impurity:

4zr eokh 2 mo = 0.53 • k x ~ ,~ ab -- m,e2 m*

(8)

The binding energy of this 1S state, Rb, is given by

m*e 4 1 m* R b - 32:rr20k2h 2~ = ~tc'--w• ~ x 13.6 eV m0

(9)

In GaAs, k = 12.85 and m*/mo = 0.067 giving us ab ~ 101 ~ and Rb ~ 5.5 meV. We can see that the binding energy of hydrogenic donors in bulk GaAs has a very small energy compared to its band gap of 1.5 eV. Therefore, this state is called a shallow donor state. An electron occupying this state has an energy of - 5 . 5 meV as measured from the bottom of the conduction band.

2.2.2. Energy of a Donor Impurity in a Quantum Well In contrast to the bulk material, the binding energy of an impurity in a quantum well depends on the properties of the well, in particular, its width L and its barrier height V0. The impurity binding energy increases as the well width decreases as long as the penetration of the quantum well wave function [X (z)] in the barriers remains small. This seems surprising at first because we intuitively associate higher kinetic energy (and, hence, lower binding energy) with the localization of a particle in a finite region of space. This is true of the energy value of the ground state of the quantum well, E1 (L), and so also of the ground state of the impurity, e(L), when measured with respect to some fixed reference such as the bottom of the well. But the binding energy of the impurity Eb(L) = E1 (L) - e(L) actually increases as L decreases because for the impurity state the confinement causes the electron to stay near the attractive center, thus experiencing a higher potential energy. In the limiting case of an infinite barrier (V0 = c~) and zero well width (L = 0), we reach the two-dimensional limit when the ground state binding energy of a hydrogenic impurity is 4Rb = 22 meV.

98

ELECTRONIC TRANSPORT PROPERTIES OF QUANTUM DOTS

lltillll,,l!,|!l,,,,l,,,,l,,,,l,,i,l,,,,l,,,,l,,lil,,,l

9 on centerimpurity o on edge impurity

_3

2

P2

~"'l'"'l'""i""'l'"'l''"i""l'"'I''"l'"'

2

4 6 8 Well Width (L/ab)

10

Fig. 3. Calculateddependences of the on-center and on-edge hydrogenic donor binding energies versus the well thickness L in a quantum well with an infinite barrier height (V0 = oo). Rb and ab are the bulk effective Rydberg and Bohr radius, respectively. (Source: Adapted from [30].)

Another important feature of impurities in quantum wells is that the impurity binding energy explicitly depends on the precise location of the impurity along the growth axis (z direction) as there is no translational invariance along that axis. This energy depends on whether the impurity is at the center of the well or at the edge of the well or within the barrier. The wave function for an impurity at the center of the well (z = 0) approaches the 1S wave function of the bulk. But the wave function for an impurity at the edge of the well (z = L/2) approaches a truncated 2pz wave function as the barrier potential forces the impurity wave function to almost vanish at the interface. The edge impurity has a lower binding energy than the center impurity. If the impurity is located within the barrier, it is still able to bind an electron in the well. The electron is physically separated from the impurity charge and such a system has lower binding energy than even an impurity at the edge. The impurity binding energy in a quantum well can be obtained numerically as has been done by Bastard [28]. The results of such a calculation for an infinite barrier quantum well (V0 = c~) are shown in Figure 3 for an impurity located at the center and for an edge impurity. The binding energy is in the units of the bulk impurity Rydberg (Rb ----5.5 meV for GaAs) and the well width is in the units of the bulk impurity Bohr radius (ab = 101 for GaAs). For our experimental system where the well width is 44 A, this figure gives us a binding energy for center impurity of approximately 16 meV and a binding energy for edge impurity of approximately 10 meV. Because the impurities are randomly distributed in the well, it is statistically possible to have two impurities close to each other particularly in large-area samples. If the separation between the two impurities is on the order of the Bohr radius of a single impurity (100/k), then the energy state of the electron is substantially modified. This is analogous to a hydrogen molecular ion problem. These impurity pairs give rise to higher binding energy states with the energy depending on the impurity separation. In the limiting case when the two impurities overlap, the situation is similar to a He + system with the resulting binding energy of the electron being four times as much as the single impurity binding energy. So far, we have assumed that the barriers are infinite. For real systems, this is not true and the binding energy of an impurity does depend on the barrier height V0. For finite barriers, as the well width decreases beyond a certain limit (~0.2ab), the impurity energy

99

REED, SLEIGHT, AND DESHPANDE

becomes comparable to the barrier height and the impurity wave function gets more and more delocalized. The effect of the Coulomb potential gets smaller and, hence, the binding energy decreases for L less than approximately 0.2ab (unlike the trend observed in Fig. 3). For the samples under study where L = 44 A, an infinite barrier approximation is shown to be a reasonable approximation [31 ].

2.2.3. Coulomb Charging Energy in the Impurity System In the impurity system, the lateral size of the device is large (a few micrometers) and the charging energy of one electron is negligible. If the impurity concentration in the device is low and the impurities are separated by a large distance (in the micrometer range), then we can assume that each impurity channel is independent of the others as the presence or absence of an electron in one would not have any effect on the others. A given hydrogenic impurity has many eigenstates. In particular, the ground state of the impurity is spin degenerate in zero magnetic field. Although we have two states with the same energy, only one of them can be occupied by an electron at a given time because of charging effects. This has important consequences on the I(V) characteristics as will be discussed later.

2.3. Current-Voltage Characteristics of Vertical Dot: Fabricated and Impurity Systems The electronic structure of the dots can be probed by studying the two-terminal currentvoltage [I(V)] characteristics as in a quantum well resonant tunneling diode. If the heterostructure barriers along the z direction have finite thickness, then the dot eigenstates (localized states) couple to the electronic states in the emitter and the collector regions on either side of the dot along the z direction. Let us first consider the simple case when the Coulomb charging energy of the dot is small compared to the size quantization energy. Any electron incident on such a structure at an energy equal to one of the localized state energies will see an increased transmission probability as it is able to couple to the eigenstate and tunnel through the structure. As bias is applied across the device, the localized states are pulled down in energy toward the emitter Fermi level. As a level crosses the Fermi energy, electrons in the emitter having the same energy as the localized state experience an enhanced transmission probability and thus there is a sharp increase in current. This current is due to single electrons tunneling one at a time through the quantum dot eigenstate and it can be written as AI ~ -

e

(10)

T

where e is the electronic charge and r is the lifetime of the dot state. The lifetime (r) depends on the heterostructure barrier thicknesses, the bias, and the density of available, occupied electronic states in the emitter. As the bias increases slightly, to first order, the current through a given localized state remains the same and, therefore, causes a current plateau or step in the I(V) characteristics. A further increase in bias brings another localized state below the Fermi level in the emitter introducing another channel for electrons to tunnel through. The I(V) characteristics of the device thus resemble a staircase structure. In the case of the fabricated dot, the bias locations of the steps correspond to the energy spectrum of the quantum dot. In the case of the impurity dot, the bias locations of the steps are random as each step is attributed to a separate impurity and the impurities are randomly distributed. This simple picture gets modified when the Coulomb charging energy becomes comparable to the size quantization energy. An additional bias, corresponding to the charging energy of a single electron, is necessary for the threshold of conduction. The energy spectrum of the dot also depends on the number of electrons occupying the dot states. The staircase structure of the I(V) characteristics is modified and the bias locations of the steps no longer just correspond to the energy spectrum of the uncharged dot but also depend on the occupancy of the dot.

100

ELECTRONIC TRANSPORT PROPERTIES OF QUANTUM DOTS

3. SAMPLE GROWTH AND FABRICATION Samples are grown using molecular beam epitaxy on a Si-doped (100) GaAs substrate [32]. For the resonant tunneling diodes of the impurity system, the epitaxial layers consist of a 1.8 x 1018-cm -3 Si-doped GaAs contact, a 150-A undoped GaAs spacer layer, an undoped A10.27Ga0.73As bottom barrier of width 85 A, a 44-/~ undoped GaAs quantum well, an undoped A10.27Ga0.73As top barrier of the same width 85 A, a 150-A undoped GaAs spacer layer, and a 1.8 x 1018-cm -3 Si-doped GaAs top contact. Square mesas with lateral dimensions ranging from 2 to 64/zm are fabricated using standard photolithography techniques. In the case of the fabricated quantum dots, the active region consists of a 50-,& In0.1Ga0.9As quantum well, enclosed by a pair of 40-A-thick Alo.25Gao.75As barriers. This region, along with 100-A spacer layers of GaAs that contact the barriers, is undoped. The spacer layers are contacted by GaAs doped with Si at a density of 3 x 1018-cm -3. Small (~ 100 nm) AuGe/Ni/Au ohmic top-contact dots are defined by electron beam lithography on the surface of the grown resonant tunneling structure. A bilayer polymethylmethacrylate (PMMA) resist and lift-off method are used. The metal dot ohmic contact serves as a self-aligned etch mask for highly anisotropic reactive ion etching (RIE) using BC13 as an etch gas. The resonant tunneling structure is etched through to the bottom n + GaAs contact. Contact to the top of the structures is achieved through a planarizing/etch-back process employing polyimide and an 02 RIE [3]. A gold contact pad is then evaporated over the columns. Bottom contact is achieved through the conductive substrate. Note that in the fabricated quantum dot samples In0.1Ga0.9As is used as the well material rather than the standard GaAs, although the contact electrodes are still GaAs. In0.1Ga0.9As has a lower band gap than GaAs. The quantum eigenstates in the In0.1Ga0.9As well thus have lower energies (measured from the bottom of the contact electrodes) as opposed to a conventional sample, which would have GaAs well material with the same well width. By using an InGaAs well, the equilibrium dot quantum states are brought down closer to, or below, the Fermi level. Lower quantum levels in the well imply longer lifetimes (i.e., less intrinsic energy broadening). Additionally, because this reduces the resonant bias voltage far less distortion of the emitter/dot/collector potential occurs while examining the density of states of the dot as compared to a conventional GaAs vertical quantum dot. Owing to the lower applied bias required, there is far less power dissipation and local electron heating in the dot region. Two-terminal direct-current (dc) I(V) characteristics are measured in a dilution refrigerator with a mixing chamber temperature (Tmix) of 35 mK.

4. EXPERIMENTAL RESULTS

4.1. Current-Voltage Characteristics

4.1.1. Fabricated Quantum Dots Several different types of transport measurements were performed to investigate the electronic properties of the vertical InGaAs quantum dot structures. Large-area resonant tunneling diodes (RTDs) are fabricated to examine the peak positions and current densities for the epitaxial material. Figure 4a shows a current versus voltage trace for a 1024-/zm 2 sample measured at 4 K. A symmetric response is observed that is consistent with the symmetric epitaxial structure. The negative differential resistance (NDR) occurs at +23 mV with a peak current density of 56 A/cm 2. The low bias conductance is 25 mS for the 1024-/zm 2 device, and this value is observed to scale linearly with device area, as expected, providing a means of extrapolating the upper limits for the electrical sizes of the smaller devices.

101

REED, SLEIGHT, AND DESHPANDE

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Fig. 4. (a) Current versus voltage for a large-area (1024/zm 2) sample fabricated from the same epitaxial material used for the small-area quantum dots (T = 4.2 K). (b) Current versus voltage for an In0.1Ga0.9As quantum dot. Note the steplike structure in current near zero bias (T = 50 mK, mixing chamber).

3 2

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Fig. 5.

-20

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Expansion of the low-bias regime of Figure 4b.

The small-area quantum dot samples are measured at millikelvin temperatures in a dilution refrigerator. Figure 4b shows a current versus voltage [I(V)] curve for a sample (R ~ 100 nm) under zero magnetic field, at a mixing chamber temperature of 50 mK. Figure 5 shows an expansion of the zero-bias region. The conductance for this sample (~0.4/zS) yields a value of approximately 800 ,~ for the electrical diameter, a. A staircase structure in current is observed in Figures 4b and 5 in both bias directions, especially at low biases. A similar structure in the low-bias regime for double-barrier resonant tunneling structures (DBRTS) has been previously reported by other groups [2, 27]. The major difference in our work is the use of an InGaAs dot, as well as the use of a symmetric epitaxial

102

ELECTRONIC TRANSPORT PROPERTIES OF QUANTUM DOTS

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Fig. 6. I(V)characteristics (zero magnetic field) at 1.4 K of the quantum well device showingthe main resonance peaks (top). The magnified prethreshold region shows two steplike structures resulting from two isolated impurities (bottom).

structure. The current steps are relatively flat at low bias, where the transmission coefficient is not a strong function of applied bias. We also note that there is an oscillatory structure on the current steps. This structure appears random but is very reproducible even after thermal cycling of the device. We will refer to this structure as the "fine structure" and discuss it in detail later.

4.1.2. Impurity Quantum Dot Figure 6 shows the I(V) characteristics for a typical resonant tunneling diode of the impurity system, (64/zm 2, 1.4 K), showing the main quantum well resonance peaks (top). Magnification of the current in the prethreshold region (bottom) shows two sharp current steps for both forward- and reverse-bias directions. This step structure is observed to be sample specific, but for a given sample it is exactly reproducible from one voltage sweep to another and independent of the voltage sweep direction. The steps are reproduced even after thermal cycling of the sample, except for slight threshold voltage shifts (< 1 mV). Similar steps are observed in other devices with different barrier thickness. These steps look similar to the steps in Figure 5 and are attributed to tunneling through single impurity states. Note that these steps also show an oscillatory fine structure on the current plateaus. To analyze the electron spectroscopy of the dot systems in greater detail, we need to determine the bias-to-energy conversion factor, or. The value of ot is a measure of the amount of voltage that is actually dropped between the emitter and the quantum dot state. As will be shown, ot can be determined from the temperature dependence of the plateau edges. 4.2. Variable-Temperature Measurements As expressed in Eq. (10), the magnitude of the current step is given by A I = e / r , where r is the lifetime of the 0D state. This r depends, among other factors, on the available

103

REED, SLEIGHT, AND DESHPANDE

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Experiment: Theory I

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Fig. 7. (a) Reverse bias I(V) characteristics of the fabricated quantum dot at different temperatures. The inset shows the subthreshold peak (in conductance) that arises as temperature is increased. (b) Experimental conductance (crosses) versus temperature [for the peak in the inset of (a)] and the theoretical fit (solid line).

and occupied density of states in the emitter. The occupancy of the electronic states in the emitter is determined by the Fermi distribution function and thus we expect the current A I to be proportional to the Fermi function. The sharpness of the current plateau edges is expected to broaden as the temperature increases, because of the broadening of the emitter Fermi distribution function. The I(V) characteristics as a function of temperature for the fabricated quantum dot in reverse bias are shown in Figure 7a. The voltage-to-energy conversion factor, or, is calculated by fitting the Fermi function to the first current plateau (I0 is the value of the current on the plateau) in the variabletemperature data, that is,

I(V, T) = I o f (otV) =

Io 1 + exp[-ea(V-

Vth)/(kT)]

(11)

Here, Vth is the threshold voltage for the current plateau and can be accurately determined from the intersection point of the I (V, T) curves in Figure 7a, because the current given by Eq. (11) does not depend on the temperature for V = Vth. The value of ot is determined to be 0.37 in the forward-bias direction and 0.50 in the reverse-bias direction for the fabricated quantum dot. The different ot values imply an asymmetry in the emitter and collector contacts of the quantum dot device (either in doping or in the barrier or spacer layer thickness) in contrast to the symmetric response seen in the large-area device (Fig. 4a). This is not surprising as we are now probing a very localized region instead of averaging over nonuniformities in barriers or series doping, as in the large-area device. The current plateau edges of the impurity system also exhibit characteristic Fermi-level thermal broadening (Fig. 8). From a Fermi function fit for this device, we get ot = 0.48 -t0.02 for forward bias and 0.42 4- 0.02 for reverse bias. Once again, the fits are done for the

104

ELECTRONIC TRANSPORT PROPERTIES OF QUANTUM DOTS

50 40 < 30 = 20 ro

10

94

+ • o [] z~

0.8K 1.0K 1.4K 2.0K 3.0K

9

4.0K

96 98 Voltage (mV)

100

Fig. 8. I(V) characteristics of the first impurity current step edge of the impurity device at different temperatures showing the Fermi-levelbroadening and the Fermi fit to these I(V) traces.

region V ~< Vth when the current is small and not affected by the occupancy of the impurity state. We note the presence of an oscillatory, reproducible fine structure on the current plateaus in both the impurity and the fabricated quantum dot systems. Recently, it has also been investigated in detail by Schmidt et al. [38]. This structure (Figs. 7a and 8) exhibits significantly less dependence on temperature, especially for those regions located far away from the plateau edges. This indicates that the structure is not due to other states in the quantum dot or the quantum well itself, as current associated with tunneling through those states would exhibit Fermi broadening. The temperature insensitivity indicates that the current under consideration is from tunneling of the electrons from below the emitter Fermi level, where the emitter state occupation is not a function of temperature. Therefore, the fine structure is attributed to emitter states below the Fermi level, which pass into and out of resonance with the narrow 0D dot levels, as the applied bias is varied. At very low temperatures, only states in the emitter at or below the Fermi level, EF, are occupied. These are the only emitter states available for tunneling. Electrons in the states nearest to the Fermi level will tunnel into the dot state first. States below the Fermi level then contribute to the tunneling as the bias is increased. If this model is correct, we expect that, as the sample temperature is increased, states above the Fermi level in the emitter will be populated. Figure 9 schematically shows how the occupation of discrete emitter levels (depicted as black lines in parts a and b of Fig. 9) is affected by increasing temperature. At finite temperature, occupation of the emitter states above the Fermi level is possible and, therefore, thermally activated resonances below the first plateau should be observed. The inset of Figure 7a shows such a resonance effect, resulting in a subthreshold thermally activated conductance peak. Because I ( V ) = Iof(otV), where I0 is a constant prefactor dependent on the transmission coefficient and f (or V) is the Fermi function, the conductance, d I / d V = Io df(ot V ) / d V . A fit of this to the subthreshold conductance peak strength (inset Fig. 7a), assuming an emitter state above the Fermi level becomes thermally activated, is shown in Figure 7b. The energy difference between the thermally activated emitter state and Fermi level (1.7 meV) is known from measuring the difference between the plateau threshold voltage at low temperatures (which determines the emitter Fermi-level position) and the thermally activated conductance peak position at higher temperatures. The only fitting parameter is I0, which is within 5% of the value used for the first

105

REED, SLEIGHT, AND DESHPANDE

Fig. 9. (a) At T = 0, the Fermi function, f (E), is a step function (black line) that results in a very sharp transition from occupied to unoccupied discrete emitter states. (b) At finite temperature, f (E) becomes rounded near the Fermi energy, EF, causing a gradual transition from states that are mostly occupied to states that are mostly unoccupied.

reverse-bias current plateau (at V = Vth). A similar thermally activated subthreshold peak is observed in the forward-bias direction as well. Similar thermally activated, prethreshold peaks are not observed in the impurity system. We will discuss the fine structure in more detail after investigating its magnetic field properties.

4.3. Magnetotunneling Measurements: Diamagnetic Shifts and Current Suppression In addition to variable-temperature measurements, magnetic field is a valuable spectroscopy tool to examine bound states. Figures 10 and 11 show the forward-bias I(V) characteristics in magnetic field parallel to current ranging from 0 to 9 T for the fabricated quantum dot and the impurity system, respectively. The traces are offset by a constant current value for clarity. Note that there is a diamagnetic movement of all steps to higher bias with the magnetic field parallel to the current. This movement can be better observed in the fan diagrams shown in Figures 19 and 21. Plots of the plateau energy shift versus magnetic field squared (not shown) yield straight lines for all plateaus. At 9 T, the diamagnetic shift is approximately 1.4 to 2.6 meV (2-4 mV), depending on the current step/dot level for the fabricated quantum dot system, while it is about 0.4 meV (0.9 mV) for the current steps in the impurity system, implying that the impurity states are more localized. In the case of the fabricated quantum dot, different current steps are due to different energy eigenstates of the quantum dot. We expect these different eigenstates to show different shifts in a magnetic field and, hence, for the rest of this section we would concentrate on the diamagnetic shift of the fabricated dot only. Table I lists the values for the diamagnetic shifts and current plateau widths for the first six steps in the reverse- and forward-bias directions of the fabricated quantum dot. From Eq. (3) (e = 0) and slope of the experimentally measured diamagnetic energy shift versus B 2 (accounting for or), the radial wave function extent is determined to be approximately 100/~ for the ground state in both bias directions. The implications of the radial wavefunction extent on the dot electron spectroscopy will be elaborated on after discussing the results for the magnetic field oriented perpendicular to the current. It should be noted here that all resonances shift to higher bias with only a diamagnetic trend. This is in contrast to the single-electron theories for two-dimensionally and three-dimensionally confined, nearly cylindrical quantum dots in a magnetic field [36]. These theories show that some states increase in energy with magnetic field, while other states decrease in energy. Starting from zero field, the ground state always shifts upward

106

ELECTRONIC TRANSPORT PROPERTIES OF QUANTUM DOTS

Fig. 10. Current-voltage characteristics in a dilution fridge with a mixing chamber temperature of 35 mK, in a magnetic field (0-9 T in 0.1875-T increments) parallel to the current for the forward-bias direction of the fabricated quantum dot. Traces are offset by a constant current value for clarity.

Fig. 11. Current-voltage characteristics in a dilution fridge with a mixing chamber temperature of 35 mK, in a magnetic field (0-9 T in 0.094-T increments) parallel to the current for the forward-bias direction of the impurity system. Traces are offset by a constant current value for clarity.

in energy, while the second state always shifts d o w n w a r d (ignoring spin). This is due to the Z e e m a n term (the term linear in B) in Eq. (3). The absence of Z e e m a n effects in the experimental data (i.e., peaks splitting and shifting in energy with a linear term) implies that either we cannot probe e > 0 states, possibly because of orthogonality b e t w e e n the emitter wave functions and e > 0 dot levels, or this simply tells us that ~ is not a g o o d q u a n t u m n u m b e r for this system. This implies that the assumed cylindrical s y m m e t r y has

107

REED, SLEIGHT, AND DESHPANDE

Table I. Experimentally Observed Diamagnetic Shifts and Current Plateau Widths for the Reverse- and Forward-Bias Directions for the Fabricated Quantum Dot Structure ~Ediamagnetic (meV, B = 9 T) (reverse, forward bias)

Plateau width (meV) (reverse,forward bias)

1

1.4, 1.6

5.0, 3.3

2

1.5, 1.6

6.5, 3.3

3

1.9, 2.6

6.5, 2.6

4

2.0, 1.6

9.0, 4.4

5

2.1, 1.6

1.1, 3.0

6

2.1, 1.0

3.5, 2.2

Plateau index (N)

40

9T

30

~J

20 r,.)

0T 10

0

20

40 60 80 Voltage (mV)

100

120

Fig. 12. Current-voltagecharacteristics in a magnetic field (0-9 T in 0.1825-T steps) perpendicular to the current for the fabricated quantum dot in the reverse-bias direction.

been distorted significantly. It should be noted that other groups [1, 2, 37] investigating similar systems also observe a diamagnetic dependence only. Figures 12 and 13 show the I(V) characteristics in the perpendicular magnetic field, for the fabricated quantum dot (reverse bias) and the impurity system (forward bias) at a mixing chamber temperature of 35 mK. As expected, the bias locations of all the current steps attributed to 0D dot states are not greatly affected by the perpendicular field, in contrast to the diamagnetic movement observed in the parallel field. This is confirmation that the current steps are the result of tunneling through the laterally localized dot states that reside in the strong confinement of the quantum well. In addition to the difference in the response of the dot energy levels (i.e., the current plateau edges) to parallel and perpendicular magnetic fields, suppression of the plateau

108

ELECTRONIC TRANSPORT PROPERTIES OF QUANTUM DOTS

Fig. 13. Current-voltage characteristics in a magnetic field (0-9 T in 0.094-T steps) perpendicular to the current for the impurity system in the forward-bias direction.

Fig. 14. Maximum (solid) and minimum (dashed) current values for the first current plateau of the fabricated quantum dot in reversebias as a function of perpendicular and parallel magnetic fields.

current is observed for both bias directions in magnetic field oriented perpendicular to the current for both dot systems. Especially noteworthy are the lower plateaus of the fabricated dot system (Fig. 12), which appear to vanish because of the current scale. Figure 14 shows how dramatic these effects are. Current versus magnetic field squared is shown for the maximum and minimum current observed on the first plateau in the reverse-bias direction, in both parallel and perpendicular field orientations. In parallel field, the difference between the current minimum and maximum remains constant on a logarithmic scale over the field range in both bias directions, and only slight suppression is observed at 9 T. The current suppression for perpendicular field at 9 T is very large for the reverse bias (a factor of 100 for the plateau current minimum and 25 for the current maximum). In forward bias, a factor of approximately 10 is observed for both the current plateau minimum and the current plateau maximum.

109

REED, SLEIGHT, AND DESHPANDE

100 9 8

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.A E even for r0 seven times larger. In Eqs. (17) and (18), we have assumed that the tunneling rates are the same at the two different biases V1 and V2, which is a good assumption because the bias difference (V1 - V2) is much smaller than the barrier potential. In the extreme limits, these equations indicate that, for Td >> Tem, p ~ 0 and 12 ~ 211, while, for Tcl ~ Vth). The experimentally measured current can be seen to be less than the theoretically expected current on the plateau.

region above the threshold (Fig. 31), we observe that the experimentally measured current is lower than the predicted value. We attribute this deviation to the Fermi behavior of the spin degeneracy of the localized state and Coulomb charging effects. This fit is strictly valid for the case of tunneling through a single state only. The current in the case of tunneling through two degenerate states can be expressed as in Eq. (18) [assuming p = pof(E)]:

AI -- Apof (E)(2 - pof (E))

(19)

where A is a constant and P0 = Tem/(Tern -k- Tcl) is the occupancy of the electron in either one of the two localized degenerate states when f(E) = 1. Po depends on the relative tunneling rates of the two potential barriers. Equation (19) can be fit to the data. Once again, the fits are done only for bias voltages V ~< Vth because of the presence of the "fine structure" on the current plateaus for V ~> Vth. However, in Figure 32, we directly show the extrapolation of the corrected fits to all bias voltages. Vth is obtained from the common intersection point of the curves at different temperatures. A and p0 are obtained from the measured current values of the plateau current (/plateau) and the threshold current Ith in the following way. If V >> Vth, then f (E) = 1 and A I --/plateau = A p 0 ( 2 - P0) If V -

Vth, then

(20)

f ( E ) - 89and AI--Ith=a(-~)(22P-------~O )

(21)

Solving these two equations simultaneously from the measured values of/plateau and Ith, we get A and p0. We get for the data shown in Figure 32, A = 81.4 pA and P0 = 0.35. Thus, once again, the only free parameter in the fit is c~, which then can be accurately determined. The c~ values obtained from this fit for this step is 0.5, which is within the experimental error of that obtained from the previous fit (0.48). This is consistent as both the fits are done at V ~< Vth I f ( E ) < 1], when the occupancy [p -- pof(E)] is small, and Eq. (19)

124

ELECTRONIC TRANSPORT PROPERTIES OF QUANTUM DOTS

50

40 < 30

=

Temperature + 0.8K x 1.0K o 1.4K [] 2 . 0 K ,~ 3 . 0 K 4.0K

20

10

94

96 98 Voltage (mV)

100

102

Fig. 32. I(V) characteristics of the first current step edge in forward bias of the impurity system with 85-A-thick barrier thickness at different temperatures and the extrapolation of the corrected fits [Eq. (19)] to these I(V) traces to voltages greater than the threshold (V ~>Vth).

reduces to that of Eq. (11). These fits and their extrapolation to bias voltages V >~ Vth now accurately determine the current plateau values as can be seen from Figure 32. It is also possible to determine the occupancy for the localized states in reverse bias. For the same device in reverse bias, we obtain P0 = 0.57 and a = 0.42. This difference in forward and reverse bias is attributed to a slight asymmetry in the growth of the device and will be discussed in detail later. The importance of this corrected fit becomes even more apparent while investigating the thermal broadening of current steps on which the fine structure is not very prominent. In such cases, the fit can be carried out over the entire range of the data unlike the earlier case where it was restricted to V ~< Vth. This is shown in Figure 33 for the 65-A-thick barrier device in forward bias. From the fit, we obtain p0 - 0.57, A = 0.56 nA, and a -- 0.42 for this particular step. Note that doing a Fermi fit only [Eq. (11)] to the data of Figure 33 would be very inaccurate. The ratio of the current at the threshold, the common intersection point of all the curves, and the current on the plateau is Ith//Iplateau = 0.275 nA/0.458 nA = 0.6. This is much larger than 0.5 as one would have expected if one had a perfect Fermi function behavior. From the experimental values of A and p0, one can determine the electron tunneling rates Tem and Td. P0 = T e m / (Tem -~- Tcl) and A = e Tcl. Thus, for the first current step in forward bias of the 85-A-thick barrier device (Fig. 32), Tcl = 509 MHz and T e m : 274 MHz. Similarly, for the first current step in forward bias of the 65-/k-thick barrier device (Fig. 33), Tcl = 3.6 GHz and Tem -- 4.7 GHz. Similar measurements of the tunneling rates can also be obtained from the magnetic field studies. Those measurements, however, require really low temperatures (less than 300 mK) and high magnetic fields. The calculation described here requires relatively moderate temperatures (greater than 1 K) and, hence, is important.

4.6.2. Tunneling Rates in a Magnetic Field For the remainder of this chapter, we confine ourselves to a discussion of the results of only one device (the device with the 85-A barrier and data from the first current step only).

125

REED, SLEIGHT, AND DESHPANDE

0.5

0.4

" 0.3

0.2

Temperatures + 0.7K o 1.2K [] 1.5K ,~ 2.0K 3.0K

0.1

0.0~ 83

84

85 86 87 Bias Voltage (mV)

88

Fig. 33. I(V) characteristics of the first current step edge in forward bias of the impurity system with 65-/~-thick barrier at different temperatures and the corrected fits [Eq. (19)] to these I(V) traces. The fits are done over the entire bias range spanning the step.

The results of the other device (65-A barrier) show similar trends. From the data shown in Figure 29 at 9 T (field perpendicular to current), we get p = 0.21 for forward bias and p = 0.62 for reverse bias. A high p value indicates that the electron tunneling rate through the collector (downstream) barrier (Td) is lower than that through the emitter (upstream) barrier (Tem), causing an accumulation in the well. A higher p value for reverse bias (as compared to forward bias) suggests an asymmetry in the heterostructure growth with one barrier being slightly thicker than the other barrier. In forward bias, the top barrier is the emitter barrier, while, in reverse bias, the top barrier is the collector barrier. This implies that the top barrier is slightly thicker than the bottom barrier. This is consistent with the difference in the measured ot values, observed asymmetry in the I(V) characteristics for this sample (the main resonance peak voltage and peak current values are higher for reverse bias as compared to forward bias), and is in agreement with previous characterization [32, 33]. We also obtain the absolute magnitude of the electron tunneling rates through the two potential barriers and study their dependence on the magnetic field. Figures 34 and 35 show the tunneling rates and the probability of occupation as a function of the magnetic field perpendicular to the current in the forward-bias and reverse-bias orientations, respectively. Note that Tern is smaller than Td in the forward-bias orientation, while Tcl is smaller than Tem in the reverse-bias orientation. This is because p is smaller than 0.5 in forward bias, while it is larger than 0.5 in reverse bias. As mentioned before, this asymmetry suggests that the top barrier of the heterostructure is slightly thicker than the bottom barrier. Despite the asymmetry, we observe that, in either orientation, Tem (and p) decreases with field strength, while Td is approximately constant. Temroughly decreases by a factor of 2 as the field increases from 6 to 11 T in both bias orientations. The probability of occupation p also decreases as the field strength increases. The oscillations in the tunneling rate are probably due to the fine structure observed on the current plateaus and its movement in magnetic field [38, 50]. The suppression of Tern results in the observed plateau current suppression with magnetic field. Figures 34 and 35 and the previous discussion indicate that the magnetic field affects the emitter-to-well tunneling process (Tem) more than it affects the well-to-collector tunneling process (Td). We, therefore, expect more current suppression when the current is emitter

126

ELECTRONIC TRANSPORT PROPERTIES OF QUANTUM DOTS

I

1400

....

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1200 N

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141

SIMON AND SCHON

block ionomer micelles, they did not transform to cylindrical domains, which is the bulk equilibrium structure of the block copolymers employed. In the samples described here, the interparticle spacing is expected to be large enough to exclude electronic interaction, but electrical investigations on these materials are still lacking.

2.3. Host/Guest Composites

2.3.1. Nanoparticles in Porous Solids Instead of covering the surface by ligands, nanoparticles can also be synthesized and protected in porous amorphous or crystalline solids. To control the size and dispersion of the particles, crystalline host lattices with well-defined pore and channel structures are expected to be promising. Therefore, molecular sieves such as zeolites or related mesoporous phases are often used to accommodate particles in colloidal dispersion [69-79]. The interest in these materials results from the principal possibility of synthesizing monodisperse nanoparticles in the confinement of the cages and herewith arranging them with defined interparticle spacing at the same time. Ideally, this would also lead to an ordered arrangement of identical nanoparticles that is an inverse lattice or superlattice similar to the crystallized, ligand-stabilized semiconductor clusters described in Section 2.1. The preparation of nanoparticles inside a host lattice can be realized for various transition metals such as Pt, Pd, Ag, or Ni [72, 80, 81] as well as for semiconductors such as sulfides or selenides of Zn, Cd, or Pb [82, 83]; ZnO [84-88]; CdO [89], or SnO2 [90]. Here, the host lattice acts as a solid electrolyte. In solution or in melts, the mobile charge compensating cations (usually Na +) are exchanged by mono- or multivalent cations, which than can be reduced by suitable agents such as hydrogen or alkali metal vapor. This process, which is illustrated in Figure 9 in a simplified manner, also requires the migration and agglomeration of the metal atoms, which, before reduction, are spatially separated, as they are located on well-defined cation sites. The formation of the nanoparticles leads, in most cases, to a local degradation of the host lattices, for example, by partial hydrolysis of the zeolite. As a consequence, the advantage of the defined pore size, which is likely to be used as a size controlling confinement, is usually deleted by this effect. Furthermore, the migration leads, in some cases, to the formation of nanoparticles or microcrystallites on the crystallite surface of the matrix. Another route, that is, the preparation of nanoparticles via decomposition of organometallic or metal carbonyl precursors, starts with the loading of the dehydrated zeolite via the gas phase or from solution. Thermal treatment then leads to ligand desorption and decomposition, which enables the metals to aggregate. Comprehensive reviews on this method are given in [69, 72]. Finally, the inclusion of ligand-stabilized nanoparticles into the channels of a porous solid has recently been demonstrated [91] and seems to be a promising approach to realize one-dimensional arrays of nanoparticles. We will discuss this in Section 3.3.1.

reductive

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I

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Fig. 9. Formationof metal nanoparticles by reduction in a porous inorganic host lattice.

142

ELECTRICAL PROPERTIES OF CHEMICALLY TAILORED NANOPARTICLES

2.3.2. Nanoparticles in Polymer Matrices The preparation of nanoparticles in an organic or inorganic polymer matrix is a wellestablished technique for obtaining thin films of nanoparticle composites with high optical quality [92-95]. Already electroluminescent devices have been developed [51 ] taking advantage of the specific electronic and optical properties of ZnS nanoparticles and the excellent film processability, that is, typically a spin coating technique. Yang et al. [51 ] described the synthesis of a ZnS nanoparticle/polymer composite, which was obtained from the reaction of styrene, zinc oxide, azoisobutyronitrile, methacrylic acid (MA), methanol, and tetrahydrofuran, via the intermediate reaction of ZnO and MA to Zn(MA)2, where the two C = C bonds in each Zn(MA)2 are copolymerized with styrene, which acts like a cross-linking agent. The particle size, which is approximately 3 nm, and crystallinity were deduced from UV-vis and transmission electron microscopy (TEM) including electron diffraction, respectively. The use of plasma polymers for metal nanoparticles is described by Kay et al. [96] and Davis and Klabunde [97], and later, in a more sophisticated technique, by Lamber et al. [98]. This technique is based on the simultaneous plasma polymerization of a fluorocarbon monomer and deposition of a metal by sputtering. Using this technique, different noble metal particles with sizes of a few nanometers and a considerable broad size distribution could be obtained [99]. In a modified technique, they introduced a metal source spatially separated from the plasma discharge region. Shown by the example of gold, nanoparticles with a size of 1.4 nm in a narrow size distribution embedded in the plasma polymer film could be synthesized. Depending on the filling factor, the composites are electrical insulators or electron hopping conductors [ 100], as might be expected from a highly disordered arrangement of metallic conductors in an insulating matrix [ 101 ].

2.4. Electrochemical Composition of Nanoparticles In 1994, Reetz and Helbig [ 102] reported on a new approach for obtaining certain transition metal nanoparticles from Pd or Ni and even from superparamagnetic Co by the use of electrochemical methods [ 102, 103]. The process, in which the particle size (with a certain size distribution) can be controlled in a simple manner by adjustment of the current density, makes use of a simple two-electrode setup, in which the sacrificial anode consists of the bulk metal to be transferred into the nanoparticles. The supporting electrolyte contains tetraalkylammonium salts, which serve as stabilizing ligands in the aforementioned way. Thus, in the overall process, the bulk metal is oxidized at the anode, the metal cations migrate to the cathode, and a consecutive reduction takes place, resulting in the formation of ligand-stabilized nanoparticles (see Fig. 10). Using this technique, particle sizes in the range of 1.4 to 4.8 nm (and above), with a considerable size distribution in comparison to the chemically tailored nanoparticles, can be obtained. The most striking advantage seems to be the broad variation range of the corresponding ligand shell. Because the tetraalkylammonium ions are simply added to the reaction mixture, the thickness of the ligand shell can easily be varied by changing the length of the alkyl chain [104].

3. ARRANGEMENTS AND DEPOSITION TECHNIQUES The main difficulty in using chemically prepared nanoparticles as quantum dots or tunnel junctions in microelectronics is the simultaneous interconnection and isolation of the dots to allow a single-electron transport between them controlled by external bias. In threedimensional arrangements of ligand-stabilized clusters, this problem is solved in an ideal way: During deposition from solution, during pressing to condensed solid, or during crystallization, the ligand shells prevent the clusters from coalescence, acting at the same time

143

SIMON AND SCHON

anodic dissolution

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o o

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as a lubricant and as a "glue." Thus, three-dimensional interconnected arrangements resuit. In contrast, the preparation of one- or two-dimensional cluster arrangements requires the development of some new deposition techniques such as Langmuir-Blodgett or selfassembly techniques. Fendler reviewed these in [105, 106]. Depending on the special requirements, suitable ligand-stabilized nanoparticles need to be synthesized and modified. As mentioned previously, in crystals as well as in compressed pellets, the ligandstabilized particles arrange themselves following the principles of closest packing. The "tunneling distance" for charge carriers is the barrier determined by the thickness and chemical nature of the ligand shell. The same situation results if the nanoparticles are attached to each other in one or two dimensions.

3.1. Three-DimensionalArrangements 3.1.1. Condensed Cluster Solids As mentioned previously, condensed solids with perfect arrangements of the nanoparticles are realized in some semiconductor superlattices that are of technical as well as academic interest [60]. The structures are suitable for X-ray structure determination and are often referred to as solids consisting of artificial atoms, that is, the nanoparticles. Although examples are given for uniform ligand-stabilized metal clusters [32-35, 107, 108], crystals have not been found up to now. Therefore, size and structure determination has been performed by different techniques such as M6ssbauer [109], high-resolution transmission electron microscopy (HRTEM) [11], or extended X-ray absorption fine structure (EXAFS) [110] instead of X-ray diffraction. Similar to crystallized semiconductor nanoparticles, the attractive interparticle interaction resulting from van der Waals forces or ionic coupling depends on the chemical nature of the protecting ligands and should be sufficient to grow a crystal, but, this problem has not been solved up to now.

144

ELECTRICAL PROPERTIES OF CHEMICALLY TAILORED NANOPARTICLES

Dense Packing

3-D Network

Insertion of spacer molecules

Fig. 11. Schemeof insertion on bifunctional spacer molecules into a dense packing of ligand-stabilized nanoparticles. The stretching of the packing results in a three-dimensional (3D) network.

3.1.2. Cluster Networks

A promising alternative for obtaining three-dimensional quasi-ordered solids of metallic nanoparticles is the interconnection of suitable metal clusters or colloids by identical bifunctional spacer molecules [8, 105] (see Fig. 11). Accordingly, Schiffrin and co-workers reported on a new preparative technique for obtaining this new class of nanomaterials, which comprises gold nanoparticles of 2.2 and 8.0 nm self-assembled into a threedimensional network by means of organic dithiols [40]. The approach involves the preparation of Au nanoparticles in a two-phase liquid-liquid system [39], where organic dithiols are used as bifunctional interconnecting ligands. This procedure leads directly to the formation of an insoluble precipitate of cross-linked nanoparticles. The existence of selfassembled nanoparticles is deduced from TEM micrographs. Using ligand-stabilized metal clusters with a defined number of atom, we actually [45] reported the insertion of bifunctional amines into a three-dimensional arrangement of Pd561phen360200, clusters. The spread of the cluster packing, that is, the insertion of the spacer molecules, starts with the deoxygenation of the clusters by hydrogen. The oxygenfree cluster Pd561phen36 provides free metal surface sites that can be coordinated by the NH2 groups of 4,4~-diamino-l,2-diphenyl-ethane. As the free cluster surface is oriented in all directions, the spacing procedure also leads to an insoluble precipitate with threedimensional cluster linkage. This network exhibits an increased interparticle spacing with respect to the closed sphere packing such as in a pressed pellet or a thick film obtained from solution of the nonmodified cluster. In both examples, the insertion of large spacer molecules is reflected by an increase in the activation energy of electron transport through the material (see Section 4.4). 3.2. Two-Dimensional Arrangements The preparation of highly ordered planar arrays of metal or semiconductor nanoparticles isolated from each other by defined tunnel barriers is one of the greatest challenges in the fabrication of microelectronic devices based on chemical nanostructures. To achieve this goal, the principles of molecular self-organization of surfactant monolayers--LangmuirBlodgett (LB) and self-assembled filmsmhave to be combined with colloid chemistry, which is the backbone of highly developed cluster preparation techniques. Fendler reviewed self-assembled nanostructured materials [ 106] developed from "wet" colloid chemistry, which was inspired by biomineralization (the in vivo formation of inorganic crystals and/or amorphous particles in biological systems [111-113]). A comparison of LB and self-assembled films is given therein and the most crucial step, that is, the deposition of preorganized layers onto solid surfaces, is emphasized. For a detailed discussion, the reader may be guided by the previously mentioned review as well as by a recently published

145

SIMON AND SCHI3N

review by Ulman [ 114], while in this section examples of two-dimensional arrangements of ligand-stabilized nanoparticles will be given.

3.2.1. Self-AssembledMonolayers Schmid et al. [ 115] reported the formation of two-dimensional arrangements of ligandstabilized gold clusters and gold colloids on various inorganic conducting and insulating surfaces. For this purpose, oxidized silicon as well as quartz glass surfaces were treated with (3-mercaptopropyl) trimethoxysilane to generate monolayers of the SHfunctionalized silane. Dipped into an aqueous solution of 13-nm gold colloids, stable S-Au bonds were formed to fix the colloids in a highly disordered arrangement. The coating of the surface was visualized by atomic force microscopy (AFM). Following a similar route, gold colloids of the same size stabilized by water-soluble P(C6H5SO3H) ligands were deposited two dimensionally on a poly(ethyleneimine)-coated mica surface. The driving force for the deposition of the colloids on the surface is the acid-base interaction between the SO3H group of the ligand and the NH group of the imine. This procedure leads to a more close packing, which was also visualized by AFM. Deposition of ligand-stabilized Au55 clusters on a conducting substrate, that is, a gold (111) surface, was realized by the initial coating of the surface by 2-mercaptoethylamine and a subsequent reaction with the water-soluble cluster Au55(Ph2PC6H4SO3H)12C16 (see Fig. 12). A close coverage of the gold surface results, which, however, is still highly disordered. The conducting substrate enables the characterization of the cluster monolayer by scanning tunneling microscopy (STM), but, unfortunately, no electrical characteristics have been obtained by these investigations besides the imaging of the surface topography. The most promising results with respect to possible utilization of the size-determined electrical properties were reported by Andres et al. [43, 116, 117]. Close-packed planar

Fig. 12. Au55(Ph2PC6H4SO3H)12C16 clusters on Au(lll) fixed on a layer of mercaptomanine molecules via NH2...HO3S interactions imagedby STM. (Source: Reprinted with permission from [115].)

146

ELECTRICAL PROPERTIES OF CHEMICALLY TAILORED NANOPARTICLES

arrays of gold nanoparticles 3.7 nm in diameter stabilized by alkylthiol molecules were cast from solution onto a flat MoS2 substrate. By adding aryldithiols or aryl di-isonitriles, the monofunctional alkylthiols are displaced, leading to a covalent linkage of adjacent nanoparticles in two dimensions. Following the same idea, Reetz et al. [ 118] realized selfassemblies of palladium clusters stabilized by tetraalkylammonium salts. In accordance with the results obtained on three-dimensional networks, a two-dimensional structure of metal nanoparticles coupled by uniform tunnel junctions could be realized. The electrical properties will be summarized in Section 4.3. Likewise regular and uniform were the two-dimensional arrangements of gold nanoparticles incorporated into micelles of A-B diblock polymers described by M611er et al. [66, 68], as discussed in Section 2.2. As an intermediate between two- and three-dimensional arrangements, Decher and coworkers [ 119] recently reported the fabrication of metal nanoparticle/polymer superlattice films. These film architectures were prepared by first depositing alternating poly(styrene sulfonate sodium salt) (PSS) and poly(allylaminehydrochloride) (PAH) onto a poly(ethyleneimine) (PEI) modified substrate. The uppermost layer of PAH provides a positively charged surface for subsequent self-assembly of a monolayer of gold nanoparticles of 15 nm diameter (see Fig. 13). From this state, the deposition procedure can be repeated to realize multilayer arrangements. Electrical investigations are also lacking in this case, but, because of its unique structure, for example highly anisotropic transport properties may be expected.

3.2.2. Langmuir-Blodgett Films Just recently, Chi et al. [120] reported access to monolayers of ligand-stabilized Au55 clusters via the Langmuir-Blodgett (LB) technique. Two different ligands, which make the cluster water insoluble, were used to spread the clusters on an air/water interface, where they could be compressed to form a closed monolayer. These could be transferred to different solid surfaces, for example, mica, silicon, and evaporated and anealed gold. From the latter, current-voltage characteristics have been recorded by STS, which will be discussed in Section 4.1.2. Close-packed monolayers with a few well-ordered arrays with partially two-dimensional crystallization were illustrated by AFM (see Fig. 14). These results are the first examples of the fabrication of ordered arrangements that fulfill the requirements of periodicity in two dimensions, for example, to enable ballistic or highly correlated electron transport. In any case, however, the method described here, by nature, does not yield sufficient sample qualities to be a routine manufacturing method.

3.2.3. Deoxyribonucleic Acid-Based Method of Self-Assembly A promising approach, which is, from the point of view of colloid chemistry, strongly related to the methods described in Sections 3.1.2 and 3.2.2, was demonstrated by Mirkin et al. [121], who developed a deoxyribonucleic acid (DNA)-based method to assemble gold nanoparticles in two dimensions. The method starts with the preparation of 13-nm gold particles, using the well-known method of synthesis [122, 123]. In a second step, the gold particles are modified by oligonucleotides, which are functionalized with alkane thiols at their 31 termini (see Fig. 15, which shows the assembly strategy). One part of the nanoparticle solution was treated with 31-thiol-TTTGCTGA, while a second part was treated with 31-thiol-TACCGTTG, so that the oligonucleotides are noncomplementary. The resulting solutions of oligonucleotide-stabilized Au nanoparticles can be combined, and no reaction takes place because of the noncomplementarity. In a third step, the assembly of the particles results from the addition of a duplex containing 8-basepair sticky ends, which are complementary to the 8-base-pair oligonucleotides, which are the ligands of the Au particles. Evidence of the polymerization/assembly process is given

147

SIMON AND SCHON

Fig. 13. (a) Process for fabricating colloidal gold/PE multilayers to a final structure with m = 3 and n = 2. (b) Schematic representation of increased gold particle layer separation achieved by changing the interlayer spacing from m = 1 (left) to m = 4 (right). On top is the PEI layer. PSS is the light-shaded layer and the PAH layer is shaded dark. Note that this drawing is an oversimplification of the actual layer structure. (Source: Reprinted with permission from [119].)

by T E M i m a g e s (see Fig. 16). A l t h o u g h it was difficult to obtain any information about the d e g r e e o f o r d e r for t h r e e - d i m e n s i o n a l aggregates, t w o - d i m e n s i o n a l aggregates p r o v i d e e v i d e n c e of the s e l f - a s s e m b l y process in small-scale images. C l o s e - p a c k e d assemblies of u n i f o r m particles and u n i f o r m particle separation of 6 n m results, whereas the interparti-

148

ELECTRICAL PROPERTIES OF CHEMICALLY TAILORED NANOPARTICLES

Fig. 14. SingleAu55(PPh3)12C16 clusters resolved by noncontact AFM on mica. The black lines indicate the ordered cluster arrays with partial crystallization.

cle distance of slightly smaller, as might be expected from the length of the DNA spacer molecules, that is, 9.5 nm if they are regarded as be rigid. This approach provides a promising way of controlling the particle topology in nanoparticle assemblies, as it allows control of the particle size as well as the spacer length by defining the oligonucleotide sequence and length.

3.3. One-Dimensional Arrangements The formation of one-dimensional (1D) arrangements of nanoparticles is, in a practical sense, the most common step toward the fabrication of single-electron devices. To realize one-dimensional arrays, which may act as multiple tunnel junctions or quantum wires, different methods are now in progress. Generally, the formation in just one dimension requires the steering influence of a substrate or a matrix, which may be chainlike molecules, linear displacements on solid surfaces, or one-dimensional channels in a, at least, "physically inert" matrix. In the following, actual examples of the development of these different techniques are given.

3.3.1. Intercalation of Ligand-Stabilized Metal Clusters into Solids with One-Dimensional Channel Structures Crystalline nanoporous solids that perform as 1D channel structures have been recognized as supports for the assembly of ligand-stabilized nanoparticles. The most prominent compounds are zeolites and related structures, which are strongly bounded open-framework aluminosilicates, wherein pores or channels of nanometer lateral extension are formed. Because of their chemical composition, these nanoporous solids have wide electronic band gaps, making these materials optically transparent as well as electrical insulators (whereas ionic conductivity is not taken into account); that is, they are physically inert. Besides this, efforts have been made to synthesize nanoporous semiconductors, as many new physical

149

SIMON AND SCHON

Au nanoparticles Q

Modificationwith

3"-thioI-TACCGTTG-5"

J

~N~

AI;

Modification with

5"-AGTCGTTT-3"-thiol

Addition of linking DNA duplex 5"'ATGGCAAC LLLLI TCAGCAAA.5-

1~ ~

.................................. L ~ Fig. 15. DNA-basedcolloidal nanoparticle assembly strategy. If a duplex with a 12-base-pair overlap but with "sticky ends" with four base mismatches (51-AAGTCAGTTATACGCGCTAG and 21-ATATGCGCGATCAAATCACA) is used in the second step, no reversible particle aggregation is observed. The scheme is not meant to imply the formation of a crystalline lattice but rather an aggregate structure that can be reversibly annealed. A is the heating above the dissociation temperature of the duplex. (Source: Adapted from [121].)

properties are expected from these "quantum antidot" solids, but, up to now, just a few examples are k n o w n [ 124]. By inclusion of nanoscaled guests inside the defined void spaces of the matrix, new nanocomposites can be obtained with tunable optical, magnetic, or electrical properties. In the case of one-dimensional structures, it was illustrated recently that, in principle, one-dimensional bundles of metallic wires can be realized by loading the uniaxial channels of zeolite L with potassium via the gas phase. The presence of conducting paths was deduced from alternating-current (ac) measurements at 3 GHz [ 125]. Numerical calculations on this material suggest that the spatial separation between neighboring metallic channels

150

ELECTRICAL PROPERTIES OF CHEMICALLY TAILORED NANOPARTICLES

Fig. 16. TEM image of a two-dimensional colloidal aggregate showing the ordering of the DNA-linked Au nanoparticles. (Source: Reprinted with permissionfrom [121].)

is not sufficient to give an electrical and optical anisotropy perpendicular to the orientation of the channels because of pronounced electronic coupling [ 126]. To avoid this problem, it might be useful to fill the channels with preformed and stabilized metal clusters. In this arrangement, the metallic core and its surrounding insulating shell replace the islands and tunnel junctions, respectively, of conventional single-electron tunneling (SET) arrangements. In practice, although these particles are labeled as uniform, certain statistical fluctuations in the atom numbers forming the core by nature have to be taken into account, leading to a finite size distribution. These deviations will directly affect the self-capacitance Co of the particles and by this the electrical properties of such an arrangement. Furthermore, it is a difficult, if not an imposible, task to avoid disorders along the array, when filling the channels with clusters, which will modify the interparticle capacitance C. A discussion of the effect of disorder on the potential distribution in such arrangements has recently been given by Simon and Gasparian [127, 128] and will be discussed in Section 4.2.1. In spite of large experimental efforts, up to now the ordered inclusion of ligandstabilized metal clusters into a zeolite or related crystalline matrix has not been realized. Besides, even examples are known about the intercalation of C60 fullerenes via the gas phase [ 129] as well as the random inclusion of Au55(PPh3)12C16 into MCM 41 for catalytic prospects. An alternative route has recently been suggested by Schmid and co-workers, who used the quasi-parallel channels of anodically generated porous alumina as a matrix for cluster inclusion [91 ] (see Fig. 17). The diameter of the quasi-parallel, penetrating channels can be controlled and varies from 2 to 100 nm and thus exhibits a complementary size for the inclusion compounds. Because the arrangement of the channels exhibits nonperiodicity in a strict sense, that is, diameter and parallelism do not fulfill the requirements for X-ray diffraction patterning, a priori, even here the problems of disorder cannot be avoided. Clusters and colloids of a corresponding size could be introduced into the channels by vacuum induction, capillary action, and electrophoretic or chemisorption/immersion

151

SIMON AND SCHON

Fig. 17. Porechannel of an alumina membrane field with ligand-stabilized gold nanoparticles. (Source: Reprinted with permission from [91]3

mechanisms. The results of initial experiments have been illustrated by means of TEM images, which proved that the arrangement of the particles inside the channels is far from being strictly one-dimensional. But, in any case, the principle developed seems to be promising and deserves to be developed.

3.3.2. Deposition on Crystalline Surfaces First attempts have been made to deposit ligand-stabilized metal clusters one dimensionally aligned on the surface of crystalline [15] or preformed solids [8], which may result from the enhanced surface energy. "String of pearls"-like alignments of superclusters consisting

152

ELECTRICAL PROPERTIES OF CHEMICALLY TAILORED NANOPARTICLES

Fig. 18. String-of-pearl-likearrangementof (Au55)l3 superclusterson HOPG. (Source: Reprintedwith permission from [15].)

of 13 Au55 self-assembled particles are known [15] (see Fig. 18). However, up to now, this technique has not been developed to give reproducible results with a high standard degree of order. Alternatively, although no nanoparticles with a defined insulating barrier are used, the deposition of metal nanoparticles from the vapor phase leads to encouraging results. Francis et al. [ 130] reported the deposition and growth of noble metal clusters on highly oriented pyrolytic graphite (HOPG). On this support, clusters of Au and Ag formed quasi-one-dimensional chains along the surface steps, resulting in a similar string-of-pearls alignment.

3.3.3. Organization along Single-Stranded Deoxyribonucleic Acid Oligonucleotides The use of chainlike molecules as organizing agents to obtain linear arrangements of nanoparticles was introduced by Alivisatos et al. [ 131 ], who described a strategy for the synthesis of "nanocrystal molecules," in which discrete numbers of defined gold nanoparticles are organized into spatially defined DNA-like structures. In contrast to the twodimensional (2D) assembly described in Section 3.2.3, in this approach parallel and antiparallel homodimer oligonucleotides react with 1.4-nm, water-soluble Au clusters. One N-propylmalinide ligand per cluster couples selectively to a sulfhydryl group incorporated into the single-stranded DNA (see Fig. 19). Oligonucleotides, modified at either the 31 or the 51 terminus with a free sulfhydryl group, were coupled with an excess of the nanoparticles. After combining with suitable oligonucleotide templates, parallel and antiparallel dimers as well as parallel trimers could be obtained. The linear alignment of the clusters, the center-to-center distance of which ranges from 2 to 6 nm, respectively, was illustrated by means of TEM images.

153

SIMON AND SCHON

~ D N A

Head-to-tail

(paralledimer l)

t!mplate

Head-to-head

(antiparallel) dimer

Paralletril mer

Fig. 19. Nanocrystalassemblybased on Watson-Crickbase-pairing interactions. Attachment of the inorganic nanoparticles (black) to either the 3t or the 5t terminus of the oligonucleotide "codon" by the linker L permits the preparation of head-to-head dimers, head-to-tail dimers, and trimers. (Source: Adapted from [131].)

4. E L E C T R I C A L P R O P E R T I E S OF ZERO- TO THREE-DIMENSIONAL ARRANGEMENTS OF NANOPARTICLES

4.1. Single-Particle Properties

4.1.1. Thin-Film Structures and Scanning Tunneling Microscopy Single-Electron Systems At present, the fabrication of "traditional" single-electron circuits, such as transistors or pumps, is carried out by the evaporation of metal (usually A1) films through a fine-pattern mask, which is often made of polymer resist by means of an electron beam lithographic process [ 132]. The mask presents a number of thin splits, determining the sizes and shapes of resulting islands, and the bridges interrupting them determine the position of the future tunnel junctions and gates. Because of the composite polymer resist layer, which is chemically undercut, the resulting mask is rigidly fixed above the substrate and its bridges

154

ELECTRICAL PROPERTIES OF CHEMICALLY TAILORED NANOPARTICLES

Fig. 20. Evaporationof metal through windows of a suspended mask to fabricate tunnel junctions. (Source: Adapted from [132].)

become suspended above it. Such arrangements of splits and bridges allow the evaporation of metals onto substrates from various angles, which allows different positions of the resulting evaporated layer (see Fig. 20). To form a set of islands connected by tunnel junctions, the evaporation is usually made from two different angles in two steps with an oxidation process in between, when aluminum is used. By adjusting the angles, the linear sizes of the resulting overlapping area of the first and the second metallic layers can be even smaller than the width of the strips, that is, somewhat less than 0.1/zm. At the same time, a gate electrode coupled to the islands only capacitively should not overlap them, which is taken into account in the mask pattern design. After double evaporation, the mask and the supporting layer are lifted off. The resulting barrier of A1203 with a desirable thickness of a few nanometers is mechanically and chemically stable. The height of the corresponding energy barrier is about 1 eV and it readily provides a tunnel resistance in the range of 50 to 500 k ~ for junctions of the aforementioned size. The resulting capacitance of such tunnel junctions is in the range of 10 -16 to 10 -15 F, which corresponds to a Coulomb energy Ec expressed in terms of temperature units, Ec/kB, of approximately 1 K. This means that such circuits operate correctly only at temperatures well below 1 K, that is, at 10-100 mK, which is just attainable with immense technical effort. Thus, the junction size and, correspondingly, the energy and temperature scale are finally restricted by resolution of the resist and critically depend on the performance of electron beam writing of the mask pattern. At present, in order to approach finer structures and, therefore, smaller sizes of tunnel junctions, the search for new materials both for resist and for metal circuits is in progress. Furthermore, efforts are also being made to improve the etching and underetching technique of the bridges. These will probably extend the operation temperature up to the routinely achievable temperature of liquid helium at 4.2 K. Nevertheless, this technique has its own natural size limit. To increase the operating temperature essentially more sophisticated technologies for the fabrication of SE structures are definitely needed. One of the most promising alternatives in metallic single-electron structures is the use of ligand-stabilized metal nanoparticles as building blocks. The drastic reduction of the sizes and, therefore, of the capacitances of tunnel junctions can be made, for example, in a single-electron structure comprising small metallic particles and the tip of the scanning tunneling microscope (STM). It is known that this instrument can probe a conducting surface with even atomic resolution because of electron tunneling through the energy barrier between the tip and the surface. The resulting tunneling space

155

SIMON AND SCHON

STM tip It

~Metal nanoparticle (droplet)

,r/l/Ill'Ill/Ill1 --I ....|~

-

I nsulating layer

Metallic ground plate

Fig. 21. Single-electron,two-junction systemconsisting of an STM tip and a metallic nanoparticle as a central electrode on a ground plane.

can also be filled with a thin dielectric, for example, oxide, coveting the metal surface. If a nanoparticle is embedded into an oxide layer or if it is fixed somehow onto an oxide surface, then the tunneling current predominantly goes through the particle. Such an arrangement presents a typical single-electron, two-junction system. One of the junctions, which is between the ground plane and the grain, is mechanically fixed, while another one, which is between the grain and the STM tip, is tunable because of displacement of the latter (see Fig. 21). The structures described previously were successfully and repeatedly realized in practice. The one-dimensional arrangement in a double-barrier tunnel junction working at room temperature has been realized by an STM tip above Au particles of approximately 4 nm in diameter obtained by metal evaporation on a 1-nm-thick layer of ZrO2 (tunnel barrier) on a fiat Au substrate. The experimentally determined capacitance of the nanoparticle-substrate junction is approximately 0.8 • 10-18 F. This value is in good agreement with the theoretically estimated capacitance of 1 • 10-18 F based on the model of a parallel-plate capacitor with ZrO2 as a defined dielectric [133]. This example shows that, by means of metal nanostructures, SET in the range of room temperature is accessible, but for SET devices particle size distribution has to be avoided, which is not possible when metal evaporation is used as the nanoparticle source. Of course, although such a procedure makes possible the fabrication of structures that are, in fact, double-junction systems with very small capacitances, the controllable gating of current seems to be practically impossible. Instead, the tunneling current is strongly affected by random charge trapped in the underlying oxide. Moreover, the size and shape of the grains are very random and are not predictable, which ruins any hopes of fabricating a system with well-defined parameters. On the other hand, the very small capacitances of such structures extend the range of observability of Coulomb blockade above helium and even up to room temperature. To take advantage of the minute grain size and to avoid the problems caused by size distribution, the use of ligand-stabilized nanoparticles seems to be a suitable method.

4,1.2. Single-Electron Tunneling on Single Chemically Tailored Nanoparticles The first results obtained on single chemically tailored nanoparticles have been reported by van Kempen et al. [20, 134]. They reported scanning tunneling spectroscopy on a Pt309phen36020 cluster at 4.2 K, which was deposited from a droplet of an aqueous solution of the clusters on a Au(111) facet (see Fig. 22). The I (U) characteristics exhibit clear charging effects, which indicates that the ligands are sufficient electrical insulators, as they act like tunnel barriers between the cluster and the substrate. The experimentally observed charging energy ranges from 50 to 500 meV, while a value of 140 meV would be expected, assuming a continuous density of states in

156

ELECTRICAL PROPERTIES OF CHEMICALLY TAILORED NANOPARTICLES

i~

V ~ kigand shell Pt309-cluster

~t Substrate (Au(11 ;I)) } Fig. 22. Singleligand-stabilized Pt309 cluster between STM tip and a Au(111) facet. The junction between the cluster and the substrate is built up by the ligand shell.

the particles and a dielectric constant er = 10 for the ligand molecules, when the "classical" formula Ec = e2/47reoerR (where R is the radius of the particle) is applied. There are different factors affecting the variation in Ec, which have been taken into account: Because the clusters have different facets (squares and triangles), Er will depend on the exact way in which the cluster lies on the substrate. Furthermore, the ligands, which, for simplification, have been assumed to be a spherical dress for the cluster, may have different orientations varying from cluster to cluster with respect to the underlying substrate, thus causing a different tunnel barrier between the cluster and the ground and, therefore, a different capacitance. Finally, the effect of residual water molecules from the solvent may be physically or chemically bound on the cluster surface or on the ligand shell and, therefore, the tunnel junction between the cluster and the substrate may differ for different clusters. Additional structures on the charging characteristics have been observed in some cases, which might be expected from a discrete electron level spectrum in the cluster caused by the quantum size effect. The effect of discrete levels on the charging characteristics has been treated theoretically by Averin and Korotkov [25], who extended the existing "orthodox" theory of correlated SET in a double normal-metal tunnel junction to the case of a nanoscaled central electrode. According to this, the I (U) characteristics should exhibit small-scale singularities reflecting the structure of the energy spectrum of the central electrode, that is, the nanoparticle. Furthermore, the energy relaxation rate becomes evident because of the small recharging time r, resulting from the small junction capacitance according to r = R-C, where R is the resistance of the tunnel barrier and C is the capacitance of the junction. Although the theoretical prediction for the level splitting A according to A = 4 E F / 3 N or to a refined approach by Halperin [21] leads to an assumed splitting of approximately 8 meV (EF is the Fermi energy of the metal and N is the number of free electrons), the fit of the spectra lies between 20 and 50 meV. Although different reasons are discussed in the cited paper, the measurements reflect the discreteness of the level spectrum in the clusters as large as 2.2-nm Pt309 clusters. On smaller ligand-stabilized metal clusters of 1.4 nm, for example, Au55(PPh3)12C16, scanning tunneling spectroscopy (STS) has been performed up to the range of room temperature. Already from cluster pellets, that is, three-dimensional compacts of the clusters, single-electron transfer has clearly been observed in the I (U) curves [19] taken at room temperature. In these investigations, however, neither the vertical nor the lateral arrangement of the clusters is well defined, as would be the case in a one-, two-, or threedimensional superlattice. As a consequence, the charging energy has a wider spread, as would be expected from the estimation of the charging energy of a single cluster according the formula mentioned previously. Excluding this problem, Chi et al. [135] reported STS on Au55 monolayers prepared on various technically relevant substrates. The samples could be obtained utilizing a two-step self-assembly (SA) process and by a combined Langmuir-Blodgett/SA process, which, in principle, have been described in Section 3.2. The spectroscopy gives clear evidence of the

157

SIMON AND SCHON

I

'

I

I

~

I

'

I

2.0-

oo

R1=1.91VE2;C1--3.1.10"19F

f

1.5

P~=1.4c~; C~=1.1"10~8F 1.0

,~

Q0---O.04 * e; T=90 K

oo y

0.5 oo

...,

~oOO~

-- 0.0

~

' '

-0.5-1,0

-1.5 -3:10

,_

I

-200

,

oooOJ fit o

I

,

-100

.

0

I

100

.

I

200

i

data

,l,

30o

i

4oo

U in m V Fig. 23. SET on a single ligand-stabilized Au55 cluster at 90 K. The junction capacitance was calculated to be 3 x 10-19 F by fitting.

Coulomb blockade originating from the double barrier at the ligand-stabilized cluster as the central electrode up to the range of room temperature. By a fit of the experimental data at 90 K, the capacitance of the cluster was calculated to be 3.9 x 10 -19 F (see Fig. 23). This value is in agreement with the value of the microscopic capacitance determined earlier by temperature-dependent impedance measurements [7]; see Section 4.4.1. Furthermore, these results are in good agreement with the capacitance data obtained from self-assembled gold nanoparticles on a dithiol-modified Au [ 111 ] surface [ 136, 137]. Here STS has been performed on 1.8-nm Au particles that were grown in the gas phase with a multiple expansion cluster source. Deposited on a suitable surface, Coulomb staircases at room temperature associated with a cluster/substrate capacitance of 1.7 x 10 -19 F could be obtained.

4.2. One-Dimensional Arrangements To the authors' knowledge, at present no experimental data about electrical properties exist from 1D arrays consisting of chemically tailored nanoparticles. In spite of the efforts to get experimental access to these most interesting structures (see Section 3.3), the electrical properties of 1D arrays have been studied theoretically up to now.

4.2.1. Potential Distribution in Nanoparticle Arrays In 1D arrays of mesoscopic tunnel junctions, time and space correlations between tunneling events may appear because of the Coulomb blockade effect [4, 138]. The time oscillations of correlated single-electron tunneling events, for example, the so-called charge soliton, can be counted very precisely in such arrangements and can be used in practice for possible metrological applications as well as for digital devices [ 138-141 ]. These arrays are usually fabricated by lithographic techniques in which the typical size of the junction is a few tens of nanometers. If chemical nanostructures are used to build up these kinds of devices, they tend to a length scale of 1-2 nm, where deviations in the number of atoms, which form the metal cluster core, influence their size and shape and have to be taken into account. Furthermore, packing defects may not be avoided on the molecular scale so that both kinds

158

ELECTRICAL PROPERTIES OF CHEMICALLY TAILORED NANOPARTICLES

of disorders will affect the form of the charge soliton and, therefore, the electrical properties of the array. Originally, charge soliton propagation would take place in a homogeneous 1D and infinitely long array of identical junctions, where the potential distribution does not change its form when an electron tunnels from one electrode to another [4, 138, 142, 143]. This means that in an infinite-chain approximation the potential profile cp~~ does not depend on the number N of junctions in the array. On the other hand, in some devices such as the "SET turnstile" and the "SET pump" [ 138, 139], the soliton can extend over approximately 6-10 tunnel junctions and, therefore, enters the same scale as the array itself. In this situation, the main condition of the infinite-array approach is not fulfilled. Then the finite number of junctions becomes crucial and starts to play an important role in the formation of the potential profile. The limits of the validity of the infinite-chain approximation have been discussed by Hu and O'Connell [ 144, 145]. They found an exact solution for the charge soliton in the case of a finite 1D array of N gated junctions with equal junction capacitances C and equal gate capacitances Co as well as for a single-electron multijunction trap. The key to the approach was, on the one hand, to adopt the semiclassical model to describe the 1D array [ 142] and, on the other hand, to rewrite the charge conservation law and Kirchhoff's laws as equations for the island potentials {q~{0)},instead of the island voltages {Vi}. Most recently, Gasparian and Simon [127, 128] found an exact analytical solution in terms of the Green's function (GF) for the potential distribution in a finite 1D array consisting of N small ligand-stabilized metal nanoparticles with a finite size distribution, which are arranged in series. The GF approach enabled them to formulate the so-called partial "solitary" problem of small mesoscopic tunnel junctions similarly to the problem of the behavior of an electron in a 1D tight binding and in a set of random delta-function models. With regard to metal nanoparticle arrays, it has been assumed that either (i) the capacitance C is the same for all junctions, whereas the self-capacitance Co can fluctuate from site to site because of the finite size distribution; or (ii) Co is the same, whereas C can fluctuate from site to site because of packing defects. Furthermore, it has been assumed that the metal nanoparticles have a continuous density of states, that is, quantum size effects, and its influence on the capacitance has been excluded from consideration. Generally, these simplifications are not necessary assumptions for the method discussed there, as such a general expression takes all these effects into account. The main results are that a decrease of the particle size at one position of the array (denoted as impurity in Fig. 24) increases the potential at this point, which may lead, at least, to localization; that is, the single excess electron in the array may be trapped. A packing defect, which affects the interparticle capacitance at one point, acts as an inhomogeneity, where the soliton will interact with its mirror-image soliton (or antisoliton) and, therefore, will be attracted. For more practical use of this method, it was pointed out that the total reflection amplitude, which was obtained by these calculations, is directly related to the Landauer resistance [ 10], which reflects the electrical characteristics of such multijunction arrays.

4.3. Two-Dimensional Arrangements

4.3.1. Electronic Conduction through Coupled Nanoparticle Networks Janes et al. [117] reported the electronic conduction across a network of 4-nm gold nanoparticles interconnected by di-isonitrile ligands [ 1,4-di(4-isocynaophenylethynyl)-2ethylbencene], which is a conjugated, rigid molecule, to give an interparticle spacing of approximately 2.2 nm. The two-dimensional assembly results from the deposition of the nanoparticles from a colloidal solution, followed by reactive addition of the linking molecules. To allow for electrical characterization, the layers were deposited on a SiO2supported GaAs wafer with gold contacts separated by 500 and 450 nm, respectively.

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SIMON AND SCHON

1.0 no impurity impurity at 1~=2

o

v

I

0.5

0.0

T -5

L -4

i -3

i -2

i -1

J 0 Position

~ 1

I 2

I 3

t 4

J 5

i

Fig. 24. Potentialdistribution in a 1D array of ligand-stabilized nanoparticles. A size fluctuation at i -- 2 (decrease of the self-capacitance) leads to an increase of the potential (black circles). (Source: Reprinted from V. Gasparian and U. Simon, Physica B 240, 289 (1997) with the kind permission of Elsevier Science-NL, Sara Burgerhartstraat 25, 1055 KV Amsterdam,The Netherlands.)

The I (U) characteristic of the arrays is linear over a broad voltage range. Because a dot-to-dot capacitance of 2 x 10 -19 F might be assumed, the total dot capacitance will be 1.2 • 10 -18 F, if each cluster is assumed to have six nearest neighbors. The corresponding charging energy thus will be approximately 11 meV, which is only about half of the characteristic thermal energy at room temperature. Therefore, a Coulomb gap at room temperature is not apparent. On the other hand, the charging energy of the nanoparticles has been obtained from comparable samples with two-dimensional cluster linkage by Andres et al. [43] from temperature direct-current (dc) measurements. According to the Arrhenius relationship Go = G ~ e x p ( - E A / k B T ) , where G ~ is the conductance as T --+ c~, EA is the activation energy, and kB is Boltzmann's constant, a Coulomb charging behavior with a charging energy (which corresponds to the activation energy) of E A = 97 meV was indicated. The interparticle resistance was revealed to be 0.9 M ~ , from which a single molecule resistance of 29 Mr2 is predicted. This value is in considerable agreement with the prediction of 43 Mr2 obtained from Htickel molecular orbital (MO) calculations. A two-dimensional tunnel junction array has also been realized by Nejoh and Aono [146] by using liquid crystal molecules (41-n-heptyl-4-cyanobiphenyl)as tunnel junctions between Pt and Pd nanoparticles deposited on a quartz substrate by dc sputtering (see Fig. 25). The average size of the particles is 1 nm and the average spacing ranges from 0.2 to 0.5 nm. This arrangement has been contacted by an STM tip and a directly connected outer electrode. The I (U) characteristics of the arrays indicate a Coulomb blockade at approximately 100 mV at room temperature with an interdroplet capacitance of 5 x 10-18 E Because the spatial distance between the STM tip and the outer electrode is about 5 mm, the number of particles participating in the charge transport is approximately 2.5 x 106. To

160

ELECTRICAL PROPERTIES OF CHEMICALLY TAILORED NANOPARTICLES

STM tip

i

LC molecules .,~ ~i~

PtPd islands

Outer electrode

Fig. 25. Schematicpicture of PtPd nanoparticles deposited on a SiO2 substrate. Liquid crystal (LC) molecules occupy the positions between the islands and support the tunneling process. (Source: Adapted from [146].)

Sn Particle

Sn02

Fig. 26. Schematicrepresentation of a Giaever-Zeller system for tunneling in parallel into a system of small metal particles. Here, both barriers are created by the oxidation of metal layers/surfaces. The basic barrier is formed by the oxidation of A1 and the barrier over the particles is formed by the oxidation of the Sn droplets themselves. (Source: Adapted from [147].)

calculate the I (U) characteristic of this kind of long array, a 1D array of 14 junctionsm just for simplicitymhas been assumed and qualitative agreement of the calculated curve (calculated with a capacitance of 5 x 10 -18 F) with the measured curve was found. Although these results are regarded as a step forward in realizing single-electron devices, the mechanism on how the liquid crystal molecules participate in the charge transport needs to be clarified. Although the former examples referred to an in-plane charge transport, electrical transport perpendicular to the orientation of a two-dimensional array has also been investigated. The most famous measuring arrangement was developed by Giaever and Zeller [2, 3], who performed tunneling experiments on 10-nm Sn particles in the 1960s. Figure 26 shows a schematic presentation of the Giaever-Zeller system for tunneling in parallel through a two-dimensional layer of small metal particles. The two tunnel barriers are formed by oxide layers on the substrate and surrounding the particles. Recent work by Ruggiero and Barner [147, 148] took advantage of this and examined layers of Ag, Pb, and Cu nanoparticles in an A1203 matrix with a considerable size distribution ranging from 3 to more than 100 nm. The I (U) characteristic gave evidence of the size distribution, as significant conductance peak spacing, determined by the capacitance of the particles, has been observed. By making the assumption that the nanoparticles are embedded in a uniform dielectric medium of constant e = 8 for A1203, they gave an expression for the conductance peak spacing A V -- e / C , where C is the junction capacitance, approximated

161

SIMON AND SCHON

by 2zr eoed and d is the particle diameter. To take into account also the self-capacitance Co of the particles, which feel the proximity of the base and outer electrode, the expression had to be extended to a model according to which a particle under consideration is surrounded by a sphere of metal and separated from it by thickness s of the barrier material, that is, A1203 in this case. According to this, they found a good correlation, when the average peak spacing is plotted as a function of diameter, for a variety of samples. What is most important to emphasize from these investigations is that obviously the information on the size distribution of nanoparticles in these arrangements is completely represented by the conductance data, implying that tunneling occurs from particles representing all size scales in the tunnel system.

4.4. Three-Dimensional Arrangements 4. 4.1. Solids a n d Networks

Various dc and ac measurements on compacts of ligand-stabilized transition metal clusters have been performed. Measurements on compressed powder samples of Au55(PPh3)12C16 as well as Pd56~(phen)360200 indicated that the temperature dependence of the dc conductivity trdc follows over a wide range of temperatures (70-350 K) the exponential law ~r ,~ ( T / T o ) -1/2 [44]. The frequency dependence of the ac conductivity as well as the nonohmic behavior at strong electric fields discloses a pronounced similarity to different heterogeneous materials, like cermets, doped and amorphous semiconductors, or metaland carbon-insulator composites. This "universal response" [ 149] was carefully analyzed by different physical models of hopping conductivity with the conclusion that the experimental data can be best fitted with a thermally activated stochastic multiple-site hopping process, whereas at high temperatures around room temperature nearest-neighbor hops dominate. Unfortunately, these models [44] do not allow any distinction between different local transport mechanisms (tunneling or hopping) or between the chemical nature of the sites (e.g., energy levels in atoms, molecules, clusters, ligand shells, aggregates of clusters, or metal particles). Hence, no principal difference was found between different cluster sizes or between the comparative substances. With respect to the application of single ligand-stabilized nanoparticles or collectives of them in SE, the authors reported temperature-dependent impedance measurements to explain or to predict local microscopic behavior. The experiments were performed on different types of ligand-stabilized clusters and have been conducted in the high-temperature range from ambient temperatures up to the respective limit of chemical stability from 253 to 333 K [7, 8, 15, 17, 107, 108]. The samples investigated by this method were pressed into disks with controlled high pressure in steps to maximum 1 GPa. Well-prepared disks revealed a gravimetrical defined density of more than 90% of the theoretical closest sphere packing of the spherical particles. By redissolution in appropriate solvents, chemical and spectroscopic analysis, and STM [19], it was verified that the protecting ligand shells were not destroyed and that the metal cores did not reveal any noticeable aggregation via coalescence. Impedance measurements on these highly compressed, close-packed samples of ligandstabilized Au55 clusters reveal in every case two relaxation domains in the kilohertz or megahertz region caused by coupled processes with macroscopic relaxation times. In contrast, samples diluted with unpolar polystyrene did not show either relaxation process. The most striking feature observed for all samples investigated was the appearance of a Debye-like relaxation as well as a Cole-Cole-like relaxation, both in the low-frequency range. Both processes, which could be resolved from the spectra by mathematical fitting of a circuit equivalent consisting of a Debye R, C link and a Cole-Cole R, CPE link, are thermally activated and follow the Arrhenius relationship, where the conductivity is cr ~ exp(--EA/kB T). It should be pointed out here that the same experimental evidence of

162

ELECTRICAL PROPERTIES OF CHEMICALLY TAILORED NANOPARTICLES

Fig. 27. Illustrationof ordered and disordered regions of a compact cluster sample. While the ordered region gives a Debye response, the Cole-Cole elementreflects the disordered regions with packing defects.

simple thermal activation has been observed in self-assembled two- and three-dimensional nanoparticle networks [40, 43, 45]. Taking into account structural details such as packing defects or the formation of superclusters, that is, superstructures consisting of several clusters in crystalline order, the authors applied a well-established physical model to a cluster solid with an inhomogeneous partially disordered system. To describe the charge transport and to explain both low-frequency relaxations, they used the so-called brick-layer model [ 150]. Whereas the Cole-Cole process was interpreted as an "intercluster" process resulting from the transport of electrons between nearest-neighboring clusters by consecutive transitions, the Debyelike process was identified as an "intracluster" process, which denotes electron transport in a band structure of cluster superstructures (see Fig. 27). The existence of the latter has been proved by STM investigations on the cluster pellets used for impedance measurements. The topography of the pellet surface showed a dense packing of the clusters with inclusions of such superstructures which have been identified to be superclusters consisting mainly of 13 Au55 clusters in a crystalline arrangement. In addition, 13-member "superclusters" of 6-nm diameter have been identified to be the building blocks of a "quantum wire," as shown in Section 3.3.2. The main advantage of the performance of temperature-dependent impedance measurements reveals that the microscopic properties of the nanoparticles could be deduced from two different measured quantities. From the temperature dependence of the conductivity of the Cole-Cole process, the height of the barrier between clusters in the disordered regions of the samples could be determined. Transferred into the "language" of SET, the activation energy is directly connected to the charging energy of two attached clusters along a current path through the sample, as it reflects the energy that has to be overcome to transfer a single electron between two initially neutral clusters and to create a charged pair. In the "language" of chemistry, this is so-called "disproportionation." In this situation, the total dot capacitance is equivalent to the dot-to-dot capacitance of two attached clusters, while the neighboring clusters in a disordered hemisphere have a minor influence. Because the activation energy E A, which is assumed to be equivalent to the charging energy Ec, is for all Au55 cluster samples between 0.15 and 0.19 eV, the dot-to-dot capacitance is in the range of 1-5 x 10 -18 F or less, deduced from a simple electrostatic approach. This value shows that the transport mechanism between the clusters even up to room temperature may be attributed to an SET mechanism. In accordance with this, Brust et al. [40], Andres et al. [43], and Terrill et al. [42] deduced single-particle properties in three-dimensional arrangements of gold nanoparticles from temperature-dependent dc measurements. The second quantity obtained from impedance measurements was the capacitance of the Debye process. Because of its attribution to a charge transport and polarization process inside crystalline-ordered grains of nanoparticle arrangements, the total or macroscopic capacitance Cmacrocould be assumed to be constituted from a three-dimensional network

163

SIMON AND SCHON

of microscopic capacitors with capacitance Cmicro, each reflecting the capacitance of a single nanoparticle in a close sphere packing according to Kirchhoff's laws. Following this argument, the "intracluster" process, which is more precisely an "intra"-ordered cluster region process, reflects the single-particle capacitance Cmicro of a Au55(PPh3)12C16 cluster even in the same range mentioned previously, that is, 1-5 • 10-18 F. Because the charge transport is attributed to consecutive single-electron transitions between attached clusters along single or multiple current paths, the quantity of the microscopic capacitance Cmicro allows the calculation of the characteristic time constant for the singular process rmicro from the estimation of the tunneling resistance RT between the nanoparticles, when an electron passes the potential barrier. According to Kirchhoff's laws, Cmacro - InlCmicro Thus, Z'macro- RT" Cmacro- RT" In lCmicro Because In l -- 105 in the samples investigated and the macroscopic relaxation time Z'macro is measured in the range of some 100 kHz, RT is approximately 100 M~. This rough estimation allows the calculation of rmicro according to Z'micro- RT" Cmicro that is, 10 -12 s, where this quantity denotes the so-called recharging time. Correspondingly, Z'macrois the operating time needed to transport an electron from one electrode to the other, while passing In l junctions in series.

4.4.2. Tailoringof the Charging Energy The chemical tailoring of the charging energy in three-dimensional arrangements of metallic nanoparticles has been reported in recent work [40, 45]. The basic idea is to stretch the close cluster package in comparison to the densest sphere packing described before and thereby increase the interparticle spacing. This should lead to an increase of the charging energy, that is, a decrease of the electrical capacitance between the clusters. Following this idea, Simon et al. [45] reported the insertion of bifunctional amines into arrangements of Pd561phen360200 clusters. The spacing started with deoxygenation of the cluster by hydrogen in a water-pyridine solution at room temperature with the formation of H202. The oxygen-free cluster Pd561phen30 then offers active surface sites that can be coordinated by the NH2 groups of 4,4'-diamino-l,2-diphenyl ethane, which was used as the spacer molecule. As the naked cluster surface sites are oriented in all directions, the spacing procedure leads to an insoluble precipitate with three-dimensional cluster linkage. This network exhibits an increased interparticle spacing with respect to the closest sphere packing of the unmodified cluster, as in the pressed pellets described previously. The charging energy Ec is dependent on the interparticle capacitance C and can be determined directly from the temperature dependence of the dc conductivity of the cluster arrangements. Earlier investigations on the electrical properties of these clusters have shown that even at high temperatures thermally activated electron hops instead of hops of variable range dominate the charge transport through the samples [44]. This was confirmed in [45] because the activated behavior over a temperature range of 80 to 300 K was found. Figure 28 shows the Arrhenius plot, in which the slope of the straight lines corresponds to the activation energy of the charge transport, that is, the charging energy of the particles in the three-dimensional arrangement. Whereas the close packing of the cluster material shows an activation energy of 0.02 eV, the insertion of the spacer molecules increases the value up to 0.05 eV. Correspondingly, the capacitance decreased from 4.0 • 10 -18 F initially to 1.6 x 10 -18 E The specific

164

ELECTRICAL PROPERTIES OF CHEMICALLY TAILORED NANOPARTICLES

Dense Packing EA = 0.02 eV

-2 -4

m

o

-6

-8

3-D Network E A = 0.05 eV

"WI,-..._ -10 -12

0.005

0.0~

0.0~5

0.02

1FF [l/K]

Fig. 28. Arrheniusplot ofPd561phen360200 clusterin (a) densest arrangement and (b) a stretched packing due to insertion of spacer molecules.

conductivity follows the same trend as might be expected because of the decrease of the volume fraction of the metal in the volume of the sample. Comparable results were found by Brust et al. [40], who investigated 2.2- and 8.8-nm colloidal gold nanoparticles with interconnecting alkyldithiols of different length. These examples show that the electrical capacitance between metal nanoparticles in a three-dimensional arrangement and thus the charging energy can be tailored chemically by the use of bifunctional spacer molecules, and thus prove the chemical control of the physical properties of cluster arrangements, which contributes to an understanding of the structure-property relationships in nanomaterials.

5. W O R K I N G P R I N C I P L E S OF S I N G L E - E L E C T R O N T U N N E L I N G DEVICES AND THE USE OF C H E M I C A L L Y BUILT NANOPARTICLES

5.1. Single-Electron Tunneling Devices and Circuits

5.1.1. Metal-Based Single-Electron Transistor The simplest circuit that reveals the peculiarities of single-electron tunneling comprises only one Coulomb island with two leads (electrodes) attached to it. In other words, this geometry presents the double tunnel junction system. If besides these parts one attaches a so-called gate electrode, which is capacitively coupled to the island, then such a system has a control and this geometry is often called a single-electron transistor (see Fig. 29). Applying a d c voltage to the outer (drain) electrodes of this circuit either may cause sequential transfer of electrons into and out of the central island or may lead to no charge transport; that is, the transistor remains in a nonconductive state. The result depends on the voltage U applied to the drain electrodes, as well as on the voltage Ug applied to the gate. Because of the small total capacitance of the island, C = C1 + Ce + Co + Co, (CI, e are the capacitances of the junctions, which, for the sake of simplicity, we shall assume to be equal, C1 -- Ce = C j, while Co, the capacitance with respect to the gate, and Co,, the capacitance of other remote conducting objects, will both be assumed to be much less than C j), the island has a large Coulomb energy, and Ec >> ka T. The total change of energy of the system A E while one electron is tunneling in one of the junctions consists of

165

SIMON AND SCHON

tunneljunctions e

2 CgC2 gate~__]_ Ug

,1+

,

,t7--

U 2

U 2

Fig. 29. Illustrationof a simple single-electron transistor, consistingof a two-junction arrangement and a gate electrode coupledcapacitivelyto the central island.

the charging energy of the island itself as well as of the work done by the voltage source. For Ug = 0, this is simply expressed by

AE= Q~ 2C

a~ 2C

qU

where Qi and Qf are the initial and final charges of the island, respectively, and q is the charge (not necessarily an integer) which passed the drain voltage source. From elementary reasoning, it is clear that if, say, ai - 0 and Qf = e, then q + e/2 (depending on the direction of electron tunneling) and, therefore, AE = e2/2C 4-eU/2. This means that - e / C , the change of energy, is always positive when - e / C ~< U ~< e/C. Hence, electron tunneling could only increase the energy of the system and this transition does not occur if the system cannot "borrow" some energy from its environment, when the temperature is assumed to be low enough. Therefore, there is a Coulombically blocked state of the singleelectron transistor when the voltage U is within the interval given previously and Ug is zero. Outside this range, the device conducts current by means of sequential tunneling of electrons. When the gate voltage Ug is finite, the calculation of the energy change resulting from one electron tunneling gives another value, because of the additional polarization of the island electrostatically induced by the gate. The result of this consideration is illustrated in Figure 30, where the U versus Ug diagram of the Coulomb blockade is shown. The diagram reflects an interesting feature; it is periodic with respect to the voltage Ug with a period of e/Co. This results from the fact that every new "portion" of the gate voltage of e/Co is compensated by one extra electron on the island and it returns to the previous conditions for electron tunneling. Therefore, at constant bias U, the current through the device is alternatively turning on and off with a sweep of voltage Ug. The behavior of the transistor outside the Coulomb blockade region also shows the single-electron peculiarities, especially for the case of a highly asymmetrical junction, where R1 >> R2 and C1 >> C2. In Figure 31, one can see the I(U) characteristics with a steplike structure fading with decreasing U. This so-called Coulomb "staircase" results from the fact that an increase in U increases the number of channels for tunneling in a steplike manner, allowing an increasingly larger number of electrons to be present on the island. Another manifestation of charging effects in the SE transistor is the offset of the linear asymptotes by e/C.

166

ELECTRICAL PROPERTIES OF CHEMICALLY TAILORED NANOPARTICLES

Fig. 30. Periodic rhomb pattern showing the Coulomb blockade region on the plane of voltages U and Ug. The value of the number n is the number of extra electrons trapped in the island in the blocked state.

Fig. 31. Dependenceof the time-averaged current I versus U for asymmetrical single-electron transistor.

The dependence of the transistor current on the gate voltage opens up the opportunity to fabricate a sensitive device that measures directly either an electric charge on the island or a charge induced on the island by the charges collected at the gate, that is, a highly sensitive electrometer. The sensitivity of such an electrometer, which has already been reached in practice, is on the level of 1 0 - 4 - 1 0 -5 parts of electronic charge and thus exceeds the charge sensitivity of conventional devices by several orders of magnitude.

5.1.2. Traps and Turnstiles The idea of effectively controling the tunneling current by means of electrostatic gating has been developed further in multiisland systems and has opened new possibilities for SE. An

167

SIMON AND SCHON

I=ef

Ul

l

1

g

Fig. 32. Four-junction (three-island) single-electron turnstile. The alternating voltage applied to the gate is Ug = Uamp sin(o)t) and at its rise an electron makes a transition. The electron remains trapped in the central

island until the negative half-wave of Ug is diminished.

I=+_ef _~ [ 1 ~j 2

~ 3 ~' 4 +U

~=.

g2

U

T 2

Fig. 33. Three-junction single-electron pump. The two sinus-waveform voltages Ug 1 and Ug2 have the phase difference, whose value can determine at small bias U the direction of single-electron current I = evsE T .

example of such a circuit is the so-called single-electron turnstile. In its simplest version, it consists of three islands aligned between two outer electrodes, as shown in Figure 32, and can be considered as two double junctions connected in series. The very central island of this chain is supplied with the capacitively connected gate, which controls electron tunneling in all four junctions. However, in contrast to the operation of the single-electron transistor, the additional two islands allow the realization of this condition. The central island works as a controllable trap for electrons, endowing the turnstile with its unique properties. If the entire chain of islands is initially blocked for small bias voltage U and the gate voltage Ug is swept, the central island first attracts one electron from the left arm. This is possible because the Coulomb blockade in the left double junction is lifted as a result of the gate voltage applied. The blockade is automatically restored after that tunneling even when Ug is increased. Hereby the electron remains trapped in the central island. Then if the voltage Ug diminishes the blockade in the right double junction, the electron sequentially passes two right junctions, completing its course through the whole array. Hence, if one applies an alternating voltage, for example, sinusoidal, to the gate of the turnstile, it should transfer exactly one electron during a period of the signal. The idea of the turnstile has been developed further in the single-electron pump device shown in Figure 33. This is a two-island (or, in other terms, a three-junction) circuit that is supplied by two sinusoidal signals applied via two gates to both of the islands. In contrast to a turnstile, this circuit can operate even at zero drain voltage U. The phase difference between these signals is 90 ~ and during one cycle exactly one electron sequentially tunnels from the left drain electrode to the left and then to the right island and, finally, to the fight drain. Such pumping of individual electrons has been likened to the mechanical pumping of a liquid. Moreover, in a similar manner, the direction of transferred matter depends on which of two oscillations is ahead of another, so the direction is changed by changing the phase from + 9 0 ~ to - 9 0 ~.

168

ELECTRICAL PROPERTIES OF CHEMICALLY TAILORED NANOPARTICLES

Frequency-controlled single-electron tunneling opens an opportunity to maintain a dc current in a lead, the value of which is determined by the frequency of an ac signal by means of the fundamental relation I -- eVSET. This is of great importance for modem quantum metrology, which could then determine the unit of dc current via the unit of frequency using one universal constant, that is, the electronic charge. In that case, taking into account the very high accuracy of the atomic standard of frequency, the accuracy of this current standard would be basically limited by the accuracy of the electron transfer cycle. At present, it is on the level of parts of 1% for currents of several picoamperes, caused by a number of factors that make the operation of the devices far from being as ideal as described previously. Among these factors are (i) the influence of thermal fluctuations, (ii) uncontrollable higher-order tunneling of an electron through all the junctions of the circuit at the same time, and (iii) rare intermittence of tunneling events in spite of their statistical character. The solution of this problem, which necessarily involves a decrease in structure size and thus an increase of the Coulomb charging energy, seems clear when taking chemical nanostructures into consideration. Accordingly, at present, ligandstabilized metal nanoparticles with this well-defined structure, seem to be the most promising candidates.

5.2. Metal Nanoparticles as Elements for Single-Electron Devices As discussed previously, the progress of lithographic methods guided by the miniaturization of conventional electronic circuits fails to satisfy the requirements arising from single electronics even operating at room temperature, a requirement that extends to a size range of a few nanometers or less [7-10]. Consequently, the use of ligand-stabilized metal nanoparticles, as it was supposed by the authors, should solve the problem and embody suitable building blocks for a new nanoscale architecture. Furthermore, in general, new techniques for a defined organization of such nanoparticles have to be developed to build up single-electron circuits of different complexity. So far, it has become evident that utilizing the principles of self-assembly by controlling intermolecular interaction, which is one of the main interests of supermolecular chemistry, will be a key feature in this development. In addition, the relatively simple theory of tunneling successfully applied to larger SE objects might now be applied with much caution and should be certainly revised for nanoparticles, where quantum size effects appear for the reasons explained in Section 1.1.3. In particular, depending on the cluster type and its bonding of the nanoparticles, the standard diffusive single-electron transport that arises from the particle nature of electrons could be converted into ballistic transport or even into resonant tunneling reflecting the wave nature of electrons. These could drastically modify the Coulomb blockade, but still leave the important role of Coulomb repulsion. Summarizing these problems, it should be noted that transition to nanoparticle SE promises incredibly high density of the elements on a chip, which is extremely important for computer-like circuits [138]. Thus, assuming a "three-nanometer design rule" (the nanoparticle size including its ligand shell) and the necessity of 10 by 10 clusters for every reliable gate, then for a two-dimensional architecture the number of gates on a 1-cm 2 chip might be about 1011. The extension of such a friable structure into the third dimension could result in an even larger number of about 1016. This is a rather conservative estimate based on the traditional paradigm for information processing. On the other hand, for nanoparticle networks, the locally interconnected architecture, such as cellular automata with neural networks, seems to be more adequate. This points out new problems in design and operation principles, the solving of which could lay a bridge to structures on the true atomic scale.

169

SIMON AND SCHON

5.2.1. Mesoscopic Arrays with Nanoparticles and First Devices It is not the purpose of this review to detail concrete microelectronic circuits. This would exceed the knowledge of the authors, and here the reader's attention should be drawn to other reviews [132, 151-153]. It should be pointed out, however, that most suggestions deal with much larger devices based on semiconductor materials, even though in the last 10 years a general understanding of the fundamental principles of conventional SET junctions between metals has been developed by extensive theoretical and experimental work. Conventional SET junctions show the SET effect only at temperatures near absolute zero and they are much larger than single nanoparticles, which show the SET at room temperature. One example of the smallest subunit of an SE device working at room temperature may be the "smallest switch with electrons" [7]. Such a switch consists of two ligand-stabilized nanoparticles and, in the ideal case, of two Au55(PPh3)12C16 clusters where the ligand shells keep the cluster cores at a distance of 0.7 nm, a barrier that can be passed by tunneling (see also Fig. 5). The electrical capacitance of this junction determines the Coulomb or switching offset as well as the temperature at which this quantum device can be used. Regarding this, it becomes clear that the fundamental principle of SET can be directly transferred to a digital technology developing more complex devices, where the information can be transported or stored by means of one electron (at a defined time and a special place) in a single nanoparticle [4]. The most detailed and concrete work utilizing the SET effect has been done in a socalled SET transistor based an metal nanoparticles. In general, this simple circuit reveals the peculiarities of SE because it includes the usual three junctions but, at least, only one metallic particle. Most recently, Sato et al. [10] reported detailed electrical characteristics of the first SET transistor utilizing charging effects on single chemically tailored gold nanoparticles. They developed a device as a hybrid system; that is, it was fabricated by means of metal electrodes formed by electron beam lithography to which a selfassembled chain of colloidal gold particles was connected. The interparticle connection as well as the connection to the electrodes results from a linkage by bifunctional organic molecules, which present the tunnel barriers, and the authors clearly demonstrated that the self-assembling nature of the gold nanoparticles helped in overcoming the size limitations of lithography. The fabrication is described as follows and is illustrated schematically in Figure 34: Gold nanoparticles with an average diameter of 10 nm were deposited on a thermally grown SiO2 surface on a Si substrate by using alkanesiloxane molecules as an adhesion agent. After formation of the Si-O-Si bond by thermal treatment, terminal amino groups of the silane attach to gold nanoparticles in an appropriate gold particle solution to form a submonolayer. Because the gold particles were obtained by the citrate method [ 154], they

Chain of nanoparticles

Drain

Sourc

'~ 3 0 n m

"

Fig. 34. SET transistor based on self-assemblingof gold nanoparticles on electrodes fabricated by electron beam epitaxy. (Source: Adapted from [10].)

170

ELECTRICAL PROPERTIES OF CHEMICALLY TAILORED NANOPARTICLES

retain their ionic charges on the surface. Therefore, the nanoparticle deposition stopped automatically before it reached a close-packing density leaving an interparticle spacing of 10-50 nm. After the submonolayer coating, 1,6-hexanedithiol was added to interconnect the particles with a more defined spacing, as described before in Sections 2 and 3. Then a second immersion into a gold particle solution increased the coverage where, again, the dithiol molecules maintained the distance between the particles. While the second layer filled the gaps between the particles of the first layer, however, chains of 2-4 particles were formed. When this procedure was performed on a SiO2 substrate, equipped with source, drain, and gate metal electrodes defined by electron beam lithography, the particles formed a chain of at least three particles bridging the gap between the outer driving electrodes. Because all steps of this procedure could not be controlled in detail, the number of nanoparticles in the bridge chain differed from device to device, but, in any case, electron conduction dominated by single-electron charging indicated by a Coulomb gap could be observed up to 77 K, whereas the nonlinearity is smeared out at room temperature. Simulation and fitting of the data with a model circuit for a three-dot (four-junction) SET transistor indicated that the capacitance of all junctions in the chain was 1.8-2 • 10 -18 F and the calculated Coulomb gap was in reasonably good agreement with the value of 150 mV obtained from the measured I (U) characteristic, which was systematically squeezed, when a gate voltage of - 0 . 4 - 0 . 4 V was applied. The plot of the current through the device was clearly dependent on the gate voltage showing the typical current oscillations, proving the desired function of the single-electron transistor. According to a Green's function-based method, which was proposed by Samanta et al. [155], the transmission function of electrons across the dithiol ligands was calculated from which the resistance R per molecule was obtained by the Landauer formula, R - (h/2e2)/T(Eg), where T(EF) is the transmission function, that is, T ~ exp[2(mEg)l/2/h]. Assuming a barrier height Eg ~ 2.8 in the dithiol molecules, the resulting resistance was estimated to be R _~ 30 Gf2. Instead of chemically tailored metal nanoparticles, however, even cluster-like molecules of the same size seem to be suitable building blocks in the fabrication of SET devices. Soldatov et al. [ 156] reported the fabrication of an SET transistor on the base of a carborane cluster, which is also a spherical-shaped molecule, working at room temperature (see Fig. 35).

Fig. 35. Closo-I,2-C2B10H12(o-carborane), which was used as the central electrode in the experiment described. The organic substituents are left out for simplification.

171

SIMON AND SCHON

STM tip

LB film I-J-] carborane It

/

/

]

m~

Fig. 36. SET transistorbased on carborane molecules in an LB film on a gold electrode array deposited on graphite (HOPG). (Source: Adaptedfrom [156].)

They deposited LB monolayers of the carborane 1,7-(CH3)2-1,2-C2B10H9T1 (OCOCF3)2 in a mixture with stearic acid dissolved in tetrahydrofuran on a preformed gate electrode system (see Fig. 36). The electrode system was formed by a conventional electron lithography technique and consisted of thin and narrow bilayer strips, where 50-nm gold on 50-nm A1203 was deposited on a graphite substrate (HOPG) with a strip width and distance of approximately 400 nm. The strips were connected in series and had the same potential. The electron transport through the layers was probed by an STM tip at room temperature. When the tip was positioned above the single carborane molecules, a transistor, consisting of a double junction (tip/molecule/HOPG) and closely situated gate electrodes (Au strips), was realized. In this arrangement, the junction capacitance was estimated to be 1 x 10-19 E In the discussion of their results, the authors pointed out that the explanation of the experimental data they obtained has to involve the discreteness of the electronic structure of the carborane molecules, which act as the central electrode. This was already emphasized in Section 4.1.2 and, furthermore, we will see in Section 5.3 that even the charge relaxation in the nanoparticles or molecular particles becomes a relevant quantity.

5.3. Time Scales of Recharging, Charge Relaxation, and Tunneling Apart from the fundamental questions in the quantum mechanical (QM) concept of time and concepts of tunneling times, which are discussed in detail by Gasparian et al. [157], practical questions arise when time-related quantities such as current determine the performance of microelectronic devices, as is the case in SE. Before dealing with time in these ultimate structures, we have to recall some facts from Section 1.1.2 about SET: SE deals with small amounts of excess electrons on islands changing their distribution over the islands in time in a desirable way. In spite of relatively complex rigorous quantum mechanical considerations, quantitatively this situation can be clearly formulated using a characteristic of the tunneling junction such as its tunneling resistance RT, which necessarily must be larger than the so-called resistance quantum Rq. Then electrons in the island can be considered to be localized and classical electrodynamics can be applied, although their number is undergoing thermodynamic fluctuations as does every statistical variable. Second, to minimize these fluctuations and, consequently, to make the exchange of electrons controllable, the Coulomb energy of an extra charge Ec = e2/2C has to be sufficiently larger than kB T. Thus, SET at ambient temperature can only be achieved with capacitances between 10 -18 and 10 -19 F, which can be realized by the use of sub-10-nm chemical nanoparticles. If the preceding conditions are met, the transfer of single electrons can be realized by means of QM tunneling if the probability of such tunneling depends on current biasing and driving voltages applied to the circuit.

172

ELECTRICAL PROPERTIES OF CHEMICALLY TAILORED NANOPARTICLES

Starting outside the Coulomb blockade region, time-dependent recharging of the junction occurs with Q = f jy dt - QT, where the first term is the charge supplied by a current source jy and the second term is the charge transferred through the barrier junction by tunneling, which is regulated by the tunneling rate. Because in metallic tunnel junctions a tunneling time of 10 -15 s is very short, external recharging of the junction in time-correlated SET will be periodic with the so-called single-electron tunneling frequency VSET -- j y / e . The smaller the current, the more regular are the SET oscillations, but generally with an inherent noise component because of the stochastic nature of the tunneling process. Although charge transport through an SET device is determined by the transit time rT [ 158], which refers to the "external" system around the single tunnel junction, supplying its current bias jy, the tunnel junction itself is characterized by "recharging time" rr = RT 9C. Depending on the approach to recharging time, it may be defined 9 either as a "decay time" of an excess charge that appears on one of the barriers after a fast tunneling step (with finite but ultrashort traversal time on the order of 10 -15 s), forming a polaron-like state together with the "hole" it left on the other side, 9 or as a "relaxation time" that the junction system needs to return to equilibrum, ready for a new cycle of external recharging. Thus, recharging time and the much faster tunneling time are additive in SET systems. As pointed out in Section 4.1.1, in nanostructured arrays with the smallest possible conventional chip architecture, the single tunnel junction comes up to a tunneling resistance of RT ~ 105 f2 and with a barrier length of L ~ 1-2 nm a capacitance C ) 10 -16 F is feasible. Thus, the recharging time with r ~ 10-11 s is still much larger than the tunneling time fT. An intermediate time scale is the "uncertainty time" r - Rq 9C, where Rq is the resistance quantum. In the theory of SET, a clear separation of time scales rT .

1.0350

~

1.0325

' -'- ' '-- ' 1.0300 -2 -1 0 1 2 3 4 Stress in SiN~ (• 9 dynes cm -2) Fig. 17. Photoluminescenceintensity and peak energy of the SiNx-coated dots as a function of the stress in the planarizing layer. SiNx ITO contact

Fig. 18.

n§ Si

n§ Si

planarization

electrical contacts

Planarization of the dot array with SiNx (left) and electrical contacts with ITO (right).

Figure 17 shows the photoluminescence intensity of the dot arrays recorded at 6 K together with the peak energy as a function of the corresponding stress of the SiNx film. When the stress in the SiNx is nearly zero, the spectrum shows the maximum photoluminescence efficiency, close to that of uncoated dots. External induced tensile as well as compressive strain drastically decreases the luminescence intensity. Thus, there is an optim u m regime for the SiNx deposition with respect to maximum luminescence yield. These experiments on the stress of the SiNx coating were very important, as in previous tests polyimide had led to unstable and shifted current-voltage ( I - V ) characteristics because of a leakage current under bias. Using high-stress PECVD SiNx removed these problems, but decreased the emission. On the other hand, stress-free SiNx reported in [72] did not alter the light emission strength and exhibited acceptable I - V characteristics. Figure 18 (left) shows a schematic of the planarized structure. Finally, a 70-nm NiCr layer was deposited as electrical top contact. Experiments are in progress to replace NiCr by an optically transparent and conducting indium tin oxide (ITO), to be used as a mask and ohmic contact in future tests. In Figure 18, NiCr has already been replaced by ITO. Figure 19 shows the electroluminescence intensity of the

252

SILICON-BASED NANOSTRUCTURES

1.100 .........

::

Energy (eV) 1.000 0.900

_

,

. . . . . . . . . .

~:

.

.

.

.

.

,~

,

....

i= 1pA/50nm d o t ~

i

107K-"

xl

75K. ~

xl

33K ~

4.2K ,/M....xl 1100 1200 1300 1400 Wavelength (nm) Fig. 19. Electroluminescencespectrum of the Si/Sil_x Gex dot array at different temperatures. This array had polyimide as the insulating material and a 70-nm NiCr top contact. For reference, the spectrum of a large mesa structure is also shown.

dots at different temperatures, compared to a low-temperature spectrum of the as-grown wafer. These spectra were recorded at an injection current of 1 pAJdot under reverse bias, 0.5 V at 293 K and 2.0 V at 4.2 K. At room temperature, an external quantum efficiency of 0.14% was estimated [70]. The results of the luminescence data have shown the crucial role of strain during the fabrication of low-dimensional structures. Tang et al. [73] found that the smaller the nanostructures, the bigger is the strain relaxation. This observation was deduced from the Raman shift of the Ge-Ge, Si-Ge, and Si-Si modes of 50-nm dots with different Ge concentration, which were accounted for by a 50% strain relaxation. Figure 20 shows the Ge content-dependent Raman shifts of the Si-Si, Si-Ge, and GeGe modes for different dot arrays of similar size. The solid line is the calculation of a corresponding unstrained pseudomorphic structure, the dashed line is the calculation with a 50% strain relaxation [74]. The solid circles represent the experimental data. In addition to the strain relaxation resulting from material removal through etching, a thin SiGe layer, redeposited on the walls of the dots, may force the atoms to rearrange and induce a lattice distortion inside the dots [75]. This hypothesis is supported by Raman spectra from etched regions away from the dot arrays pointing to the existence of a thin SiGe alloy being redeposited all over the remaining silicon substrate. To investigate the effect of size reduction on strain relaxation inside the Si/SiGe nanostructures, a series of 2.5-/zm-long and 10-to-500-nm-wide wires were fabricated of a modulation-doped p+-Si/Sil-xGex heterojunction structure [76]. Figure 21 shows room temperature photoreflectance spectra for wires with different widths compared to a mesa control sample. In this spectrum, 1 l h represents V-like 2D interband transitions between the first electron subband and the first heavy-hole subband. On reducing the wire width down to about 100 nm, the 1 l h transition is red-shifted, indicating a strain relaxation of the original comprehensive strain in the SiGe layer of the heterostructure during wire fabrication. Further reduction of the wire width to 40 and 15 nm leads to a blue shift because of lateral confinement effects, indicating a clear 2D-1D transition [77]. Similar phenomena were also observed in wires cut from Si-Sil_xGex multiple quantum wells [78]. However, a quantitative analysis of the strain and confinement shifts was not carried out.

253

SIDIKI AND SOTOMAYOR TORRES

9~e

200

"

s~i~sa~

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400

9

do

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-2

: P.

-I0

" unstrained 50% relaxed

0.0

0.1

/

~ ,

y

0.2 Ge Content x

0.3

0.4

Fig. 20. Ge content dependence of the Raman peak shift of the dot arrays compared to the as-grown superlattice. The inset on the top left shows the Raman spectra of a dot array and the corresponding as-grown samples cut from a Si-Si0.7Ge0. 3 superlattice. The sharp features at around 521 cm -1 are due to the removal of the Si TO phonon peak from the substrate.

-

i

!

T=300K 11h • 1

control sample

x 1

2.5pro x 500nm

x 2~

2.5pro x 200nm

d~

El10 > E311 > E l l l [112, 113]. In the case of SiGe, one gets the same relations [114]. Therefore, the { 111 }, { 110 }, and {311 } facets are favored during growth. Figure 32 shows a TEM

SILICON-BASED NANOSTRUCTURES

Fig. 31. Schematics of the QW structure within the oxide window. (Source: Reprinted from [110], with permission from Elsevier Science.)

Fig. 32. Transmission electron micrograph cross section of wires with (110) side-wall orientation: (a) edge of a 10-/zm wire and (b) 400-nm wire. (Source: Reprinted from [110], with permission from Elsevier Science.)

micrograph of the cross section of 10-/zm (part a) and 400-nm (part b) wires with side-wall orientations of (110). The (001) quantum wells are planar and the {311 } and (111) facets are also fiat. In contrast to the wires, the dots all show the facets during growth, because the holes in the SiO2 do not have perfect square shapes. Facet formation in this growth technique is needed to reduce the lateral dimensions of the quantum wells. However, to realize these facets, structures much thicker than the critical thickness are needed. Stoica and Vescan [ 115] attributed this higher critical thickness to an eventually hindered defect multiplication in the local structures. For x = 0.065, the size reduction leads to an increase in the critical thickness of approximately 700 nm for 30-#m-wide wires and to even more than 1 # m for 3 0 0 - # m dots. The characterization of the grown structures

263

SIDIKI AND SOTOMAYOR TORRES

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0.1 :. ; ;;;;.;, :. ; - ;;-;:. . . . . . . . . . . . . . . . . . . . . . . . 1 10 100 0.01 0.1 size of (001) region of the top quantum well (gm)

0.1 1000

Fig. 33. Integratedintensity of the SiGeNP line, normalized to the surface of the dots, for different dot samples against the size of the (001) region of the top quantum well in the dots. (Source: Reprinted from [110], with permission from Elsevier Science.) was performed optically by photoluminescence. From the presence of dislocation-related emission lines, the authors concluded that wires remain strained for sizes less than or equal to 30/zm, whereas dots are strained for diameters less than or equal to 300/zm. The photoluminescence intensity normalized to the patterned area increased by a factor of 50 for the dots less than or equal to 400 nm (see Fig. 33). This is attributed to the reduced role of nonradiative recombination channels by exciton localization. This suggests a further increase of intensity through fabricating smaller dots when the probability of the excitons reaching nonradiative center is decreased. Hobart et al. [ 116] have used solid-source MBE to grow Si on nonplanar Si substrates. The prestructured Si substrate surface consisted of truncated pyramids with { 111 } sides and (100) tops that were formed by anisotropic wet etching in KOH or EDA solutions. The height of the pyramids was about 1 /zm; the width of the tops ranged from 0.4 to 1 /zm. The pitch size was about 1 0 / z m . Because of undercutting of the SiO2 layer used as a mask for the anisotropic etching, the mesa structure typically also had {331 ) facets. Si was deposited on such templates at various temperatures and growth rates. The authors found no structural change for temperatures between 470 and 550~ In a temperature range between 650 and 700 ~ { 113 } facets formed that laterally reduced the (100) tops of the pyramids to less than 20 nm. At higher temperatures around 800 ~ only { 113 } and { 100 } facets were formed. { 113 ) facets have also been observed by Booker and Joyce [ 117] and Yang and Williams [ 118] during CVD deposition of Si, whereas the Si surface was carbon contaminated. Hirayama et al. [ 119] have observed { 113 } facets during selective epitaxial growth through a patterned SiO2 mask. The occurrence of { 113 } facets was explained by pinning of the step flow at defect sites [120] or at the edges of the SiO2 mask used for the selective growth [119]. Hirayama et al. [119] and Oshiyama [121] attributed the formation of { 113 } facets on Si(001) to bunching of double height steps. Thus, during chemical vapor deposition, surface orientation-dependent growth rates occur because of different silane and disilane deposition rates, whereas for MBE growth dynamical processes determine the facet growth. Hobart et al. [116] have used the previously described Si templates to fabricate S i l - x G e x quantum dots. Thus, a 20-period Si(20 nm)/Si0.8Ge0.2(4 nm) multiple quantum well was grown at 550~ on top of a mesa with a Si(100) surface reduced by the { 113 } facets to 10 nm. Although no optical or electrical characterization was performed

264

SILICON-BASED NANOSTRUCTURES

to confirm low dimensionality, transmission electron micrographs indicated that quantum boxes may be realized on the top as the SiGe growth rate on the { 113 } facets was 85% of that on the (100) facets for geometrical reasons. 3.7. V-Groove Growth

Kapon et al. [122] have demonstrated the growth of quantum wire arrays on V-groovepatterned GaAs substrates by MOCVD. Performing cathodoluminescence (CL), they showed the existence of quantized states resulting from the quantum wires at the bottom of the grooves. Tsukamoto et al. [ 123] fabricated GaAs "arrowhead-shaped" quantum wires by selective growth using MOCVD. Usami et al. [124] were the first to demonstrate SiGe/Si quantum wires on V-groovepatterned Si substrates. They have grown Si/SiGe/Si double-heterostructure quantum wires on V-groove-patterned p-Si(001)wafers (resistivity 5-10 f2) by gas source MBE at 740 ~ using silane and germane. Using thermal oxidation, a SiO2 film was first grown as a mask layer for the chemical etching and for the subsequent selective epitaxial growth. The fabrication process is depicted in Figure 34. With electron beam lithography and wet chemical etching in a N2H4-based solution, line patterns along the (110) direction with a period of 0.6 # m were fabricated. Because of the directional selectivity of wet etching, the V grooves have { 111 } side facets (Fig. 34a). The SiO2 mask layer was then removed by a HF dip (Fig. 34c) and subsequently the whole structure was overgrown by a thick Si overlayer (Fig 34d). Figure 35 shows a TEM micrograph of a 15-nm-high SiGe/Si crescent-shaped quantum wire revealing no misfit dislocations. The shape and the vertical height, which is higher than the nominal one, are due to anisotropy in the different orientations during gas source Si MBE. As the surface migration of adatoms on (111) surfaces is higher than on (100) surfaces, one gets an enhanced mass transport from Si(111) toward the bottom of the V grooves. The SiGe transverse optical phonon-assisted transition and the no-phonon line are clearly visible in low-temperature photoluminescence spectra, indicating a high crystalline structure in the wires. The broadening of these two peaks in the case in the wires in comparison with spectra of a two-dimensional reference structure results from the SiGe width and Ge compositional variations. The SiGe luminescence quenching temperature was determined to be 70 K. The electroluminescence spectrum is comparable to the photoluminescence spectrum, indicating that the recombination process is identical in both cases.

Si02

(a) Si (100) substrate

(c)

7

t

[o~T]

S/

/

(o)

SiGe QWR

Fig. 34. Schematics of the processing steps of SiGe quantum wires by selective epitaxial growth. (Source: Reprintedfrom [125]. 9 1994American Institute of Physics.)

265

SIDIKI AND SOTOMAYOR TORRES

Fig. 35. Transmissionelectronmicrographof a Si/SiGe/Siwiregrownon a V-groovepatterned substrate. (Source: Reprintedfrom [124]. 9 1993AmericanInstitute of Physics.)

Polarized electroluminescence was obtained in the direction of the cross section of the wires and in the growth direction. Although the wires do not show any polarization in the cross section, the single quantum well shows a strong in-plane polarization as expected from the selection rule of the hh I - e l transition. In the direction perpendicular to the sample surface, the situation changes to the opposite. Here the quantum well is optically isotropic and the wires show strong anisotropy. The polarization experiments clearly indicate successfully realized luminescent SiGe wires of high crystalline quality. From TEM micrographs, the lateral and vertical wire widths were determined to be 30 and 8 nm. However, the peak positions do not fit these dimensions as the distribution of strain and the Ge atomic fluctuations lead to a shift of these peaks. A main disadvantage of the V-groove growth technique is its limit for further reduction to quantum dots. From a scientific point of view, this method seems to be an elegant way to produce quantum wires 30-40 nm in width with high crystallinity.

3.8. Local Growth of Dots and Wires through Shadow Masks The method of local epitaxial growth through shadow masks for the homoepitaxy of Si epilayers was reported by Hammerl et al. in 1991 [126]. Brunner et al. [127] used this technique to grow directly wires and dots with SiGe quantum wells through a patterned SiO2/Si3N4 shadow mask. The dots and wires were physically detached from the surrounding material and after overgrowth they were completely embedded in Si. The dots and wires were grown on (100) Si wafers with a resistivity of 1200 f2 cm. Figure 36 shows the schematics of this growth technique. After fabrication of the LPCVD-deposited Si3N4 100-nm-thick shadow mask [ 126], the opened window is cleaned and the wafer transferred to the MBE reactor. The thickness of the SiO2 spacer layer is 1/zm. The nitride is underetched up to 5/zm. The shape of the wires and dots is determined by the growth parameters and by the angle of the incident beam with respect to the sample surface as shown in parts b and c of Figure 36. Finally, the SiO2 layer is lifted off by selective wet etching (part d). The structures mentioned here were grown at 720 ~ under an incident angle of 20 ~ consisting of a 140-nm Si buffer layer, a Ge concentration of 25% in the quantum well, and a 160-nm-thick Si cap layer. The minimum lateral dimension was 200 nm [128]. An SEM cross-sectional micrograph of a dot array is shown in Figure 37. The mask layer is not yet removed and it can be clearly seen that there is no direct contact of the structures with

266

SILICON-BASED NANOSTRUCTURES

Fig. 36. Schematics of the local MBE growth through micro shadow masks: (a) underetched SiO2 with the patterned silicon nitride, (b, c) local epitaxy with normal and off-normal incident molecular beams, and (d) mesa with smooth side walls after liftoff. (Source: Reprinted with permission from [127]. 9 1994 American Institute of Physics.)

Fig. 37. Scanningelectron micrograph of locally grown Si/SiGe/Si 2-/zm x 5-#m mesas. Note that there is no pillar support of the nitride mask over the whole dot group. (Source: Reprinted with permission from [127]. 9 1994 American Institute of Physics.)

the walls; thus, structural imperfections can be avoided during growth. Figure 38 shows a TEM micrograph of the edge of a wire with the embedded SiGe quantum well [129]. As the quantum well is completely buried in silicon, the potential problem of surface states at the side walls is eliminated. The thickness of the quantum well (QW) decreases toward the edge of the mesa; thus, the energy gap increases toward the edges confining carriers in the middle part of the mesa structure. This results in an effective passivation of the side walls without mediation of surface states. Photoluminescence experiments excited with 457 nm reveal the typical SiGe TO phonon-assisted and no-phonon lines and reflect the high structural quality of these dots and wires. The exact shape of the side walls can be controlled by the growth conditions to be nearly vertical or smoothly ascending [ 130]. Rotating the substrate during growth and positioning the e-beam evaporator off axis leads to smoothly ascending side walls as shown in Figure 36c. Figure 39 shows the peak intensities of the SiGe TO phonon replica as a function of wire width normalized to the fractional coverage of the mesa islands [ 131 ]. For comparison, the intensity of a homogeneously grown quantum well reference sample is also included. The increasing luminescence intensity with decreasing wire width from 1 /zm to 200 nm has been attributed to an effective passivation of the side walls and to confinement of excitons

267

SIDIKI AND SOTOMAYOR TORRES

Fig. 38. Cross-sectionaltransmission electron micrograph of a SiGe QW completely embedded in silicon. (Source: Reprinted from [129], with permission from Elsevier Science.)

Fig. 39. NormalizedTO phonon-assisted luminescencetransition intensity of locally grown SiGe wires as a function of wire width. The reference line is the intensity of a homogeneouslygrownquantum well. (Source: Reprinted from [131], with permission from Elsevier Science.)

within the mesa structure and thus to a smaller probability of reaching nonradiative channels. This trend is similar to observations made in GaAs-GaA1As wires [ 132]. However, as in the case of all normalized spectra of this type, one has to keep in mind that excitons in silicon have a diffusion length of about 400/zm. Thus, once generated, they can diffuse to the SiGe wires and recombine there. This effect will always contribute to an increase in intensity unless the SiGe layer is excited with light below the Si absorption edge. Some simulations to investigate this effect may be helpful to estimate the general relevance. Spatially resolved photoluminescence was used to investigate the luminescence intensity distribution and thus the exciton density distribution along a 1-/zm-long wire. From fitting the data to an exponential decay, a decay length of about 1 0 / z m could be estimated. If growth is carried out with the incident beam parallel to the mask normal direction, one obtains faceted side walls [129]. In the case of (100) substrates, the slightly lower (111) surface energy leads to { 111 } facet formation. Eisele et al. [ 129] have grown wires and pyramidal dots through submicrometer masks with the edges oriented in the (110) direction. Figure 40 shows SEM micrographs of this facet formation for a cleaved wire

268

SILICON-BASED NANOSTRUCTURES

Fig. 40. Scanningelectron micrographsof {111 } facet formation in (a) a wire structure grown at 500 ~ through a 310-nm mask and (b) a pyramidal dot structure grown at 500~ through a 350-nm square mask. (Source: Reprinted from [129], with permission from Elsevier Science.)

(part a) and a dot structure (part b). Both structures were grown at 500 ~ with a rate of 0.1 nm/s. In the case of the wire, a 310-nm mask was used, and a 350-nm square mask was used for the dot. The radius of the dot tip was estimated to be less than 5 nm. The maxim u m length of the { 111 } facets is diffusion limited. When impinging atoms have reached their diffusion limit underneath the mask, vertical (011) side walls grow as can be seen in Figure 40a. Neither thermal oxidation at 800 ~ nor thermal annealing at 1000 ~ under nitrogen atmosphere led to any facet degradation. From capacitance-voltage characteristics of metal-on-silicon (MOS) capacitors, the presence of a dense oxide with negligible leakage could be deduced. Using the same technique, Gossner et al. [133] grew silicon nanostructures through micro shadow masks. Figure 41 shows the patterned nitride film and the Si mesa structures grown through this mask. At a growth temperature of 500 ~ (111 } facets formed on the side walls. Wedge-like mesas with a top radius of about 5 nm with perfect { 111 }

SIDIKI AND SOTOMAYOR TORRES

Fig. 41. Scanning electron micrograph of a Si mesa grown through a nitride micro shadow mask at 500 ~ (Source: Reprinted from [133], with permission from Elsevier Science.)

facets were grown through (110)-oriented line-shaped masks. The formation of a perfect pyramidical shape was independent of the orientation and shape of the mask aperture. The technique of local growth through a mask allows a variety of nanostructures to be grown, as well as the realization of laboratory-scale devices as, for example, a field effect transistor with built-in one- and zero-dimensional electrical confinement (see Section 4), ultrathin tips for scanning probe microscopy and direct nanostructuring of surfaces.

3.9. Silicon Nanocrystallites 3.9.1. General Remarks

Another way of realizing nanostructures is forming nanocrystallites in, for example, a matrix. Nanocrystallites are made up of one or more clusters. A cluster consists of agglomerations of up to 105 atoms, which, in conventional terms, can be regarded as neither a bulk material nor as atoms or molecules. Clusters in the size range of 1 to 1000 nm exhibit new physical and chemical properties, which can be directly modified by controlling the cluster size. In the limit of very small clusters, the addition of a single atom can drastically modify electronic, magnetic, and other physical properties. To investigate cluster properties as a function of cluster size, it is necessary to separate the cluster by its mass. Electronic and optical properties can be probed by photoelectron, absorption, fluorescence, or photoluminescence spectroscopy, among other techniques. Chemical reactions of clusters with surfaces can be studied by depositing the cluster onto different substrates. Clusters can be classified according to their chemical bonding. For example, in a van der Waals cluster, the induced dipole-dipole interaction is the force keeping the cluster together. The stability and structure of the cluster is driven by geometric packing effects leading to closed packages with 12 nearest neighbors. Group IV semiconductor clusters, especially C, Si, and Ge, are extensively investigated. Their bonding is covalent and the clusters are not closely packed. Instead, the coordination number is given by the number

270

SILICON-BASED NANOSTRUCTURES

of valence electrons or by the degree of hybridization. A prediction of the cluster structure is very difficult because of the spatially oriented bondings. Different hybridization of the valence orbitals leads to single, double, or triple bonding, forming carbon chains, rings, or nanotubes [134]. In semiconductors, II-VI and III-V compounds have been widely investigated [135, 136] and silver halides have been widely used in the photography industry [137]. Silicon nanoparticles are found to luminesce in the red and blue region of the visible spectrum when illuminated by ultraviolet radiation or when a current is passed through them [ 138, 139]. The origin of the red luminescence is generally accepted to be due to a quantum confinement shift of the bulk silicon band gap, whereas the blue emission is not yet fully understood. Since the discovery of porous Si [49] and the interpretation of its luminescence originating from quantum confinement in nanostructures, different methods have been used to synthesize nanostructures. In the reduction of SIC14, HSiC13, or octyl SIC13 by Na [140] in nonpolar organic solvents, the synthesis is performed at temperatures around 385 ~ at relatively high pressures of around 100 atm for several days. After cooling and washing out the Na, NaC1, and hydrocarbon residue, the product is dried in vacuum. Analysis mainly reveals single crystals of 5-3000 nm with a hydrogen-terminated surface. Using octyl SIC13, one can achieve a size distribution of only 2-9 nm. Other groups have separated nanocrystals from a porous Si sample [141-144]. Here the porous silicon layer on top of the single crystalline wafer is removed mechanically. After ultrasonic agitation within a solvent for several days, one gets a colloid with particles ranging from 1 to 10 nm and some agglomerates up to 50 nm. The disadvantage of this method is the lack of size control. Thermal evaporation [145] and decomposition of silanes have also been used to fabricate silicon nanoclusters [146-148]. Well-controlled silicon nanopowder with particle sizes varying between less than 10 and 200 nm can be synthesized from gas phase reactions in a radio frequency discharge in silane. The size of the particles can be controlled by the gas flow, gas composition, and plasma characteristics, as reported by Kobayashi et al. [149] and Yasuda [ 150]. Dutta et al. [ 151 ] have published a review article on this technique. In the following, we describe some of the recently reported techniques with a high potential for crystallite size control.

3.9.2. Silicon Nanocrystals Produced by a Laser Vaporization Technique Li et al. [152] have produced weblike aggregates of coalesced Si nanoparticles on glass through laser vaporization and subsequent controlled condensation. A pulsed Nd:YAG laser with 15-30 mJ/pulse and 10 -8 s pulses evaporates Si in a chamber consisting mainly of two metal plates facing each other at different temperatures. The chamber is filled with different carrier gases such as Ar. The temperature gradient between the two metal plates leads to a strong convection. Nucleation of the Si vapor leads to the growth of Si nanoparticles, which are driven to the cold plate by convection. The temperature gradient between the two plates controls the convection and the supersaturation of the Si vapor. High supersaturation leads to smaller nuclei, which are required for the condensation of nanoparticles. The convection drives away the small nanoparticles before they can grow further. Although SEM analysis revealed spherical particles of about 10 nm in diameter connected by a weblike structure with a wall thickness of 10-20 nm, the Raman shift suggested an average particle size of approximately 4 nm. X-ray powder diffraction of these samples revealed distinct Si(111), (220), and (311) reflections, but, as the powder sample was not rotated during the scan, a possible texturing of the nanoparticles cannot be ruled out. Fourier transform infrared (FTIR) spectroscopy indicated an oxidized surface layer after exposing the nanoparticles to air consisting of SiOx with x < 2. The thickness of this SiOx was estimated to be 1-2 nm. Annealing the particles at 300 ~ in air leads to x -- 2. The freshly deposited particles do not show any luminescence until they are exposed to

271

SIDIKI AND SOTOMAYOR TORRES

30000

xloo

~

h=x= 514.5nm

20000 400

500

10000

400

500

60.0

700

800

900

Wavelength ( n m ) Fig. 42. Photoluminescence spectrum of Si nanocrystals excited with 363.8- and 415.5-nm radiation. The inset shows the weak blue luminescence excited with a 363.8-nm wavelength similar to the luminescence of

SiO2 nanoparticles. (Source: Reprintedwith permissionfrom [152]. 9 1997 AmericanChemicalSociety.)

air and their surface is passivated by SiOx. The luminescence, which shows a peak in the red and a smaller one in the blue, was excited with 363.8- and the 514.5-nm laser lines, respectively. The quantum efficiency of the red line is about 1.3%. Based on a quantum confinement model [ 153], the authors concluded that the longer wavelength excitation selects the larger particle resulting in a stronger emission to the red. The inset of Figure 42 shows a weak blue emission at 450 nm using an excitation wavelength of 363.8 nm, which is quite similar to the emission of SiO2 nanoparticles and is related to the oxidized surface layer of Si nanoparticles [154]. Based on the results of the FTIR experiments and beating in mind the approximately 8-eV band gap of SIO2, this surface layer was said to be nonstoichiometric SiOx with x between 1.4 and 1.6, resulting in a band gap of around 3-4 eV, corresponding well to the blue emission [155]. Defects in SiO2 cannot be ruled out because they luminesce in the red and blue spectral regions [ 156]. In contrast to this, pure SiO2 does not show red luminescence. Its absorption spectra in the range of 200 to 800 nm suggest that the radiative transitions are indirect. From fitting the data with the relation (othv) 1/2 -- B ( h v - Eg), the authors obtained a band gap of 1.78 eV, corresponding well to the 700-nm red luminescence. The blue shift compared to the 1.1 eV of bulk Si is attributed to quantum confinement. The great potential of this technique lies in the good size control through a simple technique. Applications such as Si powders seem reasonable. However, for any device application, the integration into the Si circuit remains an open question. 3.9.3. S i / S i 0 2 / S i M u l t i l a y e r s

Abeles and Tiedje [ 157] demonstrated the first amorphous semiconductor/insulator superlattices. In contrast to porous silicon, these regular periodic structures do not show a size distribution and suffer minimal contamination effects. Growing Si nanostructures by MBE enables a detailed study of the correlation of luminescence properties to crystallinity, interface chemistry, and nanostructure size. The commonly used insulators are SIO2, CaF2, and A1203. Lockwood et al. [86, 158, 159] fabricated a number of Si/SiO2 superlattices with a silicon layer thickness d s i - - 1-30 nm. The samples were grown by solid-source MBE and

272

SILICON-BASED NANOSTRUCTURES

~

2.3

-I '

'

"

I

. . . .

I

. . . .

30

. . . .

'

I'

,

'1

,

,

'

I , ,

,

I,

1

(Si/Si02)6 295 K

20

v

2

~" ==

0.2

.~ .=15

o o3 ._=

'

I~ CBM

25

>~ 2.1

o

' ~ ' ' I ,

0.3

(Si/SiO2)e 295 K

,

2.2

I

0.1

>,

1.9

m

10

0

~0 1.8 Q.

0

C

-0.1

1.7 . . . .

1.6 1

t 1.5

. . . .

I

,

,

,

2

Si thickness

,

I 2.5

,

,

~ , |

0

-0.2

3

' ' 0

(nm)

tiV ,

2

,

,

I

4

,,

,

I

,

,

i

6

I

8

,

,

,

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10

Si thickness (nm)

Fig. 43. Photoluminescenceenergy (open circles) and integrated intensity (full circles) for different Si layer thicknesses (left) and shift of the conduction and valence band of Si/SiO2 superlattices at room temperature for different Si layerthicknesses. The solid line in both pictures is the best fit using effective mass theory. (Source: Reprinted with permission from [159]. 9 1996 AmericanPhysical Society.) characterized by Auger electron spectroscopy (AES), X-ray photoelectron spectroscopy (XPS), photoluminescence (PL), Raman scattering, soft X-ray Si-L2,3 near-edge absorption spectroscopy (XANES), TEM, and X-ray reflectivity. The density ratio of the amorphous Si layers to c-Si was found to be 0.97, indicating little film porosity and low contamination level. Visible-to-near-infrared PL was observed at 295 K in all superlattices with dsi < 3 nm, with the maximum of the emission peak at 665 nm (1.86 eV) with a full width at half-maximum (FWHM) of 0.38 eV. The dependence of the PL peak energy and intensity on dsi is shown on the left-hand side of Figure 43, indicating a clear blue shift with decreasing Si layer thickness. The PL signal is attributed to the Si layers as the SiO2 layer thickness remains constant. The blue shift and the increasing intensity with decreasing dsi indicates quantum confinement effects [57, 58]. Using effective mass theory together with the assumption of infinite potential barriers, this energy gap dependency on layer thickness is fitted to E--Eg+

2d 2

~+ me

(1)

where Eg is the bulk material energy gap and m e* and m h* are the electron and hole effective masses. The band edge Eg obtained from fitting is in good agreement with the bulk value for amorphous Si (1.5-1.6 eV at 295 K). To obtain the shift of the conduction and valence band, XANES and XPS measurements were performed. Figure 43 (fight) shows the conduction band minimum upshifted by approximately 0.3 eV and the valence band maximum downshifted by approximately 0.1 eV when the Si layer thickness is reduced to dsi - 1.5 nm. These results are consistent with the band gap shift obtained from PL experiments (Fig. 43, left) and for the first time demonstrate unambiguously quantum confinement and direct band-to-band transitions. Figure 44 shows a photo of the National Research Council logo made of a Si/SiO2 superlattice. To obtain the PL image, the mesa structure was excited from the back by a laser. The red luminescence is visible to the naked eye. The complete integrability with conventional silicon-based technology and the good size controllability makes this technique a strong candidate for the realization of a silicon-based light-emitting diode. Quantum

273

SIDIKI AND SOTOMAYOR TORRES

Fig. 44. Visiblephotoluminescence from a Si/SiO2 superlattice mesa structure excited from the back. (Source: Reprinted from [160]. 9 1996 American Institute of Physics.) efficiency values, not published up to now, would be very desirable to gauge the technological potential of Si/SiO2 superlattices.

3.9.4. NanocrystaUine Si/CaF2 Multilayers D'Avitaya et al. [161,162] have grown nanocrystalline Si/CaF2 multilayers with periods ranging from 50 to 100 by solid-source MBE at room temperature on CaF2 and Si(111) substrates. CaF2 was chosen as the barrier layers because of its large band gap of about 12 eV and its small lattice mismatch of 0.6% to Si. For a review of Si/CaF2 superlattices, see [ 163]. As the nanocrystallinity of the whole multilayer is driven by the ionic character of CaF2 and the low growth temperature, the authors expect no effect of the substrate. However, to date, there are no published results on the growth of nanocrystalline Si/CaF2 on technologically relevant Si(100) surfaces. Whereas the CaF2 layer thickness is kept constant at 3 nm, the Si layer thickness is varied between 0.3 and 5 nm. From extended X-ray absorption fine structure (EXAFS) experiments on Si(2 nm)/CaF2(3 nm) multilayers, the Si grain size of the multilayers could be determined to be smaller than 1.5 nm. Schuppler et al. [ 164] have reported the same upper limit for the grain size in porous Si also determined by EXAFS experiments. After allowing hydrogen and oxygen to passivate the dangling bonds of the Si nanostructures, intense PL was observed at room temperature, with a peak maximum at approximately 1.65 eV and an FWHM of approximately 0.4 eV, very similar to the observed spectra of porous Si. The luminescence could be observed only if the Si layer thickness was less than 2.5 nm, similar to the 3-nm-thick Si layer reported by Lockwood et al. [ 159] for Si/SiO2 multilayers. Thus, in combination with the observed blue shift as the Si layer thickness decreased, the authors attributed the luminescence to a quantum confinement effect. Optical absorption measurements made on the same structures gave a corresponding gap value of 2.4 eV. This energy difference between the absorption and emission was ascribed to the Stokes shift. Time-resolved photoluminescence experiments revealed a slow (t > 1 /zs) and a fast (t < 1 /zs) component [165]. These two emission bands, their lifetime, and their spectral positions are very similar to porous silicon, although the monotonic temperature dependence of PL intensity differs from that of porous silicon. Moreover, Vervoort et al. [ 165] have reported a significant increase of the PL intensity upon aging of the multiple quantum wells of Si/CaF2 in air, again an effect also observed in porous silicon. This effect was attributed to a possible oxygen saturation of Si dangling bonds migrating along the grain boundaries, which most likely led to the passivation of nonradiative centers. A mesa light-emitting diode was fabricated with a transparent indium tin oxide (ITO) ohmic contact. Under forward bias (7-8 V), room temperature EL was observed. It was

274

SILICON-BASED NANOSTRUCTURES

also reported that ITO deposition has a strong effect on the luminescence. First, the PL peak position is shifted to lower energies, then the line width decreases to 100 nm, and, finally, the luminescence intensity is higher by a factor of 3. These effects are attributed to the absorption of oxygen out of the ITO layer, which modifies the surface passivation and also affects the size of the Si crystallites. This could correspond to the reported aging effect. In the case of EL, the authors attribute the excitation to tunneling of carriers through the dielectric under the high applied electric field. Bassani et al. [166] have reported a more pronounced blue shift of the optical absorption edge with decreasing Si layer thickness, adding support to the interpretation of the emission being determined by quantum confinement of carriers within Si nanocrystallites. The CaF2 thickness for all these samples is kept constant. Nevertheless, the nanocrystalline Si layers are assumed to have an indirect band gap. From Tauc's relationship ( o t h v ) 1/2 = B ( h v - Eg), the optical pseudogap could be obtained by extrapolating the experimental data to ot = 0. The dependence of the optical band gap on the Si layer thickness is consistent within the effective mass theory. The huge Stokes shift of 1 eV observed for the thinnest Si layer (1.2 nm) was attributed to relaxation of the Si atoms near the surface forming a deep luminescent center. Numerical simulations by Allan et al. [167] and Baierle et al. [ 168] have predicted a Stokes shift of approximately 1 eV for crystalline diameters of 1.5 nm, which agrees well with that reported by Bassani et al. [ 166]. The smaller blue shift of photoluminescence compared to the absorption spectrum was related to nearsurface localized states, which are less influenced by the silicon grain sizes [166]. However, quantum confinement remains a necessary condition for luminescence. Borisenko et al. [ 169] have used an improved self-consistent linear combination of atomic orbitals (LCAO) method with the extended Huckel Hamiltonian to calculate the electronic band structure of nanometer-thick (111) monocrystalline and nanocrystalline freestanding silicon films. These structures are very similar to the Si/CaF2 system. The Si dangling bonds are passivated by hydrogen. Figure 45 shows the evolution from a monocrystalline film to a "pseudofilm" and finally to a "pseudowire" and a "pseudodot" structure. On the right-hand side of Figure 45, the corresponding electronic band structure is depicted, showing the transition from an indirect to direct band gap resulting from silicon grains being formed. The calculated band gap of 2.07 eV of the "pseudodot" grain can be considered as a lower limit. For an isolated grain, the calculated band gap is 4.61 eV, which can be considered as an upper limit. Thus, the value of 2.4 eV for the gap in Si/CaF2 multiple quantum wells with grain size in the range of 0.5 to 1.5 nm would fall within the likely band gap energies in this material.

3.10. Si/III-V Light-Emitting Nanotips So far, the route favored by industry to solve temporarily the electrical wire bottleneck is to combine III-V direct band gap materials with indirect band gap silicon complementary metal on silicon (CMOS) platforms. This approach explores the excellent optical properties of III-V compounds and combines them with the existing technology of the silicon microelectronics industry. There are essentially two different ways to realize a hybrid Si/III-V device. The first is to grow directly GaAs or GaAs-based structures on Si. The second is to fabricate first the Ill-V-based optoelectronic circuit and to mount it by wafer bonding, fusion, epitaxial liftoff, or flip-chip bonding on the Si wafer. The first approach faces three different fundamental challenges [3]: 1. The high lattice mismatch of 3.88% between GaAs and Si leads to a high density of misfit dislocations and to relaxed GaAs layers. 2. There is also a polar-nonpolar surface mismatch. Whereas III-V compounds are polar, different sides of the nonpolar silicon crystal cannot be distinguished. This

275

SIDIKI AND SOTOMAYOR TORRES

3-

~-

"

(a)

~ K

r

M

K

r

M

3

(b)

. . . .

K

3

~"rr

r

-

M

-

(d)

.

K

F

M

Fig. 45. The evolution from a monocrystalline film (a) to a pseudodot structure (d) is shown on the lefthand side. The corresponding electronic band structure is shown on the right-hand side. The small circles represent H atoms; the large circles represent Si atoms. The unit cell is denoted by a dotted line. (Source: Reprinted from [169]. 9 1997 American Institute of Physics.)

mismatch leads to the growth of antiphase boundaries, as there are always atomic steps on the silicon wafer. Thus, during growth, a phase difference occurs in the stacking of GaAs between domains on opposite sites of the silicon steps, leading to G a - G a and A s - A s bonds at the so-called antiphase boundary in contrast to the G a - A s bonds. 3. Finally, there is the problem of charging of the interface. An interface that is abruptly terminated between a polar and a nonpolar semiconductor results in a heavily charged plane modifying strongly the electronic characteristics of a device. There are several groups exploring these two approaches and the reader is referred to [170-174] for recent progress in this area. One novel approach, though not specific for optical interconnects, has been proposed by Shealy et al. [175], who selectively grew a III-V alloy (GalnP) by organometallic vapor phase epitaxy on sharp silicon tips. As the thin tip behaves as a compliant substrate, the creation of misfit dislocations can be avoided as the authors showed by photoluminescence studies. The basic idea was to fabricate fieldemitting devices for high-resolution-color flat panels without the need of phosphorous

276

SILICON-BASED NANOSTRUCTURES

Fig. 46. Schematics of the fabrication process of a single pixel of Si-GalnP field-emitting tip proposed for flat panel display. (Source: Reprinted with permission from [175]. 9 1997 American Institute of Physics.)

Fig. 47. SEM micrographs of submicrometer silicon tips coated by GaInP after (a) 1 min, (b) 3 min, and (c) 5 min. At the beginning, growth takes place only on top of the tip, but, at longer deposition times, material is also deposited in between the tips. (Source: Reprinted with permission from [175]. 9 1997 American Institute of Physics.)

screens and vacuum conditions. The silicon tip can thus directly field emit electrons into the conduction band of the direct band gap material. Figure 46 shows schematically the pixel fabrication process. More details on the fabrication of the silicon tips with an onset voltage of 30 V for field emission into a vacuum are given elsewhere [ 176, 177]. It is important to cover all the bare silicon surrounding the sharp tips with Si3N4 to avoid nucleation of the III-V material. After growth of the direct gap material, the metallization is performed to connect each single pixel of the array. Fabrication of silicon field emission arrays proceeded by selective lateral thermal oxidation, which is described in more detail in [ 177]. A tip-to-tip distance of 3 / z m for the tips with a radius of curvature of 10-20 nm was thus achieved. Figure 47 shows an SEM micrograph of a silicon tip after different GalnP coating times. Photoluminescence in the visible consisted of single-peak spectra and a peak shift to higher wavelengths as compared to a GalnP reference layer grown on GaAs, indicating at least different alloy composition. Other effects may also contribute to this red shift. Both photoluminescence and cathodoluminescence images showed luminescence from the area between the tips for longer deposition times, probably coming from III-V material deposited between the tips as shown in the SEM micrographs. Thus, short deposition times, of around 1 min, have to be chosen to realize spatially well-defined tip luminescence. As the widths of the cathodoluminescence image have nearly the same dimensions as the SEM features, the authors excluded surface recombination processes.

277

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4. SINGLE-ELECTRON ELECTRONICS An electrically isolated nanostructure, such as a quantum dot, can be charged by electrons tunneling into the dot, which then become localized if the tunnel resistance is larger than the resistance quantum hie 2 and if the energy level separation e2/2C within the dot is bigger than the thermal energy k T [178]. The second condition requires nanostructures less than or equal to 5 nm to reduce the total capacitance C of the island if Coulomb blockade effects are to be observed at room temperature. The charging energy e2/2C blocks further electrons from tunneling into the dot until the applied voltage exceeds the critical value e/2C and the energy is higher than the next energy level in the dot. Thus, between - e / 2 C and +e/2C, the energy level separation of e2/2C within the dot blocks any carrier transport and steplike I-V characteristics are obtained. Extending the device structure to a single-electron transistor (SET) by applying a gate voltage V to the dot via a capacitance C to modulate the field leads to oscillations of the current through the dot as a function of the applied gate voltage. Thus, if CV/e = n is an integer value, the current is blocked. For CV/e + 89- n, the current can flow through the dot [178]. Silicon-based SETs are regarded as particularly important because of their potential role in future electronic circuits. Single-electron electronics based on silicon-on-insulator (SO1) SETs have been discussed first by Ali and Ahmed [ 179] and Takahashi et al. [ 180]. Kurihara et al. [ 181 ] reduced the size of the islands to obtain Coulomb oscillations at nearly room temperature. Yano et al. [182] used a thin polysilicon film with small islands and demonstrated a room temperature operating single-electron memory device. Carrier transport through double-barrier structures has been demonstrated with SiO2 barriers and well layers of amorphous Si [ 183], single-crystalline Si [ 184], microcrystalline Si [ 185, 186], and polycrystalline Si [187]. However, evidence of room temperature Coulomb blockade was not given in these tunneling studies. Matsumoto et al. [188] used scanning tunneling microscopy (STM) lithography to fabricate a room temperature operating SET with a Coulomb staircase of approximately 150 mV. The width of the 30-50-nm-long TiOx lines was 15-25 nm. The island size was 30-50 • 30-50 nm 2. The relevant tunnel junction area was only 2-3 nm (the thickness of the Ti film) • 30-50 nm (the length of the TiOx line). For such small sizes, the tunnel capacitance is about 10 -19 F, which enables room temperature operation of SETs with well-defined size. Possible applications of SETs, such as very accurate current standards, sensitive electrometers [ 189], and single-electron memories [ 190, 191 ], have been demonstrated. For a detailed review of single-electron devices, we refer to the chapter by Chou on quantum dot transistors and memories in this book. Eisele et al. [129] realized the use of Si wires and dots grown through micro shadow masks (see Section 3.8) for field-effect-controlled one- and zero-dimensional electronic confinement. Figure 48 shows the schematics of a MOS device on a nonplanar silicon surface. No dry etching is used in this process. The (111) faceted silicon side walls are formed by a selfassembling process. In this structure, the nonplanar surface regions exhibit different threshold voltages for inversion, where the surface potential is larger than the difference between the intrinsic semiconductor Fermi level Ei and the gate material Fermi level. By solving Poisson's equation numerically for p-type silicon, the authors showed that the surface potential is lowered at convex edges, thus forming a quasi-one-dimensional wire before the side walls start to invert. Eisele et al. [ 1129] fabricated vertical MOS transistors with 85-nm channel lengths but different planar geometries as shown in the inset of Figure 49. Thus, they realized two or four edges within the width of the transistor. Figure 49 shows the conductance against applied gate voltage for both transistors. Although the wide transistor (W = 80 lzm) shows a steplike behavior, it is not possible to resolve the structures because of the relatively large subthreshold current. Decreasing the width to 9 # m results in smaller

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SILICON-BASED NANOSTRUCTURES

Fig. 48. Schematicalcross section of the self-assembledgrowth mechanism on a nonplanar surface for 1D and 0D silicon devices. (Source: Reprinted from [129], with permissionfrom Elsevier Science.)

Fig. 49. Conductanceversus varying gate voltage for two different gate configurations (W = 80 #m and W = 9/zm). The temperature dependence is related to the narrow device. The applied source-drain voltage was 4 meV. (Source: Reprinted from [129], with permission from Elsevier Science.)

parasitic 2D current, allowing resolution of these conductance oscillations, which are not observed for transistors without edges. The authors explained the observed steplike conductance as arising from the 1D subband crossing of the Fermi level with increasing gate voltage. The mobility near the subband edges is reduced because of carrier intersubband scattering into the next subband. From the presence of the oscillations up to about 80 K, the authors deduced an energy level separation corresponding to k T of 6 meV. Coulomb staircases in the I - V characteristics [192] and Coulomb blockade effects [193, 194] were observed at room temperature owing to the strong confinement in silicon quantum dots. Fukuda et al. [193] fabricated self-assembled Si quantum dots by LPCVD on native and thermally grown SiO2 that had been etched back to a thickness of 1 nm. The height and diameter of the dots varied between 1.5 to 8 nm and 10 to 20 nm, respectively. A top barrier layer of 1 nm thickness was achieved by the same means. The I - V characteristics were measured on a single dot using AFM with a conductive cantilever. The dots had a height of 2.7 and 2.8 nm. The I - V characteristics were also simulated using the well-known transfer matrix approach [ 102, 195]. Some clear discrepancies were attributed to a possible leakage current through the SiO2 barrier and to Si/SiO2 interface states and traps, which smear out the resonance current. As a quantum dot is a three-dimensional confined electronic system, its discrete energy spectrum potentially permits the storage of single electrons. Nakajima et al. [194, 196]

279

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Fig. 50. Drain current versus gate voltage of a single-electron tunneling transistor at (a) room temperature (VDs = 500 mV), (b) room temperature and 77 K with transconductance versus gate voltage (VDs = 500 /zV), and (c) 4.2 K with down sweeps represented by the dotted line. The Coulomb oscillation peaks are denoted by the arrows. (Source: Reprinted from [194]. 9 1997 American Institute of Physics.)

realized a Si single-electron tunneling transistor with a nanoscale floating dot stacked on a Coulomb island by a self-aligned process as a possible electron memory device. The control gate consisted of polysilicon. The Coulomb island had a width of about 40-50 nm and a length of 50-60 nm. The floating dot on top of the Coulomb island had a side length of about 20-30 nm. Figure 50 shows the drain current versus the control gate voltage at 4.2 K, 77 K, and room temperature. The drain current exhibits oscillations, denoted by the arrows, because of the Coulomb blockade effect. Sweeping the voltage up and down in parts a and c of Figure 50, denoted by the dotted line for down sweeping, leads to a hysteresis effect. The oscillations in the drain current do not occur at the same voltages. Nakajima et al. [ 194, 196] demonstrated the Coulomb blockade effect via tunneling of a single electron from the channel to the floating dot gate. If one can control the device design such that the drain current change from a valley to a peak is influenced by only a single electron, this device could be used to detect single electrons and, because of the hysteresis effect in the I - V characteristics, as an ultralow-power-consumption memory. Guo et al. [ 197-199] fabricated a silicon SET memory that operates at room temperature and is suitable for ultralarge-scale integration (ULSI). A conventional floating-gate MOS memory was scaled down in order to realize a single-electron MOS memory (SEMM).

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SILICON-BASED NANOSTRUCTURES

Fig. 51. Schematic drawing of a single-electron MOS memory using single-electron charging of a polysilicon nanodot to switch the gate threshold. (Source: Reprinted from [197]. 9 1997 American Institute of Physics.)

However, the channel width was narrower than the Debye screening length of a single electron and the floating gate was a nanoscale square dot. Figure 51 shows a schematic view of this SEMM. As a floating gate, Guo et al. deposited an 11-nm-thick polysilicon film on top of the 35-nm-thick crystalline silicon layer of the SO1 wafer. In between the crystalline silicon and the polysilicon, there was an approximately 1-nm-thick native oxide layer. No additional tunnel oxide was formed to enable fast charging of the dot through the channel. Furthermore, the number of electrons stored on the dot was regulated by the Coulomb blockade mechanism, as the potential difference between the channel and the dot is minimized for a given charging voltage. In a two-level step using electron beam lithography and reactive ion etching, the widths of the floating gate and the silicon channel were patterned first; then patterning in the perpendicular direction was carried out to form the squarelike polysilicon dot. For the smallest device, the width of the channel was roughly estimated at approximately 10 nm. The approximately 7-nm • 7-nm square dot had a height of about 2 nm. To determine the electrical properties of the smallest device, a source-drain voltage of 50 meV was applied. Despite a continuous charging voltage, the threshold voltage of the device made discrete shifts of 55 meV, corresponding to a charging voltage interval of approximately 4 V. Because of the very thin native oxide in between the channel and the floating dot, the charge could be stored for about 5 s after setting the gate potential to ground. This shifted the threshold voltage to its original value. The calculated capacitance for an approximately 7-nm • 7-nm square dot is about 4.4 • 10 -20 F, giving a singleelectron charging voltage of 3.6 V, which corresponds well to the experimental value of about 4 V. The shift of the threshold voltage was estimated from the single-electron Debye screen length (~70 nm) and the channel thickness (~26 nm) to be approximately 64 meV, also corresponding well with the experimental value of 55 meV. For single-electron computing, many interesting circuits have been proposed setting up Boolean logic circuits using Coulomb interactions between bistable charge polarization states [200, 201]. The main drawback of most of the proposed schemes is the missing isolation between the input and output terminals so that the input can thus drive the output but not vice versa. As the Coulomb interaction between two identical charge polarizations is reciprocal, the output can also drive the input, violating the necessity of unidirectionality and thus leading to the so-called "catastrophic failure" [202, 203]. To realize von Neumann computing architectures, proposals for dissipationless computing [204] have been made. The drawback of this scheme is the fault tolerance. Bandyopadhyay and Roychowdhury [203,205,206] have proposed a nanoelectronic architecture to overcome these drawbacks. However, it is still too early to comment on the chances of success of any given approach for logic operations.

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SIDIKI AND SOTOMAYORTORRES

5. TIPS FOR ATOMIC FORCE MICROSCOPY AND FIELD EMISSION

The displacement of single atoms on a surface is already possible using scanning probe techniques allowing, for example, new molecular arrangements to be realized for a variety of purposes. Some of these include integrated microscopic gears, pumps, motors, membranes, and nanotweezers. Whereas silicon-based microelectronic devices switch electron fluxes through thin metallic wires, micromechanical devices could establish the contact between microelectronics and the physical world. Because of the predominance of siliconbased microelectronics, this material is favored in micromechanics research and development. For a comprehensive overview, we refer the reader to Scientific American, Special

Dossier: Microsystem Technology 1996. Silicon is also the favored material for cold field emitter devices for nanolithography and for flat panel devices. Recent studies [207-210] have shown that miniaturization of the electron beam column leads to a well-focused and bright electron beam source. Such microcolumns can be used for scanning electron microscopy and electron beam lithography with high resolution [210, 211]. The main disadvantage of electron beam lithography having a low throughput could potentially be overcome, using arrays of electron beam microcolumns. The tip sharpness, gate diameter, and gate-to-tip distance influence the turn-on voltage and the emission current of field emission devices. Thus, very sharp tips with a small gate diameter and a small gate-tip distance are desired. Rakhshandehroo and Pang [212] have fabricated 100 single Si tip arrays with a spacing o f l / z m . Using dry etching and low-temperature plasma oxidation led to a sharpening of the tips with radius from 67 down to 8 nm, leading, in turn, to a lower turn-on voltage and to a higher emission current because of the higher electric field at the tip apex. To reduce further the voltage applied to the anode, Jung et al. [213] fabricated nanosize Si tips with a tip diameter smaller than 20 nm. After reactive ion etching, a tip radius of about 300 nm was determined. To sharpen the tip to 20 nm, a low-temperature oxidation at 900 ~ with a subsequent dip in BHF was carried out. Low-temperature oxidation leads to an enhanced oxide growth in the regions with high curvature. The diameter of the tip was reduced in this fashion to less than 20 nm. A 30-nm amorphous hydrogen free diamondlike carbon (DLC) film was deposited on top of this structure by PECVD. The film is composed of a diamond-like sp 3 and a graphite-like sp 2 phase. The emission current of the DLC film is twice as high as the pure Si tip, and the onset of the field emission is shifted to smaller voltages from 700 to 600 V. At higher voltages, the emission current of the pure Si tip was zero because of deterioration, whereas the DLCcoated tip exhibited an emission current of approximately 100/zA at 1.5 kV. Figure 52 shows a silicon tip with a silicon cantilever used in atomic force microscopy (AFM) fabricated by Dr. O. Wolter GmbH in Germany. The pyramidal tip points to the (100) direction. The tips have a radius less than or equal to 15 nm and are 10-15/zm high. The thickness of the cantilever with a trapezoidal cross section ranges from 0.3 to 8, 20, 60, 125, and 450/zm, depending on the specific applications. A sharp tip of 2 nm radius has been achieved (see the fight-hand side of Fig. 52). The half cone angle is better than 10 ~ at the last 200 nm of the tip and its mechanical robustness permits fast scan rates. The ability to control single atoms could potentially enable the storage of 1012 GB/cm 2 on a silicon chip. Such a data storage system would beat all conventional systems because of its increased capacity and lack of movable parts such as a rotating disk. MacDonald et al. [214] have fabricated an STM tip with a diameter of 20 nm mounted on a floating frame with four motors, each 400/zm in diameter. These motors can pull or push the tip vertically and horizontally up to one million times per second and even tilting of the tip is possible. With a matrix of several hundred tips, a direct surface structuring in a parallel and thus a very fast process could be realized.

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Fig. 52. Silicontip together with a monolithic cantilever used in atomic force microscopy (left). Supersharp silicon tip for high-resolution imaging of nanostructures and microroughness. The tip radius is only 2 nm (right). (Source: Reprinted with permission from NANOSENSORS.)

The use of Si tips in scanning probe-based lithography is increasing fast although formally still an the laboratory scale. Madsen et al. [215] wrote patterns with feature sizes down to 50 nm with a scanning near-field optical microscope (SNOM) using Al-coated fiber probes. Nagahara et al. [216] used the tip to expose a resist to extremely low energy electrons. Minne et al. [217] used a mix-and-match lithography to fabricate a metal oxide semiconductor field effect transistor (MOSFET). The electrodes at the gate were defined by atomic force microscopy (AFM), whereas the remaining levels were defined by optical lithography. Line widths between 60 and 700 nm were achieved. Abeln et al. [218] used STM lithography to fabricate structures smaller than 10 nm. Using STM, Matsumoto et al. [188] fabricated an SET with line widths of 15-25 nm. Field-enhanced oxidation as a lithographic tool was first introduced by Dagata et al. [219]. They used a 5-10-V negatively charged STM tip under ambient air conditions. The huge electric field beneath the tip selectively desorbs passivating hydrogen atoms and molecules from the silicon surface, allowing bare silicon to oxidize under the influence of ambient air in the presence of huge fields generated at the tip. Lyding et al. [220] wrote 1.5-nm line widths in an UHV system pushing the resolution of this approach. During pattern transfer, by wet or dry etching, a high etch selectivity is essential as the oxide thickness is less than 5 nm. In many cases, AFM tips consist of Si3N4 coated with a thin layer such as Ti to lengthen its lifetime. Birkelung et al. [221] have used Ni tips coated with a 5-nm Ti adhesion layer and a 100-nm Au cap layer as a plating base between the Ni and Si. They achieved 80-nm line widths writing over 1000 lines before the tip degraded. The partial Au deposition during the first few scans onto the surface had to be removed by etching. Snow et al. [222] used AFM for local oxidation and subsequent RIE to fabricate approximately 10-nm-wide lines with a height of 30 nm. They used an n-type Si wafer hydrogen passivated in 10% aqueous solution after ozone treatment. Using a Si3N4 AFM tip coated with 30-nm Ti, they oxidized locally the Si surface by applying a negative voltage between 4 and 7 V under a scanning speed of 1-10/zm/s. To obtain fine patterns, they worked with low voltages and used slow scanning speeds. The ambient humidity was kept constant to 50% as this is a key process parameter. The addition of oxygen has been found to increase the etch selectivity to more than 20. Figure 53 shows an AFM image of several lines of varying width after dry etching to a depth of 30 nm. The two lines marked by arrows in Figure 53 have a width between 25 to 30 nm (fight) and 35 and 40 nm (left), respectively. Subtracting the convolution with the 20-nm tip diameter, a real line width for the smallest line of less than 10 nm is obtained.

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Fig. 53. AFM image of dry-etched Si nanowires of varying width etched to a depth of 30 nm. The arrows indicate two lines with widths between 25-30 nm and 35-40 nm. The real line widths are about 20 nm less because of a convolution effect with the tip diameter of the AFM. (Source: Reprinted from [222]. 9 1995 American Institute of Physics.)

Snow et al. [223] demonstrated the use of silicon as a resist material for patterning GaAs using scanning probe lithography. Thus, combining this technique with an UHV system, true nanostructures may be realized in Si as well as in III-V wafers.

6. C O N C L U S I O N S We have attempted to provide an overview concerning recent developments involving silicon-based nanostructures. It is almost certain we have not done justice to the many scientists and engineers who have contributed to the field. This is mainly a representive list of examples determined by the usual constraints of space, time, and energy. In the quest to realize a variety of nanostructures using silicon and silicon-related semiconductors, the trend to miniaturization in electronics plays an overwhelming role. To some degree, this places an enormous buxden on other developments that could potentially make use of nanostructures for other applications. The range of other applications comes under the umbrella of nanotechnology as demonstrated by the work on nanotips. It is clear that extension of the use of Si nanostructures into the biological and environmental areas has begun; however, this has not been touched upon here. The scientific and technological challenges are still formidable and there are no clear winners yet in, for example, a siliconbased light emitter suitable for optical interconnects. Our understanding is still too incomplete and we continue to learn about the impact of the local environment, in the nanometer scale, of optically active centers in silicon. On the other hand, the wealth of technological expertise developed collectively in silicon electronics ensures that any relevant scientific development in this area, which survives the acid test of industrial suitability and device specifications, could be made available to potential users because the connections to the outside world are provided by existing input and output Si-based circuitry and technology. Whereas this may well be the case in sensors and optical devices, there are significant challenges remaining in the area of quantum nanoscale electronic circuits, which is bound to keep the Si nanoelectronics community very active for years to come.

Acknowledgments We are indebted to the many authors and colleagues who kindly provided us with photos and figures of their work as well as authors who gave permission to reproduce their published figures. Of course, any misinterpretation is our sole responsibility. The dry-etched

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S i - S i G e dot w o r k r e v i e w e d here was m o s t l y carried while one of the authors ( C M S T ) was at the University of G l a s g o w jointly with Y.-S. Tang and C. D. W. W i l k i n s o n and G. V. H a n s s o n and W.-X. Ni of L i n k 6 p i n g University. S a m p l e s for the w o r k at G l a s g o w University w e r e also kindly p r o v i d e d by E. H. C. Parker of W a r w i c k University and H. Presting of D a i m l e r - B e n z R e s e a r c h L a b o r a t o r i e s in Ulm. The m o r e recent w o r k on d e e p - e t c h e d S i - S i G e dots has b e e n s u p p o r t e d by the E u r o p e a n C o m m i s s i o n E S P R I T Project 2 2 6 4 4 S I B L E . We t h a n k T. M a k a , T. K 6 p k e and our c o l l e a g u e s for their help with the preparation of this chapter. This w o r k was partially s u p p o r t e d by the University of Wuppertal.

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174. J. Liang, R Li, Y. Gao, and J. Zhao, J. Mater. Sci. 32, 4377 (1997). 175. J.R. Shealy, N. C. Macdonald, Y. Xu, K. L. Whittingham, D. T. Emerson, and B. L. Pitts, Appl. Phys. Lett. 70, 3458 (1997). 176. Z.L. Zhang and N. C. Macdonald, J. Vac. Sci. Technol., B 11,437 (1993). 177. J. E Spallas, J. H. Das, and N. C. Macdonald, J. Vac. Sci. Technol., B 11, 2538 (1993). 178. H. Ahmed, J. Vac. Sci. Technol., B 15, 2101 (1997). 179. D. Ali and H. Ahmed, Appl. Phys. Lett. 64, 2119 (1994). 180. Y. Takahashi, M. Nagase, H. Namatsu, K. Kurihara, K. Iwdate, Y. Nakajima, S. Horiguchi, K. Murase, and M. Tabe, Electron. Lett. 31,136 (1995). 181. K. Kurihara, H. Namatsu, M. Nagase, and T. Takino, Microelectron. Eng. 35, 261 (1997). 182. K. Yano, T. Ishii, T. Hashimoto, T. Kobayashi, E Murai, and K. Seki, Techn. Digest Int. Electron Device Meeting 541 (1993). 183. A.C. Seabaugh, C.-C. Cho, R. M. Steinhoff, T. S. Moise, S. Tang, R. M. Wallace, E. A. Beam, and Y.-C. Kao, in "2nd International Workshop on Quantum Functional Devices," Tokyo, 1995, p. 32. 184. K. Yuki, Y. Hirai, K. Morimoto, K. Inouse, M. Niwa, and J. Yasui, Jpn. J. Appl. Phys. 34, 860 (1995). 185. S.Y. Chou and A. E. Gordon, Appl. Phys. Lett. 60, 1827 (1992). 186. Q. Ye, R. Tsu, and E. H. Nicollian, Phys. Rev. B 44, 1806 (1991). 187. M. Hirose, M. Morita, and Y. Osaka, Jpn. J. Appl. Phys. 16, 561 (1977). 188. K. Matsumoto, M. Ishii, K. Segawa, Y. Oka, B. J. Vartanian, and J. S. Harris, Appl. Phys. Lett. 68, 34 (1996). 189. L.J. Geerlings, V. E Anderegg, E A. M. Holweg, J. E. Mooij, H. Pothier, D. Esteve, C. Urbina, and M. H. Devoret, Phys. Rev. Lett. 64, 2691 (1990). 190. K. Nakazato, R. J. BlaiNe, J. R. A. Cleaver, and H. Ahmed, Electron. Lett. 29, 384 (1993). 191. K. Yano, T. Ishii, T. Hashimoto, T. Kobayashi, E Murai, and K. Seki, IEEE Trans. Electron Devices ED4, 1628 (1994). 192. A. Dutta, M. Kimura, Y. Honda, M. Otobe, A. Itoh, and S. Oda, Jpn. J. Appl. Phys. 36, 4038 (1997). 193. M. Fukuda, K. Nakagawa, S. Miyazaki, and M. Hirose, Appl. Phys. Lett. 70, 2291 (1997). 194. A. Nakajima, T. Futatsugi, K. Kosemura, T. Fukano, and N. Yokoyama, AppI. Phys. Lett. 71,353 (1997). 195. R. Tsu and L. Esald, Appl. Phys. Lett. 22, 562 (1973). 196. A. Nakajima, T. Futatsugi, K. Kosemura, T. Fukano, and N. Yokoyama, Appl. Phys. Lett. 70, 1742 (1997). 197. L. Guo, E. Leobandung and S. Y. Chou, Appl. Phys. Lett. 70, 850 (1997). 198. L. Guo, E. Leobandung, L. Zhuang, and S. Y. Chou, J. Vac. Sci. Technol., B 15, 2840 (1997). 199. L. Guo, E. Leobandung, and S. Y. Chou, Science 275, 649 (1997). 200. C. S. Lent, E D. Tougaw, W. Porod, and G. H. Bemstein, Nanotechnology 4, 49 (1993). 201. T. Tanamoto, R. Katoh, and Y. Naruse, Jpn. J. Appl. Phys. 33, 1502 (1994). 202 A.N. Korotkov, Appl. Phys. Lett. 67, 2412 (1995). 203 S. Bandyopadhyay, B. Das, and A. E. Miller, Nanotechnology 5, 113 (1994). 204 S. Lloyd, Science 261, 1569 (1993). 205 S. Bandyopadhyay and V. Roychowdhury, Phys. Low Dimension. Syst. 8/9, 29 (1995). 206 S. Bandyopadhyay and V. Roychowdhury, Jpn. J. AppL Phys. 35, 3350 (1996). 207 T.H. E Chang, L. E Muray, U. Staufer, and D. E Kem, Jpn. J. Appl. Phys. 31, 4232 (1992). 208. T.H. E Chang, D. E Kem, and L. E Muray, J. Vac. Sci. Technol., B 6, 2743 (1992). 209. J.Y. Park, H. J. Choi, Y. Lee, S. Kang, K. Chun, S. W. Park, and Y. Kuk, J. Phys. IV C5, 258 (1996). 210. J.Y. Park, H. J. Choi, Y. Lee, S. Kang, K. Chun, S. W. Park, and Y. Kuk, J. Vac. Sci. Technol., A 15, 1499 (1997). 211. T. H. E Chang, M. G. R. Thomson, E. Kratschmer, H. S. Kim, M. L. Yu, K. Y. Lee, S. A. Rishton, and B. W. Hussey, J. Vac. Sci. Technol., B 14, 3774 (1996). 212. M.R. Rakhshandehroo and S. W. Pang, J. Vac. Sci. Technol., B 15, 2777 (1997). 213. M.-Y. Jung, D. W. Kim, S. S. Choi, Y.-S. Kim, Y. Kuk, K. C. Park, and J. Jang, Thin Solid Films 294, 157 (1997). 214. G. Stix, Scientific American 77 (February 1995). 215. S. Madsen, S. I. Bozhevolvyi, K. Birkelund, M. Mtillenbom, J. M. Hvam, and E Grey, J. Appl. Phys. 82, 493 (1997). 216. L.A. Nagahara, E I. Oden, A. Majumdar, J. E Carrejo, J. Graham, and K. Alexander, Proc. SPIE 1639, 171 (1992). 217. S.C. Minne, H. T. Sob, E Flueckiger, and C. EQuate, Appl. Phys. Lett. 66, 703 (1995). 218. G.C. Abeln, T. C. Shen, J. R. Tucker, and J. W. Lyding, Microelectron. Eng. 27, 23 (1995). 219. J.A. Dagata, J. Scheir, H. H. Harary, C. J. Evans, M. T. Postek, and J. Bennett, Appl. Phys. Lett. 56, 2001 (1990). 220. J.W. Lyding, T.-C. Shen, J. S. Hubacek, T. R. Tucker, and G. C. Abeln, Appl. Phys. Lett. 64, 2010 (1994). 221. K. Birkelung, E. V. Thomsen, J. E Rasmussen, O. Hansen, E T. Tang, E Mr and E Grey, J. Vac. Sci. Technol., B 15, 2912 (1997). 222. E. S. Snow, W. H. Juan, S. W. Pang, and E M. Campbell, Appl. Phys. Lett. 66, 1729 (1995). 223. E.S. Snow, E M. Campbell, and B. V. Shanabrook, Appl. Phys. Lett. 63, 3488 (1993).

289

Chapter 6 SEMICONDUCTOR NANOPARTICLES Prashant V. Kamat Notre Dame Radiation Laboratory, Notre Dame, Indiana, USA

Kei Murakoshi, Yuji Wada, Shizo Yanagida Chemical Process Engineering, Faculty of Engineering, Osaka University, Suita, Osaka, Japan

Contents I. 2.

3.

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Preparation and Characterization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1. Size Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2. Crystalline Phase Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3. Size Quantization Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4. Nonlinear Optical Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5. Emission Characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.6. Trapping of Charge Carriers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Inteffacial Charge Transfer Processes in Colloidal Semiconductor Systems . . . . . . . . . . . . . . . 3.1. Reductive Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2. Oxidative Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3. Kinetics of Inteffacial Electron Transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Photocatalytic Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1. Organic Synthesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2. Fixation of Carbon Dioxide into Organic Compounds . . . . . . . . . . . . . . . . . . . . . . . . 4.3. Reduction of Nitrogen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4. Decomposition of Nitrogen Oxides and Their Anions . . . . . . . . . . . . . . . . . . . . . . . . 4.5. Photocatalytic Degradation of Organic Contaminants . . . . . . . . . . . . . . . . . . . . . . . . Surface Modification of Semiconductor Colloids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1. Deposition of Metals on Semiconductors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2. Capping with Organic and Inorganic Molecules . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3. Surface Modification with Sensitizing Dyes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4. Ultrafast Charge Injection into Semiconductor Nanocrystallites . . . . . . . . . . . . . . . . . . 5.5. Designing Multicomponent Semiconductor Systems . . . . . . . . . . . . . . . . . . . . . . . . Ordered Nanostructures using Semiconductor Nanocrystallites and Their Functionality . . . . . . . . . 6. I. Preparation and Characterization of Nanostructured Semiconductor Films . . . . . . . . . . . . 6.2. Electron Storage and Photo- and Electrochromic Effects . . . . . . . . . . . . . . . . . . . . . . 6.3. As a Photosensitive Electrode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.4. Sensitization of Large-Band-Gap Semiconductors . . . . . . . . . . . . . . . . . . . . . . . . . . 6.5. Single-Electron Tunneling Devices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

292 293 293 294 296 297 297 298 299 300 300 301 303 304 304 308 308 308 309 309 310 312 314 315 318 319 322 323 325 327 329 329 329

Handbook of Nanostructured Materials and Nanotechnology, edited by H.S. Nalwa Volume3: Elec~ical Properties Copyright 9 2000 by Academic Press All rights of reproduction in any form reserved.

ISBN 0-12-513763-X/$30.00

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KAMAT ET AL.

1. INTRODUCTION The multidisciplinary research of semiconductor nanoclusters has witnessed exceptional growth during the past decade. A basic understanding of the photophysical and photochemical properties gained from colloidal semiconductor research is beneficial in the design and development of nanostructured semiconductor materials for practical applications. A great deal of attention has been focused on understanding the properties of nanostructured semiconductor systems because of their practical applications in solar energy conversion and photocatalytic degradation of organic contaminants. Some other applied areas, which can benefit from nanostructured semiconductor technology, are chemical sensors, electrooptics, microelectronics, imaging science, and photovoltaics. Possible applications that make use of the unique properties of semiconductor nanoclusters are illustrated in Figure 1. By making use of the principles of photoelectrochemistry, several semiconductor systems comprised of native and surface-modified semiconducor nanoparticles have been employed in the direct conversion of light energy into chemical or electrical energy [ 1-5]. The term colloid refers to ultrasmall particles with a particle diameter less than 100 nm with the ability to suspend in an aqueous or nonaqueous medium. These are also referred as Q particles, nanoclusters, nanoparticles, or nanophase materials. Under band gap excitation, these semiconductor nanoparticles act as short-circuited microelectrodes and initiate the oxidation and reduction processes of the adsorbed substrate. Alternatively, an adsorbed molecule can inject charge from its excited state into the semiconductor particle and the sensitizer can be regenerated with a redox couple. This process, which is commonly referred to as photosensitization, is extensively used in photoelectrochemistry and imaging science. The application of semiconductor systems in initiating and controlling various photocatalytic processes has been reviewed recently by several researchers [5-18]. Elucidation of the photophysical properties of the semiconductor colloids and the dynamics of the interfacial processes at the semiconductor-electrolyte interface has also been reviewed by many researchers [11, 19-46].

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292

SEMICONDUCTOR NANOPARTICLES

2. PREPARATION AND CHARACTERIZATION 2.1. Size Control

Several approaches have been considered to prepare size-controlled semiconductor nanocrystallites with narrow size distribution. Many of these preparation methods of the size-controlled nanocrystallites control the growth process by using stabilizers such as thiols [47-65], phosphate [22, 66], and phosphine oxide [67] and restricting the reaction space in matrices such as zeolites [68-76], glasses [71, 77-79], polymers [70, 80-84], reverse micelles [85-92], vesicles [93-102], LB films [ 103-112], multilayer film [ 113, 114], xerogels [115],/3-cyclodextrin [116, 117], and silica [118, 119]. Each step in the growth process, for example, nucleation, growth (propagation), and ripening, can be controlled by changing the preparation conditions, such as the choice of the starting materials and media (solvents), composite ratios of the reactants, and preparation temperature and time. These synthetic methods for the smaller nanocrystallites (clusters) were much more successful in the preparation and characterization of thiol-capped CdS clusters. Highly purified clusters form single crystals of (Cdl0S4(SC6H5)16) 4- [ 120], (Cd17S4(SC6H5)28) 2- [ 121 ], CdlTS4(SCH2CH2OH)26 [122], Cd32S14(SCH2CH(OH)CH3)36.4H20 [123], and Cd32S14 (SC6Hs)24.4DMF [124], which can be used as model compounds of the smallest CdS nanocrystallites. Nosaka et al. [49] reported size control of colloidal CdS nanocrystallites by changing concentration of the surface stabilizer (C2HsSH) in a reaction bath. Henglein and co-workers also reported the dependence of CdS size on concentration of long-chain alkanethiols at the stage of nucleation and growth of the nanocrystallites [52]. Apart from chemical precipitation and hydrolysis of suitable precursors, several other methods have also been considered in the synthesis of semiconductor colloids by chemical methods [11,125-127]. Electrochemical and photoelectrochemical etching of silicon wafers can yield porous film composed of nanostructured silicon [ 128, 129]. Some other techniques such as radiolysis [11, 45, 51, 130-136] and sonolysis [137] have also been employed. Sonochemical formation of Q-CdS colloids and dissolution of larger colloidal CdS particles has also been attempted by Grieser and co-workers [ 138]. Despite these various attempts to control the size and shape of the nanoclusters, two crucial problems still remain as challenging issues. (i) The size distributions of nanocrystallites prepared by the previous methods are not monodisperse (standard deviation more than 10%). A relatively narrow size distribution (standard deviation ~8%) has been achieved in the preparation of CdS nanocrystallites in vesicles of phosphatidylcholine [101 ]. (ii) The use of stabilizers or confined matrices often yield byproducts, such as metal-thiolate complexes, which makes it difficult to quantitatively assess the microscopic structure of nanocrystallites. Efforts have been made to narrow the size distribution by size fractionation using exclusion chromatography [139-141] and capillary zone electrophoresis [141-144]. The separation in electrophoresis is based on the fact that the charge-to-size ratios are different for different size particles. Size-selective precipitation [48, 67] or photocorrosion has also been considered to minimize the dispersity in particle size [ 145, 146]. Yoneyama et al. [ 145] applied the method of size-selective photocorrosion using monochromatic light irradiation. Narrower size distribution of CdS nanoparticles was achieved by irradiating light whose wavelength was close to the absorption onset of nanocrystallites in air-saturated sodium hexametaphosphate solution [145]. Photocorrosion of CdS nanocrystallites using Ar ion laser irradiation was also useful in preparing smaller nanocrystallites [ 146]. Recently, Murakoshi et al. [147] reported the size control of CdS nanocrystallites over the range from 1.8 to 4.2 nm while keeping the hexagonalcrystalline structure by varying the sulfur source (H2S and Na2S) and by regulating the preparation temperature. Strongly terminating sulfur species stabilize the nanocrystallites, thus leading to the formation of smaller size particles even in the absence of any stabilizers or matrices. Bawendi and co-workers [67] have recently adopted a novel approach of synthesizing size-controlled CdSe nanocrystallites of

293

KAMAT ET AL.

highest monodispersity (standard deviation less than 5%). Although these methods are useful for the size control of semiconductor nanocrystallites, further development of a novel and simple preparation method that excludes chemical capping or host matrices would be the topic of future research efforts.

2.2. Crystalline Phase Control II-VI semiconductor bulk materials, such as CdS and ZnS, are well known to have two crystalline structures, cubic (zincblende) and hexagonal (wurtzite) types. For the bulk materials, CdS has highly stable hexagonal phase from room temperature to the melting point (1750~ [148], while bulk ZnS has the cubic structure. Because the difference in the crystalline structure of the bulk semiconductor materials leads to considerable change in the effective masses of e and h in their electronic bands [149], the crystalline structure of semiconductor nanocrystallites should play a dominant role in determining their photochemical, photocatalytic, and photophysical properties. The crystalline structure of nanocrystallites is largely influenced by the preparation conditions. Although the hexagonal phase is the most stable phase of CdS, for example, only a few reports on the preparation of hexagonal CdS nanocrystallites have been published [48, 67, 150-153]. Hexagonal CdS nanocrystallites can be prepared by reacting Cd 2+ and S 2- (H2S or Na2S) in N,N-dimethylformamide (DMF) without using any surface stabilizers [ 147]. The mean diameter of CdS nanocrystallites can be rigorously controlled over the range from 1.8 to 4.2 nm by varying the sulfur source (H2S and Na2S) and by controlling the reacton temperature (Figs. 2 and 3). In these studies, the use of Na2 S as a sulfur source produces smaller CdS nanocrystallites than those prepared using H2S. The size control and stability of CdS nanocrystallites are discussed in terms of the surface structures that were elucidated using in situ Cd K-edge extended X-ray absorption fine structure (EXAFS) analysis. The strong terminal binding of the sulfur atoms to the surface cadmium atoms resulted in the weaker solvation of DMF molecules and the controll of their size and crystalline phase. Phase transformation of semiconductor nanocrystallites can be used to obtain a desirable crystalline structure [44]. The phase transition of semiconductor nanocrystallites can

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Wavelength / nm Fig. 2. Room temperature absorption spectra of CdS-Na2 S, which were prepared at (a) - 4 0 ~ (b) - 2 0 ~ (c) 0~ (d) 30~ and (e) 60~ Those of CdS-H2S were prepared at (f) 0~ (g) 30~ and (h) 60 ~ The inset shows the dependence of the molar extinction coefficient on the size of CdS-H2S and CdSNa2S. The experimental data were fitted in proportion to the inverse cube of the Bohr radius divided by the CdS radius (aB/R)3, aB = 26/~). (Source: Reprinted with permission from [147].)

294

SEMICONDUCTOR NANOPARTICLES

Fig. 3. Band gap dependence on the CdS radius. The experimental data are from this study (e), from Vossmeyer et al. (o), and from Herron et al. (A). The curves are predicted by the effective mass approximations with infinite (. . . . . ) and finite potential well (-.-), and the pseudopotential calculations for hexagonal (--) and cubic CdS lattice (...). (Source: Reprinted with permission from [147].)

Fig. 4. Electron diffraction patterns of (a) ZnS-DMF and (b) ZnS-DMF combined with C6FsSH. (Source: Reprinted with permission from [158].)

be achieved under high temperature [154] and pressure [155-157]. Unfortunately, these extreme conditions often cause unexpected structural deformations, such as the growth of nanocrystallites and change of their chemical composition [154]. Alivisatos and coworkers carried out a four- to six-coordinate phase transformation of CdS [ 155] and CdSe [ 156, 157] nanocrystallites without altering their size or their chemical composition. The control of crystalline structures of quantum-confined semiconductor nanocrystallites was achieved at ambient temperature and pressure through the chemical modification of the ZnS nanocrystallite surface with organic molecules (Fig. 4) [158]. Pentafluorothiophenol, thiophenol, 1-decanethiol, 1-hexanethiol, benzoic acid, and cyanoacetic acid, which chemically bind to the surface of ZnS nanocrystallites, are capable of changing the hexagonal phase of ZnS nanocrystallites to the cubic. On the other hand, similar phase transitions

295

KAMAT ET AL.

could not be observed with unreactive octanoic acid, acetic acid, and phenol, which do not bind to ZnS. The formation of the chemical bonding between surface zinc atoms of ZnS nanocrystallites and the added thiolate or carboxylate anion should lead to a change in the surface energy of ZnS nanocrystallites. This change in the surface energy could induce the phase transition from the metastable phase (hexagonal) to the stable phase (cubic) at ambient temperature and pressure. [The difference in the internal energy of ZnS between the hexagonal and the cubic phase is quite small (3.2 kcal mo1-1)]. 2.3. Size Quantization Effects A great deal of attention has been focused on the transformation from solid-state electronic properties to molecular properties of various semiconductor nanoparticles [ 11, 34, 35, 39-41, 74, 149, 159-167]. These crystallites are molecular clusters in which complete electron delocalization has not yet occurred. Quantization in these ultrafine particles arises from the confinements of charge carriers in semiconductors with potential wells of small dimensions (less than the De Broglie wavelength of the electrons and holes). Under these conditions, the energy levels available for the electrons and holes in the conduction and valence bands become discrete. In addition to the very large effects on optical properties, size quantization also leads to major changes in the effective redox potential of the photogenerated carriers. Semiconductor particles that exhibit size-dependent optical and electronic properties are termed quantized particles (or Q particles) or semiconductor clusters. The particles with diameters greater than 150 A. typically behave as bulk semiconductors. However, similarly prepared crystallites of approximately 15-50 ~ diameter that possess a bulk lattice structure differ considerably in electronic properties. Size quantization effects have been experimentally demonstrated in various laboratories around the world by controlling the synthetic procedure and monitoring the size-dependent optical effects. A few representative examples include [ 11, 24, 25, 34-36, 40, 42, 49, 51, 52, 79, 133, 137, 139, 160-162, 164, 165, 168-207]. Optical effects caused by size quantization in layered-type semiconductors have also been reported [131,170, 199, 200, 208, 209]. The absorption spectra of CdS colloids of various particle size are compared in Figure 5 [ 173]. The onset of absorption for larger colloids closely matches the absorption edge of bulk CdS. The absorption edge shifts to blue for smaller size particles as a result of the increase in the effective band gap.

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a). The spectrum of this system was discussed in [33] and also in [34, 35] where the analogy with classical paths was pointed out; (2) A~0 = ( B o p / 2 ) O ( p - a), which results in a magnetic field profile with a delta function overshoot: B ( p ) = 0 (p < a), (B0p/2)8(p - a), B0 (p > a). In [33-35], one refers to the present system as the magnetic dot system, stressing the magnetic confinement in this quantum dot. From the magnetic field point of view, one has a circular hole inside a uniform magnetic field profile and, therefore, one can also call the present system a magnetic antidot. The wave function for the single-electron states can be written as ~ ( p , 99)= eim~~ where the radial part is determined by the Schrrdinger equation

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364

HYBRID MAGNETIC-SEMICONDUCTOR NANOSTRUCTURES

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tion exhibits a maximum at p = p* > 0. With increasing a / l a , this maximum shifts toward the center of the dot. In case there is an overshoot in the magnetic field profile, when the maximum of the electron wave function is situated near p = a, the electron energy will be increased, which results in a local maximum as shown in Figure 13a. From this interpretation, it is easy to understand that the maximum in En,m/hOgcshifts to larger a / l a values with increasing angular momentum m. For large values of a/IB, most of the wave function will be situated in the dot where there is no magnetic field and, consequently, the energy decreases.

365

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a lIB) Fig. 14.

Filling of the magnetic dot in case of magnetic field overshoot.

This behavior of the electron energy has important consequences for the filling of the dot. Outside the quantum dot, the magnetic field is B0 and the electron lowest energy state is hwc/2. An electron will only be situated in the dot when its energy is lower than in the region outside the dot. For the moment, we will neglect the electron-electron interaction. From Figure 13b, we note that for a dot without magnetic field overshoot at its edges there are an infinite number of states, that is, the states with m/> 0 for n = 0, which have an energy less than ho9c/2 and, consequently, the electrons will be attracted toward the dot. For the system with magnetic overshoot, the situation is totally different. The 10, 0) state has energy below hwc/2 and two electrons (two because of spin) will be able to occupy the dot. When we add more electrons to the system, we see that for small a / l a values, the electrons are repelled and are forced outside the dot. Only when a/1a is sufficiently large will quantum dot states become available with energy less than hwc. Consequently, as a function of a/IB, we observe a discrete filling of the dots. This is depicted in Figure 14 where we show the number of electrons in the dot as a function of a/lB "~ qc-~. Including the real magnetic profile as shown in Figure 12 will not alter our conclusions qualitatively. For example, the discrete filling of the dot as shown in Figure 14 will still be present. The exact position at which the number of electrons jump to higher values will be a function of the exact magnetic field profile, and, in particular, it will strongly depend on the sharpness of the magnetic overshoot.

5. DIFFUSIVE TRANSPORT OF ELECTRONS THROUGH MAGNETIC BARRIERS In previous sections, it was assumed that the electron transport through the magnetic barriers was ballistic, and, consequently, the electrons exhibit quantum tunneling. This is valid when the width of the barriers (W) is much smaller than the mean free path (le) of the electrons and the cyclotron radius Rc > W. For wide magnetic field barriers, the charge transport is better described by a diffusive theory, which is also valid at higher temperature where the mobility is low and the electron motion is diffusive. Until now, no experiments were available of quantum transport through single or multiple magnetic barriers. Recently, Leadbeater et al. [36] reported an alternative technique to

366

HYBRID MAGNETIC-SEMICONDUCTOR NANOSTRUCTURES

5000

.

.

.

.

I

"

"

"

'

"

I

-

,,,i, ~

.

.

.

I

.

.

.

.

4000

3000 ~J

. . , . .

2000

~

....

[y

Experiment

1000

0 -10

.

.

.

.

.

I

.

.

.

.

.

.

, I

I,

111

~

|

.

-5 0 5 Applied Magnetic Field-(Tesla)

.

.

.

.

.

10

Fig. 15. Experimental (solid curve) and theoretical (dashed curve) results for the magnetoresistance as a function of the applied magnetic field. The magnetic barrier (inset) was created by faceting the 2DEG plane where the facet makes an angle of 20 ~ to the substrate and the applied magnetic field is in the plane of the substrate (i.e.,

0 = 90o).

produce effective spatially varying magnetic fields of much larger strength and gradients than could be obtained by lithographic patterned superconducting or ferromagnetic films. They constructed a nonplanar two-dimensional electron gas (2DEG) that was fabricated by growth of a GaAs/(A1Ga)As heterojunction on a wafer prepatterned with facets at 20 ~ to the substrate. Applying a uniform magnetic field (B) produces a spatially nonuniform field component perpendicular to the 2DEG (see inset of Fig. 15). With the field in the plane of the substrate, an effective magnetic barrier is created located at the facet. The resistance measured across such an etched facet showed oscillations that are periodic in 1/B and that are on top of a positive magnetoresistance background, which increases quadratically with the magnetic field for small B and quasi-linearly in B for large B (see full curve in Fig. 15). 5.1. Theoretical Formalism To explain, quantitatively, the main features of the experimental measurements of [36-38], namely, the smooth background of the magnetic field dependence of the resistance, we will rely on a classical model for magnetotransport through such a wide (typically on the order of a micrometer) magnetic barrier. This theory is also valid for 2D diffusive transport in case magnetic barriers are created through the structuring of ferromagnetic material on top of a heterostructure. The 2DEG situated in the (x, y) plane is bounded by the edges of the Hall bar where a small part of the 2DEG is subjected to a perpendicular magnetic field in the z direction. The Bz :/: 0 region corresponds to the facet region in the experimental system, that is, Bz = B sin(0), 0 = 20 ~ is the facet angle, and B is the externally applied magnetic field in the plane of the substrate. To calculate the spatial distribution of the

367

PEETERS AND DE BOECK

electrostatic potential, the electric field, and the current density, we start from the stationary continuity equation, which expresses charge conservation V .J =0

(34)

J =erE

(35)

which is supplemented by Ohm's law

In the steady state we have V x E = 0 and the electric field can be written as the gradient of a potential, that is, E = -Vq~. The previous system of equations reduces to the following 2D elliptic partial differential equation for the electrical potential 4~: V . [or (x, y)V~b(x, y)] - 0

(36)

where cr (x, y) is a spatially dependent conductivity tensor. For a homogeneous system and in the absence of a magnetic field ~r (x, y) = constant, we recover the Laplace equation. In our case, the conductivity tensor is no longer constant owing to the presence of the finite magnetic barrier: / \ -- [ O'xx tYxy(X, Y) o'(x, y) Cryx (X, y) tYyy

J

( 1 1 + (lzBz(x,

y))2

-lzBz(x, y)

lzBz(x,1 y) )

(37)

where a0 = nselz is the Drude conductivity and B z = 0 outside the facet. The 2D partial differential equation is cast into a finite-difference form and solved numerically [39] using the accelerated Gauss-Seidel iteration scheme with the boundary conditions 4~(x, 0) = 0 and 4~(x, L) = V0 (L is the length of the sample and V0 is the applied voltage) and the condition that no current can flow out the sides of the sample, that is, jx = 0 for x = 0, and x = W. The distances are normalized by the width of the sample (typically W -- 4 0 / z m taken along the x axis) and the voltages are normalized by the total voltage drop between the current probes. The magnetoresistance between any two points a and b along one side of the sample is given by R = Vab/Icd, with the voltage drop Vab = ~ (x, b) - c~(x, a), and the total current flowing normal to the facet is obtained through Icd -- fJ jy(X, y)dx, where c and d are any two points on the opposite sides of the sample. The Hall resistance at a distance y along the sample length is given by RH = VH/Icd, where VH = q~(W, y) ~b(0, y). There exist alternative approaches to solve the differential equation (36). Badalian et al. [40] used the conformal mapping method in order to find an analytic expression for the magnetic potential in an infinite long wire in the presence of a magnetic barrier. Jou and Kriman [41 ] developed a spectral expansion approach in which the magnetic potential was expanded into an orthogonal basis, which consisted of solutions of the Laplace equation in the different regions that satisfy the boundary conditions. Continuity of the magnetic potential at the boundary between the separate regions determined the expansion coefficients. In [41 ], this approach was applied to a single magnetic barrier and to a periodic array of them.

5.2. Single Magnetic Barrier In Figure 15, we show both the experimental (solid curve) and the theoretical (dashed curve) traces for the magnetoresistance across a single facet of width 3/zm where the voltage probes are situated 10/zm apart across the facet and the current probes are more than 900/~m apart for a sample with width W = 40/zm. Notice that apart from the Shubnikovde Haas (SdH) oscillations, which result from the quantizing effect of the magnetic field

368

HYBRID MAGNETIC-SEMICONDUCTOR NANOSTRUCTURES

Fig. 16. Potentialdistribution in the sample for B = -2 T.

at low temperature, the theoretical curve accounts nicely for the overall behavior of the magnetoresistance. The experimental curve is slightly asymmetric around B = 0, which is due to the fact that the voltage probes are not exactly equidistant from the facet. The classical origin of the positive magnetoresistance was confirmed experimentally where it was found that it persists even for temperatures above 100 K. Note that the experimental configuration is effectively a two-terminal measurement where the measured resistance is determined by the Hall resistance as well as the magnetoresistance. For small B fields, the Hall resistance is small and thus the resistance is determined by the magnetoresistance and is, consequently, quadratic in B. For larger magnetic fields, a quasi-linear behavior of the resistance as a function of B is found, which is due to the fact that now the Hall resistance mainly limits the current. The theoretical electric potential distribution in the sample is shown in Figure 16 for an applied magnetic field of B = - 2 T, which gives Bz = - 2 sin(20 ~ = - 0 . 6 8 4 0 T. Notice that almost all the potential drop takes place across the magnetic barrier. In the barrier region and just outside it, there is a voltage difference between the edges of the sample (i.e., across the x axis), which is nothing else than a spatially dependent Hall voltage. This is in accord with the concept that the (Bz -- 0 regions) can be thought of as extended high mobility contacts to a short and wide Hall bar (the facet region) that tends to short out most of the voltage immediately outside the facet region. Particularly interesting is the development of the Hall voltage between the opposite edges of the facet. This becomes very small but nonzero outside the facet region and gives a steep increase of the Hall potential profile at the edges of the Bz ~ 0 region, which is reminiscent of the potential profile investigated experimentally and theoretically in [42, 43] in a conventional Hall bar under the conditions of the quantum Hall regime and in the middle of a plateau in the Hall resistance.

369

PEETERS AND DE BOECK

. .

f t

t t

t t

t t

t t

t' t'

, f t

t t

t t

t t

t t

t . . . . . . t. . . . . . . .

t t t t t t

t t t t t t

t t t t t t

t t t t t t

t t t t t t

t' t' t' t' t' t

. . . . . .

. t

t

t

t

t

t.

. . . . . . .

. . . . . . . . . . . . . . . . . . . . .

'. t : t : t

t t t

t l t

t t t

t t t

t: t: t:

. . . . . . . . . . . . . . . . . . .

. . . . . . .

: t t t t t t: . . . . . . . : t t l t t t' 9 . . . . . .

0.8

. .

. .

. .

. .

. .

. .

: :

. . . . . . . . . . . . . .

'. : : : : :

. . . . . . . . . . . . .

0.6

. . . . . . . . . . . . . .

. . . . . . .

X

. . . . . .

0.4

0.2

.

.

.

.

.

.

.

" "

. . . . . . . .

9 9 9 9

. .

. .

.

. . . . . .

. . . . . . . . . . . . . . . . . .

9 . . . . . . .

.

.

.

.

.

.

0 0

0.05

0.1

0.15

0.2

0.25

Y Axis

Fig. 17. Current flow in the sample for B = - 2 T corresponding to the situation of Figure 16. The magnetic barrier region is delimited by the two dashed lines.

The spatial distribution of the components of the electric field are obtained as follows:

Ex = -Ocp(x, y)/Ox and Ey : -O~(x, y)/Oy. From Figure 16, it is clear that both components are very small outside the barrier region. Inside the magnetic barrier, Ex becomes very large close to the edges especially at the diagonally opposite comers and vanishingly small in the middle where Ey is finite and more uniform, singular at the diagonally opposite comers, and very small at the other two comers9 Accordingly, the largest part of the current will enter the magnetic barrier region from the comer where both electric field components are large and exit the barrier from the diagonally opposite comer (see Fig. 17). Once inside the barrier region, the guiding center of the electron cyclotron orbits will drift along the equipotential lines (see Fig. 16) according to the E x B drift with velocity Vdrift = -(V~b x B ) / B 2. Electrons entering or exiting the small regions of the comers of the barrier will have large velocities, which are proportional to the electric field at these locations, to account for current conservation. There are larger number of electrons drifting with slow and uniform velocities in the middle of the barrier where the electric field is smaller and more uniform. This picture is graphically represented in Figure 17 where we show the calculated results for the current distribution J(x, y) = - a ( x , y)V~p(x, y) corresponding to the experimental situation of Figure 15. Notice that even well outside the barrier the current distribution is already modified by the presence of the magnetic field barrier in the facet region and it is concentrated closer to the edges of the sample. At the diagonally opposite comers, it is strongly peaked. These results for the field and current distribution are consistent with those of [44], which were calculated for a conventional Hall geometry in the case of very low-aspect-ratio. This problem of low-aspect-ratio Hall devices in a homogeneous magnetic field was studied earlier in the context of applications for magnetic sensors (see, e.g., [45] and the references therein). 5.3.

Magnetic

Barriers

in Series

In [37], a ridge geometry (see top figure of the inset of Fig. 18) was fabricated resulting in two magnetic barriers in series (bottom figure of the inset of Fig. 18), each having the same Bz but with opposite sign. In Figure 18, both the experimental (solid) trace and the theoretical (dash-dotted and dashed) curves are shown. The experimental trace was claimed to be for 2S = 1/zm base length of the ridge (in [37], it is noted that the etch depth for a

370

HYBRID MAGNETIC-SEMICONDUCTOR NANOSTRUCTURES

,000 /

oooE 9 -~

',o

r~,, -6

-

/

~,

I.. -10-8

'

-4

~

...... 2s=1.25 p.m

-2 0 2 4 Applied B[T]

6

8

10 1

Fig. 18. Experimental(solid curve) and theoretical (dashed and dash-dotted curves) results for the magnetoresistance of the magneticbarrier created by the ridge (see inset).

ridge is less than the depth of the regrown material, which may produce some planarization during regrowth), while for the theoretical curves we found that a larger base length gives closer agreement with experiment. Notice that with this renormalization of the width of the magnetic barrier we obtain rather good agreement for the positive magnetoresistance part of the experimental curves. The oscillatory part in the experimental curves are again due to quantum effects. The more general case of two magnetic barriers in series was studied in [39]. This can be realized experimentally by producing a ridge with a fiat top, which is equivalent to introducing a zero magnetic field region between the two facets. It was shown that the relative sign of the magnetic field of the two magnetic barriers has important consequences for the magnetoresistance. For the case of two separate barriers with the same sign of Bz, the magnetoresistance at high magnetic fields is almost twice that of a single barrier and, consequently, classically the magnetoresistance of multiple barriers is additive. For not too large magnetic fields (the R ,~ B 2 region), the current path spreads across the magneticnonmagnetic interface and, consequently, the current path is shorter, leading to a smaller magnetoresistance, and the simple rule of addition of resistances in series is no longer valid [38]. For barriers in series with opposite direction of the Bz field, the situation is different. The removal point of current from the first barrier is at the same side of the sample as the injection point of the current into the second barrier and, consequently, the resistance is not sensitive to the distance of separation between the two barriers.

6. ONE-DIMENSIONAL MAGNETIC MODULATION The magnetoresistance oscillations of the two-dimensional electron gas (2DEG) subject to periodic electric (or potential) weak modulations, along one or two directions, also called Weiss oscillations, are now well established both experimentally [46-53] and theoretically [54-59]. The situation is mostly clear in the case of one-dimensional (1D) modulations where the oscillations reflect the commensurability between two length scales: the cyclotron diameter at the Fermi level, 2Rc = 2~/2zrne/2 (where ne is the electron density and l = ~/h/eB is the magnetic length), and the period a of the modulation. In this section, we consider electrical magnetotransport of a 2DEG in the presence of a weak 1D periodic modulation (of strength B0) of the magnetic field and the extreme case of a strong magnetic modulation in which the average magnetic field is zero. We will show that both situations are essentially different from each other.

371

PEETERS AND DE BOECK

Different methods of establishing a periodic magnetic field on a micrometer or nanometer scale have been used: (i) using periodically arranged flux tubes in a type II superconductor (Abrikosov lattice) that penetrate the underlying 2DEG [60-63], (ii) using patterned superconducting gates that partially shield the external magnetic field [64-66], (iii) microfabricated ferromagnetic structures whose magnetic polarization adds to the external field [65-78], or (iv) nonplanar two-dimensional electron systems [36-38, 79, 80]. The first method is limited to low magnetic fields and, furthermore, a periodic flux lattice is, in practice, not achievable in an evaporated superconducting film because of the presence of pinning centra, which leads to a rather random array of flux lines. The last method of nonplanar 2D systems can result in large magnetic field modulations, the strength of which is determined by the external magnetic field. Also sign-alternating magnetic modulations are attainable. For the second method, different superconducting periodic arrays have been made using lead [64], and niobium [66]. Different ferromagnetic materials have been patterned on top of the 2DEG, for example, nickel [65, 66, 69-72, 74, 76, 81-83], dysprosium [67, 75, 77, 82], and cobalt [73, 83]. Alternatively, metal organic chemical vapor deposition with a tunneling microscopic tip [84] was used to deposit small magnetic particles. The magnetic metallic strips also induce an electric modulation in the 2DEG and often also a strain-induced electric modulation at the 2DEG occurs because of the differential thermal contraction of the deposited magnetic material and the semiconductor. Initially [81], these built-in potential modulations dominated any effects caused by the magnetic modulation. By depositing a thin metallic film between the 2DEG and the magnetic strips, the electric modulation from the metallic strips can be shielded. For example, Weiss et al. [82] used a 10-nm thin NiCr film between the 2DEG and the magnetic strips in order to define an equipotential plane. The strain-induced modulation was removed [65, 72] by orienting the strips normal to the [ 100] direction of GaAs, which is nonpiezoelectric. The magnetic metallic strips act as a periodic gate, which causes both scalar and vector potential modulation. By applying a bias to the ferromagnetic gates, the electric field modulation can be altered. In this way, one can drive the system from a predominantly electric-dominated modulation to a magnetic field-dominated modulation.

6.1. Weak Magnetic Modulation There already exists a number of theoretical studies on the effect of a periodic magnetic modulation on the electrical transport properties of a 2DEG. Vasilopoulos and Peeters [85] predicted phase-shifted Weiss oscillations, which were later reobtained in [86]. This study was later extended [87] to the case of combined electric and magnetic 1D modulations (see also [88]). Li et al. [89] considered more general periodic magnetic field profiles by including several Fourier components in the expression for B(x). The corresponding quasiclassical band conductivity problem was studied by Gerhardts [90]. In [81], a numerical calculation of the energy spectrum for a 1D magnetic modulation of arbitrary strength was presented and the corresponding transport properties were discussed in [91]. Collective excitations of a 2DEG in a unidirectional magnetic field modulation were discussed by Wu and Ulloa [92-94]. Consider a 2DEG in the (x, y) plane, subject to the magnetic field B = (B + B0 cos Kx)ez, where K = 2n/a, and a is the modulation period. Only the first Fourier component of the periodic magnetic field is retained, which is sufficiently accurate in most situations. Here we consider only the case of a weak modulation, that is, B0 1, that is, when many Landau levels are occupied, the results of (46) can be cast into a form that exhibits explicitly both the Weiss (at low B) and the Shubnikov-de Haas (SdH) (at higher B) oscillations. The procedure has been detailed in [55, 87] and consists of using the asymptotic expressions for the Laguerre polynomials, for n >> 1, and of the density of states D(E) -- D0[1 - 2exp(-rc/COcrf)cos(2rcE/hcoc)] with the prescription ~'~n --+ 2re/2 f D ( E ) d E . The parameter rf is the electron quantum lifetime. Following verbatim this procedure and retaining only the leading terms, we obtain that Eq. (46) takes the form

o-ydif Y

akFh~176176176

o-0

2n"2 hO)c E F

cos ( 2 y r E F ) (2yrRcsin2 toe z'f

hOgc

a

+)j 4

(47)

where T G--[1-A(--Taa)]/2+A(~aa)Sin2(21rRca

1r4)

(48)

Here o-0 - nee2r/m * is the conductivity at zero magnetic field B and A(x) - x~ sinh(x). The characteristic temperatures Ta, for the Weiss oscillations, and Tc, for the SdH oscillations, are defined by kBTa = (hcoc/4zce)akF and kBTc = hOgc/2Zr2, respectively, with kF being the Fermi wavevector. In typical experiments, we have Ta/Tc -- akF/2 >> 1; for example, for ne -- 3 • 1011 cm -e and a = 3500 ~, we have akF ,~ 24. As a result, the SdH oscillations disappear much faster with temperature than the Weiss oscillations. We further

375

PEETERS AND DE BOECK

9 0.'~'_

0'I 9

3 0.2

!

'

tU--

.__'

Nickelfilm

.~

,__

'"

,. . . . .

'

,

,

Sweepup

~

ff'~'~~'-- Sweepdown

~

I "0"-0.4

-0.2

I

0.0

0.2

0.4

,",, ,, ,~' , ,, :',, I \ti

11o:o

i

l

i~/~,'

,

"

~,,f'

i

',"

l/

/i'

t

'/

'",

.,:' The_]

',

I

,, ',

!

,,

~

', ,'

0

~

' " _

0.0

,

,

0.1

,l

......

l,

,

i,

0.2

.

,I.

0.3 B

.

'

0.4

(T)

Fig. 20. Longitudinalmagnetoresistance at 1.3 K for a 1D magnetic modulation of a 2DEG for "up" (dot-dashed curve) and "down"(solidcurve) field sweeps as comparedto the calculated behavior(dashed curve). The inset shows the magnetization of the Ni strips that is responsible for the magnetic modulation. (Source: Reprinted with permission from [72]. 9 1997 AmericanPhysical Society.)

remark that in comparison with the electric case, cf. Eq. (34) of [55], the present result differs essentially by a term (akF/2sr) 2 ,~ 60 in the prefactor. Correspondingly, the amplitude will be larger in the magnetic case by this factor. In Figure 20, the commensurability oscillations in the longitudinal magnetoresistance, Rxx = Rxx (B) - Ro, of a 2DEG with mobility/x = 7 x 105 cm2/V s (corresponding to a mean free path of le -" 7.7/zm) that is subjected to a 2D magnetic modulation are shown. The 2D magnetic modulation was produced [72] by a periodic array (a = 500 nm) of Ni strips of width d = 200 nm and height h -- 100 nm that are situated a distance of 35 nm from a 22-nm-wide GaAs/A1GaAs quantum well. These magnetoresistance oscillations result from the preceding commensurability effects between the diameter of the cyclotron orbit at the Fermi level 2Rc and the period of the magnetic modulation. Notice that these magnetoresistance oscillations are clearly visible and their position agrees very well with the previous theoretical result (dashed curve). For B > 0.3 T, small SdH oscillations are superimposed on top of the Weiss oscillations. Note that the experimental result exhibits a small hysteretic behavior that is associated with the hysteresis of the magnetization of the Ni strips (see inset of figure). In the calculation (dashed curve), the strength of the magnetic modulation (B0) was taken from the magnetization (M0) given by the model hysteresis curve shown in the inset of the figure. Note that there is not only a good agreement with the position of the oscillations, confirming that the oscillations originate from a predominantly magnetic modulation, but also the magnitude of the last commensurability peak at approximately 0.27 T is well reproduced. Above about 0.2 T, the theoretical prediction involves no free parameters so this agreement confirms the accuracy of the calculated saturation modulation amplitude. Below 0.2 T, the decrease in amplitude will depend on the exact form of the M0 (Bext) curve and damping caused by scattering, which is not included in the theoretical curve, will be important.

376

HYBRID MAGNETIC-SEMICONDUCTOR NANOSTRUCTURES

6.2. Electric and Magnetic Modulations Magnetic modulations are often accompanied by an electric modulation. Therefore, we have to study how the results of a pure magnetic modulation are modified when an electric modulation with the same period is present. Two cases are of interest: that where the two modulations are in phase and that where they are out ofphase. 6.2.1. In-Phase Modulations

If a weak electric modulation described by the periodic potential Vocos(Kx), which is in phase with the magnetic one, is present, Eq. (39) will have an additional term VOFn(u)cos(Kxo). As a result, Vy, given by Eq. (43), will have an additional term -(2Vo/h K)u Fn (u)sin(Kx0). The bandwidth will be the sum of the two bandwidths. At the Fermi energy, the latter is given by the sum of those of Eqs. (40) and (41) and is equal to 2 V0

rcK Rc

v/1 + 8 -2 sin

a

4

t- 4~

(49)

where 8 = 2n Vo/akFhwo = tan(40. Notice that the flat-band condition now reads 2Rc/a = i + 1/4 - 4~/7r and depends on the relative strength of the two modulations. The changes mentioned previously will be reflected in the transport coefficients as well. As an example, the diffusion contribution to the conductivity, Eq. (46), now takes the form _die ,~, Oyy

e22Jr2rl 2

h

h

a2

E [hwoan(u) -+-gofn(u)] 2 n

(Of(E)) OE

(50)

E=en

and its asymptotic expression, obtained in the manner described earlier, reads o.dif Y ~

akF hwo hwo

o'0

2zr 2 hWc EF

(1 -+- 6 2)

X {1- A(~a)+ x sin2( 2zrRc a

T -Jr [A (-~a) - 2 e x p ( -c-~) A ( ~ c ) zr )} 4 + q~

hCOc)] (51)

Notice that the influence of the combined effect of the two modulations is to introduce the phase factor 4~ in the Weiss oscillations. In Figure 21, we plot Ap, that is, the change in resistance caused by the modulations, as a function of B (solid curve) for B0 = 0.02 T and V0 = 0.2 meV for a 2DEG with ne -- 3 x 1011 cm-2 at T = 4.2 K with a modulation period of a = 3000 ~. For comparison, we show the results when only the magnetic (dotted curve) or the electric (dashed curve) modulation is present. In line with Eq. (51) that was used for the evaluation of Ap, the solid curve is shifted from the other curves because of the phase factor 4~. We also note the zr/2 phase difference between the dashed and dotted curves, which reflects that of the corresponding bandwidths shown in Figure 19. The dependence of Ap on B and the phase factor 4~ is shown in Figure 22. B0 is again kept constant (B0 --0.02 T) but V0 is varied as indicated between positive and negative values; 8 and 4~ change accordingly. We notice that (1) the position of the peaks depends on the specific value of 8, and (2) there is a zr phase difference between large positive and large negative values of 8. Such in-phase modulation of the electric and magnetic period was studied by Iye et al. [69]. In their experiment, a GaAs/A1GaAs heterojunction containing a 2DEG, with density ne -- 4 • 1011 cm -2 and mobility/z -- 6 • 105 cmZ/V s at T = 4.2 K, was placed 75 nm below a periodic array (a -- 0.5/zm) of Ni strips with height 150 nm. By changing the voltage on the gate consisting of the Ni strips, the strength of the electric field modulation is

377

PEETERS AND DE BOECK

2.5 n,=3xlOllcm -2

](~

a=3000~ V,=O.2meV B, =O-02T

2.0

magnetic

[

1

-'--'1

+

electric/,X /

,m ,m 4,.e

1.5

, .,,=.

rr

electric

//, v /,,\

l\i

1.0

.,

2.5

-

ne=3x1011cm-2

-

a=3OOOA

"

T=4.2K

-

Bo=O.O2T

.5meV

~

=D

2.0 ell

(/j

q) rr"

./...~

1.5 1.0 0.5 9

9

.."

I

0

0.1

0.2

I

I

I

I

0.3

0.4

0.5

0.6

,

I

,

0.7

I

0.8

,

I

0.9

1

Magnetic field B(T} Fig. 24. Increaseof the magnetoresistance when magnetic and electric out-of-phase modulations are present for different values of the strengthof the electric modulation.

The result for the diffusion contribution reads e22zr2rl 2

_dif Oyy = h

h a2 ~_, n {[goFn(u)] 2 '1 [hogoGn(/1)]2 }

(Of(E)) OE E=En

(55)

There is no cross term involving the product hco0V0 in Eq. (55), as expected from Eqs. (44) and (53), because the integral over ky vanishes for this term if we neglect the very weak ky dependence of the argument of the Fermi functions. _dif The asymptotic expression for Oyy is o

.dif Y o- 0

hwohwoakF{G+32F_2exp(-rC)A(T) EF hWc2Zr2

COc--~f

(2:rEF) -~c COS hWc

D

}

(56)

where D _ 82 + (32

1) sin2(27rR c a

7r) 4

(57)

G is given by Eq. (48) and F by Eq. (48) after replacing sin2( ) by cos2(). Comparing Eq. (56) with Eq. (51), we see that changing 3 does not change the position of the extrema of Ap as a function of B because the phase factor 4) is absent from Eq. (56). This is illustrated in Figure 24 where Ap is plotted as a function of B for B0 = 0.02 T with variable V0. For the upper two curves we have 3 > 1, whereas, for the lower two curves, is smaller than 1. This results in an antiphase between the two groups of curves and reflects the corresponding behavior of the bandwidth as given by Eq. (54).

6.3. Magnetic Minibands The electronic band structure in a periodic magnetic field with zero average was investigated by several authors. Ibrahim and Peeters [96] calculated the energy spectrum of a periodic array of a delta function magnetic field oscillating in sign, which was generalized in [97] to an array with a more general unit cell. The energy spectrum and the conductivity

380

HYBRID MAGNETIC-SEMICONDUCTOR NANOSTRUCTURES

through sinusoidal [5, 98] and different periodic magnetic fields profiles was studied in [5]. Ballistic quantum transport through a periodic alternating step magnetic field profile and through a sinusoidal magnetic field structure was investigated in [99] and through a quasiperiodic magnetic superlattice in [ 100]. The surface states of a lateral magnetic superlattice were calculated in [ 101 ].

6.3.1. PeriodicSinusoidalMagnetic Fields Directing the magnetic field more and more in plane reduces the background component (B) and enhances the modulation component (B0). In the limit of B = 0, we have a pure periodic magnetic field with zero average. As an example of such a case, consider the physical system depicted in Figure 3. The magnetic field profile in the plane of the 2DEG is sinusoidal when the distance between the 2DEG and the ferromagnetic thin film is sufficiently large (see dotted curve in Fig. 3b). In such a case, only the first term of the Fourier series is important. In this subsection, we study the magnetic field profile [5, 98, 102]:

B(x)

= sin(2Zrx)

8o

-7

(58)

which has the corresponding vector potential (Fig. 25)

A(x) A0

2

m

~ --~

l(2rcx) COS

2Jr

'''1''''i''''1''''1''

(59)

---7--

' ' ' ' 1 ' ' ' ' 1

....

I ' ' ' ' 1 ' '

1

o I

0

0 m_1

-1

-2

, ,.,

l,

, ,,

l,,,,|

tl|il

-2

, , , , I , , , , I , , , , I , , , , I , , ,

J,

, , , i , , , , i , , , , i , w , , i , ,

1

1.5

o. ,~0.5 X

o.s ~>

>

0

0 ' ' ' ' 1 ' '

q

'1''''1

....

I'

~

'

'

'

'

1

'

'

'

'

|

'

'

'

'

1

'

'

'

'

1

'~

.

20 o

2

$

15 ~II

Xl l

10 x>

o

5

10

15

2o

5

10

15

20

x (eB)

x (eB)

Fig. 25. Profiles for the magnetic field, the vector potential, and the effective potential for different values of ky in the case of a sinusoidal magnetic field.

381

PEETERS AND DE BOECK

and which leads to the following Schrrdinger equation:

-d~x2 + 2E -

ky - 2---~-cos --/--

7t(x) = 0

(60)

The profiles for B(x) and A(x) are depicted in Figure 25 together with the effective potential for different ky values. When solving the Schrrdinger equation, we can restrict ourselves to one period and impose periodic boundary conditions. The potential profile V(x, ky) is shown in Figure 25 and satisfies the symmetry relation V(x, ky) --

V(x + 1/2,-ky). After making the substitutions 0 - rex~ l, co - (1/Tr) 2, p - lky/7C, and ~ - (l/rc)2(2E ky-2 1/4), the preceding equation is cast into the following form: o92 { ~--~- +

)+wpcos(20)-(~)cos(40))}~p(O)=O

(61)

which is the Wittaker-Hill equation. It is interesting to note that, in the case ky = 0, Eq. (61) reduces to Mathieu's equation with period 1/2. The numerical solution of Eq. (61) for E versus ky is shown in Figure 26 for l = 8 and in the inset for a larger period I = 16. To understand the energy spectrum, we show in Figure 9 the potential V (x, ky) for different ky values. First, note that V (x, ky) -- V(x + I/2, -ky) results in spatially separated motions for the -+ky and -ky electrons moving with E < Vmax. For ky = 0, the profile for V(x, ky) (see Fig. 25) is a periodic array of harmoniclike oscillators with finite depth and period 1/2. In this case, the first Brillouin zone (FBZ) edge is at k = 2zr/l and gaps in the spectrum appear only at k = 2nrc/1 where n is the band index. When ky takes values different from zero, the periodicity of V (x, ky) becomes twice as large and equals l and, consequently, the FBZ edge becomes k = 7r/1 and the

Fig. 26. Energy versus ky dispersion relation for a single 2D electron in the presence of a sinusoidal magnetic field modulation with period l = 8 and l = 16 (inset). The shaded regions are the lowest six energy bands. The dash-dotted curves are the maximum and minimum values of the effective potential V (x, ky).

382

HYBRID MAGNETIC-SEMICONDUCTOR NANOSTRUCTURES +

--

+

--

+

o

-1

~

-2

0

2

1

3

4

x/t Fig. 27. Possible classical trajectories with the same initial position but different initial velocities for the magnetic field model of Figure 25.

number of energy bands and gaps doubles. The bands with energy below the barrier height (the dash-dotted curves in Fig. 26 indicate the bottom and top of the potential profile), that is, E < Vmax, correspond to open orbits traveling along the y direction and oscillating around the boundary separating the two magnetic strips, which are also called snake orbits. Electrons at adjacent boundaries move in the opposite y direction. The 1D states below Vmax are similar to the so-called magnetoelectric states. Here, also, the electron motion along the + y directions are spatially separated by half a period 1/2. In Figure 27, examples of the three kinds of possible classical orbits are given: (1) 0D cyclotron motion, which occurs when the electron energy is sufficiently small such that its cyclotron diameter is less than the width of the magnetic strip (because of the spatial variation of the magnetic field, the orbit in this case is not a circle); (2) 1D drift parallel to the magnetic strips for states with the center of their cyclotron orbit near the interface between the +B0 and - B 0 regions, called snake orbits; and (3) 2D motion in the plane when the electron energy is larger than the magnetic field barriers, which results in a cyclotron diameter larger than the width of the magnetic strips. The zero-temperature density of states (DOS) for the system considered is calculated by numerically integrating the inverse of the magnitude of the energy gradient in momentum space along the constant energy contours at the Fermi energy and within the first Brillouin zone Do

= 2re

,, IVEn(k)l

(62)

where Do = m*/zch 2 is the DOS of the free 2DEG, n is the band index, and Sn is the constant energy contour. Spin splitting of the energy levels is neglected. The spin degeneracy is taken into account and no scattering is assumed other than the interaction with the magnetic field. The diagonal components of the electric conductivity tensor are calculated concurrently with the DOS and along the same constant energy contours where we used the expression - -

cro

--~

Vn,iVn,i

383

dSn

(63)

PEETERS AND DE BOECK

o-yy 0

!

6

b I,i v

b -

Dos

4

o

:

Ill Fm

2

m

0

1

2

,3

4

E (~'~c) Fig. 28. Density of states (DOS) and the diagonal components of the electric conductivity tensor versus Fermi energy for 2D electrons moving in a sinusoidal magnetic field.

where l)n,i : OEn/aki is the drift velocity and or0 is the Drude conductivity of the free 2DEG. This formula is valid for a diffusive type of transport at zero temperature. Notice that because there is no net magnetic field, that is, (B) = 0, we do not expect any Hall resistance and, consequently, O'xy : O. The density of states (DOS) (Fig. 28) is on the average the one of a free 2DEG except for singular points (1) resulting from the edges of the minibands, which occur for kx = (2n + 1)zr/l, n = 0, 1, 2, 3 . . . . ; and (2) resulting from the local minima in the energy spectrum (see Fig. 26), which occur for small ky values where Vy = 0. At these points in momentum space, the conditions for Bragg reflection are met for motion in the x direction and the average velocity in the y direction is zero. Electrons with these energies and wavevectors form standing waves with zero average velocity. This effect results in dips in the Crxx conductivity (Fig. 28). Note that no such clear structure is apparent in the O'yy conductivity because motion in the y direction does not exhibit this Bragg reflection. The tTyy conductivity is obviously the least affected by the presence of the magnetic field modulations along the x direction, because there are always states available for motion along the y direction regardless of the value of the Fermi energy. Furthermore, the number of these states increases with increasing energy. In contrast, the miniband structure has a pronounced effect on the Crxx component owing to the existence of energy gaps for motion along the x direction, where Crxx shows downward dips corresponding to the edges of the Brillouin zone where Vx ,~ O. The magnitude of Crxx does not become appreciable until the Fermi energy is near or above the magnetic potential barrier at ky : 0. The Crxx is always less than O'yy e v e n for high energies. The reason is that the effect of Bragg reflections, which does not influence tryy, persists up to high energiesma purely quantum mechanical effect. 6.3.2. Snakelike Orbits The effects of these snake orbits on the magnetotransport were investigated experimentally in [72]. They measured the magnetoresistance for different angles 0 between the external magnetic field and the 2DEG plane, which is shown in Figure 29. The results are plotted as a function of the z component of the applied field Bz, which is the component that affects the motion of the electrons in the 2DEG. The most striking feature is the appearance of

384

HYBRID MAGNETIC-SEMICONDUCTOR NANOSTRUCTURES

2.5

down ..... up

2.0 i ! ! ~

!

i

1.5

,-,,.

/

' ' " ..... " " ' , \ "'

1.0

/ t ' -/

d

\ IE 0.5

T=4.2K 0.0 -0.2

-0.1

0.0

0.1

0.2

B z (T) Fig. 29. Low-fieldmagnetoresistanceat 4 K as a function of the magnetic field componentperpendicular to the 2DEG for different tilt angles 0 of the magnetic field. (Source: Reprinted with permission from [72]. 9 1997 American Physical Society.)

a positive low-field magnetoresistance that becomes much stronger and extends to larger Bz as 0 increases. Rxx increases by a factor of up to approximately 2 on application of a Bz of only 50 mT. This can be understood from Figure 28 where increasing the magnetic field implies reducing (E = EF)/hCOc, which results in a decrease of the conductivity and, consequently, an increase of the resistance. The strong positive magnetoresistance is still observable well above 200 K, which suggests its semiclassical origin. The observed low-field magnetoresistance can be understood in terms of channeling of electrons along lines of zero magnetic field within the sample. These are the so-called snake orbits discussed previously. In this situation, two kinds of electron states coexist. Electrons that have a sufficiently large initial velocity component perpendicular to the magnetic strips will propagate across the sample in the same direction they would have in the absence of the modulation. Electrons with smaller initial velocity components cannot pass through the magnetic barriers and will be channeled in the y direction along snakelike orbits centered on the lines of zero B. The guiding center drift correction to the Dyy diffusion coefficient [58] leads to a magnetoresistance

ARxx = 2(COcr)2 (v2) RO

v2

(64)

where z is the elastic scattering time and (v2) is the appropriate average of the square drift velocity. This average was calculated [72] by numerically integrating the classical equation

385

PEETERS AND DE BOECK

2.0

1

1.5

~

1.0

0.5

.."

0=60

~

-

- ~ 1 7 6 1 7 6

O=45

0.0

0=15 i

0.00

.o

I

0.02

0=30 ,

I

~

0.04

I

0.06

~

I

0.08

B (T) Fig. 30. Measuredpositive magnetoresistance (dotted curves) for different tilt angles of the magnetic field (see Fig. 29) as compared to the calculated contribution (solid curves) from the different classical orbits. (Source: Reprinted with permission from [72]. 9 1997 American Physical Society.)

of motion for electrons traveling through the magnetic profiles. The numerical results are compared with the experimental results in Figure 30, and the dependence on the tilt angle is in good agreement with the experimental results, proving the existence of 1D electron states propagating along lines of zero magnetic field, that is, the snakelike orbits.

7. T W O - D I M E N S I O N A L M A G N E T I C M O D U L A T I O N

7.1. Periodic Two-Dimensional Modulation The energy spectrum of electrons moving in a 2D lattice in the presence of a perpendicular homogeneous magnetic field is determined by fascinating commensurability effects. When the flux through a unit cell of the lattice 9 -----Ba 2 is a rational multiple of the flux quantum ~o = c h / e , that is, ~ / ~ 0 = P / q , then the resulting energy spectrum consists of broadened Landau levels, each having the same internal structure, which is called the Hofstadter butterfly [ 103] when plotted versus the inverse flux ratio. The width of the Landau bands oscillates as a function of the Landau quantum number and the flux ratio ~ / ~ 0 . So far, this gap structure has not been observed directly in experiments. This band structure was investigated theoretically by several groups [ 104-108]. Recently, Gerhardts et al. [ 109] investigated this Hofstadter butterfly for the mixed 2D periodic electrostatic and magnetic modulation problem where they included higher harmonics and they found that the overall gap structure is similar to the one found in [103]. The classical dynamics was investigated in [ 110, 111 ]. The magnetoresitance of electrons in a periodic 2D magnetic field for different shapes of the magnetic field profile was investigated in [88, 90]. The experimental investigation of this system is still in its infancy. A 2D array of magnetic dysprosium dots on top of a GaAs/A1GaAs heterostructure was investigated in [74, 75]. The Dy micromagnets had a typical diameter of approximately 200 nm and a height of approximately 200 nm with a lattice period of a = 500 nm. No effects associated with the Hofstadter energy spectrum could be identified. The magnetoresistance was found [74] to exhibit commensurability oscillations very similar to those found in the case

386

HYBRID MAGNETIC-SEMICONDUCTOR NANOSTRUCTURES

of 1D modulation (see the previous section) with minima in the magnetoresistance occuring near 2Rc/a --n + 1 with n an integer. Also effects resulting from a strain-induced electrostatic periodic potential were observed [75]. By rotating the magnetization of the Dy dots, it was possible to induce a phase change of the magnetic stray field pattern with respect to the strain-induced electrostatic potential [75, 82].

7.2. A Random Array of Identical Magnetic Disks Here we consider a new system in which electrons are scattered by a random array of identical circular magnetic field profiles that are created by magnetic disks located a certain distance from a 2DEG. This problem is different from the magnetic flux tube problem that is encountered when a type II superconducting film is deposited on top of a heterostructure [ 112]. The essential difference is that in the present problem the local inhomogeneous magnetic fields have zero average magnetic field strength. Here the circular magnetic field profiles have an inner core with a magnetic field that is opposite to the outer part in such a way that the average magnetic field strength is zero. Recently, Van Roy et al. [6, 113] successfully fabricated a grating structure of magnetic material with a pattern of magnetic dots and antidots with period of about 600 nm. A similar structure with Dy micromagnets on top of a GaAs/A1GaAs heterostructure was realized by Ye et al. [82]. An alternative approach was demonstrated by McCord and Awschalom [114], who directly deposited nanometer-scale magnetic dots using a scanning tunneling microscope. They fabricated magnetic dots of diameter ranging from 10 to 30 nm and heights from 30 to 100 nm. The perpendicular magnetic field component produced by such a ferromagnetic disk of radius R with magnetic moment along the z direction is shown in Figure 31 a for different distances between the 2DEG and the ferromagnetic disk. The corresponding vector potential is inserted into the Schr6dinger equation. The radial equation contains an effective potential V(m, p) [see Eq. (33)], which is depicted in Figure 31b for the case of z/R = 0.02. It is clear that such a potential can only have scattered states. The scattering properties are described in terms of a phase shift 3m, which is determined by solving the Schr6dinger equation numerically. The zero-temperature magnetoresistance and Hall resistance are determined by (see, e.g., [115])

Rxx R0

= 2~

sin 2 ( 6 m

--

~m+1 )

(65)

m

and

Rxy R0 = Z

sin(Z(6m - ~ m + l ) )

(66)

m

where R0 = (h/e2)(no/n) with no the density of ferromagnetic disks and n is the electron density. The numerical results are shown in Figure 32 for b = (e/hc)MaJr R = 2, where M is the magnetization of the ferromagnetic disk and z / R -- 0.1. Notice that for small Fermi energies Rxy increases with kF as is also the case when a constant magnetic field is present. This implies that the electrons are only able to probe the outer part of the magnetic field profile of the magnetic disk. For large kF values, the electrons have sufficient energy such that they are able to penetrate the inner part of the magnetic field profile where the magnetic field is in the opposite direction. As a consequence, the average magnetic field felt by the electrons diminishes, which results in a reduction of Rxy. The oscillatory structure is a consequence of quantum mechanical resonances, which are a consequence of the quasi-bound states in the potential V (m, p). Note also that at resonance Rxy is reduced while Rxx exhibits a local maximum. The reason for the different behavior is that Rxx measures the actual resistance while Rxy is a measure of the Lorentz force.

387

PEETERS AND DE BOECK

z/R

15

0.02 10

0.05 ............ 0.1 0.2

.........

.......................

Ooo~

0

m m

.............

-5

t

- ....

~

-10

-15 I

I

I

|

I

'

'

'

I

0.5

0.0

.

1.0

.

.

,

......

I

|

,

2.0

1.5

r/R (a) I

9

I t"

t

"

I

9

I

m

"

t

"

I

9

t

:

I

_

> >

o

.~

0

"

I

9

t

"

I

9

t

".

.........

t

9

t

".

1 o,

t

t \

'='1

,

9

9**"Ooo ..... .,~176176 *

",.

I

%%

".0 " * . . . %%

0 0.0

i'" ..................

0.5

1.0

1.5

2.0

r/R (b) Fig. 31. (a) Magnetic field profile at a distance z under a ferromagnetic disk of radius R and (b) effective radial potential (in units of V0 = M/mo h2) for z/R = 0.02 and different values of the angular momentum m.

7.3. R a n d o m M a g n e t i c Fields

The p r o b l e m of electrons moving in a 2D static r a n d o m magnetic field has generated great experimental [60-63, 79, 80, 112, 116-120] and theoretical [121-123] interest. It is now understood to be distinctly different from transport in systems with ordinary potential dis-

388

HYBRID MAGNETIC-SEMICONDUCTOR NANOSTRUCTURES

lo

f'"

Rxx

""'"

e~

o

0

2

4

Fermi wavevector

6

kr

Fig. 32. Magnetoresistanceand Hall resistance of a 2DEG under the influence of a random area of magnetic field profiles producedby ferromagnetic disks.

order. This problem is closely related to the 2D quantum Hall system near half integer filling factor [124-127] and the gauge field description of the high Tc superconductivity problem [128-131]. Both problems can be mapped into a system of charged particles moving in the background of a random magnetic field. The essential issue in the theoretical studies is to determine how the random magnetic field affects the transport properties. The localization of electrons in random magnetic fields is still a controversial issue. In principle, all states of a 2D system are exponentially localized according to the scaling theory of localization [ 132]. But the presence of a magnetic field that destroys time-reversal symmetry makes a stand against localization. Perturbation renormalization group calculations show that all states remain localized [ 133, 134] but numerical simulations have not led to a definite conclusion (see, e.g., [135, 136]). It is generally accepted that, except for weak localization effects [ 137] yielding small quantum corrections to the magnetoresistance at weak fields and at low temperatures, the semiclassical approach is an adequate framework "--,1 length over which the random magnetic field varies is much larger than -~ the electrons. In [138, 139], the effect of the random magnetic )llision term of the Boltzmann equation. A different approach in c field was included in the driving force of the transport equasee also [123]) using perturbation theory. Khveshchenko [ 141] ,n in a random magnetic field with long correlation length in ! derived a nonperturbative result based on an eikonal approxa ergodic hypothesis that allowed him to study the random 'gitrary correlation length and in both the diffusive and ballis-

r/a

a 2DEG have been realized by using stochastically dissuperconducting film [60-63, 112, 142-145], supercon~G grown on substrates with prepatterned submicrometer ;copic magnets [ 116, 117], and a random distribution of The latter was achieved by depositing dysprosium dots

389

PEETERS AND DE BOECK

68

64

C~ 60 56

52

-0.6-0.4-0.2

0.0

0.2

Bo(T)

0.4

0.6

Fig. 33. Magnetoresistanceof a 2DEGresulting from a random area of Dy disks with average separation (a) = 400 nm as a function of the external magnetic field B0 for different strengths of the magnetization of the disks that are determined by the conditioning field Bmax. The asymmetry is due to the hysteresis loops of the micromagnets. (Source: Reprinted with permission from [75].)

with submicrometer diameters randomly on top of a high-mobility GaAs/A1GaAs heterojunction. This system is essentially different from the flux tube system because now the local inhomogeneous magnetic fields have zero average field strength. The circular magnetic field profiles of the dot have an inner core with a magnetic field that is opposite to the outer part in such a way that the average magnetic field strength is zero. As a typical experiment, we consider the results of Ye et al. [75]. They started from a high-mobility GaAs/A1GaAs heterostructure (/z - 1.4 • 106 cm2/V s, ne - 2.2 x 1011 cm -2 at T -- 4.2 K) in which the 2DEG was located approximately 100 nm underneath the sample surface. A 10-nm-thick NiCr film was evaporated on top of the device which defines an equipotential plane to the 2DEG. A random distribution of Dy dots with height 200 nm and with different density was defined by electron beam lithography on top of the NiCr gate. In Figure 33, the magnetoresistance of the 2DEG at 4.2 K is displayed for a random distribution of Dy dots with an average interparticle distance of (a) = 400 nm. The different traces correspond to different magnitudes of the magnetization of the micromagnets. The random magnetic field is probably accompanied by a strain-induced electrostatic random potential as discussed before for the periodic modulated magnetic field case. These random magnetic fields give rise to (1) an increase of the zero magnetic field resistance and (2) a pronounced positive magnetoresistance, both of which increase with increasing strength of the magnetization of the micromagnets. Similar behavior has been found by others in other 2DEGs with random magnetic fields.

8. H A L L E F F E C T DEVICES When a magnetic field is applied to a metallic system that carries a current, a Hall voltage develops in the direction perpendicular to the magnetic field and the current because of the Lorentz force. This phenomenon is called the Hall effect [ 146] and has been used very successfully to obtain information on the properties of the charge carriers, for example, the sign and the density of those carders. In most previous investigations of the Hall effect, the applied magnetic field is uniform and its strength is known. In [112, 147-150], the Hall effect of a known 2DEG was used as a probe of the magnetic field. In such a case, t' experimental system consists of a microfabricated Hall bar in which an inhomoge magnetic field is piercing through the Hall cross. This inhomogeneous magnetic "

390

HYBRID MAGNETIC-SEMICONDUCTOR NANOSTRUCTURES

result, for example, from magnetic or superconducting clusters [112, 149] that are placed on top of the Hall bar. Such Hall probes have become increasingly popular as local magnetometers for superconducting and ferromagnetic materials because of their (1) noninvasive nature; (2) high magnetic field sensitivity; (3) very small active region, that is, the cross region of the Hall bar, which, using modem microfabrication techniques, can be of submicrometer dimensions; and (4) broad temperature and magnetic field region over which they can be used. In [ 151-153], a quantitative theory was presented that relates the measured Hall voltage to the local flux through the Hall probe. This is needed in order to interpret the experimental data obtained from the Hall magnetometer and to understand the mechanism behind the functioning of Hall devices. Such a theory was given in the ballistic regime [152], which is applicable at low temperatures (up to liquid nitrogen temperatures) and for small Hall probes, and in the diffusive regime [148, 153], which is more applicable for larger Hall crosses and/or for higher temperatures. We find that in the ballistic regime the relation between the measured Hall voltage and the probed inhomogeneous profile is able to provide much more detailed information than the equivalent system in the diffusive regime. In this section, we investigate the effect of micrometer and submicrometer spatial variations of the magnetic field on a 2DEG. Knowing the response of a 2DEG to these magnetic field inhomogeneities is an important fundamental research problem in its own fight but, in addition, has direct consequences on the development of microelectronic devices and applications that, in recent years, have witnessed a growing interest in exploiting the versatility and added functionality of the Lorentz force on a submicrometer scale. For instance, (i) a magnetoelectronic device in the shape of a Hall cross was recently shown to have the potential of operating as a bistable memory cell or logic gate component, (ii) with Hall probe microscopy it is possible to observe the dynamics of a single flux vortex and domain walls in superconducting films and magnetic materials, and (iii) Hall components are used as magnetic field sensors for distance and speed detection in brushless engines such as used in floppy and CD-ROM disc drives.

8.1. Ballistic Hall Magnetometry In the inset of Figure 34a, we show the system under study, which consists of a Hall bar with four identical leads and a circular magnetic field profile situated in the middle of the cross junction. As an example, we consider two kinds of circular magnetic field profiles. The first profile is a superconducting disk in an external magnetic field. Because of the Meissner effect, the magnetic field will be expelled from the superconducting disk. We model the field distribution underneath the disk as zero inside a region of radius d, and constant outside it. In this way, we neglect the overshoot of the magnetic field at the edge of the disk, which is sensitive to several system parameters such as the thickness of the superconducting disk and the distance of the disk from the 2DEG. The second profile is a ferromagnetic disk that we model by a magnetic dipole placed a distance z0 above the cross junction in the absence of an external magnetic field. The Hall resistance is calculated numerically using the semiclassical formalism. The current in lead i is denoted by li, which can be expressed according to the LandauerBtittiker formula as [20]: li --

(Ni - Ri)Izi - Z TijlZj j~-i

(67)

where Tij is the transmission probability for an electron from lead j to lead i and Ri is the reflection probability for returning back into the same lead i. In practice, these probabilities are calculated at the Fermi energy EF, and satisfy ~j:fii rij -]- gi -- Ni, according to the condition of current conservation, where Ni is the number of propagating modes in lead i.

391

PEETERS AND DE BOECK

Fig. 34. (a) Hall resistance of the magnetic antidot configuration (see inset of figure) as a function of the magnetic field for different sizes (d) of the antidot. (b) Hall coefficient c~ = RH/B in the low-magnetic-field region as a function of the disk radius (lower curves). The upper curves are obtained from ct* = RH/(B), where (B) is the average magnetic field in the junction. The dotted curves are the results for a cross with rounded comers (see inset of figure).

F o r the f o u r - l e a d H a l l g e o m e t r y w i t h i d e n t i c a l leads, the H a l l r e s i s t a n c e RH c a n b e f o u n d f r o m Eq. (67) b y setting I1 = - 1 3 = I a n d 12 = 14 - 0 a n d results in RH -" (/Z2 - - / z n ) / e _ h T21 - T21 I -- 2e 2 Z

392

(68)

HYBRID MAGNETIC-SEMICONDUCTOR NANOSTRUCTURES

where Z - [T221+ T421+ 2T31(T31 ~- T21 q- T41)](T21 q- T41). For the asymmetric Hall system with either unidentical leads or asymmetric magnetic field in the cross junction, the simple formula (68) breaks down. In this case, the Hall and bend resistances should be solved from Eq. (67) by setting the same boundary conditions for the currents as used in the derivation of Eq. (68). To obtain the probabilities 7~j and Ri, we follow the semiclassical approach developed by Beenakker and van Houten [ 154]. Thus, we neglect quantum interference effects, which are expected not to be important when AF 105) toward the junction through lead 1, and follow their classical trajectories to determine the probabilities Tjl -- Nj/Ne, where Nj is the number of electrons collected in lead j. Note that for the case of unidentical leads or asymmetric magnetic field profile, similar procedures should be followed for each of the four leads. The electrons are injected uniformly over lead 1, with a Fermi velocity VF = ~/2eF/m and an angular distribution P(O) ----- I cos0, where 0 6 ( - z r / 2 , zr/2) is the injecting angle with respect to the channel axis. In the following, we will express the magnetic field in units of B0 -- mvF/2eW and the resistance in R0 = (h/2eZ)zc/2kFW, where W is the half-width of the lead, m the mass of the electron, kF = (2mEF/li2)1/2 the Fermi wavevector, and VF -- hkF/m the Fermi velocity. For electrons moving in GaAs (m = 0.067me) and for a typical channel width of 2W = 1 /zm and a Fermi energy of Er~ = 10 meV (ne = 2.8 x 1011 cm-2), we obtain B0 = 0.087 T and R0 = 0.308 k~. First, we discuss the magnetic field profile that models the situation with a superconducting disk above the junction, which may be called a magnetic antidot. In Figure 34a, we show the Hall resistance as a function of the external applied magnetic field for different disk sizes. Notice that there exists a critical magnetic field Bc = Bc(d), such that for B > Bc the Hall resistance in the presence of the disk coincides with that for the homogeneous magnetic field case (i.e., d = 0). When B < Bc, the Hall resistance is sensitive to the presence of the disk. At this critical magnetic field Bc, the diameter of the cyclotron orbit, 2Rc = 2VF/O)c, equals the distance between the edge of the dot and the comer of the cross junction: 2Rc = ~/2W - d. For B > Bc, the motion of the electron is determined by skipping orbits, located along the edge of the device, which do not feel the presence of the B = 0 region in the cross junction and the Hall resistance equals the classical 2D value: RH/Ro = 2B/zr. We have Bc/Bo = 4.4, 7.8, 18.7 for d~ W = 0.5, 0.9, 1.2, respectively. Notice that in the absence of the magnetic antidot, that is, d = 0, we find Bc/B0 = x/~ = 1.41, which is the field where the 2D Hall and bend resistance is recovered. For B/Bo L. (iv) The repulsive energy between two vortices decreases as 1/ r, similar to a Coulomb repulsion between two electric charges [23]. This implies that the repulsive interaction between vortices in a thin film is of longer range than in a bulk superconductor.

1.4.6. Flux Pinning A superconductor can carry a direct current without losses if the current density is smaller than the superconducting critical current density jc of the material [23]. Reasonable values for the critical current density in an applied field can be obtained if the flux lines are

462

QUANTIZATION AND CONFINEMENT PHENOMENA

prevented from moving, because a moving vortex induces an electric field parallel to the current density j and hence dissipates energy. The origin of the flux motion and the associated dissipation is the Lorentz force from the current density j acting on the flux lines, which is per unit length and for one vortex given by fL -- j x ~0

(36)

The Lorentz force tends to move the vortices transverse to the current. To suppress the motion of the vortices, the Lorentz force should be counteracted by a pinning force fp. The total force acting on a flux line per unit length is the sum of several contributions [26]: f = fL -- fP -- ~TVv-- fM

(37)

with 0Vv a small friction-like contribution proportional to the vortex velocity Vv, and fM the Magnus force, which usually is negligible. A general formula for fp cannot be given, because it strongly depends on the specific type of pinning center. The average macroscopic pinning force per unit volume (fp) is linked to the critical current density by the expression:

fp = jcB

(38)

The theoretical upper limit for the critical current is determined by the depairing critical current IcGL(T) at which the superconducting Cooper pairs are destroyed, and is given by the following expression [27]: 4 Hc(T) GL I c ( T ) = 3~/6 Z(T)

(39)

1.4. 7. Pinning Mechanisms A vortex can be trapped or pinned because of the presence of spatial variations in the free energy of the flux line lattice. Almost any kind of defect can create local minima in the free energy landscape (e.g., crystalline imperfections, columnar defects, grain boundaries, thickness variations of a film, etc.). Depending on the interaction between the vortex and the pinning center, a distinction can be made between two contributions to the pinning mechanism: core pinning and electromagnetic pinning [28]. Core pinning is the origin of flux pinning at most point defects, and refers to the local variation of Tc or x, which reduces the free energy if the vortex core is located at the position of the (normal) defect. Electromagnetic pinning is due to the kinetic energy of the confined screening currents around the defect and the perturbation of the magnetic field of a vortex. Theoretically, it can be described by assuming an antivortex image, in analogy with electrostatics. Thickness variations of a film can lead to the presence of the admixture of this type of pinning. The vortices are pinned at locations of smallest thickness where their energy is lowest [Eqs. (24) and (31)]. The typical length scale for this kind of pinning is the penetration depth )~. Both the core and the electromagnetic contributions define the pinning, which eventually controls the critical current density jc. After a brief introduction into the problem of optimizing the two critical parametersm Tc(H) and j c ( H ) m w e are now ready to formulate the layout of this chapter. We present the systematic analysis of the influence of the confinement geometry on the superconducting phase boundary Tc(H) in a series of nanostructured samples. We start with individual nanostructures of different topologies (lines, loops, dots) (Section 2) and then focus on "intermediate" systems: clusters of loops fabricated in the form of a 1D chain of loops (Section 3.1) or 2D antidot clusters (Section 3.2). Huge arrays of antidots are considered in Section 4 where we deal, first of all, with the Tc(H) boundary for superconducting films with antidot lattices. Having demonstrated the importance of the confinement geometry of the superconducting condensate for the optimization of the critical parameter Tc(H), we

463

MOSHCHALKOV ET AL.

move on, further in Section 4, to flux confinement phenomena in superconductors with an antidot lattice. We discuss the novel flux phases that can be stabilized by introducing regular pinning arrays. We show that lateral nanostructuring can lead to a substantial enhancement of the critical current density j c ( H ) (up to the depairing current) and to the appearance of a variety of commensurability effects between the periodic pinning potential and the vortex lattice.

2. I N D I V I D U A L N A N O S T R U C T U R E S To begin this section, we present the experimental results on the Tc(H) phase boundary of individual superconducting mesoscopic structures of different topology. It is important to keep other parameters of these structures the same, such as the material from which they are made (A1), the width of the lines (w = 0.15/zm), and the film thickness r = 25 nm, thus directly relating the differences in Tc (H) to topological effects. The magnetic field H is always applied perpendicular to the structures.

2.1.

Line

In Figure 1 la, the phase boundary Tc(H) of a mesoscopic line [29] is shown. The solid line gives the Tc(H) calculated from the well-known formula [30]:

[

zr2(w~(O)lz~

Tc ( n ) -- Tc0 1 - ~

(Do

(40)

which, in fact, describes the parabolic shape of Tc(H) for a thin film of thickness w in a parallel magnetic field. Because the cross section, exposed to the applied magnetic field, is the same for a film of thickness w in a parallel magnetic field and for a mesoscopic line of width w in a perpendicular field, the same formula can be used for both [29]. Indeed, the solid line in Figure 1 l a is a parabolic fit of the experimental data with Eq. (40) where ~(0) = 110 nm was obtained as a fitting parameter. The coherence length obtained using this method coincides reasonably well with the dirty limit

6

. . . .

,

,

,

.

L,

_

.....

,

. . . . . .

16

(a) 12

12 0.15/Jm

E

no

8

"1O

=L 4

bulk AI

':

0 0.85

0.90

0.95

1.00

0,85

0.90

0.95

1.00

T (H)/T o Fig. 11. Measured superconducting/normal phase boundary as a function of the reduced temperature

Tc(H)/Tc0for (a) the line and (b) the loop and the dot. The solid line in (a) is calculated using Eq. (40) with ~(0) = 110 nm as a fitting parameter. The dashed line represents Tc(H) for bulk A1. Comparing Tc(H) for these three different mesoscopic structures, made of the same material, one clearly sees the effect of topology on Tc(H). (Source: Reprinted with permission from [5]. 9 1998 American Institute of Physics.)

464

QUANTIZATION AND CONFINEMENT PHENOMENA

value ~(0) = 0.85(~01) 1/2 -- 132 nm calculated from the known BCS coherence length ~0 = 1600 nm for bulk A1 [23] and the mean free path l = 15 nm, estimated from the normal state resistivity p at 4.2 K [31 ]. Another simple argument can be used as well to explain the parabolic relation Tc(H) cx H 2. The expansion of the energy E ( H ) in powers of H, as given by the perturbation theory, is [32]: E ( H ) = Eo-t- A 1 L H + A2SeH 2 + . . .

(41)

where A1 and A2 are constant coefficients, the first term E0 represents the energy level in zero field, the second term is the linear field splitting with the orbital quantum number L, and the third term is the diamagnetic shift, with Se the area exposed to the applied magnetic field. Now, for the topology of the line with a width w much smaller than the Larmor radius rI-I >> w, any orbital motion is impossible because of the constraints imposed by the boundaries onto the electrons inside the line. Therefore, in this particular case, L -- 0 and E ( H ) -- Eo + A2SeH 2, which immediately leads to the parabolic relation Tc cx H 2. This diamagnetic shift of Tc(H) can be understood in terms of a partial screening of the magnetic field H caused by the nonzero width of the line [27].

2.2. Loop The To(H) of the mesoscopic loop [29], shown in Figure 1 lb, demonstrates very distinct Little-Parks (LP) oscillations [33] superimposed on a monotonic background. A closer investigation leads to the conclusion that this background is very well described by the same parabolic dependence as the one discussed for the mesoscopic line [29] (see the solid line in Fig. 11 a). As long as the width of the strips w, forming the loop, is much smaller than the loop size, the total shift of Tc(H) can be written as the sum of an oscillatory part and the monotonic background given by Eq. (40) [29, 34]: [ 7r2 ( w ~ ( 0 ) / z 0 H ) 2 Tc(H)-- Tc0 1 - ~ ~0

~2(0) ( ~)2] R2 n - ~ 0

(42)

where R 2 = R1 R2 is the product of the inner and outer loop radius, and the magnetic flux threading the loop 9 = Jr R21zoH. The integer n has to be chosen so as to maximize Tc(H) or, in other words, selecting the lowest Landau level ELLL(H). The LP oscillations originate from the fluxoid quantization requirement, which states that the complex order parameter qJs -- IqJsl exp(iqg) should be a single-valued function when integrating along a closed contour f Vqg. dl = n21r

n .....

- 2 , - 1 , 0, 1, 2 . . . .

(43)

Fluxoid quantization gives rise to a circulating supercurrent in the loop when ~ ~ n~0, which is periodic with the applied flux ~ / ~ 0 . Using the sample dimensions and the value for ~ (0) obtained before for the mesoscopic line (with the same width w = 0.15/zm), the Tc(H) for the loop can be calculated from Eq. (42) without any free parameter. The solid line in Figure 1 lb shows indeed good agreement with the experimental data [29]. It is worth noting here that the amplitude of the LP oscillations is about a few millikelvins--in qualitative agreement with the simple estimate given in Table I for LA "~ 1 /zm. The susceptibility of a single mesoscopic A1 ring, showing LP oscillations, has been studied recently by Zhang and Price [35], who found an excellent agreement with the GL theory for the susceptibility below Tc.

465

MOSHCHALKOV ET AL.

The lower critical field of a loop is found from the condition that half a flux quantum is applied, thus giving [36]: r41oop - 1 ~0 O..c l E-E2

(44)

which is totally different from the Hcl value of a bulk superconductor [see Eq. (13)]. The superconducting loop (Fig. 1lb) nicely demonstrates the classical Little-Parks oscillatory Tc(H) phase boundary [33], related to the quantization of the total flux threading the loop area. Moreover, in this simple homogeneous superconducting loop, the two supercurrents 11 and 12 flowing in the different branches of the loop gain opposite phases -4-zr~ / ~ 0 from the perpendicular applied field [37, 38]: I1 (X sin ( / 5_- o_t - T~ r o)

(45)

I2 (x sin /5 - c~ + zr

(46)

The interference of the currents flowing through the two branches of the loop produces an oscillatory dependence of the total current I = I1 + / 2 : I cx sin(/5 - or) cos zr

(47)

The current amplitude in Eq. (47) is determined by the phase difference Aq)=/5 --ot (as in the first Josephson equation I (x sin Aq)) [23, 39]. The critical current Ic for the homogeneous loop is obtained by taking sin Aq) = 1 in Eq. (47) [37]:

(~

Ic cx cos n" ~ 0

(48)

Equation (48) implies that the critical current of a mesoscopic superconducting loop without artificial Josephson weak links oscillates with the applied magnetic field in the same way as it does in a classical SQUID with extrinsic weak links. The existence of these oscillations, predicted by Fink et al. [37, 38], has been confirmed experimentally by Moshchalkov et al. [40] and is shown in Figure 12. Another interesting feature of a mesoscopic loop and other mesoscopic structures is the unique possibility they offer for studying nonlocal effects [41 ]. In fact, a single loop

Ic ,.~176176176176176

0.8 0.6 0.4 0.2 0

.:9

0

0.5

.-

1

1.5

~..

2

2.5

3

Fig. 12. Oscillations of the critical current Ic of a 1 /zm x 1 /zm square A1 loop as a function of the normalized flux ~ / ~ 0 . The solid line corresponds to the calculations based on the theory of Fink et al. [38], while the dashed line is the sinusoidal variation of Ic in a conventional SQUID with two Josephson junctions. (Source: Adapted from [40].)

466

QUANTIZATION AND CONFINEMENT PHENOMENA

can be considered as a 2D artificial quantum orbit with a fixed radius, in contrast to Bohr's description of flexible atomic orbitals. In the latter, the stable radii are found from the quasiclassical quantization rule, stating that only an integer number of wavelengths can be set along the circumference of the allowed orbits. For a superconducting loop with an arbitrary fixed circumference, however, supercurrents must flow, in order to fulfill the fluxoid quantization requirement [Eq. (43)], thus causing oscillations of the critical temperature Tc versus the magnetic field H. To measure the resistance of a mesoscopic loop, electrical contacts have, of course, to be attached to it, and, as a consequence, the confinement geometry is changed. A loop with

attached contacts and the same loop without any contacts are, strictly speaking, different mesoscopic systems. This "disturbing" or "invasive" aspect ("Schr6dinger cat") of probing a quantum object can now be exploited for the study of nonlocal effects [41 ]. Because of the divergence of the coherence length ~ (T) at T = Tc0 [Eq. (6)], the coupling of the loop with the attached leads is expected to be very strong for T --+ Tc0. Figure 13 shows the results of these measurements [41 ]. Both "local" (potential probes across the loop V1/V2) and "nonlocal" (potential probes aside of the loop V1/V3 or V2/V4) LP oscillations are clearly observed. For the "local" probes, there is an unexpected and pronounced increase of the oscillation amplitude with increasing field, in disagreement with previous measurements on A1 microcylinders [34]. In contrast to this, for the "nonlocal" LP effect, the oscillations rapidly vanish when the magnetic field is increased. When increasing the field, the background suppression of Tc [Eq. (40)] results in a decrease of ~(T). Hence, the change of the oscillation amplitude with H is directly related to the temperature-dependent coherence length. As long as the coherence of the superconducting condensate protuberates over the nonlocal voltage probes, the nonlocal LP oscillations can be observed. On the other hand, the importance of an "arm" attached to a mesoscopic loop, was already demonstrated theoretically by de Gennes in 1981 [42]. For a perfect 1D loop

16

,

,

,

l

,

,

,

l

,

,

,

,

,

~ ~ 12.._~ ~p ~ . ~ , "n~1761_I ! local

=1. 4

1'

-4

'' 1.2

,,"

1

,,fii b T N

.

, ' , . . 1.22

, . , 1.24

,

To(K)

1

, 1.26

~ 1.28

Fig. 13. Local(V1/V2) and nonlocal (V1/V3 or V2/V4) phase boundaries Tc(H). The measuring current is sent through I1/12. The solid and dashed lines correspondto the theoretical Tc(H) of an isolated loop and a one-dimensional line, respectively, both made of strips of width w. The inset shows a schematic of the structure, where the distance P = 0.4/xm. (Source: Reprinted with permission from [5]. 9 1998 American Institute of Physics.)

467

MOSHCHALKOV ET AL.

Fig. 14. Schematicview of a mesoscopic loop in (a) the multiply connected state and (b) the singly connected state, where a normal spotis spontaneouslycreated and consequentlyno supercurrent flows.

(vanishing width of the strips), adding an "arm" will result in a decrease of the LP oscillation amplitude, which was observed indeed at low magnetic fields where ~ (T) is still large. With these experiments, it has been proved that adding probes to a structure considerably changes both the confinement topology and the phase boundary Tc(H). The effect of topology on Tc(H), related to the presence of the sharp comers in a square loop, has been considered by Fomin et al. [43]. In the vicinity of the comers, the superconducting condensate sustains a higher applied magnetic field because at these locations the superfluid velocity is reduced, in comparison with the ring. Consequently, in a field-cooled experiment, superconductivity will nucleate first around the comers [43]. Eventually, for a square loop, the introduction of a local superconducting transition temperature seems to be needed. As a result of the presence of the comer, the Hc3(T) of a wedge with an angle 0 [44] will be strongly enhanced at the comer. Another interesting possibility for a superconducting ring has been analyzed [45-49]: Under certain conditions, superconductivity spontaneously breaks at some spot along the perimeter of the ring, so that the superconducting area changes from multiple to single connectivity. The physics behind this interesting theoretical prediction is the following. The oscillatory Tc(~) phase boundary is caused by a periodic variation of a circular supercurrent (when the applied flux ~ / ~ 0 is not integer; see Fig. 14a), which is induced in a ring in order to fulfill fluxoid quantization. The highest current [and, therefore, the strongest reduction of Tc(~)] is realized for half integer flux when ~ / ~ 0 - n = 1/2 (see Figs. l l b and 13). In this situation, it may turn out, however, that somewhere in the ring the order pa' rameter Us is spontaneously suppressed and a sort of "normal core" is created somewhere along the ring circumference (see Fig. 14b). The energy of this normal state core, below the Tc(~) line, is, of course, higher than the energy corresponding to a superconducting state everywhere in the ring, but, at the expense of that, the circular supercurrent is interrupted, thus effectively opening the ring for entrance and removal of flux. While Horane et al. [45] predicted the existence of the singly connected state for rings made of "ID" strips, Berger and Rubinstein [48] showed that the temperature region where the singly connected state exists can be enhanced by proper tuning of the nonuniform "strip width" profiles along the ring. 2.3. Dot

For a cylindrical symmetry, the choice of the coordinates (r, ~, z) and the gauge A = (Hr/2)e~o, where e~0 is the tangential unit vector, is well suited. The solution of the Hamiltonian [Eq. (3) with the nonlinear term neglected] in cylindrical coordinates has the following form [50]: qJs(r, ~o)=

exp(-t-iL~o)rLy(L+l)/2exp(-@)M(-N, L + 1, yr 2)

468

(49)

QUANTIZATION AND CONFINEMENT PHENOMENA

Here y - e*IzoH/h and the energy E• of the motion in the plane perpendicular to H is determined by the orbital quantum number L and parameter N, which is not necessarily an integer number, as we shall see later: E•

e*hlzoH

~ ( 2 N 2m*

4-L + L + 1)

(50)

The function M is the Kummer function defined as

a a(a -k- 1) y2 a(a + 1)(a + 2) y3 M(a, c, y)-- 1 + - y + ~ +... c c(c + 1) 2! c(c + 1)(c + 2) 3!

(51)

where a -- - N , c -- L + l, y -- y r 2. Introducing the dimensionless radius R -- v/Vr 2 = ~ / ~ 0 , the superconducting order parameter can be written in the form

The representation of the order parameter qJs - Y~L CLq~L as an expansion over states with different L for infinite samples has been analyzed in [51 ], where M (0, L + 1, R 2) -- 1 has been taken. Under these conditions, the functions Iq~LI have their maxima at R 2 -- L; that is, the area enclosed by the circle with radius corresponding to the IqJL I maximum is always penetrated by an integer number L of the flux quanta: ~ / ~ 0 - L. In this chapter, we shall analyze the case of finite samples, where the N value has to be found from the boundary condition [Eq. (8)]. It is very important to note that in the general form (Eqs. (49) and (50)) there are no limitations on the parameter N. It is not necessarily an integer number. The only argument, which is usually given in favor of taking integer N, is a possibility to get a cut off in the summation [Eq. (51)]. Indeed, if one inserts an integer N into the summation, then by adding 1 to N in each new term one eventually comes to the situation where - N + N -- 0 and all subsequent terms in the summation will be equal to zero. Thus, by the cutoff we just use a finite number of terms in the summation [Eq. (51)] and, of course, M is finite in this case. We should keep in mind, however, that any converging, but infinite row also gives a finite solution for M. Therefore, not only positive integers N in Eq. (50), but also noninteger and even negative N values are possible. In finite size samples, the N value, which we further denote as N(L, Ro), has to be found from the boundary condition at R -- R0 [Eq. (8)], where R0 is the normalized disk radius: OlWs(e)l

0R

(53)

R=Ro

Because we are looking for the lowest possible energy state, we should take the minus sign in the argument of the exponent e x p ( - i Lqg) in the solution given by Eq. (51). In this case - L and + L in Eq. (50) cancel and for any L the energy levels are given by

E•

+ ~)

(54)

where co = e*lzoH/m* is the cyclotron frequency. This result coincides with the well-known Landau quantization, but now N is any real number, including negative real number, which is to be calculated from Eq. (53). Using the expression

dM(a, c, y) a = - m ( a + 1, c + 1, y) dy c

(55)

for the derivative of the Kummer function, we can find the N(L, Ro) value, which obeys the boundary condition [Eq. (53)], from the equation:

(L-RZ)M(-N'L+

2NR 2 l'R2)

L+ 1M(-N+

469

1' L + 2 ' R~ - - 0

(56)

MOSHCHALKOV ET AL.

I

I

10

. \'L ~ -12 '

0

I

0

I

5

10

15

t

2O

~/~ 0

Fig. 15. Energylevels versus normalized flux ~/~0 for a superconducting cylinder in a parallel magnetic field. The lowest-lyingcusplike Hc3(T) line is formed because of the change of the orbital quantum number L. (Source: Reprinted with permission from [53]. (g) 1996American Physical Society.)

The remarkable thing about the N(L, Ro) values, found from the solutions of Eq. (53), is that they are negative, which immediately gives the energy E• in Eq. (54) lower than

hco/2. As a result of the confinement with the superconducting boundary conditions, the energy levels infinite samples lie below the classical value hco/2 for infinite samples [52]. The whole energy level scheme (Fig. 15), found by Saint-James [52], can be reconstructed by calculating E• versus R 2 for different L values. From this diagram, one can easily go to the field versus temperature plot, using the relation E• = -c~. The corresponding values of the Abrikosov parameter/3A, giving an idea about the flatness of I~Psl [39], are plotted in Figure 16. It should be noted that flA for certain L and H (see the levels below the dashed line in Fig. 16) is smaller than the well-known minimum possible value/TA --- 1.16 for the triangular Abrikosov vortex lattice. To conclude this discussion, we note that in finite samples N is a bad quantum number. It is rather a parameter that has to be found from the boundary condition. A good quantum number for the problem is L. By forming a superconducting condensate with a proper finite L and N(L, R0) < 0, we conserve the rotational momentum and, at the same time, reduce the energy below hoJ/2 [53]. As shown previously, because of the onset of surface superconductivity at He3 (T), corresponding to negative N in Eq. (54), the superconductivity can appear at magnetic fields well above the Hc2(T) line (found for N = 0). By changing the variable E• in Figure 15 into T, we obtain the cusplike phase boundary Hc3(T) as shown in Figure 17, which is due to switching between different orbital momenta L. The phase boundary of the superconducting disk (Fig. 17) has been observed experimentally by Buisson et al. [52] and by Moshchalkov et al. [29]. It should be emphasized here that the presence of the oscillations in the Hc3(T) curve is crucially dependent on the imposed Neumann boundary conditions [36]. Contrary to that, the equivalent eigenvalue spectrum with Dirichlet

470

QUANTIZATION AND CONFINEMENT PHENOMENA

'

I

'/

I

/ L=O


@c, modulated I%1 states, with an incommensurate fluxoid pattern, were found. At ~ / ~ 0 = 1/2, nodes appear at the center of every second common (transverse) branch. A variety of other structures (micronets, coupled tings, bolas, a yin-yang, infinite microladders, bridge circuits, such as a Wheatstone bridge, wires with dangling branches, etc.) formed by 1D wires have been analyzed in a series of publications [37, 42, 68, 69, 71-81] using the approach initiated in 1981 by de Gennes [42] and further developed by Alexander [67] and Fink et al. [37]. For all these structures, very pronounced effects of topology on Tc (~) and critical current have been predicted.

476

QUANTIZATION AND CONFINEMENT PHENOMENA

Fig. 23. AFM image of the Pb/Cu 2x2 antidot cluster (on the left) and the reference sample (on the right). (Source: Adapted from [82].)

3.2. Two-Dimensional Clusters of Antidots As a 2D intermediate structure between individual elements A and their huge arrays (Fig. 3), we shall consider the superconducting microsquare with a 2 x 2 antidot cluster [82, 83]. In this case, the symbol A from Figure 2 indicates an "antidot." This microsquare with the 2 x 2 antidot cluster consists of a 2 x 2 / z m 2 superconducting square with four antidots (i.e., square holes of 0.53 x 0.53/zm2). A Pb/Cu bilayer with 50 nm of Pb and 17 nm of Cu was used as the superconducting film for the fabrication of this structure [83]. The thin Cu layer was deposited on the Pb to protect it from oxidation and to provide a good contact layer for wire bonding to the experimental apparatus. An AFM image of the Pb/Cu 2 x 2 antidot cluster is shown in Figure 23 together with a reference sample (i.e., a Pb/Cu microsquare of 2 x ,2/zm 2 without antidots). The Pb(50 nm)/Cu(50 nm) bilayer behaves as a type II superconductor with a Tc0 = 6.05 K, a coherence length, ~(0) ,~ 35 nm, and a dirty limit penetration depth, )~(0) ,~ 76 nm. The Tc(H) measurements on the reference sample [82] revealed characteristic features originating from the confinement of the superconducting condensate by the dot geometry (see Section 2.3). The additional features observed in the Tc(H) phase boundary of the antidot cluster can, therefore, be attributed to the presence of the antidots. The experimental Tc(H) phase boundary is shown in Figure 24. It was measured by keeping the sample resistance at 10% of its normal state value and varying the magnetic field and temperature [82]. Strong oscillations are observed with a periodicity of 2.6 mT and, in each of these periods, smaller dips appear at approximately 0.75 mT, 1.3 mT, and 1.8 mT. The parabolic background superimposed on Tc(H) can again be described by Eq. (40). Defining a flux quantum per antidot as ~0 = h / 2 e = BS, where B = / z 0 H and S is an effective area per antidot cell (S = 0.8/zm2), the minima observed in the magnetoresistance and the Tc (H) phase boundary at integer multiples of 2.6 mT can be correlated with a magnetic flux quantum per antidot cell, ~ = n~0. Those observed at 0.75 mT, 1.3 roT, and 1.8 mT correspond to the values ~ / ~ o = 0.3, 0.5, and 0.7. The solutions obtained from the London model define a phase boundary that is periodic in ~ with a periodicity of ~0. Within each parabola ATc = y ( ~ / ~ 0 ) 2, where the coefficient y characterizes the effective flux penetration through the unit cell. The y value is determined by the combination of X and the effective size of the current loops. In Figure 25, the first period of this phase boundary, A Tc (~) = Tc0 - Tc (~) versus ~ / ~ 0 , is shown. There are six parabolic solutions given by a different set of flux quantum numbers {hi }, each one defining a specific vortex configuration. In Figure 25a, this is indicated by the numbers shown inside the schematic drawings of the antidot cluster. Note that some vortex configurations are degenerate.

477

M O S H C H A L K O V ET AL.

~/~o 60

-1

0

-3

0

1

2

3

5

8

50 40 v

30 20 10

Fig. 24. from [82].)

3 ].toll ( m T )

Experimental phase boundary, ATc(H), for the Pb/Cu 2•

"-.....

_................... .-

"'.

~

antidot cluster. (Source: Adapted

..

4

2

0 v'

6

-'-..;"'

?'".;.

7"

' ""..; ?'-"

-

, . . .

,

' " ']....

E 0

,3

4 2

.

,

-

,

,

,,-

.

,

-

,

-

,

.

,

-

10

E

v

0

5

0 0.0

0.2

0.4

0.6

0.8

1.0

0

Fig. 25. (a) Theoretical phase boundary, Tc(~/~0), calculated in the London limit of the GinzburgLandau theory without any fitting parameter (solid line). All possible parabolic solutions are represented by dotted lines. The dashed line indicates the nonstable parallel configuration. The schematic representation of the {ni } quantum numbers at the antidots and characteristic current flow patterns for each parabolic branch are also sketched. (b) The Tc(~/~0) phase boundary, calculated as in (a), but with the curvature "y" of the parabolas taken as a free parameter. The y value was increased by a factor of 2 with respect to its calculated value used in (a). (c) First period of the measured phase boundary shown in Figure 24 after subtraction of the parabolic background. (Source: Adapted from [82].)

478

QUANTIZATION AND CONFINEMENT PHENOMENA

From all these possible solutions, for each particular value of ~ / ~ 0 , only the branch with a minimum value of ATc(~) is stable (indicated with a solid line in Fig. 25a). For the phase boundary, calculated within the 1D model of four equivalent and properly attached squares, no fitting parameters were used because the variation of Tc(~) was calculated from the known values for ~ and the size. One period of the phase boundary of the antidot cluster is composed of five branches and in each branch a different stable vortex configuration is permitted. For the middle branch (0.37 < ~ / ~ 0 < 0.63), the stable configuration is the diagonal vortex configuration (antidots with equal ni at the diagonals) instead of the parallel state (dashed line in Fig. 25a). The net supercurrent density distribution circulating in the antidot cluster for different values of ~ / ~ 0 has been determined using the same approach. Circular currents flow around each antidot. For the states ni -- 0 and ni = 1, currents flow in the opposite direction, because currents corresponding to ni -- 0 must screen the flux to fulfill the fluxoid quantization condition [Eq. (43)], whereas for ni = 1 they have to generate flux. At low values of ~ / ~ 0 , currents are canceled in the internal strips and screening currents only flow around the cluster. When the field range corresponding to the second branch of the phase boundary is entered, a vortex (ni -- 1) is pinned around one antidot of the cluster (see Fig. 25a). At the third branch, the second vortex enters the structure and is localized in the diagonal. In the fourth branch of the phase boundary, the third vortex is pinned in the antidot cluster. And, finally, the current distribution for the fifth branch is similar to that of the first branch although currents flow in opposite direction [83]. Figure 25c shows the first period of the measured phase boundary Tc(~) after subtraction of the parabolic background. The first period of the experimental phase boundary is composed of five parabolic branches with minima at ~ / ~ 0 = 0, 0.3, 0.5, 0.7, 1. If we compare it with the theoretical prediction given in Figure 25a, the overall shape can be reproduced although the experimental plot has two major peaks at ~ / ~ 0 = 0.2 and 0.8, whereas the theoretical curve only predicts cusps around these positions. The agreement between the measured and the calculated Tc(~) is improved if we assume that the coefficient y can be considered as a fitting parameter. This seems to be feasible if we take into account the simplicity and limitation of the used 1D model. Owing to the relatively large width of the strips forming the 2 x 2 cluster, the sizes of the current loops can change because they are "soft" in this case and not defined very precisely. As a result, the coefficient y cannot be treated as a known constant. If we use it as a free parameter (Fig. 25b), then the curvature of all parabolas forming Tc(H) can be changed and the calculated Tc(H) curve becomes closer to the experimental one though the amplitude of the maxima at ~ / ~ 0 = 0.2 and 0.8 is still lower than in the experiment (Fig. 25c). The discrepancy in the amplitude of the maxima at ~ / ~ 0 = 0.2 and 0.8 could also be related to the pinning of vortices by the antidot cluster when potential barriers between different vortex configurations may appear. At the same time, the achieved agreement between the positions of the measured and calculated minima of the Tc(H) curves confirms that the observed effects are due to fluxoid quantization and the formation of certain stable vortex configurations at the antidots [82, 83]. An extrapolation of the results obtained from small to larger 2D antidot clusters (3 • 3, 4 • 4, etc.) gives an idea about possible vortex configurations, which can be expected in superconductors with huge regular arrays of antidots (antidot lattices) (see Fig. 27).

4. HUGE ARRAYS OF NANOSCOPIC PLAQUETTES IN LATERALLY NANOSTRUCTURED SUPERCONDUCTORS The periodic repetition of a certain nanoscopic plaquette A over a macroscopic area makes it possible to implement the idea of an artificial lateral modulation in nanostructured superconductors. Several different types of elementary cells A have been used for that: antidots

479

MOSHCHALKOV ET AL.

[ 1-3, 56, 84-87] (complete microholes in a film), blind holes [4, 88] (no perforation but a thickness modulation at the sites of the blind holes), magnetic [89, 90], normal metallic [89], or insulating dots [89] covered by (or grown on top of) a superconducting film. These huge regular arrays of nanoscopic plaquettes can be used for systematic studies of the confinement and quantization phenomena in the presence of a 2D artificial periodic pinning potential. We begin in this section with the effect of lateral nanostructuring on the Tc (H) phase boundary and then move on to the pinning phenomena, focusing on commensurability effects between the flux line lattice and a periodic pinning array in superconductors with an antidot lattice.

4.1. The Tc(H) Phase Boundary of Superconducting Films with an Antidot Lattice Superconducting films with a regular array of antidots are convenient models to study the effects of the confinement topology on the Tc(H) phase boundary in two different regimes [88]: (i) The first or "collective" regime corresponds to the situation where all elements A, forming an array, are coupled. From the experimental Tc(H) data on antidot clusters, we expect for films with an antidot lattice higher critical fields at 9 = n~0, which is in agreement with the appearance of the Tc(H) cusps at 9 = n~0 in superconducting networks [91 ]. Here, the flux 9 is calculated per unit cell of the antidot lattice. (ii) On the other hand, by applying sufficiently high magnetic fields, the individual circular currents flowing around antidots can be decoupled and the crossover to a "single object" behavior could be observed. In this case, the relevant area for the flux is the area of the antidot itself and we deal with surface superconductivity around an antidot. Figure 26 shows the critical field for a Pb(50 nm) sample with a square antidot lattice (period d = 1 /zm and the antidot radius ra - - 0 . 2 4 /zm). The Tc(H) boundary is

Fig. 26. Criticalfield of a superconducting Pb(50 nm) film measured at 10% Rn (Rn is the normal state resistance just above Tc), with d = 1/zm, ra = 0.24/xm. The inset shows a zoom of the Tc(H) data determined using different criteria 50% Rn, 10% Rn, and 0.5% Rn. (Source: Adapted from [84].)

480

QUANTIZATION AND CONFINEMENT PHENOMENA

1.6

1.2

0.8

[..,~

0.4

0.0 0.0

0.2

0.4

0.6

0.8

1.0

~/~ O

Fig. 27. Calculationsof the first Tc(H) period for an N x N antidot system (N = 1, 2, 3, 4, oo) in the London limit. The minima at integer ~/~0 for a single loop (N = 1) are transformed to sharp cusps as N --+ oo. (Source: Adapted from [93].)

determined at 10% of the normal state resistance, Rn. In this graph, two distinct periodicities are present: (i) Below approximately 8 mT, cusps are found with a period of 2.07 mT, corresponding to one flux quantum per lattice cell. These cusps or "collective" oscillations [88] are reminiscent of superconducting wire networks [91] and arise from the phase correlations between the different loops that constitute the network. These cusps are obtained by narrowing the minima at n~0 with increasing size N of the N x N antidot cluster (see the sharpening of the minima at 9 - 0 , ~0 in Fig. 27; note that the phase boundary in the N --+ oe case has a similar shape as the lowest energy level of the Hofstadter butterfly [19, 92]). An important observation is that the amplitude of these "collective" oscillations depends on the choice of the resistive criterion. This is similar to the case of Josephson junction arrays and weakly coupled wire networks [94] where phase fluctuations dominate the resistive behavior. The inset of Figure 26 shows the first collective period, measured using three different criteria. As the criterion is lowered, the cusps become sharper and the amplitude increases well above the prediction based on the mean field theory for strongly coupled wire networks [91]. At the same time, cusps appear at rational fields ~ / ~ 0 = 1/4, 1/3, 1/2, 2/3, and 3/4 arising from the commensurability of the vortex structure with the underlying lattice. (ii) Above approximately 8 mT, the collective oscillations die out and "single object" cusps appear, having a periodicity that roughly corresponds to one flux quantum ~0 per antidot area rrr 2. These cusps are due to the transition between localized superconducting edge states [88] having a different angular momentum L. These states are formed around the antidots and are, just as the dot in Section 2.3, described by an orbital momentum quantum number L. Figure 28 shows the same critical field as presented in Figure 26, but normalized by the upper critical field Hc2 of a plain film without antidots,/z0Hc2 = ~0/27r~Z(T) [~(0) = 36 nm]. The dashed line is the calculation of the reduced critical field for a plain film with a single circular antidot with radius ra = 0.24/zm. The positions of the cusps correspond reasonably well to the experimental ones, taking into account that the model only considers

481

MOSHCHALKOV ET AL.

. 0

9

!

9

!

.

|

9

!

9

|

,,

!

.....,/ ..... ..- ....... ............. ..........

3.8

-", -

-.y.:- y

""

1.5

""~ 1.4

N ~ 3.6

1.3

3.4

1.2

3.2

1.1 9

~

!

10

.

!

20

30

40

50

,

!

60

1.0

tlo H ( m T ) Fig. 28. The critical field of Figure 26 normalizedby r versus the applied field. The dashed line (right axis) shows the theoretical result [88] for a single circular hole with a radius ra -- 0.24/zm.

a single hole. From this comparison, an effective area ~rr2 = 0.18/zm 2 is determined which is close to the experimental value 0.16/zm 2. From Figures 26 and 28, it is possible to show that the transition from the network regime to the "single object" regime takes place at a temperature T* approximately given by the relation w ~ 1.6~ (T*) (where w is the width of the superconducting region between two adjacent antidots) [93]. Experiments on systems with other antidot sizes demonstrate that w - - d ra ratio determines the relative importance of the "collective regime" and changes the crossover temperature T*. The relation w ~ 1.6~(T*), seems to hold reasonably well and is similar to the transition from bulk nucleation of superconductivity to surface nucleation in a thin superconducting slab parallel to the magnetic field [55], which happens at a temperature Tcr satisfying w = 1.8~(Tcr). Comparing the bulk Hc2(T) curve with the Tc(H) boundary for films with an antidot lattice, we clearly see a qualitative difference between the two, caused by the lateral nanostructuring. For a superconducting network, Tc (H) can be related to the lowest ELLLlevel in the Hofstadter butterfly [19, 92] with pronounced cusps at n ~0 and a substructure within each period. In the case of an anfidot lattice, the size of the antidots is substantially smaller compared to a network. Here as well, Tc(H) is substantially modified, but the cusps at n~0 are still clearly seen [84]. Note also (Fig. 28) that in films with an antidot lattice the ratio Hc3/Hc2 is enhanced up to 3.4-3.6, which is substantially higher than the classical value Hc3/Hc2 = 1.695 [23].

4.2. Pinning in Laterally Nanostructured Superconductors Considering in the previous sections the effect of lateral nanostructuring on Tc(H), we have demonstrated that this important superconducting critical parameter can be tailored by designing a proper topology to confine the superconducting condensate. This concept has been verified on individual nanostructures, clusters containing a small number of nanoplaquettes, and finally their huge arrays in laterally nanostructured superconductors. Systematic studies of the Tc(H) phase boundaries for superconducting structures of the same material but with different confinement topologies have convincingly demonstrated that Tc (H) is determined not only by the choice of a particular superconducting material, but is also very strongly influenced by varying the applied boundary conditions. Therefore, in

482

QUANTIZATION AND CONFINEMENT PHENOMENA

nanostructured superconductors, the upper (Hc2) and lower (Hcl) critical fields are not at all good critical parameters to characterize the material, because through nanostructuring (taking, e.g., superconductors with an antidot lattice) we can strongly increase Hc2(T) and simultaneously decrease Hcl (T) while keeping the thermodynamical critical field Hc(T) almost constant. As a result, it does not make any sense to define specific values of Hc2(T) and Hcl (T) for each given superconductor when it is further used for artificial nanostructuring. Instead, these two critical parameters can intentionally be designed by changing the confinement potential through nanostructuring of the same chosen superconducting material. The suppression of the superconducting state is induced by an applied field (see the H - T plane in Fig. 7) as well as by the field generated by the currents running through a superconductor. When the generated field reaches the Hc2 value, superconductivity is destroyed. This gives the maximum possible current, the depairing current [Eq. (39)]. In type II superconductors, which are most interesting for practical applications, the problem of increasing lc up to its theoretical limit I GL is closely related to the optimization of the pinning of flux lines (FLs). In this section, we shall focus on the advantages offered for the solution of this problem by lateral nanostructuring. 4.2.1. Pinning by an Antidot or a Columnar Defect

It has been shown experimentally and theoretically that a small hole (antidot) acts as a very efficient pinning center for flux lines. The pinning force of a single hole has been calculated by Mkrtchyan and Schmidt [95] in the London approximation (high K). Buzdin and Feinberg [96] have obtained similar results for a nonsuperconducting columnar defect, by calculating the electromagnetic pinning interactions using a vortex-antivortex image method. An important conclusion of both studies is that, depending on the radius ra of the defect, more than one flux line can be trapped, up to a certain saturation number, ns, given by ra ns -~ 2~(T) (59) The radial distribution of the free energy F of a vortex around the cylindrical defect with ns > 1 is schematically shown for different values of the number of pinned vortices n in Figure 29. If no vortices are pinned (n = 0), the force on a vortex (the gradient of the energy) from an "empty" defect is attractive at all distances. As soon as a vortex is trapped (n = 1), a potential barrier develops near the edge of the defect, which grows as the number n of trapped vortices increases. If n reaches the saturation number ns, the maximum of the potential barrier reaches the edge of the defect and the force on additional vortices becomes repulsive at all distances. We should add that, in case the defect is a hole, there exists a Bean-Livingstone barrier [97] at the hole edge even if no vortices are trapped in the hole [98]. The maximum pinning force per unit length decreases with increasing n: f~nax,~ ( ~0 )2 1 ( n ) ~- 1---ns

(60)

Note that the possibility of ns vortices being trapped by the defect does not necessarily imply that this is energetically the most favorable situation. However, because the pinning force is maximum in the hole, a vortex will remain pinned by the hole once it is there. Buzdin [99] has calculated for a triangular lattice of columnar defects that, after all defects are occupied by ~0 vortices, pinning of multiquanta vortices becomes energetically advantageous in case the radius ra is larger than a critical radius rc:

re = ~/~ (T)a 2

(61)

with av the distance between the vortices in a perfect triangular lattice. The formation of multiquanta vortices has been confirmed by means of magnetization measurements [3]

483

MOSHCHALKOV ET AL.

F n=O

n-i

n - n,

r

ra

Fig. 29. Schematic presentation of the dependence of the free energy F of a vortex on its distance r from the center of a cylindrical hole with radius ra and ns > 1, showing the case with no vortex pinned by the hole (n = 0), and with n = 1, and with n -- ns flux quanta trapped by the hole.

and has been directly visualized by Bitter decoration of Nb films with circular blind holes [4, 100]. From the preceding considerations of the saturation number, one expects that small antidots (ns = 1) can trap only one flux line. In this case, other flux lines generated by the applied field will be forced to occupy interstitial positions. The interplay between weakly and strongly pinned flux lines at interstices and antidots, respectively, will be discussed. The presence of interstitial vortices for ns = 1 makes superconductors with an antidot lattice qualitatively different from superconducting networks (ns >> 1), where the vortex configuration at integer matching fields is always the same as that of the underlying network. In contrast to that, composite vortex lattices (i.e., with vortices at antidots and at interstices) show a remarkable variety of stable patterns, quite different from the underlying antidot lattice. Large antidots (ns > 1) can stabilize multiquanta vortex lattices, which do not exist in reference homogeneous superconductors without an antidot lattice. Finally, for antidot lattices with ns >> 1, the crossover to the regime of superconducting networks will be considered.

4.2.2. Regular Pinning Arrays When arranging the pinning centers in a regular lattice, interesting matching effects are observed as a consequence of commensurate vortex states in the periodic pinning potential. Because, in a homogeneous superconductor, triangular and square vortex lattices are energetically most favorable (see Fig. 10), matching effects are expected to be most pronounced for pinning arrays with a triangular or square symmetry. The presence of a regular pinning array results in a huge overall enhancement of the j c ( H ) and M(H) compared to a reference film without a pinning array. Moreover, at temperatures close to Tc, sharp matching anomalies are observed in the j c ( H ) and M(H) curves at specific field values (matching fields) where the vortex lattice matches the lattice of pinning centers. In particular, the first matching field H1 is defined as the field where the density of the vortices equals the density of the pinning centers, leading to a one-to-one correspondence between the vortex lattice

484

QUANTIZATION AND CONFINEMENT PHENOMENA

and the pinning array. Similarly, matching effects can also occur at integer and rational multiples of H1, because of a commensurability between the vortex lattice and the pinning array. These matching fields can be denoted as Hn = n • H1 and Hp/q = p / q • H1, respectively (n, p, and q integer). Pronounced peaks in the jc(H) occur at field values where an undistorted triangular vortex lattice matches the pinning potential, leading to enhanced coherent pinning and hence a maximum in jc(H) and M ( H ) . The resulting coherently pinned vortex lattice is very stable, which leads to the observed matching anomalies.

4.3. Regular Pinning Arrays with ns = 1

4.3.1. Magnetization The response of the flux lines to the presence of artificial pinning centers is a challenging problem of scientific [85, 101-104] and technological [ 105] interest. The "vortex matter" in superconductors subjected to the action of thermal fluctuations and a random or correlated pinning potential is characterized by a variety of new phases, including the vortex glass, Bose glass, and the entangled flux liquid [106-109]. These new phases are strongly influenced by the type of artificial pinning center. Especially random arrays of point defects [110-112] ("random point disorder") and columnar ("correlated disorder") defects [101, 102] have been intensively studied. The latter are convenient pins to localize the FL and enhance the critical current density jc if the vortex density at the applied field H coincides with the density of the irradiation-induced columnar tracks [ 101 ]. In spite of the progress in understanding the behavior of vortex matter in the presence of columnar pins, regular arrays of well-characterized pinning centers are much less studied [85, 104]. One of the most efficient and easiest ways to produce such centers in thin films is to make submicrometer holes (antidots) [85, 104] using modern lithographic techniques [56, 113, 114]. In the case ns = 1, the well-defined periodic pinning potential is formed by the antidots with a radius ra much smaller than the period d of the array. The opposite limit (ra ,~ d) has been studied before in superconducting networks [ 19, 115, 116]. In this section, we will focus on perforated films with ra ns, the antidot acts as a repulsive center. Because of this saturation effect, the composite flux lattice in fields corresponding to n > ns is expected to consist of FL carrying n flux quanta ~0 pinned at antidots (strong pinning) as well as at the interstices (weak pinning), as has been shown theoretically [ 117]. The well-defined lattice of antidots (d = 1/zm, ra = 0.15/zm) is usually obtained by a standard lift-off procedure [ 118]. An atomic force microscopy (AFM) study was performed that revealed a surface roughness between the antidots less than 1 nm. The very low surface roughness between the antidots ensures that the superconducting properties will mainly be influenced by the presence of the antidots. For a square antidot lattice with d = 1 #m, the matching fields are lZoHn = n • ~ o / d 2 = n • 2.07 mT, where n is an integer. Figure 30 shows the magnetization M (H) data at 6.8 K for a perforated Pb/Ge multilayer with Tc0 = 6.9 K and ~(0) -- 12 nm. A remarkably sharp drop in M ( H ) at the first matching field H1 is clearly seen [1, 98] (note that the distance between the neighboring data points is only A/z0H = 0.01 mT). The presence of weaker extra peaks at H < H1 is an indication of the fractional flux phases stabilized by the periodic pinning array [56]. To analyze these results, we will use the saturation number ns and the pinning potential

485

MOSHCHALKOV ET AL.

4

i [' T~6.SKl

2

0

Z~ -2

-4

I

i 2

1

-10-8-6-4-2

0

J 4

6

i 8 10

l.toH (mT) Fig. 30. Magnetizationloop M(H) at T = 6.8 K of a square antidot lattice (d = 1/zm, ra = 0.15/zm). The loops (see also Fig. 31) were measured for M > 0 and symmetrized for clarity for M < 0. (Source: Reprinted with permission from [1]. 9 1995 American Physical Society.)

6 _

~ o~ ~-2-4-

-6 -8

t)

T=6.5 K i

i t

.

~

i

i

-10 -8 -6, -4 -2

0

2

"

i 4

6

8

10

~toH (mT) Fig. 31. Magnetizationloop M(H) at T = 6.5 K of a [Pb(15 nm)/Ge(14 nm)]3 multilayer with a square lattice of submicrometer holes (d = 1/xm, ra =0.15/zm). (Source: Reprinted with permission from [1]. 9 1995 American Physical Society.)

at interstices Upi [117]. At T = 6.8 K, ns -- 1 and only one FL is attracted to the antidot while the second FL is repelled. This situation can be described by the Bose analog of the M o t t - H u b b a r d model for correlated electrons [ 119]. Because the pinning potential Upi oc d/~,(T) ~ 0 as T --+ Tc [117], the FLs repelled by the antidots are not localized, and they move freely between different very shallow Upi minima at interstitial positions. The motion of a very small number of excessive FLs at H > H1 leads to a sharp fieldinduced first-order phase transition from fully localized FLs at H < H1 ("insulator") to a collective delocalized state at H > H1 ("metal") when the motion of "excessive" FLs causes an effective delocalization of all the FLs trapped by antidots. The main features of this transition correspond to the Mott metal-insulator transition for the FLs [ 106]. It should be noted that previously the existence of the temperature-induced first-order transition was derived from resistivity [ 120], magnetization [ 121], and heat capacity [ 122] measurements in high-quality high-Tc single crystals. The M ( H ) jump at H = H1 is suppressed as T goes down (see Fig. 31).

486

QUANTIZATION AND CONFINEMENT PHENOMENA

0.016

.

.

.

.

.

.

0.012

~ ' 0.008

0.004 0.000

i

io

!iJ

IT6.

-10-8

-6 -4 -2

0

2

4

6

i 8 10

~t0H (mT) Fig. 32. Normalizedrelaxation rate S(H) at T = 6.5 K of a [Pb(15 nm)/Ge(14 nm)]3 multilayerwith a square lattice of submicrometerholes (d = 1/zm, ra = 0.15/zm). The solid lines are guides to the eye. The onset of the vortex formation at interstices, at H > H2, leads to a much higher flux creep rate. (Source: Reprinted with permission from [1]. 9 1995 AmericanPhysical Society.)

The evaluation of parameters H m (matching field) and T* (temperature at which matching is observed) [106] shows that, in these samples with ra > ~/2~, H * is very close to the first matching field H * ~ H1 -- H~, and T* is smaller than Tc only by a few millikelvins. In this case, the Mott insulator line/4o terminates at temperatures extremely close to Tc, where the relaxation times are very short and, therefore, the Mott insulator can be observed. As the temperature goes down, the relaxation times increase and the M(H) anomaly at H1 is suppressed (Fig. 31) because of the equilibrium time problems. Another possibility is that there is no disorder-localized Bose-glass phase at all sandwiched between the superfluid and the Mott insulator, as shown by numerical simulations [ 123]. At a lower temperature (Fig. 31), T = 6.5 K, we still have ns = 1, but the pinning potential Upi increases substantially in comparison with T = 6.8 K (Fig. 30) and enables the localization of FLs at the interstices. For fields H > H1, FLs are pushed into interstitial positions, which is confirmed by the simultaneous observation of the steplike anomaly in the M(H) curve at H = H1 (Fig. 31) and an abrupt increase of the flux creep rate also at H = H1 (Fig. 32). In the field range H1 < H < H2, the increasing S value corresponds to FLs loosely bound at the interstices. The interstitial positions are completely occupied at H --/-/2 and a reentrant flux creep rate anomaly shows up, indicating the onset of a strongly reduced mobility of the FLs. This reduction of mobility signals the onset of the formation of doubly quantized vortices at antidots, as shown in Figure 33. Because of the presence of interstitial vortices, the saturation value ns is expected to increase. This leads to the formation of two-quanta vortices at the antidots a t / / 3 (Fig. 33). The formation of multiquanta vortices will be discussed in Section 4.4.

4.3.2. Transport Measurements A straightforward way to obtain information about the mobility of the two types of vorticesmat interstices and at antidotsmis to perform low-field magnetoresistance measurements. Because flux motion leads to dissipation, the presence of the antidot lattice is expected to reduce it owing to trapping of the FLs by the antidots and hence to diminish the voltage drop over the sample. In Figure 34a, a comparison of the field dependence of the resistance R (H) is made between a film with antidots and the reference film without antidots at three different temperatures near Tc (-- 4.725 K) and with a fixed alternating-current (ac)

487

MOSHCHALKOV ET AL.

Fig. 33. Schematic representation of the evolution of the flux line lattice (arrows) for T = 6.5 K as a function of the magnetic field in a [Pb(15 nm)/Ge(14 nm)]3 multilayer with a square antidot lattice. (Source: Adapted from [1].)

density of 41 A/cm 2. For the reference film, a linear field dependence is measured with a slope that diverges near Tc as (To - T) -v (v ~ 1). This behavior is typical [ 124] for high-x superconductors in the presence of small fields (H/Hc2 < 0.1) where the Bardeen-Stephen limit [ 125], R = 13(T) H / Hc2 (0) [with fl (T) the temperature-dependent prefactor], is valid. In the case of the film with an antidot lattice, the resistance is clearly strongly suppressed when the number of FLs is less than that of available antidots (/z0H 1, two or more vortices would be trapped at a single defect [3]. Interstitial vortices were found to be randomly distributed until H reached H3/2, when vortices entered every other interstice in addition to the square array of vortices all pinned

493

M O S H C H A L K O V ET AL.

Fig. 39. Lorentz micrographs and schematics of the static stable vortex configuration in a square array of artificial defects at matching magnetic fields Hn: (a) n = 1/4, (b) n = 1/2, (c) n = 1, (d) n = 3/2, (e) n = 2, (f) n = 5/2, (g) n = 3, and (h) n = 4. Small dots and open circles in each schematic drawing to the left of the Lorentz micrographs show the positions of the defects and the vortices, respectively. Squares also indicate unit cells of the vortex lattices in each case. Vortices form regular lattices at the first matching magnetic field HI, as well as at its multiples and its fractions. (Source: Adapted from [ 133].)

494

QUANTIZATION AND CONFINEMENT PHENOMENA

Fig. 39.

(Continued.)

at defects, thus occupying just half of the available interstitial sites (Fig. 39d). Between H1 and H3/2, the interaction of distant interstitial vortices was too weak to form a regular lattice. Even for H3/2, the interstitial vortex that should be situated at the top left portion of the micrograph (see Fig. 39d) is mislocated at the interstitial position one line lower. At

495

MOSHCHALKOV ET AL.

Fig. 39. (Continued.) H = H2, all of the interstitial sites were occupied by vortices, forming a centered (1 x 1) square lattice (Fig. 39e). At H = 115/2, additional vortices entered every other interstice of the configuration at H2, thus forming a centered (2 x 2) square lattice (Fig. 39f). That is, one vortex and two vortices alternately occupied interstitial sites in both the horizontal and the vertical directions. The two interstitial vortices did not overlap but were situated side by side, separated by a distance of approximately 0.6d. They were aligned parallel to either one of the axes of the square lattice. In the present case, the direction of the two vortices is accidentally horizontal. When H reached H3, two vortices were located at every interstitial site (Fig. 39g). The line connecting these two interstitial vortices was not in the same direction but switched alternately from horizontal to vertical. When H = H4, all of the pairs of squeezed vortices were aligned in the vertical direction (Fig. 39h). Additionally, a vortex was inserted at every middle point between two adjacent sites in the vertical direction (Fig. 39h). As a result, vortices formed a slightly deformed triangular lattice. Vortices form regular lattices, and consequently stable and rigid configurations at Hn. In this case, the vortices do not move easily. Especially for n = 1, all of the defects are occupied by vortices and therefore hopping of vortices is forbidden even when the elementary force is exerted on them. In this case, the Mott-insulator phase, introduced by Nelson and Vinokur [ 106] and by B latter et al. [107] is realized. In contrast to that, interstitial vortices,

496

QUANTIZATION AND CONFINEMENT PHENOMENA

appearing at H > H1, cannot be localized by a shallow pinning potential at interstices. As a result, interstitial vortices demonstrate a metallic vortex behavior. Both localized vortices at defects and metallic vortices at interstices can be more directly observed by monitoring their dynamics. The coexistence of these two species of vortices is an excellent example of the multistage melting. For ns = 1, peaks and cusps in the critical current and the magnetization were found at H = H1/4 and H1/2 but not at 113/2 or t15/2 by macroscopic measurements [114]. This is reasonable because the pinning potential at defects (n < 1) is deeper than that at interstices (n > 1). In fact, the regular lattice was partially destroyed at H = H3/2 or H5/2, even in the field of view shown in parts d and f of Figure 39. The dynamic behavior of vortices was then observed in a changing magnetic field H. The sample was first cooled down to 4.5 K and H was gradually increased. At a few gauss, vortices began to penetrate the film from the film edge. They approached the defect region and soon occupied the front row of defects (Fig. 40a). Subsequent vortices approached

Fig. 40. Lorentzmicrographs demonstrating the dynamic behavior of vortices when H is increased and then decreased gradually (T = 4.5 K); see text. The magnetic fields in units of H 1 w e r e (a) 0.2, (b) 0.5, (c) 1.2, (d) 2.5, (e) 1.5, (f) 0.9, and (g) 0.6. Video clips showing the movement of the vortices under similar conditions are available at http://www.sciencemag.org/science/feature_data/harada.shl. (Source: Adapted from [133].)

497

MOSHCHALKOV ET AL.

this line barrier but could not easily get over it. When the vortices finally broke through the line, they jumped to defects as far away as 5d or more. When distant defects were occupied, vortices began to jump to nearer defects. When all of the defects were occupied by vortices, subsequent vortices accumulated in front of the first row (Fig. 40b) because they could not enter the defect region, since they could not find vacant defect sites to jump to. Before long, however, they began to enter interstices. The vortices continued to hop from one interstitial site to another. It can be noted in Figure 40c that the positions of interstitial vortices are displaced downward from their proper central positions because of the force in the downward direction. The manner of the vortex flow suddenly changed after all of the interstices were occupied. Without any vacant sites to hop to, they began flowing simultaneously in single lines. A few lines of vortices were flowing in the field of view in Figure 40d). When H was decreased, a force was exerted in the opposite direction and interstitial vortices began to move upward to leave the film. Vortices were displaced upward from the proper interstitial position because of this force (Fig. 40e). Even when vortices outside the defect region disappeared, vortices forming a square lattice resisted moving (Fig. 40f). When H was further decreased, vortices began to depin. For example, one vortex in the front row was depinned and then a vortex in the second row hopped to the vacant site to form a hole (shown as "h" in Fig. 40g). In the mean time, opposite vortices (antivortices) began to enter and to be trapped ("o" in Fig. 40g). The preceding experiments showed that the character of the vortex flow somehow changed every time when the vortices formed closely packed regular lattices. Consequently, this indicates that the pinning force of a whole vortex lattice can change at Hn. Peaks in the critical current could more directly be explained by the different dynamic behaviors of vortices in two cases in which H is exactly H1 and H is slightly greater than H1. In the sample that was field-cooled down to 4.5 K at a field of 3.1 mT, just above/z0H1 (2.98 mT), the interstitial vortex in Figure 41a began to hop in the downward direction w h e n / z 0 H was increased to 3.9 mT. When T was increased to 7 K to shorten

Fig. 41. Dynamicsof an excess vortex. The excess vortex hopped from one interstitial site to another when H changed from 3.1 to 3.9 mT and T increased from4.5 K (a) to 7 K (b) and then to 7.5 K (c). The arrows indicate the hopping direction. (Source: Adapted from [133].)

498

QUANTIZATION AND CONFINEMENT PHENOMENA

the time scale of the vortex hopping caused by thermal fluctuations, the interstitial vortex hopped to the next interstitial site (Fig. 4 l b). This micrograph was taken after the sample had been cooled down to 4.5 K, in order to obtain a high-contrast vortex image, but we confirmed that this cooling procedure did not change the configuration of the vortices. When T was further increased to 7.5 K, the vortex hopped to the next site again (Fig. 4 lc). The interstitial vortex hopping from one site to another reminds the hopping conductivity of charge carriers in donor-doped semiconductors. Excess vortices in a regular vortex lattice were observed to hop easily (see also flux flow results in [ 126]), whereas a change in the magnetic field two times larger was required to induce hopping of the vortices forming the lattice. The hopping of holes in a vortex lattice was also observed. A stronger force was needed to cause a vortex hole to hop than to cause an excess vortex to do so, because a vortex must be depinned from a stable defect site. Similar vortex behavior was detected at other matching fields, such as He and/-/3, although it was not as conspicuous as in the case of H -- H1. The studies by Lorentz microscopy elucidated the microscopic mechanism of the matching effect. When vortices formed a regular lattice, they could not begin to move unless a force larger than the elementary pinning force was exerted. At the same time, excess (or deficient) vortices were observed to move easily when affected by the Lorentz force, thus providing a microscopic explanation for larger critical currents at matching magnetic fields.

4.3.4. Numerical Simulations and Configuration of the Vortex Lattice in a Square Pinning Array Static and dynamic vortex phases in superconductors with a periodic pinning array have been studied by molecular dynamics simulations by Reichhardt et al. [131]. They have performed molecular dynamics simulations of the vortex configurations in superconductors with a periodic pinning array of circular pinning centers with ns = 1. In the equation of motion, the vortex-vortex interaction for a bulk superconductor [Eq. 28] is used. The vortices interact with the pinning centers only when they are within a distance k from their edge, where the attractive force is proportional to the distance between the centers of the vortex and the pinning site. Each pinning center can only pin one vortex (ns = 1). The fluxgradient-driven simulations and the simulated annealing (field-cooled) simulations result in the same vortex configurations. Figure 42 shows the resulting vortex states at the first, second, and third matching fields for a square lattice of pinning centers that can each pin not more than one vortex (ns = 1). All these simulated vortex states have also been directly observed by means of Lorentz microscopy by Harada et al. [133] in superconducting Nb films with a square lattice of small defects. At H1, a one-to-one matching between the vortex lattice and the lattice of pinning centers is established. At H2, a square vortex lattice is formed where one FL is

HIH, - 1 | i

HIH1 = 2 |

|

|

i

$ ....... $

|

|

| 0

|

|

|

|

|

|

|

|

|

|

"" 0

| |

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HIH1 - 3

| 0

| |

0 0

~-=-.@ .......@ . . | i Ui !U o |

O0

| | |

0

O0

| | | oOOo|

Fig. 42. Schematicpresentation of the vortex configurations at integer matching fields H/H 1 = 1, 2, and 3 in the presence of a square lattice of pinning sites. Open circles and dots represent vortices and artificial pinning centers, respectively. (Source: Reprinted with permission from [89].)

499

MOSHCHALKOV ET AL.

pinned at each pinning center, and one is "caged" at each interstitial position. The vortex lattice at Ha is highly ordered with pairs of interstitial FLs alternating in position, but has neither a square nor a triangular symmetry. The vortex configurations in a square pinning array have been simulated in [131] up to the 28th integer matching field. A variety of ordered, nearly ordered (e.g., distorted triangular), and disordered vortex lattices are found for integer matching fields up to H/H1 = 15. At matching fields H/H1 > 15, no overall order of the vortex lattice is found. For these high matching fields, ordered domains are observed which are separated by grain boundaries of defects. Also at rational multiples of the first matching field, matching anomalies were found, related to a stable vortex configuration in the periodic pinning potential. Molecular dynamics simulations [ 131 ] for a square lattice of pinning centers reveal ordered vortex lattices at H/H1 = 1/4 and 1/2 and partially ordered vortex lattices at H/H1 = 3/2 and 5/2. Experimentally, fractional matching anomalies have been observed in several types of periodic pinning arrays, for example, antidot lattices in Pb/Ge multilayers [2], or lattices of submicrometer insulating [89], metallic [89], or magnetic dots [89, 90], covered with a superconducting layer [89]. The matching anomalies at well-defined rational multiples of the first matching field n p / q -- p H1

q

(64)

with p and q integer numbers, can be explained by the stabilization of a flux lattice with a larger unit cell than the lattice of pinning centers. We will discuss the rational matching configurations in artificial square pinning arrays with period 1.5/zm, consisting of a lattice of submicrometer rectangular dots (insulating, metallic, or magnetic), covered with a superconducting Pb film [89]. An AFM topograph of a square lattice of Au dots is shown in Figure 43. In those systems, rational matching anomalies of two different periodicities have been observed: (i) the "binary" fractions (q = 2 n, with n integer) of the first matching field: H/H1 = 1/8, 1/4, 1/2, 3/4, 5/4, and 3/2; and (ii) the "threefold" (q = 3) fractions: H/H1 = 1/3, 2/3, and 4/3, which are only observed for T~ Tc > 0.985. Similar rational matching anomalies have also been observed by Baert et al. [2] in superconducting Pb/Ge multilayers with a square antidot lattice. In these antidot systems, rational matching peaks are observed only within the first period (IHI < H1) at slightly different fields, namely, H/H1 = 1/16, 1/8, 1/5, 1/4, and 1/2. These field values correspond exactly to those where a square lattice of flux lines with a unit cell larger than that of the antidot lattice, and if necessary rotated, can be matched onto the square lattice of pinning centers, that is, when p = 1 and q = n 2 + k 2, with n and k integer numbers. Only

Fig. 43. AFM topograph of a square lattice of rectangular Au dots with a lattice period of d = 1.5/zm. (Source: Reprinted with permission from [89].)

500

QUANTIZATION AND CONFINEMENT PHENOMENA

~',

2

!

1

0 -2

-1

0

1

2

H/H ,

8

%

4 2 0 -1

0

1

H/H 1

Fig. 44. Magnetizationcurves (M > 0) as a function of H/H1 (HI is the first matching field) for a 50-nm Pb film on a square lattice of Ge dots (d = 1.5 #m), measuredfor T very close to Tc0: T~Tc0 = 0.990 and T/Tc0 = 0.997. The matching anomalies at IH/HII= p/q are identified by the fraction p/q. (Source: Reprinted with permission from [89].)

when the radius of the antidots is increased, allowing pinning of multiquanta vortices, rational matching peaks are observed in the second period (H1 < IHI < n2). For very large antidot radii, a crossover to the network behavior is observed. In superconducting networks, anomalies in the critical current are present in all field periods at certain characteristic fractional numbers of flux quanta per unit cell: H/H1 = 1/4, 1/3, 2/5, 1/2, 3/5, 2/3, and 3/4 [91 ]. Comparison of the series of rational matching fields found in the sample with a lattice of dots with the results obtained for superconductors with a square antidot lattice, on the one hand, and superconducting square wire networks, on the other hand, reveals that these samples exhibit a different behavior. Several of the observed anomalies (H/H1 = 1/3, 2/3, 3/4, 5/4, 4/3, and 3/2) are not present when small antidots are used as pinning centers. These specific rational matching fields are also not emerging from the simulations of Reichhardt et al. [ 131] for a square lattice of pinning centers. Rational anomalies in the second period have so far mainly been observed for larger antidots, related to the formation of multiquanta vortices (ns ~> 2). The anomalies with q = 3 are typical for a superconducting network. Nevertheless, they are clearly visible in the M(H) measurements of a Pb film with a dot lattice, although this sample consists of a continuous superconducting film, far from the network limit [91 ]. These interesting differences clearly demonstrate that the details and the precise nature of the lattice of pinning centers play a determining role in the pinning phenomena and the matching effects. For the rational matching fields observed in superconducting films with a square dot lattice, the proposed stable vortex configurations are shown in Figure 45. The configuration for H/H1 = 1/8 is a square vortex pattern rotated by 45 ~ with respect to the pinning array,

501

MOSHCHALKOV ET AL.

H/H1 9

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Fig. 45. Schematic presentation of the suggested stable vortex lattices at rational matching fields, indicated by H / H 1 = p / q , for a square lattice of pinning centers. The black dots and open circles indicate pinning centers and vortices, respectively. The dashed lines are guides to the eye, showing the symmetry of the vortex lattice. (Source: Reprinted with permission from [89].)

which also corresponds to the configuration suggested by Baert et al. [2]. For H/H1 = 1/4, the flux lines can almost form a perfect triangular lattice. This configuration has been directly visualized in Lorentz microscopy measurements (see Fig. 39a). For the rather unexpected anomaly at H~ H1 -- 1/3, a configuration consisting of a distorted triangular lattice is suggested. This vortex configuration is similar to the one at H/H1 -- 1/3 in superconducting wire networks [91 ]. Although the considered sample is far from the limit of a wire network, it is still believed that this commensurate vortex configuration causes the matching anomaly in the M(H) measurements. At H/H1 = 1/2, the well-known checkerboard configuration is formed, resulting in a square vortex lattice, rotated over 45 ~ with respect to the underlying pinning lattice. For H/H1 = 2/3, an ordered vortex lattice can be formed being the inverse of the one at H/H1 = 1/3, where the occupied pinning sites are replaced by empty ones, and vice versa. Similarly, the proposed configuration for H/H1 = 3/4 consists of the inverse of the configuration at H/H1 = 1/4. The vortex configurations at rational matching fields in the second period (H1 < [HI Hns.

516

QUANTIZATION AND CONFINEMENT PHENOMENA

2 o

0

-2 -4

,a, i

-6

i

-9.6 -7.2 -4.8 -2.4

0

o

2.4

:=oi 4.8

7.2

9.6

~oH (mT) 0

................

8-

:

T=6.7K

Pb/Ge _

4-

2-

i

--

-,4,-

-8

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gtoH(mT) Fig. 61. Magnetizationloop M(H) of a [Pb(10 nm)/Ge(5 nm)]2 multilayer with and without a (triangular) antidot lattice (a) at T = 6.5 K and (b) T = 6.7 K. The arrows indicate the missing M(H) cusp. (Source: Reprinted with permission from [3]. 9 1996 American Physical Society.)

The flux phases listed previously can exist at temperatures not too far from Tc, because at lower temperatures the tendency to form a conventional Bean profile (Fig. 5 l a) starts to dominate and matching anomalies are suppressed; for example, for Pb/Ge, any M ( H ) matching anomalies below 5 K can barely be seen.

4.5. Crossover from a Pinning Array to a Network (ns >> 1) The systematic measurements of the efficiency of antidots, as artificial pinning centers, as a function of their radius ra (Fig. 63) have revealed [87] that for core pinning combined with the electromagnetic pinning the optimum size of the antidots is not ~(T) at all, but

517

MOSHCHALKOV ET AL.

_

/

/o

/ / / /

~

3 j

0

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/ / / /

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_

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0.15

)

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0.20

0.25

0.30

0.35

0.40

(1-T/Tc) 1/2 Fig. 62. Variation of the saturation number ns with temperature. The temperature dependence of ns correlates with the temperature dependence of 1/~(T) c( (1 - T/Tc)1/2 (dashed line). (Source: Reprinted with permission from [3]. 9 1996 American Physical Society.)

I withoutholes .

3-

~,

.

.

.

.

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.

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1 -,

0 -10-8-6-4-2

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laoH (mT) Fig. 63. Magnetization curves (T = 0.98Tc) of a single WGe(60 nm) film with a square lattice of antidots with radius ra = 0.075--0.3/zm. For comparison, the data for the reference multilayers without antidots are also shown. The matching fields IxoHn~ n x 2.07 mT (where n is an integer) are indicated by dashed lines. (Source: Reprinted with permission from [87]. 9 1998 American Physical Society.)

rather 2ra >> ~ ( T ) [87, 132]. As a result, the highest critical currents have been obtained for the multiquanta vortex lattices that can be stabilized by these sufficiently large antidots, because their saturation n u m b e r is ns ~ ra/2~(T) >> 1. At the same time, it is quite evident that by increasing the antidot diameter we are inducing a crossover to another regime (Fig. 64) when eventually 2ra becomes nearly the same as the antidot lattice period d. In this case, the width of the superconducting strips w between the antidots is so small that at temperatures not too far below Tc the superconducting network regime w Hn, is systematically shifted to lower matching fields as T --+ Tc.

519

MOSHCHALKOV ET AL.

T~Tc:0.98i ~ ~ 1.0[ W G e ~

(a)

::

0.80.6 0.4 0.2 0.0 -10 -8 -6 -4 -2

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m

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(b)

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r

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-10 -8 -6 -4 -2

T-n.45K T:.=4140K TM35K T !=4.30 K." I

I

0

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goH (roT) Fig. 65. (a) Normalizedmagnetization curves (T = 0.98Tc) of a single WGe(60 nm) film with a square lattice of antidots with radius ra = 0.075-0.3/xm. For comparison,the data for the reference multilayers without antidots are also shown. The matching fields IxoHn ~, n x 2.07 mT (where n is an integer) are indicated by dashed lines. (b) Magnetization curves at different temperatures of a single WGe(60 nm) film with a square lattice of antidots with radius ra = 0.25/xm. The matching fields #oHn ~ n x 2.07 mT (where n is an integer) are indicatedby dashedlines. (Source:Reprintedwith permissionfrom [87]. 9 1998AmericanPhysical Society.)

5. CONCLUSIONS We have carried out a systematic analysis of quantization and confinement phenomena in nanostructured superconductors. The main idea of this study was to vary the boundary conditions for confining the superconducting condensate by taking samples of different topology and, through that, to modify the lowest Landau level ELLL(H) and, therefore, the critical temperature Tc(H). Three different types of samples were used: (i) individual nanostructures (lines, loops, dots), (ii) clusters of nanoscopic elements--lD clusters of loops and 2D clusters of antidots, and (iii) films with huge regular arrays of antidots (antidot lattices). We have shown that in all these structures the phase boundary Tc(H) changes dramatically when the confinement topology for the superconducting condensate is varied. The induced Tc(H) variation is very well described by the calculations of ELLL(H) taking into account the imposed boundary conditions. These results convincingly demonstrate that the phase boundary Tc(H) of nanostructured superconductors differs drastically from

520

QUANTIZATION AND CONFINEMENT PHENOMENA

that of corresponding bulk materials. Moreover, because, for a known geometry, ELLL(H) can be calculated a priori, the superconducting critical parameter, that is, Tc(H), can be controlled by designing a proper confinement geometry. While before the optimization of the superconducting critical parameters has been done mostly by looking for different materials, we now have a unique alternative--to improve the superconducting critical parameters of the same material through the optimization of the confinement topology for the superconducting condensate and for the penetrating magnetic flux. The critical current enhancement, resulting from the presence of the antidots, used as artificial pinning arrays, has been analyzed. Different pinning regimes can be clearly distinguished depending on the antidot size. For small antidots with a saturation number ns = 1, the existence of the two species of vortices (weakly pinned at interstices and strongly pinned at antidots) should be taken into account. The motion of interstitial vortices gives rise to dissipation. To avoid dissipation and to obtain a further enhancement of jc, larger antidots should be used. For these antidots, the saturation number becomes sufficiently large (ns >> 1) to stabilize the multiquanta vortex lattices. In this case, the highest enhancement factor for jc can be obtained in moderate fields. The size of the antidots in this regime is considerably larger than ~(T) and, therefore, an electromagnetic contribution to pinning also plays an important role. However, the size of the antidots realizing the optimum pinning, turns out to be field dependent. For multiquanta vortex lattices, a simple approach has been applied, developed in the framework of the London limit. This approach gives an excellent fit of the M(H, T) curves at different temperatures. This implies that by making antidot lattices one can substantially expand the area on the H - T plane where the London limit is still valid. In the same framework, the variation of such a fundamental parameter as )~(T) can be achieved just by taking different antidot radii. The renormalization of ~.(T) is directly related to a different topology of films with an antidot lattice that makes the flux line penetration much easier. By a further increase of the antidot diameter, a crossover to the regime of superconducting networks can be induced, leading to the appearance of sharp M(H) peaks at integer fields Hn, in contrast with the M(H) cusps at Hn in the case of multiquanta vortex lattices. Finally, because the saturation number ns, controlling the onset of different regimes (small ns, composite flux lattices with vortices at antidots and interstices; large ns, multiquanta vortex lattices; very large ns, superconducting networks) is determined by the ratio ra/2~(T), the ns value can be tuned not only by using different antidot radii ra, but also by varying ~ (T) by taking different temperatures. Controlling the periodic pinning potential through lateral nanostructuring, the critical current density jc(H) can be eventually enhanced up to the theoretical limitmthe depairing current. Therefore, the two important superconducting critical parameters, Tc(H) and jc(H), can be drastically improved by using the concept of "quantum design": creating the proper confinement topology for the superconducting condensate and the penetrating flux lines that optimizes Tc(H) and jc(H).

Acknowledgments The authors would like to thank E. Rosseel, M. Baert, K. Temst, T. Puig, V. Metlushko, C. Strunk, J. G. Rodrigo, X. Qiu, C. Van Haesendonck, A. L6pez, H. Fink, S. Haley, A. Buzdin, J. Rubinstein, J. T. Devreese, V. Fomin, and E Peeters for fruitful discussions. We are grateful to the Flemish Fund for Scientific Research (FWO), the Flemish Concerted Action (GOA), the Belgian Inter-University Attraction Poles (IUAP), the bilateral TOURNESOL 1998 program, the ESF Program VORTEX and the European Human Capital and Mobility (HCM) research programs for financial support. M. J. Van Bael is a Postdoctoral Research Fellow of the FWO-Vlaanderen.

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525

Chapter 10 PROPERTIES AND APPLICATIONS OF NANOCRYSTALLINE ELECTRONIC JUNCTIONS Michael Gr~itzel Institute of Photonics and Interfaces, Swiss Federal Institute of Technology, Lausanne, Switzerland

Contents 1. General Properties of Nanocrystalline Semiconductor Junctions . . . . . . . . . . . . . . . . . . . . . . 2. Majority Cartier Injection Devices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1. Electrochromic Displays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2. Cross-Surface Electron Transfer on Nanocrystalline Oxide Films . . . . . . . . . . . . . . . . . 2.3. Luminescent Diodes Based on Mesoscopic Oxide Cathodes . . . . . . . . . . . . . . . . . . . . 3. Light-Induced Charge Separation in Nanocrystalline Semiconductor Films . . . . . . . . . . . . . . . 4. Nanocrystalline Injection Solar Cells . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1. Solar Light Harvesting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2. Conversion Efficiencies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3. Photovoltaic Performance Stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4. Development of Series-Connected Modules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5. Cost and Environmental Compatibility of the New Injection Solar Cell . . . . . . . . . . . . . . 4.6. Current Research Issues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5. Sensitized Solid-State Heterojunctions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6. Tandem Cells for the Cleavage of Water by Visible Light . . . . . . . . . . . . . . . . . . . . . . . . . 7. Nanocrystalline Intercalation Batteries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

527 531 531 534 534 536 537 539 539 545 545 547 547 548 550 551 552

1. G E N E R A L P R O P E R T I E S OF N A N O C R Y S T A L L I N E SEMICONDUCTOR JUNCTIONS Significant a d v a n c e s in the fields of colloid and s o l - g e l c h e m i s t r y in the last two d e c a d e s n o w allow fabrication of micro- and n a n o s i z e d structures using finely divided m o n o d i s p e r s e d c o l l o i d a l particles [1-7]. As w e a p p r o a c h the 21st century, there is a g r o w i n g trend on the part of the scientific c o m m u n i t y to apply these c o n c e p t s to d e v e l o p systems of s m a l l e r d i m e n s i o n s . H o m o g e n e o u s solid electronic devices [ t h r e e - d i m e n s i o n a l (3D)] are giving w a y to m u l t i l a y e r s with quasi t w o - d i m e n s i o n a l (2D) structures and quasi oned i m e n s i o n a l (1D) structures, such as n a n o w i r e s or clusters in an insulating matrix and finally to p o r o u s n a n o c r y s t a l l i n e films. O v e r the r e c e n t years, n a n o c r y s t a l l i n e materials h a v e attracted increasing attention f r o m the scientific c o m m u n i t y b e c a u s e of their s p e c t a c u l a r p h y s i c a l and c h e m i c a l properties. This u n u s u a l b e h a v i o r results f r o m the ultrafine structure (i.e., grain size less than 50 nm)

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of the materials. It is useful to distinguish effects related to bulk properties, such as quantum confinement [8] and monodomain grains [9], from surface effects. The latter arise from the high grain boundary to volume ratio allowing, for example, for the fabrication of ductile [10] or superplastic ceramics [11] as well as highly porous membranes [12] and electrodes [ 13]. Nanocrystalline electronic junctions are constituted by a network of mesoscopic oxide or chalcogenide particles, such as TiO2, ZnO, Fe203, NbzOs,WO3, Ta2Os, or CdS and CdSe, which are interconnected to allow electronic conduction to take place. A paste containing the nanocrystalline semiconductor particles is applied by screen printing or doctor blading on a glass coated with a transparent conducting oxide (TCO) layer made of fluorine-doped SnO2 (sheet resistance 8-10 ~2/square). Subsequent sintering produces a mesoporous film whose porosity varies from about 20% to 80%. The pores form an interconnected network that is filled with an electrolyte or with a solid charge transfer material, such as an amorphous organic hole transmitter or a p-type semiconductor, i.e. as CuI [ 14] or CuSCN [ 15]. In this way, an electronic junction of extremely large contact area is formed displaying very interesting and unique optoelectronic properties. The materials forming the junction are interdigitated on a length scale as minute as a few nanometers forming a bicontinuous phase. A schematic illustration of the nanocrystalline device is given in Figure 1. Some important features of such mesoporous films are: 1. An extremely large internal surface area, the roughness factors being in excess of 1000 for a film thickness of 8 / z m 2. The ease of charge cartier percolation across the nanoparticle network, making this huge surface electronically addressable 3. The appearance of confinement effects for films that are constituted by quantum dots, such as 5-nm-sized ZnO particles 4. The ability to form an accumulation layer under forward bias 5. For intrinsic or weakly doped semiconductors, the inability to form a depletion layer under reverse bias

Fig. 1. Typicallayout of a nanocrystalline semiconductorjunction. The network of n-type particles is interpenetrated by a p-type material used to fill the pores of the film.

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PROPERTIES AND APPLICATIONS OF NANOCRYSTALLINEELECTRONIC JUNCTIONS

6. A very rapid and highly efficient interfacial charge transfer between the oxide and redox active species anchored to the particle surface 7. A fast percolative cross-surface electron transfer involving adsorbed redox relays 8. The fast intercalation and release of Li + ions into the oxide Nanostructured materials offer many new opportunities to study fundamental surface processes in a controlled manner and this, in turn, leads to fabrication of new devices, some of which are summarized in Figure 2. The unique optical and electronic features of these films are being exploited to develop photochromic displays/switches, optical switches, chemical sensors, intercalation batteries, dielectrics/supercapacitors, heat-reflecting and ultraviolet (UV)-absorbing layers, coatings to improve chemical and mechanical stability of glass, and so on. Particularly intriguing is the observation of close to 100% conversion of photons in electric current made with films that are derivatized by charge transfer sensitizers adsorbed onto the surface of the oxide. This has led to the development of a new type of photovoltaic cell [ 16-18], which will be described in more detail later. In several recent articles [19-21 ], we have outlined some of these novel applications. The oxide material of choice for many of these systems has been TiO2. Its properties are intimately linked to the material content, chemical composition, structure, and surface morphology. Fortunately, colloid chemistry has greatly advanced in the last two decades so that it is now possible to control the processing parameters, such as precursor chemistry, hydrothermal growth temperature, binder addition, and sintering conditions, and to optimize the key parameters of the film, namely, porosity, pore size distribution, light scattering, electron percolation. On the material content and morphology, two crystalline forms of TiO2 are important, anatase and rutile (the third form brookite is difficult to obtain). Anatase is the low-temperature stable form and gives mesoscopic films that are transparent and colorless. The predominant morphology of the particles is bipyramidal exposing well-developed (101) faces. Preparation of mesoporous semiconductor films consists of two steps: First, a colloidal solution containing nanosized particles of the oxide is formed and this is used subsequently to produce a few micrometer-thick films with good electrical conduction properties. Figure 3 shows schematically the various steps involved in the preparation of nanocrystalline

( Solar Cells~ )

Oxide solution interfaces Ti02, ZnO, Nb205, W03, Ru02, Fe203 etc.

~r

Fig. 2. Applicationsof nanocrystalline oxide semiconductorfilms.

529

GR)kTZEL

Precipitation (hydrolysis of Ti-alkoxides using 0.1M HNO3)

V Peptization (8h, 80~ following by filtering

V Hydrothermal growth/autoclaving (12h, 200-250~

V Sonication (ultrasonic bath, 400 W, 15 x 2 s)

V Concentration (45~

30 mbar)

V binder addition (carbowax/PEG, MW 20000) (STOCK SOLUTION OF THE COLLOID)

V Layer deposition on conducting glass electrode (F-doped SnO2,doctor blade technique)

V Sintering / binder burnout (450~

30 min)

Fig. 3. Outlineof the steps involvedin the preparation of nanocrystalline TiO2 films.

YiO2 films. Only a brief summary is given, as detailed information on both the preparation

and the morphology of such films has been published elsewhere [22]. The precipitation process involves hydrolysis of a Ti(IV) salt, usually an alkoxide such as Ti-isopropoxide or a chloride followed by peptization. To obtain monodispersed particles of the desired size, the hydrolysis and condensation kinetics must be controlled. Ti-alkoxides with bulky groups such as butoxy hydrolyze slowly, allowing slow condensation rates. Autoclaving of these sols (heating at 200-250 ~ for 12 h) allows controlled growth of the primary particles and also, to some extent, the crystallinity. During this hydrothermal growth, smaller particles dissolve and fuse to large particles by a process known as "Ostwald ripening." After removal of the solvent and addition of a binder, the sol is now ready for deposition on the substrate. For the latter, a conducting glass sheet (R = 8-10 f2/square) is often used and the sol is deposited by doctor blading or screen printing and fired in air for sintering. The film thickness is typically 5 - 1 0 / z m and the film mass about 1-2 mg/cm 2. Analysis of the porous films shows the porosity to be about 50%, the average pore size being 15 nm. Figure 4 illustrates the morphology of such a nanocrystalline TiOz(anatase) layer deposited on a transparent conducting oxide (TCO) glass. The mean particle diameter of the oxide is 15 nm in this case. The size can be adjusted by varying the conditions of the solgel process used for film preparation. The optical properties of this film will be similar to those exhibited by bulk anatase. Ruffle is the dominant form at high temperature and its crystals are needle shaped, similarly to those of nanocrystalline Nb205 [23]. Figure 5 shows the structure of a nanocrystalline ZnO layer composed of particles whose size is in the 5-nm range. Here, confinement effects shift the optical band gap of the semiconductor to the blue [24-26].

530

PROPERTIES AND APPLICATIONS OF NANOCRYSTALLINE ELECTRONIC JUNCTIONS

Fig. 4. Scanningelectron micrographof a nanocrystalline TiO 2 film supported on conducting glass. The magnification employedis indicated as a scale bar.

2. MAJORITY CARRIER INJECTION DEVICES A schematic representation of a nanocrystalline junction operated in the charge injection mode is shown in Figure 6. The mesoscopic semiconductor, typically an oxide that is ndoped or left intrinsic, is deposited onto a current collector, which, in general, is constituted by a TCO glass. The pores present between the particles are filled with the contact medium constituted, for example, by an electrolyte, a hole-transmitting organic material, or a p-type semiconductor. This, in turn, is placed in contact with the second current collector, that is, the counterelectrode. Often, a thin compact layer of the oxide semiconductor is deposited between the conductive glass and the nanocrystalline film to avoid short circuiting of the two current collectors by the charge transport material that is infiltrated into the pores. Such a device can be used as an electrochromic or electroluminescent display, which will be discussed in more detail next.

2.1. Electrochromic Displays In this case, majority carriers are injected from outside into the junction driving the nanocrystalline oxide film into accumulation. Associated with injection is an electrochromic effect produced by the accumulation of conduction band electrons in the oxide exhibiting a very broad absorption in the visible and near-infrared wavelength range [27]. This effect has been used to determine the flat band potential of such oxide films [28].

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GRATZEL

Fig. 5.

Fig. 6.

Scanning electron microscope of a nanocrystalline ZnO film.

General layout of a nanocrystalline majority cartier injection device.

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PROPERTIES AND APPLICATIONS OF NANOCRYSTALLINE ELECTRONIC JUNCTIONS

Fig. 7. n-typeelectrochromism on nanocrystalline oxide surfaces derivatized with a molecular redox relay.

Electrochromic switching of mesoscopic films occurs rapidly because of ready compensation of the injected space charge by ion movement in the electrolyte present in the pores and fast intercalation of lithium ions [29, 30]. Viologens form a group of redox indicators that undergo drastic color changes upon oxidation/reduction. The reduced form of methyl viologen, for example, is deep blue, while the oxidized form is colorless. Efficient reduction of anchored viologen compounds by conduction band electrons of TiO2 can be used for the amplification of the optical signal, as shown schematically in Figure 7. The amplification is due to the high molecular extinction coefficients of these relays. Upon reduction, transparent nanocrystalline films of TiO2 containing viologen develop strong color and the film can be decolorized by reversing the potential. Varying the chemical structure and redox potentials of the viologens makes it possible to tune the color and, hence, build a series of electrochromic display devices [ 19, 31 ]. Such surface-derivatized oxides accomplish a performance that, in terms of figure of merit, that is, the charge required to achieve an optical density change of one, is already competitive with conventional electrochromic systems and, hence, shows great promise for practical applications. The anchoring of a redox relay, such as a viologen derivative to the surface of the oxide that turns highly colored upon reduction, allows for molecular amplification of the optical signal (see Fig. 8). The reason for this amplification is that the molecular extinction coefficient of the reduced relay is one to two orders of magnitude higher than that of the conduction band electrons. Therefore, such surface-derivatized nanocrystalline devices accomplish a performance that, in terms of figure of merit, that is, the Coulombic charge required to achieve an optical density change of one, is already competitive with conventional electrochromic systems. The exponential dependence of the change in the optical density on the applied potential allows a simple multiplexing method to be used for addressing individual pixels of the nanocrystalline film, which is important for display applications [ 19, 20].

533

GR,a.TZEL

Fig. 8. Electrochromicswitching with a mesoscopic TiO 2 film whose surface is derivatized with a dimeric viologen.Both the colored and the uncoloredstate are schematicallypresented.

2.2. Cross-Surface Electron Transfer on Nanocrystalline Oxide Films

A striking phenomenon of cross-surface electron transfer on nanocrystalline films of semiconducting and insulating oxides, such as TiO2, A1203, and ZrO2, was discovered recently [32]. These films were deposited on conducting glass and surface derivatized with a monolayer of phosphonated triarylamine acting as a redox relay. The films displayed reversible electrochemical and electrochromic behavior even though the redox potential of the triarylamine lies in the forbidden band of the semiconducting or insulating oxide. In this potential domain, the oxide is insulating, impairing any electronic charge movement across the nanocrystalline particle film. The mechanism of charge transport was found to involve hole injection from the conducting support followed by cross-surface transfer of the holes within the monolayer of the adsorbed amine. The role of the nanocrystalline oxide film is merely to support the electroactive surface layer. A sharp percolation threshold for electronic conductivity was found at about 50% coverage. 2.3. Luminescent Diodes Based on Mesoscopic Oxide Cathodes

Luminescent diodes present another important possible application of nanocrystalline junctions. In analogy to solid-state lasers, these devices operate by majority carrier injection. Organic materials have frequently been considered for the fabrication of practical electroluminescent (EL) devices. The reason for this is that a large number of organic materials are known to luminesce very efficiently in the visible region. In this respect, they are well suited for multicolor display applications. Earlier attempts to make such devices operative were plagued by the high voltage required to drive charge transport in organic crystals. Recently, the advent of thin layer cells used in conjunction with novel diamine-type organic solids as hole-transmitting layers (HTLs) has resulted in the development of systems with much improved performance characteristics [33]. The substrate is a conducting glass covered with a layer of aromatic diamine. The diamine acts as a hole conductor. Despite their amorphous character, these charge transfer materials exhibit a respectable hole mobility, which is in the range of 10 -5 to 10 -2 cm2/V s. A second layer belonging to the class of metal chelates serves as an electron conductor and light emitter. Unfortunately, the charge carrier mobility is poor in this second layer. The top electrode is an alloy of magnesium or calcium with sil-

534

PROPERTIES AND APPLICATIONS OF NANOCRYSTALLINE ELECTRONIC JUNCTIONS

ver. This organic diode was shown to behave as a rectifier emitting light under forward bias [34]. Although such devices do function as luminescent diodes, a major limiting factor for consumer display applications so far has been the short device lifetime. Amongst the many factors responsible for degradation, the low-work-function metal or alloy cathode has been recognized as a major source. Both the sensitivity toward water and oxygen as well as contact problems between the organic and the metal layer contribute to the observed instability. Work initiated in our laboratory [34] makes use of the favorable properties of mesoscopic semiconductor layers for electroluminescent display applications. Instead of using low-work-function metals, nanocrystalline oxides, such as Nb205 or Ta2Os, are employed as cathode materials for organic light-emitling diode (LED) devices. These are attractive for several reasons: (i) They have a large band gap ( E c > 3 eV) assuring transmittance of visible light. (ii) Because of the small size of the oxide particles, the scattering of light is negligible. (iii) The mesoporous morphology of the such oxide film plays an important role in favoring electroluminescent processes. The high internal surface area permits the electron injection to proceed at lower overpotentials, preventing the unwanted quenching of the excited states of the light-emitter material by energy transfer to conduction band electrons. The sensitivity of oxide cathodes toward water and air is much less critical than that of the low-work-function metals. The luminescent material may be deposited as a monomolecular layer on the nanocrystalline oxide. In such a configuration, the dye-derivatized oxide semiconductor replaces the aluminum trishydroxyquinolate film (see Fig. 9). The dye is oxidized through holes injected into a solid hole-transmitting material or a redox electrolyte. N-doping of the

Fig. 9. Energylevel diagram for an electroluminiscent device based on a nanocrystalline semiconductor oxide (SC) as an electron-injecting cathode and a counterelectrode (CE) for hole injection. The energy levels of the dye and the redox electrolyte are also indicated.

535

GRATZEL

semiconductor renders it a good electron conductor. Selecting an oxide material having a low work function assures that the electron is injected in the excited state level of the dye, producing emission of light by radiative deactivation. Although this field is still in its infancy, the outlook is bright for developing luminescent diodes based on nanocrystalline films whose characteristics are superior to state-of-the-art technology.

3. LIGHT-INDUCED CHARGE SEPARATION IN NANOCRYSTALLINE SEMICONDUCTOR FILMS The illumination of nanocrystalline junctions can be used to generate electric current from light. Because of the small size of the semiconductor oxide particles constituting the film and the fact that they are all in contact with the electrolyte, there is only a small electric field within the particles [35]. The potential gradient across the nanocrystalline film is particularly small for undoped materials [36]. The question then arises how in such a system electron-hole pairs are separated after band gap excitation. Several groups have addressed this issue and the literature has been reviewed [37]. Very recently, a detailed electrical model of nanocrystalline photovoltaic devices has been published [38]. It is now commonly agreed that charge carrier transport in the film occurs by diffusion, the rate of which is controlled by traps [39-41]. The response of the system to band gap excitation depends on the relative rate of the electron and hole reactions with the redox electrolyte present in the pores of the film. This distinguishes mesosocopic semiconductor films from conventional p/n or Schottky junction devices where the response to photoexcitation is governed by the electric field present in the junction. As an example, we consider in Figure 10 the case where the holes are scavenged more rapidly than the electrons. Here the response of the particle film to light will be that of an n-type semiconductor. In contrast, if the electrolyte contains a reactant that scavenges electrons more rapidly than holes, the film behaves like a p-type semiconductor. Thus, changing the photoresponse from n to p type becomes possible by merely modifying the composition of the electrolyte as has been shown for nanocrystalline CdSe films [42].

Fig. 10. Light-inducedcharge separationin a nanocrystalline semiconductorfilm where holes are scavenged morerapidly than electrons at the particle-electrolyte interface. As a consequence, the films exhibit n-type behavior.

536

PROPERTIES AND APPLICATIONS OF NANOCRYSTALLINEELECTRONIC JUNCTIONS

A property that is of primary concern for applications of these systems is their efficiency of operation as a quantum converter. The film absorbs photons whose energy exceeds the energy difference between the conduction and valence band. Light absorption leads to the generation of electron-hole pairs in the solid. For oxides such as TiO2, the electrons are majority carriers, while the holes constitute the minority carriers even though the material may not have been deliberately n-doped. This is due to the adventitious presence of defects such as oxygen vacancies. If such a nanocrystalline device is to be used for the generation of electricity from light, it is necessary that the holes can diffuse to the semiconductor/electrolyte junction before recombination with the electrons has occurred. In other words, the diffusion length of the minority carriers (/mc) has to be longer than the distance these carriers have to travel before they reach the junction. This diffusion length is related to the lifetime of the holes (r) via the mean square displacement expression: lmc : (2Dr) ~

(1)

For TiO2, the/mc value is typically 100 nm. Because mesoscopic semiconductor films are constituted by 5-50-nm-sized particles, their size is smaller than the minority charge carrier diffusion length. Hence, the minority carriers can reach the electrolyte interface before recombination occurs. The operation of the thin film device as an efficient quantum converter, therefore, becomes feasible, and this has been confirmed meanwhile by a number of studies [37, 42, 43]. Conversion efficiencies of incident photons to current of nearly 100% have been achieved in the wavelength range of the band-gap absorption of the semiconductor. In summary, the new mesoscopic films are constituted by nanometer-sized semiconductor particles forming an interconnected network. The internal surface of the film is much higher than its projected geometric surface. A network of interconnected pores is present at the same time within the film. Because of the small size of the particles, the film does not scatter visible light. Nor is visible light absorbed by such a film if it is constituted by an oxide because of its relatively large band gap. Thus, a mesoporous layer of TiO2 (thickness 0.1-10/zm) deposited onto a conducting glass is invisible to the naked eye. This distinguishes such films from conventional photovoltaic devices. A surprising and very important property of these nanostructured films is that a brief sintering treatment produces efficient electronic contact not only between the particles and the support but also between practically all the particles constituting the film. It has been shown that electronic charges injected into the membrane from the conducting support are able to percolate through the entire film of nanometer-sized particles at a high rate. This allows for rapid oxidation and reduction of electroactive species present at the particle surface or in the voids between particles. Alternatively, if electrons are injected into the particles from a species adsorbed at their surface or present within the voids, the injected charge can be collected with 100% efficiency at the conducting support. Given these unique properties, the film can serve as a matrix to accommodate electroactive materials within the pores or at the particle surface and to address electronically these materials. Alternatively, the pores can be filled with a solid or liquid material that forms a junction with the semiconductor particles constituting the matrix. In this case, the film functions as a photovoltaic cell that produces electricity from light. A powerful method to enhance the visible light response of such mesoscopic oxides is their sensitization by charge transfer sensitizers. This has led to the development of a new type of injection solar cell, which will be discussed in more detail in the following section. 4. NANOCRYSTALLINE INJECTION SOLAR CELLS The fundamental processes involved in any photovoltaic conversion process are: 1. The absorption of sunlight 2. The generation of electric charges by light 3. The collection of charge carriers to produce electricity

537

GRATZEL

Fig. 11. Operationalprinciple of the nanocrystalline injection solar cell.

The incident monochromatic photon-to-current conversion efficiency (IPCE) or "external quantum yield" of such a device is then given by the equation: IPCE()0 = LHE(~.) x t~inj • r/e

(2)

where IPCE(~) expresses the ratio of the measured electric current to the incident photon flux for a given wavelength, LHE is the light-harvesting efficiency, ~binjis the quantum yield for charge injection into the oxide, and r/e is the charge collection efficiency. Conventional solar cells convert light into electricity by exploiting the photovoltaic effect that exists at semiconductor junctions. They are thus closely related to transistors and integrated circuits. The semiconductor performs two processes simultaneously: absorption of light and separation of the electric charges (electrons and holes) that are formed as a consequence of that absorption. However, to avoid the premature recombination of electrons and holes, the semiconductors employed must be highly pure and defect free. The fabrication of this type of cell presents numerous difficulties, preventing the use of such devices for electricity production on a large industrial scale. In contrast, the solar cell developed in our group at the Swiss Federal Institute of Technology operates on a different principle, whereby the processes of light absorption and charge separation are differentiated (see Fig. 11). Light absorption is performed by a monolayer of dye (S) adsorbed chemically at the semiconductor surface. After having been excited (S*) by a photon of light, the dyenusually a transition metal complex whose molecular properties are specifically engineered for the taskmis able to inject an electron into the conduction band of the oxide semiconductor. The back reaction is intercepted by transferring the positive charge from the dye (S +) to a redox mediator R/R + present in the electrolyte with which the cell is filled and thence to the counterelectrode. Via this last electron transfer, in which the mediator is returned to its reduced state, the circuit is closed. The system operates as a regenerative electrochemical cell that converts light into electricity without inducing any permanent chemical transformation. The maximum voltage A V that such a device could deliver corresponds to the difference between the redox potential of the mediator and the Fermi level of the semiconductor. The electrolyte containing the mediator could be replaced by a p-type semiconductor, for example, cuprous thiocyanate, CuSCN [ 15], or cuprous iodide, CuI [14], or a hole-transmitting solid, such as the amorphous organic arylamines used in electroluminescence devices [33]. This is an attractive option that is presently being explored in our laboratory. It should be emphasized that for all embodiments of the nanocrystalline injection cell, minority carriers, that is, holes in the case of an n-type conductor such as TiOa, do not participate in the photoconversion process. This is a great advantage in comparison to

538

PROPERTIES AND APPLICATIONS OF NANOCRYSTALLINEELECTRONIC JUNCTIONS

conventional photovoltaic devices, where, without exception, the generation and transport of minority carriers is required. The performance characteristics of the conventional device are strongly influenced by the minority carrier diffusion length, which is very sensitive to the presence of imperfections and impurities in the semiconductor lattice. By contrast, the nanocrystalline injection cell operates entirely on majority carriers whose transport is not subjected to these limitations and, hence, will be much less sensitive to lattice defects.

4.1. Solar Light Harvesting As indicated previously, the absorption of light by a monolayer of dye is weak because the area occupied by one molecule is much larger than its optical cross section for light capture. A respectable photovoltaic efficiency, therefore, cannot be obtained by the use of a fiat semiconductor surface but rather by use of a porous, nanostructured film of very high surface roughness. When light penetrates the photosensitized semiconductor "sponge", it crosses hundreds of adsorbed dye monolayers. The mesoporous structure thus fulfills a function similar to the thylakoid vesicles in green leaves, which are stacked in order to enhance light harvesting. Apart from providing a folded surface having a very high roughness surface to enhance light harvesting by the adsorbed sensitizer, the role of the nanocrystalline oxide film is to serve as an electron conductor. The conduction band of the titanium dioxide accepts the electrons from the electronically excited sensitizer. The electron injected into the conduction band percolates very rapidly across the TiO2 layer. Its diffusion is much faster than that of a charged ion in solution. The time required for crossing a TiO2 film, say 5/zm thick, is at most a few milliseconds, depending on whether or not trapping of electrons is involved in the transport. During migration, the electrons maintain their high electrochemical potential, which is equal to the quasi-Fermi level of the semiconductor under illumination. Thus, the principal function of the TiO2, apart from supporting the sensitizer, is that of charge collection and conduction. The advantage of using a semiconductor membrane rather than a biological one as employed by natural photosynthesis is that such an inorganic membrane or film is more stable and allows extremely fast transmembrane electron movement. The charge transfer across the photosynthetic membrane is less rapid because it takes about 100/zs to displace the electron across the 50-,~ thick thylakoid layer. Moreover, nature has to sacrifice more than half of the absorbed photon energy to drive the transmembrane redox process at such a rate. In the case of the semiconductor film, the price to pay for the rapid vectorial charge displacement is small. It corresponds to at most 50-200 mV of voltage drop required to drive the electron injection process at the semiconductor/electrolyte junction. In contrast to chlorophyll, which is continuously being synthesized in the leaf, the sensitizer in the nanocrystalline cell must be selected to satisfy the high stability requirements encountered in practical applications. A photovoltaic device must remain serviceable for 20 years without significant loss of performance corresponding to 50-100 million turnovers for the dye. Recent work has focused on the molecular engineering of suitable ruthenium compounds, which are known for their excellent stability. Cis-dithiocyanatobis(2,21bipyridyl)-4,41-(dicarboxylate) - ruthenium(II), I, was found to be an outstanding solar light absorber and charge transfer sensitizer [ 18], which for a long time was unmatched by any other dyes. Only recently, has a black dye been discovered that has a superior performance to I as a charge transfer sensitizer in the injection solar cell [44].

4.2. Conversion Efficiencies The use of mesoporous oxide films to support the sensitizer allows sunlight to be harvested over a broad spectral range in the visible, fulfilling the first requirement for efficient light energy conversion. In order for the device to deliver a photocurrent that matches the

539

GRATZEL

performance of conventional cells, both the electron injection and the charge carrier collection must, in addition, occur with an efficiency close to unity.

4.2.1. Quantum Yield of Charge Injection The quantum yield of charge injection (~binj) is the fraction of the absorbed photons that are converted into electrons injected in the conduction band. Charge injection from an electronically excited sensitizer into the conduction band of the semiconductor is in competition with other radiative or radiationless deactivation channels. Taking the sum of the rate constants of these nonproductive channels together as keff results in kinj ~binj = keff -+-kinj

(3)

One should remain aware that the deactivation of the electronically excited state of the sensitizer is generally very rapid. Typical keff values lie in the range of 103 to 1010 s -1 . To achieve a good quantum yield, the rate constant for charge injection should be at least 100 times higher than keff. This means that injection rates in the picosecond range or below have to be attained. In fact, in recent years sensitizers have been developed that satisfy these requirements. These dyes should incorporate functional groups ("interlocking groups") as, for example, carboxylate, hydroxamate or phosphonate groups [45] that are attached to the pyridyl ligands. Besides bonding to the titanium dioxide surface, these groups also effect an enhanced electronic coupling of the sensitizer with the conduction band of the semiconductor. The electronic transition is of MLCT (metal-to-ligand charge transfer) character (see Fig. 12), which serves to channel the excitation energy into the fight ligand, that is, the

Fig. 12. Energydiagram showing the electronic orbitals involved in the MLCT excitation of a Ru(II) complex attached to the surface of the semiconducting oxide via carboxylatedbipyridyl groups.

540

PROPERTIES AND APPLICATIONS OF NANOCRYSTALLINEELECTRONIC JUNCTIONS

one from which electron injection into the semiconductor takes place. With molecules like these, the injection times are in the pico- or femtosecond range [46-49] and the quantum yield of charge injection generally exceeds 90%. In fact, for several sensitizers the electron transfer into the conduction band of the oxide is so rapid that it occurs from vibrationally hot excited states [50].

4.2.2. Light-lnduced Charge Separation As the next step of the conversion of light into electrical current, a complete charge separation must be achieved. On thermodynamic grounds, the preferred process for the electron injected into the conduction band of the titanium dioxide membrane is the back reaction with the oxidized sensitizer. Naturally, this reaction is undesirable, because instead of electrical current it merely generates heat. For the characterization of the recombination rate, an important kinetic parameter is the rate constant kb. It is of great interest to develop sensitizer systems for which the value of kinj is high and that of kb low. Fortunately, for the transition metal complexes employed as sensitizers, the ratio of the injection over that of electron recapture by the oxidized dye often exceeds one million, which significantly facilitates the charge separation. One reason for this striking behavior is that the molecular orbitals involved in the back reaction overlap less favorably with the wave function of the conduction band electron than those involved in the forward process. For the Ru complexes bound to the titanium dioxide membrane, the injecting orbital is the 7r* wave function of the carboxylated bipyridyl or phosphonated terpyridyl ligand because the excited state of this sensitizer has a metal-to-ligand charge transfer character (see Fig. 12). The carboxylate groups interact directly with the surface Ti(IV) ions, resulting in good electronic coupling of the re* wave function with the 3d orbital manifold of the conduction band of the TiO2. As a result, the electron injection from the excited sensitizer into the semiconductor membrane is an extremely rapid process occurring in the femtosecond time domain. By contrast, the back reaction of the electrons with the oxidized ruthenium complex involves d orbitals localized on the ruthenium metal whose electronic overlap with the TiO2 conduction band is small and is further reduced by the spatial contraction of the wave function upon oxidation of the Ru(II) to the Ru(III). Thus, the electronic coupling element for the back reaction is one to two orders of magnitude smaller for the back electron transfer as compared to injection reducing the back reaction rate by the same factor. A second very important contribution to the kinetic retardation of charge recombination arises from the fact that this process is characterized by a large driving force and a small reorganization energy, the respective values for sensitizer I being 1.5 and 0.3 eV, respectively. This places the electron recapture clearly in the inverted Markus region, reducing its rate by several orders of magnitude. This provides also a rationale for the observation that this interfacial redox process is almost independent of temperature and is surprisingly insensitive to the ambient that is in contact with the film [51 ]. Of great significance for the inhibition of charge recombination is the existence of an electric field at the surface of the titanium dioxide film. Although there is practically no depletion layer within the oxide because of the small size of the particles and their low doping level, a dipole field is established spontaneously by proton transfer from the protonated carboxylate or phosphonate groups of the ruthenium complex to the oxide surface, producing a charged double layer. If the film is placed in contact with a protic solvent, the latter can also act as proton donor. In aprotic media, Li + or Mg 2+ are potential determining ions for TiO2 [26] and they may be used to charge the surface positively. The local potential gradient from the negatively charged sensitizer to the positively charged oxide drives the injection in the desired direction. The same field inhibits also the electrons from exiting the solid after injection has taken place.

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4.2.3. Charge Carrier Percolation and Collection The subsequent migration of electrons within the TiO2 conduction band to the current collector involves charge carrier percolation over the mesoscopic particle network. This important process, which leads to nearly quantitative collection of injected electrons, is presently attracting a great deal of attention [20-22]. For example, the elegant experiments conceived by Hagfeldt and Lindquist [20] have given useful keys to rationalize the intriguing findings made with these films under band gap illumination. It should be noted that apart from recapture by the oxidized dye there is an additional loss channel in the nanocrystalline injection cell involving reduction of triiodide ions in the electrolyte that is present within the mesoporous network: 13 + 2e~(TiO2) ~ 3I-

(4)

Engineering the interface to impair this unwanted heterogeneous redox process from occurring will be a challenging task for future development. The efficient interception of recombination by the electron donor, for example, iodide: 2S + + 31- --+ 2S + 13

(5)

is crucial for obtaining good collection yields and high cycle life of the sensitizer. In the case of sensitizer I, our own time-resolved laser experiments have shown the interception to take place with a rate constant of about 109-108 s -1 at the iodide concentrations that are typically applied in the solar cell. This is about 100 times faster than the recombination rate and 108 times faster than the intrinsic lifetime of the oxidized sensitizer in the electrolyte in the absence of iodide. Cyclic voltammetry experiments carded out with solutions of I have shown its intrinsic lifetime in the oxidized state to be limited to a few seconds by intramolecular charge transfer from Ru(III) to the SCN- group followed by irreversible oxidation of the latter ligand. The factor of 108 explains the fact that this sensitizer can sustain 100 million turnovers in continuous solar cell operation without loss of performance.

4.2.4. Incident Photon-to-Current Conversion Efficiencies A graph that presents the monochromatic current output as a function of the wavelength of the incident light is known as a "photocurrent action spectrum". Figure 13 shows such spectra for four ruthenium complexes, illustrating the very high efficiency of quantum conversion with these complexes. When corrected for the inevitable reflection and absorption losses in the conducting glass serving to support the nanocrystalline film, yields of practically 100% of current flow per incident photon flux are obtained over a wide wavelength range. This implies that light harvesting, conversion of photons to electrons and collection of the injected electrons is quantative; see Eq. (2). Historically, RuL3 (L = 2,2'-bipyridyl4,4'-dicarboxylate) was the first efficient and stable charge transfer sensitizer to be used in conjunction with high-surface-area TiO2 films. In a long-term experiment carried out during 1988, it sustained 9 months of intense illumination without degradation. However, the visible light absorption of this sensitizer is insufficient for solar light conversion. A significant improvement of the light harvesting was achieved with the trimeric complex of ruthenium [ 16] whose two peripheral ruthenium moieties were designed to serve as antennas [52]. An even more effective charge transfer sensitizer is cis-dithiocyanatobis(2,2'bipyridyl)-4,41-(dicarboxylate)-mthenium(II). The latter achieves close to quantitative photon-to-electron conversion over the wavelength range from 350 to 600 nm [ 18]. Even at 700 nm, current generation is still 40% to 60% efficient depending on the thickness of the film. Its perfomance was only superseded recently by the discovery of a new black dye having a spectral onset at 900 nm, which is optimal for the conversion of amplitude-modulated (AM) 1.5 solar radiation to electric power in a single-junction photovoltaic cell [44].

542

PROPERTIES AND APPLICATIONS OF NANOCRYSTALLINE ELECTRONIC JUNCTIONS

Fig. 13. Photocurrentaction spectrum obtained with four different ruthenium-based sensitizers attached to the nanocrystalline TiO2 film. Data obtained with the bare TiO2 surface are shown for comparison.

4.2.5. Overall Solar-to-Electric Power Conversion Efficiencies The overall efficiency (r/global) of the photovoltaic cell can easily be calculated from the integral photocurrent density (iph), the open-circuit photovoltage (Voc), the fill factor of the cell (ff), and the intensity of the incident light (Is): r/global -----

i ph X Voc • Is

(6)

The currently obtained overall efficiencies are in the 10% to 11% range depending on the fill factor of the cell. Thus, current-voltage characteristic nanocrystalline injection cells based on sensitizer I were certified by the photovoltaic test laboratory at the PV Calibration Laboratory of the Fraunhofer Institute for Solar Energy in Freiburg, Germany. The photocurrent obtained at 1000 mW/cm 2 of simulated AM 1.5 global solar intensity was 19.40 mA/cm 2, the open-circuit voltage was 0.794 V, and the fill factor was 0.70, yielding for the conversion efficiency of the cell a value of 11%. This I / V curve is shown in Figure 14. Under optimal current collection geometry, minimizing ohmic losses resulting from the sheet resistance of the conducting glass resistance, cells with very high fill factors, that is, ff = 0.8, have already been fabricated. This yield is still significantly below the value of 33% corresponding to the upper limit for conversion of standard AM 1.5 solar radiation to electricity by a single-junction cell. The main reason for the difference is the mismatch in the redox level of the dye and that of the iodide/triioide redox system used as the electrolyte, leading to a voltage loss of 0.7 V. Adjusting the redox levels to reduce this loss to a more reasonable figure of 0.3 V would allow the overall conversion efficiency to double from 10% to 20%. An improvement of the cell current by approximately 30% should be possible through better light harvesting in the 700-800-nm range where the absorption of I is relatively weak. Applying a dye

543

GRATZEL

] =FB': il-"|-"~ Lp,~ml

ii

PV CALIBRATION L A B O R A T O R Y i

I-V Record

5.0

AM

mml

9

i

1.5 G l o b a l , 1 0 0 0 m / m 2 2 5 ~

Date

)

9

20.12.1996

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4.5

Voc

=

794. 65 m V

4.0

Isc

=

4.83 mA

3.5

19. 4 0 m A / c m 2

Jsc

=

VMa~

=

608.08 mV

3.0 '~

2.5

.~ 0

2.0

IMax

=

4.49 mA

1.5

PMax

=

2.

FF

=

70.99 %

ETA

=

10.96 %

Active Area

9

Parallel Cells

- 1

1.0

73 m W

0.5

0.0 0

400

200

600

800

Voltage [mV]

Sample Id

" PL1152/$2

Type

Basic Material" Nanocrystall. Serial c e l l s Producer

9 EPFL

Comments

9

Measurement

Simulator

Customer

Uniformity

-

File

Operator 9 K U

Correction Factors 9 9

I

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Ref.-Cell Id. 9 R - 1 2

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1 Chuck position 9

Contact

config

Comments

9

0.249 cm 2

" EPFL

Parameters

" XAT

Mismatch

9 Solar cell

Top

"

I x/-V

Bottom

9

41.4

/ x I-V

9

Fig. 14. Photocurrent-voltage curve for a sealed nanocrystalline injection cell based on cis-Ru(2,2,bipyridyl-4,4t-dicarboxylate)(SCN)2 as a sensitizer. The simulated AM 1.5 global solar radiation is 1000 W/m 2.

c o c k t a i l t h a t is c o m p l e m e n t a r y in s p e c t r a l r e s p o n s e o f f e r s a s t r a i g h t f o r w a r d w a y to a c h i e v e this g o a l . T h u s , it is f e a s i b l e to r e a c h w i t h n a n o c r y s t a l l i n e m a t e r i a l s e f f i c i e n c i e s a r o u n d 2 5 % t h a t fall in t h e s a m e r a n g e as t h o s e o b s e r v e d w i t h t o p - q u a l i t y , s i n g l e - c r y s t a l G a A s s o l a r cells.

544

PROPERTIES AND APPLICATIONS OF NANOCRYSTALLINE ELECTRONIC JUNCTIONS

An advantage of the nanocrystalline solar cell with respect to solid-state devices is that its performance is remarkably insensitive to temperature change. Thus, raising the temperature from 20 to 60 ~ has practically no effect on the power conversion efficiency. In contrast, conventional silicon cells exhibit a significant decline over the same temperature range amounting to more than 25%. Because the temperature of a solar cell will reach readily 60 ~ under full sunlight, this feature of the injection cell is particularly attractive for power generation under natural conditions.

4.3. Photovoltaic Performance Stability The stability of all the constituents of the nanocrystalline injection solar cells, that is, the conducting glass, the TiO2 film, the sensitizer, the electrolyte, the counterelectrode, and the sealant, have been subjected to close scrutiny. The stability of the TCO glass and the nanocrystalline TiO2 film being unquestionable, investigations have focused on the four other components. On long-time illumination, complex I sustained 5 x 107 redox cycles without noticeable loss of performance corresponding to approximately 10 years of continuous operation in natural sunlight [53]. By contrast, practically all organic dyes tested so far underwent photobleaching after less than 106 cycles. This clearly outlines the exceptionally stable operation of our charge transfer sensitizers, which is of great advantage for the practical application of these devices. The reason for this astonishing stability is the very rapid deactivation of the excited triplet state via charge injection into the TiO2 which--as was shown above--occurs in the femtosecond time domain. This is at least 8 orders of magnitude faster than any other competing channels of excited state deactivation including those leading to chemical transformation of the dye. These tests are very important, because--apart from the sensitizermother components of the device, such as the redox electrolyte or the sealing, may fail under long-term illumination. Indeed, a problem emerged with electrolytes based on cyclic carbonates, such as propylene or ethylene carbonate, which were found to undergo thermally activated decarboxylation in the presence of TiO2, rendering these solvents unsuitable for practical usage. They were, therefore, replaced by a highly polar and nonvolatile liquid that does not exhibit this undesirable property. Room temperature molten salts based on imidazolium iodides and triflates have revealed very attractive stability features although their high viscosity restricts applications to the low-current regime, for example, indoor power supplies. Thus, fully assembled cells showed no decline in photovoltaic performance, that is, photocurrent, photovoltage, and fill factor, when submitted to accelerated aging performed in a sun test (AM 1) chamber at 44 and 85 ~ for at least 2300 and 1000 h, respectively [53]. Direct excitation of electron-hole pairs in the anatase by k > 380-nm light was avoided in these experiments by using a polycarbonate protective film. Stability tests on sealed cells have progressed significantly over the last few years. These tests are very important as the redox electrolyte or the sealing may fail under long-term illumination. A recent stability test over 7000 h of continuous full-intensity light exposure has confirmed that this system does not exhibit an inherent instability [54], in contrast to amorphous silicon, which as a consequence of the Stabler-Wronski effect undergoes photodegradation.

4.4. Development of Series-Connected Modules Meanwhile, the development and testing of the first cell module for practical applications has begun. The layout of the module is presented in Figure 15. The cell consists of two glass plates, which are coated with a transparent conducting oxide (TCO) layer. The nanocrystalline titanium dioxide film deposited on the lower plate supports the ruthenium complex acting as a charge transfer sensitizer. On illumination, this injects an electron into the titanium dioxide conduction band. The electrons pass over the collector electrode into the

545

GRATZEL

Fig. 15. Schematic presentation of the dye-sensitized nanocrystalline solar cell and its components: (a) general view, (b) cross section, (c) blowup of the mesoporous photoanode, and (d) the structure of the ruthenium complex I serving as the charge transfer dye.

external circuit where they perform work. They are then returned to the cell via the counterelectrode. The sensitizer film is separated from the counterelectrode by the electrolyte containing the redox couple, for example, triiodide/iodide, whose role is to transport electrons from the counterelectrode to the sensitizer layer. A small amount of platinum (51 0 / z g / c m 2) is deposited onto the counterelectrode to catalyze the cathodic reduction of triiodide to iodide.

546

PROPERTIES AND APPLICATIONS OF NANOCRYSTALLINE ELECTRONIC JUNCTIONS

An alternative approach developed by Kay in our laboratory uses a monolithic triplelayer structure [55] where the nanocrystalline anatase film, a porous spacer, and the carbon counterelectrode are directly deposited on top of each other. A 21-cm2-sized working interconnected module consisting of 6 Z-type interconnected cells was recently demonstrated. Accelerated stability tests were also performed with this type of cell. Continuous exposure to full sunlight for 120 days did not result in any significant deterioriation of performance. This confirms system stability over several years of natural conditions without any indication of a decline in efficiency.

4.5. Cost and Environmental Compatibility of the New Injection Solar Cell Several industrial sources, including Asea Brown Boveri, Strategies Unlimited, and Research Triangle Institute, have performed a cost analysis which yields U.S.$0.6/Wp and U.S.$2000/kWp for module and total systems cost, respectively. Similar values were reported by Smestad [56]. It may be argued that the presence of ruthenium renders the price of the sensitizer too high for commercial exploitation or that there is insufficient supply of it. However, the required amount is only 10 -3 mol/m 2 of ruthenium complex corresponding to the small investment of approximately U.S.$0.2/m 2 for the noble metal. The world trade in ruthenium reached 10 tons in 1994 mainly because of its use as a dimensionally stable anode in electrochemical chlorine production. One ton of ruthenium alone incorporated in the charge transfer sensitizer I could provide 1 GW of electric power under full sunlight. This is more than twice the total photovoltaic capacity presently in use worldwide. Thus, the cost and supply of ruthenium-based sensitizers is of no real concern here. The price-determining material for this photovoltaic technology is undoubtedly the conducting glass. Apart from efficiency and stability, any future photovoltaic technology will be valued according to its environmental and human compatibility. There is great concern about the adverse environmental effects and acute toxicity of CdTe or CuInSe2, which are being considered for practical development as thin solar cells. Such concerns are unjustified for our nanocrystalline device. Titanium dioxide is a harmless, environmentally friendly material, remarkable for its very high stability. It occurs in nature as ilmenite, and is used in quantity as a white pigment and as an additive in toothpaste. Worldwide annual production is in excess of 1 million tons. Similarly, ruthenium has been used without adverse health effects as an additive for bone implants.

4.6. Current Research Issues Current research in the field of injection solar cells focuses on the following topics: 1. The molecular design and synthesis of new sensitizers having enhanced nearinfrared light response, examples being phthalocyanines or the black dye discussed previously 2. A better understanding of the interface, including experimental and theoretical work on dye adsorption processes 3. The analysis of the dynamics of interfacial electron transfer processes down to the femtosecond time domain 4. The unraveling of the factors that control electron transport in nanocrystalline oxide semiconductor films 5. The replacement of the liquid electrolyte by solid materials 6. The development of tandem cells and their use for the cleavage of water by visible light

547

GRATZEL

Topics 1 through 4 have already been addressed previously. In the following, we shall, therefore, restrict ourselves to the discussion of the last two items.

5. SENSITIZED SOLID-STATE HETEROJUNCTIONS Recently, great efforts have been undertaken to replace the electrolyte in liquid junction solar cells by a solid charge transport material. Thus, inorganic p-type semiconductors [ 14, 15, 58] and organic materials [57, 59, 60] have been scrutinized. These devices use holetransmitting materials that form heterojunctions with the dye-loaded n-type nanocrystalline oxide film. Suitable solid materials to replace the liquid electrolyte in the injection solar cells are large-band-gap p-type semiconductors. Light-induced electron transfer from the excited state in the conduction band of the oxide semiconductor occurs in the same manner as with liquid electrolytes. However, the dye is regenerated by electron donation from the solid charge transfer material assuming the role of the iodide ions in the liquid junction system (see Fig. 16). The advantage of this approach is that hole conduction to the counterelectrode occurs by hopping and does not involve mass transfer. In addition, judicious selection of the organic material allows its redox level to be matched to the ground state oxidation potential of the sensitizer. This is not the case for the triiodide/ioide redox electrolyte where typically 0.5 eV of the driving force is wasted in the regeneration of sensitizers, such as complex I. Judicious selection of the type of organic hole-transmitting material offers the prospect of avoiding this loss, resulting in an increased photovoltage that would permit the overall efficiency of the device to be nearly doubled. The solid nature of the cell will also foster practical applications as it avoids the technical problems associated with the use of liquid electrolytes. So far, the incident monochromatic photon-to-current conversion efficiency (IPCE) of this type of solid-state cell has remained low. However, significant progress was achieved recently by applying the novel amorphous organic hole transport material (HTM) 2,2',7,7'tetrakis-(N,N-di-p-methoxyphenyl-amine)9,9'-spirobifluorene (OMeTAD) [61, 62], whose

Fig. 16. Schematicoutline of a dye-sensitized heterojunction device. Light-induced electron transfer processes (injection, regeneration, recapture, hopping) occurring in the dye-sensitized heterojunction, as well as the approximateredox potentials and band energies of the different components.

548

PROPERTIES AND APPLICATIONS OF NANOCRYSTALLINE ELECTRONIC JUNCTIONS

oc.

OMeTAD

, (v)

--~,~/

OCH3

'~~ OCH3 H3,J@ N~

(D+/D)

_-

TiO2 Fig. 17.

N~I~ocH3OCH3

Dye

HTM

Au

Structure of arylamine used as a hole conductor in dye-sensitized heterojunctions.

structure is shown in Figure 17. Photoinduced charge cartier generation at the heterojunction is very efficient. A solar cell based on OMeTAD converts photons to electric current with a strikingly high yield of 33% [57]. The new hole conductor contains a spirocenter, which is introduced in order to improve the glass-forming properties and prevent crystallization of the organic material. Its glass transition temperature of Tg = 120~ measured by differential scanning calorimetry, is much higher than that of the widely used hole conductor TPD (Tg = 62 ~ Crystallization is undesirable as it would impair the formation of a good contact between the mesoporous surface of the TiO2 and the hole conductor. The methoxy groups are introduced in order to match the oxidation potential of the HTM to that of the sensitizer Ru(II)L2(SCN)2(L = 4,41-dicarboxy-2,21-bipyridyl) used in this study. Pulsed nanosecond laser photolysis was used in conjunction with time-resolved absorption spectroscopy to scrutinize the dynamics of the photoinduced charge separation process. It was found that electron injection from the excited sensitizer into TiO2 is immediately followed by regeneration of the dye via hole transfer to OMeTAD [Eqs. (1) and (2)]: Ru(II)L2(SCN) ~ --+ Ru(III)L2(SCN) ~- + e-(TiO2) OMeTAD + Ru(III)Lz(SCN) + --+ Ru(III)Lz(SCN)2 + OMeTAD +

(7) (8)

The latter process was too fast to be monitored with the laser equipment employed, setting an upper limit of 40 ns for the hole transfer time. The photovoltaic performance of the dye-sensitized heterojunction was studied by means of sandwich-type cells. The working electrode consisted of conducting glass (Fdoped SnO2, sheet resistance 10 f2/square) onto which a compact TiO2 layer was deposited by spray pyrolysis [63]. This avoids direct contact between the HTM layer and the SnO2, which would short-circuit the cell. A 4.2-/~m-thick mesoporous film of TiO2 was deposited by screen printing onto the compact layer [22] and derivatized with Ru(II)Lz(SCN)2 by adsorption from acetonitrile. The HTM was introduced into the mesopores by spin

549

GRATZEL

coating a solution of OMeTAD in chlorobenzene onto the TiO2 film and subsequent evaporation of the solvent. The coating solution contained 3.3 mM N(PhBr)3SbC16 and 15 mM Li[(CF3SOz)zN] in addition to 0.17 M OMeTAD. A semitransparent gold back contact was evaporated on top of the hole conductor under vacuum. The maximum IPCE is 33%, which is more than two orders of magnitude larger then the previously reported value for a similar dye-sensitized solid heterojunction [60] and only a factor of about 2 lower than with liquid electrolytes [ 18]. Further improvement of the photovoltaic performance is expected, as many parameters of the cell assembly have not yet been optimized. Preliminary stability tests performed over 80 h using the visible output of a 400-W Xe lamp showed that the photocurrent was stable within +20%, while the open-circuit voltage and the fill factor increased. The total charge passed through the cell during illumination was 300 C/cm 2, corresponding to turnover numbers of about 8400 and 60,000 for the OMeTAD and the dye, respectively. This shows that the hole conductor can sustain photovoltaic operation without significant degradation. From these findings, the concept of dye-sensitized heterojunctions emerges as a very interesting and viable option for future low-cost solid-state solar cells. Photodiodes based on interpenetrating polymer networks of poly(phenylene vinylene) derivatives [64, 65] present a related approach. The main difference to our system is that at least one component of the polymer network needs to function simultaneously as an efficient light absorber and a good charge transport material. The dye-sensitized heterojunction cell offers a greater flexibility inasmuch as the light absorber and charge transport material can be selected independently to obtain optimum solar energy harvesting and high photovoltaic output. 6. TANDEM CELLS FOR THE CLEAVAGE OF WATER BY VISIBLE L I G H T

A tandem device that achieves the direct cleavage of water into hydrogen and oxygen by visible light was developed in collaboration with two partner groups from the Universities of Geneva and Berne, CH [66]. This is based on the series connection of two photosystems. A thin film of nanocrystalline tungsten trioxide absorbs the blue part of the solar spectrum. The valence band holes created by band gap excitation of the WO3 serve to oxidize water to oxygen, while the conduction band electrons are fed into the second photosystem, which consists of the dye-sensitized nanocrystalline TiO2 film. The latter is placed directly behind the WO3 film capturing the green and red part of the solar spectrum that is transmitted through the top electrode (see Fig. 18). The photovoltage generated by the second photosystem enables the generation of hydrogen by the conduction band electrons.

Fig. 18. Circuitdiagram of the tandem cell for water cleavageby visible light.

550

PROPERTIES AND APPLICATIONS OF NANOCRYSTALLINEELECTRONIC JUNCTIONS

Fig. 19. The Z schemeof biphotonic water photolysismimicksphotosynthesisof green plants.

There is close analogy to the Z scheme operative in the light reaction of photosynthesis in green plants. This is illustrated by the electron flow diagram shown in Figure 19. In green plants, there are also two photosystems connected in series, one affording water oxidation to oxygen and the other generating the NADPH used in carbon dioxide fixation. The advantage of the tandem approach is that higher efficiencies than with single-junction cells can be reached if the two photosystems absorb complementary parts of the solar spectrum. At present, the overall AM 1.5 solar light to chemical conversion efficiency achieved with this device stands at 4.5%.

7. NANOCRYSTALLINE INTERCALATION BATTERIES The diffuse and intermittent nature of sunlight renders necessary the storage of solar energy in electrical or chemical form. There is presently a thrust for improved batteries relating to electric energy storage. In this context, the so-called "rocking chair" batteries deserve particular attention. Electric power generation is associated with the migration of lithium ions from one host, that is, TiO2, constituting the anode, to another host electrode, namely, NiO2/CoO2 or MnO2, constituting the cathode. The voltage delivered by the device is simply the difference of the chemical potential of lithium in the two host materials. It was discovered that the power output of the battery is improved if the oxides employed have a nanocrystalline morphology as compared to bulk electrodes (see Fig. 20). The reason for this behavior is that the diffusion time for lithium ions in the host oxide is dramatically shortened by using oxide particles of mesoscopic dimensions as electrodes. A standard

551

GRATZEL

Fig. 20. Mesoporouslithium ion battery using TiO2 and LiMnO4 as the anode and cathode material, respectively.

size R921 coin cell has been developed supplying 4 - 4 . 5 m A h corresponding to 50 m A h/g capacity, which compares well with the rocking chair battery having a carbon anode. These findings provide a very promising basis for the d e v e l o p m e n t of a new type of rechargeable battery [67]. In conclusion, it appears that nanocrystalline electronic junctions involving transition metal oxides form not only the heart of new display and photovoltaic devices but also offer attractive perspectives for the storage of electrical energy that is generated by sunlight.

References 1. C. J. Brinker and C. W. Scherer, "Sol--Gel Science: The Physics and Chemistry of Sol-Gel Processing." Academic Press, San Diego, 1990. 2. L.C. Klein, "Sol-Gel Optics--Processing and Applications" Kluwer Academic, Boston, 1994. 3. H.D. Gesser and P. C. Goswami, Chem. Rev. 89, 765 (1989). 4. L. C. Klein, ed., "Sol-Gel Technology for Thin Films, Fibers, Preforms, Electronics and Special Shapes." Noyes Publications, Park Ridge, NJ, 1988. 5. (a) M. Matijevic, Mater. Res. Soc. Bull 4, 18 (1989). (b) E. Matijevic, Mater. Res. Soc. Bull 5, 16 (1990). (c) R. Mehrotra, Struct. Bonding 77, 1 (1992). 6. E. Matijevic, Langmuir 10, 8 (1994); ibid. 2, 12 (1986). 7. E. Matijevic, Chem. Mater. 5,412 (1993); Ann. Rev. Mater. Sci. 15, 485 (1985). 8. W.X. Wang, D. H. Li, and S. H.,Appl. Phys. Lett. 62, 312 (1993). 9. J. S. Foresi and T. D. Moustakas, Mater. Res. Soc. Proc. 256, 77 (1992). 10. T.G. Nieh, J. Wadsworth, and E Wakai, Int. Mat. Rev. 36, 146 (1991). 11. M.M. Boutz, R. J. Olde-Schulthuis, A. J. Winnubst, and A. J. Burggraaf, in "Nanoceramics" (R. Freer, ed.), Vol. 51. London, 1993. 12. Q. Xu and M. A. Anderson, J. Am. Ceram. Soc. 77, 1939 (1994). 13. A. Hagfeldt, N. Vlachopoulos, and M. Gr~itzel,J. Electrochem. Soc. 141, L82 (1994). 14. K. Tennakone, G. R. R. A. Kumara, A. R. Kumarasinghe, K. G. U. Wijayantha, and P. M. Sirimanne, Semicond. Sci. Technol. 10, 1689 (1995). 15. B. O'Regan and D. T. Schwarz, Chem. Mater. 7, 1349 (1995).

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PROPERTIES AND APPLICATIONS OF NANOCRYSTALLINE ELECTRONIC JUNCTIONS

16. B. O'Regan and M. Gr~itzel, Nature (London) 335,737 (1991). 17. M.K. Nazeeruddin, P. Liska, J. Moser, N. Vlachopoulos, and M. Gr~itzel, Helv. Chim. Acta 73, 1788 (1990). 18. M. K. Nazeeruddin, A. Kay, I. Rodicio, R. Humphrey-Baker, E. MUller, P. Liska, N. Vlachopoulos, and M. Gr~itzel, J. Am. Chem. Soc. 115, 6382 (1993). 19. T. Gerfin, M. Gr~itzel, and L. Walder, Prog. Inorg. Chem. 44, 346 (1996). 20. M. Mayor, A. Hagfeldt, M. Gr~itzel, and L. Walder, Chimia 50, 47 (1996). 21. A. Hagfeldt and M. Gratzel, Chem. Rev. 95, 45 (1995). 22. Ch. J. Barbe, E Arendse, P. Comte, M. Jirousek, E Lenzmann, V. Shklover, and M. Gr~itzel, J. Am. Ceram. Soc. 80, 3157 (1997). 23. M. Wolf, Ph.D. Thesis, Ecole Polytechnique F6d6rale de Lausanne, 1998. 24. L.E. Brus, J. Chem. Phys. 79, 5566 (1983). 25. L. Kavan, T. Stoto, M. Gr~itzel, D. Fitzmaurice, and V. Shklover, J. Phys. Chem. 97, 9493 (1993). 26. G. Redmond and D. Fitzmaurice, J. Phys. Chem. 97, 11081 (1993). 27. U. K611e, J. Moser, and M. Gr~itzel, Inorg. Chem. 24, 2253 (1985). 28. B. Enright, G. Redmond, and D. Fitzmaurice, J. Phys. Chem. 97, 11081 (1994). 29. L.A. Lion and J. T. Hupp, J. Phys. Chem. 97, 1426 (1995). 30. S.G. Yan and J. T. Hupp, J. Phys. Chem. 100, 6867 (1996). 31. I. Bedja, S. Hotchandi, and P. V. Kamat, J. Phys. Chem. 97, 11064 (1993). 32. P. Bonhbte, E. Gogniat, S. Tingry, Ch. Barb6, N. Vlachopoulos, E Lenzmann, P. Compte, and M. Gr~itzel, J. Phys. Chem. B 102, 1498 (1998). 33. C.W. Tang and S. A. Van Slyke, Appl. Phys. Lett. 51,913 (1987). 34. J. Athanassov, E P. Rotzinger, P. Pechy, and M. Gr~itzel, J. Phys. Chem. B 101, 2558 (1997). 35. B. O'Regan, J. Moser, M. Anderson, and M. Gr~itzel, J. Phys. Chem. 94, 98720 (1990). 36. A. Zaban, A. Meier, and B. A. Gregg, J. Phys. Chem. 101, 7985 (1997). 37. A. Hagfeldt, and M. Gr~itzel, Chem. Rev. 95, 45 (1995). 38. J. Ferber, R. Stangl, and J. Luther, Sol. Energy Mater Sol. Cells 53, 29 (1998). 39. A. Hagfeldt, U. Bj6rkst6n, and S.-E. Lindquist, J. Sol. Energy Mater Sol. Cells 27, 293 (1992). 40. K. Schwarzburg and E Willig, Appl. Phys. Lett. 58, 2520 (1991). 41. R. K6nenkamp and R. Henninger, J. Appl. Phys. A 87 (1994). 42. G. Hodes, I. D. J. Howell, and L. M. Peter, J. Electrochem. Soc. 139, 3136 (1992). 43. P.V. Kamat, Prog. React. Kinet. 19, 277 (1994). 44. Md. K. Nazeeruddin, P. Pechy, and M. Gr~itzel, Chem. Commun. 1705 (1997). 45. P. Pechy, E Rotzinger, M. K. Nazeeruddin, O. Kohle, S. M. Zakeeruddin, R. Humphry-Baker, and M. Gr~itzel, J. Chem. Soc., Chem. Commun. 65 (1995). 46. Y. Tachibana, J. E. Moser, M. Gr~itzel, D. R. Klug, and J. R. Durrant, J. Phys. Chem. 100, 20056 (1996). 47. T. Hannapel, B. Burfeindt, W. Storck, and E Willig, J. Phys. Chem. B 101, 6799 (1997). 48. J. E. Moser, D. Noukakis, U. Bach, Y. Tachibana, D. R. Klug, J. R. Durrant, R. Humphry-Baker, and M. Gr~itzel, J. Phys. Chem. B 102, 3649 (1998). 49. R. J. Ellington, J. B. Achbury, S. Ferrere, H. N. Gosh, A. J. Nozik, and T. Q. Lian, J. Phys. Chem. B 102, 6455 (1998). 50. J.E. Moser and M. Gr~itzel, Chimia 52, 160 (1998). 51. J.E. Moser and M. Gratzel, Chem. Phys. 176, 493 (1993). 52. R. Amadelli, R. Argazzi, C. A. Bignozzi, and E Scandola, J. Am. Chem. Soc. 112, 7029 (1990). 53. N. Papageorgiou, Y. Athanassov, M. Armand, P. Bonh6te, H. Petterson, A. Azam, and M. Gr~itzel, J. Electrochem. Soc. 143, 3099 (1996). 54. 0. Kohle, M. Gr~itzel, A. E Meyer, and T. B. Meyer, Adv. Mater 9, 904 (1997). 55. A. Kay and M. Gr~itzel, Sol. Energy Mater Sol. Cells 44, 99 (1996). 56. G. Smestad, Sol. Energy Mater. Sol. Cells 32, 259 (1994). 57. U. Bach, D. Lupo, P. Comte, J. E. Moser, E Weiss0rtel, J. Salbeck, H. Spreitzer, M. Gr~itzel, Nature 395, 583 (1998). 58. B. O'Regan and D. T. Schwarz, Chem. Mater 10, 1501 (1998). 59. K. Murakoshi, R. Kogure, and S. Yanagida, Chem. Lett. 5, 471 (1997). 60. J. Hagen and D. Haarer, Synth. Met. 89, 215 (1998). 61. J. Salbeck, E Weiss6rtel, and J. Bauer, MacromoL Symp. 125, 121 (1997). 62. J. Salbeck, N. Yu, J. Bauer, E Weiss6rtel, and H. Bestgen, Synth. Met. 91,209 (1997). 63. L. Kavan, and M. Gr~itzel, Electrochim. Acta 40, 643 (1995). 64. J.J.M. Halls et al., Nature 376, 498 (1995). 65. G. Yu, J. Gao, J. C. Hummelen, F. Wudl, and A. J. Heeger, Science 270, 1789 (1995). 66. J. Augustynski, G. Calzaferri, J. C. Courvoisier, M. Gr~itzel, and M. Ulmann, in "Proceedings of the 10th International Conference on the Photochemical Storage of Solar Energy," Interlaken, Switzerland, 1994, p. 229. 67. S.Y. Huang, K. Kavan, I. Exnar, and M. Gr~itzel, J. Electrochem. Soc. 142, L142 (1995).

553

Chapter 11 NANOSTRUCTURE FABRICATION USING ELECTRON BEAM AND ITS APPLICATION TO NANOMETER DEVICES Shinji Matsui Laboratory of Advanced Science and Technology for Industry, Himeji Institute of Technology, Hyogo, Japan

Contents 1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2. Nanofabrication Using Electron Beam . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1. Nanometer Electron Beam Direct Writing System . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2. 10-Nanometer Lithography Using Organic Positive Resist . . . . . . . . . . . . . . . . . . . . . 2.3. 10-Nanometer Lithography Using Organic Negative Resist . . . . . . . . . . . . . . . . . . . . . 2.4. Sub-10-Nanometer Lithography Using Inorganic Resist . . . . . . . . . . . . . . . . . . . . . . . 2.5. Nanometer Fabrication Using Electron-Beam-Induced Deposition . . . . . . . . . . . . . . . . . 3. Material Wave Nanotechnology: Nanofabrication Using a de Broglie Wave . . . . . . . . . . . . . . . 3.1. Electron Beam Holography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2. Atomic Beam Holography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4. Nanometer Devices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1. 40-Nanometer-Gate-Length Metal-Oxide-Semiconductor Field-Emitter-Transistors . . . . . . . 4.2. 14-Nanometer-Gate-Length Electrically Variable Shallow Junction MOSFETs . . . . . . . . . . 4.3. Operation of Aluminum-Based Single-Electron Transistors at 100 Kelvins . . . . . . . . . . . . 4.4. Room Temperature Operation of a Silicon Single-Electron Transistor . . . . . . . . . . . . . . . 5. Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

555 556 556 558 560 561 563 565 565 569 572 572 574 576 579 582 582

1. I N T R O D U C T I O N R e c e n t y e a r s h a v e w i t n e s s e d a n u m b e r o f investigations c o n c e m i n g n a n o s t r u c t u r e technology. T h e objective o f r e s e a r c h on n a n o s t r u c t u r e t e c h n o l o g y is to e x p l o r e the basic physics, t e c h n o l o g y , and applications o f u l t r a s m a l l structures and devices with d i m e n s i o n s in the s u b - 1 0 0 - n m r e g i m e . Today, the m i n i m u m size o f Si and G a A s p r o d u c t i o n devices is d o w n to 0 . 2 5 / z m or less. N a n o s t r u c t u r e devices are n o w b e i n g fabricated in m a n y laboratories to e x p l o r e various effects, such as those c r e a t e d by d o w n s c a l i n g existing devices, q u a n t u m effects in m e s o s c o p i c devices, or t u n n e l i n g effects in s u p e r c o n d u c t o r s , and so on. In addition, n e w p h e n o m e n a are b e i n g e x p l o r e d in an a t t e m p t to build s w i t c h i n g devices with d i m e n s i o n s d o w n to the m o l e c u l a r level.

Handbook of NanostructuredMaterials and Nanotechnology, edited by H.S. Nalwa Volume3: ElectricalProperties Copyright 9 2000 by Academic Press All rights of reproduction in any form reserved.

ISBN 0-12-513763-X/$30.00

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Submicron Technology

SEM

EB

Electron

Atom (Angstrom) Technology

Nanotechnology STEM

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STM

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1

FIB

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,,

i

~

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SET

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6 Mb 9 Bacterium -~-6 4 ~16

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Mb

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SIZE (nm) Fig. 1.

Microfabrication using electrons, ions, and photons.

Figure 1 summarizes the resolution capabilities of several lithography processes that use electrons, ions, and photons. It includes the narrowest linewidth of feature size obtained with each process. Microfabrication can be classified into three regimes: submicrometer (1000-100 nm), nanometer (100-1 nm), and atom (or angstrom, less than 1 nm). A 256Mb dynamic random-access memory (DRAM) Si ultra large scale integration (ULSI) of 0.25 # m dimension can be fabricated by using an/-line stepper with a phase shift mask or an excimer laser stepper. An excimer laser or SR lithography can be applied to a 1-Gb DRAM with a 0.15-#m feature size. Electron beam (EB) lithography is the most widely used and versatile lithography tool for fabricating nanostructure devices. Because of the availability of high-quality electron sources and optics, EB can be focused to diameters of less than 10 nm. The minimum beam diameters of scanning electron microscopes (SEMs) and scanning transmission microscopes (STEMs) are 1.5 and 0.5 nm, respectively. While a focused-ion beam (FIB) can be focused close to 8 nm, EB and FIB can be used to make nanoscale features in the 100-1-nm regime. Scanning tunneling microscopy (STM) is used for atomic technology in the range of 1 to 0.1 nm. Figure 2 shows the resolution of various resists, which were confirmed by experiment for electrons and ions. Minimum sizes of 8 nm for poly(methyl methacrylate) (PMMA) [ 1, 2], 10 nm for ZEP (Nippon Zeopn Co.) positive resists [3], 20 nm for SAL601 (Shipley Co.) [4], and 10 nm for calixarene negative resists [5] have been demonstrated using EB lithography. Nanoscale patterns have also been written in inorganic resists such as A1F3, NaC1, and SiO2 using STEM [6, 7] and SEM [8]. Furthermore, carbon contamination patterns of 8 nm have been fabricated with SEM [9], and 8-nm PMMA patterns have been demonstrated by using Ga + FIB [ 10].

2. NANOFABRICATION USING ELECTRON BEAM 2.1. Nanometer Electron Beam Direct Writing System

There are some reports on EB nanolithography systems capable of exposure with a sub10-nm beam in nanofabrication [3, 11-15]. Figure 3 shows a photograph and a design

556

N A N O S T R U C T U R E FABRICATION USING E L E C T R O N B E A M

Fig. 2.

Resolution of various resists for electrons and ions.

Fig. 3.

50-kV nano-EB direct writing system.

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MATSUI

Fig. 4. Photographand schematic diagramof gas introduction system.

target of a 50-kV EB lithography system developed by modifying the JEOL-5FE 25-kV EB system [16]. The major modified points of this EB system are acceleration voltage and a gas feed system. The acceleration voltage has been changed from 25 to 50 kV. The column design with respect to the electron gun chamber is modified to withstand the high voltage in order to avoid the field emission from the electrode surface. Because a Zr/O/W thermal field emission (TFE)electron gun is used in this system, the vacuum in the electron gun chamber must be maintained under 10 -9 torr. The TFE gun has a small virtual source size and a high angular current intensity. Various gas species can be introduced into this specimen chamber to investigate the EB-induced surface reactions. The gas feed system is shown in Figure 4. The 50-cc-capacity gas cylinder contains the reaction gas. The gas is introduced through a variable leak valve and a fine nozzle with an inner diameter of 200/zm. The gas line nozzle is placed at a distance of 3 mm from the wafer. A carbon deposition pattem 14 nm in size was made by using styrene (C6HsCH=CH2) gas. The EB diameter was measured by using a knife-edge method. The result of the measurement for both the x and the y directions was less than 5 nm. The overlay and stitching accuracy were evaluated by exposing 16 chips (4 x 4 in array) with a size of 80 x 80/zm in PMMA resist at 50 kV. The stitching accuracy and overlay accuracy were 0.021 and 0.016/zm at 2~r, respectively.

2.2. 10-Nanometer Lithography Using Organic Positive Resist A PMMA positive resist was exposed to evaluate the fine pattem exposure characteristics using the preceding EB system. PMMA is known as the positive resist with high resolution. Thirty-nanometer-thick PMMA was spin coated on a bare thick Si wafer. After PMMA was prebaked at 170 ~ for 20 min, EB exposure was carried out. The line dose was 0.8 nC/cm.

558

NANOSTRUCTURE FABRICATION USING ELECTRON BEAM

Fig. 5. 10-nm-linewidthPMMA patterns.

Fig. 6. 20-nm-diameterAu-Pd patterns.

The PMMA was developed in a mixture of MIBK:IPA = 1:3 for 1 min and was then rinsed in isopropyl alcohol (IPA) for 1 min. The point EB was line scanned with a period of 50 nm. Ten-nanometer-width line patterns in PMMA resist were obtained as shown in Figure 5. Fine metal pattems are useful as conductive wires or gate metals for the investigation of mesoscopic devices and other nanostructure physics. Au-Pd metal was delineated by a liftoff method. For the exposure of dot patterns, the resist was exposed with a shot time of 7 5 / z s for each dot. After development, Au-Pd metal was deposited on the resist, at a thickness of 3 nm for dot patterns. The liftoff was performed in acetone. Figure 6 shows the

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MATSUI

Fig. 7. 10-nm-linewidthZEP patterns.

Fig. 8. Structureof calixarene.

SEM photographs of Au-Pd metal dot patterns on a Si wafer. Twenty-nanometer-diameter dot patterns with a period of 100 nm were successfully fabricated. Nanodevice fabrication requires not only high resolution but also high overlay accuracy. High-speed exposure effectively meets the requirements because overlay accuracy is improved as a result of less beam drift on the nanometer scale. Moreover, it enables the use of a highly sensitive resist such as ZEP520 [17], which has sufficient resolution and high dry etching durability for nanolithography. A 10-nm-scale resist pattern was obtained using ZEP520 positive resist. The ZEP520 resist was spin coated onto a Si wafer to a thickness of 50 nm and prebaked at 200 ~ After EB exposure, the ZEP520 was developed with hexyl acetate for 2 min and rinsed with 2-propanol. Figure 7 shows a ZEP520 resist pattern, in which the lines are 10 nm wide and have a pitch of 50 nm [3].

2.3. 10-Nanometer Lithography Using Organic Negative Resist Calixarene has a cyclic structure, as shown in Figure 8, and works as an ultrahighresolution negative EB resist. Such characteristics seem to be convenient for a nanodevice fabrication process. It is roughly a ring-shaped molecule with about a 1-nm diameter. The basic component of calixarene is a phenol derivative that seems to have high durability and stability, originating from the strong chemical coupling of the benzene ring. The threshold of sensitivity was about 800/xC/cm 2, which is almost 20 times higher than that of PMMA. Calixarene negative-resist exposure was carried out. A 30-nm-thick resist was coated on a bare Si wafer. After prebaking at 170 ~ for 30 min, EB exposure was carried out and then the resist was developed in xylene for 20 s and was rinsed in IPA for 1 min.

560

NANOSTRUCTURE FABRICATION USING ELECTRON BEAM

Fig. 9. Calixarenedot array patterns with 15-nmdiameter and 35-nmpitch.

The etching durability of calixarene was tested using a DEM-451 (ANELVA Corp.) plasma dry-etching system with CF4 gas. The etching rate of calixarene is almost comparable to that of Si, and the durability is about four times higher than that of PMMA. This durability seems to be sufficient to make a semiconductor or a metal nanostructure. Nanodot arrays are useful not only for quantum devices but also for studying exposure properties. In this experiment, the EB current was fixed at 100 pA at 50-kV accelerating voltage, for which the spot size is estimated to be about 5 nm. All the dot arrays were fabricated on Si substrates. The typical exposure dose (spot dose) was about 1 x 105 electrons/dot. Figure 9 shows typical dot array patterns having 15-nm diameter with 35-nm pitch. Germanium pattern transfer is shown in Figure 10. The 20-nm-thick Ge layer requires at least a 5-nm-thick calixarene layer to be etched down, and the resist thickness was 30 nm. Figure 10a shows the line patterns of the resist on Ge film exposed at a line dose of 20 nC/cm. Delineation was done using the S-5000 (Hitachi Corp.) SEM with a beam current of 100 pA at a 30-kV acceleration voltage. A 10-nm linewidth and a smooth line edge were clearly observed. This smoothness is the key point in fabricating quantum nanowires by etching processes. Figure 10b shows the transferred pattern treated by 1 min of overetching, followed by oxygen-plasma treatment to remove the resist residues. A G e line of 7 nm width was clearly observed without short cutting. Narrowing by overetching is a standard technique to obtain a fine line; however, side-wall roughness limits the linewidth [ 18]. The smoothness of the calixarene side wall enables the linewidth to be narrowed below the 10-nm region by overetching. Calixarene is a single molecule and thus is monodispersed with a molecular weight of 972. In contrast, other phenol-based resists have dispersive weights ranging from 1000 to 100,000, which set a resolution limit. The molecular uniformity of calixarene and its small molecular size is the origin of such surface smoothness and the resulting ultrahigh resolution.

2.4. Sub-10-Nanometer Lithography Using Inorganic Resist An inorganic resist seems to be the most promising material to achieve sub-10-nm lithography. Many previous works concerning the inorganic resist were carried out using STEM [5, 6, 19, 20], and many have attained nanometer-scale delineation. However, usage of the membrane-film substrate, which is commonly used in STEM studies, causes a crucial difficulty in device fabrication because of its delicate handling requirements. In contrast to this STEM lithography, the conventional scanning SEM should give many advantages for nanosize device fabrication if one could achieve an equally fine pattem delineation on the standard S i substrate. In general, inorganic resists have a finer resolution than organic resists. An encouraging result, using A1F3-doped LiF resist, was reported [21, 22]. It suggested the resist grain size

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MATSUI

Fig. 10. Pattern transfer to Ge. (a) 10-nm-linewidth calixarene pattern and (b) transferred 7-nmlinewidth Ge pattern. was reduced to below 10 nm on a nitrogen-cooled substrate and successfully demonstrated sub- 10-nm lithography using a STEM system. Furthermore, electron-stimulated desorption should occur under relatively low energy (20-50 keV) electron irradiation in a standard SEM lithography system. The basis for the self-developing properties on LiF(A1F3) was studied, and sub- 10-nm lithography was demonstrated using a standard SEM beam writing system [8]. The A1F3 partially doped LiF inorganic-resist films were fabricated by using conventional multitarget [LiE (Li0.9A10.1)Fx, and (Li0.7A10.3)Fx] ion beam sputtering. The chemical composition of the films was adjusted by controlling the flux ratio from each target. The sputtered particles have energy of several electronvolts. As a result, the ion beam sputtering effectively reduced the grain size below 10 nm even at room temperature deposition and even with an extremely slow growth rate of about 1 nm/min. The required dose for the (Li, A1)F resist in terms of A1F3 concentration is summarized in Figure 11, where the sensitivity of the LiF and A1F3 are cited from the STEM work, and the hatched area was obtained by extrapolating these data. A sensitivity of 0.1 C/cm 2 on the 10-nm-thick film was just below the critical dose, but the other films do not show this perfect development. The curve obtained from the 10-nm-thick films shown with solid circles are very close to those of the STEM data. This suggests that the desorption mechanism was not influenced by the electron energy, in principle, suggesting the possibility of lithography of the (Li, A1)F resist under low-energy irradiation using SEM.

562

NANOSTRUCTURE FABRICATION USING ELECTRON BEAM

Fig. 11. Requireddose versus aluminum concentration.

Fig. 12. 5-nm-linewidthpatterns with 60-nm period fabricated at 100-nC/cm line dose by 30 kV and

1.5-nmbeam diameter SEM.

By optimizing the film quality, sub- 10-nm lithography was demonstrated by using a Hitachi S-4200 (Hitachi Corp.) SEM with a fine EB produced by a field emission gun. The accelerating voltage of 30 kV and the beam diameter of 1.5 nm are the specifications of the SEM. The line dose was about 100 nC/cm. Figure 12 shows the best result of the line delineation, where a fine line of 5-nm linewidth was clearly observed. This result demonstrates that sub-10-nm lithography can be achieved by SEM using an inorganic resist.

2.5. Nanometer Fabrication Using Electron-Beam-Induced Deposition In situ processes using beam-induced chemistry are promising technologies to fabricate ultimate fine patterns and to reduce the process steps. In situ observation of W deposition by EB irradiation using a ~VF 6 gas source was carried out by transmission electron microscopy (TEM) to study the growth mechanism. The experimental arrangement is illustrated in

563

MATSUI

TEM

le-

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Fig. 13. In situ observation TEM systemof EB deposition.

Figure 13. The employed electron microscope was an EM-002A (Akashi Beam Technology Corp.) equipped with a real-time TV monitor system specially improved for in situ observation. The microscope resolution was 0.23 nm at 120 kV, which allowed imaging individual rows of atom columns in W crystals. To reduce the problems with regard to specimen contamination, the instrument was operated under ultrahigh vacuum of 3 • 10 -8 torr, attained by a dry vacuum-pumping system with turbo pumps and ion pumps. The gas injection tube had a 3-mm inner diameter and was 5 mm from the sample surface. Fine and spherical Si particles were used as TEM specimens. The small particles were made by a gas evaporation method in argon under a reduced atmosphere, where Si vapor was condensed into small particles. They were less than 100 nm in diameter and were usually covered with 1-3-nm-thick SIO2. The gas molecules were adsorbed on the fine Si particles, which were on the TEM specimen grid. The gas molecules were excited by the TEM EB and dissociated into W and F2 gas. Tungsten metal was deposited on the Si surface and growth was started. The growth process was observed in situ at the single-atom resolution level by an electron microscope equipped with a television monitor system. First, the EB was irradiated on a ~/F6 adlayer, formed on the fine Si particle surface, in order to clarify the initial growth process of EB-induced deposition. Second, the focused EB was irradiated on the Si fine particle surface, while ~ / F 6 was flowing on the surface, to study the resolution of EB-induced deposition [23, 24]. Figure 14 shows a typical series of electron micrographs of in situ TEM observations during EB irradiation of the ~ r F 6 adlayer. These micrographs were selected from a video tape record (VTR) tape, which ran for 30 min. Electron beam irradiation times for parts a-d of Figure 14 were 0, 3, 15, and 30 min, respectively. These results indicated that W atoms, dissociated by EB irradiation from the ~h/F6 adlayer, coalesced, and grew under EB irradiation. According to the real-time observation on a television screen, moving clusters often collided with each other, causing coalescence. Figure 15 shows an electron micrograph of a W rod on a fine Si particle. The W rod was made using a focused EB (STEM mode: 3 nm in diameter) scanning manually at 1 mm/s on the Si surface under 1 x 10 -6 torr source gas pressure. The W rod radius was 15 nm. This result indicated that a three-dimensional nanostructure can be fabricated using this technique. Three-dimensional STM tips as shown in Figure 16 [25] and electron field emitters as shown in Figure 17 [26] have successfully been made by EB-induced deposition with a computer-controlled writing system. Furthermore, single-electron transistor (SET) fabrication with 10-nm dimension was reported by using EB deposition with ~h/F6 gas [27].

564

NANOSTRUCTURE FABRICATION USING ELECTRON BEAM

Fig. 14. EB exposure time dependence of W cluster growth on a Si particle. Exposure times: (a) 0, (b) 3, (c) 15, and (d) 30 min.

Fig. 15. W rod with 15-nm diameter.

3. M A T E R I A L WAVE N A N O T E C H N O L O G Y : N A N O F A B R I C A T I O N U S I N G A D E B R O G L I E WAVE

3.1. Electron Beam Holography Holographic lithography has an advantage that it can produce a number of periodic patterns simultaneously. Electron holographic lithography was applied to nanofabrication. Electron interference fringes were recorded on a P M M A resist by using W(100) TFE gun and

565

MATSUI

Fig. 16. SEM micrographof a branched electron beam deposition tip.

an electron biprism, and the fabricated patterns were observed by conventional TEM and atomic force microscopy (AFM) [28, 29]. The electron optics of TEM with a W(100) TFE gun for electron holographic lithography is schematically illustrated in Figure 18. An electron beam of 40 kV is focused above an electron biprism with two condenser lenses. The M611enstedt-type electron biprism is constructed of two grounded plane electrodes and a fine-wire electrode, called a filament, between them. When a positive voltage, VB, is supplied to the filament, electron waves traveling on both sides of the filament are deflected and superimposed to form interference fringes on an observation plane. A P t wire 0.6/zm in diameter was used as the filament.

566

NANOSTRUCTURE FABRICAtTION USING ELECTRON BEAM

Fig. 17. Electronfield emitters made by EB deposition. (Source: Reprinted with permission from [26].)

,

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Fig. 18. Schemeof electron optics of TEM for electron holographic lithography.

As is well known, two coherence waves overlapping at an angle of 0 produce interference fringes with spacing, s, represented by s =

X/2 sin(0/2)

(1)

where denotes the de Broglie wavelength of 6.0 • 10 -3 nm in this case. Figure 19 shows four-wave interference fringes through an X biprism. Setting an X biprism below two condenser lenses instead of the M611enstedt-type biprism, which has two filaments placed normal to each other and both are supplied VB, four coherent waves

567

MATSUI

/"3

C~r4 , ~ = ~ . ~

~

~

X- biprism 4 planewaves

Interference fringes /

Fig. 19. Four-waveinterference fringes through an X biprism.

produce fringes like a checkerboard below the intersection of filaments, with the same spacing, s, as given by Eq. (1). Thus, electron holographic lithography could, in principle, generate line and dot patterns whose minimum spacing is ~./2, which is comparable to the crystal lattice spacing. A 30-nm-thick PMMA, spin coated on a 50-nm-thick self-supporting SiNx membrane and prebaked at 170 ~ for 20 min, was set on the observation plane 70 mm below the biprism. The self-supporting nitride (SIN) membrane was about 60/zm square and used to place the PMMA below interference fringes appropriately. Electron exposure to produce line patterns was carried out for 18 s with a dose of 25/zC/cm 2, which was measured at the fringe part. Then, the PMMA was developed in MIBK:IPA = 1:3 for 1.0 min and rinsed in IPA for 30 s. Similarly, PMMA dot patterns were exposed, at half the dose as that for the line patterns, in order to maintain whole dots. The electron exposure to produce dot patterns was carried out for 9.0 s with a dose of 13/zC/cm 2. The PMMA was developed in MIBK:IPA for 3.0 min and rinsed in IPA for 1.0 min. Figure 20a shows the interference fringes of the Mrllenstedt-type electron biprism, which was magnified 530 times by the lenses below the observation plane and recorded on a photoplate with 1.0-s exposure. Figure 20b shows the AFM image of the same interference fringes as those in Figure 20a, which was recorded on PMMA. The thickness of the PMMA is represented by a photocontrast in Figure 20b, and the thicker PMMA corresponds to the brighter part of the image. The supplied voltage to the filament of electron biprism, VB, was 5.3 V and the spacing of the fringes, s, was 108 nm in parts a and b of Figure 20. Figure 2 l a shows the interference fringes of the X biprism magnified and recorded on a photoplate, and Figure 2 lb shows the AFM image of the interference fringes recorded on PMMA. The supplied voltage to the filament, VB, was 5.0 V and the spacing of the fringes, s, was 125 nm in parts a and b of Figure 21. In Figure 21 a, dot patterns are found at the intersection where four-wave interference occurred and line patterns around the dot patterns where two-wave interference occurred. In Figure 2 lb, about 10 x 10 dots are recognized, but lines are not observed, owing to the reduction of the dose. Consequently, Figures 20b and 2 lb show that line and dot patterns were fabricated successfully, and the dose needed for lines is about twice as that for dots. More precise fabrication would be possible by optimizing the dose. To produce finer patterns than 100 nm in period, the larger overlapping angle 0, that is, the larger supplied voltage to the filament VB, should be selected. A simple assessment suggests that the spacing, s, becomes 1 nm when VB is 2.4 kV with the same electron optics. Carbon contamination line patterns with a period of 23 nm were fabiricated by a 30-kV SEM [30].

568

NANOSTRUCTURE FABRICATION USING ELECTRON BEAM

Fig. 20. (a) Two-waveinterference fringes magnified and recorded on a photoplate. (b) Interference fringes corresponding to (a) recorded on PMMA. VB: 5.3 V and s: 108 nm.

3.2. Atomic Beam Holography Atomic manipulation based on a holographic principle has been demonstrated by using a laser trap technique and a computer-generated hologram (CGH) made by EB lithography [31]. One approximation of a CGH is the binary hologram, in which the hologram takes a binary value, either 100% transparent or 100% opaque. This hologram can be directly translated to a hologram for atomic de Broglie waves, by cutting out the pattern on a film that is equal to the pattern of the 100% transmission area of the binary hologram. A monochomatic atomic wave reconstructs an atomic pattern by passing the hologram. The hologram used in this experiment was a Fourier hologram, which produced the Fourier-tranformed wavefront of the object. When the hologram is illustrated with a plane wave, the far-field pattern of the diffracted wave produces an image of the object. The object used in this experiment was a transparent F-shaped pattern, in which the transparent portion had a constant amplitude and random phase distribution. The object was represented by the complex transmission amplitude at points on a 128 x 128 matrix covering the F-shaped pattern. The two-dimensional array of numbers was Fourier transformed using a fast Fourier transform (FFT) algorithm, and the resulting 128 x 128 complex areas (cells) of the Fourier hologram. The transmission function of each cell of the hologram was expressed by a matrix of 4 x 4 subcells. A 100-nm-thick SiN membrane was used for the hologram. The binary pattern was transferred to a ZEP resist on the SiN membrane by an EB writing system. Subsequent CF4 plasma etching created through-holes in the membrane. A scanning electron micrograph

569

MATSUI

Fig. 21. (a) Two- and four-waveinterference fringes magnified and recorded on a photoplate. (b) Interference fringes correspondingto (a) recorded on PMMA. VB: 5.0 V and s: 125 nm.

of the hologram is shown in Figure 22. The size of the subcell was 0.3 • 0.3/zm square, so the size of the entire hologram was 153.6 • 153.6/zm. To increase the intensity of the deflected beam, the same pattern was repeated 10 times along the x and y directions, making the overall size of the hologram 1.5 • 1.5 mm. A schematic diagram of this experiment is shown in Figure 23. The ultracold Ne atomic beam was generated by the reported method [32]. The cloud of Ne atoms in the trap was approximately 0.3 mm in diameter, and the one-directional average velocity of the atoms was 20 cm s -1 . The hologram was placed 40 cm below the trap and was mounted on top of a 0.2-mm-diameter diaphragm. The size of the diaphragm limited the resolution of the image of the Fraunhofer hologram. The position of the hologram was not adjusted because any small portion of the hologram could produce the same image. The average atomic velocity at the hologram was 2.8 m s -1, corresponding to a de Broglie wavelength )~ of 7.1 nm. The acceleration resulting from gravity reduced the relative velocity spread to approximately 0.28%. To detect the Fraunhofer diffracted pattern from the hologram, the multichannel plate (MCP) detector was placed 45 cm below the hologram. Figure 24a shows the reconstructed F pattern. The data were accumulated for 10 h, and the total atom number of spots on the figure was 6 • 104. Figure 24b shows another example of a reconstructed pattern, which represents the characters "atom, Ne, and 7z."

570

NANOSTRUCTURE FABRICATION USING ELECTRON BEAM

......

Fig. 22.

: . . . . . .

. . . . . . . . . .

.

:

Binary CGH hologram on SiN membrane made by EB lithography.

Transfer Laser Zeeman

Deflector ~~~::::J

SlowerIMagnetoOptic .LTrap

i ~ o o l i n g Laser

I

DC Discharge

is3Ne*~,I II _~ - : . ~

Holog=

MCP Fig. 23.

Experimental apparatus of atomic beam holography.

In this experiment, a focusing lens for imaging was not used, but it is possible to combine the function of a focusing lens into the hologram [33]. In such a hologram, the resolution is determined by the same rule as applies to an optical lens. The binary hologram does not control the phase and amplitude of the wave inside a hole. When the hologram is the sole component for atomic beam manipulation, therefore, the practical limit is approximately the minimum size of the through-holes, which is in the range of 10 to 100 nm.

571

MATSUI

(a)

(b) Fig. 24. Reconstructedimage. (a) "F" pattern and (b) "atom, Ne, and ~P" pattern.

As a next step, there is a possibility of making any three-dimensional nanostructures by using CGH with an electron/atom de Broglie wave, as shown in Figure 25.

4. N A N O M E T E R DEVICES

4.1. 40-Nanometer-Gate-Length Metal-Oxide-Semiconductor Field-Emitter-Transistors Minute CMOS devices with a gate length of 100 nm or less are under extensive examination [34-36]. This is because it is expected that small feature size devices do not only realize very high density integrated circuits, but also high switching speed with low power consumption. Forty-nanometer-gate MOSFETs have been fabricated using excimer laser lithography and resist thinning technology [36]. However, to accelerate investigation of these devices, it is important to develop a sub-100-nm direct EB lithography process with good linewidth control.

572

NANOSTRUCTURE FABRICATION USING ELECTRON BEAM

Electron/Atom Beam

CGH Hologram

de Broglle w a v e

Fig. 25. Conceptof three-dimensional nanofabrication by CGH with an electron/atom de Broglie wave.

A 40-nm-gate NMOS device has been demonstrated by using direct EB lithography [37]. Figure 26 shows the fabrication process of the sub-100-nm MOS transistors by EB direct writing. A 3.5-nm-thick-gate oxide was used to obtain high current drivability. The polysilicon thickness was 150 nm. The single-layer resist was adopted as a mask to make the fabrication process simple. A SAL601 (Shipley Ltd.) chemically amplified negative resist with 200-nm thickness was coated on a 6-in. Si wafer. The thickness of the resist was decided on the basis of an etching selectivity of five for polysilicon over the resist to obtain high-aspect-ratio patterns. The gate resist patterns were exposed by a 50-kV EB lithography system as shown in Figure 3. After developing the resist, the gate pattern was transferred into polysilicon by plasma etching in which C12 + SF6 + 02 etching gas was used. The etching rate of polysilicon was 130 nm/min with a uniformity of less than -t-5%. The etching selectivity of polysilicon to SiO2 is over 40. The other lithography processes were performed using optical steppers. Parts a and b of Figure 27 show a 40-nm-gate resist pattern on polysilicon/SiO2/Si and on a NMOS transistor. The resist thickness was about 200 nm. A 40-nm line was exposed at 300/zC/cm 2 by a single line scan. NMOSFETs with various gate lengths of above 40 nm on 6-in. wafers were fabricated. The source-to-drain resistance at VD --0.1 V versus the designed gate pattern width is plotted in Figure 28. The good linearity indicated that the gate length was successfully controlled even for a less-than-100-nm gate by using a proper proximity effect correction and a high-energy nanometer EB. The Id-Vd characteristics are shown in Figure 29. Well-behaved short-channel characteristics were obtained down to a gate length of 60 nm. Operation of a 40-nm-gate FET was also confirmed, though weak punch-through occurred. Maximum transconductance (gm) at VDs was 580 mS/mm for the 40-nm NMOSFET.

573

MATSUI

negative resist

[

(200nm) ""-- I polysilicon (150nm) --....~llimmm~tmllmm

Resist coating (SAL601)

gate oxide ~

(3.5nm)

liiii iiiii li!i ii!il!iiiiiiiiii]i]i"iiiiii 'iiiiiiii i ,~,,,,~i~,,,~ii~,,,,,,,~ ~,

[!i'~::ii',!iiiii',',!iiii!!iiii!iii'~iiiiiili'~',i'~ii EB exposure (50kV EB) Development ===============================================

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

tiiiilp.-.S.ii~.bs.~a.;t.e- iiii~ ............................................... ............................................... .:.:..:::;

.............

:::::::::::;::::

........

Pattern transfer (CI2 plasma etching)

M

SiO= side wall n*-polysilicongate "~f-~m~-~/3.5nm gate source ~,,,~ i~/r / drain .............L................................................................. ...

i~iiii

oxide 9

99

Snde wall depositnon Ion implantation

Fig. 26. Gatefabrication process of a MOSFET.

4.2. 14-Nanometer-Gate-Length Electrically Variable Shallow Junction MOSFETs An electrically variable shallow junction MOSFET (EJ-MOSFET) with an ultra-shallow source/drain junction has been fabricated to investigate transistor characteristics and physical phenomena in ultrafine gate MOSFETs [38]. Figure 30 shows a schematic cross section of the EJ-MOSFET. The lower gate, which corresponds to the "gate" in conventional MOSFETs, controls the drain current. A positive upper-gate bias induces source/drain regions at the silicon surface. Because the source/drain regions are electrically induced, they are extremely shallow, typically 5 nm deep. The EJ-MOSFET was fabricated in a similar way as conventional Si-MOSFETs. To suppress short-channel effects (SCEs) caused by the lateral expansion of the depletion layers, a relatively high boron concentration of 2 x 1018 cm -3 was used within the substrate. The boron concentration was controlled by means of the boron ion implantation and the thermal drive-in. The n + regions were formed by arsenic ion implantation. A gate oxide (tox = 5 nm) was formed by thermal oxidation and a 40-nm-thick poly-Si layer was grown by chemical vapor deposition (CVD). Phosphorus was doped into the poly-Si film in a POC13 atmosphere. The ultrahigh-resolution EB resist was spin coated onto the poly-Si film and EB direct writing with a 5-nm beam diameter and a 50-kV acceleration energy was performed. After the developing procedure, the resist pattern was transferred to the poly-Si film by reactive ion etching (RIE) with CF4 gas. Figure 31 shows a TEM cross-sectional view of a 14-nm-long poly-Si lower gate. The lower gate was well defined. The 20-nm-thick intergate oxide layer was grown by

574

NANOSTRUCTURE FABRICATION USING ELECTRON BEAM

(a)

(b) Fig. 27. transistor.

(a) 40-nm-gate resist pattern with a height of 200 nm on a polysilicon layer and (b) on an NMOS

A

E =L

250 m Vg-Vth=2.0V 9 Vg-Vth=O.8V

200

v

150

m=nl

ee

100

'--

50

e-

0

_er

r

Fig. 28.

0.0

0.2

0.4

0.6

0.8

1.0

Designed Gate Length

Channel resistance versus designed gate length for different gate voltage.

575

MATSUI

.0

'

i

'

i

'

1

9

1

1.0

'

9

'

i

i

9

t

,

!

9

Lg=60nm

0.8 E

0"8 6

::I. O.
40%) and low ( 108 [34]. As a result, the uneven and slanted surface left after the substrate etch is removed by the HF, leaving a smooth, flat surface of GaAs or low Al-fraction A1GaAs. Cavity etching of the low Al-fraction A1GaAs layer to further tune the thickness for operation as an asymmetric Fabry-Prrot (ASFP), described in Section 6.3, is achieved with a 1 H202:3 H3PO4:50 H20 solution at -~3 ~ Most imaging applications of the MQW devices require perfect surface quality over large areas. In particular, surface scatter can be a problem in imaging systems, such as for biomedical applications [35, 36], while nonuniform film thickness can compromise the ASFP enhancement effects described in Section 6.3. A pressurized chemical jet has been successfully used in other applications to achieve better surface quality [37]. For use in studying ASFP effects, this chemical etching technique was modified for use in an ultrasonic agitator. For improved surface quality over large areas the substrate etch may be modified for use in an 18 ~ ultrasonic agitator bath with a concentration ratio of 1 NH4OH: 22 H202. Combined with ultrasonic agitation, this solution yields significantly improved surface quality over the nonagitated substrate etch described previously by increasing oxide removal, and thereby dramatically reducing surface scatter [36], with the additional bonus of preferentially etching the device edges. For low-temperature-grown (LTG) devices this helps to remove any remaining noninsulating etch-stop material that might be left behind after standard processing. The final fabrication step is the deposition of metal pads for use as electrical contacts. In the transverse-field or Franz-Keldysh geometry MQW devices the ~ 10 kV/cm electric field is applied along the planes of the quantum wells. For this configuration, pads of Au or

12

PHOTOREFRACTIVE SEMICONDUCTOR NANOSTRUCTURES

Fig. 9. Top (left) and side views of a fabricated transverse-fieldMQW device.

Ti/Au are evaporated onto the exposed surface of the device with an intercontact distance of 1-4 mm, shown in Figure 9.

2.3.2. Longitudinal Transmission Geometry The longitudinal-field Stark geometry operates with photocarrier transport perpendicular to the grating vector, and requires insulating cladding layers to isolate the electro-optic quantum-well layer from the electrical contacts. These devices are grown as p-i-n photorefractive diodes to give the device low leakage currents when the device is reversebiased during operation. The samples are grown by molecular beam epitaxy using a flux of As4 on n + substrates. The doped n-type and p-type contacts are used [38, 39] to replace semitransparent contacts used in previous designs [40, 41 ] and permit the operation of allsemiconductor devices without any artificial means (such as SiO2 and SiN layers) to reduce leakage currents. The active photoconductive electro-optic layer as well as the cladding layers are composed of low-temperature-grown A1GaAs [42]. The low-temperature-growth (LTG) materials have ultrafast lifetimes that extend down to picoseconds [31, 43], which produce spatial resolutions down to 1 /zm in the transverse-field geometry [44], and approximately 10/zm in the longitudinal field geometry [45-47]. The low-temperature growth (LTG) introduces large defect concentrations into the cladding layers [48], allowing the layers to perform as active buffer layers that trap and store charge. In all previous device designs, buffer layers with large defect concentrations were used [41, 47, 49, 50], based on the assumption that traps were required in these layers to efficiently trap and store space charge to screen the applied fields. However, large defect densities in the buffer layers prevented the electric field from penetrating uniformly through the device. Much of the voltage dropped across the buffer rather than dropping across the electro-optic layer. However, defects within the quantum-well electro-optic layer can perform the function of charge trapping and storage to screen applied fields for device operation without the need for defects in the buffer layers. This allows greater voltage drops across the active electrooptic layer and hence device operation at lower voltages [47]. A typical device structure grown by molecular beam epitaxy is shown in Figure 10. The photorefractive diode is grown on an n + GaAs substrate. A layer of n-GaAs ([Si] 1 x 1018 cm -3) approximately 5000/k thick is grown at 600~ to planarize the wafer to ensure good epitaxy. Next a layer of n-A10.50Ga0.50As ([Si] = 1 x 1018 cm -3) is grown for 5000 A, which acts as an etch-stop layer during wet chemical etching used in device fabrication. An AlAs layer is grown which permits the use of another technique of device fabrication known as epitaxial lift-off [33, 34]. Another layer of n-GaAs ([Si] = 1 x 1018 cm -3) is grown which performs a dual role. It acts as an etch-stop layer during an hydrofluoric acid etch and as a spacer layer which determines the final thickness of the device. The

13

NOLTE ET AL.

(1 p-OaAs 0 ~[,.

1•

IO00A L 20OO

cm-'3

p-AI0.3Ga0.7As lxlO 18 cm-1

CappingLayer

,,

LlCharge trapping and I BlockingLayer I

[ [Multiple Quantum Well J 1120.$ periods

i ll00o:, aAs

o~( 135 a A10.30Ga0.70As e~

9

I

I

Photoconductive Electro-Optic Layer

[As] = 0.2% _]~ [[

n-Al0.5Ga0.5As

5000A

lxl018 cm"3

Charge trapping and BlockingLayer Fabry-Perot& Etch stop ~ E t Lift Layer ch stop Layer

h-CaAs

5000A

lx1018 cm-3'

Planarization Layer

n + GaAs Substrate

Fig. 10.

MBE structure for a representative longitudinal-field transmission photorefractive quantum well.

final thickness of the devices are carefully tuned to meet exact Fabry-Prrot conditions to enhance the performance of the photorefractive diode [51, 52]. A spacer layer of nAlo.30Gao.7oAs ([Si] = 1 x 1017 cm -3) is grown for 3000/~ to prevent depletion of the doped contact. The active photoconductive electro-optic layer consists of a 120.5 period multiple quantum well consisting of 100 A GaAs wells and 35/~ A10.30Ga0.70As bartiers grown at 320~ The low growth temperature results in ~0.2% excess arsenic in the multiple quantum-well region. Cladding layers of 5000 A of A10.50Ga0.50As grown at 320 ~ sandwich the electro-optic layer and perform the function of charge trapping and also prevent carrier sweepout to the doped contacts. A 2000 A p-A10.30Ga0.70As ([Be] = 1 x 1018 cm -3) layer followed by a 1000 A top p-GaAs ([Be] = 1 x 1019 cm -3) layer were grown at 450 ~ The 450 ~ growth temperature for the p-doped layers acts as a weak in situ anneal of the previously grown LTG layers and results in the formation of As precipitates in the active electro-optic layer [ 14, 16]. The arsenic clusters deplete free cartiers from the surrounding material, rendering it high resistivity [53]. Thus semi-insulating quantum wells are achieved which retain excellent electro-optic properties [43] and require no postgrowth processing. The devices are fabricated as transmission devices using the following steps. The wafer is cleaved into 8 x 5 mm samples. In order to reduce surface leakage currents a mesa is etched into the quantum-well region using a phosphoric acid etch described in Section 2.3.1. Gold is evaporated on a comer of the device before the samples are epoxied

14

PHOTOREFRACTIVE SEMICONDUCTOR NANOSTRUCTURES

Fig. 11. Longitudinal-transmissiondeviceconstruction.

to a glass slide and are lapped using a fine alumina grit to a thickness of ,~ 100/zm. A small area (~0.5 x 2 mm) is covered with black wax to fabricate a mesa for the n-contact. The samples are then subject to a nonagitated ammonium hydroxide etch (19 parts H202:1 part NH4OH described earlier) at room temperature. This etch selectively removes the remaining GaAs substrate and the GaAs planarization layer and stops somewhere in the A10.50Ga0.50As stop-etch layer. After the etch the black wax is removed and gold is evaporated on the resulting mesa to form the n-contact. An ammonium hydroxide etch is used to etch to the buffed p-contact. A top and side view of the final device is shown in Figure 11. Electrical leads are connected to the contacts using silver paint.

2.3.3. Longitudinal Reflection Geometry The third photorefractive quantum-well geometry uses an electric field applied across the quantum wells along the growth axis, and has the hologram-writing beams incident from opposite faces. This geometry has the special property that the fringe spacing is extremely short and the holograms are volume holograms. The counterpropagating beams produce a fringe spacing given by A = )~/2n, where n is the refractive index of the semiconductor material. The large index n = 3.5 produces fringe spacings of only 120 nm for ~. = 840 nm. In the 1 - 2 / z m thickness of the devices, this produces only 10-15 fringes. Despite this small number of fringes, these fringes constitute volume holograms, in contrast to the two transmission geometries that produce thin gratings. The extremely short fringe spacing places severe constraints on the design of this geometry. First, extremely high defect densities are needed to trap sufficient space charge in a fringe to screen the applied field of 105 V/cm. Second, vertical transport must be suppressed to prevent overwriting the grating. These two requirements are both met by a LTG A1As/GaAs multiple quantum-well structure [43]. The low-temperature growth produces high defect concentrations, and the AlAs barriers produce small vertical mobilities.

15

NOLTE ET AL.

2000 i ' '_.___L ' ] '_....._~' ' ' ] .... "1 . Expt. ---~ ,

00

~ .... ]~

~ .... > 9

1.0

~ ....

.........

1000

-

500 -

0.5

~ "-,,. 0.0

-0.5

- 1000 .

-1500 -2000

1 the device operates in the Bragg regime, although for Q < 1 it experiences Raman-Nath diffraction. For typical two- or four-wave mixing experiments with photorefractive GaAs-based MQWs, L = 2/zm, )~ = 850 nm, n = 3.6, A = 20/zm. These values yield Q = 7 • 10 -3 and therefore place the MQWs far into the Raman-Nath regime where no Bragg matching is required for diffraction to occur. Diffraction in this regime yields two- and four-wave mixing in photorefractive MQWs.

5.2. Nondegenerate Four-Wave Mixing In the nondegenerate four-wave mixing geometry, depicted in Figure 20, two coherent pump lasers of energy at or above the bandgap of the MQW material are incident on the photorefractive material at equal angles, forming a sinusoidally varying interference pattern. A third probe beam, with a photon energy near the bandgap of the MQW, is incident at an angle 0in, and diffracts off the grating to form the "fourth" wave. Multiple diffraction orders are present due to Raman-Nath diffraction. The mth-order diffraction amplitude is calculated [5] using the Fraunhofer integral, 1 fA/2 Em -- ~ J-(A/2)IE,(x)l e-ikx(sinOa+sinOin) dx

where

(5.2)

Et (x) is the transmitted field and the diffraction angles Od are given by K sin Oct= - sin 0in + m ~ kvac

(5.3)

The diffracted amplitude is given by

Em = Ei ei(8~162

27

Jm (S1)

(5.4)

NOLTE ET AL.

where ~b is the photorefractive phase shift and the complex phase factors

t~i a r e

expressed

as

27rni L cti L ~i "- ~ ~- i ~ (5.5) 2 cos 0' )~cos 0' For small ( 95%) mirror reflectivities. The spacers in this structure consist of two A10.23Ga0.77As layers, one 1500 A thick grown at the standard temperature of 600 ~ and the other 0.75 # m thick grown at the low temperature of "-~270~ The structure was made semi-insulating by annealing at 600~ for 15 min for the low-temperature-growth (LTG) spacer and subsequent proton implantation after fabrication for the STG MQW region. The second structure is a LTG AlAs barrier MQW. The advantages of LTG A1As/GaAs quantum wells include higher breakdown field and lower leakage currents, allowing the device to perform at higher fields than A10.1Ga0.9As barriers. LTG A1As/GaAs is automatically semi-insulating when annealed [23], as described in Section 2.2.3. The LTG device structure consisted of STG-grown fabrication layers (described in Section 2.3.1) and LTG material consisting of a 2000 ~ Alo.23Gao.77As spacer layer followed by 167 periods of 100/k GaAs/20 ,~ AlAs MQWs and a 1000 A A10.23Ga0.77As spacer, grown at 315,305, and 305 ~ respectively, as measured in the Varian Gen II MBE system. A 30 s anneal at 600 ~ made the material semi-insulating. The dielectric reflector stack was deposited on the topmost layer of both structures, the device was bonded to a glass slide, and the substrate was removed according to the procedure discussed in Section 2.3.1. For both structures, the nonabsorbing spacer was etched as outlined in Section 2.3.1 to set the cavity thickness to produce the best resonance condition for each device. For the fully asymmetric Fabry-Prrots the device structure is shown in Figure 35b and the grating and probe beam configuration is the same as in Figure 39. Here, all beams are incident on the air-semiconductor interface and the reflector coating on the back of the device creates maximum diffraction efficiencies in reflection only. The reflection output diffraction efficiencies and the corresponding peak reflection input diffraction efficiencies of the two photorefractive ASFP structures are shown in Figure 41 as functions of wavelength. The diffraction peak of the STG 10% A1 barrier device is shifted toward the

47

NOLTE ET AL.

1000

,

,

i

!

I

i

r

i

,

I

'

'

'

'

t

'

'

'

'

i

.... ".... STG 10% Albarrier I --~--- LTG AlAs barrier #1 = LTG AlAs barrier #2

I

Tli n "- 0 . 1 2 %

o
'15

. - -

0 X 0

"~ 0.5 0

0

oD x

0 2 4 6 8 10 12 14 16 electronic deposited energy density (1022 keV/cm 3) Fig. 45. Optical absorption peak as a function of electronic deposited energy density for different conditions (circles -- N, diamonds = H, squares and crosses = He).

139

GONELLA AND MAZZOLDI

1.2k "~ ->" t

/ , - .... ,..~ - - - 2 x l O ' e / c m 2S" '"'.~ ......... 4xlO'6/cmS i

'~=04

0

300

350

400 450 500 wavelength (nm)

550

600

Fig. 46. Optical absorption spectra for RT, 8 /zA/cm 2, helium-irradiated silver-ion-exchanged waveguides, at the reported fluences. (Source: Reprinted from [ 163], with permission from Elsevier Science.)

'

'

'

I

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I

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'

I

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(a)

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/.~

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I (c) ~9 1.5~ r ~ -a

room 90oc ......... 150~

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t~

~0 . 0 5 0

300

375

450 525 wavelength (nm)

600

Fig. 47. Optical absorption spectra for samples irradiated at a fluence of 2 x 1016 ions/cm 2 with 100 keV (a) helium, (b) lithium, and (c) neon ions at the reported temperatures. Current densities were 2/zA/cm 2 for helium and neon beams and 1/zA/cm 2 for lithium. (Source: Reprinted from [ 163], with permission from Elsevier Science.)

140

METAL NANOCLUSTER COMPOSITE GLASSES

preciably different in the two irradiations, we can infer that the higher radiation damage caused by the lithium ions favors, in this intermediate temperature range, the migration and aggregation of silver atoms, due to the radiation-assisted diffusion. For a substrate temperature of 250 ~ the absorption bands for irradiations with helium and lithium ions differ only in minor details, probably due to a different distribution of the size of the precipitates, leading to the conclusion that at this temperature the precipitation process is mainly driven by the high thermal diffusivity of silver. At RT there is a low concentration of silver precipitates in both cases because of the smaller silver mobility. Moreover, the possibility that the precipitation of silver is favored by the substitution of lithium ions for silver ions in the implanted region is ruled out, because this substitution would be effective also at RT, whereas there is no indication of such a phenomenon occurring. Finally, in the case of neon irradiation, the intensity of the absorption band is much smaller for all temperatures and its FWHM is lower than that corresponding to the helium- and lithiumirradiated samples. In this case bigger clusters at lower concentration should have been formed [ 110]. It is possible that above a certain value of the energy deposited in elastic collisions, already formed silver precipitates dissolve in the collision cascade along the ion track, consequently decreasing their equilibrium concentration. Moreover, because of the small mean projected range, the neon-irradiation-induced clusters are formed in a thinner surface region. It can be further observed, by comparing the absorption bands for samples irradiated at RT with helium ions at a fluence of 2 • 1016 cm -2 and current densities of 8 lzA/cm 2 and 2 #A/cm 2, that the current density also plays a role in the silver precipitation under irradiation. This effect can be due to the increase in the temperature of the substrate because of deposition of the incident beam power. At high annealing temperatures (150 ~ and 250~ silver accumulation occurs in regions of the samples where the radiation damage is maximum. The shape of the profiles is clearly due to the combined fluxes of structural defects and of silver atoms (or ions) which, at these temperatures, are very mobile. X-ray-based characterizations were performed [129] on the exchanged § irradiated samples, in order to study the silver state after multistep treatment. Samples were ionexchanged in a bath of NaNO3 :AgNO3 at various molar concentrations for different times, at T = 320~ Sample A was subsequently annealed at 450~ for 48 h. Samples B and C were also irradiated with low-mass ions (He + and Li +, respectively) at different energies (1800 and 100 keV, respectively) and glass temperatures (RT up to 250~ at a fluence of 1016 at./cm 2. The electronic deposited energy density was 3 x 1022 and 1.7 x 1022 keV/cm 3, respectively, for samples B and C. Mean clusters diameters were found in the framework of the Mie theory of about 2 nm in sample B and 4 nm in sample C, while the amount of Ag atoms forming metal clusters was 12 x 1016 at./cm 2 and 7 x 1016 at./cm 2, respectively, for samples B and C. X-ray absorption measurements at the Ag K-edge were performed. In the as-exchanged samples Ag is expected to be bound to nonbridging O atoms, substituting Na in the glassy matrix. The Ag-O bonding distance is in all cases around 2.18 ,~, significantly shorter than the Na-O bond length in soda-lime glass (2.32 ~,). The values of coordination numbers N and bonding distances R in sample A agree with previous investigations [ 164, 165] while no presence of Ag colloids is found, even after annealing. In the irradiated samples the Ag-O bond distance is identical to the previous ones. In the case of high-temperature irradiated sample C, a first neighbor distance contracted to 2.86 A is found, in agreement with previous investigations on the surface stress contraction [90, 91] of Ag clusters. The case of the low-temperature irradiated sample appears to be more complicated to interpret. Indeed, the Ag-Ag bond length is expanded to 2.92/k. In the irradiated glasses the presence of Ag clusters is clearly revealed. Structural parameters of aggregates in the high-temperature irradiated glass are compatible with experimental findings and theoretical calculations on the fcc structure.

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Nanosized silver particles were also reported to precipitate from glass in the temary system Ag20:A1203:P205 (10-20 mol% of Ag20) upon irradiation with N 2+, 02+, or Ar + ions at 10-20 keV of energy [ 166]. Average radius of the particles, as deduced from optical absorption spectroscopy data, ranged from a few to about 11 nm as N 2+ energy increased from 12 to 20 keV. For the glass used in this experiment, it is supposed that the difference in the sputtering efficiency of each element in glass plays an important role in the precipitation of silver particles. In particular, an oxygen deficiency at the glass surface due to preferential oxygen sputtering should result in the enhanced reduction of Ag + to Ag ~ eventually leading to silver particle formation. When Na20 is added to the glass, irradiation-induced Ag removal is suppressed [ 167] and the amount of silver precipitates increases (up to a volume fraction of about 0.07). Electron irradiation is also effective in promoting silver aggregation in glass. Silver clusters of 4.2-nm mean diameter were formed in ion-exchanged soda-lime glass (2 h at 400 ~ in AgNO3:NaNO3 mixture with 2 wt% of silver nitrate) after 100 keV electron irradiation [ 168]. A Gaussian size distribution of the metallic particles was reported of about 2-nm FWHM, indicating the effectiveness of the method for obtaining high concentration homogeneous arrangements of metal particles, with relatively narrow size distribution. Among other--less studied--ways to exploit ion beams for creating MNCGs, high energy ion-beam-mixing has been successfully exploited for the preparation of silver clustersdoped silica glass [169]. In this technique, Si/Ag20 multilayers are prepared (150 and 15 nm of thickness for silica and silver, respectively) by stepwise vacuum deposition onto silica substrates, and then are irradiated at room temperature with 4.5-MeV Au 2+, that is, at an energy such that the ions projected range is much higher (about 1/zm) than the multilayer total thickness. Optical absorption spectroscopy measurements demonstrated that ion-beam-mixing can constitute a promising technique for forming nanometer-sized silver clusters in silica matrices at relatively low ion fluences (below 1 x 1016 atoms/cm 2) with respect to direct ion implantation. Copper clusterization within glass waveguides for MNCG formation in waveguiding structures was also studied [170]. Copper is particularly interesting because, in addition to the high n2 values of Cu-doped systems, its chemical behavior inside the glass shows a great variety with respect to parameters such as glass composition, temperature, and so forth [135]. This variety of behaviors suggests the possibility of tailoring both the linear and nonlinear optical properties of Cu-containing waveguides, through the control of the various fabrication parameters. Cu-Na ion exchange was realized [170] by immersing soda-lime slide substrates in molten baths of either pure CuC1 or CuSO4:Na2SO4 eutectic (46:54 molar ratio). The process was carried out at T -- 585 ~ in the case of the sulphates bath and at T = 550 ~ in the case of CuC1. Copper ions diffuse from the bath into the glass, replacing sodium ions that outdiffuse into the molten salt. The waveguides obtained were first optically characterized by m-line modal spectroscopy using a standard prism-coupling method. The copper-doped waveguides were then ion-irradiated with either helium or nitrogen ions. UV-VIS-IR optical absorption spectroscopy was performed before and after ion irradiation to obtain information on the chemical states of copper in the glass matrices. Cross-sectional TEM was used to detect the formation of clusters and their distribution over the metal-doped region of the waveguides. The nature of the very small clusters observed in this experiment was obtained from SAED, XPS, and XE-AES. The diffusion of copper in glass involves different copper oxidation states, with possible formation of either Cu or Cu20 clusters. In particular, the equilibrium between the copper oxidation states in glasses turns out to depend in a quite complex way on the preparation parameters and on the glass composition [ 171 ]. The experimental conditions of the copper doping, as well as the detailed nature of the substrate matrix, are therefore critical: in the glass, the equilibrium is governed by the Cannizaro's reaction 2Cu + ~ Cu 2+ + Cu ~ It is worth noting that the optical propagation constants of copper-exchanged light

142

METAL NANOCLUSTER COMPOSITE GLASSES

waveguides strongly depend on the presence of monovalent copper Cu +, because its electronic polarizability gives the major contribution to the index increase. On the other hand, the nonlinear response is related to the presence of copper clusters. After the exchange, the samples appeared transparent to pale green. Copper diffused up to a depth of several microns for a few minutes of exchange time, with copper concentrations up to some 1021 atoms/cm 3. These concentrations are much higher than the ones reachable by conventional melting techniques. Optical absorption spectra were taken in the wavelength range from 300 to 2000 nm. The only detectable structure was a faint absorption band centered at about 800 nm, ascribed to the 2Eg --+ 2Tg transition of Cu 2+ ions coordinated octahedrally with oxygen ions [171]. The ratio of the Cu2+-Cu + concentrations was around 10% for all the experimental conditions used. A first set of ion-exchanged waveguides was irradiated with a 100-keV He + beam at various fluences. Figure 48 shows the optical absorption spectra before and after He irradiation at the fluence of 1016 ions/cm 2. The spectrum appears to be only slightly modified by the ion-beam treatment, with the growth of a very broad absorption band below 500 nm, that is ascribed to the formation of Cu20 crystals [ 172]. The SPR at 580 nm of metallic copper clusters is not visible, even for fluences up to 8 • 1016 ions/cm 2. Almost the same absorption spectra were obtained in the case of nitrogen irradiation. This result suggests that the high chemical reactivity of nitrogen with soda-lime glass due to nonbridging oxygen atoms favors bonding with the glass matrix rather than with copper. The formation of SiOxNy compounds is possible [80], while the copper cluster formation depends on the electronic deposited energy (1.2 • 1023 keV/cm 3 for 8 • 1016 ions/cm 2 at 100 keV). Even if no detectable SPR absorption structures were observed, TEM analyses show the presence of high density clusters of very small dimensions (of the order of 1 nm in radius). Cluster density is observed to increase along with the fluence. Clusters are uniformly distributed over the irradiated region up to the projected range of the implanted ions. Moreover, SAED measurements indicate that both metallic and cuprous copper crystalline structures are present, as confirmed by XPS and XE-AES analyses. The absence in the optical absorption spectra of detectable SPR peaks can be explained by the extremely small cluster dimension: in both classical and quantum-corrected Mie scattering theories, the absorption cross section for copper clusters at about 580 nm abruptly decreases to zero when cluster radius is less than 1 nm [12]. Indeed, the possibility of creating extremely small-size clusters could be of great importance for the nonlinear optical response of the colloidal composite. On the other hand, when irradiated at higher energies and fluences, samples begin to exhibit the SPR structure of metallic copper clusters, as shown in Figure 49 for a sample irradiated with 1.8-MeV helium ions.

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GONELLA AND MAZZOLDI

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The Z-scan technique was used to measure the optical nonlinear features of some sampies. The samples were He-irradiated at high energies, in order to obtain thicker clusterdoped layers, with the aim to improve the analysis sensitivity. Figure 50 shows a scan on a waveguide first ion-exchanged in CuC1 and then irradiated with 5 • 1016 He+/cm 2 at the energy of 700 keV. The sample exhibited positive fast nonlinearity n2 - 10 -13 m2/W with 6-ps long pulses at high repetition rate. These values are comparable with those reported in the literature for other copper-implanted glasses [33]. It is noted that the n2 value measured at the 532-nm wavelength of the Nd:YAG laser with a pulse duration of 100 ps is almost 2 orders of magnitude higher than the value measured for 6-ps pulse duration.

3.6. Light Irradiation Irradiation of MNCG by electromagnetic radiation--most of all intense laser b e a m s - gives rise to a variety of effects connected to cluster formation or alteration. Possible mechanisms that give account for metal clusters alteration by laser light are currently un-

144

METAL NANOCLUSTER COMPOSITE GLASSES

der investigation [ 173]. Actually, UV laser light produces a pure thermal effect governed by absorption and subsequent evaporation in the composite. Metal loss observed in some experiments was explained in the framework of the Soret effect [174, 175], in which there is a differential diffusion toward the surface, with possible evaporation of implanted atoms from the surface due to the thermal gradient in that direction. On the other hand, as reported, nonthermal mechanisms can actually give rise to sizing effects [ 173], via electronic energy transfer to desorbing atoms faster than to lattice degrees of freedom. This has obvious possible application in the tailoring of nanosized composites. UV radiation can be also used to promote clusterization in glasses. For example, gold particles of a few nanometers size were grown [27] in a SiO2 :B203 :K20 glass after melt quenching followed by thermal treatment and UV irradiation, that was demonstrated to promote the cluster growing. It has been observed [173] that during Z-scan measurements of Ag:glass composites, similar to those used by Wood et al. [ 176] in their experiment, irreversible changes in the nonlinear saturation induced by the laser beam occurred. This was attributed to a reduction in the mean cluster size and the authors suggested that a possible cause could be a nonthermal removal of atoms from the cluster surface, similar to the desorption mechanism proposed in the literature [177, 178] to explain laser-induced desorption of sodium atoms from nanoclusters on LiF surfaces. The Z-scan technique was employed [ 179] to measure the nonlinear index of refraction, n2, and nonlinear absorption of an Ag:soda-lime glass composite fabricated by ion exchange and ion irradiation. After being scanned through the focal plane, the sample exhibited an irreversible change in the electronic and thermal components of n2 which reversed the sign of the intensity-dependent refractive index. This change was tentatively attributed to the formation of silver oxide at the cluster surface, a modification which appeared to have an intensity threshold and to be photochemical in origin. The modifications induced by high-power laser light irradiation of silver particles embedded in glasses, produced by the combined use of ion exchange and ion irradiation, has been explored [ 180]. Figure 51 shows the scheme of the three-step process to promote in a controlled way the formation of silver clusters in glass. Planar waveguides 5 / z m thick obtained by Ag+-Na + ion exchange were irradiated by either He + or Li + ions at the energy of 100 keV at fluences up to 1 x 1017 ions/cm 2. Silver clusters of a few nm in radius were obtained in a near-surface region about 0.6/zm thick. The transparent as-exchanged samples became brownish yellow after ion irradiation, and the optical absorption spectra exhibited a band at about 410 nm, corresponding to SPR absorption of the silver nanoparticles. As-exchanged and ion-irradiated samples were laser-treated by using a Q-switched Nd:YAG laser operated at both 1064 and 532 nm of wavelength. Pulse duration was about 10 ns. Different areas of the samples were irradiated with single pulses. Several pulses were also accumulated in the same spot to investigate possible cumulative effects. The effect of the laser irradiation is clearly visible to the naked eye. In fact, after a single pulse irradiation above a threshold value, the irradiated region became nearly transparent,

Fig. 51. Sketchof three-step methodfor fabricating MQDCwaveguides.

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GONELLA AND MAZZOLDI

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maintaining a faint yellow color. Correspondingly, the transmitted intensity of a He-Ne laser light focused onto the irradiated area suddenly increased, and the SPR optical absorption peak was dramatically reduced, as shown in Figure 52. Taking into account experimental uncertainties, which are mainly related to the not uniform spatial distribution of the laser beam, a threshold energy density was estimated for the induced transparency of E* = 0.3 + 0.1 J/cm 2 for )~ = 532 nm and E* = 5 -1- 1 J/cm 2 for )~ = 1064 nm (the corresponding power densities were 30 and 500 MW/cm 2, respectively). Multiple irradiations, at 1-Hz repetition frequency, on the same spot, with pulses at energy densities below the critical ones, did not modify the sample optical absorption, even if the integrated energy density largely exceeded E*. RBS analyses showed that the laser irradiation did not modify the silver concentration profile. From XPS and XE-AES measurements, the silver ot parameter changed from 720.3 4- 0.2 eV, close to the value of metallic silver (720.5 + 0.2 eV), before laser treatment, to 719.1 4- 0.2 eV, after the laser irradiation, in agreement with the c~ value of the Ag20 standard (718.8 + 0 . 2 eV). TEM micrographs are reported in Figure 53, which shows bright-field cross-sectional views of samples before and after laser irradiation. The sample irradiated by a laser pulse at ~. = 532 nm and E = 0.5 J/cm 2 exhibits a large reduction of the cluster size, from the mean diameter value of about 5 nm before to a mean value of about 2.5 nm after laser irradiation. This is accompanied by a corresponding increase in the number of clusters, keeping the total silver concentration constant. Similar behavior is also evident in the sample irradiated above E* at )~ = 1064 nm. The nanoclusters maintain the crystalline structure. Figure 54 shows the cluster size distribution after the laser treatment. The size reduction is in agreement with XPS and XE-AES results. In fact, the increasing ratio between the number of surface and bulk atoms with decreasing cluster size favors silver-oxygen with respect to silver-silver bonds. Moreover, because Ag20 is a direct-gap semiconductor with a calculated bandgap energy of 1.3 eV, this could explain the observed sign inversion of n2 after repeated Z-scan measurements: a negative nonlinear index of refraction is characteristic of many semiconductors. Besides the fragmentation of the silver clusters formed in the ion-irradiated region, it was observed that the laser irradiation is also effective in promoting cluster formation in as-exchanged regions, where few small clusters with a mean diameter of about 1 nm are present before irradiation. In these regions the laser irradiation causes the formation of nanoclusters about 2.5 nm in diameter. At present, the mechanisms responsible for the modification of the metal quantum dots by laser annealing are not fully understood yet. Some results can be explained in the frame-

146

METAL NANOCLUSTER COMPOSITE GLASSES

Fig. 53. Bright-field TEM micrographs of an Ag-exchanged-He-irradiated waveguide before (a) and after (b) laser irradiation with a 0.5-J/cm 2 pulse at 532 nm; (c) and (d) show an as-exchanged sample before and after the same laser irradiation.

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w o r k o f the m o d e l for the laser " p h o t o n sputtering" or ablation process, w h i c h is based on surface p l a s m o n excitation: it a s s u m e s that the a b s o r b e d e n e r g y is c o m m u n i c a t e d electronically to d e s o r b i n g a t o m s faster than it can leak a w a y into lattice degrees of freedom. B e c a u s e the surface p l a s m o n excitation exhibits a r e s o n a n c e as a function of laser fre-

147

GONELLA AND MAZZOLDI

quency and the transition frequency of this resonance depends on the particle size, this model can qualitatively explain the observed wavelength dependence of the phenomenon. On the other hand, the nonthermal desorption process does not exhibit any threshold effect for the laser intensity. The observed threshold effect may imply the occurrence of other mechanisms, like cluster photofragmentation [ 181, 182], which should be influenced by the cluster-matrix interaction. Thermal effects can also play a role. If we consider the effect of the laser irradiation on the as-exchanged region of the samples, we must take into account that silver ions introduced in glasses by the ion-exchange process have already been observed to partly reduce to neutral silver atoms (the amount of which critically depends on the glass composition), possibly aggregating to form silver clusters with a diameter of about 1 nm. These small clusters, present in the investigated samples, can dissolve under intense laser light as occurs for the larger ones. Atoms coming from dissolution eventually precipitate forming clusters with a size which is governed by the matrix properties and influenced by thermal effects. To completely understand the mechanisms responsible for the reported results, a detailed analysis of the influence of several parameters is needed. At present, the role of the wavelength, of the pulse frequency repetition rate, of the pulse length, of the cluster size and density, and of the cluster and matrix composition, are under investigation. Wood et al. [176] studied the effects of ArF laser (193 nm) annealing on the size of Ag clusters produced by ion implantation in float glass. While thermal annealing clearly reduced the average size of the nanoclusters, as evidenced by shifts in the peak of the SPR, ultraviolet-laser annealing by a KrF laser (248 nm) appeared to reduce the number of clusters without any apparent shift in the SPR wavelength. This suggests that the laser irradiation essentially vaporized clusters to a size smaller than that capable of producing a plasmon resonance, perhaps of the order of 1 nm in diameter. The effect of pulsed laser irradiation of silver clusters was also studied in the case of aqueous solutions [ 183]. After irradiation for 15 min by a pulsed laser light of 355 nm of wavelength, at 60 mJ/cm 2 of fluence, the cluster size distribution was observed to change from a mean diameter of 15 nm to a bimodal size distribution peaked at 1 and 9 nm. The authors attribute this new distribution to strong absorption of silver clusters, which gives rise to the desorption of silver atoms from the cluster surface, giving rise in turn to a decrease in the cluster size. Desorbed silver atoms can then form new silver particles with a size smaller than 3 nm. 3.7. Miscellanea

3. 7.1. Other Preparation Methods Melt-quenching and heat-treatment processes are the most simple and long-used methods for preparing glasses that contain small metal particles. An enormous amount of literature was published on this topic, especially related to the glass technology. The properties of the composites prepared by melting techniques are of course only partially tailorable, because the thermodynamics and the chemistry of the glass formation from a melting put several constraints to the possibility of control the clusters formation and (size) distribution, with definite limits concerning the metal solubility values. As a suitable example, interesting results were obtained by melt-quenching and heat-treatment processes for MNCGs containing copper and silver nanoclusters, prepared with the aim of tailoring their nonlinear optical properties [ 184]. In this experiment, 50:50 mol% BaO-P205 or CaO-P205 glasses were used as the matrix for copper and silver clusters formation. Cu and Ag were added in the form of oxides (Ag20 or Cu20) with concentration ranging from 4 to 10 additive mol%. As a reducing agent, SnO was also added to the glass. Cluster formation with different sizes and size distributions were obtained by different cooling and subsequent heat-treatment routes, obtaining metal particles with radii from 2 to 50 nm with volume fractions from 5 to 40 x 10 -4.

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METAL NANOCLUSTER COMPOSITE GLASSES

Sputtering deposition methods have found application in the last few years for the preparation of thin glass films containing metal clusters. For example, Ag/SiO2 composite films were prepared by a multitarget magnetron sputtering system [ 185, 186]. The Ag concentration was controlled by the deposition time and the input power. By depositing alternately Ag and SIO2, a more effective control of the metal particles concentration was achieved, with respect to the cosputtering method using a composite target. The main drawbacks of the method are the lack of control of both the structure of the composite and the dimensional distribution of the particle, as well as the criticity of concentration control in the case of low volume fraction of the metal with respect to the glass host. Nonlinear values of these systems are comparable to the values obtained for similar composite systems prepared by other conventional techniques. Glasses containing copper cluster were also prepared by the sputtering method [ 187, 188]. In particular, subsequent heat treatments and the control of the atmosphere during the sputtering deposition have been demonstrated to be effective in giving rise to copperruby glasses with relatively high third-order optical nonlinearity. For chemical reduction during sputtering, hydrogen was added to argon sputtering gas. In this way, it was observed that the volume fraction of copper particles in those glasses, which were heat treated in air, increased when hydrogen was added to the sputtering gas. Moreover, when heat treatments were performed in reducing atmosphere, copper particle sizes grew to 8 nm, while annealing in air gave rise to particles as large as 12 nm. A description accounting for the role played by the atmosphere in the particle formation was proposed [ 188], in which the formation of Cu clusters of radius < 1 nm is a nucleation process taking place during the heat treatment, while there are two competitive processes of particle growth, namely, gathering of clusters to form larger particles, and near-surface oxidation and subsequent migration of copper ions, eventually absorbed into the particles. Au/SiO2 films were obtained by a multitarget magnetron sputtering system, in which Au and SiO2 targets were independently manipulated [ 189]. The size of Au particles, laying in the range 3-34 nm, could be controlled by heat treatments in air, and measurements were performed of X (3) in the ns range. Large values of third-order nonlinearity at 70-ps pulse duration were also measured on cosputtered Au/SiO2 films [52]. A peculiar geometrical arrangement of the radio frequency (rf) cosputtering apparatus was set up, to achieve an effective control on the gold concentration in the deposited film, which could be continuously varied over a wide range from one end of the substrate to the other. Films as thick as 200 nm were prepared, and subsequently annealed at 850 ~ in Ar atmosphere for 1 min. In this way, film color turned from light brown to ruby, corresponding to the growth of gold clusters of inhomogeneous size distribution. Interesting results were observed when the volume fraction of gold particles, p, was varied up to the percolation threshold. In particular, the predicted linear relationship between p and X (3) was confirmed only for p < 0.15, while an almost cubic power law was observed for higher values of p, where cluster mutual interaction should be taken into account. At the percolation threshold, thirdorder nonlinear optical susceptibility abruptly decrease, corresponding to an increase of the electrical conductivity of some 8 orders of magnitudes, and to the turning of film color from ruby to goldlike. Ion-beam-assisted deposition has been explored as a suitable method for producing controlled MNCG films. Gold and silver nanoclusters were embedded in silica films by evaporating the metal species (gold or silver) simultaneously with silicon under oxygen bombardment [ 190]. It was demonstrated that the metal concentration, as well as the linear absorption and the cluster size, can be controlled by varying the processing parameters and the postdeposition heat-treatment conditions. In particular, bimodal size distribution of gold clusters was observed, with mean dimensions of a few and a few tens of nm, respectively. Pulsed laser deposition has also been used as a novel technique to synthesize metal nanoparticles in dielectric matrix. In this case, Cu clusters in A1203 matrix were formed [191].

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3.7.2. Characterization The study of MNCG is rapidly growing toward novel aspects of their physical characteristic, so new techniques are investigated to characterize the composites from optical, structural, chemical, and mechanical points of view. In the following, emphasis is given to those methods whose peculiarity when applied to the study of MNCG allow the most important deepening in the knowledge of MNCG behavior. Typically, MNCGs are first structurally and elementally characterized by the complementary usual techniques, such as SIMS, nuclear techniques, that is, RBS and nuclear reaction analysis (NRA), XPS, XE-AES, scanning Auger microscopy (SAM), TEM and the related X-ray energydispersive spectroscopy (EDS), and electron-energy loss spectroscopy (EELS). On the other hand, particular significance is assumed for the MNCGs the optical and spectroscopic characterizations. Systematic experimental characterizations have been extensively performed especially by linear and nonlinear absorption spectroscopy, saturation, photoluminescence, linear, and nonlinear refraction analyses. The corresponding properties are affected by the shape, size, and composition of the cluster and its host medium. Measurements of the optical response at low light intensities yield primarily information on the first-order susceptibilities of the irradiated material. These measurements include visible and infrared optical absorption, Raman and photoluminescence spectroscopies. While these techniques have generally been employed only to study the static properties of nanocluster composites, they can in principle be used to observe time-dependent processes, such as the growth and aggregation of nanocrystallites. Optical absorption spectroscopy has been widely used on dielectric composites containing small metal particles, because the location, amplitude, and width of the SPR are an excellent zeroth-order diagnostic of nanocluster species, size, and size distribution. However, the resonant plasmon response decreases in amplitude and broadens with increasing nanocluster size, making absorption spectroscopy a less useful tool precisely in the region where the nonlinear effects could be the strongest. For ellipsoidal particles, absorption spectra taken as a function of polarization have been shown to give a quantitative measure of the ellipticity of the particles [ 192]. In the far infrared, it is possible that one could see quantum-size effects in absorption spectroscopy; however, experimental attempts to do this have thus far been frustrated by experimental problems, notably with interactions between nanoparticles which overwhelm the expected quantum effects of level density by several orders of magnitude [ 193, 194]. Photoluminescence spectroscopy has been used on some metal-ion-implanted nanocomposite materials, but it is uncertain whether the luminescence is related to the nanoclusters or to residual defects from the ion implantation process [69]. In general, photoluminescence does not yield the same kind of indispensable information for quantum-dot composites as it does for semiconductor-doped glasses. Infrared absorption and reflectance spectroscopy are versatile and helpful tools for studying the binding arrangements of metal nanoclusters in transparent matrices. For example, IR reflectance spectroscopy has been used to study the growth of Cu and Pb nanoclusters formed by ion implantation in fused silica [70]. As the Cu ion dose increased, the Si-O stretch mode at 1111 cm -1 was observed to red-shift, indicating a decrease in the Si-O force constant; the amplitude in this mode increased, however, showing that the number of bonds recovered as the nanoclusters formed. The same stretch mode in the case of Pb nanoclusters in silica, however, showed a red-shift accompanied by a decrease in amplitude, from which it was inferred that the number of Si-O bonds was decreasing with dose, probably due to the formation of Pb-O bonds in the host matrix. Raman spectroscopy relies on three-wave mixing nonlinear phenomenon, and is useful to reveal Raman-active, particle and optical modes of the irradiated solid. Raman spectroscopy can be used to show changes in local binding occasioned by the implantation and aggregation of the quantum dots. For example, Hosono et al. [74] used Raman spectroscopy

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METAL NANOCLUSTER COMPOSITE GLASSES

to show that fluorine ions, co-implanted in a region in which Cu quantum dots had been formed by ion implantation in fused silica, were forming Si-F-Si bonds in the host matrix rather than Cu-F bonds at the surface of the Cu nanoclusters. Raman techniques were also employed by Duval et al. [195] to observe the size of mixed chromium-aluminum spinel microcrystallites in glass; the maximum in very low-frequency Raman scattering bands was shown to be inversely proportional to particle size. This technique has been employed to measure the size of Ag nanoclusters in an ion exchanged glass, and is found to give good agreement with TEM analysis for particles with diameters in the 1.5 nm range [ 196]. These last measurements were undertaken using prism coupling to inject light into the waveguide, in the same geometry used for m-line spectroscopy of the guided-wave modes. Different X-ray techniques can be used [ 126] to characterize composite systems formed by clusters embedded in glass. Due to the small amount of material in the sample the use of intense and collimated beams from synchrotron radiation machines is mandatory for this kind of application. In particular the X-ray small angle scattering (SAXS) was used to determine the morphology of the cluster system while through XRD the crystalline phases formed upon different preparation techniques were determined. X-ray absorption spectroscopy (XAS) was eventually used to study the mean valence state of the metal and the local atomic order around the metal atom. In particular, EXAFS analysis has been used as a peculiar powerful technique to study the equilibria among the different oxidation states of the dopant metal and the possible formation of mixed-metal or alloy clusters. The local structure of the metallic particles and their long-range ordering are currently investigated, as well as the possible contraction of the lattice parameter in the case of nanometer-sized clusters. Among the techniques directly sensitive to the third-order susceptibility, there are two spectroscopies in relatively common use to determine the size, speed, and dephasing of the third-order nonlinear optical effects. One, known as the Z-scan [197], is conceptually derived from the far-field intensity distribution measurements first described by Weaire and co-workers [198]. It offers, in contrast to other third-order measurement techniques, straightforward access to the real and imaginary components of the third-order susceptibility, including signs; however, in its usual experimental realization it gives no direct information about relaxation times. The electronic and thermal contributions to the nonlinear index of refraction, as well as the two-photon absorption coefficient, can be extracted from Z-scan data [ 199]. In the standard configuration, the light intensity transmitted across the nonlinear material is measured through a finite aperture in the far field as the sample is moved along the direction of propagation (Z-axis) of a focused Gaussian laser beam. When the sample moves toward the focus from negative Z, the power density increases, giving rise to self-focusing: owing to the Gaussian transverse intensity profile of the laser beam, the original plane wavefront of the beam gets progressively more distorted, in a way similar to that imposed by a positive lens (in the case of positive nonlinearity of the material), leading to a self-focusing that shifts the position of the actual focal point, because the ray propagation must be perpendicular to the wavefront. A displacement of the focal point toward negative Z gives rise to an increased divergence of the output beam, and thus to a decrease in the intensity at the detector. For positive values of the Z position of the sample, the same effect gives rise to a decreased divergence, that is, to an increased intensity at the detector. When the sample is at Z = 0 the self-focusing does not affect the output. The same occurs when the sample is far from the focal point, because the power density is low and the self-focusing effect is negligible. It is worth noting that the intensity change due to absorption effects can be evaluated by removing the aperture in front of the detector. The difference between the peak and the valley in the output intensity figure is proportional to the phase distortion of the beam, which is, in turn, related to the nonlinear refractive index, n2. Other versions of the Z-scan have been demonstrated in the evaluation of nonlinear optical materials, such as eclipsing Z-scan and pump-and-probe Z-scan [200]. With appropriate optical constructions, the Z-scan can also be implemented

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in versions suitable for two-color measurements of nondegenerate nonlinear effects [201] and for time-resolved studies [202]. The other widely used technique for measuring is the four-wave mixing. In DFWM, two pump beams and one probe beam are split off from a single laser beam; the pump beams typically contain 80-90% of the total pulse energy. The pump beams are arranged to be coincident in time in the sample volume, while the probe beam arrival time in the sample volume can be varied with respect to the pump beams by an optical delay line. The thirdorder NLO susceptibility measured in such an experiment is X O)(-w; co, co, -co), where the negative sign indicates that the complex conjugate of the electric field is to be taken. Because the relative temporal duration of the laser-induced changes in the medium is measured directly by varying the timing of the probe-and-pump beams, DFWM gives a direct indication of the speed at which the material relaxes. The ith component of the nonlinear v(3) * polarization associated with the experiment is then t% - ff-~jkl AijklEj(co)Ek (co)El(co), where the subscripts on the electric field components should be considered as including both the designation as pump or probe and the polarization of the beam. If one thinks of the beams j and k as the pump beams, the individual components of this polarization have an intuitive physical interpretation: they constitute the polarization induced by the probe beam in a material medium modified by the two pump beams; in that sense, the product of the third-order susceptibility with the two pump beams may be viewed as being an effective first-order susceptibility of the laser-modified composite material. The nonlinear polarization radiates a signal field at co in the phase-matched direction. A physical interpretation of the process can be given in terms of grating formation in the nonlinear medium: the pump and the probe waves interfere giving rise both to amplitude gratings (resulting from the nonlinear loss due to two-photon absorption) and refractive index or phase gratings (due to the intensity-dependent refractive index change), from which the waves scatter coherently. The output intensities of signal and probe are related to the nonlinear absorption and to the nonlinear gain, from which one can determine the third-order term X (3/(_co; co, _co, co), which can be in turn related to the nonlinear refractive index n2. DFWM measurements have been implemented in two geometries suitable for studies in thin nanocomposite layers. In one, the so-called phase-matched forward four-wave-mixing scheme [203], all of the beams pass through the sample in the forward direction; the probe beam is then advanced or retarded in time with respect to the pump beams. For a nanocomposite medium with cubic symmetry, one can isolate three terms that contribute to the polarization resulting from the creation of a population or electron-density grating; therefore, these terms include the effects of thermal mechanisms resulting from differential absorption, while the fourth term involves only the electronic contribution. Hence, by judicious choice of input-beam polarization, it is possible to separate the thermal from the electronic contributions to X (3). This is particularly important when four-wave-mixing measurements are made using long-pulse or high-repetition-rate laser systems. The classic DFWM geometry with counterpropagating pump beams can also be made to work in extremely thin samples [204]. Nondegenerate three-wave mixing, one of the many variations of coherent Raman scattering, is an interesting technique which has been demonstrated to yield accurate results for the nonlinear refractive index of bulk glasses [205]. Finally, we note that DFWM has also been demonstrated in a waveguide implementation, again using prism coupling to insert the pump and probe beams and extract the phase-conjugate signal [206]. Other optical techniques have been developed in the last few years for application in metal nanoclusters analysis. Pb and Sn nanoclusters embedded in amorphous SiO have been investigated [207] by means of the Brewster angle technique, giving information on the structural aspects of the composite. In [57], femtosecond transient reflectivity measurements were reported on metallic Sn nanoclusters (radii between 2 and 6 nm) embedded in the AleO3 matrix. Moreover [208, 209], femtosecond pump-and-probe spectroscopy has been successfully used to study the nonthermal generation of coherent acoustic phonons in Sn and Ga nanoparticles with radii in the range 2 to 30 nm. Other techniques are

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successfully used to determine the nonlinear optical properties of semiconductor quantum dots, but appear promising for MNCG analysis. Among these [21 ] are photon echo techniques [210, 211], nondegenerate four-wave mixing [212], electroabsorption spectroscopy [213,214], magnetoabsorption pump-probe spectroscopy [215], and interferometry [216], which is particularly suitable for waveguide systems.

3.8. Table of Metal Nanocluster Composite Glass Third-Order Nonlinearity Some measured values of the third-order nonlinearity are reported in Table I for various MNCGs. As a comparison, the intensity-dependent refractive index of the pure silica is n2 = 10 -20 m2/W, with a nonlinearity relaxation time of the order of 10 fs [19], whereas the linear absorption is ot - 1 0 -5 cm -1. In the table are also reported the experimental parameters for the nonlinearity measurement (laser light wavelength, pulse duration, and repetition rate). It is worth mentioning that the measured values for optical nonlinearity include in general both electronic and thermal contributions, and that these respective contributions can also be opposite in sign, depending on the operating time scale. This means that much experimental and theoretical work is still necessary to determine the nonlinear response of MNCGs for effective modelization and technological application.

Table I. SomeMeasuredValues of the Third-OrderNonlinearity for VariousMetal NanoclusterCompositeGlasses* Cluster Size metal (nm)

Host

Filling factor

Cu

4-~ 18

SiO 2

1 --, 6 • 10 - 2

Ag-Cu

10%). Use moderately doped (1015-1017 cm -3) p - silicon substrates. Use a constant current density (10-100 mA/cm2). Anodize in the dark.

p.type..,

CurrentI

I Anodic -

-light ~...../.~j/dark I ~

dark..'...............--f---

-

Voltage

i light .../i j/

iiii

,

Fig. 11. The effect of light on both p- and n-doped Si in the anodic and cathodic bias regions. Light absorption produces electron-hole pairs, which significantly alters the minority carrier distribution. As such, pdoped Si is most significantlyaffected by light under cathodic bias and n-doped Si showsdramatic changes under anodic bias. In both cases, the etching current is significantlyincreased when light impinges upon the sample.

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2.2. Chemical Methods Electronic holes continue to be a critical component of the reaction for producing poSi. However, the reduction of an appropriate oxidant is another way to provide those holes. A variety of chemical solutions have been used for decades to achieve particular etching objectives on Si. Most employ a mixture of nitric acid and HF, including perhaps a few other components. The series of articles by Robbins and Schwartz [6-9] thoroughly explored the etching behavior, though it was Archer [ 10] who first reported that the stain film often associated with these chemical etches was the same porous silicon film arising from the electrochemical etch. Because of this "stain," these etches are still commonly referred to as "stain etches" though the stain is really the porous silicon we want to study and is produced, not by the addition of some foreign substance but rather by the preferential removal of some silicon. The chemical reaction can be adjusted by the following parameters: 9 9 9 9 9 9

Concentration of HF and HNO3. The use of diluants other than water. Priming the solution with Si. Employing other oxidants. The doping polarity and level of the substrate. The presence of light, its intensity, and spectral distribution.

2.2.1. Reactant Concentration With two reactants and a diluant (H20), the concentration profile of the system is most readily presented in a triangle plot. This is shown in Figure 12. Each axis is a fraction or percentage of each component in the total solution. Because they must always sum to 1 or 100%, any point on the graph uniquely identifies a solution concentration. Each comer corresponds to a solution that is pure in one of the components. As before, I emphasize that both HF and HNO3 are not available as 100% "solutions," but rather are only available as either 49 or 60% solutions in water for HF and 69% in water for HNO3. It is these available solutions which are the "pure" components as plotted on the graph. Hence, 100%

Fig. 12. A ternary concentration diagram of the HF:HNO3:H20 chemical etching system.The contours approximately show the dependence of etch rate on the concentration of the various components. A solution which is 35% HNO3 and 65% HF has the greatest etch rate. Pure H20, in the lower left-hand corner has the slowest etch rate.

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nitric acid is actually only 69% HNO3 and 31% H20. However, the graph does accurately report additional dilutions with water. Clearly a solution of pure water is the one which has the lowest etch rate. This is in the lower, left-hand corner of the graph. Robbins and Schwartz found that a solution 65:35 HF:HNO3 had the greatest etch rate (measured as the thickness of material removed per time) as about 30 #m/s. The placement of a piece of Si in this solution produces a violent reaction, with clouds of brown gases evolving from the reaction vessel. The brown gas is certainly NO2. It could be produced directly in the reaction but it is also possible that NO is the gas produced and upon exposure to 02, it reacts quickly to produce NO2. Curves of constant reaction rate radiate out from this point toward slower rates. Porous silicon is formed under more modest etching conditions but many concentrations have been employed, coveting most of the reaction space. Even at the high reaction rates poSi can be formed but the vigor of the reaction along with the production of gaseous products tends to lift the film off prematurely and a uniform layer cannot be obtained. More work has been performed on this system when Di Francia and Citarella [70] reported a carefully study examining the rate of mass loss as a function of etchant composition, it depending upon the HNO3 concentration approximately as [HNO3] 071. They noted, however, that poSi morphology was more dependent upon sample characteristics rather than etching conditions. 2.2.2. Other Diluants

Robbins and Schwartz identified the amount of undissociated HNO3 as important to the reaction. The dissociation equilibrium can be shifted away from dissociation by using a solvent which is more acidic than water. They used glacial acetic acid and they confirmed that this increased the reaction rate. By using the more concentrated HF (60%) and acetic acid, they were able to analyze the kinetics of the reaction, identifying the region rich in HNO3 as one where the HF played the kinetically important role, while in the HF rich region, HNO3 was the kinetically controlling component. Acetic acid was just a more effective diluant.

2.2.3. Priming the Solution When more dilute etching solutions are employed, interesting behavior is observed in the reaction. An induction period is noted during which no etching is apparently occurring. Then, after many seconds or even several minutes, the reaction starts suddenly and progresses quickly across the surface. It is apparent that some autocatalytic reaction is involved. A slow, uncatalyzed step reacts to produce a catalytic reactant in sufficient quantity so that it can sustain further reaction. At that point the reaction can spread quickly to cover the entire sample surface. Presumably this catalyst is some nitric oxide species such as HNO2, NO2, NO, NO~-, NO +, etc. This can be further evidenced by etching the sample in a stirred solution. At slow rates, the reaction proceeds readily following the induction period, but if the solution is stirred, the reaction never starts. Apparently, the catalyst being formed is swept away from the near-surface region before it can build up to a sufficient concentration to affect the reaction rate. The reaction then, being autocatalytic, can be described as chaotic. This unpredictability can be diminished by priming the solution before etching. This can be done by pre-etching a small piece of Si in the solution to produce the desired reactant. Subsequent etches tend to proceed more smoothly and promptly.

2.2.4. OtherOxidants In a search to identify the role played by the various nitric oxides, a direct addition of NO 2 ion has proven to speed the reaction and to eliminate the induction period. A small,

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THOMAS

catalytic amount of NaNO2, Y~NO2, or NH4NO2 is commonly employed. However, another study [ 15] showed that the direct addition of NO + (by adding NOBF4) was even more effective in speeding the reaction. Other oxidizing agents have also been used, namely, KMnO4 and Na2CrO4 [15]. Without the presence of any nitrogen oxides, these reagents also etched the Si and produced poSi. The rate of reaction was very much slower than with HNO3, but it was clear that the reaction only proceeded more efficiently with the nitrogen oxides but actually only required the presence of a strong oxidant.

2.2.5. Substrate Doping and Light Exposure As with the electrochemical system, the doping of the substrate plays a critical role in determining the nature of the sample. This is particularly evident when etching with and without light. In weak etching solutions, n-type substrates are not attacked in the dark, but when illuminated, the reaction readily proceeds. Conversely, while p-type material etches readily in the dark, the reaction can be inhibited by illumination on these substrates. The photoluminescent properties of these substrates can also be influenced by the intensity and the frequency of the light used. More intense light tends to encourage more etching, shifting the luminescence toward the blue and higher frequency light also shifts the emission toward the blue end of the spectrum. This is discussed further in Section 8.3 as shown in Figure 53. For all of these processes, we have focused on the etching of Si. Under some conditions this produces poSi and in some of those cases, the poSi is luminescent. Fine tuning these various parameters can enhance and modify the spectral properties of the poSi luminescence as well as adjust the general reaction to form the porous material. These specific details will be discussed in a subsequent section. 2.3. Other Methods

The most remarkable property of porous silicon is the visible fluorescence. There are other ways to process silicon so that it also produces fluorescence of this nature. Sparkerosion [71-73] produces material that has all the features of poSi. Such treatment of a Si wafer using a high voltage, low current Tesla transformer for durations as long as a day or more, produces poSi which is reminiscent of anodically formed poSi in all ways m structurally and spectrally. This material, because of its unique production environment, has helped to elucidate the nature of poSi and the mechanisms of its production. Nanocrystallites of Si have been formed by various gas phase methods [27, 66, 74-76], often involving chemical deposition from silanelike molecules. These nanocrystallites are clearly very different from the mesoscopically and macroscopically porous materials produced anodically, but their optical characteristics have helped to clarify the luminescence properties of poSi. Other materials such as ion beam or radiation damaged Si/SiO2 interfaces have also been produced to help elucidate the nature of poSi and by various methods, the Si interface [77] has been oxidized, hydrided, or exposed to many different chemicals in an effort to study its unique properties. Siloxene is a molecular compound of Si, O, and H which has been produced [35, 78-80] to demonstrate similarities it shows with the fluorescent properties of poSi. 2.4. Postformation Conditions

The extremely high surface-to-volume ratio of poSi samples renders it very susceptible to surface reactivity. The atmospheric conditions under which it is stored dramatically effect the material properties, especially its fluorescence. We have regularly noticed how material which has been formed chemically, when withdrawn from the etching solution and

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allowed to dry, produces an intense, bright green photoluminescence for a few seconds while drying. However, as the aqueous solution evaporates to expose the sample to the atmosphere, that fluorescence is quenched, giving way to the more well-known red-orange fluorescence. Subsequent storage in air during the next few minutes and hours quenches the red-orange fluorescence, resulting in a significant drop in intensity which is usually accompanied by a red shift in the fluorescence. However, exposure to the atmosphere over the next few months helps the fluorescence to recover its initial intensity. Storage in a cold, dry nitrogen or argon atmosphere will significantly extend the performance lifetime of poSi. In addition hastening the oxidation hinted at by the long-term exposure to the atmosphere by rapid thermal oxidation (RTO), enhances either the red emission (when annealed at low temperatures) or the blue frequency emission (when annealed at higher temperatures). These high porosity samples are structurally delicate as they are left with significant stress inside the layer because of the removal of so much material. Drying can shatter the film and compromise its integrity. On the other hand, electrochemical methods have been developed to lift off the poSi film in large pieces, which can subsequently be attached to other surfaces such as a sapphire window. Control of the postetching conditions are important as we try to understand this easily formed but remarkably complex material.

3. STRUCTURAL PROPERTIES In the early days, poSi was referred to as a "brown deposit" or the "anodic film." Gas adsorption work hinted at its huge surface-to-volume ratio but it was during the mid 1970s that it started to be referred to as porous silicon. This porosity can appear in three general flavors, distinguished by the relative size of the pores--macroporous, mesoporous, and microporous. As well, the particularly controversial structural feature is its nanocrystallinity. Through the selection of the appropriate substrate and the control of the etching conditions, poSi manifesting these different properties can be obtained. The selection of the substrate doping type and density are the most important parameters determining the gross pore structure. Once this is determined, the general structure type can then be adjusted with other processing controls, such as HF concentration, etching current density, and illumination condition. As described in Section 2.1, an increase in current density or a decrease in HF concentration leads to increasing sample porosity.

3.1. Macroporosity When moderately n-doped Si is anodized with a large current density, pores with dimensions over 1 # m in diameter are formed. Shown here in Figure 13 [81] is such a sample, it being n-doped to a 5.0 f2-cm resistivity. These large pores have been used in micromachining activities to produce deep trenches, such as shown here in Figure 14 [82]. Many etching procedures demonstrate a considerable crystallographic orientation preference, and such biases in this system contribute critically to its usefulness in structure formation. Figure 15 [83] shows a plane view of these holes when etched in a (100) oriented substrate. The { 100 } planes are the most stable in this environment and so the etching structures assume features representative of this stability. Here on the (100) plane we see that the pores develop a square cross-section. Degeneratively n-doped samples can also exhibit macropore formation when heavily etched. Figure 16 [83] shows a plane view of such a sample (density, 4 x 1018 cm3; total charge transferred, 100 C/cm2). Notice how in these samples, the square cross-section is distorted by sideways pore growth from the four corners of the square. The crystallography still dictates the pore shape but now it becomes more starlike in its character. Figure 17 shows the evolution of these pores from a circular cross-section at low current densities to the heavily branched structure as the current density increases. The influence of crystallography is further demonstrated in Figure 18, which shows a heavily etched n + sample

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THOMAS

Fig. 13. When n-doped Si is anodized, it produces macropores, as much as several/xm in diameter. This electron micrograph displays this behavior. Reprinted with permission from Ref. [81].

Fig. 14. Trenches can be cut deeply into n-doped Si because of this natural pore forming ability. By pre-etching an array of spots using KOH, the etching process can be nucleated to give a regular array as seen in this SEM image. (Source: Reprinted from [82] by permission of the Electrochemical Society, Inc.)

of (111) orientation where a series of nested triangles produce a structure very m u c h like a Serpinski gasket, known from the field of theoretical fractal analysis. A nice demonstration [81 ] of the influence of current density on pore size is shown in Figure 19. Here, the current density is high (80 m A / c m 2) during the first portion of the etch

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POROUS SILICON

Fig. 15. This preferential etching is closely linked to the surface orientation. This SEM shows how the large macroporesetched in n-doped material develop into a square profile, following the {100} family of planes. (Source: Reprinted from [83] by permission of the ElectrochemicalSociety, Inc.)

Fig. 16. When etched even more heavily, the square holes start to etch into a star pattern, etching proceeding again in the [100] directions. (Source: Reprinted from [83] by permissionof the ElectrochemicalSociety, Inc.)

and then it is stepped down to 10 mA/cm 2 for the bottom portion of the etch. The dramatic drop in pore size for the milder etching conditions is obvious. Visibly luminescing poSi has been formed on n-doped structures etched in the dark [84]. Careful TEM studies revealed the presence of Si "platelets," Si planes demonstrating confinement in one dimension only. These structures were associated with the PL of these samples in contrast to the two- and three-dimensional confinement of other etch systems. Though macropore formation is the most obvious structural feature, these materials can still produce nanostructured features that are associated with the PL.

3.2. Mesoporosity When degeneratively doped, p+ or n + material, is etched, pores are produced with diameters from 10 to 100 nm, though as shown earlier, the macroporous features can be produced in the n+-doped material at high current densities.

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THOMAS

Fig. 17. A schematic of the evolution of the pore profile when etching n-doped silicon with an increasing potential bias.

Fig. 18. An etch performed on a (111) oriented substrate of n+-doping type. The triangles that form arise because of the stability of the (100) planes, which in this orientiation give the triangular profile while above in the (100) orientiation, give a square profile. (Source: Reprinted from [83] by permission of the Electrochemical Society, Inc.)

The evolution of the sample porosity with HF concentration and anodization current was nicely demonstrated in a gas adsorption study by Herino et al. [24]. Figure 20 reports their data on p + substrates for three anodization currents as a function of HF concentration. The increasing porosity with decreasing HF concentration is clearly observed. Figure 21, also employing a p + substrate, is equally convincing in demonstrating that increasing anodizing current increases the sample porosity. Their parallel studies on n + substrates reached the

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POROUS SILICON

Fig. 19. A demonstration of the dependence of pore size upon current density. The top half of this Figure was etched at 80 mA/cm2 while the bottom half was etched at 10 mA/cm2. The large pores in the heavy current density regime are clearly evident and stand in contrast to the small network of pores at the bottom. (Source: Reprinted with permission from [81].)

Fig. 20. The sample porosity was probed by gas adsorption studies which showed that an increasing current density produced greater sample porosity, while a decreasing HF concentration produced more porous material. (Source: Reprinted from [24] by permission of the Electrochemical Society, Inc.)

same conclusions regarding these trends. However, the porosity for p + was considerably greater (5 versus 30%) than for n + samples of comparable substrate resistivity, etching current density, and HF concentration. Their work was also able to deduce the pore size distribution on a sample using the BJH procedure [85]. For n + and p + substrates, the average pore size ranged from 2 to 7 n m q- 20% in diameter. Gas adsorption studies are sensitive to the pore surfaces which contribute the largest fraction of the total surface area. This comes from the small scale pore structure, as it provides the greatest surface to volume ratio. W h e n direct imaging techniques such as SEM or T E M are employed, the larger pores are more c o m m o n l y observed, because pore sizes less than 10 nm are very difficult to image. Figure 22 shows a cross-section T E M

185

THOMAS

Fig. 21. The same gas adsorption studies show how an increasing current density applied to a p+ Si sample produces material which moves from 35 to over 60% porosity as the current density rises to 250 mA/cm2. (Source: Reprinted from [24] by permission of the Electrochemical Society, Inc.)

Fig. 22. An n-doped (100) oriented sample. The pores observable by TEM are visible down to about 20 nm in this image, but gas adsorption studies suggest it should be mostly 10 nm pores. The preponderance of the porous network surface area lies below the observability by these imaging techniques. Pore growth in this sample is along the (100) direction which is also in the direction of current flow. Studies on a (110) oriented sample indicated that crystal orientation and not current flow direction dictated the pore growth direction. (Source: Reprinted with permission from [37].)

( X T E M ) i m a g e of n + - d o p e d poSi. T h e largest pore features seen here are about 20 n m across, while the bulk of the other features are apparently in the 10 n m r a n g e and thus largely agree with the gas adsorption studies.

3.3. Microporosity W h e n p - - d o p e d Si is etched, a very fine p o r o u s n e t w o r k with pore d i m e n s i o n s b e l o w 10 n m is f o r m e d . Structures of these d i m e n s i o n s are very difficult to i m a g e with any accu-

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POROUS SILICON

Fig. 23. A sample etched from p--doped silicon. A very fine network of pores, with dimensions below 10 nm is formed. The lower half of this imageshows the unetched Si substrate while the top half is poSi exhibiting features of the dimensions mentioned. (Source: Reprinted with permission from [28].)

Fig. 24. A TEM image showing a silicon crystallite embedded in an amorphous poSi layer. The crystal planes, with a spacing of 3.1 ,~, are evident. The overall diameter of the crystallite is around 5 nm. (Source: Reprinted with permission from [87].)

racy. Figure 23 [28] is a XTEM of such a sample. The lower portion of the image shows the unetched substrate with the porous layer at the top. The marker bar is 100 nm long and the porous features clearly are in the range of a few nanometers.

3.4. Nanocrystallinity in an Amorphous Layer For all of its interesting porous properties, none of this is directly responsible for the remarkable fluorescence of poSi. Although details of the fluorescence mechanism continue to be vigorously disputed, the presence of nanocrystalline material throughout the poSi layers of all porous types has been confirmed. Although early diffraction studies were unable to find evidence for crystallinity, more work confirms that poSi retains the crystallinity of the original starting material. Cullis and Canham [86] described quantum wires with dimensions as small as 3 nm. Figure 24 is a TEM image of a p - - d o p e d sample from the work of Cole et al. [87], clearly showing the presence of a small crystallite

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THOMAS

Fig. 25. A wider view TEM image of the sample showingmany crystallites, evidencedby the array of lattice planes being visible, havebeen outlined in the figure. (Source: Reprintedwith permissionfrom [87].)

embedded in an amorphous phase. From the same work, Figure 25 is a wider view TEM where a number of crystallites have been marked to show their presence. Nakajima et al. [88] associated the small Si crystallites with the columnar structures by showing their presence throughout the etching layers as consisting of strings of small crystallites. This was confirmed by Takasuka and Kamei [89] who further demonstrated the crystallographic registry of the crystallites with the underlying substrate, as shown in Figure 26. They were further able to show that the intensity of the photoluminescence scaled with the density of crystallites in the sample, concluding that these crystallites were responsible for the PL. This suggested that quantum confinement was responsible but could not rule out surface mediated emission because competing models which invoke defect sites or adsorbed species as the prime luminescent centers, locate these sites on the surface of these nanocrystals. In a TEM and electron energy loss spectroscopic imaging (ELSI) study, Teschke [90] identified nanocrystallites of Si and also he identified crystallites which were oxygen-rich, generally found at the bottom of etch channels, near the poSi/Si interface in heavily doped materials. In lightly p-doped materials, he suggested that the entire surface consisted of these oxygen-rich, H-terminated crystallites and were the source of the PL emission. The work in [91] prepared Si nanocrystals embedded in an SiO2 matrix by radio frequency (rf) magnetron deposition. These crystallites exhibited PL like that from poSi and the emission scaled with particle size. While the crystallinity of these small nanoparticles is clearly in evidence, it is equally clear that the layer in which they are found is amorphous in its structure. One finds this amorphous layer with embedded Si crystallites lining the pore walls of all types of poSi. It is this layer which is exposed to atmospheric conditions and which is subject to oxidation and attack by reactive molecules. It is also this layer which leads to confusion regarding the chemical nature of poSi, some finding Si, O, H, and F in varying and sometimes contradictory amounts. In a SIMS study, Canham et al. [39] identified freshly etched poSi as consisting mainly of H and F terminated silicon. The H was particularly stable to atmospheric exposure and actually increased in its proportion over a 10 week period. Fluorine, on the other hand showed a slow but steady decrease in its concentration over the same time frame. Carbon and oxygen contamination in-

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POROUS SILICON

Fig. 26. AnotherTEM image showingthe crystallites, manywith dimensions as small as 1 nm. It is also evident that the orientiation of the crystallites is preserved with each other and with the underlying substrate, as seen at the bottom of the image. (Source: Reprinted with permission from [89].)

creased until they became a significant portion of the sample after the 10 week exposure period. In related work, Roy et al. [92] studied poSi by X-ray photoelectron spectroscopy (XPS) on as-prepared samples, and they suggested the presence of a fluorinated siloxene species below the surface of an SiO2 outer layer as being responsible for PL. The problem, of course, is that XPS is not sensitive to hydrogen, which was noted in the preceding text to be the principal component of the layer. Vasquez et al. [93] also used XPS on samples which were chemically etched to remove the oxide layer. They found only traces of C, O, and F and they attributed the PL to an amorphous Si surface layer. It is difficult to rationalize these two studies, but the complex nature of the chemical composition of these layers is greatly effected by the handling of the material after its production. A new role for an amorphous layer has been suggested. Kim et al. [94] etched a sample which had been previously coated with an a-Si film by rf magnetron sputtering. This sample, when etched, luminesced strongly in the green at 543 nm and it was suggested that the amorphous layer protected small crystallites from oxidative attack during etching. This may be a manner by which reliable green fluorescence can be obtained. 3.5. Chemical Etch Features Si which has been etched chemically produces photoluminescence very comparable to that found in electrochemically etched samples. However, the pore structure so prevalent in the electrochemical samples is largely unseen in this material. The amorphous layer with embedded nanocrystallinity found to coat the electrochemical pores, is that which corresponds most closely to the chemically prepared poSi. Fathauer and co-workers have performed several studies on the chemically prepared material. Figures 27 (p--doped) and 28 (p+-doped) are SEM micrographs of the surface

189

THOMAS

Fig. 27. A SEM of p--doped poSi prepared by chemical etching methods. The image is approximately 4/zm across. (Source: Reprinted with permission from [95].)

Fig. 28. A SEM of p+-doped poSi prepared by chemical etching methods. The image is approximately 4/zm across. (Source: Reprinted with permission from [95].)

Fig. 29. A cross-section TEM of the poSi/Si interface. A diffraction image of each layer is shown as an inset. The crystallinity of the Si layer is obvious as is the amorphicity of the poSi layer. This is in contrast to electrochemically formed poSi which does maintain a measure of its crystallinity. It appears that chemically formed poSi is less crystalline than its electrochemical counterpart. (Source: Reprinted with permission from [95].)

190

POROUS SILICON

Fig. 30. The chemically etched samples can still display the porous features familiar with the electrochemically prepared material as seen in this SEM. The image is 5/zm wide on a side and a depth range of 300 nm. (Source: Reprinted with permission from [97].)

Fig. 31. Another common feature of chemically etched samples are small hillocks, in the range of several hundred nanometers up to a couple of microns. This AFM image is 35 #m on a side. (Source: Reprinted with permission from [229]. 9 1996 American Institute of Physics.)

of chemically etched Si(100) [95]. Both images are approximately 4 / ~ m across. A crosssectional T E M image (Fig. 29) clearly [96] shows the amorphicity of the poSi layer compared to the crystallinity of the Si substrate. The surface of chemically etched samples can display (Fig. 30) porelike features [97] but another c o m m o n structure is that of small hillocks, as in Figure 31 [ 12]. Porous structure can still be found in these samples, such as in Figure 32 [98]. The amorphous character of chemically etched poSi is dominant compared to the crystallinity of the electrochemically prepared samples. Si nanocrystals are sometimes found

191

THOMAS

Fig. 32. An electron micrographshowingboththe poSilayer and the Si substrate. The porous structurein this 200 nm poSi layer is clear in these images. (Source: Reprinted with permissionfrom [98]. 9 1995American Institute of Physics.)

within the amorphous layer, but some have argued that Si crystallinity is not common in these samples and should probably not be associated with the photoluminescence, thereby arguing against quantum confinement models [96]. By contrast, electron paramagnetic resonance (EPR) studies [99] identifying the Pb center and the dangling bond defect in chemically formed poSi suggested that the crystalline nature of the substrate must still be retained. The smallest crystallites ( 1.7-1.9 eV (the Urbach tail). As a rule, such a shape results from random local electric field on the semiconductor band structure. The absorption at hco < 1.7 eV can be attributed to the interaction between wires because it is relatively stronger for InP-A1PO and it is weaker for InP-CA. This interpretation does not contradict the quantum-size effect in InP fragments in nanotubes. However, there is not much to be gained from an estimate of the edge blue-shift within the effective mass approximation because the InP bonds are strained and it is not clear whether the actual QWR size is its diameter or the thickness of the InP layer. The effect of stress may exceed the contribution from confinement, but both are also affected by inhomogeneity of the InP network. In amorphous semiconductors selection rules do not apply and the absorption spectrum reflects a combined density of states from the valence and conduction bands. In crystalline InP the first maximum of electron density lies 2-3 eV below the Fermi level and originates from p-type bonding of In-P orbitals [43]. The distortion of a crystal lattice smears out this maximum and shifts it toward the fundamental gap. The 3.5 eV maximum of the InPCA absorption corresponds well to this picture considering the gap width. The absorption of InP-CA increases rapidly in the vicinity of the band edge with loading (Fig. 15). We interpret this as the result of an extended InP lattice formation, which increases the density of states at the edge. Thus, the absorption spectrum suggests the relative isolation of InP molecules from each other in the coating layer as well as random intermolecular distances compared to the InP lattice spacing. Accordingly, in the thin monolayer coating the InPInP interaction is much weaker than in the bulk and therefore the contribution from InPto-template interaction is important in the balance of forces in these composites. The photoluminescence (PL) spectra of InP-CA have two main bands at 1.5 and 2.2 eV if excited with 514.5 nm line (Fig. 16a) and at 1.5 and 2.4 eV if excited with 457.9 nm

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252

THREE-DIMENSIONAL LATTICES OF NANOSTRUCTURES

line. In bare CA a similar 2.2 eV band was observed (Fig. 16b), which also shifts upward with decreasing wavelength of excitation [42]. That is why the 1.5 and 2.2 eV bands were thought initially as having different origins. A comprehensive study of a number of ensembles of QWRs confined within the different hosts demonstrates similar behaviour independently of the template used [28], The low-energy band was interpreted as the band edge recombination in InP and the high-energy band as the relaxation of excited defects states (e.g,, oxygen vacancies of silica) of the template. We note that the shape of the 2.2 eV PL band for bare and loaded CA (Fig. ! 6) looks very similar, except for a distinct red shift in the PL spectrum for !nP-CA in the range 1.7-2.2 eV. Based on these observations we consider both paths in the relaxation process via the semiconductor itself and via traps in the template to be responsible for this band, The 1.5 eV PL band corresponds to the 1.6 eV width of the InP fundamental gap and can be assigned to an interband relaxation in the InP layer. This band shows the anisotropy of the PL with regard to the orientation of the electrical field in the incident laser beam EL and in the emitted light EeL. The band at 1.5 eV (Fig. 16a) appears when EpL II a. Here a a and ca denote polarisation configurations, where the first letter labels the orientation of EL and the second letter labels that of EeL, c is the direction along and a is the direction across the channel, respectively. The intensity of the 1.5 eV peak is practically independent from the orientation of EL and its polarisation rate is P - (11 - 12)/(11 + I2) = 0.31 for a a / c c , where !1 and 12 are the intensities of the recorded PL under crossed polarisation. The weakness of this band in the EpL II c configuration contradicts common experience for one-dimensional structures and the particular results for monolithic QWRs in asbestos. The 2,2 eV band is also polarisation-dependent with approximately the same values. It is believed that the main contributions to the optical anisotropy of QWRs have: (a) quantum mechanical origin, via the dependence of optical transition matrix elements upon the confinement-influenced asymmetry of the wave functions along and across QWRs and, (b) classical electrodynamic origin, via the difference of depolarisation factors for cylindrically shaped particles. For monolithic QWRs in CA the second contribution was proved to be dominant [8]. Dielectric confinement can be another source of anisotropy for nanoparticles with dimensions smaller than the wavelength of the light )~ and with a dielectric constant very different from that of the template. The latter is true for lattices of QWRs with d/)~ > d. Based on consideration of dielectric confinement it was expected that if EL II c, the field in the lattice would be homogeneous whereas if EL l c , the electric field would be highly modulated, moreover, the PL itself was assumed to be depolarised [22]. Consequently, coupling of the light to QWRs is more efficient for E II c and therefore, the PL intensity should depend on the angle between EL and c in an ensemble of collinear QWRs. However, none of these mechanisms can explain the observed anisotropy of the PL of InP-CA because all of them predict higher PL intensity for E II c. To understand the behaviour of a cylindrical shell QWR, the orientation of electric dipoles should be taken into account. In the dipole approximation, the PL amplitude is proportional to the square of the scalar product of the local electric field and the interband dipole moment. Usually, the dependence upon the dipole moment may be omitted in QWRs [22]. However, if the array of dipoles is configured in such a way that the majority of them is parallel to one plane, then the total anisotropy approachs 100% because the scalar product of two perpendicular vectors is zero. In-P bonds are known to be highly polar and a corresponding molecule can be easily oriented by the local electrostatic profile at the site where it is attached. A defect on the inner surface of the CA nanotube, usually corresponding to an electron vacancy in place of a missing oxygen in the Si-O-Si-O network results in the distortion of the local electrical field. From Figure 17b one can see that PL of these sites is weakly anisotropic. These sites are considered to be favourable for adsorbing TMIn molecules. As discussed earlier, the InP deposit inside CA is formed by weakly interacting InP molecules. Thus, it is reasonable to assume, that in the monolayer-thin coating these molecules are aligned preferentially in the radial direction. The increased anisotropy of PL

253

ROMANOV AND SOTOMAYOR TORRES

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from corresponding sites after depositing the InP layer (Fig. 17a) complies well with the preceding consideration and explains well the observed anisotropy of the 1.5 eV PL band. The polarizability, related to the dielectric constant, of the thin-wall InP QWRs is smaller than that of the monolithic QWR with the same diameter and depends upon the coating thickness [23]. Consequently, the dielectric inhomogeneity (depolarisation factors) and the dielectric confinement are both much weaker in the lattice of InP nanotubes. The foregoing arguments point to the other limit to explain the PL anisotropy, where the anisotropy due to the electric field redistribution loses out to the anisotropy due to the dipole orientation [44]. Increasing the excitation power results in the saturation of the 1.5 eV band (Fig. 18a) and the splitting of the 2.15 eV band into three bands (Fig. 18b). It is reasonable to assume that these latter bands originate from asbestos defects (see Fig. 18c) but their appearance is greatly affected by the InP deposition, because they can efficiently trap electron-hole pairs photogenerated in the InP layer. This behaviour assumes the selective population of defect states, the emission peaks of which are at 1.75 eV (Fig. 18b insert). Taken into account the higher anisotropy rate for this band, it was concluded that these defect states are situated on the channel surface. This strong deposit-template interaction is only possible in the case of incomplete coordination of an InP lattice in an atomic-thin layer. A test sample was prepared using etched asbestos (EA), which the total surface of internal voids exceeding that of CA by up to 100 x due to the removal of the magnesium layers from the roll-like asbestos structure. Additional channels in the EA structure are expected to be unevenly distributed and intersecting each other within the asbestos fibre because of the accidental shrinking of the silica frame. After InP deposition the InP-EA sample contains much more InP layers then the InP-CA sample of the same volume, moreover the 0.4 nm separation of InP layers makes their interaction more effective. The absorption spectrum of InP-EA shows a much sharper edge than InP-CA and its PL spectrum contains only the band at hw ~< 1.5 eV. The emission from InP-CA shows an intermediate case between those of InP-A1PO and InP-MCM because they contain either a PL band characteristic of the template or the InP emission. Emission spectra of the bare A1PO zeolite and InP-A1PO zeolite look very similar (Fig. 19a), that means the incorporation of InP does not affect appreciably the

254

T H R E E - D I M E N S I O N A L LATTICES O F N A N O S T R U C T U R E S

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(c) Fig. 18. (a) Redistribution of the low-temperature PL spectrum from InP-CA after increasing the excitation power by a factor of 56. Arrows show the position of emission bands. (b) Distortion of the room temperature PL spectrum of InP-CA after increasing the pumping power by a factor of 64. (Inset: Ratio of the PL spectra at Pex and 64Pex for InP-CA and bare CA.) (c) Similar to (b) for bare CA. (Inset: Absorption of bare CA showing the energy position of defect impurity bands in the forbidden energy zone of CA, which correlates with the PL spectrum of bare CA.)

way the energy relaxes. The only difference is the relative increase of the PL intensity at energies below 1.7 eV for InP-A1PO. In contrast, the PL spectrum of InP-MCM exhibits radically different behaviour. As shown in Figure 19b, the bare MCM template produces a PL spectrum typical for silica defects with the maximum following immediately the laser line at 2.2 eV, whereas the InP-MCM composite shows a strong band at 1.85 eV followed

255

ROMANOV AND SOTOMAYOR TORRES

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by a low-energy luminescence band arising from unavoidable bulklike deposit on the outer side of the MCM granules. Lowering the temperature results in: (i) an increase of the lowenergy part of the spectrum associated with transitions from the semiconductor component at h~o < 1.8 eV and, (ii) a blue-shift of the upper PL band from 1.85 to 1.93 eV. The PL spectra of three InP-MCM samples possessing channel diameters 2.8, 3.2, and 3.6 nm were infilled with InP under the same conditions. As the channel diameter decreases from 3.6 nm, the 1.85 eV PL band shifts to a longer wavelength for the 3.2 nm diameter to merge with the low-frequency band for the 2.8 nm channel (Fig. 20a). With increasing power of excitation the PL band at 1.7 eV increases faster than PL from template traps at 2.2 eV and the band-to-band transitions in the bulklike InP component (Fig. 20b). The PL spectra of structurally confined QWRs can be interpreted by a model taking into account excitation relaxation via two competing channels: one within QWR and the other through the QWR-template interface. Starting with the PL of the bare template, it is seen that excitation and relaxation in the relevant energy range involve only states of the silica defects (Fig. 21 a). When the infill concentration is small, the density of the InP electronic states is likewise small. The InP states are correlated geometrically with the states of silica defects because InP starts to grow at silica defects and also energetically, because defects accept electrons from the InP. These states overlap with the low-energy tail of the silica defect impurity band in the fundamental gap of the template. Figure 2 lb illustrates this case, where absorption of radiation takes place primarily in the InP component, but the relaxation proceeds via trapping of photoexcited electron-hole pairs by defects of the template followed by recombination between defect and valence bands of the template. As the semiconductor content increases, the band structure of QWRs themselves is formed. The band scheme of the composite (Fig. 2 lc) now looks like that of two solids in contact with their electrochemical potentials aligned. The recombination of the photoexcitation via states of QWRs dominates, because the traps in the template are spatially isolated from the body of the semiconductor [28]. The PL spectra of InP-A1PO show the radiative recombination accordingly to Figure 2 lb, so that the InP species are well isolated from each other in the zeolite channels

256

THREE-DIMENSIONAL LATTICES OF NANOSTRUCTURES

Fig. 20. (a) Red shift of the PL band of the InP deposit in MCM41 with decreasing diameter of the hollow wires. Numbers indicate the channel diameter. (b) Ratio of the PL spectra of InP wires in MCM41 after a four-fold increase of exciting pumping power. Note the discrete character of the variation assuming the superlattice type of the energy band structure.

Fig. 21. Proposed model to explain the photoluminescence of InP-loaded templates with different strengths of interface interaction. (a) Bare template, (b) lightly loaded template, PL from template traps is of the same strength as from InP, (c) heavily loaded template, absorption, and emission within InP deposit prevails.

and the interaction InP-template plays a major role. This conclusion agrees well with the assumption that polar InP molecules are very sensitive to the inhomogeneities of the template potential landscape, especially at the site of o x y g e n vacancies. The existence of two PL bands in the case of InP-CA shows the equally probable recombination via Figure 2 l b

257

ROMANOV AND SOTOMAYOR TORRES

and c. Increase the pumping power, the recombination via QWR-template interface is more efficient than within the QWR, assuming saturation of the process shown in Figure 2 l c due to the relatively weak overlap of states in adjacent fragments of InP coating. In InPEA, the InP layers can interact with each other strongly increasing the density of electron states in the semiconductor component. Therefore the PL of this material agreed with Figure 21 c. The PL of InP-MCM is qualitatively the same as that of InP-EA probably due to the same reason: interaction through the 0.8 nm thick barrier separating InP layers of adjacent QWRs. However, the recombination proceeds simultaneously along the mechanism shown in Figure 21b too as shown by the presence of the 1.85 eV band, although in this case a separation of recombination paths is hardly possible [28]. If recombination takes place according to Figure 21b, then the intensity of the corresponding PL band should increase faster than the band associated with recombination within the InP QWR with increasing pumping, which it does. In other words, the effect of energy transfer from the infill to template is an essential process taking place in lightly loaded templates, especially if the infill material has high ionicity chemical bonds. The anomalous red shift of the PL band in InP-MCM as the QWR diameter shrinks, can be related to the hollow cylindrical structure of the QWR. Assuming the walls of the nanotube have the thickness of the InP layer while the channels of the template keep the same thickness of template silica. One can see that with decreasing QWR diameter the volume fraction of semiconductor to template becomes larger. In contrast to the "blue"-shift of the PL band due to quantum-size confinement, the overlap integral of states belonging to one and the same QWR increases as well as the overlap of electron wavefunctions of adjacent wires at the QWR-QWR interface. Correspondingly, this trend to a three-dimensionallike configuration moves the electronic structure of the quasi-one-dimensional ensemble toward the bulk.

3.3. Summary Monolithic QWRs in channel templates exhibit both optical and transport anisotropy. However, in wires of ~ 10 nm diameter this anisotropy is the formal result of their geometry instead of the electron wavefunction anisotropy. The effect of the template in structurally defined QWRs is the dielectric enhancement of the optical anisotropy due to the layered structure of the ensemble. In the case of an appropriate infill, such as GaAs, the size quantisation of the electronic band structure agrees with the effective mass approximation. Hollow QWRs, made up from semiconductors with polar chemical bonds stabilised in channel templates, demonstrate an efficient energy transfer at a QWR-template interface. The potential relief of the template surface smears out the peaks of the density of electronic states characteristic to the infill due to the distortion of the crystalline structure of the infill. Optical absorption is found to be dominated by the interaction of structural elements in the wire. Moreover, the absorption edge is broadened and shows the Urbach-type tail. The relaxation of electronic excitation in such composites takes place in the semiconductor and via defects in the template. The interplay of different interfaces in the relaxation processes substantially change the PL spectra of templated nanocomposites when compared to the PL of the similar size but epitaxially grown nanostructures. The main conclusion from the preceding description is that channel templates provide a good method to make QWRs and to study the physical properties of individual wires by arranging them in macroscopically large arrays. Thus QWR ensembles in channel templates can be considered as a promising approach for nonlinear optical material, particularly optical switches.

258

THREE-DIMENSIONAL LATTICES OF NANOSTRUCTURES

4. OPAL-BASED LATTICES OF NANOSTRUCTURES

4.1. Introduction The relatively large diameter of opal voids makes size-induced quantization of minor importance when considering modification of the physical properties of guest materials. Instead, the major impact is on electron transport in opal-based ensembles by varying the strength of coupling between grains. In contrast, the optical properties of opal nanocomposites are defined by large grains and by the commensurability of the grain spacing with the wavelength of the light. In what follows we describe and discuss how the physical properties of opals infilled with semiconductors, superconductors, and insulators are modified. Figure 22 illustrates qualitatively the physical concept behind the operation of opal-based lattices of nanostructures. The general idea about these materials is the formation of a potential landscape at template-to-infill and grain-to-grain interfaces, so that a wave of any sort propagating through such a medium finds itself in a medium with well-defined periodicity. Depending on the type of infill material and physical phenomenon under consideration the electron, photon, or phonon waves, among others, can be considered.

4.2. Lattices of Semiconductor Nanoparticles A straightforward extension of the idea of QD is the construction of regular arrays of dots where the interdot coupling replaces the dot-to-bulk interface. In this case the difference between dot and antidot lattices vanishes. The points of interest in dot lattices include: resonant tunnelling throughout the array, single-electron phenomena under the Coulomb

Fig. 22. Conceptof the operation of opal-based nanocomposites. The ordered real space arrangement of nanoparticles (top) is accompanied by (i) potential profile due to the confinementof electrons in narrow constrictions, in the case of semiconductor infill, (ii) order parameter profile due to size dependence of the critical current in the case of superconducting infilI, and (iii) refractive index profile in the case of insulating infill. Infilling with a suitable guest material these compositescan be thought of as three-dimensional lattices of quantum dots-antidots (i), Josephson media (ii), or photonic crystals (iii).

259

ROMANOV AND SOTOMAYOR TORRES

blockade [45], and the coexistence of magnetotransport phenomena of classical and quantum origin [46]. In the case of an opal, the free space of which is completely infilled with a semiconductor, the potential relief formed by grain boundaries and constrictions, alters charge transport between grains (Fig. 22, upper diagram). Almost identical barriers result in similar transmission characteristics. Two cases can be distinguished: Semiconductors with large effective mass and those with small effective mass. Let us consider first the large effective mass case. If size-induced quantization of the energy band structure is insufficient to distort the energy band diagram in the hightemperature regime, the mean free path of these carriers is larger than the grain geometrical size. Thus, the impact of the geometrical periodic structure is the scattering of carriers at constrictions. Typically, the variation of the grain cross-section is about 1/ 10 between large grains and constrictions. The periodicity of the cross-section variation leads to a different temperature dependence of the conductivity (or (T)) compared to a bulk semiconductor. In the case of semiconductor possessing carriers with a small effective mass, the cartiers are confined by the constriction potential barriers, which separate grains from each other. At high temperature, carriers should tunnel sequentially through these barriers in order to complete the current path. In other words, the nearest neighbour tunnelling between grains is the dominant mechanism for carriers to be transferred through the array, whereas the next-neighbour tunnelling cannot contribute significantly due to the large distance between constrictions. Thus, the conductivity is governed by the tunnelling probability. At low temperature such a composite contains separate electron lakes, which are periodically distributed in a latticelike manner. Because the intergrain distance is comparable to the typical length of electron hopping, a discrete set of hopping distances is allowed in this material, which manifests itself in a specific dependence of the resistance R(T) at low temperatures. Furthermore, if the grains accommodate only a few free electrons, the charging energy associated with electron transfer, or Coulomb blockade, will restrict the electron transport.

4.3. Lattices of Superconductor Nanoparticles Impregnation of opals with superconducting metals results in a lattice of superconducting grains directly coupled by bottlenecklike constrictions, that is, the opal-superconductor composite can be represented by a lattice of S-c-S links, where c denotes constriction (Fig. 22, middle diagram). Generally, these constrictions behave like weak Josephson-type links. The critical current Ic, being a function of the cross-section, is different in a grain and in a bridge. Correspondingly, when such an ensemble sustains a current greater than Ic of the bridge, an ensemble of alternatively positioned and dynamically maintained superconducting and normal regions appears. The lattice regularity considers all bridges to be identical over the lattice. In this medium the transition from superconducting (S) to normal (N) states passes through the so-called resistive state as the current increases. In the S-state the phase of the order parameter (wave function) is the same over the volume of the superconductor and the whole current is carried by Cooper pairs. In the resistive state the phase slippage occurring at each link gives rise to the voltage drop A U across the weak link. The current is then carried by both Cooper pairs (supercurrent) and quasi-particles (unpaired electrons), because the number of Cooper pairs is not enough to carry the whole current. When I >> Ic the supercurrent is completely suppressed and resistance is the same as for the N-state at T > Tc. The resistive state is the most interesting state for applications of Josephson media because the S- to N-states transition can be easily externally governed. The main interest of the Josephson junction is its ability to convert the direct current (DC) to the alternating current (AC) at microwave frequency and vice versa so that the AC frequency is directly related to the voltage drop across the junction hw = eV. From this point of view a Josephson medium made out of identical junctions is an ensemble

260

THREE-DIMENSIONAL LATTICES OF NANOSTRUCTURES

of coherently operating microwave generators or detectors, the output of which can be summarised as either ,~N or ~ N 2 depending on the type of coupling mechanism [47].

4.4. Lattices of Insulating Nanoparticles The basic optical property of dielectric particle arrays is the scattering of light. Bare opal is the regular assembly of silica spheres which can efficiently scatter incident light. It is known that the scattering ability of individual scatterers approaches its maximum at Mie resonance, when the scattering cross-section exceeds by several times the geometrical cross-section of the scatterer. It is clear that the scattering strength, or the distortion of the incident wave caused by the presence of the scatterer, depends on the difference between the refractive index (RI) of the scatterer and of the surrounding medium. In disordered and ordered dense ensembles of identical scatterers, the role of Mie resonance is less important because all scatterers become optically connected. In the case of ordered ensembles the diffraction takes place, namely, the Bragg resonance. It is known that by approaching synergy of individual and collective scattering resonances, the total scattering strength increases dramatically. With increasing scattering strength, the interference between incident and reflected waves gives rise to a qualitatively different phenomenon: the formation of spectral intervals where no propagating mode is allowed. Analogously to the electronic bandgap energy structure, this optical phenomenon was called photonic bandgap (PBG). In other words, the dispersion of photons in such an ensemble acquires the sequence of forbidden zones or photonic bandgaps. The photonic energy band structure can find immediate applications to improve contemporary optoelectronic devices. This idea was suggested [48, 49] and was realised experimentally in the wavelength range from microwaves to the near infrared. Various PBG structures have been used as dissipationless resonators, perfect mirrors, and so forth. Opal is a natural diffraction grating for visible light leading to the beautiful display of colours as the opal is rotated under illumination with white light. Thus opal has been considered a precious stone since ancient times for jewellery purposes. However, bare opal possesses not a complete but a "semimetallic" photonic bandgap because of the insufficient contrast between the RI of its silica carcass and air in its empty voids [50, 51 ]. This is why the impregnation of opal with high RI semiconductors was tackled in the quest to design a true three-dimensional PBG material in the visible. Such a three-dimensional PBG is necessary to reduce energy losses in the bandgap region (Fig. 22, bottom diagram). The most interesting issue concerning PBG materials is the dissipationless control over the emission spectrum of a light emitter integrated with a photonic crystal, due to the suppression of the spontaneous emission in the photonic gap. This defines the next problem, namely, the design of light emitting structures, where the emitter is embedded in the opal framework and its emission wavelength is close to the photonic bandgap. By fulfilling these conditions, one can expect a sharp increase of the emission efficiency either at the photonic bandgap edges or in an intentionally introduced defect radiative mode within the bandgap region. The additional gain is acquired from the substantial suppression of energy leakage via spontaneous emission in the vicinity of the emission band. Further consideration of opal-based materials is limited to these three cases, although a number of experiments have been performed outside this scope. The investigation of the thermal conductivity in opal-based materials [13, 52, 53], thermo-electron emission [54], and phase transitions in ordered arrays of nanostructures [55] is worth mentioning.

4.5. Structure and Composition of Opal-Based Materials Opal consists of identical silica spheres with a size dispersion within 5% [56]. The diameter D of opal spheres can vary from 150 to 900 nm [57]. The optical diffracting properties of opal define its value as a gemstone as well as an optical material. Opals come as blocks

261

ROMANOV AND SOTOMAYOR TORRES

Fig. 23. SEM images of an accidental cleave of the opal at low (a) and high (b) magnifications. The (111) and (100) planes are clearly seen in both micrographs.

with sizes in the centimeter range while keeping a good quality of crystallinity throughout. Besides, the strength of opals is high enough for mechanical machining. The identical size spheres comprising an opal, allow their assembly in a close threedimensional lattice with fcc symmetry. Figure 23 shows the opal structure in a scanning electron micrograph (SEM) of accidental cleave of the lattice. The (100) and (111) crystalline planes are clearly seen demonstrating the three-dimensional nature of the package. These voids form their own regular lattice [58]. There are two types of alternatively positioned voids in the opal lattice. O-voids, which are eight-fold coordinated large voids with a characteristic size d l = 0.41D each connected with eight T-voids, which are four-fold coordinated small voids with d2 = 0.23D. These voids are connected via windows of a minimum characteristic diameter d3 --0.15D. The porosity of the ideal fcc package of spheres is ,~26%. Opals usually are textured polycrystals with crystallites of up to 100/zm in size, but by special means these crystallites can be made larger and oriented with (111) plane to the surface. The main opal spheres consist of smaller spheres of 30-40 nm diameter, which in turn are composed of particles of 5-10 nm diameter. Thus the total porosity of opals can approach 59 vol% arising from the 26, 19, and 14% porosity corresponding to the previous hierarchy of size [52]. The actual porosity of the opal can be either above or below this value depending on the synthesis history (sintering conditions, interstitial cement). One can refer to Ref. [59] to compare how the opal appearance depends on the amount of additional amorphous silica in large voids. The in-void synthesis routine can result in either complete or partial filling of a free space in opal: complete infilling is approached by impregnating the opal with a molten guest material whereas partial infilling is realised by, for example, chemical synthesis of the "ship-in-the-bottle" type and by chemical deposition of thin layers on the inner surface of the opal voids. The first and last methods preserve the initial ordering of the grating, whereas the second one introduces disorder due to the uncertainty of nanoparticle size and position in a void.

262

THREE-DIMENSIONAL LATTICES OF NANOSTRUCTURES

Fig. 24. SEM images of completely infilled opals. (a) The (111) plane of the In-opal. (b) Threedimensional mesh formed by a semiconductorin the InSb-opal. (c) T-grains on top of O-grains in the Te-opal.

High-pressure infilling of opals has been performed in the same manner as infilling of zeolites (see Section 2). Metals and semiconductors including In, Pb, Sn, Bi, S, Se, Te, InSb, and BiPb alloy were introduced into opal voids to study electrical conductivity and superconductivity in these composites. The common feature of all these composites, is that the guest occupies all the available volume, thus forming a precise three-dimensional replica of the opal (Fig. 24). Transmission electron micrograph (see Fig. 25) shows that metal introduced in the opal by this method occupies only O- and T-voids with connecting

263

ROMANOV AND SOTOMAYOR TORRES

Fig. 25. TEM image of a completely infilled Te-opal. (Source: Reprinted with permission from [60]. 9 1997 American Institute of Physics.)

Fig. 26. Schematics of the grain lattice in the opal. Full circles: O-grains. Shadowed circles: T-grains. Each pair of O-grains is connected by two equivalent channels via T-grains.

bridges [2, 58]. In this case the guest grains arrangement looks like that shown schematically in Figure 26. In principle, depending on the synthesis method, there could be a difference of the actual position of nucleation centres, where the guest material starts to grow. Nevertheless, TEM investigations of opal-based composites show that only large O- and T-voids take part in the in-void synthesis [58, 60]. In order to examine these possibilities the opal was

264

THREE-DIMENSIONAL LATTICES OF NANOSTRUCTURES

Fig. 27. TEM images of Te grains in the opal. Space coordination with respect to spheres (top) and bottleneck bridge between O- and T-grains. (Source: Reprinted with permission from [60]. 9 1997 American Institute of Physics.)

impregnated with tellurium both under the high pressure and by wet chemical synthesis. In the case of pressure-made composites, the shape of the Te particle corresponds well to the geometry of the opal void (Fig. 27). Moreover, it was shown that Te keeps the same crystallographic orientation, or monocrystalline structure, over several adjacent voids and bridges, that is, as the melt temperature of the melt is lowered the directional crystallisation takes place [60]. On the other hand, the in-void chemical synthesis of Te resulted in a different distribution of the infill. Moreover, after seven repetitions of the synthesis procedure, the homogeneity and ordering of the particle lattice was still not approached. In fact the following was noticed: some voids remained empty, nanoparticles tended to adopt the oval shape, they are separated from each other by vacuum gaps, and they do not make

265

ROMANOV AND SOTOMAYOR TORRES

Fig. 28. TEM images of semiconductor grains prepared in the opal by multiple-step in-void synthesis. Top: Te-opal. Reprinted with permission from Ref. [60]. Bottom: CdS-opal. (Source: Reprinted with permission from [63]. 9 1995 SociettaItaliana di Fisica.)

contact with the void surface over the void perimeter while the void surface is accidentally partially coated with a 4-6 nm thick Te film (Fig. 28, top). The following model was proposed for nanoparticle growth: (i) during the first synthesis cycle tellurium forms as thin film areas on the void surface, (ii) any subsequent cycle continues the growth of tellurium on this site. In fact, microdiffraction shows that even after the first cycle the Te film is of polycrystalline structure. Similarly, indium nanoparticles have been synthesised in opal voids by chemical process: (i) impregnation of the opal with a solution of indium nitrate, (ii) thermal

266

THREE-DIMENSIONAL LATTICES OF NANOSTRUCTURES

CdSe-opal

CdS-opal InP-opal GaP-opal TiO2-opal 3.4 vol.% TiO2-opal 0.4 vol.% ,

I

200

,,

....

I

,

,

,

I

400 600 Raman Shift (cm

,

,,

I,

,

800

Fig. 29. Roomtemperature Raman spectra of semiconductors synthesisedin opal voids. CdSe- and CdSopals contain the semiconductornanocrystallites similarto those in Figure 28 bottom. InP-, GAP-,and TiO2-opals were produced by a thin film coating of the inner surface of the opal.

decomposition of the nitrate to indium oxide, and (iii) reduction of this oxide toward metallic indium in a flow of hydrogen [61 ]. This method results in the partial infilling of opal voids with metal so that 16.9 vol% of the O- and T-voids is occupied. For the majority of semiconductors high-pressure impregnation is not suitable because their melting temperatures are above the temperature at which opal becomes soft ( ~ 1000 ~ and loses its porosity. Therefore, the synthesis of the guest should be made in-void to avoid damage to the opal structure. Composites with CdS and CdSe guests occupying a fraction from 0.1 to 10% of free internal volume [39] have been prepared by a multiple-step procedure. It starts with the impregnation of the opal with a Cd(COO)2 water solution. After drying, this composite is exposed to a flow of H2Se (H2S) that results in the formation of CdSe (CdS). To vary the content of the guest in the opal the dilution rate may be changed or, alternatively, the procedure may be repeated. It is difficult to approach the homogeneity of the semiconductor distribution across the opal volume because the solution disperses to separate drops if dried. The Raman phonon spectrum of CdSe in the opal shows the LO phonon at 209 cm -1, which corresponds to the bulk phonon of CdSe (Fig. 29). An improved technique of CdS synthesis employs the catalytic activity of the void surface for a more homogeneous infilling of the opal internal volume [62]. In this case the semiconductor synthesis occurs in the liquid phase without drying and the reagents are delivered to the voids continuously via

267

ROMANOV AND SOTOMAYOR TORRES

diffusion in the solution. With this method more than 90% of the free volume was loaded with CdS. However, the structure of synthesised CdS is far from crystallinity as the Raman spectrum revealed (Fig. 29). Another approach consisting of a simultaneous treatment of the opal in a flow of Cd and sulphur vapour results in a homogeneous loading of opal voids with CdS [63]. Scanning transmission electron microscopy (STEM) revealed the semiconductor in the form of nanoparticles with typical average size "~ 10 nm, occasionally filling up the intemal voids of the opal (Fig. 28, bottom). Because the Cd vapour flow temperature is near 900 ~ the porosity of the opal was reduced to 4 vol% as a result of the distortion suffered by the spheres, which acquired a shape with a truncated cubelike appearance. A thin layer coating of the void walls was achieved by absorption of, for example, S, by CVD, for example, TiO2 and by MOCVD, for example, InP. The gas-phase reactions taking place in the opal is essentially due to the catalytic activity of the defects on the surface of the spheres. Correspondingly, the guest material is smoothly spread over the inner surface of the voids. MOCVD was used to grow InP and GaP inside the opal. First, trimethylindium (1.9 x 10 -5 mol min -1) was added in a flow of H2 at 52~ forup to 4 h. Second, phosphine (8.9x 10 -4 mol min -1) was passed through the reactor for several hours at 350 ~ to decompose the hydride. For higher loading of InP a cyclic growth was carried out with the preceding cycle repeated. Although the growth temperature is very low compared to that normally employed in InP MOCVD, the procedure resulted in a measurable InP growth within the opal. InP is incorporated with a highly distorted lattice due to the interaction of the InP layer with the incommensurable substrate, as demonstrated by the phonons shift in the Raman spectrum of InP in the opal, where lines at 319 and 328 cm -1 are related to the TO and LO phonons of bulk InP at 303 and 345 cm -1, respectively (Fig. 29). The homogeneity of the guest loading was analysed by EPMA scanning a length of 20/zm with a resolution of ,~0.5/zm and by SEM for in-void inspection. The guest content was found to be within 0.5 % of the mean value on the sample cross-section [41]. TiO2 coating was grown in the opal by sequential deposition of monolayers [64, 65]. Each step consists of the adsorption of TIC14 molecules which substitute surface O H groups. This is followed by exposure to water vapour for the transformation of TIC14 into TiO2. Up to 20 repetitions TiO2 crystallises as anatase and with further thickness increments the rutile structure dominates. Phonon lines similar to rutile are observed at 143, 447, 612, and 826 cm-1 together with a two-phonon band at 200-300 cm-1 in the Raman spectrum of the opal containing over 3 vol% of TiO2. These lines are quite distinct from the anatase phase of TiO2, where the 139 cm -1 line dominates (Fig. 29). Absorption spectra show the absorption edge near 3.2 eV, which is blue-shifted from the 3.05 eV band edge of bulk ruffle. PbSe was synthesised in opal voids by impregnating the bare opal first with a water soluble salt of lead and then treated in H2Se flow [13]. The volume fraction of PbSe was up to 63 vol% of the void volume. X-ray diffraction analysis showed the crystal structure of the PbSe deposit to be comparable to that of the bulk semiconductor. The silicon nanoparticles were formed in opal voids using a CVD process of thermal decomposition of 5% monosilane mixed with argon. The pressure gradient inside the opal, due to the high hydraulic resistance of the porous structure, results in an infill profile which decreases as a function of depth away from the surface of the sample. The concentration profile of a 300/zm thick sample starts from a 100% filling of opal voids at a depth of ,~ 100/zm and decreases to 0% at 200/xm deep [66]. The Raman spectrum of the Si-opal shows a feature at 480 cm -1 with a half-width of 70 cm -1, characteristic of amorphous silicon. Further annealing of the Si-opal at 800 ~ in vacuum, results in the formation of nanocrystalline Si, accordingly to the changes observed in the Raman spectrum. Using the model of optical phonons confinement, the crystallite size was estimated as 4 nm and their volume fraction in the double amorphous-nanocrystalline phase was estimated as 52%.

268

THREE-DIMENSIONAL LATTICES OF NANOSTRUCTURES

The X-ray diffraction pattern of the Si-opal has a very weak peak which is correlated with that of bulk silicon. An alternative determination of the crystallite sizes was performed by modelling the width of diffraction lines as a function only of the volume where coherent scattering of X-rays occurs. According to this method the size of crystallites was found to be about 13-19 nm. The correlation seems reasonably good taking into account the dispersion in crystallite sizes [66]. The distribution homogeneity of the chemically synthesised indium and that of silicon inside the opal was examined by photoelectron absorption of X-rays for samples of different thickness. For impregnation, the opal with 42% of total porosity is chosen, whereas the volume fraction of T- and O-voids is 26%. Correspondingly, the exact place of the In particles formation as well as distribution of the indium infill between voids remains unclear due to insufficient resolution of this method of compositional analysis. Quantitative EPMA was used to study the distribution of infill in opal voids along a 2 5 / z m path on cleaved composites with the resolution "~0.5/zm. In the case of a completely impregnated In-opal and a CVD coated TiO2-opal the homogeneity of the infill distribution stays within 4-0.5 %. In contrast, in the case of a CdSe-opal, prepared by liquidphase synthesis, the guest distribution was found to be highly inhomogeneous. The regions of high concentration of semiconductors scales are within an ~ 1 - 1 0 / z m cross-section surrounded by un-infilled zones of the same size. Depending on how the Cd-salt solution is dried, different inhomogeneous configurations were observed from isolated regions to dendritelike formations across the whole sample.

5. OPAL-BASED LATTICES AS J O S E P H S O N MEDIA

5.1. The Superconducting Transition The superconductor transition in the lattice of coupled In or Sn grains was found to be very different from that taking place in bulk metals (Fig. 30) due to the size dependence of the transition temperature Tc(d) of these "soft" superconductors [67]. For superconductors with a strong electron-phonon coupling, like Pb and the BiPb alloy, Tc remains unchanged. In the following text, considering the superconductor transition effects, we see the dependence of the resistance as a function of temperature, R(T), of these soft superconductors. The coherence length of the low-dimensional superconductor is restricted by its size to = .~-~0d3, where ~0 = 360 nm in bulk In. The coherence length can be interpreted as the shortest distance within which the order parameter (wave function) of superconductivity

t~

~

1

2

50

J.o5

J.55

r

r,K

Fig. 30. Resistivesuperconducting transition normalised to the resistance at T = 4.2 K (curve 1) and its first derivative dR/dT (curve 2) in the In-opal. Arrows identify the positions of maxima of the derivative and numbers at arrows give the size of fragments in nanometers reconstructed from the transition temperature according to empirical correlation. Note that the transition temperature is far above Tc in bulk In.

269

ROMANOV AND SOTOMAYOR TORRES

-

A''

0

_

3.J

_. . . . . .

~

......

r,K

1

.......

_

J.5

Fig. 31. Shift of the superconducting transition of the same sample as Figure 30 from zero (1-dotted line) to H = 30 Oe applied magnetic field (2-solid line). Horizontal arrows show the shift for O- and T-grains, ATcl and ATc2,respectively.

remains unchanged. If ~ < dl, one can expect the co-existence of S- and N-states within one grain, in the opposite case no S - N boundary is available. That is the physical reason which allows us to distinguish two types of superconducting transitions. Experimentally, they were observed as: (i) inhomogeneously broadened transitions in the case of relatively shallow modulation of the superconductor cross-section [67] and (ii) transitions with resistance anomalies and negative magnetoresistance in the grain lattice, where grains are well separated from each other [68]. With the structure of opal voids in mind and taking into account the increase of Tc in the superconductor with reduced dimensionality, one can expect that the fluctuating pairing of quasi-particles first takes place at constrictions and then extends successively to small and large grains. The first derivative of the R(T) curve reveals three well separated peaks (Fig. 30). Using the empirical correlation for In, Tc = 3.41 + 51/d, where d (in nm) is the characteristic size of the superconducting particle and Tc = 3.41 K for bulk In [69], these peaks were ascribed to the successive superconducting transitions of different parts of the d3-d2-d3-dl-d3 nanostructure formed in opal voids: the transition starts in d3, spreads to d3-d2-d3, and ends in dl. Estimations of Tc correlate well with the microscopically determined geometrical size of these parts [58]. It is seen that the final transition leading to zero resistance of the lattice is determined by the transition in the large grains and its Tc (R = 0) lies above that of bulk In by 0.1-0.5 K. It is essential to emphasise, that the appearance of distinct features in the R(T) curve becomes possible only for well-ordered lattices. The critical magnetic field Hc of the superconductor increases as soon as its size falls below the London penetration depth d < )~L [70]. Typically, for In-opal composites with dl ~ 100 nm, Hc increases by a factor of 10 from Hc = 283 Oe of bulk In. Under the external magnetic field the Zci of each i th nanostructure component shifts, thus increasing the broadening of the transition region, as seen in Figure 31, because of the difference in size. The smaller the size of the nanostructure component the smaller the shift A Tcl/A Tc2 = dl/d2, which correlates well with experiments. Another type of superconducting transition was found in the case of deeper modulation of the channel cross-section (Fig. 32). A higher dl/d3 ratio was realised by depositing several tens of monolayers of SiO2 or TiO2 on the inner surface of the opal [68]. The total thickness of deposit was around 15 nm. SEM demonstrated the smoothness of the deposit, from which it can be estimated, that the dl/d3 = 2.7 ratio in untreated opal changes after deposition to 8.5 for the opal with D = 260 nm. The R(T) curve of this sample exhibits a resistance spike of --,5% in magnitude just above the abrupt drop of the resistance to its zero value, which is called the low-T resistance anomaly (LTA). Increasing the dl/d3

270

THREE-DIMENSIONAL LATTICES OF NANOSTRUCTURES

H=OOe

C

,10 1

a.3

1t

~.4

|11

....

t

;J.5 .... a,e

_1___

3,7

1

a.8

I

!

~.9 r.~

Fig. 32. Changeof resistance anomalyas a function of temperature near the superconducting transition temperature as a function of magnetic field. Curves are displaced for clarity and the applied magnetic field in given in Oersteds.

ratio, the Tc(R = 0) decreases in contrast to the size-determined tendency to get larger. This is apparently the result of weakening Josephson links to overcome the size dependence [71]. A smaller resistance peak was found at higher temperature and was called the high-T anomaly (HTA). The LTA disappears under the application of a magnetic field of H = 3 - 5 0 e . Typically, such anomalies have been observed in superconducting nanostructures, parts of which possess critical temperatures, which differ at least by several percent of Tcs. They were explained as the result of imbalance of quasi-particles and Cooper pairs at S-N boundaries [72-74]. The magnitude of the anomaly and its weakness in a magnetic field are common features of the LTA anomaly in an In-opal composite. To use this analogy, the necessary conditions are the absence of quasi-particles-to-pairs equilibrium at the temperature at which the anomaly occurs throughout the components of the In nanostructures and, the summation of this effect over the lattice of identical nanostructures. The nonequilibrium in the grain length scale means that the coherence length should fall below the grain size ~ < 100 nm, otherwise no appreciable change of the order parameter is allowed. Thus, the modulation of the channel cross-section should be high enough to suppress the coherence length. An important message from previous considerations is that any small current at an intermediate temperature between T (R = 0) and T (R = R N) is carried both by quasi-particles and Cooper pairs and that is important for further discussion on the penetration of magnetic field in opal-based networks. The suppression of the LTA by a magnetic field, induces a pronounced negative slope in the resistance which persists in R-H coordinates at a temperature where the superconducting gap is developed (Fig. 33, left). The HTA corresponds to the temperature range of the superconducting transition in the constrictions Tcct3(d = 10 nm). Similar to the LTA, a negative magnetoresistance is found to accompany this anomaly, but the field scale is around 100 x higher in proportion to the size-dependent increase of the critical magnetic field (Fig. 33, fight). Thus the difference between lattices exhibiting R(T) transitions obeying these mechanisms is the difference between nanostructured material and the ensemble of coupled nanostructures.

5.2. Dynamic Properties of the Grain Lattice The important question to be answered with regard to lattices of superconducting nanostructures in the opal host is the type of superconductivity they belong to. In practice, this is a problem of critical current Ic and/or critical magnetic field Hc. There are three structural arguments that make opal-based superconducting composites very different from other granular superconductors. We have already mentioned that Hc is enhanced because

271

ROMANOV AND SOTOMAYOR TORRES

a

3.492

%

l _ d

-10

-5

.

0

~

5

....

I

H, Oe

1.76

3.61 1.74

"t

4.11

O

1.72 t

3.475 4 t

I 3.41

'*'~.

1.70

0

100

50

H, Oe 150

Fig. 33. Changein the magnetoresistance at T < Tc (a) and at T > Tc (b). The curve labels are temperatures in K.

the London penetration depth exceeds the characteristic size of the nanostructure components. Another relevant structural parameter is the multiple loop arrangement defined by the superconducting network. Certain effects should also come from weak links incorporated regularly in any current path crossing this network. In contrast to nonordered granular superconductors, the discreteness and strict hierarchy of loop diameters has a major effect. The current-voltage (I-V) characteristics of all superconducting metals incorporated in opal voids exhibit the characteristic shape of individual Josephson junctions (Figs. 34 and 35). This is the well-defined superconducting state at I < Ic, the extended hyperbolic shaped resistive state V ,~ ( I - Ic) n (n < 1) at I > Ic and the Ohm law branch, where resistance is equal to that of the normal state just above the Tc [47]. Most of granular superconductors can be characterised by the same behaviour with one exception: the parabolic I-V curve of the resistive state instead of the hyperbolic I-V curve. The latter is characteristic of the Josephson junction and two-dimensional arrays of superconducting antidots. In both cases the hyperbolic I-V curve can be ascribed to the strictly pinned magnetic vortices, either Josephson vortices confined in the junction area or to Abrikosov vertices pinned on the regular lattice of antidots. It was demonstrated experimentally that a hyperbolic I-V curve could be transformed into a parabolic one by intentional disordering the grain lattice in opal. The essential difference of the Josephson medium from the single Josephson junction is the magnitude of Ic -- 0.1-10 A, which is at least a factor of 104 larger than that of a single bridge. However, the Vc = I c R N , where RN is the resistance in the normal state, is

272

THREE-DIMENSIONAL LATTICES OF NANOSTRUCTURES

~f

1.5

-1

.m

(A) 1.2

I

(At ,0.8

---

S

.....

0.9

1.0

G

I

0.6

..w

,p, ' J

.

0.6

0.4 T-4.2K 3 37 K

0.3

.0

,! .

,,t

l ....

t

~

I .....

A

_

,

J

0.2

0.0

w

0

40

80 U (mV)

T ..........

- F

" .......

0 l

0.4

~

|

"

9

0.8

' "

!

-

U (mV)

--!-

I

9

(A)

.-o

600

200

,//

..... ....Jr

.

t r

i

400

H = 30Oe I f 100

r .... • . . . . O-Sn T=3.97 K

0

L

0

..

Z.

0.1

i

,J

O-Sn T = 3.925 K

. . . . . . . . . . .

0.2U(mV) 0

i_ . . . .

, .....

h

200

---_-C

0.4 U(mV) 0.8

Fig. 34. Current-voltagecharacteristics of opal-based superconducting nanocomposites. (a) BiPb-opal at T 4-6 T, which is higher than for b u ~ samples. In general, geometrical confinement effects can be neglected when considering the density of states, which is then described by Landau levels [45], if 2lcycl 1 T) comprise the background. The midscale (AB ~ 1 T) and short-scale (AB < 1 T) fluctuations were extracted from the background (Fig. 52). Their Fourier transforms show that they are quasi-periodical fluctuations (QPF) with a characteristic period 0.96 and 0.28 T, respectively. Midscale patterns demonstrate the correlation through the whole temperature range with a small change at T < 200 mK. Near the 1 K limit the oscillations appear more periodic than at 0.05 K. It means that the source of these QPFs is not temperature sensitive. In contrast, short-scale QPFs are less correlated with each other and their correlation energy [103] can be estimated to be Ec ~ kT = 0.04-0.05 meV. At 0.06 K the short-scale Fourier spectrum peak spreads over a wide range maintaining the periodicity. To understand this magnetoresistance it is necessary to refer back to the structure of the QD lattice. It has been shown that tunnelling is the only mechanism for charge transfer between QDs. Due to the lattice arrangement, QDs within the first coordination sphere can be reached by hops of the same length, then there is a gap up to the next neighbours and so

290

THREE-DIMENSIONAL LATTICES OF NANOSTRUCTURES

1,2

~ . 5000[.,

~,~ 4000I

mmm

/ 9

II

1,1

/ t:'/

77

/ 1,0

'

0

i

'

,;,'

;

B (T) Fig. 50. Magnetoresistance of the InSb-opal at T = 3.2 K. Inset: Semilogarithmic R(I) dependence at B = 0. Note the similarity with Figure 40. Increasing the homogeneity of the current distribution in the near-zero field the negative magnetoresistance becomes less pronounced, probably due to the delocalisation of carriers. Curve labels are the bias current in nA.

3x10 s

E O 2xl 0 5 I:Z:

lx10 s

0

8

4

e (T)

12

Fig. 51. Change of the magnetoresistance with decreasing temperature in the InSb-opal. Labels are temperatures in millikelvins. The source of R (B) curves distortion is unclear. Apparently the magnetoresistance maximum can be associated with a resonance of the/cycl with the size of constriction. Because/cycl ~ n 1/3/B, with decreasing concentration this resonance appears at a higher field.

on, that is, there is only a discrete set of h o p lengths available. T h e probability of interdot t u n n e l l i n g is affected by the m a g n e t i c field b e c a u s e the w a v e f u n c t i o n overlap for electrons in different dots d e c r e a s e s and, in turn, the overlap can differ for hops within different c o o r d i n a t i o n spheres. This is a s s u m e d to be a source of the large-scale m a g n e t o r e s i s t a n c e

291

ROMANOV AND SOTOMAYOR TORRES

Fig. 52. Short-(a, c) and mid- (b, d) scale fluctuation patterns of the magnetoresistance of the InSb-opal at T = 1 K and 60 mK. Fourier transforms demonstrate the appropriate length-scale of these oscillations, which are related to the T-grain size (d2 = 50 nm) and the diameter of the minimum loop for carriers circulating between two adjacent O-grains via T-grains (--90 nm).

pattern. It is worth noting the strong contrast between the magnetoresistance of ordered and disordered materials because, for the latter, the magnetoresistance increases exponentially with the field [ 102]. On the other hand, the background underlying these peaks shows a continuous distortion with temperature. The shift of the curve maximum to larger field can be associated with the resonance of the cyclotron orbit diameter with a particular geometrical characteristic of the grain structure. Freezing out free carriers with decreasing temperature leads to a permanent increase of the magnetic field magnitude needed to meet resonance conditions. Considering the similarities of these fluctuations to the A h a r o n o v - B o h m oscillations, it seems likely that these QPFs are due to quantum interference, because loop diameters extracted from the oscillation period,

where A B is the oscillation period, are 46 and 86 nm (Fig. 52) which in turn are similar to d2 and dl in this sample, respectively. Another contribution to the short-scale QPF

292

THREE-DIMENSIONAL LATTICES OF NANOSTRUCTURES

can arise from the interference of the electron virtually visiting neighbouring QDs during the hop [ 104]. For example, with D = 227 nm the smallest loop formed in the (100) plane is a square with D / ~ -- 92 nm side. Due to Coulomb barriers the probability of performing Aharonov-Bohm oscillations in large loops in a geometrically ordered lattice is suppressed. Moreover, different orientations of loops with respect to the magnetic field together with lattice imperfections wash out the Aharanov-Bohm oscillations. The fluctuation patterns superimposed on the smooth magnetoresistance background contain information about the phase-coherence length l~0 due to the quantum interference term arising from the annular structure [ 105]. An analysis of the power spectrum can be used to estimate the localisation length in this network of conducting wires. In the case of noncoplanar loops randomly distributed in three-dimensional the Fourier components F~ of magnetoresistence fluctuations are related to the average phase-breaking length ~ by F/~ "~ C e x p ( - 2 ( L ~ ) ) where C corresponds to the number of loops of a given area in the sample and (L~) is the length of the shortest path starting and finishing at the same point. Therefore, the power spectrum of magnetoresistence fluctuations should decay exponentially with an exponent inversely proportional to the average length. An order of magnitude of the phase-breaking length can be obtained using the approximation function, 8(zra)0.5) 2 lOgl0(F/~) = 0.434 c where am~

(L~) 4~r

Parameters c and ~ can be estimated from the least-squares fit of this function to experimental data shown in Figure 52. This fit yields ~ to be 320 and 305 nm at 60 mK and 1.02 K, respectively, which is longer than the separation from the first coordination sphere. This length exceeds the circumference of smallest loops d ,~ D / ~ in the network and the next small loop with d ,~ D. For a sample with a higher electron population ~ was found to be 10 • larger, consistent with lower barriers resulting from their better transparency when the system has a higher Fermi energy. The Hall resistance behaviour (Fig. 53) also correlates with the Coulomb blockade. The low-temperature Hall concentration increases linearly with bias, that is, n n "~ I , which is a direct consequence of the increase of sample volume involved in the charge transfer. The zero-field anomaly of the Hall resistance (Fig. 53a) is apparently due to electron focusing in the multiple coordinated QD network. Another result of the blockade is the saturation of the Hall resistance with field because the Hall potential developed across the QD is not enough to overcome the Coulomb barrier. Thus, the electron reservoir is only partly involved in the formation of the Hall voltage across the sample. Increasing further the magnetic field leads to smaller wavefunction overlaps which result in a diminished probability of electrons reaching the Hall probes (Fig. 53b). This is manifested as a decrease of the Hall resistance. For the semiconductor, the electrons of which do not suffer from confinement in sizescale provided by the opal, the main difference in conductivity modifications between bulk and opal-embedded is the change in scattering mechanism. In the PbSe-opal [85] the resistivity does not change its functional behaviour when the volume fraction of PbSe in voids changes from 82 to 63%, which correlates with the absence of the confinement mechanism (Fig. 54, top). The mobility of carriers is much smaller in the PbSe-opal than in bulk PbSe and exhibits another type of temperature dependence (Fig. 54, bottom). To explain this difference, a diffuse scattering at the PbSe-template interface was invoked in addition to

293

ROMANOV AND SOTOMAYOR TORRES

5'0X104

~ '0x104

,

E

cO

0,0

O, 0,0

-5,0xl0 4

-5,0xl0 4

) i

-1

I

0

|

I

1

i

I

2

,

3

-15-10

B (T)

-5

0

5

10 15

B (T)

Fig. 53. Low-fieldscale (a) and high-field scale (b) traces of the Hall resistance of the InSb-opal. They show the fluctuation pattern and the change of sign of the Hall voltage. The former is the result of carriers encircling the structurally defined loops. The latter can be associated with the change of the transmission of intergrain barriers in a high magnetic field.

ionised impurity scattering. This structure-dependent scattering mechanism dominates all over in nanostructured composite.

6.3. Conclusions We have demonstrated that the conductivity of a three-dimensional QD lattice of semiconductor grains in the opal is dominated either by interdot tunnelling or scattering at the semiconductor-template interface. Intergrain tunnelling is accompanied by thermal activation in the high-temperature regime and becomes macroscopic quantum tunnelling at low temperatures under the Coulomb blockade regime. The lattice arrangement of QDs results in a softening of the Coulomb gap in the single-electron regime. For highly resistive arrays, the Coulomb blockade appears as a staircase in the I-V curves denoting single-electron transport. The classical magnetosize effects due to electron scattering in the periodically modulated confining potential of the three-dimensional lattice, results in a pronounced negative magnetoresistance (NMR). At low temperature, the quantization of the magnetic flux penetrating through the lattice induces multiple periodic oscillations which appear superimposed on the smooth magnetoresistance background. Due to the discrete arrangement of QDs in the opal-semiconductor lattice, the high-field magnetoresistance behaviour deviates from the classical law. In addition, saturation of the Hall resistance with respect to the linear behaviour in the large-field scale appears due to the Coulomb blockade, whereas its shortscale deviations near zero field may be attributed to the electron focusing within QDs as multiple-terminal junctions. The change of the scattering mechanisms results in a much weaker effect, but it can also be used for modification of the semiconductor properties with a proper design of the nanocomposite material.

294

THREE-DIMENSIONAL LATTICES OF NANOSTRUCTURES

o [] ~

~a

~

oo~o

o ~

II

~z

--

-_

+

+""+"~'+""'1"~

%

++..+~.~_ + +§f ++

-

"

4+

-

+

I

1

I IlJll

I

i

I

1 JJlJl

10

1 .

T,K

100

/os

/0 ~ Q

l"

10-I

1

~ I

11111

l

1

t

I J anll

10

1oo

..,

l

1

n__

3OO T, K

Fig. 54. Top: Resistivity of the PbSe-opal for different PbSe loading as 82% (1) or 63% (2) of void volume fraction. Bottom: Mobility in PbSe-opal (1, 2) and bulk PbSe (3). (Source: Reprinted from [85].)

7. OPAL LATTICES AS PHOTONIC CRYSTALS 7.1. Introduction

Photonic bandgap (PBG) materials have been designed to control the spontaneous emission and to modify the light-to-matter interaction in solids by introducing an energy band

295

ROMANOV AND SOTOMAYOR TORRES

structure for the propagating light. By definition, a PBG crystal is a three-dimensional periodic structure made of "optical atoms" (scatterers), in which the multidimensional optical reflection results in forbidden energy gaps for the propagation of electromagnetic waves. For simplicity of calculations, the material of scatterers was chosen as the insulator with a zero imaginary part of its dielectric constant e2 (o9) = 0. The main reason for the crucial difference between the PBG structure and a diffraction grating is the use of scatterers with the real part of the dielectric constant (or refractive index (RI)) contrasting sharply with that of the surrounding medium. These structures were successfully realised in the microwave region of the spectrum and their performance was successfully modelled. A PBG structure for photons is analogous to the electronic band structure for electrons due to the crystal lattice, taking into account the absence of photon-photon interaction, because forbidden energy gaps appear as a result of constructive interference of propagating and scattered waves describing an electron or a photon. The structure then contains a sequence of allowed and forbidden energy bands that makes possible the control of the spontaneous emission. Numerous applications have been proposed for PBG materials as perfect mirrors, single-mode waveguides, and highly effective emitting structures, when light emitters are incorporated in the PBG structure [ 106]. Three-dimensional PBG structures are highly desirable because they possess a photonic gap irrespectively of the propagation direction and the polarisation of light. Twodimensional and one-dimensional PBGs inevitably suffer from radiation leakage in certain directions. The first three-dimensional photonic crystals possessing a complete PBG were fabricated for millimeter wavelengths by Yablonovitch [107]. These structures were realised by drilling holes in a slab of an appropriate insulator. Later, a variety of structures were made by layer-by-layer stacking of micromachined wafers [ 108]. The photonic crystal performance in the microwave regime is very impressive, for example, the 4-5 orders of magnitude suppression of the electromagnetic radiation intensity in the gap is routinely obtained. In principle, photonic crystals in the visible can be prepared by scaling down the dimensions of grating to the submicron range. However, a mechanical approach does not suit the precision requirements in a length scale below 0.5 mm. Moreover, the choice of high-RI contrast materials is progressively reduced for higher operating frequencies, where energy losses rapidly destroy the photonic gap. Three-dimensional photonic structures are thus a target for passive PBG devices. The incorporation of light emitters in photonic crystals designed to work in the visible range gives rise to further complexities, because the operation of composite ensembles of insulator and semiconductor nanometer-size structures is based upon the strong interaction of photons localised within the photonic crystal and electrons confined within individual nanostructures [109]. If the photonic energy structure is highly sensitive to the spacing of nanostructures, the electronic band structure is subjected to the nanostructure size and impurity content. Therefore, a nonlinear response of an ensemble as a whole becomes possible only by approaching both the identity of nanostructures in the ensemble and its long-range order. Device applications require a measurable intensity of light, which makes the design of large three-dimensional ordered ensembles of nanostructures increasingly important in order to enhance their output [2]. This is a target to be met by future lightemitting PBG devices. At least three basic methods of fabrication three-dimensional photonic crystals can be distinguished: subtractive, constructive, and template approaches. According to the subtractive approach one starts with a block of material and removes fractions of material to produce a periodical sequence of interfaces. The submicron range is nowadays accessible by nanolithography, however fabrication of large-area arrays and extension to the third dimension remain a challenge. Using a combination of high-resolution electron beam lithography and dry etching technology, face centred cubic (fcc) photonic crystals were fabricated in GaAs with a 40 x 40/zm 2 area and a thickness of 3 repeated (111) planes [110]. The main result is a photonic bandgap centred at 1300-1500 nm. In spite of the high-RI

296

THREE-DIMENSIONAL LATTICES OF NANOSTRUCTURES

Fig. 55. Schematicsof opal-based photonic crystals (top). Three different configurations are shownfurther in the followingtext: a bare opal grating, where the refractive index of the spheres is abovethat of the filling material; a replica grating, where the refractive index of the filling material exceeds that of balls and a coated opal, wherethe inner surface of voids is coated with a high refractive index film.

contrast (RIC = n 1/ n2 ~ 3.6), where n 1 and n2 are the RIs of scatterer (GaAs) and medium (air), respectively, the transmission dip exhibited by this crystal was very shallow ( ~ 15%), probably because of the insufficient thickness and homogeneity of the grating. The number of layers in this structure is a real limitation, because holes must have a uniform shape throughout. An example of the constructive technique employs a layer-by-layer construction of three-dimensional wire frame. For example, a three-dimensional PBG was built up by laser-induced direct-write chemical vapour deposition of A1203. In this approach the volume of the PBG crystal is basically unlimited, although only 3 • 3 mm 2 area structures with 13 planes were reported [111]. The periodicity of about 130/zm was obtained, which defined the shortest wavelength scale of the Bragg resonance. The transmission spectrum exhibited a 35% deep minimum as the stop-band. This method offers excellent flexibility to design structures with various symmetries, including incorporation of intentional defects, but its resolution is limited to at best 1 /zm by the laser spot size. A constructive approach in nanolithography is represented by layer-by-layer deposition of 1 /xm thick metal layers followed by reactive ion etching [ 112]. These metallodielectric photonic crystals demonstrated up to 15 dB deep suppression in a stop-band with only three layers at 2300-3000 nm irrespective of the light angle of incidence. However, the energy dissipation is still a problem for these structures. The template approach is based on porous structures to be infilled with guests with another RI (Fig. 55). Following the first publication of transmission of the water-impregnated opal by V. N. Astratov et al. in 1995 [113], a number of groups have reported on the photonic properties of opal templates. Basically, the properties of the liquid-impregnated opal with RIC below 1.05 are very similar to that of colloidal crystals [114-116]. For

297

ROMANOV AND SOTOMAYOR TORRES

liquid-impregnated opals, the PBG structure has been modelled [117]: As the RIC increases a pronounced dip in the transmission spectrum develops. In the dry bare opal (airopal) with RIC ~ 1.45, the suppression of the light propagation at the stop-band by 2 orders of magnitude has already been demonstrated [57]. By varying D from 180 to 500 nm it is possible to centre a stop-band anywhere in the frequency range from 1 to 3 eV [118]. However, the RIC in air-opals is insufficient to form a photonic band structure, where stopbands overlap in all directions in the Brillouin zone of the photonic crystal. So far, there is no theoretical modelling for opals with moderate RIC contrast. In order to improve the RIC, opals were impregnated either partly or completely with semiconductors. The template method has not yet resulted in a complete photonic gap although good progress has been made. Up to now all methods mentioned previously have not succeeded to make a true threedimensional PBG crystal in the visible light, however opal-based materials are those operating in the visible as incomplete PBGs and they hold the promise of completeness in the not too distant future. It is worth mentioning that combinations of the preceding methods can be used, for example, the microfabrication technique for the construction of three-dimensional far-IR photonic crystals was combined with preparation of an artificial template made by deep X-ray lithography in PMMA resistance followed by subsequent infilling of pores with preceramic polymer and pyrolisis-induced conversion of this composite in the free standing framework made of SiCN ceramic [ 119]. Two important problems can be studied with regard to opal-based photonic crystals: (i) the PBG structure of the three-dimensional photonic crystal with a deep modulation of the RI and (ii) the optical gain for light emitted within a three-dimensional photonic crystal. The merit of opal-based PBGs is their three dimensionality, operation at visible wavelengths [57, 120, 63, 121,122] and the possibility to be integrated in light-emitting devices.

7.2. Photonic Bandgap Characterisation The optical properties of ensembles of scatterers can be described applying the concept of optical localisation. This is a universal concept, which applies to perfect and disordered ensembles as well as to complete and incomplete photonic crystals [ 123-125]. There are two different issues concerning the localisation of light in photonic bandgap (PBG) crystals. The first concerns the scattering of externally generated light when its wavelength satisfies the Bragg conditions for the PBG grating. The second issue is the light emission from a source coupled to the photonic crystal, if its emission band overlaps with the photonic bandgap. The most convenient measurements are those revealing the transmission characteristics (T-spectra) of opal-based PBGs [63, 126], because they allow a quantitative estimation of the suppression of light intensity for a beam passing through the sample (Fig. 56). However, for high-RIC crystals, reliable data can only be obtained for light propagating normal to the surface of the sample taking special precautions in order to diminish the effect of the diffuse scattering by imperfections of the opal lattice [126]. In order to reveal the completeness of the PBG structure, the energy-wavevector (E-k) dispersion needs to be demonstrated. Measuring the angular dispersion of the Bragg resonance in reflectance spectra (R-spectra) alone (see Fig. 57) [ 127] cannot demonstrate this characteristic in full because the external light does not excite all modes available in a photonic crystal. The characterisation of a PBG also requires a complementary study of the emission from the photonic crystal. The correspondence between the angle of the incident light and the orientation of the k-vector for light propagating in the photonic crystal, requires further theoretical analysis because of the uncertainty in the direction of propagation after refraction. This is especially the case when stop-bands overlap over a wide range of angles but, as a rule, only the modes

298

THREE-DIMENSIONAL LATTICES OF NANOSTRUCTURES

1.0

0.8 0.6 .o ~D

0.4

0.2 0

-100 9 r~ r~

E -200 r~

2

[-.

1 -300 1.5

l

i

2.0

2.5

_~.0

Photonenergy (eV)

i

-100

E

. .

-..

r

.o o~

-200

...,..

- . - .

...

. .

...

...

-300 -

-400

]_.l!l

I I a 1, 2

I J I I J ! I J 1 I I I !

3

4

5

6

Photon energy (eV) Fig. 56. Top: Reflection spectrum of the air-opal taken at normal incidence to the (111) plane (A); transmission spectra of the air-opal (B) taken at normal incidence to the (111) plane (spectrum 1) and to the (110) plane (spectrum 2). Bottom: Transmission spectra of the air-opal taken at normal incidence to the (111) plane. (Source: Reprinted from [ 128], with permission from Elsevier Science.)

of crystal with the same k-vector as for incident light can be coupled efficiently. In this context it is important to notice that the angular dispersion is the relevant parameter for the device applications of these materials. In opal-based PBGs, especially those with a semimetallic PBG structure, if the angles for incoming and outgoing light are kept equal and the beam divergence is less than the angular width of the resonance, then the position of the Bragg resonance at oblique light incidence corresponds to that of the stop-band. In practice, angular dispersion is measured with a beam collimated within a solid angle of 1o. Diffuse reflectance spectra (DR-spectra), where the scattered light is averaged over all angles using an integration sphere, are useful to confirm both Bragg features and the absorption band edge.

299

ROMANOV AND SOTOMAYOR TORRES

=6.8~

m=2

52.1~

~D

r ~D

% 0=72.7~

I 450

!

'

I

500

, //I ,,In

650

I

I

I

700 ~. (nm)

I

750

'

I

800

'

I

'

850

Fig. 57. Reflectance from the opal as a function of wavelength for a series of incident angles (first and last ones in each series labelled in degrees). The first- and second-order Bragg diffraction are clearly seen. (Source: Reprinted with permission from [127].)

The optical spectra (Fig. 56) of an opal show the different features. To correctly assign these features the comparison of transmission and reflectance spectra was made. The similarity of the line shape and width of 2.23 eV peak (dip) in reflectance (transmission) strongly suggests their scattering origin, that allows ascribing this peak to the variation of the real part el (w) of dielectric constant, that is, it is the Bragg resonance. Obviously, the optical diffraction pattern of the three-dimensional opal lattice consists of reflections from all crystallographic planes, but they should be taken with a weight factor proportional to the density of scatterers in the plane. Intuitively, the main contribution would be expected to come from the most dense packed (111) plane irrespective of whether this plane faces up the sample surface or not. Thus, the detected positions of the Bragg resonance at different angles of the light incidence describe the dispersion of the stop-band near the L-point of the Brillouin zone of the fcc photonic crystal. Over a wider spectral range the well packed opals have other scattering resonances. For example, in an opal with D = 440 nm spheres, two peaks of different behaviour were found, as shown in Figure 57. The main (111) resonance is at 957.5 nm and the less pronounced (220) resonance is seen at 525 nm for normally incident light [118]. Moreover, the observation of the first- and second-order diffraction was reported at 2.23 and 3.9 eV, respectively (Fig. 56) [128]. Therefore, the opal possesses a complex optical transmission (reflectance) spectrum. The Bragg resonance appears at different energies depending on the sphere diameter. This shift correlates with the diameter of the opal sphere via the Bragg law ),1/),2 = D1 / D2. Optical spectra for opals with sphere diameters from 220 to 535 nm and the Bragg law fit for the positions of the Bragg resonances are shown in Figure 58 [ 118]. The slope of the fit gives the average RI of the sphere lattice nay = 1.349 in accordance with an estimate using nay -- ~ i ft" X h i , where fi is the volume fraction in the opal package occupied by a matter with RI ni. It was observed that reflection maxima at normal incidence 0 = 90 ~ of the light are very wide, whereas for inclined incidence (0 < 85 ~ the peak becomes narrower and better resolved. It is reasonable to assume that the overestimation of the stop-band width at

300

THREE-DIMENSIONAL LATTICES OF NANOSTRUCTURES !

,--1,,

v

Iv0 _J

400

600

800

100012001400

~. ( n m ) 1200

'

,.,,0"

1000

E

.d

.d o9

800

O,"

,,,9 ,.0" 600

9" 0 400

'

200

'

'

300

'

400 0 (nm)

'

'

500

Fig. 58. Top: Optical transmission at q = 90~ for opal-like structures made of spheres with different diameter: (1) 535, (2) 480, (3) 415, (4) 350, (5) 305, (6) 245, and (7) 220 nm. Spectra have been vertically shifted for the sake of clarity. Bottom: The Bragg reflection maximum wavelength plotted against the sphere size and fit to Bragg law (dashed line). (Source: Reprinted with permission from [118]. 9 1997 American Institute of Physics.)

normal incidence comes from contributions to the Bragg peak from other sources. Several possible wavelength-dependent scattering mechanisms which may contribute to the T- or R-spectra can be mentioned: scattering resonances associated with individual particles in a well structured medium reminiscent of Mie resonances, the enhanced backscattering characteristic of the light localisation in an inhomogeneous medium [ 129] and the effect of the anomalous reflection due to the smooth variation of grating parameters, compared to the wavelength [ 130]. There are several parameters to be considered with respect to scattering from opal lattices with different infills, such as the width, shift, dispersion, and resolution of the stopband and, the effect of the infill. In the following text an illustration is given of the impact of varying these parameters on the T- and R-spectra by discussing experiments with opal immersed in air (air-opal, RIC = nsio2/nair -- 1.45) and in sulphur (S-opal, RIC = ns/nsio2 -- 1.38) (Fig. 59). In addition, other data concerning the incomplete infills will be used to generalise the discussion.

7.2.1. Stop-Band Width In general terms the width of the stop-band is governed by the RIC. Figure 60 shows the development of the stop-band with increasing RI contrast for an opal filled with various

301

ROMANOV AND SOTOMAYOR TORRES

Fig. 59. (a) Bragg resonances from the air-opal at different light incident angles (top) and the angular dispersion of the stop-band (bottom) extracted from reflectance spectra. (b) Similar plots here for the S-opal.

Fig. 60. Transmission (T) spectra of a wedged opal infilled with various liquids, taken at normal incidence to the (111) plane for D = 210 nm. Spectra 1, 2, and 3 correspond to different refractive indices of the pores n b = 1.33, 1.37, and 1.47, respectively. The dotted curve gives the dependence T cx k 4. Inset: Thickness dependence of the attenuation at the centre of a stop-band. Circles, squares, and triangles correspond to different nb. Solid lines are least-square exponential fits to the experimental data. (Source: Reprinted with permission from [126]. 9 1997 American Physical Society.)

liquids. Similar trends for this range of R I C variation have b e e n reported [ 126, 128]. It is clearly seen that as the stop-band develops, the scattering strength at the r e s o n a n c e freq u e n c y of the e n s e m b l e increases (see inset, Fig. 60).

302

THREE-DIMENSIONAL LATTICES OF NANOSTRUCTURES

Following the idea of John [49] the scattering from a dense lattice of scatterers is the combination of components from individual scatterers and the scattering by the ensemble. If the microscopic resonance (Mie resonance [131,132]) and the macroscopic Bragg resonances of the lattice of scatterers occur close to each other in wavelength, the synergy of these resonances maximises the scattering strength of the ensemble and, consequently, the width AE of the stop-band. In order to approach this maximum, for a given ratio nr of the refractive indices of scatterers relative to air, optimisation of the filling factor of dielectric spheres is required [133, 125]. From this point of view, the optimal filling factor of dielectric spheres immersed in air was estimated as f = 1/(2nr), where nr is the RI of scatterers relative to air [ 133, 125]. From this viewpoint the optimal filling factor for silica spheres is fsphere ~'~ 0.36, which is far from the actual factor fsphere ~'~ 0.87 for the air-opal. The same opal immersed in sulphur has a lower RI ratio, but in this case the optimal silica sphere filling factor is found to be fsphere ~ 0.72, which is significantly closer to the actual value for the S-opal. For this reason the relative gap width A E / E c , defined as the width of the Bragg peak relatively to its central energy, appears wider in the S-opal than in the air-opal, while their RIC values are 1.38 and 1.45, respectively. A E / E c values of about 0.05 and 0.09 for air- and S-opals, respectively, are very close to those reported in the microwave regime for fcc ensembles of alumina spheres at the L point of the Brillouin zone [134], with a RIC of 3.06. An exact bandstructure calculation is necessary to demonstrate what the photonic bandstructure looks like for the air-opal and the inverted opal. Because real opal structures are not perfectly regular, the formation of the PBG may be more adequately treated in terms of light localisation. We point out that it is a matter of language how to discuss light scattering phenomenon in ordered ensembles of scatterers. A convenient estimate of the optimal volume fraction of scatterers is based upon the idea of the relative fluctuation of the dielectric constant (permittivity) from its average magnitude in the fcc lattice of scatterers [ 135],

fin4 + f2n4 8r-

- 1] 1/2

[ (fln 2 + f2n2) 2

The increase of 8r is taken as corresponding to the localisation length. It was thought that a significant deviation of the density of photon modes appears if 8r ~ 1. Because Er "~ 0.25 for the air-opal and Er ~ 0.31 for the S-opal, this approach may apply. However, the small difference of estimates for these lattices does not reflect the actual difference of their PBG behaviour. This is because this model does not take into account the change in the electromagnetic field distribution in favour of the high-index fraction of the photonic crystal structure, which occurs when opal voids are infilled with guest semiconductors. Correspondingly, the prospects for PBG material design on the base of opals [ 126, 128] might seem inadequate.

7.2.2. Shift of the Stop-Band A red shift of the Bragg peak occurs after complete impregnation of the opal matrix with sulphur due to the increase of the average RI of the grating ngr (Fig. 59). In a multiplecomponent composite the average RI was estimated using rtgr = Y~-i fi X ni as discussed earlier. Thus, for the opal with fball ~ 0.87, the average indices are calculated to be nair-opal -- 1.39 for the air-opal and ns-opal ~ 1.52 for the S-opal. The linear Bragg approximation predicts a shift of the scattering peak as ~.S-opal/)Vair-opal = ns-opal/nair-opal, where ns-opal/nair-opal = 1.09 was estimated. Experimentally, the shift of the scattering resonance (0 = 85 ~ after impregnation was found in agreement with the Bragg prediction.

303

ROMANOV AND SOTOMAYOR TORRES

7.2.3. Dispersion of the Stop-Band The scattering cross-section of individual scatterers at the Mie resonance is several times greater than their geometrical cross-sections, indicating that in the dense ensemble all scatterers are optically connected. The most densely packed planes of a fcc lattice are (111) planes, where maximum scattering occurs. Therefore, in first approximation, opal lattices can be represented as a stack of planes. With this assumption, the problem of Bragg scattering from a three-dimensional opal grating can be reduced to that of scattering from a one-dimensional grating. The position of the scattering resonance from the array of (111) planes has been traced with varying angle of incidence of the light. The stop-band of the opal immersed in liquid shows the Bragg-like behaviour with changing the angle of incidence [136]. In water-filled opals Ec(O) exhibits a sinelike behaviour [137], the same trend was confirmed for air-opals [57] (Fig. 57). If RIC > 1.1 the stop-band becomes detectable at any angle [57, 63, 121, 122]. The angular dispersion of the (220) resonance appears much smoother than that of the (111) resonance and its trend to longer wavelengths with decreasing 0-angle is opposite to that of the (111) resonance [ 118]. A quantitative comparison of different gratings can proceed via the relative stop-band width A E/Ec and the relative shift of the stop-band with the changing of the angle of incidencet Eshift/A E. The latter characterises the completeness of PBG because for a complete PBG Eshift/AE < 1. In water-filled opals with a RIC ~ 1.05, the stop-band is characterised by A E / E c ,~ 0.035 and Eshift/AE ,~ 9 for 0 from 90 to 45 ~ In practice, it is easily observed how an opal with a low RIC changes colours very fast with an angle due to its narrow stop-band. This very same feature is characteristic of colloidal suspensions, which are commonly considered as the prototype of opals. For the air-opal A E / E c ~ 0.049 and Eshift/AE ,~ 3.25 were estimated [138, 139]. From the data on the air-opal in Ref. [118], A E / E c ,~ 0.08 and Eshift/AE ,~ 2.24 were extracted. This excess broadening of the Bragg resonance is most likely due to other scattering contributions to the transmission, possibly disorder of the lattice. It is worth noticing that the modelling of the RIC-dependent width of the Bragg resonance applied to the opal structure [140] gives A E / E c ,~ 0.054, which emphasises the reliability of reflectance spectroscopy to characterise these materials as PBG. For the S-opal these values are A E / E c ,~ 0.089 and Eshift/AE ~ 1.2, that is, the stop-bands nearly overlap in the examined range. The difference between the average RI values of the air-opal and the S-opal is about 0.1, which cannot drastically change the refraction of light, so the angle-dependent change in the stop-band position (Ec(O)) were treated in a similar manner for both cases. It is seen from Figure 61 that sphere (normal opal) and O-void (inverted opal) lattices are identical and, therefore, their reciprocal lattices are also identical. Thus, the Bragg resonance corresponding to the scattered wave, which adds the vector of the reciprocal lattice to the incident wave, occurs at the same point of the Brillouin zone for both configurations. The basic difference between these lattices is the basis of the unit cell, which is a sphere in the air-opal and one O-void plus two T-voids in the S-opal. This change from one-point scatterers to multiple-point scatterers affects the scattering efficiency, but not the range of wavevector variation. If the angular dispersions are similar for both lattices, the ratio of the peak spectral energy positions at 0 = 85 and 45 ~ should be the same, following a linear approximation. However, at 0 = 45 ~ Eair-opal/Es-opal = 1.17 was found, which exceeds EaJr-opal/ES-opal = 1.09 at 0 = 85 ~ This deviation suggests a stronger angle-dependent shift of the resonance peak when the sphere lattice is substituted by its replica. The angular shift of the Bragg resonance is evidence of the anisotropy of light transmission in the lattice. This anisotropy can be considered to be related to the anisotropy of the localisation length which follows the lattice symmetry or, using a different language, to the different mode structure in normal and inverted opal lattices. The Fourier transform of the variable part of the RI in the ensemble of scatterers can be factorised into the structure factor, which describes the symmetry and ordering of the

304

THREE-DIMENSIONAL LATTICES OF NANOSTRUCTURES

Fig. 61. Left: Schematics of the ball and O-void lattices arranged in the (111) plane of a fcc package. Right: (a) Photonic DOS of a fcc lattice of high dielectric spheres in a low dielectric background, with a 25% dielectric filling ratio. For comparison, the free-photon DOS is shown by the dotted line. Frequencies are expressed in dimensionless units of co/A, where co is the speed of light and A is the fcc lattice constant. DOS is in units of photon states per unit cell. (b) Calculated photon DOS for the fcc lattice of dielectric spheres (radius Rb) connected by thin cylindrical rods (radius Rr) to form an interconnected network, displaying a higher frequency gap. The filling ratio is 25%. (c) The photon DOS for the fcc lattice of large dielectric spheres surrounded by smaller dielectric spheres (Rs) in the 110 directions. Each large sphere has 12 smaller spheres as neighbours for a filling ratio of 27%. As in (b), a higher frequency gap is found. (Source: Reprinted with permission from [142]. 9 1998 American Physical Society.)

lattice, and the form-factor, which describes individual properties of the scatterers [ 125]. Clearly, the structure factor remains the same after infilling of the opal with sulphur. The form-factors of sphere and replica lattices are different due to the space distribution of the high-RI component, where the speed of light is lower. The replacement of the sphere by the inverted lattice means a three-fold increase in the density of scatterers and an improvement of the spatial localisation of the scatterers. Because the linear scale of this variation is less than a quarter wavelength it can appreciably affect the resolution of the RI modulation. Concerning the structure of electromagnetic modes in the crystal, this is more pronounced in the inverted lattice due to the spatial localisation of these modes. In the air-opal the spheres effectively overlap with each other because fsio2 = 0.87, for this particular sample, instead of fsio2 > / 0 . 7 4 in an ideal fcc package, that is, the form factor reduces the effect of the structural factor. In contrast, in the S-opal the grains are clearly separated from each other, that is, the form factor is improved.

305

ROMANOV AND SOTOMAYORTORRES

Band structure calculations of the complete photonic crystals based on colloidal crystalline packages [141], show the effect of the complex unit cell upon the width of the bandgap [142]. The demonstrated effect is in line with the foregoing considerations on scattering from opal replicas. Scattering resonances from planes other than (111) ones contribute to the optical localisation. Obviously, the contribution from other planes is enhanced with increasing scattering strength. The large number of resonances simultaneously available in many directions cannot be resolved experimentally. It is reasonable to assume that precisely this background contributes to the bandgap formation, which results in the observed squeezing of the Bragg resonance angular dispersion. This squeezing, which is observed in the S-opal compared to the dispersion in the air-opal, is further enhanced in the case of a guest material with higher RI, such as the CdS-opal [143] or the GaP-opal [144].

7.2.4. Resolution of the Stop-Band R- and T-spectra of air-opals have well-defined peaks (dips) (see Fig. 56) for (111) crystal planes facing upward. The peak energy shifts with changing sphere diameters and with varying the angle 0 of the incident light [ 118]. The resonant scattering typically exceeds the background scattering by 1-2 orders of magnitude [ 127]. In infilled opals, increasing the volume fraction of the semiconductor in the nanocomposite material, results in the Bragg feature becoming less pronounced (Figs. 59 and 62) [ 144], although the resolution can be preserved in good quality samples using strongly collimated incident and scattered light [ 126]. A reasonable assumption is that the diffuse scattering due to opal lattice imperfections and the inhomogeneity of the guest distribution smears out the sharpness of the Bragg resonance by averaging over fragments of opal with different PBG structures. The infill inhomogeneity has been clearly documented by AFM and SEM studies of the CdS-opal [ 145]. Choosing the areas with homogeneous infill, attenuation length measurements have been performed [63, 126]. These showed that the attenuation length is around 180 layers along the (111 ) direction in the air-opal with fball = 0.96 which, after infilling a quarter of voids free volume with CdS, decreases by a factor of 2, assuming negligible dissipative losses in the CdS-opal. This example illustrates how strong the increase of the scattering strength is with infilling the opal voids. Figure 62 shows the interplay between the electronic and the photonic energy band structures and how it manifests itself in transmission and reflectance spectra of the CdSopal, the InP-opal, and the GaP-opal. In general a two-peak spectrum is observed. One peak is of Bragg nature and the other peak corresponds to the absorption edge of the parficular semiconducting infill. Increasing the loading, the scattering strength increases, but the resolution of the Bragg peak decreases (Fig. 62, right). The inhomogeneity of the semiconductor loading is probably the main source of this distortion. When the stop-band overlaps with the electronic band edge of the guest material, inelastic scattering takes place in the photonic crystal (e2(w) ~ 0 contribution). This dissipation can entirely destroy the upper edge of the stop-band [146] and can contribute to the attenuation length. In addition, the in-void chemical synthesis of semiconductoropal nanocomposites results in a nonperfect crystalline structure and contamination of the semiconductor. These are direct consequences of the opal not being precisely a chemically clean material and of the stoichiometry resulting from the gas-phase synthesis of semiconductors. This synthesis is in turn affected by the opal internal surface curvature, which alternatively changes its sign along the cavity diameter. Both give rise to a nonnegligible density of electronic states within the electronic gap of the semiconductor. We illustrate the interplay between scattering strength and the opal inhomogeneity with the discussion of the following example. For the polycrystalline bare opal, the T- and DRspectra are of the edge type. This is a result of the random orientation of the crystallites that mixes scattered light. Nevertheless, this edge has a diffraction nature. It indicates the lowest

306

THREE-DIMENSIONAL LATTICES OF NANOSTRUCTURES

Bragg

I CdS-opal

1

-250

~

~,

5 .soo

~[ InP -750

~

"

gc

.lOOO i

1.8

2.0

2.2

2.4

2.6

2.8

1,6

Photon energy (eV)

J

,

2,0

Energy (eV)

Energy (eV)

Fig. 62. Left:Transmission spectra of the CdS-opal measured at incidence normal to the (111) plane in the region (1) with embedded CdS nanocrystals and (2) in the reference region (air-opal). The contribution of incoherent scattering is subtracted as discussed in the text. Curve (3) is a second-order derivative of the spectrum (1). The arrow shows the photon energy of the A exciton of the bulk CdS at 300 K. Middle and right: Coexistence of features from the electronic spectrum of guest and coherent Bragg scattering from the guest grating in reflectance spectra. Right panel shows the variation of the Bragg resonance with increasing CdS loading. (Source: Reprinted with permission from [126]. 9 1997 American Physical Society.)

possible stop-band position and it shifts with changing nay and D [64]. Furthermore, this edge spreads over a wider spectral range for opals with poor order as has been confirmed by SEM. In order to demonstrate the improvement of the PBG overlap in different directions these polycrystalline opals were coated internally with high RI semiconductors [50]. DRspectra of the polycrystalline opal with InP, CdS, and TiO2 coatings exhibit two maxima in contrast to the bare opal. One of them corresponds to the interband transition within the electronic structure of the coating at ~ 1.4 eV for InP, ,~3.2 eV for TiO2, and ,~2.5 eV for CdS. The other peak seen in DR-spectra comes from coherent scattering. Using the idea of angular dispersion squeezing of the stop-band, we conclude that particular resonances at different angles come closer together thus forming a common region or pseudo-gap. Thus, the higher the RIC, the less the homogeneity of the lattice required to construct the photonic bandgap. This observation confirms the theoretical assumption that the essential parameter for optical localisation effects is the short-order regularity of the structure factor. With this consideration in mind photon localisation effects can be considered even in the case of a partially disordered lattice. In this sense the system being studied, possessing a well-ordered porosity but an uneven void filling, may well satisfy the conditions for photon localisation.

7.2.5. Effect of the Infill From calculations it is deduced that the scattering strength of light by a shell-shaped scatterer is the same as a monolithic scatterer of the same shape, provided that the shell thickness is about 10% of the scattering diameter [ 132]. This means that the effective medium approximation is invalid if a thin coating is deposited on the inner surface of the opal because the interaction of the electromagnetic field with the thin wall may be far too weak. By thin here we refer to a few nm thickness. The implications of this for the design of photonic crystals is to soften the requirements for coating homogeneity above a certain thickness. However, if the infill is composed by a random collection of nanoparticles in the void volume, the effective medium approximation can be legitimately used.

307

ROMANOV AND SOTOMAYOR TORRES .

1.0

. . . . . .

/ I/',, \

0.5

0 t~

.~~ o z

. . . . .

Air-opal 85,/~ 60,i~ (~ 45* 1

,

.....

,B

I

,.

~

!

!

.

0.0

1,0

CdS..opal

0.5

0.0

. . . . . . . .

'

.....

'

1.0

0.5

0.0

QaP-opa|

~ s/~/~~i ~ ' 2.0

-

2'.4

.....

21a

Energy (eV) Fig. 63. Top:Normalisedreflectance of the air-opal at three angles of incidence. Middle and bottom: Effect of squeezing the angulardispersionof the Bragg resonance after infillingthe opal voids. Note the overlapping of Bragg peaks for the CdS-opalin a given interval of angles of the light incidence.

For the same matrix, the CdS filling factor gives rise to a Bragg resonance positioned at 2.22 eV [147], whereas the GaP filling factor results in the resonance occurring at 2.2 eV, [ 144] (see Fig. 63). The small difference in resonance frequencies suggests a similar average RI for both lattices. Taking into account the difference of the RIs of these semiconductors, a filling factor ratio fGaP/fCdS "~ 0.71 is found. Using the measured CdS fraction fCOS ~ 0.076 of the crystal volume, the estimated fraction of GaP is fGaP ~ 0.055. However, this value overestimates the actual amount of GaP by a factor of 5. Moreover, the infill inhomogeneity precludes a more precise determination. Thus, it may be advantageous to use coated inner opal surfaces than randomly infilled opals. Increasing the guest volume fraction makes the Bragg resonance shift progressively to longer wavelengths. Figure 64 illustrates this showing the shift of Bragg resonance for nearly normal beam incidence (0 -- 85 ~ from 2.34 eV in the air-opal to 2.26 eV for the CdS-opal with a fraction fCdS = 5.4 vol% (or ~45% void filling). Further increments in the CdS fraction to 7.5 vol% (58 vol% filling of the opal voids) and to 12.5 vol% (97 vol% filling of the voids) shift the resonance Ec to 2.22 and 2.17 eV, respectively. This shift is directly proportional to the volume fraction of the semiconductor in the opal or to the average RI of the composite. The width of the transmission dip A E increases rapidly with loading, AE/Ec = 0.06, 0.13, 0.28 for fCdS = 5.4, 7.5, and 12.5 vol%, respectively. The gap is wide enough to form a complete PBG crystal. At nay -- 1.41 the ratio AE/Ec = 0 is found, reflecting the disappearance of the stop-band if RIC = 0, that is, the RI of the infill matches the RI of the opal carcass. The region of very small RIC = i 0 . 0 7 was thoroughly studied with liquid-impregnated opals [ 148] and a similar linear dependence of the gap width upon RI of the infill was found. The key feature shown in the fight-hand side of Figure 64 is the steeper slope of AE/Ec when the RI of the infill exceeds that of silica compared to the slope in the region where the RI of the infill is less than that. This change reflects the difference in the localisation of the electric field, which is concentrated in the

308

THREE-DIMENSIONAL LATTICES OF NANOSTRUCTURES

#i II

0.3

# # #

I

#

I

#

#I

#

g

,f r~

I

I

I

O.2

I I

i I

I

#

#

# #

1

O- 1

11

W,,,I

540

r o, bo

nn ,,' -'-0.00

' o.io

u

u

(a)

I

, .

,..

0.05

9

o.lo

(b)

Fig. 64. (a) Red shift of the Bragg resonance for a grating with the same lattice parameter, but with different loading of CdS with 4.5, 9, and 18 vol%. (b) Linear increase of the relative stop-band width with increasing loading.

component with the higher RI, either the spheres or the guest material, depending on the sign of the RIC. Control of the PBG behaviour of the opal-based photonic crystal can be achieved changing the RIC in the lattice. Therefore, keeping the same lattice parameter it is possible to move from the highly anisotropic semimetallic PBG to the nearly isotropic "semiconducting" PBG. The most relevant parameter from the point of view of material design is the proper sequence of interface formation seen by the photon waves in the photonic crystal. The homogeneity of the infill from void to void is a decisive factor, otherwise the coexistence of different PBG fractions reduces the overall PBG effect. Apparently, the fine structure of the interface in the nm scale is of less importance, if the roughness is less than about one tenth of the wavelength. This is why opals with partially infilled voids and those with completely occupied voids exhibit the same trend of the PBG change. It is an important experimental finding that the shell-shaped scatterers, produced by coating the inner surface of the opal template, behave similar to monolithic scatterers. Such a configuration of an opal-based photonic crystal opens a possibility for further processing the composite material by coimpregnation with another guest material. 7.3. Photoluminescence from Opal-Based Photonic Crystals In the context of emission spectroscopy opal composites can be considered as ensembles of emitters and nondissipative selective couplers integrated in one material. Consequently, the emission spectrum depends upon both the guest and the host materials. In this section the anisotropy of the PL spectrum of silica defects in the bare opal, the changing PL spectra with increasing RIC, and the change of PL spectrum of silica defects with ZnS infill is discussed. The latter is an example of the spontaneous emission rate redistribution due to the interplay of the PBG and electronic energy band structures.

309

ROMANOV AND SOTOMAYOR TORRES

7.3.1. Anisotropy of Photoluminescence Spectrum of Silica Defects in Bare Opal Bare opals have a broadband luminescence spectrum, which is attributed to the radiative relaxation of predominantly oxygen vacancy-related defects in the silica carcass. These defects form an impurity band within the forbidden electronic gap of the SiO2 energy band structure [149], the radiative recombination emission of which appears from the photon energy hOgL of the exciting laser line in the visible down to ,~ 1.5 eV [64]. The study of this broadband PL reveals the PBG effect upon the bare opal spectrum. From the PL of colloidal systems it is known [ 114], that the stop-band suppresses the spontaneous emission causing a dip in spectrum, which shows the effect of the stop-band. A similar effect has been observed in the air-opal (Fig. 65a). In contrast, the disordered opal, which was synthesised by the same method as the ordered one but consists of randomly shaped particles of different sizes, does not exhibit such a dip. Using the PL of the disordered opal as the standard for PL of silica defects, the relative PL spectrum illustrates the decrease in the density of photon modes coupled to this emission in a solid angle around the specified direction in the opal (Fig. 66b) [ 144]. This dip can be associated with the Bragg resonance, because its appearance in the airopal is subjected to the spacing of the opal lattice. However, if the reflection spectrum mirrors variations in the number of photon modes coupled to the external light of the same wavevector, the intraPBG emission is coupled to all available modes and can be referred to a sharp feature in the local density of photon states (DOPS). Because the PBG of opal photonic crystals is incomplete and is due to a certain amount of disorder, the structure is not perfectly organised. This is why the dip depth in the transmission spectrum is greater that 2 orders of magnitude, whereas the PL dip is only about 10-50% of the background signal. With further improvements in the crystallinity and increasing the RIC, the dip in the DOPS is expected to be more pronounced. The restriction in the probability of a photon being emitted in certain directions can be treated as the anisotropy of photonic energy band structure. In terms of optical localisation, the emitted photon is strongly bound to the atom from where it originates because, after

I disordered - - - . - ~ "J ":"1 _~_,,o I:L :3 opal ........ 50 o) ~ ~9

.-"~'"~

........

...... .....-

...................... ...................... 0 s ''J'' i~:::.: ----..,..., ....... ,.,,,..s .,70 ,,"

7o_=

:3 v

n 0 a

J

50o (b)

Fig. 65. (a) PL spectra of ordered air-opal at different angles of the PL collection and the PL spectrum from disordered opal at T = 300 K, under excitation with radiation of 351.2 nm. The signal was collected from the solid angle of 4 ~ (b) Density of states of photons extracted from a comparison of PL spectra of ordered and disordered opals.

310

THREE-DIMENSIONAL LATTICES OF NANOSTRUCTURES

5

Observation angle (deg): 0 15 ~~, .......... 20

(a)

v

4 r

~--

C:

~

c:

3

8 8

2

e-

60

/

f/)

.r o

30

9

1

.....

LL

500

550

600

Wavelength 1.2

'

;

....

'

- 9

-

~'."Y,

1.0

650

(nm)

i

(b)

J '--. Pd~F

r.-

0.8 v

,,%

0.6 Observation angle (dell): 0 . . . . . . 15 .......... 20 25

0.4 0.2 =

0.0

5 0

I

,

-

550 Wavelength

I

600

,,

m

650

(nm)

Fig. 66. Fluorescencespectra of dye molecules (rhodamine 6G) embedded in opal. Panel (a) shows spectra measuredat various observationangles withrespect to the normalto the samplesurface. Squaresrepresent the emissionspectrumof the samedye embeddedin the samplewiththe stopband locatedoutsidethe fluorescence emission range ("vacuum" spectrum). Panel (b) contains the same spectra divided by the latter one. (Source: Reprinted with permission from [51]. 9 1997American Physical Society.)

travelling a short distance within the area defined by the localisation length, that is, after several elastic scattering events, this photon is reabsorbed by the same atom. By analogy with an atom emitting in a perfect microcavity, this emitter is "dressed" in radiation, when the emission frequency falls within the bandgap. Whether or not the photon can escape from the photonic crystal depends on the localisation strength. If the PBG environment is of an incomplete nature, the localisation is anisotropic and the emission intensity is different in different directions in the photonic crystal. The probability of recovering the emitted photon after several scattering events is much lower than in a fully PBG crystal but is not zero [ 125]. Therefore, the relative PL spectrum provides a measure of the anisotropy of the probability for a photon to escape from the photonic crystal in a given direction in an incomplete PBG structure. The PBG structure has to be proved by the correspondence of the angular dispersion of the stop-band measured by reflectance spectroscopy and by PL spectroscopy [147]. The angular dispersion of the PBG-related dip (Fig. 65b) demonstrates the correlation with the Bragg resonance in reflection spectra, when the angle of detection 0 is changed for both emitted and scattered light. Assuming that there is no dependence of the angle of incidence upon the UV excitation, the 0-dependence of PL dip is caused by anisotropy of the PBG structure in the air-opal.

311

ROMANOV AND SOTOMAYOR TORRES

Comparable fluorescence spectra have been reported from the dye molecules rhodamine 6G embedded in opal [51 ] (Fig. 66). Spectra showing the anisotropy of the photon localisation were reconstructed from PL spectra using an opal sample with smaller spheres as the reference. The dip in DOPS spectra is less pronounced than for the air-opal probably due to the smaller RIC in this material.

7.3.2. Photoluminescence Spectra Dependence on Refractive Index Contrast In order to change the RIC three wide-gap semiconductors, namely, CdS (Eg ~ 2.5 eV), CdSe (1.7 eV), and ZnS (3.7 eV), were synthesised in opals with spheres of diameter D ~ 239 (fsio2 = 0.87). After impregnation of the opal samples with semiconductors the resulting PL spectrum was found to consist of two components: one associated with transitions in the semiconductor and the other associated with oxygen defects in the silica carcass as its origin. As in many semiconductors, it is expected that oxygen defects trap electron-hole pairs from the semiconductor thus creating a competing channel for energy relaxation. In general, it is virtually impossible to distinguish between these components in the total PL signal, especially in the case of lightly loaded opals, that is, those with a low volume fraction of the semiconductor. In fact, this mixed origin can be misinterpreted: in Ref. [ 150], the authors ignored the extrinsic recombination channel when explaining the origin of the photoluminescence in the CdS-opal and they relied only on the apparent correspondence of the amplified spontaneous emission (ASE) band position and the Bragg resonance in the lattice. The rapid growth of the additional ASE band under increasing pumping power is probably due to different emission rates from available radiative recombination channels (see Fig. 67), as discussed in the case of InP-asbestos. A detailed examination of this experiment [ 151] also shows the inconsistency of angular dependence of this peak and that of the stop-band as well as incorrect extending of ASE analysis from homogeneous to highly RI contrasting medium [154, 155]. A schematic of the PBG effect upon the broad-band emission from opal-based nanocomposites is shown in Figure 68. The line shape and the intensity of the PL from the semiconductor-opal composites depend strongly on the homogeneity of the semiconductor distribution within the opal grating. Clearly, an inhomogeneity in the 10 lzm scale leads to the co-existing of crystallites with different PBGs comprising each ,, .~--

"~ | i

g

.:

.

........

"'_

2.0

1.5 o~

i

=

|

i

|

,

.s.,

9

|

s

i

2.5 - 0=600 2

=.=.

.

..

(c)

20

n

C~

15

.

10 2.0

I

2.2

2.4

2.6

Energy (eV) Fig. 72. PL (a) and PL ratio spectra (b, c) of the ZnS-opal taken at different levels of excitation power at q = 85 and 60 ~ Numbers on curves show incremental increases of pumping level. Arrows indicate the stop-band position accordingly to reflectance spectra.

'

''

''

~"

'

9

i

i

i

,

I

,

D-A

'

"

'""

I

"

" ~

"

D-h

o.=4 C~

a) ,.=4

b)

c)

2.001

2.25

2.50

2.75

3.00

p h o t o n e n e r g y (eV) Fig. 73. Photoluminescence spectra of the CdS-opal measured as a function of time delay at T = 2 K under pulsed excitation with N2-1aser. Time delay for spectra (a)-(c) is 0, 50, 300 ns correspondingly. (Source: Reprinted with permission from [63]. 9 1995 Societ~ Italiana di Fisica.)

318

THREE-DIMENSIONAL LATTICES OF NANOSTRUCTURES

8. C O N C L U D I N G R E M A R K S In this chapter we have presented the nanocomposite family based on porous templates with emphasis on the opal. From the synthesis, using the template technique, to their potential applications in electronics and optics, it has been shown that these nanostructured materials offer a wealth of possibilities to tailor their properties for specific purposes. We have shown how the crystalline porous template can be viewed as a host for a threedimensional lattice array, where issues of cluster formation meet the concepts of quantum dots and wires. In particular the schematic view of infilled opals as lattices of semiconductors, superconductors, and insulating nanoparticles was amply discussed. The underlying science is challenging both at the experimental and theoretical level because opal-based nanocomposites are not perfect. A tour of superconductivity on board an opal-based Josephson medium provided an insight into the commeasurability of magnetic flux and nanostructure size. The magnetotransport properties of the InSb-opal treated as a quantum dot lattice illustrated the several quantum and classical transport regimes taking place in such arrays. Finally, the potential use of opal-based photonic crystals as three-dimensional photonic bandgaps operating in the visible was illustrated with many examples pointing out the issue of photon localisation and the control of the spontaneous emission. Characterisation techniques such as scanning probes of assorted nature are still to be deployed systematically in the study of these nanocomposites. We expect much activity in this area. The template approach to realise nanostructures is in its infancy. One can imagine the progression of activities to make templated nanocomposites with molecules and polymers, or with biological matter. From sensors to multiaddressable three-dimensional memories with a number of parameters that allow specific functions, the science and potential applications offered by templated nanostructures are just beginning.

Acknowledgments The authors are grateful to Professor V. N. Bogomolov for introducing them to the template method and its wide ranging scientific and technical issues. We are indebted to our many collaborators over the years who have contributed to this body of knowledge. Special thanks are due to Torsten Maka for his assistance with the preparation of this manuscript.

References 1. D.J. Bergman and D. Stroud, eds., in "Solid State Physics Series," Academic Press, Boston, p. 147, 1992. 2. V. Bogomolov, Y. Kumzerov, and S. G. Romanov, in "Physics of Nanostructures" (J. H. Davies and A. R. Long, eds.), lOP, Bristol, p. 317, 1992. 3. U. Woggon, "Optical Properties of Semiconductor Quantum Dots," Springer-Verlag,Berlin, 1997. 4. P.M. Petroff, M. Tsuchiya, and L. A. Coldren, Surf. Sci. 228, 24 (1990). 5. N.N. Ledentsov, M. V. Maximov,P. S. Kop'ev, V. M. Ustinov, M. V. Belousov, B. Y. Meltser, S. V. Ivanov, V. A. Schukin, Z. I. Alferov, M. Grundmann, D. Bimberg, S. S. Ruvimov,W. Richter, P. Werner, U. Grsele, U. Heidenreich, P. D. Wang, and C. M. SotomayorTorres, Microelectron. J. 26, 871 (1995). 6. T. Ohsuna, O. Terasaki, and K. Hiraga, Mater Sci. Eng. A 217, 135 (1996). 7. J.H.P. Watson, Phys. Rev. B 2, 1282 (1970). 8. V.N. Bogomolov,Sov. Phys. Uspehi 21, 77 (1978). 9. V.N. Bogomolov,V. V. Poborchii, S. V. Kholodkevich, and S. I. Shagin, JETP Lett. 38, 532 (1983). 10. V.N. Bogomolovand Y. A. Kumzerov, JETP Lett. 21,198 (1975). 11. V.N. Bogomolovand A. I. Zadorozhnii, Sov. Phys. Solid State 17, 1078 (1975). 12. V.N. Bogomolov,N. A. Klushin, and Y. A. Kumzerov,JETP Lett. 26, 72 (1977). 13. L. I. Arutyunan, V. N. Bogomolov, N. E Kartenko, D. A. Kurdukov, V. V. Popov, A. V. Prokofiev, I. A. Smirnov, and N. V. Sharenkova, Phys. Solid State 39, 510 (1997). 14. J.R. Agger, M. W. Anderson, M. E. Pemble, O. Terasaki, and Y. Nozue, J. Phys. Chem. B 102, 3345 (1998).

319

R O M A N O V AND SOTOMAYOR TORRES

15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31.

32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43. 44. 45. 46. 47. 48. 49. 50. 51. 52. 53. 54. 55. 56.

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Chapter 5 FLUORESCENCE, THERMOLUMINESCENCE, AND PHOTOSTIMULATED LUMINESCENCE OF NANOPARTICLES Wei Chen Laboratory of Semiconductor Materials Science, Institute of Semiconductors, Chinese Academy of Sciences, Beijing, People's Republic of China

Contents 1. 2.

3. 4.

5.

6.

7.

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Measurement of Split Levels of Quantum Confinement . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1. Optical Absorption Spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2. Photoluminescence Excitation Spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Excitation Energy Dependence of Fluorescence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Absorption and Luminescence of Surface States in Nanoparticles . . . . . . . . . . . . . . . . . . . . . 4.1. General Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2. Excitonic and Trapped Fluorescence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3. Absorption of Surface States . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4. Size Dependence of Trapped Luminescence from Surface States . . . . . . . . . . . . . . . . . . Thermoluminescence of Nanoparticles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2. Thermoluminescence of CdS Clusters in Zeolite-Y . . . . . . . .................. 5.3. Thermoluminescence of ZnS Nanoparticles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4. A Schematic Luminescence Model of Surface States . . . . . . . . . . . . . . . . . . . . . . . . Photostimulated Luminescence of Ag and AgI Clusters in Zeolite-Y . . . . . . . . . . . . . . . . . . . 6.1. Photostimulated Luminescence of Silver Clusters in Zeolite-Y . . . . . . . . . . . . . . . . . . . 6.2. Photostimulated Luminescence of AgI Clusters in Zeolite-Y . . . . . . . . . . . . . . . . . . . . Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

325 328 328 329 339 346 346 348 364 366 371 371 371 376 378 379 381 384 390 390 390

1. I N T R O D U C T I O N O n e o f t h e m o s t i n t e r e s t i n g s u b j e c t s in m a t e r i a l s s c i e n c e is a q u a n t u m c o n f i n e m e n t e f f e c t in l o w - d i m e n s i o n a l s y s t e m s as q u a n t u m w e l l s , q u a n t u m w i r e s , a n d q u a n t u m dots. T h e int e r e s t o f this s u b j e c t r e l i e s o n t w o a s p e c t s , o n e is t h e d e s i r e to u n d e r s t a n d t h e t r a n s i t i o n f r o m m o l e c u l a r to b u l k e l e c t r o n i c p r o p e r t i e s , t h e o t h e r is t h e p r o s p e c t o f p r a c t i c a l a p p l i c a t i o n o f t h e s e m a t e r i a l s to o p t o e l e c t r o n i c d e v i c e s [ 1 ], p h o t o c a t a l y s t s [2, 3], a n d c h e m i c a l

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325

CHEN

sensors [4]. The most striking property of low-structured semiconductors is the massive change in optical properties as a function of the size. This is the quantum confinement that is observed as a blue shift in absorption spectra with a decrease of particle size [5]. As the size is reduced to approach the exciton Bohr radius, there is a drastic change in the electronic structure and physical properties, such as a shift to higher energy, the development of discrete features in the spectra, and concentration of the oscillator strength into just a few transitions. The electronic states in the limiting three-dimensional confinement lead to molecular orbitals (strong confinement). The electronic states of a quantum dot are better described with a linear combination of atomic orbitals than bulk B loch functions in momentum space [6]. However, it is still unknown how the bulk electronic properties develop with the size of the nanoparticles. Thus it is interesting to investigate three-dimensional evolution of molecular to bulk properties in a quantum box. Theoretical models based on the effective-mass approximation have established two limiting regimes [7]: the weak and the strong confinement regimes. The first one occurs when the particle radius is larger than the exciton radius. In these regime, the exciton translation motion is confined. The second limiting regime occurs when the particle radius is smaller than the exciton radius. In these regimes, the individual motions of electrons and holes are independently quantized. In both regimes the main experimental effect of the confinement is the blue shift of the absorption edge, which is roughly proportional to the inverse of the square of the particle radius and the appearance of a structured absorption spectrum due to the presence of discrete energy levels. However, some electronic properties are expected to be modified only in the strong confinement regime, for example, the enhancement of electron-hole interaction. This is due to the increase of spatial overlap of electron and hole functions with decreasing size. As a consequence, the splitting between the radiative and nonradiative exciton state is enhanced largely in the strong confinement regime. The quantum confinement not only causes the increase of the energy gap (blue shift of the absorption edge) and the splitting of the electronic states, but also changes the densities of states and the exciton oscillator strength [6]. It was revealed that many of the differences between the electronic behaviors of the bulk and of the quantum-confined low-dimensional semiconductors are due to their difference in densities of states [8-11]. Figure 1 [ 11 ] shows the variation of density of states with dimensionality. Passing from three dimensions to two dimensions the density N ( E ) of states changes from a continuous dependence N ( E ) ~ E 1/2 to a steplike dependence. Thus the optical absorption features are different for the bulk and for the quantum well structure. The optical absorption edge for a quantum well is now at a higher photon energy than for the bulk semiconductor and,

2d ul

Energy Fig. 1. Variationof density of states of electrons withincrease of the quantization dimensionin quantum structures. (Source: Reprinted with permissionfrom [11]. 9 1996AmericanChemicalSociety.)

326

PHOTOLUMINESCENCE AND STIMULATED LUMINESCENCE OF NANOPARTICLES

above the absorption edge, the spectrum is stepped rather than smooth, the steps corresponding to allowed transitions between valence-band states and conduction-band states, while, at each step, sharp peaks appear corresponding to confined electron-hole (exciton) pairs states. In the case of zero-dimensional systems (quantum boxes, dots, nanocrystallites, clusters, nanoparticles and colloids, etc.), the density of states is illustrated as a delta function. Optically, large absorption coefficients are observed, which is illustrated in Section 2.1. The low-dimensional structure has proven to be very promising for application to semiconductor lasers, which is mainly due to the quantum confinement of the carriers and the variation of the density of states with dimensionality [12]. The density of states has a more peaked structure with the decrease of the dimensionality. This leads to a change in the gain profile, a reduction of threshold current density and a reduction of the temperature dependence of the threshold current. Furthermore, improvements of the dynamic properties are also expected. Owing to the steplike density of states, high gain with lower spontaneous emission rate has been realized in a GaAs/A1GaAs graded index-separate confinement heterostructure single quantum well (GRIN-SCH SQW) laser [13]. The quantum structured laser is a promising light source for various applications and many new optical devices based on low-dimensional structures have been proposed and demonstrated. These include optical modulators [ 14, 15], optical bistable devices [ 16], tunable p-i-n QW photodetectors [ 17, 18], size effect modulation light sources [ 19], Q-switching laser light source [ 12], modulation-doped detectors [20, 21 ], and single-electron devices [22-26] (single-electron transistors [23], single-electron storage [24], single-electron computing [25], etc.). The preceding text demonstrates that low-dimensional structured materials are interesting, both for basic research and for practical applications. Low-dimensional semiconductor structures are usually fabricated by highly sophisticated growth techniques like molecular beam epitaxy (MBE) and metallorganic chemical vapor deposition (MOCVD). Those methods may provide low-dimensional structures of high quality. However, some difficulties or problems existed [ 10]. On the other hand, quantum dots can be grown in a relatively easy way, that is the chemical methods, including the colloidal method, sol-gel, Langmuir-Blodgett (LB) thin films, self-assembly, embedding in polymers, encapsulation in zeolites or in glasses, and so forth. Many terms have been used to describe these ultrasmall particles, such as quantum dots, Q-particles, clusters, nanoparticles, nanocrystals, and others. Usually, the zero-dimensional structures prepared in physical methods like MBE and MOCVD are called quantum dots by physicists, while the small particles formed in chemical methods are called nanoparticles, nanoclusters, Q-particles, or nanocrystallites by chemists. We think that the quantum dot is the same in physics as the nanoparticle (nanocrystal, nanocluster, etc.), by definition a system, where the motion of the carriers is confined in all three dimensions. Here we adapt the term nanoparticles to loosely describe semiconductors in the size regime from a few to hundreds of angstroms, which possess hybrid molecular and bulk properties and truly represent a new class of materials. Obviously, the study of these systems is a new interdisciplinary branch of the materials science developing on a border between chemistry and physics. For example, the linear combination of atomic orbitals-molecular orbitals (LCAOMO) approach provides a natural framework to understand the evolution of nanoparticles from molecule to bulk and the size dependence of the lowest excited-state energy (energy gap), while the enhancement in the excited-state oscillator strength can be best appreciated with the exciton concept in semiconductor physics [6]. There are many publications on nanoparticles, mostly on their preparation and optical characterization. Fluorescence of nanoparticles is the subject that is studied most widely but still has some problems that are not clear even at present. Here we review the experimental results and we discuss the fluorescence mechanism. In our group, we have studied the absorption and photoluminescence excitation spectra of nanoparticles systematically [43, 51, 96]. The absorption spectra of the surface states in ZnS nanoparticles were first observed by us [29] and the energy transfer from the exciton

327

CHEN

to the surface states was discussed. We also observed the thermoluminescence (TL) and the photostimulated luminescence (PSL) of nanoparticles [27-31 ]. The thermoluminescence is related to the surface states and the PSL is caused by the carrier migration or energy transfer from the matrix to the particles or between the two domains of the clusters. The appearance of PSL indicates that nanoparticles may find application as a medium for erasable optical storage. This is a new direction of nanoparticle application which is introduced here.

2. M E A S U R E M E N T OF SPLIT L E V E L S OF QUANTUM C O N F I N E M E N T

2.1. Optical Absorption Spectra Optical spectroscopy has played a key role in the study of nanoparticles. The quantum confinement is clearly evidenced by the blue shift of the absorption edge with decreasing size. There will be a series of discrete features appearing near the onset of absorption in the spectra. As the size is becoming smaller, these transitions occur at higher energies and are more widely spaced, as predicted by standard models of quantum confinement. These features are shown clearly in the absorption spectra of CdSe nanoparticles with very narrow size distribution [32] (Fig. 2). The quantum-size effects not only include the blue shift of the exciton energy but they also cover the increase of the exciton oscillator strength and the increase of the binding energy. The exciton absorption in bulk materials is not able to be observed at room temperature, but becomes visible in nanoparticles. This is attributed to the increase of the exciton binding energies and of the oscillator strength. The size dependence of the exciton oscillator strength is one of the most interesting subjects. In a bulk semiconductor, the electron and the hole are bounded by the screened Coulomb interaction with a binding energy of a few to tens of millielectron volts. This exciton is easily ionized at thermal energies, which accounts for the absence of a strong exciton absorption band in a bulk semiconductor at room temperature. By confining the electron and the hole in a nanoparticle, the binding energy and the oscillator strength can increase due to the enhanced spatial overlap between the electron and the hole wavefunction and the coherent motion of the exciton. This confinement effect is responsible for the appearance of the exciton absorption in nanoparticles at room temperature which is illustrated as follows [6].

-

_

.-

~

.

~

-

===

-

:

=

__

-

~

21 A diameter

27

, ,'

o 3oX.111, O

.

.

1.8

.

.

.

2.0 2.2 2.4 2.6 2.8 3.0 3.2 3.4 3.6 Energy (eV)

Fig. 2. Low-temperature(10 K) linear-absorption spectra of CdSe nanocrystals.Mean particle diameters are shown. These spectra have been scaled for clarity. (Source: Reprinted with permission from [32]. 9 1994 American Physical Society.)

328

PHOTOLUMINESCENCE AND STIMULATED LUMINESCENCE OF NANOPARTICLES

The exciton oscillator strength is given by [33],

f-

2m* h---:--~-' - A E IMI21U(o) I2

(1)

where E is the transition energy, M is the transition dipole moment and is concerned with the probability of finding an electron and hole on the same site (the overlap). The oscillator strength per unit volume f l y (v being the cluster volume) determines the magnitude of the absorption coefficient [6]. In the strong confinement (R < a s ) regime, there is an increased overlap of the electron and the hole wavefunctions, and increases with decreasing cluster volume. As a result, f is now only weakly dependent on cluster size [34]. However, the oscillator strength f l y per unit volume now increases with decreasing cluster size and scales roughly as (aB/R) 3 [35, 36]. The exciton absorption band should therefore become stronger as R decreases, and so the excitonic-type features in the absorption spectra become visible even at room temperature [6]. Thus the absorption features of semiconductor nanoparticles are totally different from that of the bulk.

2.2. Photoluminescence Excitation Spectra Optical absorption spectroscopy is of course an effective method to study the quantum-size effects, particularly the enlargement of the energy gap and the enhancement of the exciton energy. However, some difficulties exist in the study of quantum-size effects by optical absorption spectroscopy. Puzzling is the fact that many of the semiconductor nanoparticles synthesized so far show no exciton absorption bands at all, in spite of the positive identification of their existence by X-ray. One of the original and basic experimental questions about quantum dots--how their electronic spectra evolve with size in the strong confinement regimemremains largely unanswered. Early work on this question was constrained by difficulties in preparing high-quality, monodisperse samples. Inhomogeneities such as distribution in size and shape cancel the higher transitions. This size fluctuation gives rise to an inhomogeneous broadening of absorption and luminescence bands that mask information about a single size. Such difficulties have been settled down. Extremely monodisperse ( n,'

$

I |

~_,,...J

_0

i

i

I

i

i

250

300

350

400

450

.....

i

500

Wavelength(nm) Fig. 10. Reflectance absorption (ABS), photoluminescence excitation (PLE), and emission (PL) spectra of 2.38 nm radius CdS nanoparticles. (Source: Reprinted with permission from [54].)

Table II. Experimental and Theoretical Results of the Interband Transitions of CdS Nanoparticles with a Radius of 23.8 ,~ [54] PLE (eV)

120 100

t

Calculated (eV)

Assignment

3.35

3.22

1S-IS

4.06

3.90

1S-1P

4.84

4.75

1S-1D

ZnS/Y

ABS -"t 9

,"7,.

PLE

80 60

PL

40

i

\ 20 0

I

I

I

400

500

600

I

200

300

Wavelength(rim) Fig. 11. Reflectance absorption (ABS), photoluminescence excitation (PLE, ~,em -- 375.5 nm), and emission (PL, ~,ex = 319 nm) spectra of ZnS clusters in zeolite-Y. (Source: Reprinted with permission from [43].)

no longer valid [56]. This is why we can see the 1S-1P transitions that are forbidden in spherical approximation. It was reported by Norris and Bawendi [44] that the absorption features are most efficiently resolved in PLE when the emission is monitored on the blue edge of the lumines-

337

CHEN

Table III. Experimental and Calculated Excitation Peaks of ZnS Clusters in Zeolite-Y Experimental (eV)

Calculated (eV)

Assignment

5.35

1S-1D

4.66

1S-1P

4.12

1S-1S

--

Surface states

5.42* 5.45 t 4.50* 4.50 t 3.94* 3.75 t 3.15t * ~.em = 357.5 nm. t ~.em = 535 nm [43].

Wavelength(nm) 550 500 450 400 350 a)

PLE - - - " FIT

- - -

.,..

"1

i

xl

i

i

i

o

I

. . .

I ~ L . .

!

..

9 I

~.

- l -

- ~ 1

9 -

9 I

b) ~a)

~,i (b)

(a)

.................

=-0

2.2 2.4 2.6 2.8 3.0 3.2 3.4 3.6 3.8 Energy(eV) Fig. 12. (a) Demonstration of the fitting procedure used to extract PLE peak positions. The PLE scan (solid line) is compared to the fit (dashed line) for a "~1.8 nm radius CdSe nanoparticle sample. (b) The individual Gauss,an components (solid line) and the cubic background peak is decomposed into two narrow features lightly to the red of a broader absorption peak. (Source: Reprinted with permission from [44]. 9 1996 American Physical Society.)

cence. Thus in their P L E m e a s u r e m e n t , the detection energy was selected to the e m i s s i o n e n e r g y w h e r e the blue e d g e intensity is ~ 1 / 3 of the p e a k height. As m a n y as eight features were o b s e r v e d in their P L E spectrum of C d S e nanoparticles (Fig. 3). T h r o u g h comparison of the spectra with theoretical predictions (Figs. 12 and 13), the P L E lines were assigned as follows: (a) 1S3/21Se, (b) 2S3/21Se, (c) 1S1/21Se, (d) 1P3/21Pe, (e) 2S1/21Se,

338

PHOTOLUMINESCENCE AND STIMULATED LUMINESCENCE OF NANOPARTICLES

Decreasing Radius 1.2 -

a~

,.."' .,~

,.,

>

(h)

(i)

j.-

1.0

10

(O)

..

..:::.

.-

.~

*"~

/~'

o,

'~

J'"

0.6

0

~0.4

C I

~ w

.... ......

0.2

,

i 0.0 . . . . .i . 9

.,~..+.**.~..~,~-.~

'

(el .

' .

.

!

I L

9

9

I

.

,,

.

I

9

,,,.

9

I

I

2.0 2.2 2.4 2.6 2.8 Energy of 1st ExcitedState (eV)

Fig. 13. Transitionenergies (relative to the first excited states) versus the energy of the first excited state. Strong (weak) transitions are denoted by circles (crosses). The solid (dashed) lines are visual guides for the strong (weak) transitions to clarify their size evolution. (Source: Reprinted with permission from [44]. 9 1996 American Physical Society.) (f) 1Ps/21Pe (1P]/21Pe), (g) 3SI/21Se, (i)4S3/22Se (1S1/22Se, 1P~21Pe). However the assignments of lines h and j are not certain, the possible assignments are: (h) (1S1/21De, 2S3/22Se, 1S3/22Se, 2S3/21De, IDs/21De, and 4P3/21Pe), and (j) (2P~/22P e, 3S3/23Se, 2P3/22Pe, 4P3/22Pe, 2Ps/22Pe, 4Ps/22Pe, and 3S3/22De). It can be seen from Figure 13 that as the radius is decreased, the energy of the excited states is increased and the separation between the excited states is wider. Five PLE lines in Figures 6 and 7 were reported in CdTe nanocrystals doped in glasses by Oliveira et al. [40]. According to the calculation based on a modified multiband envelope function model [57, 58], the five PLE lines are assigned to h 1- --+ e +, h 2- --+ e +, h 1+ --+ e - , h 2+ ~ e - , s o - --+ e - , respectively, [40]. The calculated results also show that the excited-state energy is increased as the radius is decreased and the separation between the excited states becomes wider except for that between the two highest excited states [40]. The previous results show clearly, that the splitted absorption features by quantum-size confinement may be revealed by PLE spectroscopy due to the effective reduction of the inhomogeneous broadening. PLE has become a standard technique to obtain quantum dot absorption information.

3. EXCITATION E N E R G Y D E P E N D E N C E OF F L U O R E S C E N C E We can see in the foregoing text that in the same sample the PLE spectrum is dependent on the monitored emission wavelength. Similarly, the photoluminescence spectrum is dependent on the excitation energy or wavelength. In the following, we will introduce the dependence of the fluorescence on the excitation energy. The dependence of nanocrystal luminescence on the excitation energy has been pointed out by several researchers [7, 38, 41, 54]. However, the detailed results were reported by Chamarro et al. [7], Hoheisel et al. [38], and Rodrigues et al. [41]. It was pointed out that [38], while size is an important factor in determining the energy and relative type

339

CHEN

of emission from the nanocrystals, an equally important issue is the excitation energy or wavelength. By tuning the excitation source to the far red edge of the cluster absorption the extent of inhomogeneous versus homogeneous broadening can be ascertained because only the largest nanocrystals in the sample are excited, and line-narrowing effects are observed [59]. An opposite effect, "line-broadening," can also be expected when the excitation source is tuned far blue of the absorption edge where the homogeneous and inhomogeneous linewidths are comparable. In this limit all the nanocrystals are excited simultaneously, and the complete inhomogeneous profile of the luminescence is observed. Between the far red and deep blue excitation it is possible to generate emission starting with different initially prepared excited states leading to complex but predicated changes in the emission spectrum. This is predicated on the assumption that each nanocrystal luminescence at an energy that is determined only by its size, regardless of what photon energy it is excited with. The features of the nanocrystal fluorescence on the excitation energy may be reflected in Figure 14 and the variation follows these expected patterns [38]: line narrowing in the red, followed by complex behavior when the excitation occurs on top of overlapping states, culminating in an emission spectrum independent of the excitation wavelength. In Figure 14, as the photon energy is increased above the absorption edge of 2.1 eV one peak is observed whose emission energy shifts smoothly with excitation energy. Such a result is expected for an inhomogeneous, single state system (2.175-2.225 eV). However, because there are multiple states present, there is a photon energy (2.29 eV) where the largest nanocrystals can be excited into their second excited state, while a smaller size is excited into their first excited state. Because each nanocrystal emits at one photon energy, regardless of excitation energy, at this point the emission spectrum shows two peaks in it, one from the smaller set of clusters absorbing into their first state and the second from the larger clusters excited into their second state. As the photon energy is tuned further to the blue, this pattern is repeated between states 2 and 3. Unlike the first double peak structure, this spectrum has only a disappearing shoulder on the blue edge due to the limited range of the size distribution (at 2.34 eV). The pattern that emerges from this data is that whenever excitation

E x c i t a t i o n [eV]: 2.175

2.175

2.214

2.214

2.255 2.296

^

2.318

2.

2.340

I1

2.385 2.431 2.455

~

5

2.480

J c

2.531 2.583 2.695 , 2.818 2.952

r-1

~ 71- ' | ~ i

9

.i

9

9" 9

9 1

s" ~

i

1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 $ Photon E n e ~ (eV)

fll !

1 II Wlil !

W

I

m

9

1.8 2 2.2 2.4 2.6 Photon Energy (,V)

Fig. 14. (a) Experimental fluorescence spectra for CdSe-nanocrystals (R = 16 A) for various excitation energies at 77 K. The spectrum at the bottomrepresents the absorption spectrum. (b) Simulatedfluorescence spectra to modelthe evolutionof the multiplepeak structure of the particle ensemble in the previous text. All considered excitation energies correspondto those of the experimental spectra. (Source: Reprinted with permission from [38]. 9 1994American Institute of Physics.)

340

PHOTOLUMINESCENCE AND STIMULATED LUMINESCENCE OF NANOPARTICLES

2.8

~" 2.6 c9 I,U r

~

2.4 2.2

2

2

2.2

2.4

2.6

2.8

3

3.2

Excitation Energy (eV)

Fig. 15. Positionof the emission peak versus excitation energy. This plot is composed from five different samples with various particle radii (9, 13, 16, 21, 26/~). There are three different line groups indicating the emission peak due to excitation of the first (a), second (b), third and higher [all (c)] excited states. Within each line group the peak positions measured of a single sample are connected by thin lines. Note that the emission energies of all samples upon excitation of the first two excited states line up very well. They spread out for higher energy (smaller particles) indicating the effect of quantum confinement. The excitation of the third state merges into the continuum excitation indicated by the almost horizontal line at higher excitation energy. (Source: Reprinted with permission from [38]. 9 1994 American Institute of Physics.)

occurs at an energy where the sample is absorbing into two different, yet overlapping electronic states, a dual peak emission spectrum is observed. At still higher excitation energies a different behavior is observed. The new peak apparently from state 3 moves due to its inhomogeneous width to 2.175 eV, but rather than being followed by a new state from 4 at higher excitation, the emission wavelength becomes independent of excitation even when the sample is illuminated with more than 2.6 eV [38]. By plotting the peak of the emission spectrum versus its corresponding excitation source (Fig. 15) [38], the shift of the emission spectra versus excitation wavelength can be seen more graphically. A sample with no Stokes shift in this graph gives a line of slope 1 (solid line), while a size-independent Stokes shift also has a slope of 1, but with a different intercept [38]. If the emission is independent of excitation, as it is when the sample is excited in the blue of its absorption, then a horizontal line is observed. Figure 15 contains the data from each state in the nanocrystal spectrum. Even though this data was compiled from many different sizes of clusters, a consistent pattern emerges. The first group of lines (labeled as a in Fig. 15) shows [38] the position of the luminescence peak due to excitation near the red edge for all particle sizes. Like the second peak (labeled b) the behavior is nearly linear. At higher energies, corresponding to excitation of smaller particles, all the line groups fan out. The third emission peak (c) stops shifting when the excitation energy in increased further, giving roughly horizontal lines (dashed) [38]. A similar result was reported in CdSe nanocrystals embedded in a silicate glass matrix [41]. The absorption spectrum of the CdSe doped glass sample is shown in Figure 16 [41 ], it has a broad peak centered at ~ 2 . 2 4 eV and a broad shoulder at ,~2.65 eV. The blue shift of the absorption edge relative to the band gap of bulk CdSe indicates the strong confinement of the carriers. From the shift of the absorption edge, the average particle radius is estimated to be ~ 2 . 7 nm. The PL spectrum of the sample consists of a very broad band centered at ~ 1.7 eV and additional structures in the photon energy range of 2.0 ,-~ 2.3 eV. The former band is usually attributed to deep traps [60, 61 ], it is not considered further here. The sharper structure between 2.0 ,-~ 2.3 eV close to the low-energy absorption peak is referred to as band-edge emission. These structures are found to be dependent on the excitation energy (hvL) as seen in Figure 16. The behavior of the PL spectra in CdSe doped glass may be divided into three regions according to the excitation energy (hvL) [41].

341

CHEN

CdSe T-80K

~W 0.0 C

"e 0.0 v

9~raw

m C

o

t

0.0

._=

j 2.o

2.3

~ 0.0 O.,t- :1.1111eV

0.0

Owt,,~W

| I 0.0 t O.O

2.0

2.2

2.4

2.6

2.8

3.0

PhOtOn energy (eV)

Fig. 16. Photoluminescence(PL) spectra of the CdSe doped glass sample at 80 K (curves a-f). For each spectrum the excitation energy (hvL) is markedby an arrow. The identifiable peaks have been labeled AI, A-D. Curve g is the linear absorption spectrum of the same sample. The inset shows the fitting of the PL spectrumwith hvL = 2.41 eV: open circles are the experimental data, dotted lines are the individual Gaussian to which each peak was fitted, and the full line in the sum of the Gaussians. (Source: Reprinted from [41], with permission from Elsevier Science.)

When h vL < 2.2 eV (region I) the PL spectra contain two peaks whose positions vary with h vL in almost the same way [41 ]. In this region the lower energy peak (A') is weaker than the higher energy peak (A) but its intensity increases faster with hvL. Also, the widths of both peaks increase with h vL. In this region the excitation energies lie within the tails of the first absorption peak and therefore only the largest nanocrystals are excited. For hvL in this region, the allowed electronic transition in the nanocrystals must involve the lowest energy confined electrons and holes. Hence, the smaller is h vL the larger is the radius of the resonantly excited nanocrystals. Therefore, the energies of peaks A and A" shift with h VL due to change in the size of the nanocrystals that are resonantly excited. In region II (2.4 eV < hvL < 2.6 eV) [41 ] the behavior of the PL spectra are more complex. When hvL = 2.41 eV the PL has two intense peaks at -~2.09 eV (B) and ,~2.19 eV (C) and a much weaker one at ~2.31 eV (D). For higher hvL peak D disappears while peak C shifts to higher energies while its intensity decreases relatively to that of peak B. Peak B often overlaps with peak A ~. The two appear to be partly resolved for h VL = 2.497 eV. The earlier complex behavior of the PL spectra may be explained in terms of the selectively excited PL. The energy levels in CdSe nanocrystals were calculated theoretically using an envelope function approximation [55, 56]. Combining the theoretical eigenenergy values and a bulk CdSe bandgap (1.84 eV at 80 K), the size of nanocrystals which are excited by incident photos with h vL in region II can be estimated. For example, while a nanocrystal with a radius of 2.3 nm would be excited via the 1S3/2 ~ 1Se transition by a 2.41 eV photon another one with a radius of 4.0 nm would be excited by the same photon via the 1S3/2 --+ 1De transition. The excited electron-hole pairs in both nanocrystals would relax and would recombine radiatively through the 1Se ~ 1S3/2 transition. The resultant PL spectrum will consist of two peaks at ,~2.41 eV and ,-~2.03 eV due to the 2.3 and the 4.0 nm

342

PHOTOLUMINESCENCE AND STIMULATED LUMINESCENCE OF NANOPARTICLES

nanocrystals, respectively. As h VL is varied, some crystals with different radii are brought into resonance while others go out of resonance. As a result a complex and rich variety of dependence of the PL spectra on h vL is observed. In region III where hvL > 2.55 eV there are so many transitions allowed for nanocrystals with different radii that the PL spectra contain signals from almost the entire distribution of nanocrystals. Therefore only a very small dependence of the PL spectra on hvL is observed [41]. Photoluminescence of CdSe nanocrystals in a glass matrix was also investigated by Chamarro et al. [7] at low temperature with size-selective excitation. Figure 17 [7] shows low-temperature absorption spectra of CdSe nanoparticles in oxide glasses at 5 K. The radii of the four samples are 15, 17, 18, and 27 A, respectively. Absorption bands from confined states at higher energy are clearly resolved, indicating a narrow size distribution. The size selectively excited PL spectra of sample 3 are shown in Figure 18 [7]. It is seen that luminescence mainly originates from band-edge state transitions. Curve a in Figure 18

1.2 /

.

'

" ...... "

'-

"

4'

/

1.0 0.8

3

'

~

0.6

2

"

~

0.4

~.8

-,

2.O

2.2

2.4

2.6

2.8

3.O

3.2

ENERGY (eV} Fig. 17. Absorptionspectra of CdSe nanocrystals in oxide glasses at 5 K. The mean radii are 1.5, 1.7, 1.8, and 2.7 nm for samples 1, 2, 3, and 4, respectively. (Source: Reprinted with permission from [7]. 9 1996 American Physical Society.)

II

),

c

W U)

=L

o

,a t,, t v

=0 "a

-I

m it 17 I= we. Im

1.9

2

2.1 2 . 2 2 . 3 ENERGY (eV)

2.4

2.5

Fig. 18. Photoluminescence spectra of CdSe nanocrystals in oxide glasses (sample 3 of [7]) obtained at 5 K with excitation at (curve a) 3.645 eV, (curve b) 2.39 eV, (curve c) 2.344 eV, (curve e) 2.26 eV, (curve f) 2.216 eV, (curve g) 2.17 eV, and (curve h) 2.142 eV. The black dots indicate the position of the F-line. The dashed curve is the absorption spectrum. (Source: Reprinted with permission from [7]. 9 1996 American Physical Society.)

343

CHEN

is obtained with an excitation energy well above the band edge, thus the emission is contributed from the entire size distribution. Curves b-h in Figure 18 are the PL spectra measured by tuning the excitation energy through the first absorption peak. For low-energy excitation, the luminescence spectrum, close to the laser position, is dominated by three lines: a line (denoted as an F-line) with an energy shift of a few meV from the laser and two lines about 26 and 52 meV from the F-line energy position. These two lines are assigned to the 1LO and 2LO phonon replica of the F-line [7]. The three lines are hardly distinguishable and the spectrum consists of two broad bands (curves b and c). For an excitation energy higher than 2.31 eV, the F-line is not observed anymore. This is similar to the results observed by Rodrigues et al. [41 ]. The size-selective technique makes it possible to study the size dependence of the PL spectra [7]. The energy difference A E between the laser energy and the F-line is plotted as a function of the particle radius. It shows clearly that AE is increased with decreasing size. From the analysis of the time decay and the steady-state and time-dependent degree of linear polarization, the F-line is attributed to the recombination of the optically forbidden A exciton [7]. The size dependence of the F-line shift (AE) was considered to be originated mainly from the size dependence of the electron-hole exchange energy which varies as 1/R 3 for small nanocrystals owing to the increasing overlap of the electron and hole wavefunctions. The small deviation of the F-line shift from the 1/R 3 dependence [7] was considered to be caused by the size dependence of the acoustical-phonon energy. Because the radiation recombination was considered to be possible through a phonon-assisted virtual transition to the confined B-exciton state [7]. This work tells us that size selectively excited PL may provide much information to the intrinsic properties of single size nanocrystals. Similar results were observed by us [51, 54] in CdS nanoparticles deposited from chemical colloids or embedded in a mesoporous zeolite. The reflectance absorption (ABS), photoluminescence (PL), and excitation (PLE) spectra of the CdS nanoparticles deposited from chemical colloids are shown in Figure 10. The average size of the particles estimated from an X-ray diffraction pattern is around 23.8 ,~ [54]. Two emission bands at 385 and 465 nm were observed and were attributed to the excitonic and trapped luminescence, respectively, [54]. The excitonic emission is much stronger than the trapped emission, demonstrating a good surface passivation of the nanoparticles. Actually, the excitonic emission band consists of two peaks and the relative intensity of the two peaks is dependent on the photoexcitation energy (Fig. 19) [54]. Excitation at 370 nm, the high-energy peak is stronger than the low-energy peak, but the low-energy peak is stronger when the excitation is at 260 or 310 nm [54]. Figure 20 shows the reflectance absorption (ABS), photoluminescence excitation (PLE), and emission (PL) spectra of CdS clusters in a mesoporous zeolite [51 ]. The average size of the clusters is around 18.5/~. The strong emission around 550 nm is assigned to the trapped luminescence arising from surface states. A small shoulder around 420 nm is probably the excitonic fluorescence. The trapped luminescence is much stronger than the excitonic fluorescence, indicating poor passivation of the surface states. Figure 21 [51] shows the emission spectra excited at 288, 368, and 434 nm, respectively. These excitation energies are corresponding to the three excitation bands in Figure 20, respectively. At high-energy excitation, both the excitonic and the trapped emission bands were observed. While at lowenergy excitation, only the trapped emission band was observed and the band was sharpened largely as the excitation energy was lower. Our observations demonstrate that not only the excitonic, but also the trapped fluorescence are dependent on the excitation energy [51 ]. It was pointed out [41] that the behavior of these selectively excited PL spectra is dependent on the nanocrystal size distribution. If the distribution is very broad, a large number of particles of different sizes are always excited. Hence a broad PL spectrum with no distinct features will be observed independent of excitation energy (hvL). On the other hand if the distribution is extremely narrow, the emission peak always occurs at the same energy determined by the unique crystal size. Only in the intermediate case of a distribution can

344

PHOTOLUMINESCENCE AND STIMULATED LUMINESCENCE OF NANOPARTICLES

v>,, .i t,t) ri

r-

J

.i

EX: 310nm

i

n,"

EX: 260nm

360

I

I

I

1

I

I

380

400

420

440

460

480

500

Wavelength(nm) Fig. 19. Photoluminescence spectra of 2.38 nm-CdS nanoparticles excited at 260 nm (bottom), 310 nm (middle), and 370 nm (top), respectively. (Source: Reprinted with permission from [54].) Size:l.85nm PL

"C3 (D ,IN

ABS

PLE

600 Z

4ow eIu

-= 2 0 ,I It l

/%~"~ex?tons

'k

lg

0

I

I

I

I

300

400

500

600

700

Wavelength(nm)

Fig. 20. Reflectance absorption (ABS), photoluminescence excitation (PLE, ~emission --553 nm), and emission (PL, ~.excitation= 312 nm) spectra of CdS clusters in a mesoporous zeolite. (Source: Reprinted from [51], with permission from Elsevier Science.)

appropriate excitation energy excited several nanocrystals simultaneously producing a PL spectra which contains more than one peak and whose relative intensities and peak positions vary with h vL. We [96] have studied the excitation-energy dependence of the photoluminescence of CdS clusters in zeolite-Y in which the size distribution is very narrow. We found that the emission position is not varied with excitation energy but the emission intensity is related to the excitation energy. The luminescence intensity excited at 250 nm is lower than that excited at 310 nm (Fig. 22 [96]). This indicates that the luminescence efficiency is lower at higher energy excitation, which is contrary to that in the bulk from which the luminescence efficiency is higher at higher excitation energy. Because more nonradiative channels occurred at upper levels of the quantum box [ 104], the radiative recombination rate is lower by higher excitation into higher levels at higher excitation energy and thus the luminescence is weaker. Our observation supports the intrinsic mechanism proposed by Benisty et al. [104] for the poor luminescence properties of quantum-box systems.

345

CHEN

80 Size:1.85nm 34nm

.~ 60 :5 .,~ e-

40-

r

._> n,'

20Ex:288nm

\

I

I

I

400

500

600

700

Wavelength(nm)

Fig. 21. Photoluminescence spectra of CdS clusters in a mesoporous zeolite excited at 288, 368, and 434 nm, respectively. (Source: Reprinted from [51], with permission from Elsevier Science.) 120 ABS

,-:,. l O 0 -

._z- 8 O -

PLE

PL

~'~/

Ex: 310nm

e-

--" c

60-

ID g9

t~

40

-

20-

0

200

I

I

I

300

400

500

600

Wavelength(nm)

Fig. 22. Absorption (ABS), photoluminescence excitation (PLE), and emission (PL) spectra of CdS clusters in zeolite-Y (5 wt%). (Source: Reprinted from [96], with permission from Elsevier Science.)

From the selectively excited PL results the size distribution and the energies of excitedstate transitions can be determined by comparing with the theoretical calculation [41]. These observations tell us that selectively excited PL is a good method to study the sizedependent optical properties of nanoparticles and from which much useful information may be obtained.

4. A B S O R P T I O N A N D L U M I N E S C E N C E O F S U R F A C E STATES IN N A N O P A R T I C L E S 4.1. G e n e r a l I n t r o d u c t i o n

Optical excitation of semiconductor nanoparticles leads to band-edge and deep trap luminescence. The size dependence of the exciting or band-edge fluorescence has been studied extensively and is now well understood [10]. It is noted that the fluorescence process in

346

PHOTOLUMINESCENCE AND STIMULATED LUMINESCENCE OF NANOPARTICLES

semiconductor nanoparticles is very complex and that most nanoparticles exhibit broad and Stokes-shifted luminescence arising from the deep traps of surface states [59, 62-66]. Only clusters with good surface passivation may show high band-edge emission [37]. The absence of band-edge emission has been previously attributed to a large nonradiative decay rate of the free electrons to the deep-trapped states [67]. As the particles become smaller, the surface-volume ratio and the surface states increase rapidly, thus reducing the excitonic emission via nonradiative surface recombination [68]. The earlier text indicates that the surface states are very important to the physical properties, especially the optical properties, of the nanoparticles. However, little is known about the physical properties of the surface states. Some reports [69, 70] said that the trapped fluorescence of the surface states does not vary as much upon decreasing size, while others [28, 29, 38, 61, 71 ] showed that the surface luminescence shifts to the blue as the size is decreased. These results indicate that the surface states of semiconductor nanoparticles should be investigated further. Furthermore, no absorption properties of the surface states have been reported, even if the fluorescence of surface states has been widely reported. It has been pointed out [61 ] that the surface states are not able to be detected in the optical absorption spectra. The absorption features of the surface states in ZnS nanoparticles were reported by us [29]. Here we will summarize the absorption and luminescence of the surface states in semiconductor nanoparticles. First, we introduce some basic concepts of the surface states and then we show how the surface states influence the intrinsic properties of the nanoparticles. For particles in such a small size regime, a large percentage of the atoms is on or near the surface, for example, 99% of the atoms are on the surface for a 1 nm sized particle (Table IV). The existence of this vast interface between the nanoparticles and the surrounding medium can have a profound effect on the particle properties. The imperfect surface of the nanoparticles may act as electron and/or hole traps upon optical excitation. Thus the presence of these trapped electrons and holes can in turn modify the optical properties of the particles. They can also lead to further photochemical reactions which are of considerable interest in the field of photocatalysts [72]. For example, the presence of surface-trapped electron-hole pairs can reduce the exciton oscillator strength [73], thus may modify the absorption and luminescence of excitons. The effect of a surface-trapped electron-hole pair on the optical absorption spectrum of CdS nanoparticles has been studied with timeresolved laser spectroscopic techniques [73]. Experimentally [6], it was found that the exciton absorption is bleached during the presence of the trapped electron-hole pair and recovers as the trapped electron-hole pair decays away. It was pointed out [6] that one trapped electron-hole pair can bleach the exciton absorption for the whole cluster. There must exist, therefore, a strong interaction between the trapped electron-hole pair and the exciton to cause the loss of the exciton oscillator strength [6]. The effective mass models consider crystallite internal molecular orbitals that evolve into the continuous valence and conduction bands in the bulk crystal. It may illustrate the

Table IV. Relationbetween Size and Surface Atoms

Size (nm)

Atoms

Percentage of Atoms at Surface (%)

10

3* 10 4

20

4

4* 103

40

2

2.5* 102

80

1

30

99

347

CHEN

Fig. 23. Sketchshowinginfluence of surface states on the spatial overlap of the electron and the hole wavefunction. (Source: Reprintedwith permissionfrom [6]. 9 1991AmericanChemical Society.)

blue shift of the absorption edge upon size qualitatively but it cannot explain many of the other physical properties, such as the fluorescence efficiency, because it ignores possible surface states and surface construction. Each 32 ~ diameter CdSe QC has an internal F = 3/2 highest occupied molecular orbital (HOMO). This state lies about 0.1 eV below the top of the bulk valence band [59]. Theory predicts a surface HOMO band of narrow width, composed of lone pairs on Se atoms that have three covalent bonds into the bulk lattice [74]. This surface band actually lies within the bandgap if the surface geometry is held unchanged from bulk tetrahedral angles and bond lengths. That is, an internal HOMO hole could localize spontaneously on the surface. Because there is a large increase in effective mass from a delocalized hole to one localized in the surface band, the kinetic energy of the hole is not increased substantially upon localization, as would be expected from bulk arguments alone [59]. The behavior of the surface states within the energy bandgap just like the impurity levels within the bandgap of bulk materials, will influence the physical properties largely [61]. It was predicted by theoretical calculation that in the presence of a surface trapped electron-hole pair, the exciton energy shifts to the red by only "~50 meV but its oscillator strength is reduced by 90% for a 25 A-radius CdS particle [6]. The basic physics can be easily understood by considering the overlap of the electron and hole wavefunction [6]. Without the trapped electron-hole pair (Fig. 23a [6]), the hole wavefunction (smaller, dark circle) is located at the center of the cluster and has good overlap with the electron wavefunction (shade circle). By introduction of a trapped electron and a hole to the cluster surface, the hole wavefunction is now localized in the presence of the trapped electron because of the behavior is still delocalized (Fig. 23b [6]). This may reduce the spatial overlap of the electron and the hole wavefunction and thus of the oscillator strength of the exciton. It was also expected [6] that the trapped electron is more efficient than the trapped hole in bleaching the exciton absorption because the trapped hole is not capable of localizing the electron (with small effect mass) and therefore is inefficient in reducing the electron-hole overlap. This prediction does quite well with the pulse radiolysis experiments performed by Henglein [75] and Henglein et al. [76]. It clearly seems that the surface effects of nanoparticles play a key role in their properties, from structural transformation to light emission and to solubility [ 11 ]. Furthermore, it was predicted [46, 59] that surface states near the gap can mix with interior levels to a substantial degree, and these effects may also influence the spacing of the energy levels. It was established that in many cases it is the surface of the particles rather than the particle size which determines their properties. It is, therefore, a major goal to characterize the surface states and to control them chemically [6, 11, 71].

4.2. Excitonic and Trapped Fluorescence In the following we will introduce the fluorescence of semiconductor nanoparticles with emphasis in the fluorescence of surface states and the influence of the surface states in the

348

PHOTOLUMINESCENCE AND STIMULATED LUMINESCENCE OF NANOPARTICLES

1

\

J!

iI

,,..a

I!

I' II

(D r

9 ca~ 9

i

4O0

~ I ~ ~f~,i Ct 9

_~mple II "~'~ample I%. i 600

,

~--

800 wavelength [nm]

,..d

-i'~-

1000

Fig. 24. Absorptionand fluorescence spectraof CdS nanoparticles (samplesI and II). (Source: Reprinted from [71], with permission from Elsevier Science.) fluorescence of the particles. As we know, the spectral position, the ratio of excitonic to trapped fluorescence, as well as the absolute intensity are influenced not only by the particle size but also by the surface modification. Usually the band-edge emission due to the exciton recombination is very weak, and the red-shifted emission from the deep-trapped states is strong. As pointed out that, in many cases, it is the surface of the particles rather than the particle size which determines their properties. In semiconductor particles an electron-hole pair is generated by absorption of light. After being trapped on the surface, the charge carriers may recombine either under the emission of light or nonradiatively. Fluorescence spectroscopy is, therefore, an easy and sensitive method of studying the surface states of nanoparticles [71]. It is also a convenient method with which to obtain information on the energetics and dynamics of photogenerated charge carriers in small particles. The spectral distribution may give information on the occurrences, population, and depths of the surface traps. The relaxation kinetics of the charge carriers can be obtained from timeresolved measurements. It was concluded from the temperature-dependent fluorescence of quantum-sized CdS and CdSe particles that one of the charge carriers is trapped in shallow traps and the other one in deep traps [71 ]. However, which one is trapped in the shallow or in the deep traps should be studied further. The fluorescence and absorption spectra of two samples of CdS nanoparticles are shown in Figure 24 [71 ]. The sizes of the two samples estimated from the absorption edge are 34 and 43/k, respectively. Both of the two samples exhibit a sharp excitonic fluorescence band (at 435 nm for sample 1 and 480 nm for sample 2), as well as a broad fluorescence band at longer wavelengths arising from the recombination of trapped charge carriers at the surface states. The fluorescence quantum yield of the samples is in the order of 0.1 [71 ]. Cooling the sample to 4 K increases the quantum yield to 1 without significantly changing the spectral shape. Thus, it was concluded that the fluorescence spectra at room temperature may reflect the energetic distribution of the entirety of the photoexcited charge carriers [71 ]. As seen from Figure 25 [71] the addition of nitromethane (or methylviologen can quench the fluorescence of CdS nanoparticles effectively and may shift the emission to the red. In order to explain the fluorescence quenching experiments, it was assumed that the electron traps are fixed relative to the conduction band of differently sized particles. Therefore, energetically, the main difference between the two samples is the bandgap energy. Considering these assumptions and the positive reduction potentials, the fluorescence quenching behavior of CdS nanoparticles by nitromethane or by methylviologen may be explained reasonably [71 ]. It may be seen later that this assumption is consistent reasonably with the thermoluminescence results of semiconductor nanoparticles [27-29]. Although there are many publications on the fluorescence of nanoparticles [38, 59, 63, 64, 77-81], it is not clear now about the nature of the emitting states and the lumines-

349

CHEN

[

I

AI

i

sample I o~,,~ r~

~D

,l,,,a

o~,,~

10 -3 M C H 3 N O 2

r r r~

o

sample II All

,-d ~D

9

9

400

S

I

10-3 M CH3NO2

600 800 wavelength [nm]

1000

Fig. 25. Fluorescencespectraof CdS nanoparticlesbefore (solidline) and after (dottedline) the addition of 10-3 M nitromethane. (Source: Reprinted from [71], with permissionfrom Elsevier Science.)

cence mechanism. Rosseti et al. [5] and Wang and Herron [66, 82] have published data on low-temperature fluorescence measurements on colloidal CdS and CdSe particles in solution and in zeolite frameworks. The fluorescence quantum yields of their samples were extremely low and even at liquid helium temperature they were far from unity. Therefore, fluorescence was only a side reaction when compared to the main process of radiationless recombination. Due to the broad size distribution, the samples showed only a broad fluorescence band from the recombination of trapped charge carriers. Detailed conclusions on the nature of the emitting states and on the trap depths for electrons and holes could hardly be drawn. O'Neil et al. [77] have published results on both static and time-resolved fluorescence experiments performed with CdS particles which exhibited higher fluorescence quantum yield but rather broad size distribution. However, the clear differentiation between excitonic and trapped fluorescence could be made. In the meantime some highly mondisperse CdS particles have been prepared and showed high fluorescence quantum yields at room temperature [63, 83]. Eychmuller et al. [64] had reported the temperature-dependent static and the time-resolved fluorescence of CdS nanoparticles and they showed how surface chemistry influence the trap depths and how the population of traps with electrons and holes changes as a function of temperature. Their work is representative of one type of semiconductor nanoparticle fluorescence which is introduced as follows. Two samples of CdS nanoparticles were studied by Eychmuller et al. [64], sample 1 shows only the excitonic fluorescence (Fig. 26, upper), while sample 2 shows both the excitonic and the trapped fluorescence (Fig. 26, lower). The temperature dependence of the fluorescence of the two samples is shown in Figures 27 and 28, respectively. The most obvious features are a general increase in fluorescence intensity and a blue shift of the fluorescence maximum with decreasing temperature. Both the excitonic and the trapped fluorescence increase with decreasing temperature. Figure 29 [64] shows the spectral position of the maxima of the two fluorescence bands as a function of temperature. It is seen that the spectral shift of the trapped emission is much larger than that of the excitonic fluorescence. It is noted that the energetic difference between the excitonic and trapped

350

P H O T O L U M I N E S C E N C E A N D S T I M U L A T E D L U M I N E S C E N C E OF N A N O P A R T I C L E S

Fig. 26. Absorption and fluorescence spectra of CdS nanoparticles at room temperature. (~,ex -- 360 nm, upper: sample I, lower: sample II). (Source: Reprinted with permission from [64].)

Fig. 27. Fluorescence spectra of CdS nanoparticles (sample I) at different temperatures. ()~ex -- 360 nm). (Source: Reprinted with permission from [64].)

Fig. 28. Fluorescence spectra of CdS nanoparticles (sample II) at different temperatures. (~,ex -- 360 nm). (Source: Reprinted with permission from [64].)

351

CHEN

~" 22.0 ~

........

....

17.4 .

0

excitonic E 21.5-

-16.9

o

-

.

N ~

trapped

o .

"16.4

21.0

O ~

,

0

0

"

= 20.5 -, , , , , ~ " , , , , ~ . ; , , ~ - , ' . . . . . , ,,15.9 ~, 0 50 100 150 200 250 ...7 Temperature (K) Fig. 29. Spectralposition of the trapped (circles) and excitonic (dots) fluorescence maxima as a function of temperature (sample II). (Source: Reprinted with permission from [64].)

r~

700 600 500

"~_~=~=~400300

~ , 8 ~

= 200 O

100 IJ

9

0

"

"

~ ."."~ '.:,, . . . . . ~..~......... . 50 100 150 200 250 Temperature (K) "

i

i

i

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"

9

300

Fig. 30. Excitonic(dots) and trapped (circles) fluorescence intensities as a function of temperature (sample II). (Source: Reprinted with permission from [64].)

fluorescence amounts to 0.6 "~ 0.7 eV which is considered mainly due to the energy loss of hole trapping and it was concluded that the electron traps are much more shallow than the hole traps [64]. Figure 30 [64] shows the intensity of the excitonic fluorescence (dots) and the trapped fluorescence (circles) of sample 2 as a function of temperature. It is seen that the temperature dependence of the fluorescence is very complex and that the dependence of the trapped fluorescence is different from that of the excitonic fluorescence, the latter is more complex. The decay curves of the excitonic and trapped fluorescence at different temperatures are shown in Figure 31 a and b, respectively, [64]. The decay curves of both the excitonic and the trapped fluorescence are multiexponential, but, there are some differences in the decay behavior of the two types of fluorescence [64]. It was noted [64] that a simple explanation, that is, the photogenerated electron-hole pair (exciton) gives rise to spontaneous fluorescence, cannot explain the complex behavior of the temperature dependence of the fluorescence and decay rate. It was also found that in CdS and ZnS nanoparticles the trapping of electrons is an extremely fast process occurring in the 10-13-10 -14 s time range [78, 84]. Therefore, spontaneous fluorescence has no chance to compete with this process. Thus, excitonic fluorescence was considered to be arisen via detrapping of the trapped electrons. In this sense, the traps work as a reservoir for electrons and they lead to a delayed fluorescence [71, 64]. Considering the preceding

352

PHOTOLUMINESCENCE AND STIMULATEDLUMINESCENCE OF NANOPARTICLES

4K

t/)

.,::; eo

.,.,.,

i/} 0,1 .4. r.....,.

0

100

200

300

T~me (ns)

~4s

_3o~~

b

er

C

,I

0

100 2oo The Ins)

300

Fig. 31. Decaycurvesfor the excitonic fluorescence (a) and for the trapped fluorescence (b) at different temperatures (sampleII). (Source: Reprinted with permissionfrom [64].)

measurement, a model was proposed by Eychmuller et al. [64] to explain the excitonic and the trapped fluorescence of CdS nanoparticles. They [64] proposed that the trap population depends on the temperature as schematically shown in Figure 32 for two temperatures. They distinguished between shallow and deeper traps and they considered that nonradiative processes (Knr) mainly take place out of deeper traps. The fluorescence decay rate is determined by detrapping (K d) and Knr. With decreasing temperature two effects influence the fluorescence decay in opposite ways: detrapping out of a given trap becomes slower as it is a thermally activated process, on the other hand the trap population shifts closer to the conduction band, that is, most of the electrons are then trapped in very shallow traps. It seems that the temperature dependence of the fluorescence may be explained reasonably based on the previous assumptions. Some interesting results on the luminescence of CdSe nanocrystallites have been observed by Bawendi et al. [59] who used time-, wavelength-, temperature-, polarization-

353

CHEN

m u

shallow traps .-!.-'~I

270 K

4K

Fig. 32. Modelfor the excitonic fluorescence in a CdS quantum dot with a temperature-dependent trap population. (Source: Reprinted with permission from [64].)

LumlMm:uwe

,A~orpt.~n

[,,llllrtll'14~l~t

~tlcm

Fig. 33. (Top) Absorption and luminescence spectra of 3.2 nm CdSe nanocrystals at 15 K ( ~ . e x " 440 nm); (Bottom) The same absorption spectrum but the luminescence excitation wavelength is on the red edge of the absorption band (~.ex= 550 nm) for size selection. (Source: Reprinted with permission from [59]. 9 1992 American Institute of Physics.)

resolved luminescence to elucidate the nature of the absorption and "band-edge" luminescing states in 3 2 / ~ wurtzite CdSe particles. Figure 33 shows the absorption and excitation dependent luminescence spectra of the CdSe particles [59]. The results shows that excitation in the blue gives a symmetric band-edge emission with high quantum yield (Fig. 33, upper). The entire size distribution contributes to this emission. In contrast, only the "largest" crystallites are excited selectively on their zero phonon lines by spectrally narrow excitation on the red edge of the absorption spectrum. Thus the same sample shows the cw structured emission by 550 nm excitation (Fig. 33, lower). This emission approaches

354

PHOTOLUMINESCENCE AND STIMULATED LUMINESCENCE OF NANOPARTICLES

that of a perceptively monodisperse sample. There is a Frank-Condon LO phonon emission progression with bulk spacing of 200 cm -1, with a shift of ~75 cm -1 between the excitation energy and the peak of the LO zero phonon line in emission. The shape of the structured emission spectrum is nearly insensitive to excitation wavelengths on the red side of absorption, but a blur light is used, the apparent ratio of the intensities of the zero to first LO phonon decreases until the first LO phonon appears more intense than the zero LO phonon. This is a direct result of the size distribution_bluer wavelength exciting a broader distribution by exciting larger crystallites on the first LO phonon and smaller ones on their zero phonon line [59]. Such phenomena have been discussed in Section 3. Figure 34 [59] shows the time-resolved emission spectra constructed from decay curves at different emission wavelengths. There is a clear red shift of the structured spectrum during the first nanosecond. In Figure 34, the highest intensity at each time is scaled to the same absolute value; there is no resolved rise time in emission at any wavelength in this region. Figures 35 and 36 show the emission decay at the peak of the zero LO phonon lines

Time Resolved Luminescence ,,1.

9

50-250 ps

u

~50-650 !

~

550

-

ps

!

5

ns

5;5

560

565

Wavelength (nm) Fig. 34. Time-resolvedluminescence spectra showing a red slide (75 cm-1) of the spectrum as a function of time during the first nanosecond. The intensities are all scaled to the same value for comparison of line shapes. (~.ex = 549 nm). (Source: Reprinted with permission from [59]. 9 1992 American Institute of Physics.)

I.uminwoenc~m

~uto

Intenmltios) ~OK 20K 101


?oc lc>

Yea

la> Fig. 39. The three-state model. ~tbais the radiative decay from b to a, ~c is the radiationless decay from b to c, and Ycb represents the rate of repopulation of b fixed by microscopic reversibility. There is an energy offset E between b and c. A nonradiative pathway Ynr has been put to account for the decrease in quantum yield with temperature and b and c were assumed to have equal degeneracies. (Source: Reprinted with permissionfrom [59]. 9 1992 American Institute of Physics.)

mal equilibrium is excited between a weakly emitting, long-lived lower state, and a strong emitting, upper state. These results can be modeled phenomenologically by assuming that both fast and slow components occur in one nanoparticle and do not represent emission from a separate group of nanoparticles. The model is shown in Figure 39 [59], "(a)" is the ground state, "(b)" represents initially populated states which carry most of the oscillator strength in absorption, while "(c)" represents "darker" states populated principally by radiationless transitions from (b). State c has an extremely long lifetime implying that at least one carrier is localized or "trapped," producing a very poor overlap with the other carriers. It was proposed that [59] the hole is surface localized, essentially at the same energy as the internal 1Sh MO, as suggested as the surface band calculation. The experimental results can be understood if there is strong resonant mixing among the zero-order A and B internal MOs and the zero-order surface Se lone lair states. Some of the surface Se atoms will couple strongly and some will couple weakly to the interior A and B MOs. The model based on the resonance between interior and surface localized states is able

357

CHEN

i

ii

ii

LUMINESCENCE

,

i

i

it

_

S'PEC TR A

/

-- 22~,~

DIAMETER

)..

I.-tn z w tz:

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, ,

_

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I

d

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J

440 EMISSION

"r

v

t

L

I

~

~

s2o

. e ~

/

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6oo

WAVELENGTH

DIAMETER

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(nm}

Fig. 40. Time-resolvedemission spectra of CdS nanoparticles at 10 K. The dashed lines refer to integrated emissionin the 0 ~ 1.5/zs time period after excitation. The solid lines refer to the 16 --~32/zs time period. (Source: Reprinted with permission from [61]. 9 1986 American Chemical Society.)

to illustrate the influence of the surface states on the intrinsic properties of the particles reasonably. Similar fluorescence behavior in CdS clusters was investigated by Chestnoy et al. [61 ]. They also measured the time, wavelength, temperature, and physical size dependence of the CdS cluster luminescence, focusing on the excited relaxation and luminescence process following optical excitation. Excitation of the colloidal clusters produces a broad luminescence band in the visible region of the spectrum as shown in Figure 40 [61]. Through analysis, they attributed the luminescence to a photogenerated, trapped electron tunneling to a preexisting, trapped hole and they pointed out that the range of tunneling distance is almost independent of cluster size. The optical line shape and the temperature dependence of the lifetime indicate that the carriers are very strongly coupled to lattice phonons. All these phenomena indicate that the luminescence processes in these particles are quite complex and await to be studied further. A growing part of the present activities on semiconductor nanoparticles is motivated by the search for mechanism of energy relaxation, because the study of the energy or carrier relaxation by time-resolved PL is helpful for understanding the luminescence process that is still a controversial subject. For example, Bawendi et al. [59] have argued that the bandedge emission comes from the recombination of a shallow surface trapped hole with a delocalized electron, whereas Eychmuller et al. [64] considered that in CdS nanoparticles it is the electron that becomes surface trapped. These need to be revealed further. In bulk semiconductors, the energy relaxation of nonequilibrium electrons and holes is mainly mediated through interaction with an LO phonon or, in highly excited materials, proceeds by carrier-cartier scattering. In systems with a discrete energy level structure, the relaxation process is modified when the level spacing grows with increasing confinement. It has been suggested that the cartier relaxation is suppressed unless the level separation equals the LO-phonon energy. This slowing down of the relaxation rate of nonequilibrium charge carriers is referred to as the phonon bottleneck [79]. The survival of a hot carriers

358

PHOTOLUMINESCENCE AND STIMULATED LUMINESCENCE OF NANOPARTICLES

9

II 9 ' . r " 1

.

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. . . .

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2.3

i = . . l l l . l l *

2.4

2.5

2.6

~_

I I L J l l

2.7

l,J*

2.8

!.9

Energy (eV) Fig. 41. Time-resolved(solid lines) and cw (dashed line) photoluminescence spectra of CdS nanoparticles measured at pump flounce COp= 5 #J cm-1 . (Source: Reprinted with permission from [80]. 9 1996American Physical Society.)

system over a long time increases the probability of carriers escaping from the quantum dot into the matrix and therefore would cause nonradiative recombination. The hindered relaxation could provide an intrinsic mechanism for low luminescence efficiency [79]. Femtosecond measurement is important in the study of such processes as well as the carrier dynamics in semiconductor nanoparticles. Such measurements have been carried out on CdS [80], CdSe [7, 79, 81, 85-87] and lnAs [88] quantum dots. Here we introduce some of these results. The time-resolved spectra of the band-edge emission of CdS nanocrystals recorded at different delay times are shown in Figure 41 (solid lines) along with a cw (time-integrated) spectrum (dashed line) recorded at the same pump intensity [80]. The up-converted PL spectra exhibit a number of discrete features which are not resolved in the cw spectrum. The striking feature of the recorded spectra is the extremely fast buildup dynamics in the whole spectral range. The initial relaxation time of spectrally integrated PL derived from the spectra in Figure 41 is ~ 1 ps. The analysis of the relaxation dynamics performed shows that transitions ~r2 and or4 (as denoted in Fig. 41) have relatively slow and nearly the same relaxation dynamics with time constant 20-23 ps. Whereas the transitions Orl and nr3 are characterized by much shorter relaxation times of about 1 and 3 ps, respectively. As seen from Figure 41 as well as reported in the literature, there is a red shift from the lowest absorption peak to the band-edge emission. The shift amounts to several tens of meV and has been explained either by strong electron-phonon interaction [89] or by the presence of localized states (surface and/or defects) involved in the band-edge emission [90]. Two maxima were observed in the femtosecond spectra of CdS particles (Fig. 41 [80]): one (short-lived) at the transition between the lowest extended states (or1), and the other (long-lived) at the position of the cw-emission maximum (~2). This observation excludes the explanation of the PL red shift by strong coupling of extended states to lattice vibrations and it supports the presence of the localized states in the energy bandgap which are involved in the band-edge emission. A model (Fig. 42 [80]) was proposed to illustrate the femotsecond PL discrete features in CdS nanocrystals. The trapping of carriers

359

CHEN

e

Is e

~2 = 20 - 30 ps Band-Edge Emission

El' t o a

% [c~

!%

o e e

'Deep-Center, ' Emission t

t I n

A~ _

Ao

i

:,

A i

~n= lps h

I sh

Fig. 42. The tentative scheme of energy levels in CdS nanocrystals which accounts for the PL spectra: lse and lsh are the lowest electron and hole extended states, A0 and A- are the levels of the neutral and the

charged acceptors, respectively. ET is a deep electron trap. Thin solid and dashed arrows show the transitions leading to the band-edge and the deep-center emission, respectively.Thick solid arrows show the carrier trapping. (Source: Reprinted with permission from [80]. 9 1996 American Physical Society.)

to deep centers or surface states is an ultrafast process and the carrier trapping is directly related to the relaxation time. The involvement of the surface states in the edge or excitonic emission may explain the time-resolved PL of the nanocrystals reasonably. The dynamics of photoluminescence in CdSe quantum crystallites was studied by Lefebvre et al. [81 ] via time-resolved photoluminescence measurement. The medium-size CdSe nanocrystallites with diameters larger than the bulk exciton Bohr diameter were chosen for the studies because it was considered that size distribution is a severe obstacle for absorption and luminescence properties of small particles and that in the case of small crystal radii, even small size fluctuation causes important variations of transition energies [81]. It appeared that in such small crystallites, extrinsic states localized at the interface between the semiconductor and the matrix play a major role in recombination dynamics and it has been shown that near band-edge emission in small CdSe or CdS crystallites results from quantum mechanical resonance between exceptions and "extrinsic" surface states. In the medium-size particles, both the size fluctuation and the surface effects may be reduced efficiently, thus the medium-size particles should be good candidates for detailed studies of the dynamics of recombination processes [81 ]. The absorption and PL spectra of four samples of CdSe nanoparticles are shown in Figure 43 [81]. The absorption blue shift, particle sizes, and decay time constants of corresponding PL peak are given in Table V. The radii were deduced and the free exciton radiative lifetime was estimated by using the model of Kayanuma [35]. Sample 4 corresponds to a stronger confinement regime, while samples 1-3 belong to a moderate quantum confinement. In samples 1-3, the excitonic lines (A-C) of hexagonal CdSe were observed in the absorption spectra and sharp excitonic emission lines were measured. While in sample 4 excitonic lines are no longer resolved. This indicates that in moderate-size nanocrystallites, the inhomogeneous broadening due to size distribution is quite small. In samples 1-3, the sharp lines above 1.85 eV are mainly due to recombination of "free" excitons, while in sample 4 (also sample 3), the broad low-energy bands are assigned to the interface or surface states [81 ].

360

PHOTOLUMINESCENCE AND STIMULATED LUMINESCENCE OF NANOPARTICLES

9

I

~

|

,.

9

i

"

1

9

s

"

I

"

!

,~_~

,-'* .... %,.

.~

.'.;2:::"'"" ....

-

r,13


.

3

d 9-~ 10r

4 5

e,(D

_= 5

0 250

I

I

I

300

350

400

450

Temperature(K)

Fig. 59. Glowcurves of CdS clusters in zeolite-Y with CdS loading of 1, 3, 5, and 20 wt% (from 1 to 4), respectively. Curves 5 and 6 represent the bulk CdS and the mechanical mixture of CdS with zeolite-Y powders, respectively. (Source: Reprinted from [27], with permission from Elsevier Science.)

from pure CdS powders, but much weaker in intensity. The TL intensity of CdS in zeolite mechanically mixed is even lower than that of the pure CdS. In order to reveal the cause of the thermoluminescence, the glow curves of Cd2+-exchanged zeolite-Y (Cd2+/Y) and zeolite-Y exposed to Na2S solution (Na2S/Y) are also measured (Fig. 60 [27]). The glow peak of Cd2+/Y is higher than that of CdS/Y, while no obvious signal is detected from zeolite-Y exposed to Na2S solution. The foregoing results indicate that the TL of CdS/Y is caused by CdS clusters. As no irradiation was made before the measurement of the samples, the TL must be caused by the intrinsic defects or surface states of the clusters. It can be seen from Figures 58 and 59 that as the CdS loading in zeolite-Y decreases, the TL intensity increases. One may think that the glow peak of CdS/Y is caused by the bulk CdS, because the glow peak of CdS is located around the same temperature region. In fact, it is not true, although some CdS may be formed outside the zeolite pores, but it only occurs at sufficient high loading. At low loading, all CdS would be confined in the pores of zeolite as clusters. In our experience, more CdS are formed outside the pores as the loading increases. Suppose the glow curve is caused by the bulk CdS, it becomes stronger as the CdS

373

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=. 6 o~

CdS/Y(2Owt%)

Cd2+/Y

~ A

rr ~D r 4,,.=,

(D

._> "~ n,' 2 -

0

I

I

I'

J

i

'

250 300 350 400 450 500 550 Temperature(K)

Fig. 60. Glowcurves of CdS clusters in zeolite-Y (20 wt%), Cd2+-exchangedzeolite-Y (Cd2+/Y) and zeolite-Y powders exposed to Na2S solution (Na2S/Y). (Source: Reprinted from [27], with permission from Elsevier Science.) loading increases, just like the situation of curves 5 and 6 (Fig. 59), which represent the bulk CdS and the mechanical mixture of equal CdS with zeolite-Y powders, respectively. The inverse dependence of the TL intensity on the CdS loading indicates that the TL efficiency is dependent on the cluster properties. As we point out, as the loading increases, the cluster density goes up and the sizes of clusters are bigger [96, 97]. This means that the TL intensity is not dependent on the cluster density but is dependent on the cluster sizes. The luminescence intensity increases as the cluster size decreases. We have mentioned in the Introduction that the trapping of electrons in semiconductor clusters is a very fast process, spontaneous fluorescence has no chance to compete with it [78, 84]. Thus the quantum yield of fluorescence of clusters is very low [63]. However, traps and trapped carders in clusters are abundant, luminescence might be improved if the trapped carders are effectively released from the traps by stimulation with energy equal to the trap depth. Thermoluminescence is a good method to detect the recombination emission caused by the detrapping of carriers thermally. The energy corresponding to the glow peak is equal to the trap depth. The glow peaks in Figure 59 are caused by trapped carders produced during sample processing. Because in nanoparticles or clusters, most ions at the surface are not saturated in coordination, electrons or holes may be excited easily and may escape from the ions, then are trapped at surface states located in the forbidden gap [53]. In the thermoluminescence process, electrons or holes may be ionized from the surface states and may recombine to emit luminescence. According to the theories of thermoluminescence [ 101,102], the TL intensity of clusters may be given by dm I -- - ~ dt

= mnA

(5)

where m and n represent the density of holes and electrons for recombination, respectively. A is the carder recombination probability. Obviously, m and n are proportional to the surface states. As we have pointed out, as the size of clusters decreases, surface ions and states increase rapidly, thus enhancing TL efficiency. Furthermore, in clusters the wavefunctions of the electron and the hole are overlapped effectively, which may result in the increase of their recombination probability (A). Theses two effects may make the TL of clusters much stronger than that of the bulk and may increase as cluster size decreases. Besides the two effects we discussed previously there may be some other possibilities that may cause the TL of CdS/Y to decrease as the loading increases. One is the reabsorption of luminescence by the bulk CdS, because as the loading increases, some bulk CdS may be formed outside the zeolite pores. However, this effect is significant only at

374

PHOTOLUMINESCENCE AND STIMULATED LUMINESCENCE OF NANOPARTICLES

high loading. According to our works [96, 97], at low loading, no or very little bulk CdS are formed. Below 10 wt%, the photoluminescence (PL) increases as loading increases, indicating reabsorption is not important. Above 10 wt%, the PL decreases (Fig. 58), reflecting strong reabsorption, thus the increase of TL as loading increases is not so obvious. Another possibility is the carrier transport between neighboring clusters, because it was reported [98] that as the loading increases, the clusters in the cages of the zeolite may be interconnected and carriers may transport or may transfer between the neighboring cages. The carrier transport reduces the recombination rate of carriers and thus reduces the TL efficiency and causes the TL decrease as the loading or connectivity increases. However, it may be deduced from the change of the PL upon the CdS loading that this effect is minor. Suppose that the carrier transport reduces the carrier recombination, it also affects the PL of the clusters and causes the PL decrease as the loading or connectivity of the clusters increases. However, we observed that the PL first increases then decreases as the loading increases. It was also reported in Ref. [98] that at low CdS concentration, no emission can be seen even down to 4 K, but obvious emission exhibits from the so-called "superclusters" at high loading. It seems that the increase of the "connectivity" of the clusters does not decrease the rate of the carrier recombination. We think that the CdS clusters formed in the supercages of zeolite-Y cannot be connected. Because the supercages are isolated or separated, each supercage is surrounded by several sodalite cages. It is hard for them to be interconnected. It was found that the dependence of PL on CdS loading or on cluster size is different from that of TL. Because these two processes are different, in the PL process, the increase of surface states enhances nonradiation and thus decreases PL efficiency [96]. While in the TL process, the increase of surface states provides more accessible carriers for recombination and therefore enhances TL efficiency. It can be seen from Figure 59 that the clusters of different sizes have almost the same glow peak positions and shapes, reflecting that the properties of traps or surface states are not sensitive to the cluster size. In summary, the thermoluminescence of CdS clusters encapsulated in zeolite-Y is observed successfully and is revealed to be caused by the CdS clusters, not by other defects in the zeolite. The TL intensity increases as CdS loading decreases. The thermoluminescence is considered to be related to the surface states of the clusters. Carriers trapped at the surface states may be ionized by heating and may recombine to give luminescence. The increase of the TL intensity upon CdS loading is mainly caused by two effects. The clusters formed are smaller at lower loading, having higher surface to volume ratio and containing more accessible trapped carriers for TL. Meanwhile in smaller clusters, the recombination probability increases due to stronger quantum-confinement effect. Thus it is not surprising that the TL increases as the cluster size increases. However, in this kind of material, we cannot rule out the quenching of the luminescence by reabsorption of bulk CdS, although this effect is not so important as the size effect and only occurs at sufficient high loading. The position and shape of the glow curves do not change very much upon the cluster loading or size, indicating that traps or surface states are not sensitive to the cluster sizes. However the glow peak shape of the clusters is a little different from that of the bulk, revealing that the probabilities and dynamics of carriers recombination in CdS clusters and in the bulk are different. All these await to be accomplished. In fact, much work awaits to be done, such as the precise correlation between the TL efficiency and the cluster sizes, emission or energy spectra of thermostimulation, the assignment of the glow peaks, the estimation of physical parameters of the traps, the change of TL upon preparation conditions, etc. We also found that the TL of semiconductor clusters is very sensitive to light irradiation with different energy. The dependence of TL upon irradiation might be an interesting subject, it may provide an opportunity for searching new and more sensitive materials for optical storage and dosimeter.

375

CHEN

5.3. Thermoluminescence of ZnS Nanoparticles [28, 29] Two methods were used to prepare the ZnS nanoparticles. One [28] is capped with organic stabilizer agents, the other [29] is deposited from the colloids directly without capping. In both cases, the sizes of the clusters were adjusted by the reaction temperature. There are some differences in the physical properties of the "two" ZnS nanoparticles. Their structure, optical absorption, and photoluminescence have been introduced in Sections 2.4.1 and 2.4.2, respectively. Here we illustrate their thermoluminescence.

5.3.1. Thermoluminescence of Capped ZnS Nanoparticles [28] Figure 61 shows the glow curves of the capped ZnS nanoparticles which were recorded without any irradiation. An equal amount (15 mg) of sample was taken for each measurement. The sizes of the particles are 18.1, 25.0, 27.4, and 30.1 ,~, respectively, [28]. An obvious glow peak around 380 K is exhibited from the nanoparticles. All four samples show the glow peaks at almost the same position and the TL intensity increases as the particle size decreases. The change of the TL is consistent with that of the surface fluorescence. It is reasonable to consider that the TL of the nanoparticles is correlated to the surface states. The glow signal is caused by the recombination of trapped carriers released by heating. The glow peaks in Figure 61 are caused by the trapped carriers which are produced during the sample processing, because no irradiation was carried out before the measurement. Carriers trapped at the surface states or defect sites may be released by heating to recombine to give out the so-called thermoluminescence (TL). According to Eq. (5), the increase of TL upon decreasing size may be explained reasonably. Because the decrease of the particle size may enhance the surface ions and states rapidly and, as the content of the surface states increase, the particles may provide more accessible carriers (holes and electrons) for the TL recombination, that is, the m and n are proportional to the surface states. Furthermore, in nanoparticles the wavefunctions of electron and hole are overlapped effectively, which may result in the increase of their recombination probability or rate (A). These two effects may make the TL of small particles much stronger than that of the bulk and may increase as the size is decreased. We plot the TL intensity versus the particle radius (Fig. 62), hopefully to figure out which of the two effects is more important. Because surface effects should vary as surfacevolume (i.e., 1/ R), while quantum confinement should vary as 1/vol (i.e., 1/ R 3). However,

10-

8 -

::= ~C

6-

_=

esSS"~

//

W 4-

,/s

99

,"

X

,

3

,, ',, \

2

_

300

r

1

I

320

340

360

T 380

400

Temperature(K) Fig. 61. Glow curves of capped ZnS nanoparticles. (Source: Reprinted with permission from [28]. 9 1997 American Institute of Physics.)

376

PHOTOLUMINESCENCE AND STIMULATEDLUMINESCENCE OF NANOPARTICLES

70 IV I / R 3

56. . . . . .

:5

"7".

.'~.~,.. .

(11

m-

=~ 4 2 -

tll v

r

._Z"

ffl e--

C

|C

-=

28-

..A IX.

,,.I

I--

14-

0

0

I

I

I

I

I

1

2

3

4

5

1/Rn 10~*1,(n=1,3)

Fig. 62. Curvesof TL and PL intensities versusparticle size (R) in capped ZnS nanoparticles. (Source: Reprinted with permissionfrom [28]. 9 1997AmericanInstitute of Physics.)

the results in Figure 62 cannot tell us which of the two effects is more important. Probably, the surface and the quantum confinement effects do the same contribution to the increase of the TL upon decreasing size. We have mentioned that the measurement of TL is desiring to get some useful information about the surface states of the particles. Here we attempt to figure out what we can learn about the surface states from the TL investigations. The appearance of TL prior to radiation indicates that some trapped carriers have been pre-existed. The pre-existing carriers or occupation of the localized states have been proposed by Chestnoy et al. [61] to explain the very weak dependence of the fluorescence decay lifetime upon CdS cluster size and have been explained by Klimov et al. [80] to explain the extremely fast buildup dynamics of the low-energy emission bands of CdS nanocrystals. TL from semiconductor nanoparticles without any radiation has been observed in CdS clusters in zeolite-Y [27], CdS [103], and ZnS [28, 29] nanoparticles. Our observations provide direct evidence for the pre-existing trapped carriers and support the suggestions of Chestnoy et al. [61 ] and of Klimov et al. [80].

5.3.2. Thermoluminescence of Uncapped ZnS Nanoparticles [29] Figure 63 shows the glow curves of the uncapped ZnS nanoparticles [29]. An obvious glow peak around 396 K is observed. The three samples show the glow peaks at almost the same position and the TL intensity increases as the particle size decreases. The change of the glow curves of the uncapped ZnS particles upon size is similar to that of the capped ZnS particles. However, the glow peak maximum is different, indicating that the trap depth related to the glow peak is correlated to the condition of sample preparation. Furthermore, the TL intensity-size curves of the uncapped particles are different from that of the capped particles, indicating a different TL mechanism occurring in the two particles. As pointed out earlier, there are two effects, that is, surface effect and quantum confinement, that may make the TL of small particles increase as the size decreases. In the capped ZnS particles, the surface and the quantum confinement effects do the same contribution to the increase the TL upon decreasing size. To figure out which of the two effects is more significant in the uncapped ZnS particles, we plot the TL intensity versus the particle radius (Fig. 64). As pointed out, the surface effect should vary as surface-volume (i.e., 1/ R), while quantum confinement should vary as 1/vol (i.e., 1/R3). The results in Figure 64 show

377

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10 1.24nm _

,,.->

~,,

_

.65nm

ell)

_=

'~t ,~2.;28nm

_

/'

.--I

_

#.#

j

~,

i

I

I

I

I

I

I

340

360

380

400

420

440

Temperature(K)

Fig. 63. Glowcurves of uncapped ZnS nanoparticles. (Source: Reprinted with permission from [29]. 9 1997 American Institute of Physics.) 12

~

::i

.._~.

9-

.._~.. ,,-:,. :3 v

e-

~

t~ r tD r

6

e,_,1

_.1

g-

_

0

0

IX.

g-

I

I

I

1

2

4

6

8

10

1/R".10"*~,(n=1,3)

Fig. 64. Curvesof TL and PL intensities versus particle size (R) in uncapped ZnS nanoparticles.

that the increase of TL and of PL upon 1/R is faster than that upon 1/R 3, indicating that the surface effect does more contribution to the luminescence of the particles. It is also indicated that the surface effect is more significant in the uncapped particles than in the capped particles. This is reasonable, because in the uncapped particles the content of surface states is higher than in the capped particles, therefore the surface effect is more important.

5.4. A S c h e m a t i c L u m i n e s c e n c e M o d e l of Surface States

Surface states or defect sites in nanoparticles are so abundant that the trapping of carders is a very fast process [78, 84]. Fluorescence has been considered to occur via detrapping of carriers from the surface states or traps. The detrapping of carriers is an important process to determine the fluorescence efficiency and to reveal the luminescence mechanism. The detrapping rate is correlated to the trap depth which is measured with respect to the bottom of the conduction band for electron traps and to the top of the valence band for hole traps

378

PHOTOLUMINESCENCE AND STIMULATED LUMINESCENCE OF NANOPARTICLES

Dp

,,

S

"

,,,,m

~trap depth~~._ I surface fluorescence I

o,,

P ft.- small size

big size

Fig. 65. A schematicfor the sizedependenceof the trapped fluorescencefrom surface states in semiconductor nanoparticles. (Source: Reprinted with permissionfrom [28, 29]. 9 1997American Institute of Physics.)

in bulk materials. In nanoparticles (clusters, nanocrystals, and quantum dots), we define the trap depth to the lowest excited state or exciton state for electron traps. The trap depth determining the activation energy of detrapping may be estimated from the glow curves. The glow peak maximum does not change upon size, reflecting that the trap depth does not vary as much upon decreasing size. As in the conventional TL theories [101, 102], only the electron traps were involved. Also, in our work, we only consider the electron traps. The physical properties of these traps may be reflected from the temperature, shape or symmetry of the glow peak. It can be seen that the glow peak temperature and shape (or symmetry) of all the samples are similar, indicating that the physical properties of the traps (i.e., surface states and/or defect sites) are not sensitive to the particle size. The trap depths of the capped and of the uncapped ZnS nanoparticles, estimating from the glow peaks according to the methods in Ref. [101], are around 0.75 [28] and 0.96 eV [29], respectively. Considering these results, the size dependence of the surface fluorescence may be explained reasonably. The schematic is shown in Figure 65 [28, 29]. As the trap depth does not change as much upon the size, while the bandgap increases as the size decreases, the separation between the electron-hole states (similar to the donor-acceptor pairs [61 ]) increases upon decreasing size. Thus the luminescence of surface states shifts to the blue as the size is decreased. This is the case for most nanoparticles reported. In summary, the thermoluminescence of ZnS nanoparticles is studied. Both the TL and the surface fluorescence increase as the particle size decreases. The consistence of the TL with the surface fluorescence indicates that the TL is related to the surface states. TL may occur via detrapping of carriers by heating. As the size becomes smaller, the surface to volume ratio increases, the particles contain more accessible trapped carriers for TL. This is one factor to make the TL increase upon decreasing size. Another factor is the increase of the carrier recombination rate upon decreasing size due to the increase of the overlap between the electron and the hole wavefunctions. In the capped ZnS particles, the two effects are equally important, while in the uncapped particles the surface effect is more significant than the quantum confinement, because in the uncapped particles, the content of surface states is higher. The appearance of TL prior to any radiation reveals that trapped carriers have existed previously. The glow peak of the particles is not sensitive to the size, indicating the trap depth does not change as much upon decreasing size. The size dependence of the surface fluorescence may be explained well with the model based on the TL results.

6. PHOTOSTIMULATED LUMINESCENCE OF Ag AND CLUSTERS IN ZEOLITE-Y

AgI

A strong luminescence should be observed in quantum structured materials, because the carrier recombination rate should be increased due to the increase of the overlap of the

379

CHEN

Energy c~176

- -

nonr~iative channels

---I c -e-

il adisttve ;hannel$ llmul

iil

111111111111

61,m,.=O

_ -

I,m,n

"..':'..'..::~ Fig. 66. (a) Energyrelaxationin a continuum. Radiative recombinationis possible even though K = Kt is needed because both band edges are populated. (b) Energyrelaxationthrough a fully quantized box level can be very slow. (l, m, n) = (lt, mt, n~) then is needed to decay radiatively, but this rarely occurs because nonradiative channels are efficient on electrons storedmorethan nanoseconds. (Source:Reprinted with permission from [104]. 9 1991 American Physical Society.)

electron and the hole wavefunctions. However, the fluorescence efficiency of most quantum crystals is very low. Three models have been proposed to explain the low luminescence efficiency of nanoparticles. One is attributed to the fast trapping of carriers to the surface states where nonradiation recombination occurs [59, 61, 71, 78, 80, 81, 84]. However, it was considered by Benisty et al. [ 104] that the poor radiative efficiency in quantum boxes in photoluminescence and laser action is due to the combination of inefficient energy relaxation and orthogonality of carrier quantum states, rather than to a major increase in extrinsic defect density. It was proposed that electrons captured from barriers in the upper levels of quantum boxes are retained in their cascade to the fundamental states for more than nanoseconds. Due to the mutual orthogonality of quantum states in a box, no luminescence, or much less than bulk, can be obtained from these stored electrons with reasonable assumptions for the hole population. The model in Figure 66 [104] shows clearly why the radiative rate is low due to the efficient nonradiative channels occurring in the upper levels of the quantum box. The third mechanism [79] for low luminescence efficiency in nanoparticles is the trapping of carriers escaping from the quantum dot into the matrix. This therefore, would cause nonradiative recombination processes. If the weak luminescence is caused by the intrinsic effect proposed by Benisty et al. [ 104], it is probably hard to enhance the luminescence efficiency. If the luminescence is quenched by surface states or defects, it may be improved via surface passivation. As the fluorescence of most nanoparticles may be enhanced by surface passivation, thus we believe that surface states play a key role in determining the fluorescence efficiency. To avoid the obstacle of the surface states, Bhargava et al. [68] and Bhargava [105] have worked out a new way to enhance the fluorescence efficiency of nanoparticles by incorporating an impurity into the quantum-confined structure, because the dominant recombination route can be transferred from the surface states to the impurity states by doping. These doped nanocrystals may make an impact on the next generation bright, high resolution, and high contrast emissive displays [105]. Because most clusters are stabilized in a matrix like polymers [ 106], zeolites [ 1], and glasses [79, 52], and others, charge or carrier transfer from quantum dots and their surround matrix have been noted [30, 31, 79]. Electrons or holes trapped at the defect sites of the matrix are metastable, they may be ionized and they may return to the quantum dot states [30, 31]. This indicates that charge transfer between quantum dots and the matrix

380

PHOTOLUMINESCENCE AND STIMULATED LUMINESCENCE OF NANOPARTICLES

is reversible. This reversible process may find applications for optical storage. The photostimulated luminescence (PSL) of Ag [30] and AgI [31 ] clusters in zeolite-Y were observed supporting the preceding views.

6.1, Photostimulated Luminescence of Silver Clusters in Zeolite-Y [30] Silver clusters have been studied extensively [3, 4, 52, 107, 108], because they are very sensitive to light stimulation and they may find applications as photocatalysts for solar energy conversion [3] and as optical materials for information or image storage [4]. It was reported [108] that silver microclusters on silver halide grains may work as latent images and reduction sensitization centers which play a dominant role in the photographic process. Silver clusters may be formed simply by encapsulation in the cages of zeolites. The structure and chemistry of silver clusters in zeolites have been reviewed by Sun and Serf [107]. The spectroscopy and photoprocesses of silver clusters in zeolites have been discussed by Ozin et al. [109]. Ozin et al. [4] also have a patent entitled "photosensitive, radiation sensitive, thermally sensitive, and pressure sensitive silver sodalite materials." A Japanese patent (SHO-61-61894, Yokono et al.) describes an optical recording medium consisting of a silver halide and a large pore zeolite compound. The material darkens when exposed to light and may fade back to its original color on heating. These indicate that silver clusters are novel materials with potential applications in optical and chemical sensors. For the first time, we observed the photostimulated luminescence (PSL) of silver clusters encapsulated in zeolite-Y [30]. PSL is different from PL (photoluminescence), in PL the excitation energy is higher than the emission energy, while in PSL the stimulation (excitation) energy is lower than the emission energy. The PSL is caused by the recombination of luminescence centers with electrons released from their traps by photostimulation [ 1 !0]. The photostimulatable materials may find applications as image plates for X-ray computerized radiography [ 111 ] and as a medium for erasable optical memory [112]. Our observations here indicate that silver clusters encapsulated in zeolite-Y (Ag-zeolite-Y) exhibit PSL and may be used as erasable optical storage materials. In the preparation of silver clusters inside the zeolite, the zeolite powder was slurried in deionized water with pH adjusted to 6 with nitric acid. The silver nitrate was added and the mixture was stirred at room temperature for 30 h. The Ag+-ion-exchanged zeolite was collected by filtration, washed with deionized water until no Ag + was detected in the filtrate by C1- solution, then suction dried to a damp powder, and finally dried and calcined at 250 ~ in dark and in vacuum for 10 h. The PL and PSL spectra were recorded with a Hitachi M-850 fluorescence spectrophotometer. The light source for stimulation or excitation was a 150 watt Xe lamp, and the emitted light was detected with a R3788 photomultiplier tube with resolution of 0.15 nm. In the PL measurement, the excitation light is chosen at 305 nm, which is shorter in wavelength than the emitted light (505 nm). In the PSL measurement, the stimulation (or excitation) light is chosen at 840 nm, which is longer in wavelength than the emitted light. The reported spectra were corrected automatically for the photomutiplier response. All measurements were carried out at room temperature. The silver clusters in the zeolite show an excitation maximum at 305 nm and an emission peak at 505 nm (Fig. 67) [30], respectively. The fluorescence of sliver clusters in zeolite-Y has been studied extensively [109]. The appearance of an absorption band at 306 nm, a fluorescence emission at 490 nm, as well as an excitation spectrum with maximum at 306 nm are considered to be strong evidence for the existence of zeolite entrapped silver atoms from comparison with the corresponding data for gaseous and rare gas matrix isolated Ag o atoms [ 113]. The excitation and emission spectra of our sample are consistent with the observation of Kellerman and Texter [113]. Thus the fluorescence is tentatively

381

CHEN

6 a

5 4

~

2 1 0

l

i

i

i

i

J

240

320

400

480

560

640

Wavelength(nm)

Fig. 67. Photoluminescenceexcitation (a, ~em = 505 nm) and emission (b, ~.ex = 305 nm) spectra of silver clusters in zeolite-Y. (Source: Reprinted from [30], with permission from Elsevier Science.) 6 1

5

2 3

4

, ~

5

ttt

2

4

0

350

I

I

400

450

I

500

550

600

650

Wavelength(nm)

Fig. 68. Photoluminescenceof silver clusters in zeolite-Y. 1. sample without UV-irradiation; 2. sample after UV-irradiation at 254 nm for 1 min; 3. sample after UV-irradiation at 254 nm for 10 min; 4. sample after UV-irradiation at 254 nm for 30 rain; 5. sample after UV-irradiation at 254 nm for 30 min and then optically bleached at 840 nm for 10 min. (Source: Reprinted from [30], with permission from Elsevier Science.)

assigned to the transition between the ground state (2S1/2) and the excited state (2p1/2) of Ag atoms [ 109]. It was found that the emission from Ag o decreased under the UV-irradiation at 254 n m (Fig. 68) [30]. Figure 69 shows the photostimulation spectra of Ag-zeolite-Y after UVirradiation for 10 min and for 30 min, respectively. An absorption appears at around 840 n m in the stimulation spectrum under UV-irradiation. A similar absorption band around 850 n m was reported in the optical stimulation spectra of natural silicates (feldspar [ 114]) after y-irradiation. However, no assignment was made to the stimulation spectra of the natural minerals [ 114]. We think the absorption is related to the electron centers or F-centers correlated to the oxygen vacancies in the zeolite framework. An obvious fluorescence is detected by stimulation with the light corresponding to the absorption band in the stimulation spectrum (Fig. 70). This is the so-called photostimulated luminescence (PSL). The

382

PHOTOLUMINESCENCE AND STIMULATED LUMINESCENCE OF NANOPARTICLES

2.0 A

1.5

ai

1.o

m t-.

_= 0.5

0.0 750

780

840

810

870

900

Wavelength(nm)

Fig. 69. Photostimulatedspectra of silver clusters in zeolite-Y after UV-irradiation at 254 nm for 10 min (dotted) and for 30 min (solid), respectively. (Source: Reprinted from [30], with permission from Elsevier Science.) 2.0

1.5

-

::3

d -~ 1 . 0 9 te....,

0.5

--

t

0.0

1

1

1

I

I

350 400 450 500 550 600 650 Wavelength(nm)

Fig. 70. Photostimulated luminescence spectra of silver clusters in zeolite-Y after UV-irradiation at 254 nm for 10 min (dotted) and for 30 min (dash), respectively. (Source: Reprinted from [30], with permission from Elsevier Science.)

PSL is the same in wavelength as the PL (photoluminescence), but much weaker in intensity. The PSL is also assigned to the fluorescence of Ag atoms. It was found that the PSL intensity of Ag-zeolite-Y increased with increasing irradiation time. The PSL phenomenon in BaFBr:Eu 2+ phosphors has been studied extensively [ 100, 110, 111, 115]. In BaFBr:Eu 2+, the PSL occurs via the recombination of [Eu 2+ + h] [ 115] or Eu 3+ [110] with the electrons released from the F-centers by photostimualtion. In Agzeolite-Y, it was observed that the Ag o emission decreased under UV-irradiation, indicating the decrease of Ag ~ Under photostimulation at 840 nm, the emission of Ag o increases slightly (Fig. 68). These observations tell us that under irradiation, some Ag o atoms converted to Ag +, while the electrons were captured by the oxygen vacancies in the zeolite framework to form electron centers. Under photostimulation, the electrons are released from the centers and recombine with Ag + to give the fluorescence of Ag ~ In fact, the charge transfer from the zeolite framework to the entrapped silver atoms or clusters has been discussed previously [116]. It was reported that dehydrated Ag +exchanged zeolite-A (Ag-A) is very sensitive to even small amounts of moisture [ 117]. Upon absorption of water, the brick red of dehydrated Ag-A changed to orange, then to yellow, and finally to white. The color changes were attributed to a charge transfer from the framework oxygen to silver cations by Kim and Serf [ 116]. A similar phenomenon was described in a Japanese patent (SHO-61-61894), that is, the materials composed by silver

383

CHEN

halides and zeolite compound darkens when exposed to light and fades back to its original color by heating. These results support that charge can transfer from the zeolite framework to the entrapped Ag + by thermo- or photostimulation. In the following, we attempt to illustrate why Ag atoms can be formed within the zeolite and how can the charge transfer between the framework and the encapsulated silver cations. The molecular formula of zeolite-Y is Na64[A164Si1280384].256H20, some silicon ions (Si 4+) in the tetrahedra are substituted by aluminum ions (A13+). Because of the valence difference between aluminum and silicon, the zeolite lattice possesses a negative charge equal to the number of aluminum atoms. Thus the zeolite crystallites have large electrostatic potentials that may absorb some cations in their cavities. Ion exchange is a popular way to encapsulate cations into the cavities of zeolites. In the solution exchange, it should be Ag + cations rather than Ag o atoms that enter into the zeolite cages. However, as indicated by the fluorescence, it is Ag o atoms rather than Ag + cations that appear in the zeolite. We think that the "autoreduction" mechanism proposed in the Ag +exchanged-zeolite-A [ 118] may be borrowed to explain the appearance of Ag o atoms in Ag+-exchanged-zeolite-Y. According to the temperature-programmed desorption experiment on hydrated Ag+-exchanged-zeolite-A, oxygen gas was evolved by heat treatment at a high temperature above 400 K and the Ag + may be "autoreduced" to Ag ~ The overall stoichiometry of this reaction can be represented symbolically as [118], 2Ag + +

ZO 2- ~

1 0 2 --[--2Ag ~ + Z

where ZO 2- represents a zeolite framework and one of its oxygens, and Z represents a zeolite framework with a missing oxygen link, that is, with a Lewis acid site (oxygen vacancy). The autoreduction may occur in Ag+-exchanged zeolite-Y by heat treatment in dark and in vacuum. Thus it was Ag o atoms rather than Ag + cations that appeared in the zeolite. Ag o may be ionized to Ag + by UV-irradiation (Ag o ~ Ag+). The ionized electron may be captured in the Lewis acid sites (oxygen vacancies) that are the acceptors of electrons. The trapped electrons in the Lewis sites are metastable and may be released by light stimulation. The photoreleased electron may recombine with Ag + to give the emission of Ag ~ These processes are revisable, reflecting that Ag-zeolite-Y has potential application as a medium for erasable optical memory. Here we propose that the production of UV-irradiation is Ag + rather than [Ag + + h] complex, because the irradiation energy (4.96 eV) is much lower than the energy gap of the zeolite (10.5 eV as estimated from the empirical method proposed by Maj [ 119]). No electron-hole pairs could be created under UV-irradiation. The irradiation can only ionize the electrons from Ag o atoms. In summary, the photostimulated luminescence of silver-exchanged zeolite-Y is reported. Under UV-irradiation, the PL intensity of silver atoms decreased and an absorption band showed up around 840 nm. Under photostimulation at 840 nm, the fluorescence of silver atoms was observed and the PL intensity of silver atoms increased slightly. These phenomena were considered to be caused by the charge transfer from the zeolite framework to the entrapped silver atoms. These reversible processes make the material have potential applications in erasable optical memory.

6.2. Photostimulated Luminescence of AgI Clusters in Zeolite-Y [31] Silver halide clusters have been studied extensively [3, 107, 120-125], because they are very sensitive to light stimulation and they may find applications as photocatalysts for solar energy conversion [3] and as a medium for optical information or image storage [4]. Silver halide clusters may be formed simply by encapsulation in the cages of zeolites. The synthesis of silver halide clusters in zeolites has been reported by several investigators [ 121-124]. An optical recording medium consisting of a silver halide and a large pore

384

PHOTOLUMINESCENCE AND STIMULATED LUMINESCENCE OF NANOPARTICLES

zeolite compound has been described in a Japanese patent (SHO-61-61894, Yokono et al.). The synthesis, structure, and optical properties of sliver halide clusters in halosodalites have been studied by Stein et al. [121-123]. Calculations showed that electronic transitions took place between the clusters and the sodalite framework [ 122]. The photosensitive properties of AgI inclusion in modenite have been reported by Hirono et al. [ 124] and were considered to be caused by a photoinduced intermediate state. The roles of silver and silver iodide nanoclusters in silver halide photographic emulsion grains have been discussed widely [108, 125]. It is agreed that silver and silver iodide microclusters play a very important role in the photographic process in mixed-halide emulsions and have a great influence on their spectral sensitization, light absorption, chemical sensitization, pressure sensitivity, and developability [ 125]. All these indicate that silver iodide clusters are novel optical materials with potential applications. For the first time, we observed the photostimulated luminescence (PSL) of silver iodide clusters in zeolite-Y. Our observations demonstrate that silver iodide clusters encapsulated in zeolites may work as a medium for erasable optical memory. In the preparation of AgI clusters in zeolite-Y (henceforth Agl/Y), Ag + ions were first exchanged into the cages of the zeolite. The zeolite powders were slurred in deionized water with pH adjusted to 6 with nitric acid. The silver nitrate was added and the mixture was stirred at room temperature for 30 h. The Ag+-ion-exchanged zeolite was collected by filtration, washed with deionized water until no Ag + was detected in the filtrate by C1- solution. Then the Ag+-ion-exchanged zeolite powder was slurried in a sodium iodide solution by stirring at 100 ~ for 20 h. The color of the materials changed from gray to yellow as the interaction was going on. Then the materials were collected by filtration and washed extensively with deionized water and finally dried and calcined at 250 ~ in dark and in vacuum for 20 h. The transmission electron microscopy (TEM) observations were made on the ultrathin films which were prepared as follows: the powder samples were mixed with a diluted organic binder which was made from nitrocellulose, ethyl acetate, and n-butanol. Then the films were formed simply by spin coating or formed on a water surface by dropping. The films were moved to a copper grid and were thinned by low energy ion-beam bombardment. The Auger electron spectra were measured on a PHI 4~550-AES spectrophotometer. The PL and PSL spectra were recorded with a Hitachi M-850 fluorescence spectrophotometer. In the PL measurement, the excitation light was chosen at 274 or 303 nm, which is shorter in wavelength than the emitted light. In the PSL measurement, the stimulation (or excitation) light was chosen at 625,675, or 840 nm, which is longer in wavelength than the emitted light. In the measurement of the PL excitation spectrum, the scan was taken from 200 to 400 nm by monitoring the emitted light at 474 or 510 nm. In the measurement of the photostimulation spectrum, the scan was taken from 550 to 900 nm by monitoring the emitted light at 474 or 510 nm. The reported spectra were corrected automatically for the photomutiplier response. All measurements were carried out at room temperature. The TEM observations show that the clusters are quite uniform and even in size. The mean size of the clusters is 1.0-2.0 nm which is in agreement with the space in the zeolite supercages (1.3 nm in diameter), indicating that the clusters are formed inside the cavities of the zeolite. It is worth noting that the actual size of a cluster or a quantum dot is less than that measured by TEM because the distributions measured by TEM are affected by strain, which tends to overestimate the size. In order to determine the formation of AgI clusters, the energy spectrum corresponding to the TEM picture was recorded (Fig. 71 [31 ]). Iodine was detected in the reaction products of Ag+-exchanged zeolite-Y with NaI solution, but no iodine was measured in the zeolite exposed to NaI solution, because the I - ions can be reacted with Ag + to form the AgI deposit. Otherwise, the iodine could not be deposited in the zeolite. It can be seen from the energy spectrum that the content of iodide is lower than that of silver. This means that silver clusters may also be formed along with the formation of AgI

385

CHEN

Fig. 71. Energyspectrum of AgI clusters in zeolite-Y. (Source: Reprinted with permission from [31]. 9 1998 AmericanInstitute of Physics.)

0

:3 v

200

I

I

I

I

300

400

500

600

700

Electron Energy (eV)

Fig. 72. Augerelectron spectra of zeolite-Y loaded with AgI and of zeolite-Y exposed to NaI solution. (Source: Reprinted with permission from [31]. 9 1998 AmericanInstitute of Physics.)

clusters. Because in preparation, the samples were annealed at 250 ~ in vacuum, this may cause some loss of iodine and may convert part of the AgI into Ag. It was found that the color of the sample changed during the TEM observation, and finally some clusters or dots "disappeared" or became colorless, indicating that the clusters are not stable under electron beam irradiation. The Auger electron spectra (AES) of the zeolite loaded with AgI (AgI/Y) and of the zeolite exposed to NaI solution were measured (Fig. 72). After sputtering for 60 s, both Ag and I were detected in Agl/Y samples, but no I signal was found in the latter. These results indicate further that AgI clusters are really formed in the zeolite. The PL excitation and emission spectra of Agl/Y are displayed in Figures 73 and 74, respectively. In order to reveal the origin of the fluorescence, the PL excitation and emission spectra of silver clusters in zeolite (Ag/Y) prepared in the same way are displayed along with that of Agl/Y, respectively. We also made the measurement on zeolite-Y powders exposed to NaI solution and zeolite-Y loaded with 12 by vapor inclusion, but no fluorescence was detected from these samples. These observations show clearly that the emission at 474 nm and the excitation at 274 nm are attributable to the AgI clusters, while the emission at 510 nm and the excitation at 303 nm are assigned to silver clusters. The fluorescence results indicate that both Ag and AgI clusters were formed inside the zeolite. This is in agreement with the TEM observations.

386

PHOTOLUMINESCENCE AND STIMULATED LUMINESCENCE OF NANOPARTICLES

10 Emission

Wavelength S~

II

8

474nm--~/~ "3".

,'/

6-

t'r-

~

/'

_ _

0 200

I

I

250

300

350

Wavelength(nm)

Fig. 73. Photoluminescenceexcitation spectra of Agl/Y (dash and dotted lines) and Ag~ (solid line). (Source: Reprinted with permission from [31]. 9 1998 American Institute of Physics.) 12

citationWavelength

10--:5

8-

9=~

6-

303nm /

.~274nm

,

t

4

2

I

I

I

I

I

400

450

500

550

600

650

Wavelength(nm)

Fig. 74. Photoluminescenceemission spectra of AgI/Y (dash and dotted lines) and Ag/Y (solid line). (Source: Reprinted with permission from [31]. (~) 1998 AmericanInstitute of Physics.)

It is reported [ 108, 125] that silver microclusters usually appear on silver halide emulsion grains and may work as a latent image and reduction sensitization centers which play a dominant role in the photographic process. Here we find that some interactions exist between the AgI and Ag clusters in zeolite-Y. Because when silver clusters are excited, not only the emission of silver clusters, but also the emission of AgI clusters are observed. Similarly, when AgI clusters are excited, both the emission of Ag and AgI clusters are detected. This demonstrates that energy or charge carriers can transfer from Ag clusters to AgI clusters and vice versa. It is interesting to find that the emission of AgI clusters is stronger than that of Ag clusters when excitation is at the absorption band of Ag clusters. The emission of Ag clusters is stronger by indirect excitation into the excited states of AgI clusters than that by direct excitation into the excited states of Ag clusters. Similarly, the emission of AgI clusters is stronger by indirect excitation into the excited states of Ag clusters than that by direct excitation into the excited states of AgI clusters. These phenomena indicate that,

387

CHEN

1.0 0 . 8

--

~i 0.6

0.4-

~

3

,

,

0.2 1 ..

o.o|

,

; T , -

550 600 650 700 750 800 850 900 Wavelength(nm)

Fig. 75. Photostimulationspectra of AgI/Y. (1) ~.em = 474 nm, UV-irradiation for 5 min; (2) Xem - 510 nm, UV-irradiation for 5 min; (3) ~.em = 5 1 0 n m , UV-irradiationfor 5 min. (Source: Reprinted with permission from [31]. 9 1998AmericanInstitute of Physics.)

in photoexcitation, energy transfer or carrier migration between Ag and AgI clusters is a dominant process. Details about the interaction and energy transfer between the two clusters are not very clear now, but they are probably related to the structure of the two clusters. We have demonstrated the presence of both Ag and AgI clusters in the zeolite and the conversion of part of AgI into Ag by annealing at 250 ~ in vacuum. Thus a type of composite clusters, that is, the clusters each containing some Ag as well as AgI, may be formed. Each of these composite clusters may have two domains with a sharp boundary separating the Ag from AgI. The structure of the composite AgI-Ag clusters is probably similar to that of mixed CdS-CdSe nanoparticles [126]. As Ag and AgI clusters have different energy gaps, there must be a potential difference between the Ag and the AgI clusters, and therefore the dominant mobile carrier is the electron in one and the hole in the other. Thus, under light stimulation, charge carrier migration or energy transfer between the two clusters can be expected. This is similar to the result observed in the coupled composite CdS-CdSe and in the core-shell type mixed (CdS) CdSe and (CdSe) CdS nanoparticles [126]. Three absorption bands at 625,675, and 840 nm were measured in the photostimulation spectra of Agl/Y (Fig. 75) and the absorption increased with increasing UV-irradiation time. Two absorption bands around 630 and 850 nm were reported in the optical stimulation spectra of natural silicate (feldspar [ 114]) after v-irradiation. However, no assignment was made to the optical stimulation spectra of the natural mineral. We think these absorption bands are related to the electron centers or F-centers correlated to the oxygen vacancies in the framework of the silicate. Thus the two absorption bands at 625 and 840 nm of Agl/Y are tentatively assigned to the electron centers in the zeolite framework. The absorption at 675 nm was not observed in the optical stimulation spectra of pure zeolite-Y or Ag/Y [15]. This indicates that this absorption is not related to the zeolite, but it is probably caused by the AgI clusters. However, at present, we do not know clearly what causes the 675 nm absorption. One possibility is the interstitial silver ions produced by UV-irradiation, the other is F-centers, because an absorption at 672 nm in KI crystal [127] was assigned to F-centers. We think the interstitial silver ions are the most likely, because they are easily produced by irradiation. The irradiation energy at 254 nm is probably not high enough to create F-centers in silver halides. Luminescence was detected by photostimulation at 675 or at 840 nm, which is called photostimulated luminescence (PSL). The PSL intensity increased with the UV-irradiation time (Fig. 76). The PSL spectrum is different from the emission spectrum of Agl/Y, but it is consistent with the emission spectrum of Ag/Y. The PSL spectrum by stimulation at 625 nm cannot be measured, probably because the absorption band at 625 nm is partly overlapped with the emission band and thus the emission signal is masked by the stimula-

388

PHOTOLUMINESCENCE AND STIMULATED LUMINESCENCE OF NANOPARTICLES

0.8 3

,\ 0.6

-

l

'

,,->.

=.

: 2_

\

i _">, \

0.4-

II

0.2

0.0

I

I

I

I

450

500

550

600

Wavelength(nm) Fig. 76. Photostimulated luminescence spectra of AgI/Y. (1))~em = 474 nm, UV-irradiation for 5 min; (2))~em -- 510 nm, UV-irradiation for 5 min; (3) ~.em = 510 nm, UV-irradiation for 5 min. (Source: Reprinted with permission from [31]. 9 1998 American Institute of Physics.)

tion light. The appearance of PSL from AgI/Y indicates that these materials may find an application as a medium for optical memory. In AgI/Y, the PSL may be caused by the recombination of luminescence centers with electrons released by optical stimulation. However, in AgI/Y the PSL process is probably more complex, because there are two luminescence centers in AgI/Y, that is, AgI and Ag clusters, and energy or charge carriers may transfer or may migrate between the two kinds of clusters. Besides, electrons may be stored in the zeolite framework, and they can also be trapped in the AgI clusters. As the emission from Ag clusters is dominant in the PSL, we mainly consider the PSL process involving Ag clusters. It is known from comparison with the fluorescence of silver clusters in zeolites [109] that the emission of Ag cluster in AgI/Y is mainly from Ag o atoms, because the absorption band at 306 nm, a fluorescence emission at 490 nm, as well as an excitation spectrum with maximum at 306 nm are considered to be strong evidence for the existence of zeolite entrapped silver atoms [113]. The clusters were prepared by ion exchange. In the solution exchange, it should be Ag + cations rather than Ag o atoms that enter into the zeolite cages. However, as indicated by the fluorescence, it is Ag o atoms rather than Ag + cations that appear in the zeolite. The autoreduction mechanism proposed in the Ag+-exchanged zeolite-A [118] may be borrowed to explain the appearance of Ag o atoms in the zeolite as we mentioned in the previous section. We found that the emission from silver clusters was decreased by UV-irradiation, but it was recovered by optical stimulation at 840 or at 675 nm. This indicates that part of the Ag o atoms might be ionized to Ag + cations by UV-irradiation. The ionized electrons may be captured in the zeolite Lewis acid sites (oxygen vacancies) that are the electron acceptors, or trapped at the surface states or defects in AgI clusters. The trapped electrons may be released by optical stimulation and the photoreleased electrons may recombine with Ag + to give the emission of Ag o clusters. In summary, AgI clusters were formed in zeolite-Y. The fluorescence of AgI/Y consists of the emission of both AgI and Ag clusters. Reversible energy transfer or charge cartier migration may occur between the two types of clusters. Photostimulated luminescence (PSL) from AgI/Y was observed by photostimulation at 675 or at 840 nm. The PSL spectrum of AgI/Y is consistent with the emission of Ag clusters. It was considered to be caused by the charge transfer from the zeolite framework or from the AgI clusters to Ag clusters. These observations indicate that clusters of silver halides or silver clusters encapsulated in zeolites may be used for optical storage.

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CHEN

7. SUMMARY Here the fluorescence, thermoluminescence, and photostimulated luminescence of nanoparticles have been reviewed. The quantum-size and surface effects and their influence on the exciton oscillator strength, absorption, and fluorescence were also discussed. The photoluminescence excitation spectra and the excitation energy dependence of fluorescence of nanoparticles were illustrated. Photoluminescence excitation spectrum is better than absorption spectrum in the detection of splitted levels by quantum-size effect and has become a standard technique to obtain quantum dot absorption features, while the size selectively excited PL technique provides a good method to study the size dependence of the photoluminescence of nanoparticles in only one sample. Thus the photoluminescence excitation spectrum and the size selectively excited PL technique may provide much information of the intrinsic properties of nanoparticles. The fluorescence process in nanoparticles is very complex and is not clear even at present, but it is agreed that surface states are involved and play an important role in the luminescence of nanoparticles. Our results demonstrate further that not only the exciton, but also the trapped carders at the surface states are confined by quantum-size effect. Both the exciton and the surface luminescence may be adjusted by quantum-size confinement. Thermoluminescence from semiconductor nanoparticles was observed and was discussed. The appearance of thermoluminescence of nanoparticles before any irradiation demonstrates the pre-existed trapped carders and the little change of the glow peak upon size indicates that the trap depth of surface states is not sensitive to particle size. Based on the thermoluminescence, a model proposed may explain the size dependence of the trapped luminescence from surface states of nanoparticles reasonably. The observations of photostimulated luminescence from Ag and AgI clusters in zeolites indicate that these materials may find an application as a medium for erasable optical memory. This represents a new direction for the practical applications of nanoparticles. As these phenomena have just been observed, much work is to be accomplished, both for basic research and for practical applications.

Acknowledgments I thank my students, Zhaojun Lin and Yan Xu, and my co-workers, for their help in experiments. I thank Jianhui Zhang for his help in the reprinting of the literature figures. I am grateful to Professors Lanying Lin, Zhanguo Wang at my Institute and Professor Mianzeng Su at Peking University, for their continued encouragement and support. I also thank my wife, Chunying Liang and my lovely daughter, Dandan Chen, for their support of my research works. This subject is supported by the President's Foundation of the Chinese Academy of Sciences and the National Natural Science Foundation of China.

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392

Chapter 6 SURFACE-ENHANCED OPTICAL P H E N O M E N A IN NANOSTRUCTURED FRACTAL MATERIALS Vladimir M. Shalaev Department of Physics, New Mexico State University, Las Cruces, New Mexico, USA

Contents 1. 2.

3.

4.

5.

6.

1.

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Surface-Enhanced Optical Responses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1. Kerr-Type Nonlinearity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2. Four-Wave Mixing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3. Raman Scattering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4. Harmonic Generation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Fractal Aggregates of Colloidal Particles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1. Coupled-Dipole Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2. Absorption Spectra in Fractal Aggregates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3. Local-Field Enhancements in Fractal Aggregates . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4. Surface-Enhanced Optical Phenomena in Fractal Aggregates . . . . . . . . . . . . . . . . . . . . 3.5. Selective Photomodification of Fractal Aggregates . . . . . . . . . . . . . . . . . . . . . . . . . 3.6. Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Self-Affine Thin Films . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1. General Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2. Linear Optical Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.3. Enhanced Optical Phenomena on a Self-Affine Surface . . . . . . . . . . . . . . . . . . . . . . . Random Metal-Dielectric Films . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1. Linear Response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2. Numerical Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3. Field Distributions on a Semicontinuous Film . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4. Scaling Theory of the Field Fluctuations and the Surface-Enhanced Optical Nonlinearities 5.5. Surface-Enhanced Raman Scattering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.6. Nonlinear Optical Processes on Semicontinuous Metal Films . . . . . . . . . . . . . . . . . . . . Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

393 395 395 396 396 397 397 398 401 404 406 409 413 414 414 416 419 424 428 429 430 . . . 435 440 444 444 446 446

INTRODUCTION

A giant enhancement

o f o p t i c a l r e s p o n s e s in m e t a l n a n o c o m p o s i t e s

consisting of small nanometer-sized

particles or roughness

studied during the last few years. This enhancement

and rough thin films

features has been intensively

is a s s o c i a t e d w i t h o p t i c a l e x c i t a t i o n o f

Handbook of Nanostructured Materials and Nanotechnology, edited by H.S. Nalwa Volume 4: Optical Properties Copyright 9 2000 by Academic Press All rights of reproduction in any form reserved.

ISBN 0-12-513764-8/$30.00

393

SHALAEV

surface plasmons which are collective electromagnetic modes and which strongly depend on the geometrical structure of the material. Typically, random nanocomposites and rough thin films are characterized by fractal geometry within a certain interval of sizes. The emergence of the concept of fractals was a significant breakthrough in the description of irregularity. Fractal objects are not translationally invariant and, therefore, cannot transmit running waves. Accordingly, collective excitations, such as surface plasmons, tend to be localized in fractals [1, 2]. Mathematically, this is a consequence of the fact that plane running waves are not eigenfunctions of the operator of dilation symmetry that characterizes fractals. In fractals, collective plasmon oscillations are strongly affected by the fractal morphology, leading to the existence of "hot" and "cold" spots (i.e., areas of high and low local fields). In many cases local enhancements in the hot spots exceed the average surface enhancement by many orders of magnitude because the local peaks of the enhancement are spatially separated by distances much larger than the peak sizes. Also, the spatial distributions of these high-field regions are very sensitive to the frequency and polarization of the applied field [2-7]. The positions of the "hot spots" change chaotically but reproducibly with frequency and/or polarization. This is similar to speckle created by laser light scattered from a rough surface with the important difference that the scale size for fractal plasmons in the hot spots is in the nanometer range rather than in the micrometer range for photons. Two classes of surface plasmons are commonly recognized: localized surface plasmons (LSP) and surface plasmon waves (SPW). [SPW are also called surface plasmon polaritons (SPP)--coherent mixture of plasmons and photons.] SPW propagate laterally along a metal surface whereas LSP are confined to metal particles that are much smaller in size than the wavelength of the incident light. However, in fractal media plasmon oscillations in different particles (roughness features) strongly interact with each other via dipolar or, more generally, multipolar forces. Thus, plasmon oscillations on a self-affine surface and in a fractal aggregate are neither conventional SPW nor independent LSP. Rather, they should be treated as collective eigenmodes arising from multipolar interactions in a fractal object. Fractal nanostructured materials can be fabricated with the aid of well-established chemical and depositional methods. For example, colloidal clusters with the fractal dimension D = 1.78 can be grown in colloidal solutions via the aggregation process which is known as the cluster-cluster aggregation [8]. Alternatively, clusters with fractal dimension D = 2.5 can be grown by the particle-cluster aggregation process (termed the WittenSander aggregation or WSA [8]). Also, by controlling conditions of atomic beam deposition and substrate temperature, self-affine thin films may be grown with various fractal dimensions [9]. Finally, random metal-dielectric films (called also semicontinuous metal films) produced by metal sputtering onto an insulating substrate also include fractal clusters of metal granules near the percolation threshold [8, 9]. The fractal plasmon, as any wave, is scattered from density fluctuations. The strongest scattering occurs from inhomogeneities of the same scale as the wavelength. In this case, interference in the process of multiple scattering results in Anderson localization. Anderson localization corresponds typically to uncorrelated disorder. A fractal structure is in some sense disordered, but it is also correlated for all length scales, from the size of constituent particles, in the lower limit, to the total size of the fractal, in the upper limit. Thus, what is unique for fractals is that because of their scale invariance, there is no characteristic size of inhomogeneity--inhomogeneities of all sizes are present from the lower to the upper limit. Therefore, whatever the plasmon wavelength, there are always fluctuations in a fractal with similar sizes, so that the plasmon is always strongly scattered and, consequently, localized [2, 10]. Large fluctuations of local electromagnetic fields in inhomogeneous metal nanostructures result in several optical effects. A well-known effect of this type is the surface-

394

SURFACE-ENHANCED OPTICAL PHENOMENA

enhanced Raman scattering (SERS) by molecules adsorbed on a rough metal surface or on aggregated colloid particles [ 11 ]. A giant enhancement of nonlinear optical responses was predicted [ 12] for metal fractals. In an intense electromagnetic field, a dipole moment induced in a particle can be expanded into power series: d = c~(1)E(r) + c~(2)[E(r)] 2 + o~(3)[E(r)] 3 + . . . , where ot(1~ is the linear polarizability of a particle, ot(2), ot(3) are the nonlinear polarizabilities, and E (r) is the local field at the site r. The polarization of the medium (dipole moment per unit volume), which is an additional source of an electromagnetic field in a medium, can be represented in an analogous form with the coefficients called susceptibilities. When the local field considerably exceeds the applied field, E (~ huge enhancements of nonlinear optical responses occur. Our chapter is concerned with theoretical and experimental results obtained in this promising area.

2. SURFACE-ENHANCED O P T I C A L RESPONSES In the following text we consider enhancement of optical responses on different fractal surfaces, such as aggregates of colloidal particles, self-affine thin films, and semicontinuous metal films. We assume that each site of the surface possesses a required nonlinear polarizability, in addition to the linear one. The local fields associated with the light-induced eigenmodes of a fractal surface can significantly exceed the applied macroscopic field, E (~ For metal surfaces, this enhancement increases toward the infrared part of the spectrum where resonance quality factors are significantly larger, in accordance with the Drude model of metal [2, 5].

2.1. Kerr-Type Nonlinearity We begin our consideration with the Kerr-type nonlinearity, X (3)(--O); 09, 09,--0)), that is responsible for nonlinear corrections to absorption and refraction. This type of optical nonlinearities can be used, in particular, for optical switches and optical limiters. The local nonlinear dipole, in this case, is proportional to IE(r)laE(r), where E(r) is the local field at the site r. For the resonant eigenmodes, the local fields exceed the macroscopic (average) field by a quality factor, q. The fields generated by the nonlinear dipoles can also excite resonant eigenmodes of a fractal surface resulting in an additional "secondary" enhancement cx E ( r ) / E (~ Accordingly, the surface-enhanced Kerr-susceptibility, )~(3), can be represented as (the angular brackets in the following formulas denote an ensemble average) [2, 5, 13], )~~3~ (IE(r) 12[E(r)]2) [E(0)] 4 px(3 ) = GK =

(1)

Here X (3) is the initial "seed" susceptibility; it can be associated with some adsorbed molecules (then,)~ (3) represents the nonlinear susceptibility of the composite material consisting of the adsorbed nonlinear molecules and a surface providing the enhancement). The seed X (3) can be also associated with an isolated colloidal particle. Then, G K represents the enhancement due to the clustering of initially isolated particles into aggregates, with the average volume fraction of metal given by p. The applied field with the frequency in the visible, near IR or IR parts of the spectrum is typically off resonance for an isolated colloidal particle (e.g., silver) but it does efficiently excite the eigenmodes of fractal aggregates of the particles; the fractal eigenmodes cover a large frequency interval including the visible and infrared parts of the spectrum [2, 5]. For simplicity, we assume that E (~ in (1) is linearly polarized and therefore can be chosen real. The previous formula was proven [5] from rigorous first-principle considerations. Note also that GK depends on the local-field phases and it contains both real and imaginary parts.

395

SHALAEV

2.2. Four-Wave Mixing The high local fields associated with the localized eigenmodes experience strong spatial fluctuations on a random fractal surface. Because a nonlinear optical process is proportional to the local fields raised to some high power, the resultant enhancement associated with the fluctuation area (hot spot) can be extremely large. In a sense, one can say that enhancement of optical nonlinearities is especially large in fractals because of very strong field fluctuations. Four-wave mixing (FWM) is determined by the nonlinear susceptibility similar to (1) ((3) a/~y~(-Ws; Wl,Wl,-w2), where Ws --2Wl -092 is the generated frequency, and o91 and w2 are the frequencies of the applied waves. Coherent anti-Stokes Raman scattering (CARS) is an example of FWM. In one elementary CARS process, two Wl photons are transformed into the w2 and Ws photons. Another example is degenerate FWM (DFWM); this process is used for optical phase conjugation (OPC) that can result in complete removal of optical aberrations [14]. In DFWM, all waves have the same frequency (Ws - Wl - 092) and they differ only by their propagation directions and, in general, by polarizations. In a typical OPC experiment, two oppositely directed pump beams, with field amplitudes E (1) and E ~(1), and a probe beam, with amplitude E (2) (and propagating at a small angle to the pump beams), result in an OPC beam which propagates against the probe beam. Because of the interaction geometry, the wave vectors of the beams satisfy the equation k l -F k~ -- k2 -F ks - 0. Clearly, for the two pairs of oppositely directed beams, that have the same frequency o9, the phase-matching conditions are automatically fulfilled [ 14]. The third-order nonlinear susceptibility, X (3), that results in DFWM, also leads to the considered nonlinear refraction and absorption that are associated with the Kerr optical nonlinearity. Note also that as in the foregoing text the nonlinear susceptibility, X (3), can be associated with either the fractal surface itself or the molecules adsorbed on the surface. For coherent effects, including the ones discussed in this section, averaging is performed for the generated field amplitude (rather than intensity) or, equally, for the nonlinear polarization of a medium. The average polarization, p(3)(w), is proportional to the nonlinear susceptibility, p(3)(o9) oc )~(3) _ Z(3)GK. The measured signal for coherent processes is proportional to 1~(3)12. Thus we conclude that the resultant enhancement for degenerate (or near degenerate) four-wave mixing can be expressed in terms of the enhancement for the Kerr-susceptibility as follows [5], GFWM = IGrl 2 -

(IE(r)le[E(r)]2) 2 [E(0)] 4

(2)

Note that one can equally describe a medium optical response in terms of the nonlinear currents rather than the nonlinear polarizations; these two approaches are completely equivalent [7] (see Section 5).

2.3. Raman Scattering Although Raman scattering is a linear optical process, the surface-enhanced Raman scattering at small Stokes shifts is proportional to the fourth power of the local fields [5, 11], so that the average enhancement factor is [5], (IE(r)l 4)

GRs = [E(0)] 4

(3)

Note that in contrast to the enhanced Kerr-nonlinearity considered earlier, GRs is real and the local enhancement is phase insensitive, so that there is no destructive interference of signals from different points of a surface. As a result, GRs is, typically, larger than GK.

396

SURFACE-ENHANCED OPTICAL PHENOMENA

2.4. Harmonic Generation

Under some simplifying conditions, the enhancement for the second harmonic generation (SHG) can be written as [2], GSHG --

( [ E~ O E()

] 2 [ E2~ ] ) 12 E(0)

(4)

where "-'2co ~(0) and Ezco(r) are the macroscopic and local linear fields at frequency 2w. If there is no enhancement at frequency 2w, then E2co(r) - E 2o9" (0) The previous formula can be easily generalized for the nth harmonic generation (nHG), GnHG :

E(O)

E(nO 2

(5)

Note that the previous formulas are valid for an arbitrary surface fractal or nonfractal. In fractals, however, because of the extremely large field fluctuations the ensemble-average enhancements are typically much larger than for nonfractal surfaces. In addition, the fractal modes provide enhancements in a very large spectral range including the infrared part, where the enhancement is particularly large because of the high quality factor for metal surfaces in this spectral range [2]. We also show in the following text that the local enhancements in the hot zones (associated with the localized eigenmodes) can exceed the ensemble-average enhancement by many orders of magnitude.

3. FRACTAL AGGREGATES OF COLLOIDAL PARTICLES As well known, there is only one dipolar mode that can be excited by a homogeneous field in a spherical object. For a three-dimensional (nonfractal) collection of small particles, such as randomly close-packed hard spheres of particles or a random gas of particles, absorption spectra are peaked near the relatively narrow resonance of the individual particles, that is, all eigenmodes of a collection of particles are located within a small spectral interval [5]. In contrast to such conventional (nonfractal) three-dimensional systems, dipolar interactions in low-dimensional fractal clusters are not long range. This results in the spatial localization of the eigenmodes at various random locations in the cluster [2-7, 10]. The spectrum of these eigenmodes exhibits strong inhomogeneous broadening as a result of the spatial variability of the local environment. It is also important to note that, despite the asymptotically zero mean density of particles in a fractal cluster, a high probability always exists of finding a number of particles in close proximity to a given particle (stated more precisely, in fractals, the pair correlation g cx r D-d (D < d), where D is the fractal dimension and d is the dimension of the embedding space; accordingly, g becomes large at small r). Thus, objects with fractal morphology possess an unusual combination of properties. Namely, despite the fact that the volume fraction, p, filled by N = (Rc/Ro) ~ particles in a fractal (Re and R0 are the size of a fractal cluster and a typical separation between neighbor particles, respectively) is very small, p cx N l - d / ~ __+ O, strong interactions nevertheless exist between neighboring particles [2]. These strong interactions between neighboring particles, which are highly variable because of the variability of local particle configurations in a cluster, lead to the formation of inhomogeneously broadened eigenmodes covering a broad spectral range [2, 4, 5]. Localization of eigenmodes in fractals leads to a patchworklike distribution of the local fields associated with hot and cold zones [2-5, 10]. This, in turn, results in large spatial fluctuations of local fields in fractal composites and in giant enhancements of various optical effects [2-7, 10, 12, 15]. For the special case of fractals formed by metal particles, the dipole eigenmodes span the visible and the infrared regions of the spectrum; because the mode quality factors

397

SHALAEV

Fig. 1. Electronmicroscopepicture of a fractal aggregate of silver colloidalparticles. (Source: Reprinted with permission from I. Stockman, V. M. Shalaev, M. Moskovits, R. Botet, and T. F. George, Phys. Rev. B 46, 2821 [1992]. 9 1992American Physical Society.)

increase with wavelength, local fields are especially large in the long-wavelength part of the spectrum [2, 5]. An electron microscope picture of a fractal aggregate of silver colloidal particles is shown in Figure 1. The fractal dimension of these aggregates is D ~ 1.78. Using the wellknown model of cluster-cluster aggregation, colloidal aggregates can be readily simulated numerically [8]. Note that voids are present at all scales from the minimum one (about the size of a single particle) to the maximum one (about the size of the whole cluster). This is an indication of the statistical self-similarity of a fractal cluster. The size of an individual particle is ~ 10 nm, whereas the size of the whole cluster is ~ 1/zm. The process of aggregation can be described as follows. A large number of initially isolated silver nanoparticles execute random walks in the solution. Encounters with other nanoparticles result in their sticking together, first to form small groups, which then aggregate into larger formations, and so on. The "cluster-cluster aggregates" (CCA) having fractal dimension D ~ 1.78 are eventually formed.

3.1. Coupled-Dipole Equations As shown in Section 2, enhancement for various optical phenomena on random surfaces can be expressed in terms of the local fields. For calculations of the local fields we solve the coupled-dipole equations (CDE) describing an optical response of an arbitrary collection of N identical polarizable particles (monomers) possessing a linear scalar polarizability ct. When irradiated by a plane monochromatic incident wave of the form, Einc (r, t) -- E (~ exp(ik 9r - iogt)

398

(6)

SURFACE-ENHANCED OPTICAL PHENOMENA

the monomers interact with the incident field and with each other through induced dipole moments. The local electric field Ei at the monomer's position ri is given by the sum of the incident wave and all the scattered (secondary) waves: Ei = Einc(ri, t) + Esc(ri, t). The dipole moment di at the ith site is determined as di = ot0Ei

(7)

The field Esc(ri), scattered from all other dipoles, generally, contains the near-, intermediate-, and far-zone terms. We restrict our consideration to the quasi-static limit, that is, the characteristic system size L is assumed to be much smaller than the wavelength = 2Jrc/og. In this approximation, we leave only the near field term in the expression for Esc(ri) and the factor exp(ik.ri) is always close to unity. In addition, the time dependence, exp(-iogt), is the same for all time-varying fields, so that the whole exponential factor can be omitted. After that, the coupled-dipole equations (CDE) for the induced dipoles acquire the following form [2, 10],

di,a -- a 0 ( E (~ -t- ~ Wij,afldj,~) jr

(8)

3rij,arij,fl -- 8aflr 2 rS.. ij

(9)

Wij,otfl --

where Wij,a~ is the quasi-static interaction operator between two dipoles, ri is the radius vector of the i th monomer, and rij = ri - rj. The Greek indices denote Cartesian components of vectors and should not be confused with the polarizability, c~0. Hereafter, summation over repeated Greek indices is implied, except if stated otherwise. The linear polarizability of an elementary dipole representing a spherical monomer, c~0, is given by the Lorenz-Lorentz formula (see, for example, [ 16]), 8 - 8h

otO - R3m 8 -+-28h

(10)

where e = 8 t + i8" is the bulk dielectric permittivity of the film material and 6h is the dielectric constant of the host material. Because Wij,a~ is independent of the frequency co in the quasi-static approximation, the spectral dependence of solutions to (8) is manifested only through ot0(og). For convenience, we introduce the variable Z(og) = 1/c~(og) = -[X(og) + i8(o9)]. Using Eq. (10), we obtain [ 38h(8'--Sh)] X _= -Re[c~o 1] = - e m 3 1 -+- 18 - 8hi 2 8 -- --Im[oto 1] = 3Rm 3

8hStt

18-8h12

(11)

(12)

The variable X indicates the proximity of o9 to an individual particle resonance occurring at 8' = --28h and it plays a role of a frequency parameter; 8 characterizes dielectric losses. The resonance quality factor is proportional to 8 -1 . One can find X (Z) and 8(~.) for any material using theoretical or experimental data for 8(~.) and formulas (11) and (12). In Figure 2a and b, we plot X and 8 as functions of the wavelength ~. for silver in water and vacuum using the tabulated data for 8 [17], (the units in which (4:r/3)R3m = 1 are used). As seen in the figure, X changes significantly from 400 to 800 nm and then, for longer wavelengths, remains almost constant, X ~ -4zr/3. The relaxation constant is small in the visible spectral range and decreases toward the infrared. For metal particles, the dielectric function is well described by the Drude formula 2 ogp 8 =e0 (13) o9(o9 + iF) where 80 includes the contribution to the dielectric constant associated with interband transitions in bulk material, COp is the plasma frequency and 1-' is the relaxation constant.

399

SHALAEV

IX

I

I

I

I

I

I

I

8 water vacuum ...........

6 4 2 0 -2 -4

400

200

600.

800

1000 1200 1400 1600 1800 (a)

101

i6

i

I

I

!

I

I

I

-2 water vacuum ...........

10-1

"~..,..., 10-9.

i

i

200

400

600

800 1000 1200 1400 1600 1800 (b)

Fig. 2. Spectraldependence of the frequency parameter, X, and loss parameter, 8, for silver. (Source: Reprinted with permission from V. A. Markel, V. M. Shalaev, E. B. Stechel, W. Kim, and R. L. Armstrong,Phys. Rev. B 53, 2425 [1996]. 9 1996 American Physical Society.) Now we write Eq. (8) in a matrix form. Following Refs. [2, 5, 10], we introduce a 3Ndimensional vector space R 3N and an orthonormal basis Iiot). The 3N-dimensional vector of dipole moments is denoted by Id), and the incident field is denoted by IEinc). The Cartesian components of three-dimensional vectors di and Einc are given by (ic~ld) = di,~ and (iotlEinc) = E0,~. The last equality follows from the assumption that the incident field is uniform throughout the film. The matrix elements of the interaction operator are defined by (iotl W l j f l ) - Wij,=~. Then Eq. (8) can be written as [Z(w) - W i l d ) = [Einc)

(14)

The interaction operator W in (14) is real and symmetrical, as it can be easily seen from the expression (9) for its matrix elements. By diagonalizing the interaction matrix W with W i n ) = wnln) and by expanding the 3N-dimensional dipole vectors in terms of the eigenvectors In) (as Id) = E n Cn In)), we obtain a relation between the local fields and the amplitudes of linear dipoles induced by

400

SURFACE-ENHANCED OPTICAL PHENOMENA

the incident wave (6) [2, 5, 10],

Ei,~ -- otol di,~ -- otol oti,u~Eo,~

(15)

where we introduced the polarizability tensor of the i th dipole, ~i (O9), with its matrix elements, c~i,,~, given by

oti,afl =-oti,c~fl(o))- Z

(ialn) (nljfl) Z(co) -

j,n

(16)

w.

The local dipoles, according to (15), are expressed in terms of the eigenmodes as follows,

di ~ - Z '

n

(ic~ln)(nlEinc) = Z Z (co) -

w,,

(i~ln)(nljfl) Eo,~

n,j

Z(w)

-

(17)

w,,

Equations (15) and (16) allow one to express the local fields in terms of the eigenfunctions and eigenfrequencies of the interaction operator; the local fields then can be used to calculate enhancements of optical phenomena, using the formulas of Section 2. The average cluster polarizability is given by

1

o t - 3N LTr[c~;'~J

(18)

i

The extinction cross-section O'e is expressed through the imaginary part of the polarizability as O" e - -

4JrkN Im~

(19)

For small clusters scattering can be neglected so that the extinction cross-section is approximately equal to the absorption cross-section. From (16) and (18) the following useful sum rules can be obtained [10], f Imt~(X) -- rr

fXlma(X)dX-O

(20)

3.2. Absorption Spectra in Fractal Aggregates In the following text we discuss results of our numerical and experimental studies of the extinction (absorption) spectra of fractal aggregates of nanoparticles. To simulate the silver colloid aggregates studied in our experiment, we used the clustercluster aggregation model [8]. The cluster-cluster aggregates (CCA) have fractal dimension, structure, and aggregation pattern very similar to those observed in the experiment. The CCA were built on a cubic lattice with periodic boundary conditions using a wellknown algorithm [8]. In Figure 3, the absorption spectrum, Im ot(X), as function of the frequency parameter X is shown for CCA (the units a = 1 are used, where a is the lattice period). The simulations were performed for clusters consisting of N = 500 and N -- 10,000 particles each. Note the spectrum reflects a strong inhomogeneous broadening in CCA; the spectrum width is much larger than the resonance width for an individual monomer which is 3 (in the simulations we used 6 = 0.1). The used CCA model contains two adjustable parameters, the lattice period, a, which defines the relative distances, rij, between particles, and the radius of a monomer, Rm. Clearly, solutions of the CDE are very sensitive to the ratio a/Rm, because this parameter determines the interaction strength. The model of geometrically touching spheres, which seems to be the most natural, implies that a/Rm -- 2. However, as was shown in Ref. [18], this model fails to describe the long-wavelength resonances observed in a group of particles; it also fails to describe the long-wavelength tail observed in the absorption spectra of colloid aggregates (see, for example, Refs. [15] and [19]). The physical reason for the failure of this model is that the dipole approximation is not strictly applicable for touching spheres [ 18, 20-23]. Indeed, the dipole field produced

401

SHALAEV

0.5

Ima

,

0 . 4

-

I

,

,-i~--

t~ I

i ~

'*

0.3-

0.2-

0.1-

CCA . . . . . N=500 ........ N= 1,000 N= 10,000

I

'~ 'i\ ',\ ~ t "-%.._

0.0

-6

,

'

-~4

'

-'2

'

()

'

i

2

'"

|

J~

6

X Fig. 3. Calculatedabsorption spctra, Im c~(X), for cluster-cluster aggregatescontaining a different number of particles, N = 500, N = 1000, and N = 10,000. (Source: Reprinted with permission from V. A. Markel, V. M. Shalaev, E. B. Stechel, W. Kim, and R. L. Armstrong, Phys. Rev. B 53, 2425 [1996]. 9 1996 American Physical Society.) by one of the touching monomers is highly inhomogeneous (c~ r -3) within the volume of the other one. This inhomogeneous field should result in high-order multipole moments, coupled both to each other and to the incident field. The high-order moments, when they are taken into account, effectively increase depolarization factors, and lead to the lowfrequency resonances observed in experiments [18]. However, incorporating these highorder moments into the calculation results in an essentially intractable problem for the large fractal clusters considered here. As suggested by Purcell and Pennypacker [24], and developed by Draine [25], a description of the optical response of an arbitrary shaped object can be obtained, remaining within the dipole approximation. (It is worth noting that the macroscopic Maxwell equations also contain only dipolar terms, i.e., polarization.) In the following text we generalize these ideas for fractal aggregates. To account for multipolar effects in the CDE, real touching spheres may be replaced by effective spheres which geometrically intersect. Formally, this requires the ratio a/Rm to be taken less than 2. The physical reason underlying this procedure can be understood from the following arguments. Consider a pair of touching spheres and ascribe to the first sphere a dipole moment d located at its center. Because we would like to remain within the dipole approximation, the second sphere should also be replaced by a point dipole located at a certain distance from the first sphere. Clearly, because the field associated with the first sphere decreases nonlinearly, ~ d / r 3, the second dipole should be placed somewhere closer than 2Rm from the center of the first sphere (otherwise, the interaction between the spheres would be underestimated). In other words, in order to correctly describe the interaction between the spheres remaining within the dipolar approximation, the distance between the dipoles must be taken less than 2Rm. This is equivalent to replacing the original touching spheres by overlapping spheres with the dipole moments located at their centers. To gain insight concerning selection of the ratio a/Rm, we first consider cases for which a/Rm is known exactly. As shown in Refs. [24-26], the correct description of the optical response of a small object of arbitrary shape was obtained by considering the dipolar interactions of a set of spherical monomers placed on a simple cubic lattice inside the volume of the object; the lattice period, a, was chosen such that a 3 = (4:r/3)R3m . This relation which provides equality of the total volume of the spheres and the original object under

402

SURFACE-ENHANCED OPTICAL PHENOMENA

consideration, gives the ratio a/Rm -- (47r/3) 1/3 ~ 1.612. In Ref. [27] it was shown that, within the dipole approximation, correct depolarization coefficients for a linear array of spherical monomers are obtained provided a/Rm is chosen to be (4(3) 1/3 ~ 1.688 ((3 = ~ k k-3), that is, close to the previously mentioned value. We used a/Rm --(4zr/3) 1/3 in our calculations. We also require that the radius of gyration Rc and the total mass of clusters used in the simulations must be the same as in the experiment. This condition, combined with a/Rm (4zr/3) 1/3, can be satisfied for fractals (D ~ 3) if one chooses Rm Rexp(yg/6) D/[3(3-D)], where Rexp is the radius of monomers used in experiments. In our experiments described later, the radius of silver particles forming colloidal aggregates was Rexp ~ 7 nm, so that Rm ~ 5 nm for D = 1.78. For a light beam propagating in a system which contains randomly distributed clusters far away from each other (so that the clusters do not interact), the intensity dependence is given by the expression I(z) = I(O)exp(-(regZ), where 9 is the cluster density, ff = p/[(4rc/3) R3xp(N) ], and p is the volume fraction filled by spherical particles. Introducing the extinction efficiency, -

-

4k Im ot R2xp

((r e )

O e - (N)TrR2xp

(21)

the intensity dependence I (z) acquires the form,

z 1

I (z) -- I (0) exp - ~ Qe p ~exp "

(22)

As follows from (22) the extinction efficiency Qe is the quantity that is measured in experiments on light transmission (rather than (re). In Refs. [4, 5, 15] experiments were performed to measure extinction in silver colloid aggregates. In [5] fractal aggregates of silver colloid particles were produced from a silver sol generated by reducing silver nitrate with sodium borohydride [28]. The color of fresh (nonaggregated) colloidal solution is opaque yellow; the corresponding extinction spectrum (see Fig. 4) peaks at 400 nm with the halfwidth about 40 nm. Addition of adsorbent 1.5

-

Qe Monomers

1.0

-

0.5

-

Calculation (N= 1;N=500) Experiment ooooo Calculation (N--10,000)

t

\

Aggregates

. .0

.

.

.

.

~-

.=_

--

200

400

600

Wavelength,

800

1000

ilm

Fig. 4. Experimentaland calculated extinction spectra of silver colloid CCA. The theoretical spectra are presented for 500-particle and 10,000-particle CCA. (Source: Reprinted with permission from V. A. Markel, V. M. Shalaev, E. B. Stechel, W. Kim, and R. L. Armstrong, Phys. Rev. B 53, 2425 [1996]. (g) 1996 American Physical Society.)

403

SHALAEV

(fumaric acid) promoted aggregation, and fractal colloid clusters formed. When adding the fumaric acid (0.1 cm 3 of 0.5 M aqueous solution) into the colloids (2.0 cm3), the colloid's color changed through dark orange and violet to dark grey over 10 h. Following aggregation, a large wing in the long wavelength part of the spectrum appeared in the extinction, as seen from Figure 4. Note to plot Figure 4, we used the results of Figure 3, where X was expressed in terms of )~ for silver particles (see Fig. 2). A broadening of absorption spectra of silver colloidal aggregates due to the interaction between particles constituting the aggregates is well seen in Figure 4 [5, 29, 30]. The results of calculation of the absorption wing shape by the coupled-dipoles method describe experimental data fairly well [5, 29, 30]. The calculations were performed for 500-particle CCA (solid line with a large wing) and for 10,000-particle CCA (circles) [5]. Clearly, the aggregation results in a large tail in the red and infrared part of the spectrum, which is well described by the simulations. The discrepancy in the central part of the spectrum probably occurs because, in the experiments, a number of particles remained nonaggregated and led to additional (not related to fractal aggregates) absorption near 400 nm.

3.3. Local-Field Enhancements in Fractal Aggregates We now discuss the enhancement of local fields in small-particle composites. The parameter characterizing the enhancement of local-field intensity can be defined as G=

(IEil 2) IE(0)l 2

(23)

The enhancement G is related to Imc~(X) as follows [10] (see (15), (16), and (18)), a-8

1+-~-

Imot

(24)

According to Eq. (24), the enhancement factor G ~ (X2/8)Imc~ for IXI >> 6, that is, it can be very large. Note that, because in fractals the fluctuations are very large so that (IEI 2) >> (IEI) 2 [2, 10], we have (IAEI 2) ~ (IEI2); therefore, in this case, G characterizes both the enhancement of local fields and their fluctuations as well. In other words, the larger the fluctuations, the stronger the enhancement. In the following text we consider results of numerical simulations of G for clustercluster aggregates (CCA) having fractal dimension D ~ 1.78, and for two nonfractal ensembles of particles: a random gas of particles (RGP) and a close-packed sphere of particles (CPSP). While RGP is a very dilute system of particles randomly distributed in space, CPSP represents a dense (but still random) system of particles. In both cases D = d = 3 and the correlation function g(r) is constant. The particles were assumed to be hard spheres. To provide better comparison with CCA, the RGP was generated in a spherical volume that would be occupied by a CCA with the same number of particles; this means that particles in CCA and RGP fill the same volume fraction, p (p was small, p ~ 0.05 for N = 500). In contrast, a fairly dense packing of spherical particles, with p ~ 0.44, was used for CPSR In Figure 5 results of the simulations for the enhancement factor G in silver CCA in vacuum are compared with those for nonfractal composites, RGP and CPSP [5]. (The material optical constants for silver were taken from Ref. [17].) As seen in Figure 5, the enhancement of local-field intensities in fractal CCA is significantly larger than in nonfractal RGP and CPSP clusters, as was anticipated. The enhancement can reach very high values, ,~ 103, and increases with )~. This occurs because both the localization of fractal eigenmodes and their mode quality factor (q ~ 1/8 ~ le - ehl2/3e"eh) increase for the modes in the longwavelength part of the spectrum. We next consider a more detailed comparison between fractal small-particle composites and nonfractal inhomogeneous media. The simulations were performed for RGP and CCA

404

SURFACE-ENHANCED OPTICAL PHENOMENA

1000

G

"CCA~"

_

~

/

lOO

IO~

;,....................................

~

460

~60

~..G..r'. .....

860

Wavelength,

i0'00

izoo

nm

Fig. 5. Enhancementfactors, G, of local-field intensities plotted against ~. for 500-particle aggregates: CCA (solid line), a random gas of particles (RGP) with the same as for a CCA volume fraction of metal (shortdashed line), and a close-packed sphereof particles, CPSP,(long-dashedline). (Source:Reprintedwithpermission from V. M. Shalaev, E. Y. Poliakov, and V. A. Markel, Phys. Rev. B 53, 2437 [1996]. 9 1996American Physical Society.) having the same volume fraction p filled by metal. The volume fraction p of particles in a fractal cluster is very small. (In fact, p ~ 0 at Rc ~ ex~;but p is, of course, finite for a finite number of particles.) According to the Maxwell-Garnett theory [2], there is only one resonant frequency in conventional (d = D) media with p 0 G~.o

o

a~> l~, where ~" = 2(d + 1)/(d + 2) = 2 - H; here, l is the linear size of a system and d is the dimension of the embedding space. Our simulations satisfied this condition, and the foregoing scaling relation was well manifested. In the simulations, we removed the bulk (regular) part of the computer-generated film so that the resultant sample had, at least, one hole. Clearly, the removal of the bulk part of a film does not affect the scaling condition (26). A typical simulated self-affine film is shown in Figure 13. Unlike for "conventional" random surfaces, the contribution of higher spatial harmonics (with amplitudes larger than the harmonic wavelengths) plays an important role in the

Fig. 13. Self-affinefilm obtained in the restricted solid-on-solidmodel. The scaling exponent H --0.4 and the fractal dimension D = 3 - H = 2.6. (Source: Reprinted with permission from V. M. Shalaev, R. Botet, J. Mercer, and E. B. Stechel, Phys. Rev. B 54, 8235 [1996]. 9 1996American Physical Society.)

415

SHALAEV

Fourier expansion of a self-affine surface profile. This means that neither the Rayleigh perturbation approximation [45] nor the Kirchoff (geometrical optics) approach can be directly applied to describe optical properties of self-affine structures [48]. Apart from these two basic approaches, there exists a phase perturbation method [49, 50], which is intermediate between the former two methods, and cannot be applied to self-affine surfaces either. Our approach is based on the discrete dipole approximation (DDA) [6]. As mentioned in the previous section, the DDA was originally suggested by Purcell and Pennypacker [24] and was developed in later articles [25] and [51-53] to calculate optical responses from an object of an arbitrary shape. It is based on replacing an original dielectric medium by an array of pointlike elementary dipoles. The DDA has been also applied to fractal clusters built from a large number of small interacting monomers [2, 10, 54, 55] (see Section 3). We briefly recapitulate the DDA and the related method based on solving the coupled-dipole equations [2, 6, 10]. Following the main idea of the DDA, we model self-affine films by point dipoles placed according to an algorithm described in the following text in sites of a simple cubic lattice with a period a, which is assumed to be much smaller than the size of spatial inhomogeneities. The occupied sites correspond to the spatial regions filled by the film, while empty sites correspond to the empty space. The linear polarizability of an elementary dipole (monomer), c~0, is given by the Lorenz-Lorentz formula having the same form as the polarizability of a dielectric sphere with radius Rm -- (3/47r) 1/3a (see, for example, [ 16]), e- 1 or0 -- R3me + 2

(27)

where as earlier e -- e I + ie" is the bulk dielectric permittivity of the film material (note that (27) coincides with (10), if eh -- 1). The choice of the sphere radius, Rm, provides equality of the cubic lattice elementary cell volume (a 3) and the volume of an imaginary sphere (monomer) that represents a pointlike dipole (4zr Rm/3 3 ) [24, 25, 52]. Consequently, for large films consisting of many elementary dipoles, the volume of the film is equal to the total volume of the imaginary spheres. Note that the neighboring spheres intersect geometrically because a < 2Rm. Using the intersecting spheres allows one, to some extent, to take into account the effects of the multipolar interaction within the pure dipole approximation [2, 6, 24, 25, 52] (cf., Section 3). We also note that using the DDA allows us to treat a film as a cluster of polarizable monomers that interact with each other via the light-induced dipoles which makes this problem similar to the problem of fractal aggregates considered previously in Section 3.

4.2. Linear Optical Properties Being given the coordinates of all dipoles in a self-affine film we can find its optical eigenmodes, the local fields, and the film polarizability, in the same way it was done for smallparticle aggregates (see (15)-(18)). In Figure 14, we show plots for the imaginary parts (describing absorption) of the "parallel" and "perpendicular" components of the mean polarizability per particle, Ctll - (1/2)(oti,xx + Oli,yy) and ct_t_------ (oli,zz). The parallel component, Ctll, characterizes the polarizability of a self-affine film in the (x, y)-plane, whereas the perpendicular component, or_L,gives the polarizability in the normal, z, direction. The polarizability components satisfy the sum rule: f ct• I(X) dX = 7r (see (20)). From the figure it is clear that there is a strong dichroism expressed in the difference between the two spectra, Ctll(X) and or• (X). The modes contributing most to Ctll (the "longitudinal" modes) are located in the long wavelength part of the spectrum (negative X; cf. (11)), whereas the "transverse" modes tend to occupy the short wavelength part of the spectrum (positive X). To some extent, this can be understood by roughly considering a film as an oblate spheroid, where the longitudinal and transverse modes are shifted to the red and blue, respectively, in comparison with the eigenmode of a sphere. However, in contrast to the case of a spheroid, there is a large variety of eigenmodes in self-affine films, as

416

SURFACE-ENHANCED OPTICAL PHENOMENA

1.6-I

1.2-

.8-

Im(~l) 11

\11

Im(otl__), _/

,

2

6

/

.4-

-10

-8

-6

-4

-2

0

4

8

10

Fig. 14. The imaginaryparts of the parallel, Otll,and the perpendicular, c~_t_,components of the polarizability. The results for samples with N ~, 104 and N ~ 103 dipoles each (solid and dashed lines, respectively) are shown. (Source: Reprinted with permission from V. M. Shalaev,R. Botet, J. Mercer, and E. B. Stechel, Phys. Rev. B 54, 8235 [1996]. 9 1996AmericanPhysical Society.)

follows from Figure 14. Really, the widths of the spectra in Figure 14 are much larger than the width of an individual resonance, 8; this indicates a strong inhomogeneous broadening associated with a variety of the dipolar eigenmodes on a self-affine surface. Thus, the dipole-dipole interactions of constituent monomers in a self-affine film generate a wide spectral range of resonant modes, similar as it was in the case of fractal aggregates. From Figure 14, we also make an important conclusion that in the quasi-static approximation, the optical properties of a self-affine film do not depend on the number of monomers, N, and, therefore, on the linear size, l, of the film. The calculations that were performed for the ensembles of samples with very different numbers of particles and linear sizes give similar results. Note also that the fact that the spectra are almost independent of the number of the dipoles, N, justifies the used discrete dipole approximation. The field distributions of eigenmodes on a self-affine surface are extremely inhomogeneous. On such a surface, there are hot spots associated with areas of high local fields, and cold zones with small local fields. (A similar patchworklike picture of the field distribution is observed in fractal clusters [2, 3, 10, 31, 56].) Spatial locations of the modes are very sensitive to both frequency and polarization of the applied field. To demonstrate this, in Figure 15, we show the intensity distributions for the local fields, IE(Ri)I 2, on the film-air interface [Ei,~ =- Ec~(Ri) -- otoldi,ot, where di,a are defined in (15)-(17), and Ri ~ (xi, yi), with xi and yi being the coordinates of the dipoles on the surface of a film]. The results are shown for different values of frequency parameter, X. Note that the local-field distributions, ]E(Ri )12, can be measured with the use of a near-field scanning optical microscope, provided the probe is passive [57]. As seen in Figure 15, for a modest value of 8 -- 0.03, which is typical for metals in the visible and near-infrared parts of the spectrum, the local-field intensities in the hot zones can significantly, up to 3 orders of magnitude, exceed the intensity of the applied field

417

SHALAEV

Fig. 15. Spatial distributions of the local-field intensities, [E(Ri)I 2, on the self-affine surface for different values of frequency parameter, X. (a) X = - 3 (Z = 500 nm, (b) X = - 2 (Z = 400 nm). The decay parameter ~ = 0.03 in both cases. The applied field is polarized in the (x, y)-plane, E (0) = (2)-1/2(1, 1, 0). (Source: Reprinted with permission from V. M. Shalaev, R. Botet, J. Mercer, and E. B. Stechel, Phys. Rev. B 54, 8235

[1996]. 9 1996American Physical Society.)

(for smaller values of 8, the enhancements can be even larger). The high frequency and polarization sensitivity of the field distributions are also obvious from the figure. Strongly inhomogeneous distributions of local fields on a self-affine surface bring about large spatial fluctuations of local fields and strong enhancements of optical processes. These enhancements are especially large for nonlinear optical phenomena which are proportional to the local fields raised to some high power. To study localization of eigenmodes on a self-affine surface, we calculated the mode pair-correlation function defined as

i,jEs;ot,fl

where the normalization constant C is defined by the requirement v(R - - 0 ) = 1, and the summations are over dipoles on the surface only. If the mode is localized within a certain area of radius R0, then v(R) is small for R > R0 and the rate of decay of v(R) at R > R0 reflects a character of localization (strong or weak) for the state n [58]. The calculated v(R, X) (see Fig. 16) are well approximated by the formula v(R, X) = exp{-[R/L(X)]X}, where !< ~ 0.7. When the exponent is larger than 1, x > 1, the modes

418

SURFACE-ENHANCED OPTICAL PHENOMENA

Fig. 16. The mode correlation function, v(R, X). (Source: Reprinted with permission from V. M. Shalaev, R. Botet, J. Mercer, and E. B. Stechel, Phys. Rev. B 54, 8235 [1996]. 9 1996AmericanPhysical Society.) are commonly called superlocalized; in our case, with tc ~ 0.7, the modes can be referred to as sublocalized (or quasi-localized), on average. 4.3. Enhanced Optical Phenomena on a Self-Affine Surface

Calculating the local fields with (15) and (16) and substituting them to the general formulas of Section 2, we find enhancement factors for different optical phenomena. In Figure 17, we show results of our theoretical calculations for the average enhancement of Raman scattering for both small and large Stokes shifts on self-affine films generated in the RSS model. GRS, II and G Rs,• describe enhancements for the applied field polarized in the plane of the film and perpendicular to it, respectively, (see (3)). As seen in the figure, the enhancement increases toward the long-wavelength part of the spectrum and it reaches very large values, -~ 10 7. This agrees well with the experimental observations of SERS on cold-deposited thin films [ 11 ]. In Figure 18, the field spatial distributions at the fundamental and Stokes frequencies are shown. As seen in the figure, the distributions contain hot spots, where the fields are very high. Although the Stokes signal is proportional to the local field at the fundamental frequency, 09, the generated Stokes field, with frequency COs,excites, in general, other eigenmodes. Hence the field spatial distributions produced by the applied field and by the Raman signal can be different, as clearly seen in the figure. This pattern is expected to be typical for various optical processes in strongly disordered fractal systems, such as self-affine thin films. Specifically, hot spots associated with fields at different frequencies and polarizations can be localized in spatially separated nm-sized areas. These novel nano-optical effects can be probed with NSOM providing subwavelength resolution [3, 31, 57]. If molecules possess the second-order nonlinear susceptibility, X (2), then second harmonic generation (SHG) can be strongly enhanced when adsorbing the molecules on a metal self-affine surface (see (4)). In Figure 19, we plot the calculated enhancement for SHG from molecules on a silver self-affine surface (for the applied field polarized parallel and perpendicular to the surface, GSHG, II and GSHG,_t_,respectively). As seen in the figure, the enhancement is very large and increases toward larger wavelengths. We see that the anticipated inequality G II >> G• holds, because the linear dipoles and corresponding local fields (17) are, on average, larger for the incident field polarized in the

419

SHALAEV

Fig. 17. EnhancementfactorforRamanscattering, GRS, II = [GRS,x +GRS, y]/2 and GRs, A_= GRS,z, on silver self-affine films for small and large Stokes shifts. (Source: Reprinted with permission from E. Y. Poliakov, V. M. Shalaev, V. A. Markel, and R. Botet, Opt. Lett. 21, 1628 [1996]. 9 1996 American Institute of Physics.)

Fig. 18. Spatial distributions for the local fields at the fundamental frequency, ~ = 550 nm, (bottom; the field distribution is magnified by 3) and for the Stokes fields, ~.s = 600 nm, (top). [The applied field is linearly polarized in the plane of the film.] (b) and (c) The contour plots for the field distributions shown on (a). (Source: Reprinted with permission from E. Y. Poliakov, V. M. Shalaev, V. A. Markel, and R. Botet, Opt. Lett. 21, 1628 [1996]. 9 1996 American Institute of Physics.)

p l a n e of the film than in the n o r m a l direction; this is b e c a u s e a thin film can be r o u g h l y t h o u g h t as an oblate spheroid with a high aspect ratio. T h e largest average e n h a n c e m e n t for S H G is ~ 107. In F i g u r e 20, we show the e n h a n c e m e n t factor for T H G , GTHG, calculated using f o r m u l a (5) with n -- 3. T h e values of GTH6 are even larger than for GSH6, reaching ~ 1011 values.

420

SURFACE-ENHANCED OPTICAL PHENOMENA

i

l0 T

,

,

i

,

,

j

GSHG

7

10~

103

~j~

?, I', "i

/"

I

I

.~:Y

,IVl

II r

il'l fl I

I^

p~t~ LJ r

'I

l

A (nm) I

400

r,.

[

i I~1 I I II

" V'

I''\''

I01

,"I i!

/~

600

I

800

I

,

I

1000 1200 1400

I

1600

1800

Fig. 19. Average enhancement factors for second harmonic generation (SHG) from a self-affine silver surface, for the light polarized in the (x, y)-plane of the film (GsH G = all) and in the normal z-direction (GSHG = G_L). (Source: Reprinted with permission from E. Y. Poliakov, V. A. Markel, V. M. Shalaev, and R. Botet, Phys. Rev. B 57, 14901 [1998]. 9 1998 American Physical Society.) w

i

i

i

i

#[

GTItG

10 lo

108

10 6

10 4

t"

!,,,

10 2

1 [~ 600

I ,, I 800 1000

,,, I

1200

i

1400

~1 (nm)

1600

1800

Fig. 20. Average enhancement factors for the third harmonic generation (THG) from a self-affine silver surface, for the light polarized in the (x, y)-plane of the film (GTHG ~ GII), and in the normal z-direction (GTHG ~ G_L). (Source: Reprinted with permission from E. Y. Poliakov, V. A. Markel, V. M. Shalaev, and R. Botet, Phys. Rev. B 57, 14901 [1998]. 9 1998 American Physical Society.)

The T H G involves a higher power of electric fields, so that the d o m i n a n c e of local fields Ei over E0 leads to larger values of e n h a n c e m e n t factors. In Figure 21a and b, we plot spatial distributions for local-field e n h a n c e m e n t s at the fundamental frequency, g = I ( E i ) / E o ] 2 and for the local e n h a n c e m e n t s of S H G and THG, g S H G - g S H G ( r i ) = IdNL(2co)lZ/Id~VL(2w)l 2 and g T H G - g T H G ( r i ) -

IdNL(3~o)I2/IdNL(3~o)I

(where d NL and d NL are the nonlinear dipoles in v a c u u m and on the film surface, respectively). The interactions of the nonlinear dipoles at the generated frequency is taken into account for both S H G and T H G effects. The distributions of local e n h a n c e m e n t s are calculated for two wavelengths, 1 and 1 0 / z m , for the light polarized

421

SHALAEV

Fig. 21. Spatial distributions of the local enhancements for the field at the fundamental wavelength, g, for SHG signal, gSHG, and for THG signal. The corresponding counterplots for the spatial distributions are also shown, in all cases. (a) The fundamental wavelength is ~. = 1/xm. The linear scales are used in all cases. The highest enhancement values in the figures are as follows: g -- 5 x 103, gSHG = 5 x 10 8, and gTHG = 2 x 1 0 1 2 . (b) Same as in (a) but for ~. = 10/xm. The highest enhancement values are as follows: g --- 3 x 104, gSHG = 1013, and gTHG = 2 x 1019. (Source: Reprinted with permission from E. Y. Poliakov, V. A. Markel, V. M. Shalaev, and R. Botet, Phys. Rev. B 57, 14901 [1998]. @ 1998 American Physical Society.)

in the plane of the film. As was discussed earlier, the largest average enhancements are achieved in the infrared region, for the incident light polarized in the plane of the film. The local enhancements are also very large in this case. In the counterplots of Figure 21 a and b, the white spots correspond to higher intensities whereas the dark areas represent the low-intensity zones. We can see that spatial positions of the hot and cold spots in the local enhancements at the fundamental and generated frequencies are localized in small spatially separated parts of the film. Because the fundamental and generated frequencies are different, the fundamental and generated waves excite different optical modes of the film surface and, therefore, produce different localfield distributions. With the frequency alternation, the locations of the hot and cold change for all the fields, at the fundamental and generated frequencies. Thus different waves involved in the nonlinear interactions in a self-affine thin film produce nanometer-sized hot spots spatially separated for different waves. A similar effect was shown in the preceding text for R a m a n scattering from self-affine film [6]. The values of the local field intensities in Figure 2 l a and b, grow with the wavelength. The highest local enhancement factor in the spatial distribution g changes from 5 x 103 at )~ = 1 # m to 3 x 104 at )~ = 10 # m . For the S H G and the T H G spatial distributions, the m a x i m u m increases from 5 x 10 8 to 1013 and from 2 x 1012 to 2 x 1019, respectively. Such behavior correlates with the fact that the average enhancement factor also increases

422

SURFACE-ENHANCED OPTICAL PHENOMENA

Fig. 21. (Continued.) toward the infrared spectral region. We emphasize that the local enhancements can exceed the average one by several orders of magnitude. For example, comparison of the maximum local enhancement with the average enhancement for )~ = 1/zm shows that the maximum intensity peaks exceed the average intensity by approximately 2 orders of magnitude for SHG (cf. Figs. 19 and 21) and by 4 orders of magnitude, for THG (cf. Figs. 20 and 21). This occurs, in part, due to the fact that the spatial separation between the hot spots can be significantly larger than their characteristic sizes, and, in part, due to destructive interference between the generated fields in different peaks. The giant local enhancements of nonlinear processes (e.g., up to 1019 for THG at 10/zm) open a fascinating possibility of the fractal-surface-enhanced nonlinear optics and spectroscopy of single molecules. Also, if the near-field scanning optical microscopy is employed, nonlinear nano-optics and nanospectroscopy (with nanometer spatial resolution) become possible. In contrast, with the conventional far-zone optics only the average enhancement of optical processes can typically be measured. The huge average enhancement for DFWM on a self-affine film is illustrated in Figure 22 (see (2)). The larger values of enhancement for DFWM, compared to THG, are explained by the fact that the interaction of nonlinear dipoles is stronger when the generated frequency is equal to the fundamental one. Also, the role of destructive interference for the field generated in different points is much larger for high-order harmonic generation than for DFWM. In Figure 23a and b, we show the calculated real and imaginary parts of the Kerr enhancement factor. We calculated the enhancements using formula (1). The calculations show that [G~cl > IG~ [, and both are especially large in the nearinfrared. Note however that the signs of both real and imaginary parts of GK strongly vary with ~; this means that the sign of nonlinear correction to refraction and absorption strongly

423

SHALAEV

1016 I

i

,

,

I01210 s GDFW~" I

.

~ll

~

.

! In

9 ,~,,, I'N~! ~llJt I ~"1, .I It

I

t I

~ I i,i!

_

"

?,f

ff I,,

i

IJ

t(

I ~ ~h.

./ % ;

v

Gll

lO4

G•

1 A (nm) 10-4

200

I

I

I

400

600

800

I

I

I

I

1000 1200 1400 1600 1800

Fig. 22. Average DFWM enhancement factors from a self-affine silver surface, for the light polarized in the (x, y)-plane of the film (GDFWM = GII) and in the normal z-direction (GDFWM --= G_L). (Source: Reprinted with permission from E. Y. Poliakov, V. A. Markel, V. M. Shalaev, and R. Botet, Phys. Rev. B 57, 14901 [1998]. 9 1998 American Physical Society.)

107

I

I

I'

I

I

!

I

I

"'_J

lOs

103

101

10-x A (nm) 200

I

I

I

I

400

600

800

I

I

I

1000 1200 1400 1600 1800 (a) !

Fig. 23. Absolute values of (a) the real, IGK[, and (b) imaginary, IG%[, parts of the average enhancement factors for the Kerr-nonlinearity for the light polarized in the (x, y)-plane of the film. (Source: Reprinted with permission from E. Y. Poliakov, V. A. Markel, V. M. Shalaev, and R. Botet, Phys. Rev. B 57, 14901 [1998]. (g) 1998 American Physical Society.)

d e p e n d s on the w a v e l e n g t h that can be a very useful p r o p e r t y in d e s i g n i n g p h o t o n i c devices, such as optical switches.

5. R A N D O M

METAL-DIELECTRIC

FILMS

F o r applications, it is i m p o r t a n t to have fractal films that retain their fractal m o r p h o l o g y at r o o m t e m p e r a t u r e s , such as t w o - d i m e n s i o n a l r a n d o m metal-dielectric films (referred to

424

SURFACE-ENHANCED OPTICAL PHENOMENA

10 7

I

I

I

I

I I

I

I

!,,

I

400

600

800

Im(Gg)l

105

103

101

10-1

200

i

i

A (nm)

i

1000 1200 1400 1600 1800 (b)

Fig. 23. (Continued.)

also as semicontinuous metal films) near the percolation threshold. In contrast to colddeposited self-affine films that are essentially three-dimensional and do change their morphology when annealed, two-dimensional semicontinuous films remain stable at room temperatures. Many of optical properties of particle aggregates are similar to those observed in metalinsulator random films. A semicontinuous metal film can be viewed as a two-dimensional (2d) composite material. Semicontinuous metal films can be produced by thermal evaporation or sputtering of metal onto an insulating substrate. In the growing process, first, small metallic grains are formed on the substrate. As the film grows, the metal filling factor increases and coalescences occur, so that irregularly shaped clusters are formed on the substrate eventually resulting in 2d fractal structures. The sizes of the fractal structures diverge in a vicinity of the percolation threshold. A percolating cluster of metal is eventually formed, when a continuous conducting path appears between the ends of a sample. The metal-insulator transition (the conductivity threshold) is very close to this point, even in the presence of quantum tunneling. At higher surface coverage, the film is mostly metallic, with voids of irregular shape; at further coverage increase, the film becomes uniform. The optical properties of metal-dielectric films show anomalous phenomena that are absent for bulk metal and dielectric components. For example, the anomalous absorption in the near-infrared spectral range leads to anomalous behavior of the transmittance and reflectance. Typically, the transmittance is much higher than that of continuous metal films, whereas the reflectance is much lower (see Refs. [ 13, 59-64] and references therein). Near and well below the conductivity threshold, the anomalous absorptance can be as high as 50% [63, 65-68]. A number of the effective-medium theories were proposed for the calculation of the optical properties of semicontinuous random films, including the Maxwell-Garnett [69] and Bruggeman [70] approaches and their various modifications [ 13, 63, 64]. The renormalization group method is also widely used to calculate the effective dielectric response of 2d percolating films near the percolation threshold (see [71-73] and references therein). A new theory based on the direct solution of the Maxwell equations have been suggested [74]. This new theory allows one to quantitatively describe the anomalous

425

SHALAEV

absorption and other optical properties of semicontinuous films. However, the field fluctuations in semicontinuous metal films and the effects resulting from these fluctuations were not considered neither by the effective-medium theories nor by the theory of Ref. [74]. Nonlinear electrical and optical properties of percolating composites have attracted much attention. At zero frequency, strong nonlinearity may result in breaking down conducting elements when the electric current exceeds some critical value [75]. This fuse model can be also applied for the description of fractures in disordered media and related problem of weak tensility of materials in comparison to the strength of the atomic bonds (see [76] and references therein). The tension concentrates around weak points of materials and a crack spreads out starting from these weak points. Another example of unusual nonlinear behavior was observed for the ac and dc conductivity in the percolating mixture of carbon particles embedded in the wax matrix [77]. In this case, neither carbon particles nor wax matrix have any nonlinearity in their conductivities; nevertheless, the conductivity of a macroscopic composite sample increases twice when applied voltage is increased by a few volts. Such a strong nonlinear response can be attributed to the quantum tunneling between carbon particles; this is a distinguished feature of the electric transport in composites near the percolation threshold [78]. The current and electric field are concentrated in few hot junctions and they make it possible to change their conductances under action of the high local fields, whereas the external field is relatively small. Percolating systems are very sensitive to the external electric field because their transport and optical properties are determined by a rather sparse network of conducting channels and the field concentrates in the weak points of the channels. Therefore composite materials can have much larger nonlinear susceptibilities at zero and finite frequencies than those of ordinary bulk materials. In particular, the cubic nonlinearity, which is of particular interest for a number of applications, was intensively studied (see, for example, [79, 80] and references therein). The local-field fluctuations can be strongly enhanced in the optical and IR spectral ranges for a composite material consisting of a dielectric host and embedded in the host metallic elements that are characterized by the dielectric constant with negative real and small imaginary parts. Then the enhancement is due to the plasmon resonances in the metallic granules [2, 5-7, 32, 38, 79-83]. Nanostructured composite materials are potentially of great practical importance as media with an intensity-dependent dielectric function and, in particular, as nonlinear filters and optical bistable elements [80]. The response of a nonlinear composite can be tuned by controlling the volume fraction and the morphology of constitutes. The enhancements of the optical nonlinearities associated with strong field fluctuations are especially large in composites with fractal morphology where the local fields experience giant fluctuations [2, 5, 6, 10, 56, 84] (see Sections 3 and 4). Nonlinear optical properties of fractal aggregates were studied in [2, 5, 15, 82], where the authors showed that the aggregation of initially isolated particles into fractal clusters results in a huge enhancement of the nonlinear response within the spectral range of cluster modes associated with surface-plasmon resonances (see Section 3). The eigenmodes were found by diagonalizing the interaction operator of the dipoles induced by light on particles forming the cluster. Giant fluctuations of the local fields were studied by Markel et al. [ 10], Shalaev [2], Tsai et al. [3], Shalaev et al. [5, 6, 82] for the fractal aggregates, and Brouers et al. [84] for 2d percolating composites. The areas of large field fluctuations are localized in different parts of the conducting clusters with random local structure [2, 3, 5, 6, 10, 40, 56, 84]. The prediction of large enhancements of optical nonlinearities in fractal clusters was confirmed experimentally for the example of degenerate four-wave mixing (DFWM) and nonlinear refraction and absorption [ 15, 30]. As shown in Section 3, aggregation of initially isolated silver particles into fractal clusters in these experiments led to a 106-fold enhancement of the efficiency of the nonlinear four-wave process and ~ 103 enhanced nonlinear refraction and absorption.

426

SURFACE-ENHANCED OPTICAL PHENOMENA

The localized and strongly fluctuating modes of fractal composites were also imaged by means of near-field optical spectroscopy in [3, 31 ]. Enhanced optical processes in composites of various (nonfractal and nonpercolating) morphology were also studied by Sipe, Boyd, and their co-workers both theoretically and experimentally [38]. If the skin effect in the metal grains is small, a semicontinuous film can be considered as a 2d object. Then in the optical spectral range where the frequency o9 is much larger than the relaxation rate ogr - r -1, a semicontinuous metal film can be modeled as a 2d L - R m C lattice [13, 85, 86]. The capacitance C stands for the gaps between metal grains that are filled by dielectric material (substrate) with the dielectric constant ed; the inductive elements, L-R, represent the metallic grains that for the Drude metal are characterized by the following dielectric function,

(o9p/o9)2 8m (o9) -- 8b --

1 +iogr/o9

(29)

where eb is a contribution to e due to the interband transitions, COp is the plasma frequency, and ogr - 1 / r 3. Because in the visible, infrared, and far-infrared spectral ranges the real l >> ed, and losses are small, part of the dielectric constant of a typical metal is large, leml igmlt >> gm," the values of the field moments ([EI n) exceed the corresponding moments of the incident field, IE (~ [", by several orders of magnitude. This indicates the presence of the giant field fluctuations in semicontinuous metal films in the visible and, especially, in the infrared spectral ranges. For the Drude metal, we can simplify Eq. (47) for sufficiently small frequencies, co 1), the electron and hole motions are strongly correlated via the Coulomb interaction and NC energy spectra are determined by quantization of the motion of the exciton center of mass [ 1]. In the intermediate-confinement regime (a lax "~ 1), energy structures in NCs are determined by a complex interplay between quantum confinement and the Coulomb e-h interaction. Molecular beam epitaxy has been a standard technique for making high quality twodimensional quantum wells and superlattices [6]. Epitaxial techniques also allow the preparation of three-dimensionally-confined islands with lateral dimensions down to 10 nm [7], which, however is not sufficient to reach the interesting regime of strong confinement. The alternative approach to making high-quality three-dimensionally-confined nanostructures is a chemical synthesis based on the control of homogeneous nucleation. There are two main chemical routes for preparation of NCs: high-temperature inorganic precipitation in molten glasses, producing NCs embedded in transparent glass matrices [8, 9] and moderate-temperature organometallic reactions, resulting in colloidal NCs [3, 5]. Glass samples provide rigidity and environmental stability, but they have a broad NC-size distribution (typically greater than 15%) and a large number of surface defects. A much higher level of control is provided by colloidal NCs, which can be chemically manipulated in a variety of ways, including size-selective techniques (resulting in less than 5% size variations [5]), surface modification by exchanging the organic passivation layer [10], heterostructuring with formation of layered NCs [ 11-13], immobilization in sol-gel [ 14-16] and polymer [ 17-19] matrices, and self-assembly into three-dimensional superlattices [20]. Systematic research into NC materials began with the first observations of effects of quantum confinement in the optical absorption of semiconductor-doped glasses [21]. Since then, tremendous progress has been made in both the theory of three-dimensionallyconfined systems and experimental studies. Theoretical descriptions of electronic structures in NCs have advanced from simple particle-in-the-box models [1] to much more sophisticated approaches, including finite-well effects [22-24], Coulomb interactions [22, 25-27], nonparabolicity of the conduction band [28, 29], and confinement-induced mixing of valence subbands [27, 29, 30]. A great deal of experimental work has been performed to detect and to carefully map the structure of electron and hole quantized states in different confinement regimes [29, 31-33], to study confined phonon modes [34-37] and the processes of electron-phonon [34, 35, 38-41] and many-particle Auger-type interactions [42-44], to investigate biexciton effects [45-47] and the effects of three-dimensional confinement and surface properties on cartier energy relaxation and recombination dynamics [31, 48-50]. New insight into the physics of three-dimensionally-confined structures has been provided by experiments on single NC spectroscopy [51-53].

452

LINEAR AND NONLINEAR OPTICAL SPECTROSCOPY

Apart from exciting new physics and chemistry, NCs offer a number of device applications which can benefit from size-controlled spectral tunability, confinement-induced concentration of the oscillator strength, and ultrafast relaxation dynamics, which can be controlled by NC surface properties. Applications of NCs in laser emitters [54], electroluminescent devices [55], switching elements [56], and solar cells [57] have been reported. This review summarizes some progress in NC research with a special emphasis on optical spectroscopy of II-VI NCs such as CdSe and CdS. Because of the highly developed preparation technology, these NCs have been prototype systems for studies of the effects of three-dimensional confinement on the electronic and optical properties of semiconductors. Due to a relatively large exciton Bohr radius (~5 nm in CdSe and ~3 nm in CdS), II-VI NCs are convenient systems for studies of the strong- and intermediate-confinement regimes, the focus of this review. Experimental results are reviewed for two types of sampies: NCs prepared by high-temperature precipitation in glass matrices (referred to as NCglass composites or glass samples) and NCs made by colloidal synthesis (referred to as colloidal NCs). The remainder of the chapter is organized into six sections entitled: 2. Energy states and optical transitions in semiconductor nanocrystals: Theoretical models; 3. Experimental studies of energy structures in semiconductor nanocrystals; 4. Fine structure of the lowest exciton state; 5. Effects of electron-phonon interactions on the optical spectra of semiconductor nanocrystals; 6. Band-edge optical nonlinearities in semiconductor nanocrystals; 7. Carrier dynamics in semiconductor nanocrystals. In Section 2, energy structures in NCs are considered using a well-developed effective mass approach. The section begins with a description of the simple parabolic-band model, and then outlines the effects of valence-band mixing, Coulomb interactions, finite height of the confinement barrier, and nonparabolicity of the conduction band, and their impact on the energy structures and optical transitions in NCs. Section 3 contains some experimental results on the size dependence of the energy gap in NCs and the observations of discrete electron and hole energy states in NC-based structures. Section 4 gives a brief overview of theoretical and experimental studies of the fine structure of the lowest exciton state, associated with the effects of nonspherical NC shape, crystal-field splitting, and exchange interactions. Section 5 outlines the effects of electron-phonon interactions on the optical spectra of NCs. It starts with a description of the model of a "displaced" oscillator, which is then used to analyze the effects of carrier interactions with optical and acoustic phonons. This section also contains results of experimental studies of electron-phonon coupling performed by various optical techniques. Section 6 examines the results of studies of resonant optical nonlinearities in NCs observed at spectral energies near the band edge. It concentrates on several topics, including the role of state-filling and Coulomb many-particle interactions on the nonlinear optical response of NCs, the third-order nonlinear susceptibility of NC-based structures, optical nonlinearities in direct- and indirect-gap semiconductor NCs, and optical gain and lasing in NCs. Section 7 surveys some results on carrier dynamics in NCs, including those on intraband energy relaxation, radiative decay, carrier trapping, and nonradiative Auger recombination and associated ionization of NCs.

2. ENERGY STATES AND OPTICAL TRANSITIONS IN SEMICONDUCTOR NANOCRYSTALS: T H E O R E T I C A L MODELS The effective mass approximation (EMA) has proven to be a powerful tool for describing energy structures in semiconductor NCs [ 1, 2, 22, 30]. Although it fails in the limit of very small NCs, it nevertheless allows a correct prediction of important trends in most of the NC sizes which have been synthesized and which have been studied experimentally. In the following text we briefly review several EMA models developed for strongly confined NCs.

453

KLIMOV

2.1. Parabolic-Band Model The first theoretical descriptions of NCs were based on the model of a spherical quantum well with an infinite potential barrier assuming a parabolic dispersion of electron and hole bands [1, 2]. However, even within this simple model, analytical solutions of the corresponding quantum mechanical problem are not possible if the Coulomb e-h interaction is explicitly taken into account. The Coulomb interaction scales with the NC radius as a - 1 , whereas confinement energies are proportional to a -2. Therefore, in the strong confinement regime (a 10. The magnitude of kl (as well as the electron confinement energy) reduces sharply at 77 < 2-3. In the limit r/--+ (2Jr) -1 , kl approaches its minimum value of zr/(2a). This simple model can be improved by including the Coulomb effects [22, 24] and interactions between conduction and valence bands [42] which allow one to account for the nonparabolicity of the electron energy spectrum.

3. EXPERIMENTAL STUDIES OF ENERGY STRUCTURES IN S E M I C O N D U C T O R NANOCRYSTALS

3.1. Energy Gap in Semiconductor Nanocrystals Synthetic efforts have resulted in the development of procedures for preparation of high quality NCs with narrow size distributions using both high-temperature precipitation [8] and colloidal synthesis [5, 68]. The best results have been achieved using organometallic synthesis followed by a size-selective precipitation which allows isolation of samples with size dispersion [] 9

2.2 ~0

~"

2.0

Z

1.8

NCs/glass NCs/colloids

1.6 ,I 2

I

I

!

!

!

I

3

4

5

6

7

8

Radius (nm) Fig. 9. The position of the lowest optical transition (NC energy gap) in CdSe NCs (room temperature) plotted versus NC mean radius. The data are derived from absorption spectra of colloidal (solid circles; Fig. 8) and glass (open squares; Fig. 7) samples, and compared with the bandgap energies (solid line) calculated within parabolic-band approximation, corrected for the Coulomb e-h interaction.

3.2. O b s e r v a t i o n s of E l e c t r o n Q u a n t i z e d States

As was mentioned, inhomogeneous broadening resulting from the size distribution masks discrete energy structures related to size quantization. Inhomogeneous broadening can be significantly suppressed using spectroscopic size-selective techniques such as fluorescence line narrowing (FLN) [31, 33, 69, 70], photoluminescence excitation (PLE) [31, 33], and spectral "hole burning" [31, 32, 71-73]. In these techniques, a narrow spectral window is used for resonance excitation (FLN and hole burning) or detection (PLE) of a small portion of NC sizes from the broad size distribution as is discussed in more detail in Sections 4.2 and 4.3 in the context of studies of electron-phonon interactions. Size-selective techniques are most efficient using excitation (detection) wavelengths on the red edge of the absorption spectrum (the lowest optical transition) which corresponds to the selective excitation of the largest NCs from the size distribution [33, 69]. However, excitation into higher lying states also provides some size-selective effect [74] which was used in Refs. [32, 54, 75] to resolve excited electron states in nonlinear differential transmission (DT). DT gives a measure of pump-induced transmission changes and is defined as follows: D = ( T - To)/To = A T / T o , where To and T are transmissions of the unexcited and excited samples, respectively. In the small-signal limit (D v

1.0

"13

(i)

(g) (f)

.

j+~j

,

..#+~.+

.4.

s

+.+.4.e"r

0.8

~

++~ +,#"

4.,, ~

,,

",,"

+.4"

,-- 0.6

4:+

4

o

(e)

+

o

+..',

o x W r

+'.t4-

o)

..i.+

L_

c LM

f

(h)

i., 4. §A-

f

0.4 "

I

"''''''"

0.2

(b)

(c)

...... ,r.r247

"~.~."

,~Q

tI.IJ

(a)

0.0

-

I

I

,

,

,

I

,

,

,

I

,

,

,

I

,

,

,

-

-

A

I

2.0 2.2 2.4 2.6 2.8 Energy of 1st Excited State (eV) Fig. 13. Transitionenergies derived from PLE data of CdSe colloidal NCs of various sizes plotted versus the energy of the lowest 1S transition which gives a measure of the radius of NCs probed in PLE measurements. Strong (weak) transitions are denoted by circles (crosses). The lines are visual guides for transitions to clarify their size evolution. Based on comparison with calculated transition energies, the PLE features (a)-(g) were assigned as follows: (a) 1S(e)-lS3/2(h), (b) 1S(e)-2S3/z(h), (c) 1S(e)-lS1/2(h ), (d) 1P(e)-lP3/2(h), (e) 1S(e)-2S1/2(h), (f) 1P(e)-lP5/z(h ) and/or 1P(e)-lP1/z(lh), (g) 1S(e)-3S1/z(h). The features (h)-(j) were in the region with a high density of allowed optical transitions which complicated their accurate assignment. (Source: Reprinted with permission from [33]. 9 1996 American Physical Society.)

Several hole states of P symmetry were also resolved in the spectra. A minimum in the second-derivative spectra at around 2.3 eV seen in a sample with a -- 3.8 nm were assigned to the transition involving the 11'3/2 state (transition 5) with a possible contribution from the transition involving the 1 P1/2 light-hole state (transition 6). These two P-type hole states were resolved as separate minima in the spectra of samples with a = 2.6 and 2.3 nm. The P state originating from the spin-orbit split-off subband (1 pso) was possibly seen as transition 9 in the spectrum of the sample with a = 3.8 nm. Detailed studies of the size dependence of hole spectra were performed in Ref. [33] using a series of high-quality colloidal samples with mean radii from ~ 1.2 to ~ 5 . 3 nm and size dispersion < 5 % rms. To further reduce the effects of inhomogeneous broadening, the size-selective PLE technique was used to detect discrete absorption features, allowing resolution of up to eight bands in a single PLE spectrum. The results of size-dependent measurements of positions of these bands are plotted in Figure 13 as AEi versus Els, where A Ei is the high-energy shift of the band number i with respect to the lowest 1S transition, and E ls is the energy of the 1S transition. This choice of x axis allows one to minimize errors caused by uncertainty in the sizes of NCs actually probed in the PLE spectra. A comparison of the experimental data with calculations which take into account band-mixing effects [29, 30] allowed a confident assignment of the six lowest transitions

469

KLIMOV

involving five S-type (1S3/2, 2S3/2, 1S1/2, 2S1/2, and 3S3/2) and one P-type (1P3/2) hole states. Four more higher lying transitions were resolved in the spectra, but they were only tentatively assigned because of the high spectral density of allowed transitions at large confinement energies. The important result of these studies was the observation of the avoided-crossing behavior for states 2S3/2 and 3S3/2 [transitions (e) and (g) in Fig. 13] at ElS ~ 2 eV, and for states 1S1/2 and 2S1/2 [transitions (c) and (e) in Fig. 13] at ~2.2 eV. This clearly indicates the important role of band-mixing effects in the valence-band energy spectra of NCs. The effects of the band mixing were also manifested in the size dependence of the oscillator strength of transitions involving S1/2 states. These states represent a mixture of the D- and S-type wave functions from the J = 3/2 and 1/2 subbands, respectively. The 1S1/2 state, for instance, in large NCs is dominated by the D-type wave function which is not coupled to the 1S electron level. For small sizes the dominant contribution to this state comes from the S-type component which is strongly coupled to the lowest electron state. This size-dependent behavior of the wave function should result in increasing oscillator strength for the 1S(e)- 1S1/2 transition with decreasing NC radius, which was observed experimentally.

4. FINE STRUCTURE OF THE LOWEST EXCITON STATE In spherical quantum dots with a cubic lattice the lowest e-h pair state [1S3/2(h)lS(e)] (the lowest exciton) is eightfold degenerate. However, the effects of the crystal field in the hexagonal lattice [77], nonspherical NC shape [78], and the electron-hole exchange interaction [79-81 ] lift this degeneracy, leading to fine structure of the lowest exciton. In the case of the exchange interaction, a good quantum number is the total momentum of the e-h pair N - Fe + Fh. When the anisotropy of the lattice and the nonspherical shape are included in the model, the only conserved quantity is a projection of the total exciton momentum Nm along a unique crystal axis. The crystal field of the wurtzite lattice leads to a splitting of states with Mh -- +1/2 and 4-3/2 (Mh is a projection fo the hole momentum Fh) (see Fig. 14a) which is analogous to the A - B splitting in bulk semiconductors (see Fig. 2). In the strong confinement regime, this splitting (3A8) is independent of the NC radius and is only determined by the ratio (13) between the light- and heavy-hole masses along the c axis (13 = mlh/mhh) [77]: r "-- tO(fl)AAB, where A A B is the crystal-field-induced splitting in bulk materials. For /3 = 0, w(0) ~ 0.2, meaning that the A - B splitting in this case is 5 x smaller than in bulk semiconductors. When the crystal-field-induced splitting is taken into account, the hole ground state is characterized by the momentum projection Mh = 4-3/2. Holes in this state and 1S electrons can form e-h pair states (excitons) with total momentum projection Nm = 4-2 or 4-1. The exciton with INm[ - 1 is coupled to the ground state by an allowed dipole transition, whereas the INml = 2 exciton is not optically active, because a single-photon emission (absorption) cannot account for the two-unit change of the angular momentum. The INml = 2 excitons cannot be directly excited by light, but they can be created as a result of carrier relaxation after excitation into higher lying exciton states (associated, e.g., with the Mh = + 1 / 2 holes); this can significantly alter cartier recombination dynamics [77]. The A - B splitting is further affected by effects of the nonspherical shape [78]. The deviation from the spherical shape can be characterized by the parameter X = al/a2 - 1, where al and a2 are the major and minor axes of a NC, respectively. X is positive in prolate NCs and is negative in oblate ones. Due to the nonspherical NC shape, the hole states with IMhl = 3/2 and 1/2 shift in opposite directions. For the lowest 1S3/2 hole states, these shifts are [78], AE•

"- -- AE•

-- - g v(fl) E (1 $3/2)

470

(28)

LINEAR AND NONLINEAR OPTICAL SPECTROSCOPY

"A-B splitting"

(a)

Exchange splitting INml = 0v

INmi = 0, l(IMhl = 1/2) INml = lU

F e = 1/2, F h = 3/2

[Nm[ = 0 L AB

INto[ = 1L INm] = 2, 1 (IMhl =

INml = 2 "Dark exciton"

Strong exchange interaction

(b)

N=I

F e = 1/2, F h = 3/

~ST

N=2 "Dark exciton" Fig. 14. (a) The splitting of the lowest exciton (Fe = 1/2, Fh = 3/2) due to the crystal field and/or the NC nonspherical shape (the A-B splitting). The A and B excitons are further split by the e-h exchange interaction into five sublevels (the limit of weak exchange interaction). (b) The splitting of the N = 1 and N = 2 excitons in the limit of strong exchange interaction which overwhelms the A-B splitting.

where E(1S3/2) is the ground-state hole energy given by Eq. (14) and v(/3) is a parameter determined by the ratio of the light- to heavy-hole masses. With increasing 13, v(/3) decreases from 4/15 at 13 - 0 to ~ ( - 0 . 2 6 ) at/3 - 0 . 3 with a crossover to positive v at /~ ~ 0.14; v(/~) increases in the range 13 > 0.3 until it reaches zero at/~ = 1 [78]. Due to the fact that energy corrections induced by the nonspherical shape are proportional to the hole energy, they show a size dependence, increasing as a -2 with decreasing NC radius. The sign of the energy shifts, which determines the alignment of the states with IMhl - 3/2 and 1/2, depends on the sign of X and the magnitude of/3. For example, in the case of CdSe (/3 ~ 0.3 [29]), the parameter v is negative (v ~ - 0 . 2 6 ) . Therefore, in prolate NCs (X > 0) (which is typical for CdSe colloids [82]), the effects of the nonspherical shape tend to reduce the A - B splitting resulting from the crystal field, which can ultimately lead to switching the ground hole state from one with IMhl = 3/2 to that with IMhl = 1/2. The A and B exciton levels are further split by the e-h exchange interaction into five sublevels (Fig. 14a). These sublevels are labeled by the modulus of the projection of the total angular momentum INml with a superscript which denotes the upper (U) or the lower (L) states with the same INm I. The states with IN m l = 2, 1L, and 0 U'L, 1 u originate from the A and B excitons, respectively. The exchange splitting is proportional to the overlap of the electron and hole wave functions and, therefore, is strongly enhanced by spatial confinement, following an a -3 dependence [80]. Because the crystal-field-induced contribution to the A - B splitting is size independent and the contribution due to nonspherical shape has the a -2 dependence, the exchange interaction overwhelms the A - B splitting effects in small NCs. In the limit of strong exchange interaction (Fig. 14b), the lowest exciton is split into two states with N - 1 (threefold degenerate) and N - 2 (fivefold degenerate). The state with N = 1 is strongly coupled to the ground state by dipole transitions, whereas the lowest state with N - 2 is optically forbidden. This can lead to the existence of so

471

KLIMOV

called "dark excitons" which are passive in optical absorption but can be detected in photoluminescence (PL) by their weak emission [80]. The splitting between the N = 2 and N -- 1 states can be expressed in terms of the singlet-triplet splitting in bulk semiconductors (AST),

~ST 4(

Asr

-

(29)

where ~" is a constant on the order of unity. In bulk CdSe, for example, the exchange interaction leads to only a 0.13-meV difference in the energies of singlet and triplet excitons. However, due to quantum confinement, this splitting increases up to ~20 meV in NCs of ,~ 1.4 nm radius [80]. The fine structure of the lowest exciton state was studied experimentally in both colloidal [80, 82] and glass [70, 83, 84] NC samples. These studies were performed using high-resolution PLE and FLN techniques. Low-temperature PLE spectra of CdSe colloidal NCs show fine structure in the band-edge absorption in which up to three features can be resolved [82]. The lowest of these features (c~) was assigned to the ]Nml-- 1L exciton, whereas the other two were attributed to states with INml-- 1U and 0 U (see Fig. 14a). In small NCs (a ~< 3 nm) two latter features merged into a single band (/3). The ot - / 3 splitting increased with decreasing NC radius (up to "-~50 meV for a = 1.5 nm), which was explained in terms of the confinement-enhanced exchange interaction [79-82]. The FLN studies of CdSe NCs indicate that the emitting state is different from the absorbing one [70, 80, 82-84] [see Fig. 15a], consistent with the predicted exchangeinteraction induced splitting of the lowest exciton (A exciton) into the optically active state with INml-- 1 L (absorbing state) and the optically passive "dark exciton" with INml -- 2 (emitting state). In agreement with theory [79, 80], experimental data indicate that the energy spacing between these states (the Stokes shift) increases with decreasing NC radius (see Fig. 15a and b) [70, 80, 82-84]. In CdSe colloids, the Stokes shift is only 1-2 meV

20

~" ~= E.,

x

A

•>----•' 15 E . =,,.,=

t-

oo

lO

t-"

c: 10K

O (D

k X

|,,I

x

5

....

~~Energy 10

20

I ....

I ....

-60-40-20

I ....

0

I

20

(mxeV)

30 40 Radius (A)

50

Fig. 15. (a) Normalized FLN spectra of CdSe colloidal NCs with radii from 12-42/~. A small amount of the pump laser light is included for reference in each spectrum and set to zero energy for comparison. (b) Size dependence of the Stokes shift (crosses) between the pump-photon energy and the position of the zero-phonon line in the FLN spectra. The solid line is the calculated size dependence of the splitting between the ]Nml = 2 and 1L states. (Source: Reprinted with permission from [80]. 9 1995 American Physical Society.)

472

LINEAR AND NONLINEAR OPTICAL SPECTROSCOPY

in large NCs (a ~ 4-5 nm), however, due to the confinement-induced enhancement in the exchange interaction, it increases up to about 20 meV in NCs of small radius (a ,~ 1.4 nm) [80, 82]. The fact that two different states are involved in the absorption and emission processes is confirmed by PL polarization studies [70, 83, 84] which indicate that the polarization of the resonantly excited PL is different from that of the absorbed light. The effect of the magnetic field on the PL dynamics support the assignment of the emitting state to the INm l = 2 dark exciton [80]. Without a magnetic field, the PL exhibits a long/zs decay, characteristic of the optically passive "dark" exciton. The decay rate increases with increasing magnetic field which can be explained in terms of the magneticfield induced mixing of the dark INml = 2 state with the optically active INml = 1L state.

5. E F F E C T S OF ELECTRON-PHONON INTERACTIONS ON THE OPTICAL SPECTRA OF SEMICONDUCTOR NANOCRYSTALS

Electron-phonon interactions in semiconductor NCs are significantly modified with respect to those in bulk materials. Spatial confinement leads to quantization of the phonon modes. In spherical NCs, these modes are classified by their orbital momentum I and are ( 2 / + 1)fold degenerate with respect to momentum projection m [85, 86]. However, in contrast to the discrete electronic energy structures clearly manifested in optical spectra, the discrete structure of vibrational modes is difficult to resolve due to the close mode spacing resulting from the large ion masses. The electron-phonon interactions in NCs are strongly effected by the discrete structure of electronic energies, significantly reducing the efficiency of firstorder processes involving a change in the electron (hole) state. These processes can only efficiently occur between states separated by integer numbers of phonons and are strongly hindered due to the scarcity of the electronic states [87]. 5.1. The Model of a Displaced Oscillator

In strongly confined NCs with large energy-level separations, the mixing between electronic (exciton) states resulting from electron-phonon coupling can be ignored. Therefore, electron (exciton)-phonon interactions in these systems can be treated within the independent boson model [88], which has been traditionally used to describe a localized state coupled to lattice vibrations (the model of a displaced harmonic oscillator) [89, 90]. In the simple case of coupling to single-frequency phonons (Einstein model), the electron-phonon interaction can be characterized by a coupling parameter S (Huang-Rhys parameter). S is related to the dimensionless mode displacements A~ (k denotes the phonon mode) (see Fig. 16a) and further to the diagonal matrix element of the exciton-phonon interaction Mk.. JJ (j denotes the exciton state interacting with phonons) by the expression, s-

:

k

(30

k

where hw0 is the phonon-mode energy. In this model, the electron-phonon coupling gives rise to a series of equally spaced phonon sidebands in both emission and absorption spectra. These sidebands are associated with multiple phonon emission (absorption) processes accompanying the optical transition. The optical absorption spectrum taking into account the phonon progression can be presented as follows, cx)

ot(hw) ~ ~__~pn~(hw- EO - nhwo) mOO

473

(31)

KLIMOV

(a)

o

Lattice-displacement Coordinate

(b)

2Sh0~0 - "

h%

s s

s

L', /

l'(

....... .,,tl ]

N Photon Energy

Fig. 16. (a) Configuration diagram representing the dependence of electronic energies of the ground and the first excited states on the lattice-displacement coordinate. A is the lattice relaxation accompanying the electronic excitation. Arrowsshowvertical transitions which determinethe positions of the emission and absorption maxima. (b) Phonon progressions in absorption and emission; envelop functions for these two processes are shownby solid and dashed lines, respectively.

where E0 is the energy of the zero-phonon transition (Fig. 16a). The corresponding emission spectrum is a mirror image of the absorption spectrum with respect to the energy E0. At low temperatures when kT 1), the zero-phonon line is suppressed due to an exponential factor e -S(2N+I)

474

LINEAR AND NONLINEAR OPTICAL SPECTROSCOPY

and the maximum of the absorption (emission) spectrum shifts upward (downward) in energy to the phonon replica with n - S, which corresponds to vertical transitions in the configuration diagram in Figure 16a. This results in a large Stokes shift (As -- 2ShCO0) between absorption and emission maxima (Fig. 16b). In the low-temperature limit (T ~ 0), the function in the fight-hand side of Eq. (32) reduces to the Poisson distribution, e-S Sn Pn -

n!

(33)

which further reduces to a Gaussian distribution centered at n - S in the limit S >> 1. The approach described in the previous text can be applied to both optical and acoustic modes. However, exciton interaction with these two types of lattice vibrations affects the optical spectra in different ways. Because the optical modes have relatively large frequencies and a narrow energy dispersion, the corresponding phonon side bands are spectrally well separated, leading to the appearance of the phonon progressions in absorption and emission spectra [31, 82, 91]. In contrast, acoustic modes have small energies and are characterized by almost continuous energy spectra. Therefore, the side bands associated with acoustic phonons tend to merge into a continuous band contributing to the homogeneous linewidth of optical transitions. Next we will examine in more detail the effects of carrier coupling to optical and acoustic phonons on optical spectra.

5.2. Electron-Optical Phonon Interactions In NCs, electronic excitations are coupled to two different types of optical modes associated with longitudinal optical (LO) and surface optical (SO) vibrations [85, 86]. As shown by resonance Raman studies [34, 35], the LO-phonon frequencies in NCs are essentially identical to those in bulk materials. The frequencies of the SO modes corresponding to the orbital momentum l (COl)can be determined from the equation, l+ 1

T6m

CO2_ o)2 ~

-- ~cx~CO2 CO20

(34)

where COLO and COTO are longitudinal and transverse phonon modes, respectively, related by the expression (COLO~COt0) 2 -- ~0/E~, G0 and e~ are the high- and low-frequency dielectric constants of a NC, and ~:m is the dielectric-response function of the surrounding matrix which is usually assumed to be frequency independent. The frequencies of the SO modes are slightly smaller than those of the LO phonons. In the case of CdSe (COLO - - 2 1 0 cm-1), for instance, they are in the range 194-200 cm -1 [39]. In bulk semiconductors, the electron-optical phonon coupling is dominated by the polar Fr6hlich interaction [92]. However, due to spatial confinement, this interaction is significantly suppressed in NCs. This suppression can be understood from the following simple arguments [60]. The polar coupling of the e-h pair (exciton) to optical modes is determined by the product of the exciton local charge density Peh and the electric potential (/)opt associated with optical (LO and SO) vibrations,

MJP~

fNCvolume~bopt(r)peJh(r)dr

(35)

where peJh(r) -- e([~e(r)[ 2 --I~h(r)[2), and ~e and ~h are the electron and hole wave functions corresponding to the [j) exciton (e-h pair) state. In the parabolic-band model applied to the spherical quantum well with an infinite barrier, the electron and hole groundstate wave functions have exactly the same shape, resulting in a zero local charge density in a NC. This immediately leads to the conclusion that the polar coupling dominating the electron-phonon interaction in bulk materials is completely suppressed in strongly confined NCs. However, the real situation is more complex, because any deviations in electron and/or hole wave functions which may result from such effects as penetration of the wave

475

KLIMOV

function into the potential barrier, mixing of valence subbands or the Coulomb e-h interaction lead to a nonzero local charge density with the associated restoration of the polar coupling. The interaction of the ground-state exciton with optical vibrations in NCs is dominated by LO phonons with a minor contribution from coupling to the SO vibrations via the I = 2 component of the hole wave function [93] (in the case of purely I = 0 wave functions the exciton does not interact with the SO phonons [39, 94]). The results obtained for the absolute magnitudes of the exciton-LO-phonon coupling strength and its size dependence are strongly affected by the assumptions made regarding the electron and hole charge distributions. In calculations, electrons have been usually described by a simple parabolic-band model, whereas different assumptions have been made regarding the hole wave function. In the case of extremely high hole localization (3-functionlike charge distribution), calculations predict a size independence for the coupling parameter S [39]. The use of more realistic hole wave functions which account for the band-mixing effects leads to the dependence S cx 1/a [93]. If the Coulomb e-h interaction is also taken into account, the coupling parameter shows a nonmonotonic size dependence with a minimum at "~7 nm in CdSe NCs [94]. This nonmonotonic behavior occurs because the parameter S increases due to increasing coupling to short-wavelength phonons [60] for smaller sizes, whereas in the range a > 7 nm, the coupling strength increases, approaching its bulk-exciton value due to increasing difference in the electron and hole wave functions caused by a large difference in the electron and hole masses. Calculations using extended wave functions for both an electron and a hole result in small magnitudes for the coupling parameter S, typically below 0.01 [93, 94]. However, experimental studies indicate a much stronger coupling strength with S on the order of 0.1-1. The enhancement of the carrier-phonon polar interaction can be explained by carrier localization (due to, e.g., surface trapping or hole localization in the donorlike-exciton model [95, 96]) which leads to charge separation with an associated increase in the local charge density. The coupling strength for transitions involving localized states is much higher than for those involving extended states, being ~ 1 for the case of CdSe NCs [94, 96]. Experimental studies of the carrier LO-phonon coupling have been performed by PL [31, 82, 91, 97], absorption [31, 82], Raman [34, 35, 39, 41 ], and time-resolved degenerate four-wave mixing (FWM) [38, 98] spectroscopies. If the pump-photon energy significantly exceeds the energy of the lowest optical transition, NCs exhibit a broad structureless PL band, red shifted with respect to the absorption maximum, Figure 17a. This shift is typically several tens of meV in colloidal samples, and can be greater than 100 meV in glass samples. In early studies, particularly in those performed on NC-glass samples, the large PL band broadening and its low-energy shift were explained in terms of the strong coupling to LO phonons, with the coupling parameter estimated to be S > 1 [99-101]. However, the studies using spectroscopic size-selective techniques such as FLN and PLE [31, 69, 82], as well as time-resolved PL measurements [49, 91 ], indicate that the actual Stokes shift is relatively small. In CdSe NCs, it is in the range of 1-20 meV depending on the NC radius [80, 82] (see previous section). The large displacement of the PL maximum with respect to the absorption peak, seen without using size-selective techniques (in measurements of global PL and global absorption), can result from the effects of inhomogeneous broadening [69] and/or carrier trapping [91,102], with the latter mechanism being particularly important in glass samples. In colloidal NCs, the global PL and the global absorption profiles as well as their energy shift can be modeled by summing contributions from "single-dot" LOprogression spectra of NCs of different radii, weighted using a size-distribution function [31, 82] (see illustration in Fig. 18). In FLN experiments, a narrow-band laser with photon energy in the red part of the absorption peak is used to selectively excite only the largest NCs from the size distribution. This type of excitation results in a significant suppression of the inhomogeneous broadening and allows the observation of structured PL spectra in colloidal NCs which clearly

476

LINEAR A N D N O N L I N E A R OPTICAL S P E C T R O S C O P Y

Wavelength (nm) 580 560 540 ,>

520

500

480

,

,

,

,

460 1.5 O

t.t} e-

/i

t-

.o

1.0 5" 0.5 CO =

t,O

E IJ.I

0.0

b)

~

a

,

10K

r

c--

LE

_= t-

.o r

E I.IJ ,

~

,

,

t

,

,

2.2

I

,

,

~

,

2.3

I

I

I

I

I

2.4

I

I

i

I

,

2.5

I

J

,

2.6

,

,

I

,

-

2.7

Energy (eV) Fig. 17. Absorption (solid line) and PL (dotted line) spectra (a) of CdSe colloidal NCs (a = 1.9 nm; T = 10 K) in comparison to FLN and PLE spectra (b) of the same sample. The downward (upward) arrows denote the excitation (emission) positions for FLN (PLE). (Source: Reprinted with permission from [80]. (g) 1995 American Physical Society.)

PL --___d ~ o

AS

Absorption

7"

O d~

a 1> a2 > a3


10 ps), the DT band starts to shift downward in energy until

510

LINEAR AND NONLINEAR OPTICAL SPECTROSCOPY

~=11 ps

r~

10 8-

~.

('

~

o

5-

9 M

9

PL(2.6eV) TA (2.6 eV)

]

x=l

"

ps

--i

(a! 2

IaiiIiI,,l,,Ii

I

I J , I I , , I I l I I , I I i I I i l , , I i I i I , J l n l l

-1

0

1

2

3

4

Delay Time (ps) I III

III

III

I I I I I I'II

III

' I I'II

III

I I I 'I'III

I III

I I I Ill

I I I I

I

100 8

.i.

t--

6

.

"N t-

-

_1

~ 121

9 ~lb

2

10

z - 70 ps

,[.

:

[]

.

I

8

Q ,,,I

....

PL(2.6eV)

1

DT (2.6 eV)

9

9 = 90 ps

(b,)

6 4

9

I-I

I ........

0

I ....

10

I ....

I,,,,I

....

20

I ....

30

I,,,ll

....

40

Delay Time (ps) Fig. 43. Room-temperature single-wavelength [hw = 2.6 eV (the 1S transition)] short- (a) and longterm (b) dynamics of PL (solid circles) and DT (open squares) in CdS NCs (a ~ 4 nm; glass sample). Solid lines show fits to a double-exponential decay. (Source: Reprinted with permission from [ 153].)

it finally reaches (at At > 250 ps) the position of the cw-PL maximum at 2.56 eV (see normalized spectra in Fig. 44b). This can be explained by the increasing relative contribution from the long-lived bleaching of the transition coupling the shallow hole trap to the lowest electron quantized state. At long delay times, after the electron state is completely depopulated, the bleaching of this transition is solely due to the trapped holes. A detailed analysis of the up-converted PL spectra [49] (see Fig. 45) shows the presence of several discrete features (09]-094) which are not resolved in cw emission. The data shown in the preceding text allows one to identify the high-energy band o91 with the 1S transition coupling the lowest electron and hole quantized states. The 092 band can be attributed to the transition involving the 1S electron and the hole-trap state. The low-energy bands o93 and 094 are red shifted from the 1S bleaching by "-~170 and ~270 meV, respectively, indicating that they are due to transitions involving localized carriers. Interestingly, the low-energy portion of PL spectrum in the range of the 093-094 bands has extremely fast buildup dynamics (time constant ~800 fs), essentially identical to those of the 091 feature (see inset to Fig. 45). These data can be understood under the assumption that the 093 and

511

KLIMOV

I

I

0.4 -

I

I

I

DT (0.45 ps) DT (300 ps) cw-PL ."

.t

/

e"S m~n

I

0.1

.....-"

-

...........

...

,......"

/ i~/

2.2

/

t ~.

/

I

/

/

', ",.,

,., ~ ~

. ~ , , t

_ 9

99

,.

-

/

~

!

\

,',/,,., "'.......

I

I

,*

.

. . _ - ~ -

I

....... --,..:;.,.~,~tr..-

-,

, ~ L_

~,. ~.

',

,,,

-,

" # ~ O "' ~

I*

I

I~. I ~.

"/

, tl

.." /,,,

~9

0.0

;

.,."

.s. S

I

I

,/~.o'

.s"

I

-

,.,.;~" - ' . , , , /

O

CW-I"L

I

~.p

0.3

0.2 _

I

70 meV

,,,

9t . ,I

tl

"

I

I

I

I

1

2.3

2.4

2.5

2.6

2.7

t i

, t t, ,

I

i

2.8

2.9

P h o t o n E n e r g y (eV) Fig. 44. Normalized DT spectra of CdS NCs (a -~ 4 nm; glass sample) measured at At = 0.45 ps (solid line) and 300 ps (dashed line) in comparison to the cw-PL spectrum (T = 300 K). (Source: Reprinted with permission from [44]. 9 1997 American Physical Society.)

18 r

i

i

~ .~

1.0

~

0.4

~

0.2

16 laL 14

0)2

- CO1

~ o

12 -

t,~_

~/

~

-

2

2

0

4

Delay Time (ps) ~

10

M

8

,..

m

6

u

R

I

I

I

I

I

2.2

2.4

2.6

2.8

3.0

Photon Energy (eV) Fig. 45. The up-converted PL spectrum measured at 2 ps after excitation demonstrating four features labeled as o91-o94. Inset: Short-term PL dynamics measured at 2.6 (091) and 2.45 eV (093) along with fitting curves calculated for the exponential rise (time constant rb) followed by the exponential decay (time constant rd).

512

LINEAR AND NONLINEAR OPTICAL SPECTROSCOPY

1S(e)

i (,01

(short-lived)

Band-Ed[ Emission

~e > 10ps

I Deep-Trap Emission

Zh -- 1 ps

1S3/2(h) Fig. 46. Schematicof the trapping processes and optical transitions leading to principal emission features in CdS NCs. A short-lived 091 feature is located at the position of the 1S transition. It decays rapidly due to a fast 1-ps hole trapping (localization). The transition coupling the hole localized state and the 1S electron level dominates the cw band-edge emission. Electron gets trapped at a deep-trap state on the tens-of-ps time scale. The transition coupling this deep trap and the hole localized level gives rise to the low-energy deep-trap emission.

O94 PL bands are due to transitions coupling extended IS electron state to localized hole

states which are occupied in the absence of the pump. These hole states can be associated, with uncompensated acceptors [49]. In discussing the nature of the defect states contributing to the band-edge PL, it is natural to consider first surface located native defects such as sulfur or cadmium vacancies or add atoms. As was discussed in the previous text, the deep-trap emission in CdS NCs (band at 1.98 eV in Fig. 38) can be assigned to a surface sulfur vacancy with a level located "-~0.7 eV below the conduction band [ 163]. A Cd vacancy can create two acceptor states in the energy band gap: One (singly ionized) above the valence band and the other (doubly ionized) below the conduction band [ 171, 172]. The other possible acceptor states are complexes associated with the Cd vacancy, such as a complex with a donor at the next lattice site [ 173]. Bulk CdS is an n-type material with a conductivity dominated by foreign donor atoms. However, one may expect a different situation in NCs (at least in a portion of them) with a large number of surface located native defects which can lead to the existence of uncompensated acceptors along with compensated ones. The presence of negatively charged compensated acceptors can explain a fast capture of the photoexcited holes resulting in a 1-ps decay of the o91 PL band associated with the 1S transition, whereas the processes involving the uncompensated neutral acceptors can account for a fast buildup of the emission in the NC energy gap. A schematic of the trapping processes and principal emission features in CdS NCs is given in Figure 46.

7.3. Auger Recombination in Semiconductor Nanocrystals Three-dimensional carrier confinement leads to the enhancement of Auger-type processes and in particular, of Auger recombination [42, 160]. Auger recombination is a nonradiative process which involves three particles [ 174, 175]. Two particles (an electron and a hole)

513

KL]MOV

e

i ,,L h

(a)

(b)

Fig. 47. Schematicof the Augerrecombination accompaniedby reexcitation of an electron (a) or a hole (b).

recombine, and the recombination energy is transferred to a third particle which can be either an electron or a hole (see Fig. 47). Auger recombination is mediated by the Coulomb electron-electron (hole) interactions which are much stronger than carder interactions with the electromagnetic field. As a result, in strongly confined atomic and molecular systems, the Auger processes dominate cartier recombination in the case of multielectron excitations [160]. The efficiency of Auger processes is significantly reduced in bulk crystalline materials because of the kinematic restrictions imposed by the energy and momentum conservation [ 175]. These restrictions lead to the existence of the energy threshold for the Auger recombination and a temperature-activated behavior of the corresponding recombination rate RA ~ exp(-(Eg/kT))n3eh (neh is the e-h pair concentration) [160]. In spherical NCs, the momentum conservation is replaced with a less-restrictive conservation of the angular momentum, which removes the energy threshold for the Auger process and results in a significant enhancement of the corresponding recombination rate [42, 160]. In NCs, Auger recombination is a confinement enhanced process. Calculations performed assuming that the confinement-induced energy shifts are significantly smaller than the confinement potential indicate a strong size dependence of the Augerrecombination rate which scales as 1/a 7 [42, 160]. The first experimental indications of highly efficient Auger recombination in semiconductor NCs were obtained in pump-intensity-dependent studies of carrier decay in NC-glass composites [131, 162, 176-178]. In Refs. [162, 178] these studies were performed using streak-camera measurements of PL relaxation in CdSe NCs (a ~ 3.5, 6, and 6.5 nm) cooled down to the liquid-nitrogen temperature. In NCs with the largest mean radius (a ~ 6.5 nm), at low-pump intensifies (pump fluence below ,~0.5 mJ cm -2) the PL decay was essentially exponential with a ~2.4-ns time constant. At pump fluences above ~0.5 mJ cm -2 the PL traces displayed strongly nonexponential behavior (see Fig. 48) indicating a significant role played by nonlinear recombination processes. The initial decay time (r) rapidly shortened with increasing pump fluence (down to ~40 ps at 2.8 mJ cm -2) following the Wp2 dependence (see Fig. 49). Two other samples (a ~ 6 and 3.5 nm) showed a similar relaxation behavior at high-pump fluences, although the low-intensity PL dynamics for them were different from those in the sample with a ~ 6.5 nm. In the case of ps excitation used in Refs. [162, 178], the number of e-h pairs excited per NC (Neh) was proportional to the pump fluence, therefore the pump dependence of the relaxation time observed at high-pump intensities could also be presented as r c~ N ~ 2. This type of dependence indicates that the carrier decay at high-pump fluences is a cubic process governed by the rate equation dNeh ~dr cx --Ne3h, characteristic of Auger recombination. The difference in low-pump-intensity PL dynamics observed in samples with different radii was explained in terms of the competition between the radiative decay and cartier trapping. In the sample

514

LINEAR AND NONLINEAR OPTICAL SPECTROSCOPY

C d S e N C s (80 K ) Wp = 2 8 m J / c m 2 lO

e O Xl = 4 0 p s

~ 1,,,i

%

I,,,,w

Ikl

r 9

oJ

.

x2= 3 0 0 p s

~

E o

pump pulse 9

e64.,o

.

0

100

200

300

400

500

Time (ps) Fig. 48. PL dynamics (symbols) in CdSe NC-glass sample (a -~ 6.5 nm, T = 80 K) recorded at Wp = 2.8 mJ cm -2. The PL relaxation is fit to a double-exponential decay (dashed line) with time constants of 40 and 300 ps. Dotted line shows a ps pump pulse9

I0

....... . ,,. CdSe NCs (80 K) ,

R nm l

.....

',, 9 =2.4ns

',

I 9

6.5 i

1o

6 I

[ A

3.5 I

-- - T l -- 11"- fill- - i - ' ~ - - - j

1L

o

~

'

i"

"

o

1:=n[ 12 (l+exp[(EF-En)/kT]) \ Lw~h 2 ]Mmn x In 1 + exp[(Er -- Em)/kT] 9

(h/z.) 2

"]

x (Em - En - hw) 2 + (h/r) 2 1

(2.23)

where/1.0 is the permeability in a vacuum, s is the dielectric constant, Lw is the total quantum well width, r is the lifetime, and EF is the Fermi level of the system. The dipole matrix element Mmn is given by

Lw/2 Mmn -"

~* (z)lzlcbn(Z) dz

,I-Lw /2

(2.24)

The integrated absorption strength can be expressed as

IA =

f0

ot(w) dw

(2.25)

and the dipole oscillator strength is given by

4rcm*c fos = ~ l M m m l h~

2

(2.26)

The Fermi level EF can be calculated from [28],

m*kT ~n l n [ l + e x p ( E F - E n ) ] N o - zrh2Lw kT

(2.27)

Equation (2.27) is valid for summation over the subband levels En below the Fermi level E F. It is noted from Eq. (2.24) that the normal incidence radiation is not absorbed because there is no electric field component along the z-axis (i.e., the growth direction of quantum well). Therefore, both 45 ~ polished facet illumination and grating coupler [53-55] are commonly used to characterize the spectral responsivity of n-type QWIPs. For p-type strained-layer QWIPs, in order to determine the intersubband transitions and their corresponding absorption coefficients a 6 • 6 simplified Hamiltonian is used to predict the p-like properties of coherently strained layers. This matrix treats the s-like conduction band states as a perturbation and includes the k. p Hamiltonian [47-56] and the strain Hamiltonian [57]. Because the strain and spin-orbit coupling terms do not lift the spin degeneracy, the 6 x 6 Hamiltonian can be factorized into two 3 x 3 irreducible matrices. The assumption that the Fermi distribution function is equal to 1 for the confined ground state and is equal to 0 for the excited states in equilibrium is used to simplify the calculation without loss of accuracy. The absorption coefficient for the transition between the initial ground state, i, and the final state, f , in the valence band is given by [58],

oti(co)_Z4rcZq2fB 2dk[ 2 1-'/2 ](2.28) f nrcmoco z ~ 3 " (fi - ff)ls" Pi, fl [Ai, f(k) _ hw]2 + (1-,2/4) where nr is the refractive index in the quantum well; mo is the hole effective m a s s ; Ai, f is the energy difference between the initial ground state, i, of energy Ei (k) and the final state, f , of energy Ef(k); ~ and co are the unit polarization vector and frequency of the incident IR radiation, respectively; f f and fi are the Fermi distribution functions of the final and initial states, and F - - h/72if is the full width of level broadening with 72if being the lifetime between the initial and final states. I~" Pi, fl are the optical transition elements between the quantum well valence subband ground states, i, and the extended states, f , in the heavy-hole, light-hole, and spin-orbit bands. One important aspect that must not be overlooked in the design of reliable and functional p-type QWIPs is the limitation of layer thickness imposed by the induced biaxial

570

QUANTUM WELL INFRARED PHOTODETECTORS

compressive strain. If the biaxial stress introduced between the quantum well layer and the barrier layer (or the superlattice barrier layers for the B-M QWIP) is smaller than the biaxial stress needed for the quantum well to reach the critical layer thickness, then pseudomorphic or coherent interfaces can%e grown without creating defects between the quantum well and the barrier layers. Based on the force balance model [59, 60], the equilibrium critical layer thickness Lc, for an epilayer with lattice constant a, grown on a substrate with lattice constant as, is given as ( a )

LC--

~3o

l-re~174 [l+ln/qa~ 8Jr(l+v)cosol

]

(2.29)

where lq is the epilayer thickness, | is the angle between the dislocation line and the Burgesf vector, ot is the angle between the slip direction and the layer plane direction, 60 is the lattice mismatch or the in-plane strain, and v is the Poisson ratio. The Poisson ratio is defined as v -C12/Cll. =

2.4. Detector Performance Parameters

2.4.1. Absorption Quantum Efficiency The spectral responsivity of QWIPs depends on the absorption quantum efficiency and the photoconductive gain. The absorption quantum efficiency r/can be defined as [61], -- P(1 - R)[1 -exp(-Botlqw)]

(2.30)

where P is a polarization dependent constant, oe is the absorption coefficient, lqw is the total thickness of the whole quantum wells, R is the reflection coefficient. B is a constant depending on the number of paths the IR radiation made through the QWIP active region. For p-type QWIPs, P = 1, because both the TE and TM polarization of the incident IR radiation can be absorbed, whereas P is equal to 0.5 for n-type QWIPs. The absorption quantum efficiency r/ in a QWIP can be enhanced by increasing the doping density, the number of quantum wells, and the number of light paths through the quantum wells. The performance of QWIPs is very sensitive to the doping density. Increasing doping density lowers the activation energy of the dark current, and hence increases the thermionic emission dark current, which is undesirable for high temperature operation. However, for low temperature operation (e.g., T < 40 K), the dark current is not dominated by the thermionic emission, and an increase of doping density would be beneficial. Increasing the number of quantum wells results in an increase of the absorption but reduction of the photoconductive gain, results in little or no increase of spectral responsivity. Increasing the number of light paths can be achieved by using different optical coupling schemes, and considerable efforts have been devoted to developing new optical coupling techniques in n-type QWIPs. If the doping density in the quantum wells remains constant, the absorption quantum efficiency, r/, is determined by the oscillator strength (see Eq. (2.26)) and the density of states. The oscillator strength is at its maximum when the incoming photon energy h v is in resonance with the transition energy Ef - Ei. The value of r/in a QWIP can be obtained experimentally by using Fourier transform IR (FTIR) absorption or transmission measurements. The IR radiation is usually incident at the Brewster angle of 73 ~ with a polarizer. Appropriate background and baseline subtraction are needed to obtain the absorption spectrum of a QWIR Studies of absorption spectra for a wide variety of n-type QWIPs have been reported [12]. We next discuss the intersubband transitions in the B-M, BQB, and B-C QWIPs. In a B-M QWIP structure, the electron transition is based on the B-M transition. The electron wave functions are well confined in both the initial and final states. Because the well width in a B-M QWIP is much wider than that of the B-C and BQB QWIPs, there is a large overlap of wave functions between the initial and the final states, and the interaction is strong. The density of states are delta functions and the absorption spectrum is sharp with

571

LI AND TIDROW

narrow absorption bandwidth. The absorption bandwidth can be changed by adjusting the relative positions of the miniband and the excited state. A blue shift of the peak detection wavelength is obtained by aligning the excited state to the top of the miniband, while maximum bandwidth is achieved when the excited state is lined up in the middle of the miniband. In a BQB QWIP, the wave function of the upper excited state is only half confined and the interaction between the initial and the final states is relatively smaller at the resonant photon energy. The absorption spectral width is wider than the B-B QWIP. In a B-C QWIP, the wave function of the upper excited state is spreading over the barrier region so that the peak absorption is even smaller. However, the increase of the density of states at the upper level gives a wider absorption width when compared with the BQB QWlP. The width of spectral response can be controlled, and the optimized structure can be obtained when the energy spacing between the excited state and the barrier height is equal to one half the absorption width. In general, the peak responsivity of QWIPs is smaller when the photoresponse spectral width is wider and vice versa. As a result, the integrated absorption is nearly identical for either the B-C, BQB, or B-M QWIP. 2.4.2. Photoconductive Gain

QWIPs are photoconductors with majority carrier conduction. The signal detection is not only decided by the absorption quantum efficiency but is also decided by the photoconductive gain which is a measure of the hot electron transport after absorbing photons. The photoconductive gain of a QWIP is defined by the ratio of the electron lifetime and the transit time across the active quantum well region to the contact electrode. In general, the photoconductive gain will increase with increasing bias voltage across the QWIP. For photo-excited electrons, higher electron mobility will also lead to higher photoconductive gain. The photoconductive gain of a QWIP can be varied via detector design to meet various applications. For a B-C QWIP, the excited states are above the barrier height and electrons can easily escape from the well region even at small bias voltages. Because electrons do not have to tunnel through the barriers during the transport, the electron lifetime is longer and the photoconductive gain is larger compared to the BQB and B-M QWIPs. The transport mechanism for a BQB QWIP is similar to the B-C QWIP when the bias is large and the effective barrier is below the excited state. The photoconductive gain is smaller at lower biases due to the difficulty of electron tunneling through the barrier, and the photo-excited electrons are more likely to be recaptured in the quantum well at lower biases. The photoconductive gain for a B-M QWIP is usually smaller than the B-C QWIP because the electron transport through the miniband is via thermal-assisted resonant tunneling, which has a smaller probability than transport through the continuum states. When the bias voltage is large, the miniband becomes misaligned with the excited state. The scattering of electrons in the misaligned miniband prevents the increase of photoconductive gain with increasing bias. A wider miniband in the superlattice barrier layers can make electron transport easier and more efficient. For a given QWIP structure, the photoconductive gain can be varied by varying the number of quantum wells. A typical QWIP structure consists of 20-50 periods of quantum wells. Reducing the number of wells decreases the thickness of the active region and gives a shorter electron transit time. Using a smaller number of quantum wells is feasible, and high performance QWIPs have been reported using three quantum wells [63, 64]. At high operating temperatures, the photoconductive gain of a QWIP is nearly identical to the noise current gain due to the device dark current because enough thermal electrons have the same energy as the photo-excited electrons. At lower operating temperatures, a transport mechanism of thermal electrons is quite different from the photo-excited electrons. For a LWIR QWIP operating at 40 K, the thermal electrons are mostly bound in

572

QUANTUM WELL INFRARED PHOTODETECTORS

the ground state. Due to the thick barrier used in a QWIP, no sequential tunneling is expected at the operating bias. The defect-assisted tunneling (DAT) or direct tunneling (DT) dominates the dark current. The electron escape probability from the quantum well is very small and the transit time is very long. Thus, the noise currrent gain is much smaller than the photoconductive gain at low temperatures. The noise current gain of a QWIP can be measured by using a spectral analyzer and a low noise preamplifier. For example, a Brookdeal low noise amplifier (LNA) with an input reference noise of Sia 4 • 10-27 A2/Hz is used to amplify the signal generated by incident IR radiation in the QWIP. The spectral density from the output of the LNA is measured using an HP spectrum analyzer. The photoconductive gain is usually deduced from the measured noise current gain at T = 77 K or higher. To differentiate the noise current gain with the photoconductive gain, a cold shutter is used inside the cryostat. The shutter is opened to measure the photoconductive gain and is closed to measure the noise current gain due to the device dark current [65]. ~"

2.4.3. Spectral Responsivity

The peak responsivity of a QWIP is defined as e

R p = -~v rlg P e

(2.31)

where h v is the photon energy, r! is the absorption quantum efficiency, Pe is the escape probability of a hot electron from the well region, and g is the photoconductive gain. Note that the value of pe depends on how easy an electron can escape out of the quantum well region after absorbing photons; its value usually increases with increasing bias voltage. In a B-C QW!P, Pe is large even at very small bias voltage because the excited state is above the barrier. In general, B-C QWIPs have a relatively large photoconductive gain due to the easy electron transport in the continuum states above the barrier. The responsivity of B-C QW!Ps is usually larger than that of BQB and B-M QWIPs under the same bias condition, while the B-M QW!P has the smallest responsivity among these three QWIPs due to the lower electron mobility in the miniband. For a given QWIP structure, the responsivity can be increased by reducing the number of quantum wells. As discussed in the previous section, reducing the number of wells increases the photoconductive gain. However, reducing the number of quantum wells also reduces the absorption quantum efficiency if the light paths and the doping density are fixed. If the absorption is kept constant by using effective optical coupling schemes, then the responsivity increases with the decreasing number of quantum wells. Certain light coupling schemes give effective coupling with a thinner active region. For example, the spiral antenna grating reported by Beck et al. [66] is estimated to have 20-30% absorption quantum efficiency with 12 quantum wells and 10-20% for five quantum wells. Enhancement QWIP (E QWIP) reported by Dodd and Claiborn [67] is another grating structure that gives effective light coupling with fewer quantum wells. The spectral response of a QWIP can be measured using a monochrometer and a blackbody IR source, or an FTIR system. The absolute value of the responsivity can be determined using a calibrated blackbody source. For n-type QWIPs at single device level, the IR radiation is usually incident through a 45 ~ facet on the edge of the substrate. Either frontor backside illumination can be used depending on the contact metal geometry. 2.4. 4. D a r k Current

The dark current of a QWIP is determined by three basic conduction mechanisms, depending on the operating temperature as shown in Figure 6. At very low temperatures (e.g., T < 50 K for 10/zm cutoff), the dark current is mostly controlled by the DAT or DT mechanism. With mature III-V semiconductor growth and processing, this dark current is

573

LI AND TIDROW

52 .

.

.

.

.

A,

......................

TE

-= . . . . . . . . . .

-)

PC

Ii .......... -'q

Fig. 6. Dark current conduction mechanisms in an n-type B-C QWIP: (a) thermionic emission (TE), (b) thermally assisted tunneling (TAT), and (c) direct tunneling (DT).

usually very small. At medium operating temperatures (e.g., 50 K < T < 70 K for 10 lzm cutoff), the thermally assisted tunneling (TAT) current becomes dominant. At higher temperatures (e.g., T > 70 K for 10/xm cutoff), dark current is dominated by electron transport above the barrier via thermionic emission (TE) process [68]. Calculations of the dark current for a B-C QWIP have been reported by Levine et al. [62]. Under dark conditions, electrons can transfer out of quantum wells and can produce the dark current via three mechanisms: TE, TAT, and DT as shown in Figure 6. In the low-field regime, the thermionic emission current is related to the density of electrons nt and the average drift velocity vd, and can be expressed as [69],

Ith =eAdvdnt

(2.32)

where A,t is the active detector area, e is the electronic charge, and #F [1 + (#e/Vs)2] 1/2

(2.33)

m*kBT [ Ecf - EF ] exp -rch2L kB T

(2.34)

v~ = and

nt --

In the foregoing equations,/z is the electron mobility, F is the electric field, Vs is the saturation velocity, EcT is the cutoff energy related to the cutoff wavelength ~c, and m*/rrh 2 is the two-dimensional density of states. The Fermi energy, EF, can be determined from the expression of the doping density ND, No -

zrh

~ln I

I

1 +exp

ksT

(2.35)

,

m*

zrh2 ~ Z ( E F -

En)

(2.36)

n

Equation (2.35) for No is valid when summed over the subband levels En below the Fermi level, and Eq. (2.36) is only valid at cryogenic temperatures. Using the previous results in the cryogenic temperature regime, we see that the dark current due to thermionic emission is exponentially dependent on the doping density in the quantum well; that is,

EF

Ith 0(. exp( k---~) o( exp ( ~ T )

\

574

(2.37)

QUANTUM WELL INFRARED PHOTODETECTORS

Therefore, as the doping density in the quantum well increases, the dark current due to thermionic emission also increases exponentially. In contrast to this, the intersubband absorption is directly proportional to the doping density. Thus, a tradeoff between the dark current and the intersubband absorption is required in order to optimize the QWIP performance. However, for p-type QWIPs, the Fermi level in the quantum well is pinned at or slightly above the ground bound state for highly doped quantum wells. As a result of the pinning of Fermi level at high doping density, a higher doping density in the quantum wells can be used to increase the optical absorption without increasing the dark current in p-type QWlPs. The dark current for p-type QWIPs can be expressed as [70],

Jd = =

ITs. Ts[g(E, V) dE1 4rrqm*kBTfo~ h3 •

(l+exp[(Ef-E1)/kBT]) ITs" Tslln 1 + e x p [ ( E f - E1 - q V a ) / k B T ]

dE1 (2.38)

where m* is the hole effective mass; E1 is the longitudinal energy of the holes along the barrier layer; k8 is the Boltzmann constant; ITs * Tsl is the transmission coefficient; T is the temperature, and Va is the applied bias across one period of quantum well. Using Eq. (2.38) the dark current densities in both n- and p-type QWIPs can be calculated when current transport is dominated by the thermionic emission process. The dark current of a QWIP can be measured using an HP semiconductor parameter analyzer. The dark currents measured are usually not symmetric under positive and negative bias conditions due to a doping impurity migration effect. For n-type QWIPs, the theoretical modeling is in good agreement with the measured dark current under the negative bias condition, but not under the positive bias condition. The reason is that the doping impurities in the QW region undergo migration toward the surface during the MBE growth, which results in an asymmetrical impurity ion segregation and reducing the effective barrier thickness when an n-type QWIP is under positive bias [71 ]. Under the same temperature condition, the dark current also depends slightly on the detector structure. At high temperatures, the dark current in a B-C QWIP is usually higher than other types of QWIPs (i.e., B-B, B-M, BQB QWIPs) due to the easier hot electron transport in the continuum states. The lower dark current achieved in a BQB QWIP is due to the slightly higher barrier for the thermal electrons at the same cutoff wavelength as compared to the B-C QWIP. In a B-M QWIP, due to the high barrier created by the superlattice barrier layers and the fact that the excited state and the superlattice miniband are well below the barrier, the thermionic emission dark current is very small at 77 K.

2.4.5. Noise Detector noise can be distinguished in two types: radiation noise and intrinsic detector noise. Radiation noise includes the photon signal fluctuation noise and the background photon fluctuation noise. Intrinsic detector noises could have many sources, such as shot noise, Johnson noise, g-r noise, 1 / f noise, and pattern noise. At the FPA level, the pattern noise is the major limitation to the array performance at low temperature. The fixed pattern noise results from local variation of the dark current, photoresponse, and the cutoff wavelength. In QWIPs, the device dark current is the main source of noise at high temperature. This dark current related shot noise can be expressed by

in -- v/4eglagdA f

(2.39)

where Id is the dark current, gd is the dark current noise gain, and A f is the noise bandwidth. When the detector is operating under background limited performance (BLIP) conditions, the noise is dominated by the background photocurrent, which is given by

in = v/4eg libgpA f where Ib is the background photocurrent, and g p is the photoconductive gain.

575

(2.40)

LI AND TIDROW

Fixed pattern noise is a limiting factor for QWIP array performance when D* is above 101~ c m H z l / 2 w -1. The fixed pattern noise is very small due to its excellent material quality and controlled cutoff wavelength. There is very little 1 / f noise observed in QWIPs owing to its stable surface properties. 2.4.6. Detectivity (D*) The detectivity D* is an important figure of merit for IR detectors. Values of D* can be determined from the measured responsivity and the noise of the detector. In general, D* is a function of operating temperature, detector bias, and cutoff wavelength. Therefore, a typical detector characterization should include measurements of both the responsivity and noise as a function of each of these parameters. Obviously, one cannot make measurements at all combinations, so all parameters but one are usually held constant, with only one parameter being varied. When data are presented, the significant parametric variations are presented along with D* values as a function of these parameters. If single D* values are given, it is imperative that the values of all parameters be given. The peak detectivity of a QWIP can be calculated using [72], , Ri,p~/AdAf Dp -in

(2.41)

where Ri,p is the peak current responsivity, A f is the noise spectral bandwidth, and in is the overall root-mean-square noise current of a QWIE The noise current consists of two components: one is the device noise current ind and the other is the background photon noise current inb. There are two main noise sources in a QWIP device: one is the g-r noise (in the PC mode) and the other is the Johnson noise (in the PV mode). The BLIP peak detectivity can be determined [62] using DBLIP --

hv-isc

(2.42)

where ri is the absorption quantum efficiency, and 186 is the intensity of the incident background photons, which can be expressed as ISG -- sin 2

cos(0)

W(X) d~

(2.43)

1

where f2 is the solid angle; 0 is the angle between the incident IR radiation and the normal of the quantum well plane, and W(X) is the blackbody spectral density given by W()O

--

2zcj c 2 1 )~5 ehc/~kTSc -- 1

(2.44)

where c is the speed of light, X is the wavelength, h is the Planck constant, k is the Boltzmann constant, and TBG is the background temperature. The D* value also depends on the detector structure. For example, a B-M QWIP can have a higher D* at high temperatures when the miniband width is very narrow and resonant with the excited state. The miniband blocks more dark current than the photocurrent in this situation and gives a higher signal to noise ratio. At low operating temperatures (T < 50 K at 10/~m cutoff), the dark current is low, and D* is varied with the photoresponse. The B-C QWIP usually has a higher value of D* at low temperatures and small bias due to its larger responsivity compared with other types of QWIPs. 2.4. 7. Noise Equivalent Temperature Difference and Noise Equivalent Power (NETD and NEP) Noise equivalent temperature difference (NETD) is a key figure of merit for the performance of a FPA thermal imaging system. NETD is the minimum temperature change of a

576

QUANTUM WELL INFRARED PHOTODETECTORS

scene required to produce a signal equal to the rms (root-mean-square) noise. For low background applications, noise equivalent power (NEP), or noise equivalent irradiance (NEI) is usually used as a figure of merit. It is the radiant flux power necessary to produce a signal equal to the rms noise. The relationship between the NEP and NETD is NETD =

NEP

dPb/dT

(2.45)

where Pb is the background photon power. The spectral detectivity given in Eq. (2.41) can be related to NEP by D* (~., f ) --

4AdAf NEP

(2.46)

where Ad is the detector area. A low NETD or NEP is desirable for high FPA performance. At the FPA level, the fixed pattern noise, readout noise, charge handling capacity, together with D* are considered in evaluating a QWIP to fit into the applications. The nonuniformity of the FPA is a major limiting factor when the D* is sufficiently high. The importance of the uniformity for thermal imaging can be reflected by NETD, as reported by Levine [12]. When the D* value is approaching a certain limit, increasing D* no longer increases NETD. The nonuniformity factor becomes the key parameter and an improvement of nonuniformity from 0.1 to 0.01% after correction could lower the NETD from 63 to 6.3 mK for an IR FPA with D* > 1010 c m H z l / 2 w -1.

3. n-TYPE QUANTUM W E L L INFRARED P H O T O D E T E C T O R S Since the first observation of intersubband transitions in a GaAs quantum well [7], rapid progress has been made in the development of high performance QWIPs and FPAs using an n-type GaAs/A1GaAs materials system for IR imaging applications [ 12]. The intersubband detection schemes for these n-type QWIPs are based on B-B, B-C, BQB, and B-M transitions, as are illustrated in Figure 2. Large area, highly uniform focal plane arrays (FPAs) using n-type GaAs/A1GaAs QWIPs have been demonstrated [73-77]. Due to the quantum mechanical selection rules, normal incidence absorption is forbidden in the direct gap n-type QWIPs. As a result, efficient light coupling in the n-type QWIP FPAs is achieved by using various grating structures in each pixel of the FPA for normal incidence backside illumination. In the next section, the device structures, properties, and performance parameters for a wide variety of n-type QWIPs using B-B, B-C, BQB, and B-M transition schemes are discussed. 3.1. Bound-to-Bound Quantum Well Infrared Photodetectors The first B-B QWIP using GaAs/A1GaAs material were reported by Levine et al. [9]. The device consists of 50 periods of 6.5 nm GaAs quantum wells doped to 1.4 • 1018 cm -3 and 9.5 nm undoped A10.zsGa0.75As barrier layers sandwiched between the top and bottom n+--GaAs contact layers grown by MBE technique. The thickness and composition of this QWIP were chosen to produce two bound states in the quantum well with an energy separation that corresponds to a 10/zm detection peak. The schematic energy band diagram for an n-type B-B QWIP is given in Figure 2a. The intersubband absorption of an IR radiation excites an electron from the filled ground state to the second bound state where it can tunnel out, thereby producing a photocurrent. The measured absorption peak for this QWIP is at )~p = 10.9/zm, which is in good agreement with the calculated value. The measured absorption coefficient is 600 cm -1 which corresponds to an oscillator strength of f = 0.6. The dark current in a B-B QWIP is usually very low because the thick barrier

577

LI AND TIDROW

A1As/Ino.53 Gao.47As/A1As

Ino.52Alo.48As

Ino.szAlo.48As

I II

I II --" E F El

Fig. 7. Schematic energy band diagram and transition scheme of a double-barrier (DB-)InGaAs/ A1As/A1GaAsQWIPfor MWIRdetection.

layer effectively blocks the transport of electrons in the ground bound state of the quantum well. The first demonstration of a B-B QWIP using the lattice-matched In0.53Ga0.47As/ In0.52A10.48As grown on the InP substrate were reported by Levine et al. [78] for MWIR detection. A conduction band discontinuity of A Ec = 550 meV, which is significantly higher than that of a direct gap GaAs/A1GaAs system, allows a much shorter wavelength detection for such a direct gap n-type QWIP. The device structure consists of 50 periods of alternating layers of the doped In0.53Ga0.47As quantum well (5 nm, 1 x 1018 cm -3 doping) and the undoped In0.52A10.48As barrier (30 nm). This QWIP structure contains two bound states separated by 281 meV in the quantum well, corresponding to an intersubband transition at )~p -- 4.4/zm for MWIR detection. The intersubband absorption for this device was strong and relatively broad (A~./~ -----33%) with an oscillator strength f = 0.44. A peak detectivity of D* = 1.5 x 1012 cmHzl/2/W at 77 K and a BLIP detectivity of 9 DBLIP -- 2.3 X 10 1 0 cmHzl/2/W at 120 K were obtained for this device at )~p = 4.4/zm. We next present a double-barrier (DB) QWIP using lattice-matched InA1As/A1As/ InGaAs materials system grown on the InP substrate for 3.4/zm MWlR detection. The device structure consists of 10 periods of alternating layers of doped InGaAs well (4.4 nm), two thin (1.5 nm) undoped AlAs double barriers, and a thick (30 nm) undoped InA1As bartier sandwiched between two 0.5/zm n+-InGaAs top and bottom contact layers, which were grown on the InP substrate by MBE technique. The InGaAs quantum wells and InA1As barrier layers were lattice-matched to InP substrate, and the thin AlAs double barriers were used to enhance the barrier height of the quantum well and served as tunneling barriers for the PC mode detection. Figure 7 shows the schematic conduction band diagram and the transition scheme for this DB QWIP with an intersubband transition energy ( E l - E 2 ) of 365 meV for the 3.4 # m peak detection wavelength. The transition scheme is from the localized ground state (El) to the bound excited state (E2) inside the quantum well. A shorter wavelength detection peak can be achieved by reducing the well width to push up the bound excited state (E2) and hence increasing the energy separation between the E2 and E1 states for intersubband absorption. The light coupling for this device was achieved by using 45 ~ facet illumination. This DB QWIP can be operated in both the PV and PC mode detection in the MWIR band.

578

QUANTUM WELL INFRARED PHOTODETECTORS

10 -2

10-4 < v

10-6 LI.I n," n" Z3 rO 10 -8 nc ,< a 163 K 137 K 109 K 77 K 40 K

10-10

10-12 -5

-4

-3

-2

-1

0

1

2

BIAS V O L T A G E

(V)

3

4

5

Fig. 8. DarkI-V characteristics as a function of temperature for the InGaAs/A1As/A1GaAsDB QWIP shown in Figure 7.

Figure 8 shows the dark current versus bias voltage (I-V) curves measured at T = 40, 77, 109, 137, and 163 K. The spectral responsivity was measured at T = 40, 77, 109, and 137 K. Figure 9 shows the responsivity as a function of bias voltage at T = 40 and 77 K. The peak responsivity is 0.247 A/W at T = 40 K, Vb = --3.5 V, and )~p = 3.4/zm, with peak detection wavelength nearly independent of the temperature and applied bias. The peak detectivity (D*) for this device was found to be 7.28 • 101~ cmHzl/2/W at T = 77 K and Vg = - 2 . 5 V.

3.2. Bound-to-Continuum Quantum Well Infrared Photodetectors In a B-B QWIE the optical absorption in the continuum states above the top of the barrier is usually very weak, because most of the oscillator strength is confined in the bound states (i.e., E l - E 2 ) transition. However, by reducing the quantum well width the strong oscillator strength of the excited bound state can be pushed up into the continuum states resulting in a strong bound-to-continuum state absorption [6]. The B-C-QWIP structure (see Fig. 2b) has the major advantage in that the photo-excited electrons can escape from the quantum well without tunneling through the thick energy barrier as in the B-B QWIP case. Thus, the bias voltage required for the transport of photoexcited electrons out of the quantum well region can be greatly reduced, which in turn drastically lowers the dark current. In addition, the barrier thickness can be increased substantially, thereby reducing the ground state sequential tunneling dark current by many orders of magnitude. By making use of these improvements, Levine et al. [ 10] have demonstrated the first B-C QWIP and have achieved a dramatic increase in the performance of the B-C QWIP over the B-B QWIP. We next discuss several reported B-C QWIPs fabricated from the GaAs/A1GaAs and InGaAs/A1GaAs material systems.

579

LI AND TIDROW

0.3

T=40 K

-3.5 V -3 V

v>.. 0.2 I-> 03

-2.5 V

z

0 0.1 13. 03 u..I n,"

0V

0 2.5

3

3.5

4

4.5

5

W A V E L E N G T H (prn)

(a)

0.25 [E ~'

T=77 K

0.2 ~'-

-3.5V

0.15

I

-.

0.1 0.05 0 2.5

3

3.5

4

4.5

5

W A V E L E N G T H (pm)

(b) Fig. 9. Peakresponsivityversus wavelengthmeasuredat (a) 40 K and (b) 77 K for the DB QWIP shown in Figure 7.

3.2.1. GaAs/AIGaAs Bound-to-Continuum Quantum Well Infrared Ptotodetectors To illustrate the device characteristics and the performance of a B-C QWIE we present a GaAs/A1GaAs B-C QWIP grown on GaAs substrates. The device structure consists of 20 periods of alternating layers of doped GaAs well (5.5 nm) and undoped A10.z7Ga0.73As barrier (50 nm) as the active region sandwiched between two 0 . 5 / z m highly doped n + GaAs top and bottom contact layers. The doping densities are 7 x 1017 cm -3 and 1 x 1018 cm -3 for the GaAs quantum well and contact layers, respectively. The thickness of the quantum well and the composition of the barrier layer are chosen so that the energy separation ( A E - 132 meV) between the ground bound state (El) in the well and the continuum states above the barrier corresponds to a peak detection wavelength at kp = 9.4/zm. The schematic conduction band diagram and intersubband transition scheme for this GaAs/A1GaAs B-C QWIP is illustrated in Figure 39, which is used as the LWIR stack for a two-color QWIP [79]. Figure 10 shows the dark current density versus bias voltage (J-V) curves for T = 35, 66, and 77 K along with the 300 K background window current measured at 30 K with a 180 ~ field of view (FOV) [79]. The BLIP temperature for this device is around 70 K for bias up to 4-2 V with a cutoff wavelength at ~.c - 10 lzm. It should be noted that 77 K

580

QUANTUM WELL INFRARED PHOTODETECTORS

lO o LWIR t"q

77 K

300 K BG

IE

Z LU

o 10-5 I-Z LU n" n,'

35 K

r

a

10-1o -5

-4

-3

-2

-1

0

1

2

3

4

5

BIAS VOLTAGE (V) Fig. 10. Dark I-V curves measured at 35, 66, and 77 K, along with 300 K window current measured at 30 K with a 180 ~ FOV for the GaAs/A1GaAs B-C QWIP. (Source: Reprinted with permission from [79]. 9 1997 American Institute of Physics.)

operation could be achieved by shifting the cutoff wavelength to 9 lzm. The 300 K window current was also calculated using the integration of the measured responsivity times the 300 K blackbody radiation spectrum with a 180 ~ FOV [80]. The calculated window current density at 2 V is 1.93 x 10 -3 A/cm 2, which is in excellent agreement with the measured value shown in Figure 10. Figure 11 shows the responsivity versus the wavelength plot for this device at 77 K and 2 V with a 45 ~ facet light coupling and normal incidence illumination without grating (dashed line). The peak detection wavelength is at Xp = 9.4 lzm. The cut-on full width half maximum (FWHM) is at 8.6/zm, and the cutoff FWHM is at 10/zm with a spectral bandwidth of 1.4/zm. The responsivity increases linearly with bias voltage up to -+-2V and reaches a maximum value of 0.55 M W at 3 V with 45 ~ facet incidence. The BLIP temper, ature is 70 K at 2 V, and the corresponding DBLIP is 1.8 • 1010 cmHzl/2/W, assuming a 13% quantum efficiency.

3.2.2. InGaAs/A1GaAs Bound-to.Continuum Quantum Well Infrared Photodetectors We next discuss a B-C QWIP with peak detection wavelength at 4.3/zm using high-train InGaAs/A1GaAs materials grown on the semi-insulating GaAs substrate for MWIR detection [79]. The schematic conduction band diagram and transition scheme for this B-C QWIP is also shown in Figure 39 for the MWIR stack. The device structure consists of 20 periods of alternating layers of undoped A10.38Ga0.62As barriers (30 nm) and doped (2.5 • 1018 cm -3) GaAs/Ino.35Gao.65As/GaAs (thickness: 0.5/2.4/0.5 nm) wells sandwiched between two 0.5 # m highly doped n+-GaAs top and bottom contact layers. The well width and composition of this device are chosen so that the peak detection wavelength is at 4.3/zm in the MWIR band. The low dark current and the excellent uniformity of the device dark current and responsivity show that this high-strain QWIP is of high quality despite the high indium concentration (35%) used in the quantum well. Figure 12 shows the dark current versus bias voltage measured at 77, 122, and 140 K, along with the 300 K window current measured at 30 K with a 180 ~ FOV. The BLIP temperature is at 125 K up to 4-2 V and 120 K up to 4-3 V.

581

LI AND TIDROW

0.6 LWIR: T = 77 K, bias = 2 V A

(a)

0.5 incidence

~

0.4

oo 0.3 z o

i

~

no.rmal

IX oo LU

n,, 0.2 0.1 0.0

9

,,

- . .

6

7

8 9 10 WAVELENGTH (pm)

11

12

(a) 0.7 t 0.6 _

LWIR: T = 77 K

45 ~ incidence 2tp = 9.4 i.tm

I

'"1

_ _

~

0.5

~-> 0.4 Or) Z

normal incidence 7tp = 9.2 .l.t,.~m....

o13. 0.3 CO LU n,'


I-

0.'I,

_> r Z O Q. O9

ua 0.05

n," v < uJ r

0

0.5

1

1.5

BIAS VOLTAGE (V) Fig. 17. The peak responsivity versus the bias voltage for the GaAs/A1GaAs B-M QWIP measured at T = 50 K with 45 ~ facet incidence illumination.

The performance of GaAs/A1GaAs B-M QWIP FPAs is comparable to that of the B-C and BQB GaAs/A1GaAs QWIP FPAs reported by Bethea et al. [74] and Gunapala et al. [77], respectively.

3.5. Strained Layer Quantum Well Infrared Photodetectors QWIPs based on compressively strained layer InxGal_xAs/AlyGal_yAsmaterials grown on semi-insulating GaAs substrates have been widely investigated for MWIR and LWIR detection [21, 79, 90-92]. Based on the theory of intersubband transitions and carrier transport in n-type QWIPs, a larger responsivity in the high-strain InGaAs-based QWIPs as opposed to unstrained QWIPs is expected due to the reduction of electron effective mass and the compressive-strain enhanced intersubband absorption. In addition, large normal incidence photoresponse has been consistently observed in these strained layer n-QWIPs [21, 79, 90-92]. For example, a peak responsivity of 0.25 A/W was obtained in the In0.35Gao.65As/A10.38Ga0.62As B-C QWIP at ~.p = 4.4/zm under normal incidence illumination without using a grating coupler [79]. Wang and Lee [91, 92] also reported a normal incidence responsivity of 0.23 A/W at )~p = 8.8 /zm in an n-type In0.32Ga0.68As/GaAs QWIP. We shall next describe a high sensitivity voltage-tunable triple-coupled (TC) QWIP using high-strain (HS) InGaAs/A1GaAs materials grown on the semi-insulating GaAs for LWIR multicolor detection. The basic structure of a TC QWIP consists of asymmetrical triple-coupled quantum wells separated by two ultrathin AlyGal_yAs barrier layers, which are sandwiched between the wider A1GaAs barrier layers to form an active absorption region (see Figure 18a) [21, 22]. Figure 18 shows (a) the schematic conduction band diagram and (b) transmission coefficients of a high-strain (HS) InGaAs/A1GaAs/InGaAs TC QWIP for LWIR detection [90]. Using a quantum-confined Stark effect, the B-B transition scheme, and a reduced effective mass, a linear wavelength tunability and enhanced optical absorption can be obtained in this HS-TC QWIP. The basic device structure consists of 10 periods of triple-coupled quantum wells with a doped In0.zsGa0.75As quantum well (5.5nm, 7x 1017cm -3) and two undoped thin A10.11Ga0.s9As/In0.12Ga0.ssAs quantum well (2/3.5 and 2/4 nm) separated by a 50 nm A10.11Ga0.s9As barrier layer. Finally, a 0.1/zm thick undoped GaAs spacer layer was grown between the triple-coupled quantum

588

QUANTUM WELL INFRARED PHOTODETECTORS

Ea

E2 I

I

Elli

i

(a) m

-.

-5

ii

i

Z'13 = 10.9 lam

E3

; L I C = 8 . 8 I.tm

~j]

@0v

-10 A

"~-15

o ....I

-20

-

l

-25 .

I

-30

|

0

0.05

0.1 0.15 0.2 'Energy (eV)

0.25

|

0.3

(b) Fig. 18. (a) The schematic conduction band diagram and (b) transmission coefficients of a high-strain (HS) InGaAs/AIGaAs/InGaAs TC QWIP for LWIR detection. (Source: Reprinted with permission from [90].)

well and the top and bottom GaAs ohmic contact layers to reduce the tunneling current from contacts to quantum well, and hence to lower the device dark current. Figure 18a shows the schematic diagram of the conduction band and bound state energy levels of this device under zero bias condition. For a TC QWIP, due to the strong coupling effect of the three asymmetrical quantum wells and the two thin A1GaAs barriers, the bound states in the thin quantum well and the first excited state in the deep quantum well are coupled to form the second (E2) and the third (E3) bound states inside the quantum well, as is illustrated in Figure 18b. The intersubband transition is dominated by the E1 --+ E3 B-B transition, while a second photoresponse peak due to the E1 --+ Ec B-C transition was also observed in this device. Figure 19 shows the dark J-V curves measured at 30, 65, and 77 K, along with the 300 K background window currents measured at 180 ~ FOV, for the 5- and 10-period devices, respectively. The BLIP temperature was found at 65 K for Vb ~< --5 V, which is 5 K higher than our previously reported value for a lightly strained layer In0.05Ga0.95As/ A10.21Ga0.79As/GaAs TC QWIP [21, 22]. Figure 20a and b shows the spectral responsivity measured at T = 30 K for the 5- and 10-period devices, respectively. The highest peak responsivity was found to be 2.72 A/W at ~.p = 9.6 lzm and Vb = --5 V for the 10-period device, and similar results were also obtained for the 5-period device at - 3 V. The inset shows a linear dependence of the peak wavelength on the applied bias voltage for both the E1 --+ E3 and E1 --+ Ec transitions. The wavelength tunability for both devices is in the range from 6.9 to 7.3/xm and from 9.6 to 10.1 # m for the E1 --4 Ec and the E1 --+ E3 transitions, respectively. The interpolated peak wavelengths at zero

589

LI AND TIDROW

10 2 r

1~0

_ 10-2

r Z ILl

0-4 Z

~

0-6

~

l o .8

lo-lO -1 0 1 BIAS VOLTAGE (V~

-2

-3

2

3

10 2

(b) t",4

10 0

~ 10 -2 e~ z

77

K

UJ

~i-- 10-4 z

'~x~oo K

W

~ r

0.6

~ a

10 -8

30 K

10-10 -5

-4

-3

-2 -1 0 1 2 BIAS V O L T A G E (V)

3

4

5

Fig. 19. Measured dark J-V curves for (a) 5-period and (b) 10-period HS TC QWIPs. Device area: 216 x 216 lzm 2.

bias were found to be 8.6 and 11.1 /zm for the E] --+ Ec and the E] --+ E3 transitions, respectively, which are in good agreement with the calculated peak wavelengths at zero bias: ~.p = 8.8 and 10.9 ~m. Figure 21 shows a comparison of the peak responsivity versus the wavelength for (a) a lightly strained InGaAs/GaAs/A1GaAs TC QWIE and (b) the HS-TC QWIP shown in Figure 20b. The results show that using this HS-Ino.zsGao.75As/A10.11Gao.s9As/Ino.lzGa0.ssAs materials system, the peak responsivity was increased by more than 1 order of magnitude over the lightly strained (LS) In0.05Ga0.95As/A10.zlGa0.v9As/GaAs TC QWIP reported earlier by [22, 90]. For example, the peak responsivity was increased from 0.16 A/W for the lightly strained TC QWIP to 2.71 A/W for the HS-TC QWIP (an increase of 17.5) at 9.6 # m with same doping concentration in the quantum well. Figure 22 shows the peak detectivity versus electric field for the 5- and 10-period devices at 77 K. The maximum peak detectivity (D*) is 2.93 x 1010 cmHzl/2/W at ~.p -- 9.8/zm, V b - - - 4 . 5 V, and T - 77 K for the 10-period device, and 1.65 x 101~ cmHzl/2/W at ~.p -- 9.6/zm, Vb = --2.6 V and T - 77 K for the 5-period device [90]. In this subsection we have discussed several high performance strained-layer n-QWIPs using InGaAs/A1GaAs materials grown on GaAs substrates. The results reveal that all ntype QWIPs formed on the strained-layer InGaAs/A1GaAs or on the InGaAs/GaAs material systems show excellent performance characteristics. A high-sensitivity TC-QWIP

590

QUANTUM WELL INFRARED PHOTODETECTORS

-3V

30 K

12

2.5

(a)

!

~

10

2 ~'~ 8

~O9 Z

1.5

ft. co

w

9

6

o

-4

I

-

-2

1

0

B~AS (V)

0.5

7

8

9

10

11

12

13

14

WAVELENGTH (pm)

12

-5 V

30 K 2.5

10

A

(b)

E=

v

2

8

5

1.5

Z

o Q. 09

w

n,"

6

1

I

I

l

-6

-4

-2

BIAS (V)

0.5

7

8

9

10

11

12

13

14

WAVELENGTH (IJm)

Fig. 20. The spectral responsivity for (a) 5-period and (b) 10-period HS TC QWIPs with a 45~ facet incidence measured at 30 K. (Source: Reprinted with permission from [90].)

formed on high-strain InGaAs/A1GaAs material systems has been illustrated in this section, which shows 1 order of magnitude improvement in peak responsivity over the lightly strained TC QWIP reported previously [22]. Furthermore, using a quantum-confined Stark effect, a linear dependence of the peak detection wavelength on the applied bias has also been demonstrated in a TC QWIE

3.6. Optical Coupling in n-Type Quantum Well Infrared Photodetectors It is well known that the electric dipole matrix element existing between the subbands of a quantum well is relatively large. However, only the component of IR radiation with the electric field e• vector perpendicular to the quantum well layers will give rise to intersubband transition in the quantum well. Thus, no intersubband IR absorption in the quantum well is expected in the ordinarily bare surface at normal incidence for n-type direct gap

591

LI AND TIDROW

0.25

(a) LS TC-QWIP 0.2

7v

11 A

E 10

~0.15

,-e" 9

N Z o

0.1 8 0

2

~ uJ 0.05

4

6

8

BIAS (V)

n,"

0 IL

7

8

9

10

11

12

13

14

WAVELENGTH (pm)

-5 V

(b) HS TC-QWIP

2.5 "~

2

1.5 Z

6 i

o o.. 03 UJ n,"

1

-6

i

i

-4

-2

0

BIAS (V)

0.5

7

8

9

10 11 12 WAVELENGTH (pro)

13

14

Fig. 21. The spectral responsivity of (a) an LS-InGaAs/GaAs/A1GaAs TC QWIP and (b) an HSInGaAs/A1GaAs/InGaAs TC QWIP,measured with a 45~ facet illumination. (Source: Reprinted with permission from [90].)

QWIPs. Even tilted at a Brewster's angle of 73 ~ due to the large refractive index (n = 3.3) of III-V semiconductors and the anisotropic character of the absorption, only a small fraction (cos 2 0 8 / s i n 08 = 9%, where 08 is the angle between the incident IR beam and the normal of the quantum well plane) of the incident IR radiation can be absorbed. In fact, the practical net absorption is only about 4% [93, 94]. For a large and uniform surface illumination, a texture diffraction surface, or metal grating, is needed to induce the perpendicular electric field component for intersubband resonance [96]. Therefore, to fabricate large format QWIP FPAs using n-type direct-gap materials, diffraction gratings are an excellent means for achieving efficient optical coupling. These have been demonstrated in the early work reported by a number of researchers [72, 96, 97]. Hasnain et al. [98] have reported an optical coupling scheme in a 50-period QWIP using triangular gratings that were monolithically etched into the top contact or in the substrate. They have found that the absolute peak responsivity of the grating coupled QWIP is similar to a 45 ~ facet illuminated QWIP. Planar two-dimensional metal gratings have also been used in the B-M QWIP reported by Yu and Li [ 11, 97] in the evanescent geometry (i.e., when the wavelength in the medium is larger than the grating period) and in the propagating diffracted wave geometry. These gratings are simple to fabricate, and give a collection quantum efficiency from 10 to 15%. Wang and Li [54] have also reported a two-dimensional double periodic reflection metal gratings with collection quantum efficiency over 20%. The most detailed analysis and measurements on the QWIP grating coupling efficiency and optimization were done

592

QUANTUM WELL INFRARED PHOTODETECTORS

1011

iii

77 K

10-period t'N N

z, E

J'/"

O

~ " 1010

~%5-period

i-w I-uJ a

(D*) max @-4"5 V (10-period) (D*)max @-2.6 V (5-period) t

109

~

-55

-

n

n

t

,

-50

n

t

l

n

-45

,

n

t

l

m

n

-

-

I

-40

n

n

~

n

-35

-30

ELECTRIC FIELD (KV/cm)

Fig. 22. Detectivityversus electric field for the HS-InGaAs/A1GaAs/InGaAs TC QWIP measured at T = 77 K. (Source: Reprinted with permission from [90].)

(a)

(b)

RANDOM REFLECTOR /4 ~

~k

-

2D GRATING GRATING AND CAVITY

v PIXEL

I

"

'-7

RADIATION INCIDENT -RADIATION

THIN GaAs SUBSTRATE

Fig. 23. (a) A randomly roughened reflecting surface, and (b) a two-dimensional grating coupler for light coupling in n-type QWIPs. (Source: Reprinted from [88], with kind permission from Kluwer Academic Publishers.) by Andersson et al. [82] and Andersson and Lundqvist [99] who considered both linear and two-dimensional grating couplers (see Fig. 23b). They calculated the optimum period, shape, and depth of the grating as well as the enhancement produced by a 3 / z m thick AlAs total internal reflecting layer beneath the QWIP active region to reflect the unabsorbed radiation back into the quantum wells. Multiple paths of IR radiation and higher optical absorption can be achieved with a randomly roughened reflecting surface as shown in Figure 23a [ 101-102]. Sarusi et al. have shown experimentally that by careful design of surface texture randomization, efficient light coupling can be obtained under normal incidence illumination [ 101 ]. They reported nearly 1 order of magnitude enhancement in responsivity compared to 45 ~ facet illumination geometry. Bandara et al. [88] have conducted a detailed study of the optical coupling in n-type QWIPs using random reflector and two-dimensional gratings. Figure 24 shows the normalized responsivity spectra for the two-dimensional periodic grating coupled QWIPs as a function of grating period D for D = 2.2, 2.4, 2.6 . . . . . 3.2/xm and with fixed groove

593

LI AND TIDROW

1.2

I

I

I

I

I

DETECTOR AREA 200 ~m x 200 ~m .

1.0 2.2 ~m

,,,,,

-> (n

0.8

2.4 pm

z

o O.

2.6 pm

(/) U.I

r,- 0.6 3.0 pm

ILl N ..I

< X CC o z

0.4

I

/

0.2

/

/

II]

/

/

/

5

6

7

3.2~m

4

2.8 .rn

Xd,/X./' I

0.0

,,l,,,~

45 DEG

I

I

8

9

1 .-I

10

11

WAVELENGTH (mm)

Fig. 24. Normalizedresponsivityspectrafor the two-dimensionalperiodic grating coupled QWIPsas a function of grating period D for D = 2.2, 2.4, 2.6..... 3.2/zm with fixed groovedepth, and comparedwith the 45~ facet incidence. (Source: Reprintedfrom [88], withkind permissionfrom KluwerAcademicPublishers.)

depth, compared with the 45 ~ facet incidence [88]. Note that the normalized spectral peak shifts from 7.5 to 8.8/zm as the grating period increases from 2.2 to 3.2/zm. Enhancement in responsivity for these two-dimensional grating coupled QWIPs varies by a factor of 0.83.5 over the 45 ~ facet incidence, depending on the feature size, grating peak wavelength, and groove depth used. Another enhancement (E) QWIP structure developed at Lockheed Martin Vought Systems [67] utilizes diffracting resonant optical cavity in place of the optical grating. The cavity requires a relatively thin active layer to resonate at the desired wavelength [67]. By being a resonant cavity, the quantum efficiency of the E QWIP is enhanced over that of a two-dimensional grating coupled QWIP, typically by a factor of 1.5-2. The photoconductive gain of an E QWIP could be increased by a factor of 2-3 due to the thinner structure. The resonant cavity is created by etching away a portion of the active region, creating a waffle pattern, The removal of portion of the active region reduces the dark current density by a factor of 3-4. The net result of the E QWIP performance could improve the D* value by a factor of 5. This translates to a 10-15 K increase in the operating temperature for a given performance level. The disadvantage of the E QWIP is its strong wavelength dependence, which makes the multicolor and tuning of wavelength difficult to achieve. Another optical coupling scheme has been reported by Choi et al. [ 103]. They proposed a corrugated (C)QWIP structure using total internal reflection to couple the normal incident IR beam into the detectors. Similar to E QWIPs, the grating is built in the active region of the C QWIP by removing part of the active volume, resulting in reduced dark current. Compared with a 45 ~ edge coupling, a C QWIP structure has shown an increase of the background photocurrent to dark current ratio by a factor between 2.4 and 4.4, thereby increasing the BLIP temperature by 3-5 K, and increasing the D* by a factor of 2.4. Using the C QWIP structure, a 256 x 256 FPA has been demonstrated by them with N E A T of 17 mK at 63 K and 11.2/zm cutoff wavelength. A major advantage of the C QWIP is that it is wavelength independent, and hence has potential for multicolor QWIP FPAs applications.

594

QUANTUM WELL INFRARED PHOTODETECTORS

3.7. Normal Incidence Absorption in n-Type Quantum Wave Infrared Photodetectors As discussed in Section 2.3, normal incidence absorption in n-type QWIPs is forbidden due to the quantum mechanical selection rules to the first order of perturbation. However, normal incidence absorption in n-type direct gap QWIPs has been observed consistently in experiments. Peng et al. [104] and Smet et al. [105] first reported the normal incidence absorption in InGaAs/InA1As material systems. Since then, normal incidence absorption has been observed in several n-type QWIPs including InGaAs/ InA1As [42, 91], InGaAs/GaAs [43, 93], InGaAs/A1GaAs [79, 90], GaAs/A1GaAs and InGaAs/GaAs/A1GaAs [79, 106]. Experimental results of normal incidence photoresponse in strained-layer n-type QWIPs will be shown in this section. The causes of the normal incidence absorption phenomenon in n-type QWIPs can be either from the sample processing and testing conditions in which the normal incidence light could be directed to the in-plane direction, or due to intrinsic normal incidence absorption. In Ref. [95], different quantum well structures, processing procedures, and experimental conditions were used to experimentally determine the possible origin of the normal incidence absorption of the QWIP samples. Several theoretical models have also been proposed, including space-variant electron effective mass, interaction of the spin-orbit splitting states, 4-, 8-, and 16-band Kane models, and the role of higher conduction bands. Some of the theories could explain, to a certain extent, the normal incidence absorption phenomenon in n-type direct bandgap quantum well structures. However, none of these theories are able to quantitatively explain the experimental observation, particularly in the high-strain InGaAs-based QWIPs. Although normal incidence absorption is allowed in both p-type QWIPs and indirect band gap n-type QWIPs, considering the sensitivity and speed associated with the low electron effective mass and the high electron mobility in the 1-" valley of the conduction band, n-type direct gap QWIPs are more desirable for a wide variety of IR detection and imaging applications. Normal incidence n-type QWIPs without grating are especially attractive and are important for large format FPA applications. Even though large normal incidence absorption has been observed in single n-type QWIP devices, a single beam scan has also shown that the responsivity is much larger at the edge than in the center of the detector [95]. Experiments show that when the substrate is removed, the normal incidence absorption in an n-type QWIP is drastically reduced. Further studies are needed to see the feasibility of using normal incidence absorption in n-type QWIPs for FPA applications.

3.8. Performance of n-Type Quantum Well Infrared Photodetectors Unlike the responsivity spectra of intrinsic IR detectors, the spectral response of QWIPs is much narrower and much sharper due to their resonance intersubband absorption. Figure 25 shows the normalized responsivity spectra for the B-B, B-C, B-M, and BQB transition QWIPs. As shown in this figure, the spectral width for the B-B (curve 1) and B-M (curve 3, 6), BQB (curve 4) QWIPs is much narrower than that of the B-C QWIPs (curve 2, 5, 7, 8). This is due to the fact that with the bound excited state placed in the continuum states above the barrier of the quantum well of the B-C QWIP, the energy width associated with the intersubband transition becomes broader than the bound excited state in the quantum well for the B-B, B.-M, and BQB QWIPs. The spectral bandwidth of QWIPs can be made wider by using coupled wells [20], stepped wells, or using multiple stacked quantum well structures with each stack peaked at slightly different peak wavelengths [ 107]. To compare the performance of various n-QWIPs reported in the literature, Figure 26 shows the peak detectivity versus cutoff wavelength for different n-type QWIPs reported in this work and those published in the literature. The straight line is the result calculated from an empirical formula given by Levine [ 12], Dc* -- 1.1 x 106eEc/(2kT) cmV/-H-~/W

595

(3.1)

LI AND TIDROW

I ,:1~ o.~[ " l l i

9 ;

I

'/i ~

.;,,l;il ~

L::/ I ~liiY.. 0.2

\

"~, ~!t. , ,I

',

/

I

0

9

4

2

6

8

10

12

14

16

18

20

Wavelength (lxm)

Fig. 25. Normalized responsivity spectra for the B-B, B-C, B-M, and BQB QWIPs. Curve 1: DB n-QWlP; curves 2,5, 8: B-C n-QWIPs; curve 3, 6: B-M n-QWIP; curve 7: type II n-QWlP; curve 4: CSL-ptype QWlP.

1013

n-QWlPs 1012

IB-QWlP (PV), 40 K

~.

9

E IO 1 o

:) BTQB, 70 K

HS-QWIP N

o E-QWlP, 60 K HS TC-QWIP, 77 K BTM 9

~

01o

BTC

w I-. w a

~. 9 TC-QWIP BTC 50 K

10 9

10 8 3

5

7

9

11

13

15

17

19

CUTOFF WAVELENGTH (pm)

Fig. 26. Detectivity versus cutoff wavelength for n-type QWIPs described in this work and for those published in the literature.

where Ec is the cutoff energy and T = 77 K is the operating temperature. The results show that D* values for these n-QWlPs are in the range of low 101~ cmHzl/2/W in the 8 - 1 2 / z m LWIR band with operating temperatures ranging from 60 to 77 K. Currently, the most mature QWIP technology is based on the GaAs/A1GaAs multiple quantum well

596

QUANTUM WELL INFRARED PHOTODETECTORS

structures grown on GaAs substrates using the B-M and BQB transition schemes. Large format (640 • 480) QWIP FPAs have been developed from this material system [108].

4. p-TYPE QUANTUM WELL INFRARED PHOTODETECTORS p-type QWIPs offer intrinsic normal incidence intersubband absorption due to the mixing between the off-zone center (i.e., k ~- 0) heavy-hole and light-hole states in the valence bands [4, 110-114]. However, because of the large hole effective mass and the low hole mobility, especially for heavy holes, the absorption coefficient, the photoconductive gain, and the spectral responsivity of p-type QWIPs are substantially lower than those of n-type QWIPs. This maybe attributed to the fact that the optical absorption coefficient is inversely proportional to the effective mass of holes [109]. To solve these problems, p-type QWIPs using compressive- and tensile-strain in the quantum wells have been investigated [25]. A p-type tensile strained-layer (TSL) InGaAs/A1GaAs QWIP grown on InP substrate has been reported by Wang et al. [ 110]. However, problems associated with the epitaxial growth of this structure, especially with cross-hatching on the wafer surface, still need to be resolved. On the other hand, p-type QWIPs using an InGaAs/A1GaAs materials system grown on the GaAs substrate will introduce the biaxial compressive strain in the InGaAs quantum well. The compressive strain in the quantum well reduces the effective mass of heavy holes and hence increases the intersubband absorption coefficient under strain [ 111]. As a result, it improves the overall device performance, making the GaAs/InGaAs or the InGaAs/A1GaAs system grown on GaAs substrates possible for fabricating high performance p-type QWIPs. Figure 27 shows the schematic drawings of the effect of compressive- and tensile-strain on the valence and conduction band shifts as compared to the unstrained case.

4.1. Strain Layer p-Type Quantum Well Infrared Photodetectors In this subsection, we present three different strained-layer p-type QWIPs grown on semiinsulating GaAs substrates by using the MBE technique. The quantum well-barrier layer is composed of InGaAs/GaAs for the QWIP-A device. In the second device (QWIP B), the GaAs barrier layer was replaced by an A1GaAs, while the third device (QWIP C) consists of doped InGaAs quantum wells and undoped thin short-period (e.g., six-eight periods) A1GaAs/GaAs superlattice barrier layers. In all three structures, the quantum well region is under biaxial compressive strain (ranging from -0.7 to -2.8% lattice mismatch), and

I k=0

I

CB

k=0

k=O

CB

I

1

CB I

~\,/

, I I I

\.d

I I

HH

I

HH

f I

C o m p r e s s i v e Strain

i

N o Strain

S

HH I I |

LH

Tensile Strain

Fig. 27. The effect of compressive- and tensile-strain on the valence and conduction band shifts as compared to the unstrained case.

597

LI AND TIDROW

Table I. DevicePhysical, Structural, and Performance Parameters for Three Compressively Strained-Layer (CSL) p-QWlPs Device characteristic

QWlP A

QWIP B

QWIP C

Quantum well (Thickness)

In0.4Ga0.6As 4 nm

In0.2Ga0.8As 4.8 nm

In0.12Ga0.88As 9 nm

4 x 1018

2 x 1018

2 x 1018

Barrier (Thickness)

GaAs 35 nm

A10.15Ga0.85As 50 nm

GaAs/A10.35 Ga0.65As 2.7/2.0 nm (10 periods)

QW periods

20

20

20

% strain

-2.8

- 1.4

-0.8

Transition scheme

B-C

BQB

SB-M

Peak wavelengths (/zm)

8.9, 8.4, 5.5

7.4, 5.5

10.4

Cutoff wavelengths (/zm)

10, 6

8.5, 6.5

13

Spectral bandwidths

35%

30%

20%

45, 45, 13 75 K, 0.7 V

38, 8 81 K, 5 V

28 65 K, 3 V

12.5%

15.1%

6.5%

Dark current density (A/cm2) @ 77 K, 1 V

1.7 x 10-2

1.07 x 10-4

1.28 x 10-1

Detectivity (cm Hzl/2/W) (Temperature and bias)

4.0 x 109 75 K, 0.3 V

1.06 • 1010 81 K, 1.0 V

1.4 x 109 65 K, 1.0 V

Doping density (cm-3)

Peak responsivity (mA/W) (Temperature and bias) Quantum efficiency

the quantum well thickness for each well is within the critical thickness calculated for each strained-layer. The peak detection wavelength for each structure was designed for 7 1 4 / z m LWIR detection, with QWIP A having a double-hump detection peak at 8.4 and 8.9/zm, QWIP B having a detection peak at 7.5 # m , and QWIP C having a detection peak at 10.4/zm. The transition schemes for these devices are B-C for QWIP A, BQB for QWIP B, and B-M for QWIP C. Table I summarizes the material and the performance parameters for these three devices. Figure 28 shows the schematic valence band diagrams of the heavy- and light-hole subband states in the quantum well, the intersubband transition schemes, and the calculated ITs * Tsl for each device. A comparison of the calculated peak detection wavelengths and the measured results will be discussed later. Using linearly interpolated values for the heavy-hole and light-hole effective masses and the bandgaps at 77 K for the III-V semiconductor materials used in this study, we have determined the LWIR absorption peaks for each of these p-QWIPs by taking into account the effect of biaxial compressive strain in the calculation. Under these conditions, absorption peaks at ~.p = 8.2, 7.4, and 1 0 / z m were obtained for QWIP A, QWIP B, and QWIP C, respectively. All of the material and physical parameters used in the calculations can be found in [ 112, 113].

4.2. Characterization of Strain-Layer p-Type Quantum Well Infrared Photodetectors The first compressive-strained-layer p-type QWIP device (QWIP A) studied, the ground bound state, HH1, is occupied by the highly populated heavy holes. In addition to the

598

QUANTUM WELL INFRARED PHOTODETECTORS

InGaAs

GaAs :~and

QWlP-A

~and

0

20

40

60

80 100 120 140 160 180 200 InGaAs

AIGaAs .

.

.

.

.

.

.

.

.

.

.

InGaAs .

.

.

HH3

HH2 HH2 HH1

HH4

QWIP-B

0

25 50 75 100 125 150 175 200 225 250 In 12Ga.88As

HH4 & MB1

AI.3sGa.65As/-r.'~'"~:! .".."2.- ~,

a,s

I

QWlP-C

0

50

100

150

200

250

rl

.... 1""'

....

ill

300

Energy (meV)

awlP-C

Fig. 28. The calculated transmissioncoefficient and the correspondingenergylevels and the schematic energy band diagrams for three compressive strained-layer p-type QWIPs. (Source: Reprinted with permission from [25]. 9 1997IEEE.)

reduction of the hole effective mass by the compressive strain in the quantum well, the combined type I (for the heavy-hole) and type II (for the light-hole) energy band configurations (see Fig. 28) can improve the performance of this QWIP by giving rise to a quantum state coupling effect due to the resonance between the heavy-hole and the light-hole states. It is this resonantly lining up effect that makes the conducting holes behave like light holes with higher hole mobility, smaller effective mass, and a longer mean free path. Finally, the heavy-hole excited continuum states (i.e., HH3) are resonant with the GaAs barrier; which can maximize the absorption oscillator strength. The layer structure and other important material parameters such as quantum well-barrier layer composition and thickness, and the number of quantum well periods are summarized in Table I for all three devices (QWIP A, QWIP B, and QWIP C), while the schematic valence band diagrams and the bound heavyhole-light-hole state levels as well as the transition schemes and calculated transmission coefficients are shown in Figure 28 for each strained-layer p-type QWIP device studied.

599

LI AND TIDROW

In QWIP B, the transition is from the ground heavy-hole state (HH1) to the second bound excited heavy-hole state (HH3), which is slightly below the top of the quantum well. This configuration (BQB transition) along with the applied strain should maximize the intersubband absorption and the expected spectral characteristics. The QWIP-C configuration uses the step bound-to-miniband (SBM) transition scheme, from which we expect a slightly decreased responsivity but a lower dark current, when compared with the BQB QWIP or B-C QWlP. The dark I-V characteristics for each QWIP device were measured using the procedure described in Section 2. The responsivity for each QWIP was measured under normal incidence illumination as a function of temperature, applied bias, and incident IR radiation wavelength. In the QWIP B device, the noise characterization was performed using standard noise measurement procedures described previously [ 115]. 4.3. Results a n d D i s c u s s i o n

Figure 29 shows the dark current (I-V) characteristic of QWIP A as a function of the applied bias and device temperature. The I-V characteristic is asymmetrical under positive and negative bias, which is attributed to band bending due to the dopant migration effect occurring during the MBE layer growth [ 116]. For the responsivity measurements, the device was illuminated from the backside with the substrate thinned down to about 50/zm. Two dominant peaks were detected: a twin LWIR peak at ~.pl,p2 = 8.9, 8.4/zm, as shown in Figure 30a, and a MWIR peak at ~.p3 = 5.5/zm as shown in Figure 30b. Peak responsivity values of 24 and 45 mA/W for biases of 0.3 and 0.7 V, respectively, were measured at T ~< 75 K for the two LWIR peak wavelengths, and 7 and 13 mA/W for the MWIR peaks under the same conditions. The cutoff wavelength for the LWIR detection band was found to be at )~c = 10/zm, which yields a spectral bandwidth of A~./~.p = 35%. The detectivity at )~pl - 8.9/zm was determined to be 4.0 x 109 cm Hzl/2/W at Vb = 0.3 V and T -- 75 K. The spectral bandwidth of A~./~.p = 27% for the MWIR peak was determined with a cutoff wavelength of ~.c = 6/zm. Figure 31 shows the linear increase of responsivity with applied bias for the LWIR ()~pl = 8.9/zm) and MWIR ()~p = 5.5/zm) peaks. The difference in the responsivity under positive and negative bias conditions was attributed to the built-in electric field arising from the doping impurity migration effect. The linear increase in the

10.2 t

InGaAs/GAaASp.QWlP

_ b...'"-10"4

I-. z 10"6

ILl rr

o

10"8

T=77K

b,..

30 K

10"10

10"12 -2.0

-1.2

-0.4

0.4

1.2

2.0

VOLTAGE (V)

Fig. 29. DarkI-V curves for the p-type InGaAs/GaAs B-C QWIP (QWIPA) as a function of temperature. (Source: Reprinted with permission from [25]. 9 1997 IEEE.)

600

QUANTUM WELL INFRARED PHOTODETECTORS

50 (a)

p-QWIPA

'40

E

LWIR

30

0 5

6

7

14

8 9 10 11 12 WAVELENGTH (~m)

13

,

(b)

12

A

p~Wp A . -

10

/

I

\

I

8 6 4 2 0

3

4

5 6 7 WAVELENGTH (l~m)

8

Fig. 30. Peak responsivity versus wavelength for (a) LWlR and (b) MWIR detection peaks for QWIP A. (Source: Reprinted with permission from [25]. 9 1997 IEEE.)

responsivity with applied bias is attributed to the linear increase of photoconductive gain with increasing bias. From the results of the responsivity measurements, a collection quantum efficiency of r/c = 0.63% at ~.pl = 8.9 lzm, V = 0.7 V, and T = 75 K was obtained for this device. Using the approximation that the photoexcited hole travels on an average of one period before capturing (as demonstrated by the noise current gain measurements for QWIP B) and the fact that the noise current gain is equal to the photoconductive gain at moderate biases (1 V 7 V or Vb ~< --5 V. In addition, it is shown that this two-stack IB-TC QWIP can be used as a voltage-tunable IR detector for the MWIR and LWIR dual band detection. In this section we have described the multicolor detection in the MWIR and LWIR bands using the two-stack QWIPs and voltage tunable TC QWIP structures. The peak wavelengths of these QWIP devices can be tuned to the desirable wavelength by selecting

612

QUANTUM WELL INFRARED PHOTODETECTORS

the proper structural and compositional parameters in the stacked QWIPs or by varying the applied bias voltage in a TC QWIR In addition to the multicolor QWIPs described earlier, other multicolor QWIPs operating in the MWlR and LWIR bands have also been reported in the literature [122-125].

6. FOCAL PLANE ARRAYS

Large format (640 x 480) QWIP FPAs using a GaAs/A1GaAs materials system have been developed for 8 - 1 2 / x m LWIR imaging applications. With the advent of III-V material growth (MBE) and processing technologies, it is now possible to grow large and highly uniform QWIP FPAs with tunable wavelengths from 3 to 16/xm using GaAs/AlxGal_xAs grown on GaAs substrates. Currently, there is a great interest in LWIR QWIPs due to IR imaging systems that require large area, uniform FPAs for a wide variety of applications, including night vision, tracking, navigation, flight control, early warning systems, earth resources observation, astronomy, and medical diagnosis. In this section we present QWIP FPAs for LWIR imaging applications. GaAs/A1GaAs QWIP FPAs using B-C-, B-M- and BQB-transition schemes have been reported in the literature [26, 73, 75, 89, 126-129]. These QWIP FPAs have shown excellent imagery in the 8-12/xm LWIR atmospheric spectral window. Bethea et al. [73] reported a 128 x 128 GaAs/A1GaAs B-C QWIP FPA operating at an 8.5/xm peak wavelength and 65 K. This QWIP FPA, incorporating an integral grating structure for efficient optical coupling, was hybridized to the silicon CMOS MUX readout circuits in the IR imaging camera. Excellent imagery with low noise equivalent temperature difference (NETD < 10 mK) and high image contrast signal-to-noise ratio was achieved in this QWIP FPA camera. Detectivity (D*) for this QWIP is 2 x 101~ cm ~/Hz/W at 77 K, and pixel-to-pixel uniformity is 2% with 99% pixels operating. Beck et al. [75] have reported a 256 x 256 (also 512 x 512) GaAs/A1GaAs B-M QWIP FPA with NETD of 21 mK and minimum resolvable temperature (MRT) of 7 mK using an f~ 1.7 camera with excellent imagery. The peak detection wavelength for this B-M QWIP is 9.1/zm and the operating temperature is 65 K. Finally, a hand-held IR camera has been developed by Gunapala et al. [26] using a 256 x 256 GaAs/A1GaAs BQB QWIP FPA indium-bumped on Si complementary-metal-oxide-fieldeffect transistor multiplexer (CMOS MUX) readout circuits. This QWIP FPA IR camera is operating at 70 K with a 9/xm cutoff wavelength. Excellent imagery with NETD of 25 mK has been achieved in this BQB QWIP FPA camera. It is noted that 99.98% of the QWIP pixels are operable for this FPA. Figure 44 shows (a) a schematic of the hybridized QWIP FPAs indium-bumped bond on a silicon CMOS MUX and (b) 12 processed 640 x 486 QWIP FPAs formed on a 3 in GaAs wafer. A large format (640 x 486) high uniformity GaAs QWIP FPA camera with cutoff wavelength at 9/zm has also been demonstrated by Gunapala et al. [89]. This QWIP FPA was installed in a palm size hand-held camera capable of operating at a temperature as high as 70 K. This large QWIP FPA was hybridized with the silicon CMOS readout electronics for the IR imaging camera. Excellent imagery, with very low NETD and MRT has been achieved in this BQB QWIP FPA. Figure 45 shows the photo of a 640 x 486 LWIR QWIP camera, which was jointly developed by AMBER and the Jet Propulsion Laboratory (JPL) [89]. Video images were taken from this QWIP camera at a frame rate of 30 Hz at temperatures as high as 70 K using a readout integrated circuit (ROIC) capacitor with a charge capacity of 9 x 106 electrons. Figure 46 shows two frames of video images taken with this LWIR 640 x 486 QWIP camera [89]. The image in Figure 45a was taken around midnight, and it clearly showed where the cars were parked (dark shaded areas) during the daytime. This image demonstrates the high sensitivity of the QWIP FPA camera. Figure 45b shows blades of a fast turning chopper wheel. The sharp straight edges of the chopper wheel

613

LI AND TIDROW

Fig. 44. (a) Schematic of a two-dimensional QWIP FPA indium-bumped bond to Si MUX, (b) 12 640 • 486 QWIP FPAs on a 3 in GaAs wafer. (Source: Reprinted from [89], with kind permission from Kluwer Academic Publishers.)

Fig. 45. The picture of a 640 • 486 LWIR QWIP camera developed by JPL and AMBER. (Source: Reprinted from [89], with kind permission from Kluwer Academic Publishers.)

demonstrate the snap-shot m o d e of operation. It should be noted that Q W I P FPA used in the camera shown in Figure 44 was not optimized, and further improvements in Q W I P FPA structures such as adding antireflection coating and optimizing the grating structures and the ROIC design should significantly increase the Q W I P FPA operating temperature to 77 K with a 9 / z m cutoff wavelength.

614

QUANTUM WELL INFRARED PHOTODETECTORS

Fig. 46. (a) The image of cars taken around midnight which clearly shows the parked area (the dark shaded area) during the daytime, and (b) blades of a fast turning chopper wheel. (Source: Reprinted from [89], with kind permissionfrom KluwerAcademic Publishers.)

7. CONCLUSIONS In this work we have reviewed the device physics, structures, characteristics, and performance parameters for a wide variety of n- and p-type QWIPs. Using intersubband transitions and bandgap engineering, single- and multicolor QWIPs with detection wavelengths ranging from 3.4 to 16/zm have been presented in this work. A comparison of the performance parameters for both n- and p-type QWIPs reveals that n-type QWIPs have responsivity and detectivity 3-5 x higher than p-type QWIPs, when two-dimensional grating and random reflectors are used in n-type QWIPs for light coupling. However, p-type QWIPs have the advantage of intrinsic normal incidence absorption without using grating couplers, which makes it much simpler to fabricate large format FPAs. This is particularly attractive for large format and low cost FPAs applications. Multicolor QWIPs for both MWIR and LWIR bands have been developed using multistack QWIPs and voltage tunable asymmetrical coupled quantum well structures. Large format (640 x 480), high uniformity FPAs have been developed using n-type GaAs/A1GaAs B-M and BQB QWIPs for LWIR camera applications. In comparing with HgCdTe LWIR detectors, QWIPs have the advantages

615

LI AND TIDROW

of h i g h e r uniformity, h i g h e r reproducibility, and h i g h e r operability in large f o r m a t FPAs with the potential of higher yields and l o w e r costs due to the m a t u r e III-V s e m i c o n d u c t o r epitaxial g r o w t h ( M B E ) and p r o c e s s i n g t e c h n o l o g i e s . D e v e l o p m e n t of Q W I P FPAs using I n G a A s - b a s e d material systems could further e n h a n c e the p e r f o r m a n c e of Q W I P FPAs for a w i d e variety of IR applications.

Acknowledgments T h e authors t h a n k Dr. J. C. C h i a n g and Dr. J. C h u for their contributions to the Q W I P s r e p o r t e d in this work. We also thank Dr. S. B a n d a r a and Dr. S. G u n a p a l a for p r o v i d i n g s o m e of the figures and p h o t o s used in Sections 4 and 6, and Dr. H. P o l l h e n and Dr. S. K e n n e r l y for their c o m m e n t s and corrections in the manuscript.

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619

Chapter 10 NANOSCOPIC OPTICAL SENSORS AND PROBES Weihong Tan Department of Chemistry, and The UF Brain Institute, University of Florida, Gainesville, Florida, USA

Raoul Kopelman Departments of Chemistry, Physics, and Applied Physics, The University of Michigan, Ann Arbor, Michigan, USA

Contents 1.

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

622

2.

Near-Field Optics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

622

2.1. 2.2. 2.3.

622 624 625

3.

Near-Field Optics Principle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Near-Field Optics Probes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Near-Field Optics Application . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Photonanofabrication Based on Near-Field Optics

.............................

629 631

3.3.

Multiple Dye Doping and Multiple Photopolymerization Step Approach . . . . . . . . . . . . . .

4.1. 4.2.

N a n o m e t e r p H Sensors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Calcium Sensors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

633 635 636 640

4.3. 4.4. 4.5. 4.6.

Sodium Sensors (Sodium Selective Optodes) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Other Ion-Selective Sensors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Glucose Sensors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Oxygen Sensors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

642 643 644 646

4.7.

Glutamate Sensors

647

4. Miniaturized Biochemical Sensors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5.

629

3.1. Photonanofabrication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2. Doped Polymer Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

...........................................

4.8. Anion Sensors . . . . . ............. ............................ Nanosensor Application . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1. Single Embryo pH Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2. Single Cell Calcium Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3. Diffusion Induced Self-Recovery from Photobleaching . . . . . . . . ............... 5.4. The World's Smallest Devices? Optical Nanosensors Based and Entirely Cell Embedded Chemical Analysis Laboratory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Molecular Nanostructures and Supertips . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1. Nanocrystal Designer Probes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2. Polymer Matrix Supertip . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.3. Single Dendrimer Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

650 652 652 654 656 658 660 661 662 663

Summary and Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

665 666

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

666

Handbookof NanostructuredMaterialsandNanotechnology, edited by H.S. Nalwa Volume4: OpticalProperties Copyright 9 2000 by Academic Press All rights of reproduction in any form reserved.

ISBN 0-12-513764-8/$30.00

621

TAN AND KOPELMAN

1. INTRODUCTION Nanotechnology, "the manufacturing technology of the 21st century," has been the driving force for many new devices and novel applications. Potentially, it will enable us to efficiently build a broad range of complex molecular machines. The field has evolved rapidly over the past decade. In nanotechnology development, one of the most widely used techniques is scanning probe microscopy (SPM). There are many different types of SPMs, among which an optical microscope, using near-field scanning optical microscopy (NSOM), based on near-field optics (NFO), has begun to gain its recognition in several fields, including microscopy, spectroscopy, photofabrication, single-molecule detection and imaging, and biochemical sensing [1, 2]. In this chapter, we review the progress in a newly evolving nanotechnology: ultrasmall optical biochemical sensors. Near-field optics is the crucial technology for the preparation, characterization, and application of these miniaturized sensors, including the first devices smaller than 100 nm in all three dimensions. We first briefly cover NFO, then we discuss photonanofabrication and a variety of micrometer and submicrometer biochemical sensors, and then we discuss the application of these sensors in different areas.

2. NEAR-FIELD OPTICS The unique advantages of optical microscopy and spectroscopy have led to their success and wide application in many areas of science and technology. Most optical techniques involve conventional optics which are based on focusing elements such as a lens. The sample is usually positioned at a distance relatively large from the light source. In such "farfield optics," the standard rules of interference and diffraction lead to the Abb~ diffraction limit [3] on the resolution of optical microscopes. This limit is approximately ~./2, where )~ is the wavelength of light. No classical optical microscope can overcome this diffraction barrier. Electron and X-ray microscopes do not overcome it either, except that their ~. is significantly shorter. Their better absolute resolution comes, however, at the price of their use of highly ionizing radiation, which may cause severe damage to some samples. Through the years, as technological and scientific studies required finer and finer resolution, the bounds imposed by far-field diffraction pushed the optical microscope to its fundamental limits. The search for better resolution has led to the concept of near-field optics [4, 5]. NFO has enabled researchers to examine optically a variety of specimens without being limited in resolution to one-half the wavelength of light. NFO is generating considerable interest and has been applied in microscopy, spectroscopy, single molecule studies, biochemical analysis, and photonanofabrication, as discussed in the following text.

2.1. Near-Field Optics Principle NFO enables us to bypass the optical diffraction limit by utilizing a small light source which effectively focuses photons through a tiny aperture that may be as small as ~./50. The principle underlying this concept is schematically shown in Figure 1. The near-field apparatus consists of a near-field light source, with the sample in the near-field and a farfield detector. To form a subwavelength optical probe, light is directed to an opaque screen containing a small aperture. The radiation emanating through the aperture and into the region beyond the screen is first highly collimated, with dimension equal to the aperture size, which is independent of the wavelength of the light employed. The region of collimated light is known as the "near-field" region. The highly collimated emissive photons only occur in the near-field regime. To generate a high resolution image, a sample has to be placed within the near-field region of the illuminated aperture. The aperture then acts as a subwavelength sized light probe which can be used as a scanning tip to generate an image.

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Fig. 1. Schematicof near-field optics. L: Active or passive light source; O: Opaque material; S: Sample (support not shown); D: Far-fielddetection system.

That is why this optical microscopy is called near-field scanning optical microscopy. Let us take an example to illustrate the realization of the NFO concept. In a gedanken experiment, corresponding to Figure 1, we use a tiny flash lamp, say only 100 nm across. A 100 nm cover will stop the light, while a 50 nm cover will not. Imagine now a sample made of a glass plate with aluminum spots on its front surface. If we scan this plate very close to the light source, we can image spots of the size of 100 nm or larger, with an effective resolution of about 100 nm. The resolution in the "green" (with wavelength around 500 nm) is now about ~./5. Furthermore, if we use a far-infrared light source with )~ = 100 lzm (but geometrical size still 100 nm) the resolution is ~./1000, or thereabouts. As with many scientific developments, the expression of the fundamental concepts behind NFO considerably predated their successful implementation. The NFO principle has been discovered and rediscovered several times [4-8]. In the 1920s, Edward Hutchinson Synge discussed an instrument very similar to today's NSOM with Albert Einstein, and published his ideas in The PhilosophicalMagazine. His basic vision included the design of a subwavelength aperture scanned in the near field of a sample. Synge's ideas were independently rediscovered several times in the 1950s but it was not until 1972 that we saw the first experimental demonstration of near-field scanning microscopy by Ash and Nichols. They used microwaves (wavelength 3 cm) to obtain a subwavelength line scan. The photon "scanning probe technique" preceded all other scanning probe microscopies (SPM), such as scanning tunneling microscopy (STM) [9] and atomic force microscopy (AFM) [10]. However, only in the 1980s was the principle followed by optical experiments. Major advances in SPM that provide sample and probe manipulation with subnanometer precision and for three-dimensional computer imaging from a series of line scans have facilitated the development of visible NSOM. Today's NSOM has indeed borrowed some of the electromechanical and computer control scanning techniques from STM, AFM, and others. What are the major technical difficulties in NFO? One is that we need such a small subwavelength light source with enough intensity. Another is that the sample has to be scanned closely and quickly. The latter requirement is not too difficult nowadays (magnetic memories are scanned extremely quickly at even closer distances). There are other problems, such as a "feedback" mechanism to avoid physical contact and damage to the source. There are also wonderful solutions, like combined NFO and force, or combined NFO and STM operation. These further enrich the contrast mechanisms of near-field optics: refraction, reflection, polarization, luminescence, lateral force interactions, and so on. However, the first requirement of a tiny but intense and scannable light source has been

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much more challenging. NFO is realized by subwavelength optical probes. Light can be

apertured down to sizes much smaller than its wavelength, with no obvious theoretical limit until one reaches the size of an atom.

2.2. Near-Field Optics Probes Subwavelength probe development has been the key to the advances in NFO instrumentation and application. Originally, tiny nanofabricated orifices in a thin metal sheet or film were used as light sources. However, the photon throughput was very limited. In addition, a flat sheet or film (with a nanohole) can be used as a scanning probe only with completely fiat samples. This led, among others, to the idea of a glass micropipette used for intracellular measurements. Further development has led to the advent of active subwavelength light sources (fiber-optic tips and luminescent probes) [11-14]. Now glass micropipette and optical-fiber tips are both used for NFO applications, with the most frequently used being the fiber-optic tip, as shown in Figure 2. In a coated fiber-optic tip, an intense light point is seen at the tip end, as shown in Figure 3. The first step in the probe nanofabrication process is the pulling of micropipettes or fiber-optic tips of appropriate size and shape. For example, fiber tip is produced by drawing an optical fiber in the puller with appropriate heating by a CO2 laser and pulling force. The second step is the metal coating of such tips. The optical-fiber tip is coated with aluminum, by vapor deposition, to form a small aperture. A specially built high vacuum chamber is employed for coating these pulled fiber tips. Only the fiber-tip sides are coated with aluminum, leaving the end face as a transmissive aperture. Pulling such micropipettes or fibers is mostly done today with a commercial puller (such as Sutter Instrument Corp., Novato, CA, P-97 or P-2000). One can now reproducibly pull robust and efficient fiberoptic tips with orifices as small as 20 nm, optically streamlined and clean enough on the outside to facilitate metal coating. Fiber-optic tips can also be prepared by etching with chemical solutions [ 15]. There is a difference in light throughput between the pulled and the etched optical-fiber probes. Etched tips may provide 2-4 orders of magnitude higher light throughput. One of the major concerns troubling today's NFO technology is the quality of

Fig. 2. Scanningelectron microscopymicrographof a subwavelengthoptical-fiberprobe.

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Fig. 3. Microphotographof a NFO optical-fiber probe.

NFO tips. The major problems in this area are: Reproducibility, limited light throughput for probes with sizes smaller than 50 nm, and leakage of light through pinholes. Many factors affect the taper length and tip size of the pulled fiber probe [ 16], with heating power and pulling force as the most critical ones. To improve NFO technologies, there is still a great need for better optical-fiber tip quality, that is, probe size and light throughput.

2.3. Near-Field Optics Application NFO has generated considerable interest and has been successfully applied in microscopy, spectroscopy, single-molecule localization, photonanofabrication, and subwavelength optical biochemical probes and sensors [ 1, 2]. Here we summarize some of the most important achievements of NFO's applications in a few areas.

2.3.1. Near-Field Scanning Optical Microscopy NSOM belongs to the SPM family, sometimes referred to as the "children of the STM." However, the rich contrast mechanisms in optics and the ability to image a broad range of samples in a variety of environments make NSOM unique. The very same tip can be scanned over the same sample with an alternation of the contrast mechanism (for example, fluorescence and shear force), yielding images with a high degree of fidelity, as well as additional information content (this is like adding the natural color to a three-dimensional topographic map). One of the major advantages of NSOM is its ability to obtain simultaneous optical and topographic images. The optical image is obtained through the optical signal, while the topographic image is obtained through shear force. This is potentially very useful for a variety of studies where the functionality is closely linked to the sample's morphological conditions. NSOM has led to a revolution in physical science by providing optical resolution at the level of 120 A with rigid samples [17]. Very impressive biological images with about 50 nm resolution have been obtained for cytoskeletal actin and cellular protrusions [ 18] formed in the process of wound healing, as well as for blood cells (see Fig. 4) [19], DNA molecules, and photosynthetic units [20]. These images are of major interest to biology and medicine. However, images of Langmuir-Blodgett and polymeric films are also of much interest in chemistry and materials science.

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Fig. 4. NFO image of red blood cells. Left, lowerresolution image; Right, three consecutiveimages of the samecell.

2.3.2. Near-Field Scanning Optical Spectroscopy NSOS is based on near-field optical microscopy. It basically adds one more dimension, spectroscopy, to NSOM and can be used to obtain the spectrum of various nanostructures, such as subcellular organelles and quantum wells. NSOS inherits all the advantages of NSOM: its noninvasive nature, its ability to look at nonconducting and soft surfaces, and the addition of the spectral dimension. The ability to obtain spectroscopic information with a nanometer-sized resolution makes NSOS very promising for a wide variety of biomedical and chemical research. Examples include the detection of fluorescent labels on biological samples and isolating local nanometer-sized heterogeneity in microscopic samples. Using NSOS, tetracene and perylene doped in polymethylmethacrylate as well as microscopic crystals were studied, which demonstrated that nanoscopic inhomogeneity can be detected in what might at first appear to be homogeneous. In NSOS, an optical probe with an emissive aperture that is subwavelength in size is positioned so that the sample is within the near-field region. With piezoelectric control of the fiber tip, the tip can be accurately positioned over a fluorescing region of the sample and a spectrum is recorded. Excitation of the sample can be, alternatively, external with detection through the fiber tip. This means that it is not necessary for the sample to be of any particular thickness or opacity; however it should be a relatively smooth surface. The experimental apparatus for measuring fluorescence spectra with high spatial resolution is very similar to that in NSOM. The fluorescence spectra are obtained through an optical multichannel analyzer or a charge coupled device. For example, spatially resolved spectra of films of a 1.0% wt mixture of tetracene in polymethylmethacrylate are obtained [21 ]. Similar results have been obtained for microcrystals of perylene with different crystal structures [22] (shown in Fig. 5), and

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quantum wells [23, 24]. Near-field microscopy-spectroscopy provides a means to obtain optical information from a variety of samples on a nanometer scale.

2.3.3. Single-Molecule Detection and Localization Traditionally, molecular structure and dynamics have only been inferred through averaging techniques, such as X-ray crystallography, electron diffraction, and various spectroscopies. On the other hand, electron microscopy and related methods do indeed directly image single molecules but at a heavy cost to their integrity---observing them in a vacuum and/or under highly perturbative conditions. Methods such as STM and AFM come closer to the ideal but the molecules are still exposed to electric fields or contact forces. These problems are particularly acute for the soft organic-biological molecules. In addition, the observation cannot be performed in situ or in vivo, and rarely even in vitro. Furthermore, it has been impossible or nearly impossible to observe the molecular dynamics. Near-field optical microscopy and spectroscopy are new tools providing hopes for highly improved imaging at a relatively low cost to the sample. Among the most exciting advances in NFO research are studies of single molecules [25, 26]. Impressive progress has been made with NFO in single-molecule localization, spectroscopic, and photodynamic studies. Using NFO to localize and to detect single molecules has its unique advantages. Actually, there is no need for a molecular size NFO probe for single-molecule localization and detection, as is schematically shown in Figure 6. The size of the probe can be quite large compared to that of one molecule (100 nm versus 1 nm). Single-molecule localization is not single-molecule imaging. The sample is prepared with a very low surface concentration of the molecule of interest. The reason a 100 nm probe can localize one molecule (1 nm) is that there are no other molecules within this 100 nm area. Therefore, one molecule can be localized and can be detected. Very elegant observations of single molecules together with their optical spectroscopy have been performed by a variety of techniques. Individual carbocyanine dye molecules were localized with NSOM [25]. The imaging resolution is about 50 nm, and the molecular location is resolved within about 25 nm in the horizontal plane and 5 nm in the vertical direction.

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Fig. 6. Schematicof single-molecule studies by near-field optic probes.

About two dozen isolated dye molecules are imaged within minutes. Information has also been obtained on the orientation of these individual molecules. Along with single-molecule localization, studies of single-molecule spectroscopy, dynamics, photochemistry, and photophysics have also been performed by NFO. The ability to observe the optical spectrum of a single molecule or, alternatively, of molecular aggregates can afford insights into the interactions that distinguish one molecular environment from another [27]. Near-field spectroscopy of single molecules has been performed in air at room temperature. In this experiment, time-dependent emission spectra of a single molecule have been obtained. The spectra of individual molecules exhibit wavelength shifts from, and have typically smaller line widths than, those from the bulk material, as is expected because the spectral lines from the bulk material are broadened by the range of local environments of the individual molecules. This variety in wavelength, line width (and also shape and time dependence) can be understood with a model of broadening which recognizes that there is a distribution of barrier heights to the molecular arrangement, within the bulk sample. Thus individual molecular properties can be understood thoroughly. NFO has also been used to study the molecular dynamics of individual molecules dispersed on a glass surface. The fluorescence lifetimes of single molecules are measured on a nanosecond time scale, and their excited-state energy transfer to the aluminum coating of the near-field probe is characterized [28]. The feasibility of fluorescence lifetime imaging with singlemolecule sensitivity, picosecond temporal resolution, and a spatial resolving power beyond the diffraction limit has been demonstrated. NFO has opened a new avenue in singlemolecule studies. This may facilitate the manipulation of single molecules in the basic physical sciences as well as in medical diagnostics and in biotechnology. In addition, laser desorption and Raman studies have been carried out using NFO probes [15, 29]. Biological applications have also been attempted [2, 18-19, 30-32]. A novel nanotechnology, photonanofabrication, has been developed [ 13]. Nanometer biochemical probes have been prepared and have been applied in rat embryo organogenesis studies [2, 32]. Despite NFO's success in the physical sciences, the constraints of imag-

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ing biological samples prevent NSOM from being applied to living cells efficiently. The complexity and fragility of biological systems have hampered the application of NFO in biology. There remain a few difficulties, such as scanning feedback, signal collection, biological sample thickness, and cell fragility. So far NFO technology has been mainly developed for rigid solid surfaces. Most of the feedback mechanisms cannot be applied to soft biological membranes and cannot function well inside the aqueous melieu of cells. However, there are some efforts toward NFO's application in biology and it is expected that NFO's potential will be fully explored for a variety of applications [2].

3. PHOTONANOFABRICATION BASED ON NEAR-FIELD OPTICS

Nanofabrication based on conventional optics has been widely used in photolithography. However, it has not been able to produce nanometer structures and devices due to the diffraction limit. Using near field optics, we have developed a novel nanofabrication technology for the preparation of nanometer structures. 3.1. Photonanofabrication

NFO enables a revolution in nanofabrication techniques. A novel nanofabrication technique has been developed, based on NFO: photonanofabrication, a new and controllable nanofabrication technology [13]. Using the near-field optics principle, photonanofabrication controls the size of the luminescent material grown at the end of a light transmitter, such as a micropipette or optical-fiber tip, by photochemical reactions. These reactions are initiated and are driven by an appropriate wavelength of light. The luminescent material is formed (synthesized) only in the presence of light and is "bonded" only to the area where light is emitted. We notice that the key to photonanofabrication is a near-field photochemical reaction, in which the electromagnetic waves of the light source are mapped by the photochemical process. Thus the size of the luminescent probe is defined by the light emitting aperture and is independent of the wavelength of the light used to promote the chemical reaction. The photochemical reaction only occurs in the near-field region, where the photon flux and the absorption cross-section are the highest [2]. NFO has thus revolutionized nanofabrication techniques for ultrasmall nanometer devices and patterns. The NFO based nanofabrication process is shown in Figure 7. To illustrate the principle of photonanofabrication, here we describe the near-field photopolymerization process, by which submicrometer optical-fiber pH sensors have been prepared. The metal-coated fiber tip is first silanized. The silanization solution (2% v/v) is prepared by dissolving 200/zl of 3-(trimethoxysilyl)propyl methacrylate in 10 ml of H20 that was previously adjusted to pH 3.45 with HC1. The fiber ends are placed in the silanization solution for 1 h then were rinsed with deionized H20 and were placed under nitrogen for 1 h. The silanized ends are then sensitized by placing them in a solution of 2 g benzophenone in 10 ml of cyclohexane for 15 min. After silanization of the metal-coated fiber-optic tip, the photopolymerization is controlled by the light emanating from the nearfield light source. The size of the light source and the near-field evanescent photon profile control the size and the shape of the immobilized photoactive polymer. The pH sensors are prepared by incorporating a fluorescein-amine derivative, acryloylfluorescein (FLAC), into an acrylamide-methylenebis(acrylamide) copolymer that is attached covalently to a silanized fiber-tip surface by photopolymerization. The silanized tip end is positioned into a small Petri dish containing 1 ml of polymerization solution 40/zl of triethylamine on the stage of an inverted microscope. The proximal end is coupled to an air-cooled argon ion laser exciting at 488 nm. The rate and size of polymer formation is controlled by visually monitoring the distal tip through the microscope. This process enables the incorporation

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Fig. 7. Schematic of near-field nanofabrication: photonanofabrication of a nanometer biochemical sensor probe. The probe is prepared with a near-field optics controlled biochemical immobilization process. Depending on the molecules or biomolecules in the solution, different types of probes can be prepared with a variety of biochemical sensitivities.

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Fig. 8. Schematic of polymerization for optical-fiber pH sensor. This is a cross-link reaction. The dye molecules possess double bonds by derivatization.

o f p H - s e n s i t i v e d y e m o l e c u l e s covalently b o n d e d to the optical-fiber surface and the prod u c t i o n o f n a n o m e t e r b i o c h e m i c a l sensors [33]. T h e p r o c e s s is s c h e m a t i c a l l y s h o w n in F i g u r e 8.

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Fig. 9. Top: Scanning electron micrograph of a pH nanosensor probe; Bottom: Microphotograph of a NFO biochemical sensor. It is prepared by photonanofabrication. Bright tip area shows that sensing molecules are attached to the tip end surface.

The size of the polymer grown on the aperture of the optical-fiber tip is equal to or smaller than that of the aperture. By photonanofabrication, one is able to produce submicrometer structures at the end of an NFO probe, as shown in Figure 9a and b.

3.2. Doped Polymer Approach We have generalized the photonanofabrication technique by using fluorescent dye or fluorescent dextran doped polymers through photopolymerization [34]. These doped polymers have been successfully used in biochemical sensors. The new methodologies make it possible to further miniaturize optical-fiber sensors with multiple biochemical sensitivities by multiple step nanofabrication processes. In the previous photonanofabrication approach, one of the important requirements for the monomers is their polymerizability. To achieve this goal, one has to derivatize the fluorescent dye into a polymerizable one [33]. In the pH sensor preparation, fluorescein-amine, the pH sensitive dye, is derivatized into N-acryloylfluorescein-amine (FLAC) through several steps of organic synthesis, separation, and purification. The double bond in the acryloyl group of FLAC is polymerizable like the other two components in the monomer solution. However, there are many excellent chemically sensitive dyes which cannot be used in the same manner. They either do not have double bonds or it is difficult to derivatize them. In some cases, even though the dyes may be derivatized into such a polymerizable form, still the chemical sensitivities or the optical properties of the dye may vary a lot. Thus it is sometimes difficult to generalize the photonanofabrication technique and to prepare other chemical sensors with available first rate intracellular fluorophores. One approach to circumvent this problem is to use fluorophore doped polymers. The basic idea of this approach is to photopolymerize polyacrylamide gel with a fluorescent dye or a fluorescent dextran. The latter has been used for chemical sensor applications. Polyacrylamide gel results from the polymerization of an acrylamide monomer into long chains and the cross-linking of these by bifunctional compounds such as N , N 1methylenebisacrylamide (it is often abbreviated as bisacrylamide) reacting with free functional groups at chain termini, as shown in Figure 10. The pore structures of the polyacrylamide gel have been well investigated for gel electrophoresis [35]. The pore structure of the polyacrylamide gel can be controlled to be small enough so that the dye molecules or dye dextrans are not released from the polymer once trapped during the process of photopolymerization [34]. However, the pore structure is still large enough for chemical

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Fig. 10. Schematicof polymerization for optical-fiber pH sensor. This is a cross-link reaction. The dye molecules possess double bonds by derivatization.

species, such as hydrogen ions, calcium ions, and others, to enter into or exit from the copolymer freely. Thus, the equilibrium required for chemical sensing is established. This forms the basis for the use of dye doped polymers in chemical sensing. Using this technique, our groups have prepared different fluorescent dye or fluorescent dextran doped polymers and their capabilities as chemical sensors have been examined. In this doped polymer nanofabrication process, there is no modification of the dye molecules. Thus the dyes preserve and exhibit their optical properties even after being trapped inside the polyacrylamide gel. We have used different dextrans for miniaturized chemical sensor preparation. BCECFdextran, SNARL-dextran and SNARF-dextran (pH sensitive), calcium green-dextran, indodextran and fura-dextran (calcium sensitive), and ABQ-dextran (chloride ion sensitive) have all been used in doped polymer experiments. (SNARL: seminaphthofluoresceins; SNARF: seminaphthorhodafluors; BCECF: 2t,7t-bis-(2-carboxyethyl)-5-(and-6)carboxyfluorescein; ABQ: N-(4-aminobutyl)-6-methoxyquinolinium chloride.) For example, BCECF is typically used as a dual-excitation indicator, with the ratio of the emission intensity from excitations near the absorption maximum (505 nm) and the isosbestic point (439 nm) providing the pH determination. Using different molecular weight (MW) of BCECF-dextrans, miniaturized fiber-optic sensors have been prepared, with excellent pH sensitivity. By using near-field photochemical synthesis, BCECF-dextran is trapped inside the meshwork of the polyacrylamide gel. The polymeric matrix is attached to the opticalfiber tip through spatially controlled photopolymerization. Under conventional optical microscopy, the BCECF-dextran doped polyacrylamide gel pH sensor is a cone-shaped polymer formed on the top surface of an optical-fiber tip. There are two major solutions for the photopolymerization: acrylamide-bisacrylamide stock solution and the dextran solution [34]. In order to have the fight pore structure for BCECF-dextrans, 30:0.8% was chosen for acrylamide-bisacrylamide. This ratio for acrylamide-bisacrylamide may not be the best for BCECF-dextran to be trapped inside the pore structures of the polymer, but it works for the sensor preparation. Acrylamidebisacrylamide (30:0.8) stock solution is prepared by dissolving 30 g of acrylamide and 0.8 g bisacrylamide in a total volume of 100 ml phosphate buffer (pH = 6.5) solution. The solution is filtered through a Whatman No. 1 filter paper, and stored at 4 ~ in a dark bottle. For different MW BCECF-dextrans solution, 10 mg of each of these dextrans is dissolved into 20 ml distilled water. Usually 200/zl of the dextran solution is mixed with about 1 ml stock solution of acrylamide-bisacrylamide (30:0.8) for one sensor preparation. The procedures for growing the doped polymer are quite similar to what we described for photonanofabrication. We have combined photopolymerization with the use of a catalyst (ammonium persulfate aqueous solution), and thus we have controlled the dimension of the polymer formed onto the optical-fiber probe.

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The fluorescent spectra of the BCECF-dextrans in aqueous solution and in the polyacrylamide gel are very similar. The pH testing of such an optical-fiber sensor has been successful, as shown in Figure 11. It is interesting to notice that the pH sensitivity is almost the same for both forms of the BCECF-dextrans, in aqueous solution and in the polyacrylamide gel. We have not observed any visible dye leaching out of the polymer after the sensor was immersed in water overnight. The significance of this experiment is not only the demonstration of successful fabrication of a BCECF-dextran optical-fiber pH sensor, but, more importantly, the generalization of the newly developed photonanofabrication technique. It provides a means to extend the approach of near-field photochemical synthesis to other biochemically sensitive dyes. In the doped polymer approach, a polymerizable dye species is not a requirement anymore for the near-field photopolymerization process for the preparation of subwavelength optical-fiber chemical sensors.

3.3. Multiple Dye Doping and Multiple Photopolymerization Step Approach The feasibility of measuring two or more parameters with one sensor has been studied [36]. Multidye doped polymer and multistep photopolymerization have been tested with fluorescent dye doped polymers. By using a multidye solution for photochemical synthesis, we prepared multifunctional optic probes with micrometer to submicrometer size. These probes emit multiwavelength photons and thus have multiple sensitivity potentials, providing either internal calibration or the scheme to build supertip sensors based on energy transfer. There are two different ways to prepare a multidye sensor. The first is to use two or more dye molecules with polymerizable functional groups upon photochemical promotion. Thus a cross-linked copolymer is synthesized and all the dyes are covalently bonded to the surface of the light probe. The second way is to use a dye doped polymer, just as the BCECF-dextran probe, where the dyes are either bonded covalently to the probe or "trapped" inside the polymer. We used double-dye systems, such as rhodamine B (Rh B) with FLAC, or calcium green (a calcium sensitive dye from Molecular Probes, Inc.) with

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FLAC to prepare sensors and optical nanoprobes. We have obtained the spectra of a few Rh B-FLAC polymer probes prepared with different Rh B concentrations in the monomer solutions. In the emission spectra for Rh B-FLAC polymer fiber tips, it is clear that even with a very low concentration of Rh B (10 -7 M), there is still significant Rh B emission in the spectrum, as shown in Figure 12. Comparing to the pure FLAC polymer spectrum (on the left) there are always some red shifts. The higher the concentration of Rh B, the larger the red shift, and the Rh B emission becomes more and more dominant in the spectra. The disappearance of the FLAC spectral peak clearly indicates energy transfer from FLAC to rhodamine B. This demonstrated that one can incorporate two dyes into the copolymer, and thus one may be able to create multisensitivity miniaturized optical sensor probes. By using multistep photochemical synthesis, we further miniaturized optical probes to sizes much smaller than the sizes of the original light conductors. Just like in the preparation of a double-dye optic probe, they developed a multistep near-field photopolymerization to fabricate even smaller probes, shown in Figure 13. In the previously described Rh B doped FLAC polymer system, what is important is the distribution of Rh B inside the polymer at the top of the fiber tip. It is reasonable to assume that Rh B is homogeneously distributed inside the polymer, thus there is essentially no effective size reduction for the probe if Rh B fluorescence is targeted. However, performing a multistep polymerization will assure one of a size reduction in preparing the doped polymer probe. We note that usually a cone-shaped polymer on the fiber tip is obtained in the near-field photonanofabrication, which makes the miniaturization possible. A step-by-step approach has been used for the preparation of a Rh B-FLAC tip via multistep photopolymerization. In the beginning of the multistep polymerization, only FLAC monomer solution is used for near-field photopolymerization. By controlling the reaction time, one should be able to know how much polymer is grown on a fiber tip. When the polymer is grown to a certain thickness, the Rh B solution is added to the polymerization solution. The idea is to keep the disturbance of the polymerization process to a minimum, and then the polymerization process on the fiber tip is continued as usual. Thus one obtains a polymer tip with Rh B only at the cone-shaped polymer tip. In multistep photochemical synthesis, the location of the active center is controlled to be only at the very tip of the probe. The principle for miniaturization of doped polymer probes by a multistep nanofabrication process has been successfully demonstrated. The ultimate goal of our

634

NANOSCOPIC OPTICAL SENSORS AND PROBES

Fig. 13. Schematicof multistep photonanofabrication with rhodamine B and FLAC.

photonanofabrication technique is to produce optical sensor probes with molecular size for NSOM by controllable molecular engineering. Indeed, a single-molecule light source based on a near-field optical nanoprobe has been prepared and characterized [ 14]. A single carbocyanine dye C18 (DiI) molecule is immobilized on a near-field optical-fiber probe. Photobleaching of the single DiI molecule on the probe occurs as a discrete and total extinction of its fluorescence. The single-molecule light sources are the first step in an effort to developing a variety of single-molecule sensors and probes for single-molecule optical microscopy and single-molecule interaction studies with extremely high spatial resolution and sensitivity.

4. MINIATURIZED BIOCHEMICAL SENSORS Photonanofabrication produces nanometer-sized optical probes with or without a specific biochemical sensitivity. Probes with a specific chemical sensitivity are nanometer optochemical sensors. For the fabrication of the nanometer sensor, the polymerization reaction temperature, polymerization time, and laser power had to be optimized in order to grow nanometer-sized polymers on the activated fiber-tip surfaces. The reduced size of the light sources, together with the near-field enhanced molecular excitation cross-section and the good spectral and time resolution have enabled the development of rugged, ultrasmall, ultrasensitive, and ultrafast fiber-optic biochemical sensors. The size of the sensors ranges between 50 nm to a few micrometers, and no mechanical confinement is used. Thus the analytes have immediate access to the dye on the sensor tip. This gives the NFO sensors the shortest response times among any reported optical-fiber sensors. These nanometer intracellular sensors require only attoliters (10 -18 1) of sample, zeptomoles (10 -21 mole) of unknown and milliseconds or microseconds of response times. The sensing occurs in the near-field regime of the optical excitation, thus highly increasing the sensitivity per photon and per sensor molecule. This has decreased the volume needed for (nondestructive) analysis. Since the initial pH sensor research in 1992, many different optical sensors have been successfully prepared for direct, real-time chemical analysis of intracellular processes and other studies. These sensors monitor pH, calcium, sodium, potassium, chloride, oxygen, and glucose [13, 33, 34, 37-41]. In the following, we will discuss the preparation and the characterization of these sensors.

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TAN AND KOPELMAN

Even smaller probes, so-called probes encapsulated by biologically localized embedding (PEBBLE) optochemical sensors, have been developed [42]. These fiberless probes have all their dimensions in the nanoscale range and typically are spheres with a radius of 100 nm. The major reason for their development has been their application to biological samples, such as single mammalian cells. The name PEBBLE stands for "probes encapsulated by biologically localized embedding," referring to the "biologically localized" method of "shooting" the probes into the cell with a "gene gun," that is, a particle delivery system usually used for the "dry" insertion into viable cells of DNA molecules. It is also possible to insert PEBBLEs into a cell by "wet" methods, that is, with a "pico-injector"-a syringelike microsystem. The disadvantage of the latter method is the additional inclusion into the cell of a liquid solution (in contrast to the helium gas that carries the PEBBLEs in the biolistic approach). Alternatively, PEBBLE type probes have been manipulated with "laser tweezers" and there exist other potential methods for steering them inside cells.

4.1. Nanometer pH Sensors

4.1.1. Subwavelength pH Sensors Nanometer pH sensors have been prepared with different dye molecules [13, 34, 39]. As shown in Figure 9, the pH probes have subwavelength dimension. The bright point of light at the end of the fiber probe in Figure 9b is the fluorescence from the fluorescent dye embedded in the copolymer covalently bonded to the activated fiber surface. Nanometer pH sensor preparation needs careful design of the preparation procedures. Here we briefly describe the detailed experimental procedures by which an optical pH sensor was prepared. Into a small vial was placed 1 ml of catalyst prepared by mixing 0.4 g of potassium persulfate in 10 ml of H20. Then, 70 ml of the monomer solution were added. The sensitized end of the optical-fiber was placed in contact with the monomer solution. This assures size control of the formed polymer. A 30 mW laser beam at 488 nm was coupled into the opposite end of the optical fiber via a microscope objective with a 0.25 numerical aperture which initiated the polymerization. This polymerization was allowed to continue for 12 min. The sensors were rinsed in deionized water then placed in a neutral pH phosphate buffer prior to use.

4.1.2. pH Measurements Inside Membrane holes [33] To demonstrate the resolution of the subwavelength optical sensors, the submicrometer pH sensors were tested using "nucleopore" porous polycarbonate membranes. The samples are similar to biological cells in size and shape. The different hole sizes available in these membranes [43] range from 0.02 to 20/zm, and the hole depths are about 6 / z m for a 10/xm hole membrane, deep enough to hold pH buffer solutions inside. Before testing, the membranes were first immersed inside a pH buffer solution, then taken out and put on the microscope viewing stage where the sensor was aligned with a specific hole using the microscope. By driving a Z translational stage, the sensor could be inserted into one of the holes. The position of the sensor could be controlled easily. The sizes of the membrane pores used in our experiments were from 2 to 10/zm. Eight different buffers were used in the pH tests of the submicrometer pH sensors in the experiments. Measurements were cycled several times from pH 4 to 9 and then back to 4. The data of photon counts shown in Figure 14 are the averages of a few measurements in different cycles.

4.1.3. Photostability and Sensor Sensitivity The nanometer pH sensors have good photostability and excellent detection sensitivity. We tested these properties with different pH buffer solutions. The results at each pH measurement in the preceding membrane experiment were always slightly lower than the previous

636

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one because there was some photobleaching of the dye inside the copolymer. We note that with the highest intensity (up to about 103 W/cm2), the sensor output drops about 10% after 40 min of continuous excitation. Routinely one can easily work with 5% of this power, so that the photobleaching becomes much less significant. Thus, the bleaching is practically imperceptible at the lower laser power operating conditions. The reversibility of the submicrometer pH sensor is good. The history, that is, the order of how data are taken, does not affect the fluorescence intensity for a specific pH buffer solution. This greatly enhances its ability in dealing with biological cells where an abrupt change often happens (i.e., upon cell death) and in applications as scanning tips. The submicrometer pH sensor has a low detection limit. We notice that the smallest volume that gave definite pH measurements had less than 3000 hydrogen ions (at pH = 8) [33].

4.1.4. Sensor Response Times The nanometer sensors have extremely short response times. Response times of the opticalfiber pH sensors have been determined by a microscope-based sensor apparatus. Accordingly 10 ms were used as the data acquisition time with a photon counter. The submicrometer pH sensor has a response time shorter than 50 ms, as shown in Figure 15.

4.1.5. p H Sensor Based on Ratiometric Measurements Aiming at enhancing the working ability of the miniaturized optical-fiber sensors, new internal calibration methods have been developed to quantify pH [13]. Their method is based on the fluorescence intensity ratio at different wavelengths of the same emission spectrum for a single dye. It is highly effective for small-sized sensors, especially when the dye species absorption differences are also utilized. Because various ratios can be obtained by selecting the intensities at different wavelengths of the same spectrum, this approach gives more than a double check for a single experiment. The change in the ratio per pH unit can be increased up to 10x if two different excitation sources are used, as shown in Figure 16. Thus it greatly enhances the sensitivity and the accuracy of the measurements and greatly improves the working ability of these miniaturized sensors in a variety of sampies. The internal calibration methods developed here have helped our efforts in fabricating nanometer-sized optical-fiber biochemical sensors. To a certain degree, these methods minimize the effects of the photobleaching of the sensor molecules and of geometric changes

637

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and of other parameters in using the nanometer pH sensors. Errors introduced by leaching, quenching, and excitation source fluctuations are thus minimized.

4.1.6. NanometerpH Sensors Based on Other Dye Molecules [34, 39, 441 Miniaturized pH sensors have been prepared with other dye molecules, such as B C E C F dye [34] and 5-(and-6)-carboxynaphthofluorescein (CNF) [39]. For example, a fast and durable ratiometric pH micro-optode that is highly accurate, precise, sensitive, reversible, and reproducible over the physiological ranges of pH, ionic strength, and temperature has been developed with CNF [39]. The sensing site consists of CNF entrapped in a polyacrylamide gel matrix via photopolymerization at the silanized end of either a pulled or

638

NANOSCOPIC OPTICAL SENSORS AND PROBES

unpulled optical fiber. The fabricated sensor was air-dried and was stored in air, buffer, or water. The optode's precision for the pH 6.3-8.4 range in rat embryos, sera, or physiological (Earle's and Tyrode's) buffers was found to be better than +0.03 pH units. The pulled and unpulled optodes have respective upper limit response times of 1 and 400 ms for 1 pH unit change. Over a 7-week period, they retain sensitivity for 600 and 10,000 measurements, respectively. Ratiometric measurements are made using a pH-sensitive emission peak on each side of an isosbestic point. The results show that it is possible to make precise pH measurements using dual-emission wavelength ratios even when photobleaching causes drastic reductions in emission intensity. The ratiometric method gives the optode stability, reproducibility, and durability, which are indispensable for practical applications. An unpulled CNF optode has a response time of 200-400 ms and a long operating lifetime in both real time (months) and the number of measurements (~> 10,000). The CNF dual-emission optode correlates with a pH electrode extremely well over the physiological regions of pH, ionic strength and temperature. The CNF optode is most suitable for biological applications because of its essentially linear response over the pH 7-8 range, high sensitivity (slope about 2), and its almost perfect correlation with a pH macro-electrode.

4.1.7. PEBBLE pH Sensors PEBBLE sensors based on the CNF indicator dye and the polyacrylamide gel matrix were also prepared by photopolymerization, or alternatively by reverse micelle polymerization [42]. The photopolymerization method can be carried out by ordinary far-field illumination of the solution (with no fiber inserted). The resulting polymer nuggets are then ground with a mortar and pestle. Occasionally glass beads are added to improve on the grinding procedure, that is, to obtain a finer powder. Particle sizes range from 20/zm to submicrometer, depending on the procedure, with a broad size distribution. An example of a calibration curve is given in Figure 17. The result is quite similar to that from the analog fiber-tip sensor discussed earlier. Submicrometer pH and other PEBBLE sensors, prepared by reverse micelle polymerization, are discussed in the following text.

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639

TAN AND KOPELMAN

4.2. Calcium Sensors

4.2.1. Covalently Bound Indicator Sensor [38] The important role that calcium ions (Ca 2+) play in biological systems cannot be overemphasized. Many physiological processes are triggered, regulated, or influenced by Ca 2+. A new optical sensor based on covalent immobilization of a newly synthesized calciumselective, long-wavelength, fluorescent indicator has been constructed, with a response dynamic range optimal for physiological measurements [38]. Immobilization occurs via photopolymerization of the indicator with acrylamide on the distal end of a silanized optical-fiber probe. The working lifetime of this sensor is limited only by photobleaching of the indicator. Due to the inherent hydrophilic nature of the acrylamide polymer, the response time of this new sensor is governed by simple aqueous diffusion of the Ca 2+. This results in sensor response times fast enough to monitor concentration fluctuations at physiological rates. The ability to monitor Ca 2+ concentration fluctuations in a high background level of magnesium was also demonstrated with a calculated selectivity of 10 -4"5. The fiber tips were pretreated the same way as that in the preparation of a pH sensor. Calcium green was derivatized to contain an amine group as shown in Figure 18. The 51-amino-calcium green tetramethyl ester-diacetate molecule prepared was further derivatized using a procedure analogous to that of the pH sensor for derivatizing fluorescein. The result of this derivatization was conversion of the added amine functionality to an amide with an extending vinyl group. The vinyl group is necessary to covalently link the fluorescent indicator to the acrylamide polymer through free radical polymerization. The copolymer solution was then prepared as described for the pH sensor, with a slight modification to accommodate the special solubility requirements of the aminated form of calcium green. Then 5 ml of a 1:1:1 mixture (by volume) of THE ethanol, and H20 were added to the vial containing the calcium green monomer. To this solution were added 0.376 g acrylamide and 0.086 g N,N1-methylenebisacrylamide. The newly synthesized calcium green was then treated in the same manner as that applied in the fabrication of the pH sensor. The fluorescent calcium green derivatized polymer material, immobilized on the end of the optical fiber, was excited by an Ar + laser lasing at 488 nm. The laser light was coupled into the optical fiber to excite the dye bound polymer. During each measurement, the fluorescent material was illuminated for approximately 0.1 s. The sensor was placed in a small vial with approximately 2 ml total volume with an optically clear bottom directly above

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the objective of the microscope. The position of the sensor was optimized to achieve the highest possible throughput of fluorescence to the detector prior to the measurement. The position was then held constant. The solution in the vial was changed after each measurement. The sensor was allowed to equilibrate for 2 min in the new solution prior to the next measurement. All of the measurements were done at pH 7.2. The fluorescence spectra of the calcium sensor in various concentrations of free calcium show an excellent response to calcium changes. The increase in fluorescence produced by increasing the concentration from zero free calcium to 38 nM is clearly resolved and has a good signal to noise ratio. To further show the potential utility of this sensor in biological samples, the sensor's calcium response was measured with a physiological background level of magnesium (1 mM). In Figure 19, the spectra of this set of experiments are shown. The ability to distinctly monitor a small change in free calcium concentration, zero free Ca 2+ to 38 nM, with such a high background of ionic magnesium indicates that this sensor should have adequate selectivity for most intraceilular applications. The detection limit of this sensor for Ca 2+ in a 1 mM magnesium background was slightly higher (31 nM free calcium). The values for the activity of calcium, aca2+, at the detection limit in the presence of a constant background activity of magnesium, aMg2+, are used in calculating the selectivity. We find that, based on the following equation, 3 . 1 . 1 0 .8 M aca2+ = -4.5 log Kfa2+ ' Mg2+ = log Zca2+/zMg2+ = log 1.10-3M aMg2+ the selectivity for calcium over magnesium is thus 10 -4"5. As a measure of the working lifetime of the sensor, fluorescence photobleaching measurements were carried out. The data indicate that the working lifetime of the calcium sensor should be more than 3 x that of the similarly constructed pH sensor. The advantages of this device over similar optical calcium sensors include: (1) a linear response in the physiological range of calcium found in most biological cells; (2) the sensor responds

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641

TAN AND KOPELMAN

at a physiological pH of 7.2; and, (3) it has good selectivity against magnesium, permitting measurements under normal physiological concentrations (1-5 mM Mg2+). 4.2.2. Doped Indicator Calcium Sensors The major problem with the foregoing sensor is the need for overall intensity measurements (rather than ratios). Therefore, different designs of nanosensors have been tried out, such as adding an indicator dye (e.g., Texas red) for calibration purposes. This work is based on the simple approach of doping dyes into a hydrophillic matrix, that is, acrylamide. Alternatively, the "calibration dye" could also be an indicator dye. Specifically, SNARF or CNF have been used. The isosbestic point of the pH indicator serves as a fixed calibration point. The main problem lies in the partial overlap of the spectral emissions of these dyes. It is also helpful if the depletion rate of the two dyes (combining photobleaching and leaching) are similar, so that the measured intensity ratio is valid over time (this problem does not exist with the tautomer intensity ratio measurements for the pH indicators, as there is an equilibrium between them, compensating for any differential leaching or bleaching of one tautomer over the other). 4.2.3. PEBBLE Calcium Sensors Due to the similarity between doped gel pH sensors and doped gel calcium sensors, calcium PEBBLE sensors can be prepared in much the same way. This has indeed been demonstrated [42]. Micrometer and submicrometer calcium sensors have been prepared using calcium green, calcium orange, or calcium crimson [42] as the dyes embedded into the matrix.

4.3. Sodium Sensors (Sodium Selective Optodes) It is convenient to make use of ionophores already developed for use in ion-selective electrodes for optical sensors. Ion-selective micro-electrodes have been developed which can reliably measure several of the most interesting electrolytes in intracellular media including potassium, calcium, magnesium, and hydrogen ions. However, the measurement of intracellular levels of sodium (5-18 mM Na +) has remained a challenge to analytical chemists considering the high level of potassium (80-160 mM K +) and the absence of an ionophore with sufficient selectivity toward sodium. An ultrasmall fluorescent fiberoptic sodium sensor was constructed [37] based on a highly sodium-selective, crown-ether capped calix[4]arene ionophore. Three optode membrane configurations have been developed, employing different lipophilic, fluorescent pH chromo-ionophores (Nile blue derivatives), demonstrating the ability to improve the detection limit and to tune the dynamic range to the desired region of interest. Two of the membrane configurations are of special interest in that their working ranges lie within those desired for measuring intracellular cytosolic or blood levels of sodium at the respective physiological pH. These membranes also have excellent selectivity toward potassium, calcium, and magnesium. The three membrane configurations use three versatile fluorescent signal transduction mechanisms based on intensity, intensity ratios, or energy transfer (inner filter) effects. These optodes measure the sample's sodium activity, rather than the concentration, provided that the sample's pH is measured simultaneously by another sensor, such as a glass electrode. The sensing principle of the sodium sensor is based on the optode response mechanisms developed by Morf et al. [45, 46] and later expatiated on extensively by Simon and co-workers [47]. Two liquid phases, one hydrophobic and one hydrophilic, define the system. The hydrophilic, or aqueous phase, is the sample. The hydrophobic, or organic phase, which is approximately one-third polymer and two-thirds plasticizer by weight, retain the various components: lipophilic ion-selective ionophores; pH-sensitive chromo-ionophores;

642

NANOSCOPIC OPTICAL SENSORS AND PROBES

and, in many cases, inert lipophilic anions and/or sensitizing dyes. Predefined concentrations of these components determine the response of the optode. The lipophilic anionic sites (tetraphenyl-borates) require a counterion for electroneutrality reasons. The nature and concentration of this counterion are given by a competitive ion-exchange equilibrium where both the ionophore and the chromo-ionophore compete for the ions for which they have complexation selectivity. The following equation shows the relevant ion-exchange equilibrium, + q- L(org) + nt- CH(org) + + R(org) + ~ R;rg) + C(org) nt- LI(org + ) q- H (aq) + l(aq)

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The metal ion activity ai+ is a function of the hydrogen ion activity all+ and a number of constants including: [Ltot], the total ionophore concentration; [Ctot], the total chromoionophore concentration; and [R~ot], the total liphophilic charge site concentration. The equilibrium constant Kexch associated with Eq. (1) is the product of the ion-extraction coefficient, the ion to ionophore stability constant and the acidity, or pKa, of the chromoionophore species. Replacing the chromo-ionophore with another whose p Ka differs directly changes the overall membrane exchange constant. The effect is to shift both the range of sensitivity and the detection limit while retaining the selectivity. This leads to a highly versatile sensing methodology. There are three fundamental considerations when selecting chromo-ionophores for use in a fluorescence based optode: 1. the acidity or basicity, that is, the pKa; 2. the brightness of the fluorescent signal produced; and 3. the relative change in the signal brought on by altering the pH of the solution in contact with the indicator. An important function of the chromo-ionophore is its ability to vary, in a controlled fashion, the detection limit and the dynamic range of the optode. Figure 20 is a plot of the response functions of the three optodes developed for use here, each with the 1,3-bridged calix[4]crown derivative but with a different chromo-ionophore. As is shown in Figure 20, these shifts are predicted from theory and they demonstrate the versatility of such optodes as sensors. It is important to point out that no analogous detection or range extension mechanisms exist for ion-selective electrodes. It is also important to note the co-dependance of the response on pH. Hydrogen ion activity measurements must be carded out in buffered solutions or the pH must be simultaneously monitored in order to achieve accurate determinations. The sodium optode is reproducible and has short response times. The preparation of the optode is extremely simple. The optical-fiber or optical-fiber tip is dipped into the solution "cocktail" for 89s or less. Regular fibers get thus covered with 12/zm films. Pulled fiber tips end up with submicron size films, down to about 100 nm [37]. 4.4. Other Ion-Selective Sensors

The principle underlying the previously described sodium selective optode has been generalized to other ions, both cations and anions [47]. The only significant difference is in

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replacing the sodium selective ionophore with a potassium, or chloride, or nitrite selective ionophore. Obviously, the specific value of the pertinent equilibrium constants affect the optimal composition of the cocktail. The thermodynamic framework works extremely well (ibid.) in contrast to the often "non-Nernstion" curves describing electrochemical sensors such as ion-selective electrodes. Keeping the same polymeric matrix (PVC) throughout, all these optochemical sensors have essentially the same "mechanochemical" behavior and therefore have similar film thickness and dimensions (with given fibers or fiber tips). In addition, they also share the universal fluorescent chromo-ionophores (fluorescent pH indicators) and thus have similar behaviors regarding the spectral distribution, quantum efficiency, photobleaching probability, and leaching coefficients. Only the nonuniversal ion-specific ionophores differ in their selectivity and leaching coefficients. Some anion sensors are described in greater detail in Section 4.8.

4.5. Glucose Sensors The development of glucose sensors displaying high sensitivity, fast response, reproducibility, and long term stability has been a main target in sensor research during the last three decades. Amperometric glucose sensors were developed in the early 1960s [48] and they continue to receive considerable attention [49]. Much effort is devoted to the development of new and improved amperometric glucose sensors that continuously monitor physiological levels of glucose in blood over an extended period of time [50]. An interesting direction is the development of needle type amperometric glucose sensors that are suitable for long term implantation in diabetes patients. A micrometer sized fiber-optic fluorescence biosensor for glucose has been fabricated [40]. The sensor is 100• smaller than previous glucose optodes. It is based on the enzymatic reaction of glucose oxidase that catalyses the oxidation of glucose to gluconic acid and hydrogen peroxide while consuming oxygen. Tris(1,10 phenanthroline) ruthenium chloride, an oxygen indicator, is used as a transducer. The common glucose sensing scheme involves the employment of glucose oxidase which catalyzes the oxidation of glu-

644

NANOSCOPIC OPTICAL SENSORS AND PROBES

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The measurement of the reduced oxygen level or the reduced pH when glucose is oxidized by the enzyme, serves as an indirect indication of the glucose concentration. In preparing the sensor preparation, ruthenium complex and glucose oxidase are incorporated into an acrylamide polymer that is attached covalently to a silanized optical-fiber-tip surface by photocontrolled polymerization. Leaching of dye and enzyme molecules from the polymeric matrix is minimized due to electrostatic interactions with charged residues in the polymer, and due to the relative insolubility of the ruthenium dye molecules in water. The oxygen indicator serves as a transducer for the rate at which oxygen is consumed during the enzymatic oxidation. Hence, the response of the sensor is the result of a dynamic balance between the diffusion of glucose and oxygen into the sensor, and the consumption of oxygen in the reaction, resulting in a steady-state decreased oxygen level and consequently, an increase in fluorescence. As with oxygen sensors we find that the maximum response of our glucose sensors is realized when the solution used for polymerization contains 35 % acrylamide monomer, 5% cross-linker N,N-methylene-bis-acrylamide, and 5 • 10 -4 M tris(1,10 phenanthroline) ruthenium chloride. The additional parameter--glucose oxidase concentration in the polymerization mixture--is optimized to achieve a maximum response to glucose. A study of the dependence of the fluorescence intensity on sensor size shows that under normal operating conditions the signal decreases with the sensor diameter rather than its volume [40]. Also, the response of micrometer sized sensors is improved by about 20% compared to that of larger fiber-optic glucose sensors. Due to its small size and the lack of membrane support the response time of the sensor is only 2 s. An absolute detection limit of around 1 x 1015 mol is achieved. The miniaturized glucose sensor is at least 25 • faster and its absolute sensitivity is 5-6 orders of magnitude higher than that of previous glucose optodes. The response of the fiber-optic fluorescence sensors for glucose is seen in Figure 21. The enhancement in the sensor response of small sensors partly negates the loss in fluorescence signal resulting from the sensor miniaturization, a most welcome effect. 1

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10

TAN AND KOPELMAN

A strong pH dependence of an enzyme activity is a common phenomena. We find that the maximum activity of glucose oxidase in solution is at pH 5.5. When the enzyme is immobilized at the end of a 100/zm glucose optode the maximum activity is observed at pH 7.5. Both of these observations are in agreement with previous studies. The lifetime of sensors, especially those employing bioactive materials such as enzymes or antibodies is a major concern. Under the appropriate storage conditions a typical lifetime of the biosensor is only 4-6 days. A degradation in the sensor's response is observed after a week of intensive use. The relatively short lifetime of this sensor is attributed to a possible leaching of dye molecules from the polymeric support as well as to a degradation in the enzymatic activity. Leaching of the ruthenium dye molecules from the polymeric matrix is minimized by optimizing the ratio between the concentration of the acrylamide monomer and the cross-linking reagent. This microsensor can be used for the measurements of glucose levels in the range of 1-10 mM with at least 25 • faster response time compared to larger fiber-optic fuorescence sensors.

4.6. Oxygen Sensors The determination of molecular oxygen levels in solution is of great importance in environmental, biomedical as well as in industrial analysis. The development of in situ and real time measurements using on-line fiber-optics systems is a possible alternative to the current environmental monitoring systems. Using the photonanofabrication technology, a submicron optical-fiber oxygen sensor has been fabricated [41 ]. The sensor is based on the fluorescence quenching of tris(1,10 phenanthroline) Ru(II) chloride in the presence of oxygen or dissolved oxygen. The Ru compound has been incorporated into an acrylamide polymer that is attached covalently to a silanized optical-fiber-tip surface by photo-initiated polymerization. The sensor is 100• smaller than other oxygen optodes. Due to its small size and the lack of membrane support the response time of the sensor is in the subseconds regime. The sensor is fully reversible and no difference between the response time and the recovery time could be observed. The sample volume required for measurements is 0.1 pl. An absolute detection limit of 1 x 10 -18 mol is achieved. This is an improvement by a factor of 106 compared to larger optical-fiber oxygen sensors [41 ]. The fabrication of a working submicron optical-fiber oxygen sensor based on Ru compounds is more difficult relative to the submicron optical-fiber pH sensors. That is because the quantum efficiency of tris(1,10 phenanthroline) Ru(II) chloride is 10x lower than the quantum efficiency of fluorescein-amine or other fluorescein derivatives The photostability of the Ru compounds is higher than that of fluorescein-amine and it is less subject to photobleaching or other photodegradation processes. The analytical range of an oxygen optode is governed by the respective quenching curve and the Stern-Volmer constant. The variation in the fluorescence intensity as a function of the dissolved oxygen concentration is given by the Stern-Volmer equation, I o / I c - 1 + Ksv [02]

(4)

where I0 is the fluorescence intensity of the sensor dipped into a nitrogen saturated solution, Ic is the fluorescence intensity of the sensor in a given dissolved oxygen concentration, and Ksv is the Stem-Volmer constant. In principle, higher quenching constants result in a better accuracy at a low level of oxygen because of a larger relative signal change per oxygen concentration interval. However, high quenching constants result in a limited linear dynamic range. The design of the sensor was for the detection of low oxygen levels in water solution (0-15 ppm). The fluorescence spectra obtained from a 0.8/zm opticalfiber oxygen sensor at different dissolved oxygen concentrations are shown in Figure 22. It can be seen that the relative change in fluorescence between 7.5 and 15 ppm dissolved oxygen (air saturated solution--i.e., 0.25 mM) is comparable with the change in fluorescence between 15-75 ppm dissolved oxygen (oxygen saturated solution). The sensitivity

646

NANOSCOPIC OPTICAL SENSORS AND PROBES 2000

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factor, I (N2)/I ( 0 2 ) - - 3.2, is comparable with other oxygen optodes using organic polymer matrices [41]. A Stern-Volmer analysis of the submicron optical-fiber oxygen sensor results in a Ksv of 5420 M -1, with a correlation coefficient of 0.997 between 0 and 20 ppm dissolved oxygen. The accuracy of the oxygen optode is governed by the uncertainties in the determination of I0 (nitrogen saturated solution), Ksv and Ic. A precise determination of I0 is essential for obtaining a sufficiently precise calibration curve and a Ksv value. The accuracy of the sensor is demonstrated in Figure 22, where Ic is shown for different oxygen levels. The sensor is fully reversible. The limit of detection of the sensor is around 0.75 ppm dissolved oxygen. This is comparable with other oxygen optodes that are 15100-fold larger. It should be noted that a sudden change in the oxygen level is not easily achieved experimentally. Based on measurements in gas phase, the response time was estimated to be shorter than 1 s. Due to its small size the recovery time of the sensor is almost equal to its response time. Obviously, there may be a difference between the response time and the recovery time which cannot be observed under the experimental conditions.

4.7. Glutamate Sensors

In addition to the previous photonanofabrication method for nanometer sensors, direct covalent immobilization techniques have also been developed for biomolecule sensors. A variety of biomolecules (enzymes, antibody, antigen, proteins, and DNA) can be immobilized onto solid supports for the study of biomolecule interactions [51 ]. These solid supported biomolecules have proven to be useful for many biological studies. However, these solid supports cannot be used to study biological processes at the subcellular level. The NFO probes should easily allow preparation techniques for biomolecule probes sufficiently small for studies in nanoscopic regions. Photonanofabrication is one such preparation technique for ultrasmall biochemical sensors. However, to have biomolecules covalently bonded to a NFO tip, special functional groups, such as vinyl monomer, are required. We have generalized the immobilization technique for most biomolecules by creating a procedure applicable to the synthesis of various nanometer biomolecule probes. New immobilization procedures, including tip silanization, conjugation, and chemical binding of these compounds, are being created to coordinate the NFO tip's characteristics with the specific properties of biological compounds. As shown in Figure 23, biomolecules with free amine functional groups can be immobilized to NFO probes, thus preparing NFO

647

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Fig. 23.

Immobilization of enzyme molecules on NFO fiber probe. A: GDH; B" GDH and LDH.

NANOSCOPIC OPTICAL SENSORS AND PROBES

biosensors. These sensors operate by detecting distinct changes in optical properties of the specific biomolecules adhered to the tips. Using this method, a nanometer glutamate dehydrogenase (GDH) probe has been prepared and has been used to detect glutamate (Glu) down to 0.2/zM [52]. By covalent bonding, GDH enzymes can be immobilized on a fiber-tip surface. The fiber is first silanized with trimethylacylpropyldiethylenetriamine to cover the tip with amine groups. As amines are found in most enzymes as well as in other biomolecules, it is then necessary to incorporate a homobifunctional cross-linker as a conjugate reagent between the enzyme molecules and the amine groups on the fiber-tip surface. Therefore, the carboxyl group will conjugate to the amino acid side chains of the enzyme. Using this approach, we have successfully immobilized GDH on optical-fiber probes. The probes' enzymatic activities have been tested and have been found to be steady after being washed more than 20 • with phosphate buffer. This indicates that GDH molecules are indeed covalently immobilized on the optical-fiber probe surface and can be used as biosensors. Further miniaturization of GDH probes to approximately 100 nm will increase the probe's sensitivity and the ability to work with minute biological samples. GDH has been used to detect Glu efficiently. The principle is to detect the fluorescence of NADH which is produced by a GDH catalyzed reaction involving Glu and NAD +. As shown in Figure 24, the GDH probe has been used to detect Glu in the sub-/zM concentration range (0.2/zM). The GDH probe is inserted into a small sample vial containing a pH 8.0 phosphate buffer of 1 mM NAD + and Glu. NADH produced by the reaction catalyzed by GDH immobilized on the fiber probe is excited by light emanating from the same probe. This greatly enhances the detection efficiency of NADH. The GDH probe is highly selective in detecting Glu due to the specificity of the GDH enzymatic reaction.

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649

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TAN AND KOPELMAN

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The optimization of the immobilization procedures will enable achievement of better Glu sensitivity (down to nM). The miniaturization of Glu sensor has resulted in fast response times. As shown in Figure 25, these GDH probes have less than 50 ms response times.

4.8. A n i o n S e n s o r s

As mentioned, nanosensors can also be prepared for anions, and, in particular, ion-correlation-based sensors. These optodes utilize standard ion-selective electrode ionophores with universal pH chromo-ionophores that have been selected for their fluorescence efficiency, photostability, and pKa based tenability of the optimal activity range. The miniaturization of the photo-excitation zone enhances the optode lifetime, due to fast diffusion of unbleached chromo-ionophores into this zone. Specifically, we provide here examples of charged and neutral-carrier ionophore based fluorescent optodes, one highly selective for nitrite and the other selective for thiocyanate. The dynamic range of the nitrite-selective optode is tunable. The operation of these anion optodes is based on a competitive ion coextraction across the interface between an aqueous sample solution and the hydrophobic liquid-polymer optode film (see Fig. 26). The neutral ionophore L or the charged ionophore L + are responsible for the selective extraction of the anion X - . Concomitant with this anion extraction is the coextraction of a proton H + by an acidic chromo-ionophore C or a basic chromo-ionophore C - . This coextraction is brought about by the condition of nonseparation of charge. The chromo-ionophores are assumed to be ideally hydrogen-ion selective and produce an optical change (absorbance or fluorescence) by which the signal is measured. If the anion-selective ionophore is capable of producing its own optical signal, then a nonoptically sensitive proton-selective ionophore can be exchanged for the protonselective chromo-ionophore. The lipophilic ionic additives R + and R - are used in conjunction with the chromo-ionophores to maintain constant the ionic strength in the organic optode film phase. This yields an anion optode capable of performing activity measurements. It is important here to draw attention to the sensitivity of these optodes to changing pH. Samples must be buffered or the pH simultaneously monitored in order to make accurate determinations of the anion activity.

650

NANOSCOPIC OPTICAL SENSORS AND PROBES

Organic LiquidPolymeric Optode Films

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651

TAN AND KOPELMAN

5. NANOSENSOR APPLICATION Conventional fiber-optic sensors currently in use have tip diameters larger than 100/zm and are thus inappropriate for single cell applications and other nanotechnological applications. In addition, response times have been relatively long, typically in the range of seconds to min, making determinations of rapid, real-time responses impractical. Size reduction in sensors can be utilized in many different areas. These ultrasmall optical-fiber sensors are capable of spatially resolved measurements in small organisms and single cells. These sensors are capable of very rapid (millisecond) monitoring of chemical and biological reactions. The working range of optical-fiber sensors includes probes with tip dimensions in the submicrometer to about 10/zm ranges. Here we will mainly discuss three examples: rat embryo studies; single cell studies, and diffusion studies.

5.1. Single Embryo pH Measurements 5.1.1. In Vivo Monitoring of lntracellular Biochemical Species The nanometer sensors are small enough (e.g., 100 nm) to slip in and out of a living biological cell's membrane without any damage or leakage. Such biochemical sensors have been used to investigate the developmental biology of rat embryos. The NFO based optical-fiber sensors have been successfully applied in static and dynamic studies of rat embryos. The ability to control cellular homeostasis is important throughout development for the timing and the regulation of critical events in metabolism, differentiation, and cell growth. The mechanisms underlying these processes in development have, however, not been clearly elucidated and are difficult to assess due to the small size of the organism and the rapidly changing cellular environment. Many traditional methods for determination of cellular, biochemical, and molecular functions have, of necessity, been invasive, requiring destruction of the cell or organism. Measurements of pH by conventional methods have been determined by sensors, remote to the biological sample, following the uptake of a chemical indicator substrate or following tissue disruption. One of the limitations of these conventional techniques has been the need to introduce chemicals into the cells or tissues that could interfere with normal function or, by themselves, alter the very aspects of homeostasis being monitored. The development of probes small enough to be used in extremely small, fragile and dynamic biological systems, such as early embryos and single cells, will circumvent some of these limitations. The use of fiber-optic chemical biosensors has been growing for both environmental and biological applications. There is a common understanding that if the probe size is smaller than one-tenth of the biological sample, the probe insertion into the biological unit is considered minimally invasive. In vivo experiments then are possible. The nanoprobe size is well below the onetenth limit for all the samples tested. The probe can be inserted into different regions of a single cell with the help of a micromanipulator. Therefore in vivo subcellular structure analysis becomes possible. We have successfully applied the miniaturized optical-fiber sensors to rat conceptuses studies [32]. The rat whole embryo culture system [53] was used for these studies. Explanted, cultured, viable, gestational day 10-12 (GD 10-12) rat conceptuses are carefully placed inside a customized perfusion chamber, which is positioned on the stage of an inverted fluorescence microscope. This apparatus is able to maintain the viability of GD 10--12 rat conceptuses in a serum-free medium for over an hour of monitoring. The miniaturized fiber-optic biosensors are inserted noninvasively into the extraembryonic space of the rat conceptus, suspended in the customized perfusion chamber, causing little damage to or leakage from the surrounding visceral yolk sac (VYS). The probe is first mounted on a translational stage, such as a micromanipulator. Then it is gently directed toward the cell membrane to punch a small hole in the cell membrane. A schematic of how the miniaturized fiber-optic chemical sensor is inserted and positioned in the extraembryonic fluid

652

NANOSCOPIC OPTICAL SENSORS AND PROBES

Fig. 28. Schematicof the rat conceptus with its associated tissues, showing placement of the ultramicrofiber-optic sensor inside the extraembryonicfluid compartment.

(EEF) space of the conceptus is shown in Figure 28. The insertion of the ultrasmall sensor through the visceral yolk sac appeared to cause no damage to or leakage from the involved tissues. This demonstrates the advantage of an essentially noninvasive approach, as compared to conventional means, necessitating the disruption of large numbers of conceptuses to obtain less sensitive and indirect measurements. Some difficulties were experienced in punching the biological membrane, especially for red blood cells which are much smaller than rat embryos. However, after careful localization and punching, it became possible to insert the probe into a single blood cell.

5.1.2. Static pH Measurement of Rat Conceptuses Intracellular and extracellular pH are differentially regulated throughout the course of mammalian embryogenesis. These fluctuations play an important role in the control of cell proliferation, metabolic regulation, and differentiation. Significant changes in pH in the intracellular and intraconceptual milieu are also important in determining the relative distribution of chemicals from mother to embryo, especially during the teratogen-sensitive period of early organogenesis and prior to establishment of a functional placenta. The extent to which chemical, environmental, and physiological factors influence the regulation of pH and lead to alterations of normal development is not well known. Experiments, using Hanks buffer salt solution (HBSS), without the embryo present, verified the ability of the ultramicrofiber-optic sensor to discriminate less than 0.1 pH unit changes in the pH range of 6.6-8.6. Next, GD 10-12 conceptuses were analyzed for differences in pH as a function of advancing gestational age. EEF pH measurements, determined by using the fiber-optic sensor, show values of 7.50-7.56 in the 10-16 somite, GD 10 rat conceptus and pH values of 7.24-7.27 in the 32-34 somite, GD 12 conceptus. These data agree well with the mouse data presented for a conceptus of the same relative stage of development, based on somite number [54-56]. Comparison of GD 12 rat data using the same reference sources [56] shows that the fiber-optic pH sensor records pH in the EEF

653

TAN AND KOPELMAN

at a level approximately 0.20 pH units lower than that reported. The discrepancies may be due to the differences between EEF alone and the pH of the whole conceptus or real differences in the tissues themselves. In evaluating these discrepancies, it is important to note that the measurements are direct and can be accurately compared to other determinations regardless of size, age, or relative fluid volume of the cell or organism being monitored. The current application of our method does not require pools of conceptuses for determinations and can utilize single live conceptuses for the pH measurements. Traditional methods are based on relative concentration differences between matemal and embryonic tissues that occur as a radio-labeled weak acid diffuses preferentially into compartments of high relative pH. These methods also fail to account for differences in weak acid metabolism and altered distribution that may occur with time and between species. The use of a single embryo has numerous advantages over pooled embryos, in that it is possible to maintain structural and functional integrity while monitoring static and dynamic pH changes in the EEF. The conceptus also serves as its own control, can be accurately characterized as to developmental stage, can be monitored spatially and temporally in real time, and can be returned to whole embryo culture to evaluate other relevant endpoints later in development.

5.1.3. Real Time Monitoring during Environmental Changes and Direct Chemical Exposure The miniaturization of this fiber-optical sensor has not occurred at the expense of response times, with current sensors able to respond to events of shorter than 50 ms [13]. Tan et al. have made use of this feature in determining the dynamic response of a rat conceptus to alterations in its in vitro environment. A perfusion system for dynamic experiments has been built. Experiments were conducted to ascertain the ability of the GD 12 rat conceptus to respond to changes in its environment and to selected chemical agents. Three different experimental protocols were used. First, the perifusate bathing the embryo was saturated with 100% nitrogen, to create a condition of hypoxia. The measured pH over time did not vary significantly from the initial control readings. Even though hypoxia does not immediately alter hydrogen ion concentrations in the conceptus as determined by measuring EEF pH, it does not preclude the possibility of intracellular changes taking place within cells of the embryo proper which do not affect the equilibrium between EEF and intracellular fluid compartments. Second, conceptual response was determined by monitoring EEF for pH, when the perifusate, containing HBSS, was altered over a pH range of 6.6-8.6. Again, the measured pH in EEF did not result in any significant variations from control levels. A 500/zM solution of diamide in the perifusate (HBSS, pH 7.4) results in an initial rapid decrease in pH over the first 30 s, followed by a slower downward trend thereafter. An absolute decrease of about 0.3 pH units occurs within 3 min, as shown in Figure 29. A decrease in pHi of this magnitude has been shown to have significant effects on the activity of a number of enzymes which are critical for normal growth and development.

5.2. Single Cell Calcium Measurements Another way to use NFO to study biological samples is to use a NFO light probe directly. We have used the NFO probes to penetrate vascular smooth muscle cells (VSMC) to monitor Ca 2+ fluctuations during cell stimulation. As shown in Figure 30, a NFO probe has entered a single VSMC, without any visible damage or leakage. Fluorescence images of these cells have confirmed that the cells are still alive after the penetration of the probe. The penetration of the probe into a cell is very similar to cell microinjection. The NFO fiber probe is controlled by a micromanipulator. The experiment is done on an inverted optical microscope with live images taken by a frame transfer charge-coupled device (CCD)

654

NANOSCOPIC OPTICAL SENSORS AND PROBES

Fig. 29. Intracellular pH changes with time upon 50/zM diamide administration.

Fig. 30. A NFO probe inserted into a vascular smooth muscle cell. Measurements are done by monitoring fluorescence intensity of a calcium ion dye excited by light exiting from the NFO probe. Very localized quantitative measurements are due to the near-field optical excitation of the probe.

camera during the penetration procedure. The NFO fiber probe is connected to an argon ion laser, from which a variety of laser beams from UV to visible can be obtained. The tip

of the NFO probe defines the spatial resolution of the localized subcellular measurements. This is its advantage compared to the conventional far-field illumination. Bui et al. [57] report single cell responses to neurohormone stimulation--in this case, to angiotensin II (ang II), a hormone which contracts VSMC by increasing intracellular [Ca2+]i. The results indicate that this technique is useful for detecting resting [Ca2+]l and [Ca2+]i increases after ang II administration. The cells were loaded with fura-2/AM. After a short equilibration period, resting [Ca 2+]I images were acquired and ang II (1 uM) was added. This produced an increase in fluorescence intensity, followed by a return to baseline levels. The Ca 2+ concentration increased at 30 s and maximized at 60 s. The concentration returned

655

TAN AND KOPELMAN

Fig. 31. Representativefluorescence images of the NFO probe inside the VSMC at different time. A: after 30 s; B: 60 s; C: 90 s. Background signals are subtracted from all images.

to its initial value within 90 s as shown in Figure 31. This has demonstrated the ability of probing of a single cell with a NFO probe.

5.3. Diffusion Induced Self-Recovery from Photobleaching The major concern with optodes, especially miniaturized ones, has been their photobleaching limited lifetime. Liquid-polymer (highly plasticized poly(vinyl chloride)) films are commonly used to prepare fluorescent optical-fiber sensors. A major advantage is the ease of their fabrication. It was demonstrated that, with proper choice of excitation power and illumination time, the sensor completely recovered from photobleaching after each measurement. This self-recovery was demonstrated on single-mode optical fibers with 80/zm diameter (3.1/zm active region) and on near field scanning optical microscope pulled fiber tips with submicrometer diameter (250 nm active region). The single-mode optode can be used for 30,000 measurements with only a 5% signal loss at a signal-noise >66. This opens the way for prolonged ratiometric application of such optodes. Using a technique developed originally to study the motion of fluorescent molecules and fluorescently tagged proteins and lipids in thin membranes and films, Shortreed et al. have demonstrated the efficacy of diffusion in dramatically enhancing the working lifetime of fluorescent optodes. The fluorescence recovery after photobleaching (FRAP) technique [58] is based on using a brief, intense pulse of light to photobleach a small circular or Gaussian-shaped region in a thin film, followed by the monitoring of an increase in fluorescence intensity (with a greatly attenuated beam) as unbleached molecules outside of the bleached zone diffuse in. The recovery kinetics are characterized by the diffusion coefficient of the fluorophore, the size of the bleached spot, and the extent or depth of photobleaching. The results of FRAP experiments performed on the ends of single-mode optical-fibers and on NSOM light sources, used to study thin, plasticized PVC films doped with fluorescent chromo-ionophores, enable a simple procedure for quick total regeneration of the microsensor while in use on the microscope stage. Liquid-polymeric membrane based optodes are typically fabricated by a dip-coating procedure which takes ,~ 10 min (most of it being drying time, which could be accelerated). Once an optode film is deemed no longer usable, it can be dissolved in THF and a new

656

NANOSCOPIC OPTICAL SENSORS AND PROBES

film can be applied. This procedure does not require the fiber to be uncoupled from the excitation optics and yields sensors with a thin (2/zm or less) film. For flat cleaved singlemode optical fibers, the total diameter of the film can be as large as 80-100/zm with only a small 3 /zm active region. For sensors prepared from NSOM light sources, the active region of the plasticized PVC film is submicrometer, yet this region remains in contact with a relatively large reservoir of film which extends up the sides of the tip. The FRAP (fluorescence recovery after photobleaching) process in a liquid-polymeric membrane is detailed in a schematic (Fig. 32). The topmost frame (A) shows a side-on view of homogeneously distributed chromo-ionophore molecules in a thin liquid-polymer film. Only those chromo-ionophore molecules directly in the path of light leaving the optical fiber (labeled excitation zone) are excited. Depending on the photochemistry of the chromo-ionophore, the molecule may undergo several thousand transitions before becoming photobleached. For a typical experiment, this means a relatively constant fluorescence produced by an extremely low power excitation source (B). The role of diffusion in replenishing the photobleached molecules to the excitation zone (C-G) is highlighted in the remaining frames. The shutter blocking the high power bleach beam is opened (C), consequently photobleaching many of the molecules in the local region of excitation (D), the amount of which is dependent upon the duration and intensity of the pulse. Once the shutter is closed only a weak fluorescence signal is produced by the probe beam (E). Through rapid lateral diffusion, photobleached molecules leave the area of the liquid-polymer film and chromo-ionophore molecules that have not been bleached enter (F), returning to its original level the fluorescence produced by excitation from the probe beam (part G).

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5.4. The World's Smallest Devices? Optical Nanosensors Based and Entirely Cell Embedded Chemical Analysis Laboratory Practical optochemical sensors, sphere-shaped, and down to 10 nm radius, have been developed for measuring pH, calcium, magnesium, oxygen, or potassium. They can be entirely embedded into a single mammalian cell with negligible effects on its viability. These PEBBLE (probe embedded by biologically localized encapsulation) sensors can be inserted into the cell, singly or in groups, by wet (pico-injector, lypsome delivery, cell ingestion) or dry (gene-gun) delivery methods. Their small size assures excellent spatial resolution (submicrometer), time resolution (milliseconds), and detectability (zeptomoles), while good signal noise and stability are retained. These nanosensors promise to turn into reality the ultimate goal of spatially, temporally and chemically resolved studies on the cell's primary physiological processes, processes that occur during natural or pathological cell developments, as well as in the presence of remedies or pathogen countermeasures. Is smaller better? For optochemical biosensors the answer is yes, due to three major rationales [59]: (1) Minimal perturbation to the sample, especially a viable cell; (2) Optimal detectability of the analyte, especially if it consists of only a small number of molecules or ions; (3) Maximal sensing speed. Ultraminiaturization also allows the simultaneous operation of many such sensors, adding up to a chemical analysis nanolab whose components can all be entirely embedded inside a single mammalian cell. Such a nanolab makes it feasible to study, with both spatial and temporal resolution, the primary chemical-physiological processes of the cell, whether they occur naturally or occur due to pathogenic or counterpathogenic impacts. What has been available so far for the on-line, in situ chemical analysis of a single viable cell? (I) Miniaturized electrochemical and optochemical microprobes have been cast in the form of micro-electrodes or micro-"optodes," the latter based on pulled optical-fibers [2]. We note that even with nanoscale tips of electrodes or optodes, the connecting fiber or wire (not to mention the encasing capillary used with electrodes) present a major mechanical and electrical perturbation to the cell. It is especially difficult to introduce into a cell simultaneously several such probes. (II) Free floating fluorescent molecular probes have been routinely introduced into cells. However, in contrast to the new nanodevices described in the following text, these free molecular probes invade the entire cell, with the following major consequences: (1) parallel operation of two or more indicators (for two or more analytes), with the aid of spatial resolution, is not possible. (2) Uneven sequestration of the dye (at organelles) biases the results. (3) Interference with and poisoning of various cell activities. (4) Relative rapid leaching back out of the cell. (5) Photobleaching cannot be alleviated by "antifade" additives (mainly antioxidants) that perturb or poison the cell. (6) Cell autofluoresence is a serious problem. (7) Quenching of the probe fluorescence by heavy metals. (8) Global radiation damage to the cell. (9) Low sensitivity. (10) Need a separate indicator dye for each analyte (e.g., works well for pH or calcium, but no selective dyes yet available for sodium, nitrite, or glucose). Like free molecular probes, the new PEBBLE nanosensors described in the following text are entirely embedded inside the cell and communication with them is truly remote (wireless and fiberless). They too are energized from a distance with photons, and they too report back via emitted photons. However, in contrast to free molecular probes, these PEBBLE sensors only occupy a negligible fraction (1 PPM-1 PPB) of the cell's volume, allowing thus parallel operation of multi-analyte sensors (spatially resolved). Most importantly, in contrast to the free molecular probes, a PEBBLE is not just a capsule with a single kind of indicator molecules. The PEBBLE sensor can be a multicomponent, multifunction device. For instance, it may contain the fight combination of (1) ionophores, (2) fluorescent indicators, (3) sensitizing dyes, (4) antifade agents, (5) ionic additives, and (6) stabilizing additives, as well as (7) the protective shell polymer (so as to make an ion-correlation

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sensor). Thus the PEBBLE is a true nanodevice that has no free molecular probe analog. Potentially, the PEBBLE could also contain a magnetic steering unit (ferromagnetic), or it could be steered by a laser tweezer (photon trapping). Many such single- or multi-analyte PEBBLEs could be located at strategic locations inside the cell, where they continuously monitor its chemical composition (i.e., by spatially and spectrally resolved optical imaging in real time). PEBBLE sensors were originally prepared by grinding with mortar and pestle (a stoneage nanofabrication method). However, to better control their size, size-distribution, and shape, a microemulsion polymerization technique [42] was developed. The microemulsion technique, where the probes are formed from monomers, makes it easy to change the size of the PEBBLEs formed, by simply varying the concentration of the monomers, or the concentration of the surfactant. Another advantage is the resulting spherical shape of the probe, instead of the jagged, irregular shapes produced by polymer grinding. In the case of the acrylamide sensors, PEBBLEs were produced in sizes ranging from 20 nm to 1/zm in diameter, as indicated by TEM or SEM, or optical microscopy, depending on the size. How are the PEBBLE sensors introduced into the cell? The original plan was to use pico-injectors, delivering an appropriate liquid solution containing the PEBBLEs in colloidal form. This "wet delivery" method has both the advantages and disadvantages of micropipette injection methods, with the major challenges being micromanipulation, cell viability maintenance, and cell "flooding." An alternative method was developed, based on a "dry delivery" method, that is, "biolistic" embedding into the cell via a gene gun system (BioRad). A sample result is shown in Figure 33. The reliability and applicability of PEBBLE sensors is demonstrated in Figure 34. Shown is the clear-cut differentiation between intracellular and extracellular chemical environments, exhibited by potassium sensitive PEBBLEs. Independent optical micrographs (not given here) show PEBBLEs #3-5 to be embedded in neuroblastoma cells while #1, 2, and 6 are located in the buffer solution. Clearly, the extracellularly embedded three PEBBLE sensors give the fluorescence ratio "2," while the first three, cellularly embedded sensors, give a ratio regime between 5 and 8, indicative of the very different intracellular chemical environment. The variations found within this last set are expected, due to the specific location of the PEBBLE in the cell or due to the different age and/or viability of the three cells. This example demonstrates both the dependability and the utility of PEBBLE sensors. The stability of the PEBBLE sensors is excellent. For instance, while photobleaching is always an issue for optical sensors, typical PEBBLEs show only a 20% loss of signal

Fig. 33. A transmissionelectron micrographof two 200 nm PEBBLEs,embeddedbiolistically (viagene gun), at 900 psi, into the cytoplasmof a neuroblastomacell, close to its nucleus.

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Fig. 34. Potassium selective fluorescent PEBBLES "short" (by gene gun) into a neuroblastoma cell culture. PEBBLES#1, 2, and 6 landed into the homogeneous extracellular solution (based on independent microscopic observation) while #2, 3, and 4 got embedded into individual cells. The latter's fluorescence ratio spread is likely due to different positioning inside the cell, and/or different degrees of the individual cell's stage of development and/or viability.

over 200 acquisitions (each acquisition is 100 ms). This is an acceptable photostability, because a 20% loss has only a marginal effect on the intensity ratio measurements. The effects of photobleaching are thus minimized by the use of a ratiometric dye (CNF) and by short exposure times (100 ms). Leaching of the dyes from the PEBBLE sensor also does not present a serious problem. When left in aqueous solution for up to 2 days, the PEBBLEs remain distinct points of fluorescent light when excited. This indicates that the dye is retained by the polymer matrix. After 3 days or longer periods, the dye seems to diffuse into the solution, and may no longer be discerned as distinct sensor points of light. Here it should be noted that, in contrast to other sensors where stability is expected for the duration of 1 year, PEBBLE sensors do not have to last longer than their host cell. As the viability of most cells, when on a microscope stage, is on the order of only 1 h, this defines the lifetime expected for the sensors. Having shown that leaching is negligible over such periods and photobleaching is easily tolerable (even in the absence of antifade agents), the durability of these PEBBLE sensors is quite satisfactory.

6. M O L E C U L A R NANOSTRUCTURES AND SUPERTIPS For better resolution in biochemical analysis, smaller probes are required and are in the making. In principle, an exciton light source can be as small as a single-molecule or atom. At the same time, its position and scanning have to be defined in space equally well to those of an STM tip (a randomly flying atom does not qualify). Existing designs for optical supertips [60] are based on the same principle as the green plant photosynthetic system. A submicrometer antenna collects the photons by absorption and transfers the excitation energy to a single active center, as shown in Figure 35 [2, 14]. From there the energy is either (i) radiated as a photon or (ii) transferred to the sample in an energy transfer process (Ftrster-Dexter) [61]. In either case the result is generally affected by the nearby sample

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molecule: (i) The radiated excitation may be effected, for example, by intermolecular spinorbit coupling (Kasha effect) [62]. (ii) The energy transfer results in a fluorescence or phosphorescence typical of the sample molecule. In the latter case, only virtual photons are produced by the supertip; this gives an excitation transfer tip ("exciton tip") and only sample luminescence is detected. There are many methods and reasons for making supertips. For example, the opticalfiber tip can be treated, in principle, chemically, so as to produce specific supertips for a variety of purposes: (1) Wavelength shifters, for example, crystallites that fluoresce to the red of the tip emission; (2) Time "extenders," same as (1), utilizing prompt or delayed fluorescence or even phosphorescence; (3) Highly sensitive optochemical nanosensors; (4) Energy transfer supertips; (5) Heavy-atom sensors. Supertip development is the key to scanning probe microscopy which relies on quantum optics mechanisms, such as Frrster energy transfer [61 ] or Kasha effect (external heavy-atom effect) [62]. These interactions occur at the interface of the tip (its active center) and the sample (which are quantum mechanically coupled). For the highest resolution, this active center would consist of a single molecule, or molecular cluster, that does the imaging. This molecule is then the energy donor site for the Frrster energy transfer, or the spin-orbit interaction site for the Kasha effect. Figure 35 shows the relation between the tip, the supertip, and the active center. As much as the supertip is part of the tip, the active center is part of the supertip. We note that a completely analogous situation is found in atomic force microscopy, where the active center is the force contact site at the tip of the supertip. In NSOM the active center has to be optically excited repeatedly. The design of the system of tips is thus geared toward the need of supplying the active center with plenty of excitation quanta. We describe later several approaches for the present developments of supertips. Supertips have been constructed on both micropipette tips and optical-fiber tips. The following gives a few examples of supertips.

6.1. Nanocrystal Designer Probes One approach employs exciton conducting crystallites that absorb the light of the fiberoptic tip, convert it into excitons, which ultimately again produce photons. We have successfully grown such crystals of perylene, diphenyl-anthracene, etc. onto the fiber tip. Alternatively, the crystallite is grown at the tip of a micropipette and the fiber-optic tip is pushed deep into the pipette, very close to the crystal tip as shown in Figure 36. The crystallite acts as an antenna (compare photosynthetic antenna) that channels the excitons to an

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Fig. 36. Nanometerperylene crystalprobe.

active center which acts as an exciton trap [63]. This trap collects excitation from as far as 500-1000/~. The active center is the key of the molecular engineering. The single impurity molecule (the "supertrap") creates a host "funnel" around it [61 ]. This funnel consists of host crystal molecules perturbed by the impurity ("guest") molecule. The closer the host molecule is to the trap, the lower its excitation energy. The molecules in the funnel act as exciton traps, catching the excitation from the host crystal and passing it deeper and deeper (in energy) to the deepest of themall, the supertrap. For molecular exciton microscopy (MEM) the guest molecule is deposited onto the surface of a molecular microcrystal and thus creates an energy funnel at its apex (active center). The best microcrystals are grown onto the tip of a micropipette. This tip is excited internally by a fiber-optic tip. It gives as much intensity as with epiluminescence, that is, external excitation method [64]. We have observed acceptable levels of luminescence intensities from a few molecules of rhodamine B embedded onto the surface of a DPA crystal [65], as shown in Figure 37. From the spectra, it is clear that even for dipping into very dilute rhodamine B solutions (10 -7 M), the emission of a tiny rhodamine B active center is still detectable in an optical multichannel analyzer (OMA) apparatus. This preliminary work clearly demonstrates that supertips can be prepared by dipping nanometer crystal tips into dye solutions. The crystal tips absorb the incident light, create excitons, and emit light again (with their typical fluorescence spectrum) or transfer energy to the active center and emit a lower energy fluorescence. These tips are exciton supertips. By optimizing the selection of host-crystal guest-supertrap pairs, we have been able to prepare supertips with high intensity and good stability [63, 65].

6.2. Polymer Matrix Supertip Another approach altogether involves a polymeric matrix attached to the optical-fiber tip by spatially controlled photopolymerization. The polymer is a copolymer, consisting of acrylamide, N,N-methylenebis(acrylamide)(BIS) and appropriate dye monomer groups [13]. This polymer supertip acts as an antenna, even though a less efficient one compared to a molecular crystal. However, with the large photon flux emanating out of the tip this lower

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NANOSCOPIC OPTICAL SENSORS AND PROBES

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efficiency should suffice. At the very tip of this supertip the "active center" is attached by physical and chemical methods. The dye molecule on the top surface of the polymer is produced by a photochemical reaction from a layer of precursor molecules deposited on the polymer tip by dipping into a solution. The highest probability for the photochemical reaction is at the center of the tip, thus making it likely that the first and only active molecule is produced at this center. Several parameters can be used to control this operation: Depth and duration of dipping, precursor concentration, and the intensity and/or exposure time and the photochemical reaction light intensity. By using a multidye solution for photochemical synthesis, we have prepared multifunctional optic and excitonic probes with extremely small size. These probes emit multiwavelength photons or produce excitons of different energy levels. By using multistep photochemical synthesis, we have miniaturized optical and exciton probes to sizes much smaller than the sizes of the original light conductors. The multistep near field photopolymerization [ 13] has been very effective in fabricating extremely small optical and excitonic supertips [66, 67]. 6.3. S i n g l e D e n d r i m e r

Design

We have also designed a supertip made of a single symmetric macromolecule by using newly developed dendrimer supermolecules [66, 67]. The so-called starburst phenylacetylene dendrimers include the largest so far synthesized structurally ordered molecule (D127, See Fig. 38). These fractal, treelike supermolecules have spatially localized eigenfunctions, and, in particular, localized electronic states. Furthermore, in the so-called SYNDROME family of dendrimers [66, 67], simple theory leads to selectively lower excitation energies at the central locus of the ordered macromolecule, with energies increasing toward the rim. This is borne out experimentally by the vibronic spectra of the entire family of molecules (D-2 to D-127), with full internal consistency in the observed electronic energies (red shifts), vibrational quanta, Franck-Condon factors, overall transition moments, and picosecond spectral diffusion. The architecture of this series of dendrimers is controlled by organic synthetic methods. For example, the overall shape of a "D-127" molecule is bowllike with a molecular size around 125 ~. It can thus act as both optical and force active center. The large "rim" is bound to the tip by cumulative van der Waals bonding or covalent bonds. D-127 may be used in supertip preparation in two ways. The first is to make supertips in the range of 100 A. In this case, D-127 is an energy transfer acceptor. It traps

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Fig. 38. Dendrimermolecule (top) and nanostar molecule (bottom).

most of the energy quanta from the bulk of the tip, as shown in the following text. D-127 is the light emitting active center. The supertip prepared in this way follows this scheme,

Tip ==~ supertip ==~ active center ==~ sample The second way for supertip preparation is to achieve about 10 A resolution. To further demonstrate our "energy funnel" model (see the preceding text) we synthesized partial dendrimeric wedges with (and without) an excitation acceptor, a perylene derivative pendant, at the locus. As expected, the energy transfer from the large antenna ("tree canopy") to the small acceptor center is indeed dramatic. The presence of the antenna (39 phenyl groups) increases the yield of the yellow perylenic emission by 3 orders of magnitude for a given excitation wavelength. This molecule is an ordered supermolecule transducer of absorbed radiation (STAR) [60] in analogy to the primary excitation energy collecting antenna of some natural photosynthetic systems. Overall, such a photonic subwavelength nanolens may play a role in developing molecular excitonics, including luminescent

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optical nanoprobes, scanning exciton tunneling microscopy, and nanometer-scale fiberoptic chemical and biochemical sensors. In order to synthesize such a STAR molecule, the nanoarchitecture process is modified to prepare a D-127 molecule with a supertrap in the center. D-127 is synthesized with phenylacetylene [66, 67]. The synthesizing route has been modified to prepare similar dendrimers containing higher aromatic rings. A single such substituted group acts as a supertrap [68], collecting most of the excitation. This intramolecular exciton supertrap plays the role of the active center. It may act as an exciton donor, transferring excitation to an acceptor on the sample, and as the smallest possible light source. The modified dendrimer has a supertrap in the center with a size of about 10 ~. In such a supertip case, the supertrap center have different optical and excitonic properties from its surrounding molecules. The center can be used as a scanning tip which defines the scanning resolution. The supertip prepared in this way follows the following scheme: Tip ==~ supertip ==~ antenna ==~ active center ==~ sample

The design of the STAR molecule is not only for accelerated energy transfer but also for backward "spill over" of redundant energy in the pendant group. For instance, if a second excitation arrives while the first is still there, the two excitations are expected to "fuse" [70] and the resulting higher energy excitation transfers backward into the dendrimeric antenna state. There, having many more nonradiative energy decay channels, it is reduced from an Sn to an $1 excitation. Then the $1 excitation will flow again into the pendant "supertrap." This mechanism prevents photobleaching. Indeed, both theoretical and experimental work has borne out the high efficiency of energy funneling and the high degree of resistance to photobleaching. The nanostar represents a new class of "designer" molecules, tailor made for single-molecule light and exciton sources [2]. We note that its large size (125 for D-127), stability, and efficiency will allow it to be used as a "supertip" for optical nanoprobes and nanosensors. The superresolution imaging of biologically interesting species relies on this dual function. The MEM operation itself involves different mechanisms: (1) Active energy transfer (F/Srster-Dexter) [61 ] where the supertip is the exciton (energy) donor and the sample is the acceptor. (2) Passive interaction (sensor mode), exemplified by the Kasha effect [62], where the sample either quenches the supertip's exciton or transforms it from "singlet" to "triplet." We have prepared a single-molecule light source [14]. It is based on a dye molecule immobilized onto a NFO probe. This probe can be developed as a single-molecule sensor. Potential applications, that are unique to single-molecule probes, include sequencing DNA, probing nanometer scale environments, monitoring individual molecule reactivities, studying the variability of molecular conformations, detecting disease infection at an early stage, and devising nanostructures and molecular-scale imaging probes for single-molecule microscopy. 7. SUMMARY AND O U T L O O K Many theoretical and technical problems still have to be solvedmfrom understanding the NSOM contrast mechanism to the nanofabrication of molecular sized probes to the control of photobleaching. However, the future looks bright. Growth in NFO research in its early days has not been as spectacular as that of its SPM predecessors, scanning tunneling microscopy (STM) and AFM. On the other hand, NFO is increasingly making its appearance in new areas of research as well as in established areas as its capabilities expand: the number of NFO microscopes, worldwide, has risen in 5 years, from about 5 to about 300. The ability to image in-solution environments has been demonstrated, and the combination of better resolution and biochemical identification capabilities seems ideally suited to a number of biomedical investigations. Biosamples, including living cells and even ion channels,

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c o u l d be i m a g e d d o w n to the m o l e c u l a r level and a n a l y z e d s p e c t r o s c o p i c a l l y by either N F O p r o b e s or b i o c h e m i c a l sensors. T h e intracellular m o l e c u l a r d y n a m i c s of o r g a n o g e n esis, m e t a b o l i s m , splitting, and b i o c h e m i c a l d a m a g e c o u l d be f o l l o w e d in v i v o and in real time.

Acknowledgments We t h a n k our c o l l e a g u e s at the University of Florida and at the University of Michigan. W.T. thanks the N S F Faculty C a r e e r Award 9 7 3 3 6 5 0 , W h i t a k e r F o u n d a t i o n B i o m e d ical E n g i n e e r i n g P r o g r a m , and the Office of N a v y R e s e a r c h Young Investigator A w a r d N 0 0 0 1 4 - 9 8 - 1 - 0 6 2 1 . R.K. thanks N I H G r a n t 1 R 0 1 G M 5 0 3 0 0 , N S F G r a n t D M R 9 4 1 0 7 0 9 , and D A R P A G r a n t M D A 9 7 2 - 9 7 - 0 0 0 6 .

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NANOSCOPIC OPTICAL SENSORS AND PROBES

40. 41. 42. 43. 44. 45. 46. 47. 48. 49. 50. 51. 52. 53. 54. 55. 56. 57. 58. 59. 60. 61. 62. 63. 64. 65. 66. 67. 68. 69. 70.

Z. Rosenzweig and R. Kopelman, Anal. Chem. 68, 1408 (1996). Z. Rosenzweig and R. Kopelman, Anal. Chem. 67, 2650 (1995). H. Clark et al., Sensors and Actuators, B, Chem. 51, 12 (1998). W. Tan and E. S. Yeung, Anal. Chem. 69, 4242 (1997). S. McCulloch and D. Uttamchandani, lEE Proc. Optoelectron. 144, 162 (1997). W. E. Morf, K. Seiler, B. Lehmann, C. Behringer, S. S. S. Tan, K. Hartman, P. R. Sorensen, and W. Simon, "Ion Selective Electrodes," Vol. 115, Budapest, 1989. W. E. Morf, K. Seiler, P. R. Sorensen, and W. Simon, Vol. 141, Akad. Kiad6, Budapest, 1992. E. Bakker and W. Simon, AnaL Chem. 64, 1805 (1992). G. P. Updike and S. P. Hicks, Nature (London) 214, 986 (1967). H. P. T. Ammon, W. Ege, M. Oppermann, W. Gopel, and S. Eisele, Anal. Chem. 67, 466 (1995). T. Hoshi, J. Anzai, and T. Osa, Anal. Chem. 67, 770 (1995). C. Ingersoll and E Bright, Anal. Chem. 69, 403A (1997). J. Cordek, X. Wang, and W. Tan, Anal. Chem. 71, 1529 (1999). R. Hiranruengchok and C. Harris, Toxicol. Appl. Pharmacol. 120, 62 (1993). W. J. Scott, Jr. et al., in "Approaches to Elucidate Mechanisms in Teratogenesis" (E Weisch, ed.), Vol. 99, Hemisphere, New York, 1987. M. D. Collins, C. A. Duggan, C. M. Schreiner, and W. J. Scott, Jr.,Am. J. Physiol. 257, R542 (1989). G. E. Dean, H. Fishkes, P. J. Nelson, and G. Rudnick, J. Biol. Chem. 259, 9569 (1984). J. Bui, T. Zelles, H. Lou, V. Gallion, I. Phillips, and W. Tan, J. Neuroscience Methods 89, 1 (1999). M. Shortreed, E. Monson, and R. Kopelman, Anal. Chem. (1997). R. Kopelman and S. Dourado, SPIE (Int. Soc. Opt. Eng.) Proc. 2836 (1996). R. Kopelman, M. Shortreed, Z. Shi, W. Tan, Z. Xu. J. Moore, A. Bar-Haim, and J. Klafter, Phys. Rev. Lett. 78, 1239 (1997). M. Pope and E. Swenberg, "Electronic Processes in Organic Crystals," Oxford Univ. Press, New York, 1982. M. Kasha, J. Chem. Phys. 20, 71 (1952). W. Tan and R. Kopelman, in "Molecular Electronics, Chemistry for 21st Century Monographs" (J. Jortner and M. Ratner, eds.), p. 393, Blackwell Sci., Oxford, U.K., 1997. A. Lewis and K. Lieberman, Anal. Chem. 63, 625A (1991). W. Tan, Ph.D. Dissertation, University of Michigan, 1993. Z. Xu and J. S. Moore, Angew. Chem. 32, 1354 (1993). Z. Xu, Z. Shi, W. Tan, R. Kopelman, and J. Moore, Polymer Prepr. 33, 130 (1993). M. Shortreed, Z. Shi, and R. Kopelman, Mol. Cryst. Liq. Cryst. 283, 95 (1996). R. Kopelman and W. Tan, Science 262, 1382 (1993). M. Shortreed, S. Swallen, Z.-Y. Shi, W. Tan, Z. Xu, J. Moore, and R. Kopelman, J. Phys. Chem. B 101, 6318 (1997).

667

Chapter 1 INTERCALATION COMPOUNDS IN LAYERED HOST LATTICES: SUPRAMOLECULAR CHEMISTRY IN NANODIMENSIONS Anton Left

Walther Meissner Institute, D-85748 Garching, Germany

Contents 1. 2.

3.

4.

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Intercalation Chemistry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1. "Story Lines" in Intercalation Chemistry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2. Present State of Intercalation Chemistry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Structural Organization of Intercalated Species: Supramolecular Chemistry in Constrained Space or "Nano" Aspects of Intercalation Chemistry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1. Structural Arrangements of Metals and Inorganic Compounds in the Interlayer Space . . . . . . 3.2. Water in the Interlayer Space . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3. Arrangements of Small Organic Molecules or Molecular Cations in the Interlayer Space . . . . 3.4. Self-Assembled Layers of Amphiphilic Molecules in the Interlayer Gap . . . . . . . . . . . . . 3.5. Formation of Nanoporous Solids: "Pillaring" (2D-3D Transitions) . . . . . . . . . . . . . . . . . 3.6. Self-Assembly of Multicomponent Artificial Layer Composites . . . . . . . . . . . . . . . . . . 3.7. Molecular Recognition in the Interlayer Space . . . . . . . . . . . . . . . . . . . . . . . . . . . . Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1 6 6 14

77 79 92 107 120 131 138 145 151 152 152

1. INTRODUCTION

The term intercalation is deduced from the Latin verb intercalare and assigns (as the Latin origin) the insertion of an additional day in special years to synchronize the calendar with the solar year. 1 The german verb einlagern was used for the first time by Schleede and Wellmann [1] to describe the process of potassium uptake into graphite, when they discussed the structure of these compounds (prepared a few years ago by Fredenhagen and Cadenbach [2]). As far as I could see, the English terms to intercalate and intercalation were used for the first time by McDonnell et al. in 1951 [3]. At the end of the 1950s 1 See for this meaning The New Encyclopaedia Brittanica, Vol. 6, 15th ed. Micropedia, 1985. The underlying verb intercalare has undergone an interesting development showing roman practice. It is derived from the verb calare which means to cry, to call, or to shout. Intercalare means then to proclaim the leap-year day. According to Langenscheidt's Enzyklopiidischem WOrterbuch der englischen und deutschen Sprache (Teil I, English-Deutsch, Bd. 1, Berlin, 1962), this verb can be used figuratively to mean "to insert" or "to introduce," and it is given as the direct English translation of the German verb einlagern.

Handbook of Nanostructured Materials and Nanotechnology, edited by H.S. Nalwa Volume 5: Organics, Polymers, and Biological Materials ISBN 0-12-513765-6/$30.00

Copyright 9 2000 by Academic Press All rights of reproduction in any form reserved.

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Rtidorff used the term Einlagerungsverbindungen to assign the graphite-alkali-metal compounds [4] and extended the English translation intercalation compounds to all chemical derivatives of graphite [5]. Atoms or ions have been inserted in these compounds (alternatively, intercalated, or in German, eingelagert) under expansion of the lattice perpendicular to the nearly unchanged graphite layers. It is worth noting that Henning used the term "interstitial compounds" to name the same compounds at the same time [6]. This term was applied to assign compounds like the hydrides, the carbides, or the nitrides of the early transition metals, in which there are also close topological relationships between the structure of the starting metals and the products obtained and in which the ratio of the inserted atoms with respect to the host lattice is nonstoichiometric [7]. Some years later Barrer merged the graphite compounds, the zeolites, the clay minerals, and other solids, which can take up additional ions or molecules without severe structural reconstructions of the host lattices, under the new heading "inclusion complexes" [8]. Up to the 1980s intercalation compounds were subsumed under this term [9]. In my view these three terms (inclusion complexes, interstitial compounds, and intercalation compounds) should not be intermixed but should be used to assign definite groups of complex solids. I would guess that the term inclusion complexes should be used exclusively for such solids, in which the guest component is occluded in the host during preparation (see the chapters of H. M. Powell, J. Lipkowski, J. Hannotier, P. de Radzitzky, and G. A. Jeffrey in Vols. 1 and 2 of [9]. The guest species can only be removed from the intracrystalline cavities by destruction of the complex. A further characteristic feature of these systems is that the crystal structure of the host can be different from the structure of the host adopted in the presence of the guest species. By this definition it is clear that only molecules can form such inclusion compounds in the solid state. The term interstitial compounds should be restricted to those inorganic solids in which the additional atoms occupy empty lattice sites of the host structure with small crystal expansions and without other structural changes. These compounds are normally prepared at very high temperatures, and the atoms taken up in the solid are immobile at room temperature. To keep electrical neutrality, the host lattice must have the tendency to change the oxidation state. These compounds have strong relationships to nonstoichiometric compounds (examples are the above-mentioned hydrides, carbides, or nitrides of the early transition metals [ 10, 11 ]. Peculiar for solids forming intercalation compounds are anisotropic bonding relationships leading to stable structural elements like chains, layers, or three-dimensional frameworks (Fig. 1). If these structural elements are electrically neutral, they are held together by weak van der Waals forces or they contain empty one-dimensional channels (running parallel through the structure or intersecting each other) or interconnected cavities. If these structural elements carry electrical charges, these are compensated for by small counterions between them or occupying the channels and cavities [8, 12-18]. In most of these compounds there are many more empty lattice sites than can be occupied by additional atoms or molecules. Therefore the mobility of the interstitial atoms can be very high if their interaction with the host structure is not too strong [ 14, 19]. This led to the discovery that many intercalation reactions can be carried out at room temperature or slightly above, making new compounds accessible that are not stable at high temperatures. In conclusion, intercalation is considered to be the reversible uptake of atoms, ions, molecular cations, or molecules at low temperature while the structure of the host lattices is conserved. The term intercalation does not tell anything about the nature of the chemical reaction underlying this process. It mainly stresses the topological relationships between the host and the final product of the reaction. Whereas in the framework structures only those compounds can be taken up, that fit into the channels or cavities, the layered or chain host lattices can expand in one or two dimensions without serious restriction. This allows the accommodation of species other than atoms, like large metal complexes or organic cations. Layer expansions up to 5 nm have

SUPRAMOLECULAR CHEMISTRY IN NANODIMENSIONS

Fig. 2. Schematicdrawing of a layer structure and definitions of the vocabularyused in this review.

been observed (Figs. 1 and 2). One intercalation compound showing such a high layer distance is (octadecylamine)xTaS2 [20]; a drawing of the proposed structure (see Fig. 3) has been the focus of great attention and has been reproduced many times, even in general textbooks of solid-state chemistry [21 ]. In channel compounds defects can block the diffusion totally, and so it can be hard to achieve homogeneous filling of the possible lattice sites. In the chain and layer compounds the species to be intercalated can have access from all or at least two directions. However, in chain structures the insertion of additional species, even if they are bulky, weakens the interaction between the chains, thus leading to an easy disintegration of the solid. In the layer compounds the two-dimensional structural elements give enough stability to prevent this disintegration, at least for moderate layer separations. This ideal combination of easy access to the interlayer galleries and the stability of the final products is why layer compounds are preferred for intercalation reactions and why most of the intercalation compounds are layered structures [8, 12-19, 22-28].

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Fig. 3. Proposed structure of the intercalation compound (octadecylamine)xTaS2. (Source: Reprinted with permission from [20]. 9 1971 American Association for the Advancement of Science.)

The term "nanodimension" used in the title also deserves some comments. The venture into the realms of the "nanodimension" seems to be the leading motif of materials science in the 1990s. In literature one can find a large number of new key words beginning with the prefix n a n o , like nanotechnology, nanochemistry, nanoclusters, nanotubes, nanowires, nanomachining, nanomaterials, and nanostructures, and these key words stand for new research areas. 2 As the prefix suggests, researchers working in these new fields are dealing with or are learning to handle objects with dimensions on the order of the nanometer. This is the same size scale as the colloids, which were an important research area at the be2 In a visionary lecture 39 years ago, Richard Feynman predicted many of the advances that are the subject of this new area of science [29].

SUPRAMOLECULAR CHEMISTRY IN NANODIMENSIONS

ginning of this century. Ostwald brought it to the limelight in his famous book, Welt der vernachliissigten Dimensionen [30]. In nanoscience or nanotechnology we are doing nothing more than colloid science, so to speak, enriched by the knowledge we have gained in this century and armed with very potent and highly sophisticated new methods. The metaphor used in the title of Ostwald's book is as true today as at the beginning of the century, but things are changing now. The prefix nano- has two different meanings: the first is a reference to the relevant dimension of the objects treated; the second is connected to the observation that really new phenomena appear if one examines the realm of "nanodimensions." Thus, for example, if the dimensions of semiconductor structures are in the submicrometer range (quantum wires or quantum dots), their conducting properties will be dominated by quantum effects [31, 32]. The electronic properties of the nanocluster show new features that take a position between the band structure in bulk solids and the separated energy levels of small molecular species [33]. Another phenomenon is related to surface effects. For particles on the nanoscale, the ratio of atoms lying on the bulk to the atoms forming the bulk comes close to unity; consequently, these particles are highly reactive, as demonstrated by interesting elastic properties of genuine ceramic materials [34]. The starting point of these new research lines was the progress in cluster research by physicists and chemists [32] and the formation of artificial layer structures by molecular beam epitaxy [35], based on purely physical methods. The latter is a key invention that gives the methods of synthesis of solids a completely new direction. Other key events for the foundation of nanoscience were the development of supramolecular chemistry [36, 37] and the rapid progress of all experimental methods related to scanning tunneling microscopy [38-41 ], including the manipulation of surfaces. Interesting nanosystems related to the topic of this review are artificial semiconducting [42], metallic [43], or magnetic [44] superlattices. They are formed by chemical or physical deposition methods and are built up from alternating layers of different metals/elements. The thickness of the individual layers is on the order of 1-20 nm. With respect to these structures one can also consider intercalation compounds as artificial layered structures built up of alternating layers from more complex chemical individuals. The thicknesses of inorganic host lattices are normally in the range of 0.3-1 nm, whereas the thickness of the intercalated layers varies from 0.3 to 5 nm. The chemical nature of these intercalated layers varies from metals to membrane-like arrangements of amphiphilic molecules or to polymers (including biopolymers). According to their physical properties, these complex assemblies can be considered as conducting/insulating, conducting/ semiconducting, or metallic multilayers depending on the nature of the host and the guests. Intercalation reactions are in this sense nothing more than a preparative method for building artificial superlattices, and intercalation chemistry is noting more than nanochemistry [45, 46]. In this view intercalation chemistry is nanochemistry from its early beginning in the 1920s. Up to now there has been no evidence that we have new phenomena like quantum effects connected with these nanometer-thick layers. It is just the dimension and the artificial nature of these highly metastable arrangements that justifies placing intercalation compounds under the heading "nanosystems." In contrast to the metallic superlattices, the intercalation compounds can be modified after preparation. In addition, the confined space between two solid surfaces can lead to special arrangements in the interlayer space different from that on outer surfaces, to some sort of shape selectivity influencing chemical reactions in the interlayer galleries [47], or to some kind of molecular recognition (e.g., [48]). Thus I guess we could consider intercalation chemistry as a sort of supramolecular chemistry in confined nanodimensions. The scope of this review is as follows. Because there are a large number of reviews about the different aspects of intercalation chemistry, I will give--after a historical introduction---only a general review of the host lattices known, the intercalated species, and the methods of intercalation. I will stress the common features of all of these

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reactions, which are not so evident, if the intercalation compounds of fairly similar host lattices are discussed separately, which is the case in most of the reviews available. The main part of this review is devoted to the organization of the intercalate in the interlayer galleries. I shall discuss first the problems in determining the structure of the intercalated layers. Then some organization schemes found in intercalated layers will be shown. Concerning the large family of organic compounds intercalated up to now, I will choose examples known to intercalate in different types of host lattices and discuss the consequence for the structure. Special reference will be made to the more complex systems that show interesting functional properties of the intercalation compounds, like molecular recognition, molecular sieve properties, catalysis, and so on.

2. INTERCALATION CHEMISTRY

2.1. "Story Lines" in Intercalation Chemistry Table I shows a time line of the essential events in the history of intercalation research. I endeavored to find out the first publication for each topic listed in the table. Aside from some observations made in the last century, which we would interpret now as intercalation phenomena, the intercalation research starts in the 1920s, after the introduction of X-ray diffraction. This method allowed for the first time the detection of the close relationship between the structure of the starting materials and the products of intercalation reactions [ 1, 59]. Hofmann and Frenzel [59] were the first to realize this structural relationship and called the uptake of sulfuric acid into graphite a topochemical process, in accordance with Kohlschtitter and Haenni [172]. It is interesting to note that in 1897 Weinschenk [173] proposed, from microscopic investigation of graphite oxide only, that the structure of this new compound should be similar to that of the starting material. The first intercalation compounds studied were graphite compounds and clay minerals. Both systems are layer compounds, but they represent two different intercalation systems: graphite is a neutral host lattice with electronic conductivity, whereas the clay minerals are electronically insulating systems consisting of negatively charged host layers whose charges are compensated for by hydrated alkali metals between the layers. The chemical and physical properties of the two groups of compounds are so different that the two different research traditions that arose have undergone nearly no interaction up to now. The only exception is graphite oxide, whose properties are more similar to those of the clays than to the other graphite compounds [59, 68]. That these compounds were studied first is connected to research activity at the beginning of the century. Graphite and carbon in general were of major interest in the early stages of scientific metallurgy and were widely studied. The same was true for the clays, because it was realized that they are the mayor constituents of soils and understanding them could be of advantage for agriculture and the ceramics industry. Because of the different properties of the two groups of compounds, the invention of different preparation and handling properties was necessary, and parallel to the progress in research, a new vocabulary was created [4-6]. Thus, for example, the alkali metal intercalation compounds of graphite were prepared at high temperatures under careful exclusion of air and moisture. They were compared with the known interstitial compounds of some metals or with nonstoichiometric compounds, which were studied in inorganic solid-state chemistry at the same time. From this point of view it is not surprising that the review of Henning is titled "Interstitial Compounds of Graphite" [6]. The interest in graphite intercalation chemistry increased after the Second World War, when new research groups joined this field. Great progress has been made by the following persons and their research groups: Herold in France, Croft in Australia, Ubbelode in England, Henning in the United States, and Hooley in Canada.

S U P R A M O L E C U L A R CHEMISTRY IN N A N O D I M E N S I O N S

Table I.

Time Schedule for Essential Steps in Intercalation Research

....

Year of invention

Authors

Topic

Ref.

1841

Schafh~iutl

Swelling of graphite in sulfuric acid

[49]

1850

Thompson

Cation exchange in soils

[50]

1850

Way

Cation exchange in soils accompanied by the clay fraction of soils

[51]

1855/59

Brodie

Graphite oxide

1897

Hofmann and Ktispert

Nickel cyanide inclusion complexes

[54]

1926

Fredenhagen and Cadenbach

Intercalation of K, Rb, Cs into graphite out of the vapor phase

[2]

1926-31

Ross and Shannon Hendricks and Fry Kelley etal.

Clay mineral concept

[55] [56] [57]

1929

Demolin and Barbier

Fixation of humic acids and proteins by clays

[58]

1930

Hofmann and Frenzel

Intracrystalline swelling of graphite oxide

[59]

1930

Pauling

Structure of micas and related minerals

[60]

1930

Houdry (cited in Ballantine 1986)

Acid-treated montmorillonite as catalyst for petroleum cracking

[61]

1932

Schleede and Wellmann

Crystal structure of K graphite

[1]

1932

Thiele

Intercalation of ferric chloride into graphite Intercalation of bromine into graphite (crystal structure Rtidorff 1941)

[62]

[52,53]

[631

1932

Thiele Rtidorff and Hofmann (1938)

Anodic swelling of graphite Electrointercalation into graphite

1933

Hofmann et al.

Intracrystalline swelling of montmorillonite Structure of montmorillonite

[67]

1934

Hofmann, Frenzel and Csalan

Model for the structure of graphite oxide

[68]

1934

Hofmann and Frenzel Rtidorff and Hofmann (1938)

Structure of graphite sulfate Graphite salts

[69] [66]

1934

Ruff and Bretschneider

Graphite monofluoride

[7O]

1935

Noll

Laboratory synthesis of clay minerals

[71]

1934/36

Smith (1934) Gieseking and Jenny (1936)

Base exchange for organic cations in montmorillonite

[72, 73]

1938

RUdorff

Graphite salts; stepwise uptake (staging) followed for the first time by X-ray up to the 5th stage

[74]

1939

Ensminger and Gieseking (1939)

Reduction in base exchange capacity by complexing clay with protein

[75]

1942

Feitknecht Feitknecht and Gerber

Synthesis and structural analysis of layered double hydroxyds of the hydrotalcit type

[64-66]

[76-78]

(continues)

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Table I.

(Continued)

Year of invention

Authors

Topic

Ref.

1945/48

Bradley Mac Ewan

Adsorption of organic compounds with polar active groups on clay minerals

[79] [80]

1946

MacEwan

Halloysite organic complexes

[81]

1949

Jordan

Alkylamine uptake of montmorillonite; swelling of organo clays in organic solvents

[82]

1949/50

Juza et al. Goldsmith

Magnetic susceptibility of graphite intercalation compounds

[83] [841

1949/52

Powell and Rayner

Structure of the nickel cyanide inclusion complex Ni(CN) 2 NH 3 C6H 6

1951

McDonnell et al. Hennig

Electrical resistivity and magnetic susceptibility of graphite intercalation compounds

[3] [87]

1951

Weiss and Hofmann

Formation of a nickel complex in the interlayer galleries of batavit

[88]

1953

Weiss et al.

A Hofmann-type compound with negatively charged layers

[89]

1954/55

Schulze et al.

Electrointercalation into graphite out of ammonia solutions; ammoniated phases of the alkali graphite compounds

1955

Barrer and McLeod

Permanent porosity by formation of tetralkylammonium clays

[92]

1956

Weiss et al.

Uptake of alkylammonium species in mica-type layer silicates

[93, 941

1959

Rtidorff and Sick

Intercalation of alkali metals out of liquid ammonia into MoS2 and WS2

[95]

1960

Weiss and Weiss

Alkylammonium exchange in the layered ternary oxide Na2Ti205

[96]

1960

Baur and Schwarzenbach

Creation of Hofmann-type compounds by replacement of nickel with other two-valent metals

[97]

1961

Wada Weiss

Intercalation of organic molecules in kaolinite

1962

Hagenmuller et al.

Ammonia intercalation into FeOCI

[lOO]

1964

Clearfield and Stynes

Crystallisation of zirconium phosphate

[lOl1

1965/67

Michel and Weiss

Cation exchange, swelling, and alkylammonium uptake in layered phosphates

1965

Hannay et al.

Superconductivity of the alkali metal graphite compounds

[104]

1965

Saehr and Hrrold

Hydrogenation of KC8

[105]

1966ff.

Allmann et al. Taylor et al.

Reinterpretation of the structure of the layered double hydroxydes

[85, 86]

[90, 91]

[98, 99]

[ 102, 103]

[106-109]

(continues)

S U P R A M O L E C U L A R CHEMISTRY IN N A N O D I M E N S I O N S

Table I.

(Continued)

Year of invention

Authors

Topic

Ref.

1967

Hagenmuller et al.

Intercalation of amines into FeOC1

[355]

1967

Nomine and Bonnetain

Intercalation of THF in KC24

[110]

1969

Weiss and Ruthardt

Intercalation of organic molecules into TiS2

[lll]

1969

Clearfield and Smith

Structure of ot-Zr(HPO3) 2 H20

[112]

1969

Daumas and H6rold

New model for the staging phenomenon

[113]

1970

Gamble et al.

Superconductivity of the dichalcogenide intercalation compounds

[114] [20]

1970

Furdin et al.

Ternary intercalation compounds of graphite involving two halogens

[115]

1973/74

Sch611hom and Weiss

Solvation and cation exchange of alkali intercalation compounds of the layered dichalcogenides

1973

Moore

HOPG

[118]

1973

Miyata et al.

Synthesis of new layered double hydroxides (with new anions, including organic anions)

[119]

1973/76

Knudsen and McAtee Shabtai et al.

Pillaring of montmorillonite by metal chelates

1974

Lagrange et al.

Graphite compounds with different intercalates in alternating layers

[122]

1974

Whittingham Subba Rao and Tsang Sch611horn and Meyer

Electrointercalation into the layered dichalcogenides

[123-125]

1975/78

Dines Clement et al. (1978)

Intercalation of metallocenes in the layered dichalcogenides

[126] [127]

1975/76

Yamanaka and Koizumi Behrendt et al.

Organic complexes of the zirconium phosphate

[128] [129]

1976

Yamanaka

First intercalation (alkylamines) into a MPX 3 compound

[1301

1976

Mortland and Berkheiser Shabtai et al.

Pillaring of montmorillonite by bicyclic amine cations

[1311 [1211

1976

Hamwi et al.

Benzene intercalation in KC24

[1321

1976

Besenhard

Electrointercalation of solvated alkali metals in graphite; solvents DME, DMSO, PC, or NM

[133]

1977

B6hm et al.

New double hydroxide, anion exchange, intercalation of surfactant anions

[134]

1977

Vogel

Very high conductivity of graphite intercalation compounds

[1351

1977ff.

Brindley and Sempels Lahav et al. Vaughan and Lussier

Pillaring of montmorillonite by polyoxycations

[116, 117]

[120, 121]

[136-138]

(continues)

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Table I. Year of invention

(Continued)

Authors

Topic

Ref.

1977

Kato and Kawada

LaCrS3 identified as an alternating sequence of CrS2 and LaS layers with a NaCl-like arrangement

[1391

1978

Alberti et al.

Organic derivatives Zr(RPO 3)2 and Zr(ROPO3)2 of ot-Zr(HPO3)2

[1401

1979

E1 Makrini et al.

Multiple metal layer intercalates in graphite: phases K1VIxC4, M = Hg, T1, Bi

[141]

1980

Sch611horn

Concept of topotactic redox reactions

[142]

1980

Johnson

Cobaltocene intercalation of zirconium hydrogen phosphate accompanied by reduction of protons

[1431

1980

Krenske et al.

Photocatalysis on organometallic compounds intercalated in clays

[144]

1980

Clarke et al. Wada et al.

High-temperature/high-pressure phase diagrams of alkali metal graphite compounds; staging transformations

[145, 146]

1981/82

Yamagishi and Soma

Racemic adsorption

[147, 148]

1982

lye and Tanuma Wachnik et al.

Superconductivity of the ternary phases KMxC4, M = Hg, T1, Bi

[149, 150]

1983

York et al.

Heterostructures with two heavy alkali metals in graphite

[151]

1985

Vliers et al.

Photophysics of metalorganic intercalation compounds of zirconium phosphates

[152]

1986

Kijima and Matsui

Intercalation of cyclodextrin into c~-zirconium phosphate

[153]

1986

Nazar and Jacobson Gee et al.

Exfoliation/flocculation as new preparative method in dichalcogenide intercalation chemistry

1987

Giannelis et al.

Photophysics of metalorganic intercalation compounds of double hydroxides

1987ff.

Clayden Christensen et al.

y-ZrP is y-Zr(PO4) (H2 PO4)

[ 157, 158]

1988

Williams and Hyde Wiegers et al. Guemas et al.

Misfit layer compounds of the type (MIS) 1 + xMS2, where M I = Sn, Pb, rare earth; M = Ti, V, Cr, Nb, Ta

[159-161]

1988

Coleman et al.

Organic clay: sodium-calix[4]arene sulfonate with a layer structure

[162]

1988

Clearfield and Roberts

Pillaring of metal phosphates with the aluminium polyoxycation

[163]

1988

Kwon et al. Drezdzon

Pillaring of layered double hydroxides with polyoxometalate anions

[164, 165]

1989

Johnson et al.

Molecular recognition in layered phosphates

[154, 155]

[156]

[481

(continues)

10

SUPRAMOLECULAR CHEMISTRY IN NANODIMENSIONS

Table I. Year of invention

(Continued)

Authors

Topic

Ref.

1992

Vermeuelenand Thompson

Stable photoinduced charge separation in the viologen intercalation compound of c~-zirconiumphosphate

[166]

1992

Ogawa et al.

Solid-state intercalation of naphthalene and anthracene in alkylammonium montmorillonite

[167]

1993

Thompsonet al.

Solid-state intercalation of alkali halides in kaolinite

[168]

1993/94

Albertiet al.

Covalently pillared zirconium phosphate-phosphonates

1994

Keller et al.

Layer-by-layer assembly of intercalation compounds

[169, 170] [171]

One will not find these terms (the same is true for the term intercalation) in clay chemistry. The properties of the most studied clays (montmorillonites, bentonites) are dominated by the very small particle size and swelling behavior in pure water under special conditions [26]. There was a long controversy about the chemical nature of these soil colloids [26] until the clay mineral concept was developed in the 1920s by Ross, Hendricks, and co-workers [55-57]. The terminology of this research field and the investigation methods are closely related to colloid chemistry, which was in a very active state at nearly the same time. Examples of related phenomena are ion exchange, swelling, electric double layer formation, gel formation, flocculation, and so on. The phenomenon of swelling in particular received much attention [67]. It was the first time that the swelling of a solid could be investigated directly; because of the layer structure it was easy to determine the layer distance during swelling of the solid by following the decreasing ionic strength in the surrounding solution from a very low layer expansion of about 0.3 nm (the thickness of one water layer) up to about 10 nm immediately before the full disintegration of the solid; this process was reversible and was called "one-dimensional intracrystalline swelling" [67, 174]. The natural examples in soils led to the discovery that a large number of organic molecular cations, neutral molecules, polymers, and biochemicals can be adsorbed or taken up in the interlayer space of the clay minerals [26, 27]. This result has guided researchers, who have tried similar intercalation processes in other host lattices since the 1970s. Barrer [8] was the first to bring together the two research fields in his review under the heading of "inclusion complexes," but this had no influence on interdisciplinary cooperation. Up to the 1950s no one had tried to find new host lattices. Weiss found for the first time that uranium micas [ 175, 176] and ternary oxides [96, 177] with layer structures are accessible to the same reactions as clay minerals. A breakthrough for intercalation chemistry was achieved in the 1960s, starting with the observation of Rtidorff that the method of intercalation of alkali metals into graphite out of liquid ammonia solutions leads to successful insertion of these metals into the electronically conducting layered dichalcogenides [95]. Encouraged by this success, Weiss and Ruthardt tried to transfer his successful intercalation of hydrazine and other hydrogen bond-breaking molecules into kaolinite [99, 178] to the layered dichalcogenides and has found a new class of intercalation compounds [ 111 ]. According to the suggestions of

11

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Weiss, the products have been interpreted as the insertion of neutral molecules in neutral host lattices, and the interaction between the constituents has been considered as a sort of Lewis acid-base interaction. It took nearly 10 years to establish the view that the intercalation of these molecules is accompanied by a redox process and that the products contain negatively charged dichalcogenide layers and charge-compensating molecular cations in the interlayer galleries [ 142, 179, 180]. One year later, a group of physicists at Bell Laboratories extended the reaction of Weiss to the layered metals TaS2 and NbS2 and found that intercalation can dramatically increase the transition temperature to the superconducting state [20, 114]. It should be mentioned that some members of this research group at Bell Labs had tried a few years before to increase the superconducting transition temperature (Tc) of metals by adsorption of polyaromatic hydrocarbons at the outer surface of these metals [181, 182]. They explained their disappointing results with the low number of molecules that could be brought into contact with the metals and proposed the idea that the effect could be improved if it were possible to increase the surface of the metals dramatically to maximize the interaction with the organic molecules. It was evident that this group was well prepared to take up the results of Weiss to continue their search for Tc enhancement by the interaction of small molecules with metal surfaces (intercalation makes accessible the whole interlayer surfaces of the crystals, which increases dramatically the contact area between the metal and the molecules). Whereas earlier determination of physical properties of intercalation compounds, like the increase in the electrical conductivity of graphite compounds [3, 87] or the superconducting properties of graphite alkali metal derivatives [104], have found nearly no resonance in the physics community, the discovery of superconductivity in the intercalation compounds of the layered dichalcogenides initiated very broad investigation of these compounds by physicists. The activity was also prepared by the excellent review of Wilson and Yoffe [183], who have collected all information about the physical properties of the transition metal dichalcogenides. To understand this great interest, it must be remembered that about 1965 physicists started to investigate the electronic properties of more complex solids, perhaps encouraged by the hypothesis of Little that electron/exciton interactions could increase Tc to room temperature. At nearly the same time a search for purely organic metals has been initiated. Because of the discovery of Tc, intercalation compounds were increasingly in the limelight of the solid-state sciences, and for more than 10 years the physical properties of these compounds were the main research subject in intercalation science, but the ressearch in clay minerals could not take profit from this extended interest. For graphite compounds the situation was improved dramatically by two events: the successful preparation of highly oriented pyrolytic graphite [118] made accessible a highly ordered sample, which made it possible to prepare high-quality intercalation compounds and strongly improved the determination of their structure and of their physical properties; the second was the detection of electronic conductivity values as high as that of Cu for the graphite intercalation compound Cx (AsF6) [135]. Interest first concentrated on the superconducting properties [ 184-187]. Later it was extended to the anisotropic magnetic properties of the transition metal intercalation compounds [187-190]. With the discovery of charge density waves in the layered dichalcogenides [191 ], research moved to the problem of how charge density waves (CDWs) can be influenced by intercalation or doping and how they are related to superconductivity [ 185, 186]. The discovery of Vogel has led to revival of research on graphite compounds, carried on by physicists. First electronic transport properties have been on the agenda [192, 193], followed by the preparation of a large number of new intercalation compounds (mainly ternary compounds) [193, 194] and the investigation of staging phenomena [195]. Advances in experimental methods have led to great progress in determination of the structure of graphite compounds [ 194, 196], even of very complex ones. The latter activities have

12

SUPRAMOLECULAR CHEMISTRY IN NANODIMENSIONS

led to the investigation of structural phase transitions in intercalated matter [194, 196]. In the 1980s the interest of physicists in intercalation compounds decreased continuously, triggered by the discovery of high Tc superconductors and the fullerene compounds. The phenomenon of anodic swelling of graphite was observed as early as 1932 [64], and it was interpreted as the electrochemical insertion of sulfuric acid in 1938 [66]; electrointercalation received more attention in the 1970s. After the first successful electrointercalation reactions in the layered dichalcogenides [123-125], it was soon recognized that the intercalation compounds are mixed electron/ion conductors and that some conventional battery electrodes are intercalation compounds [19, 197]. From this point on, large efforts were directed toward the search for new battery electrodes based on conducting host lattices for intercalation reactions. This dramatically extended the number of new host lattices suitable for intercalation, but it was mainly restricted to showing that small ions can be taken up. This result does not say anything about the possibility of intercalating larger and more complex species. Great progress has also been made in the improvement of the electrode properties of carbons used in battery applications [197]. Based on these results on electrointercalation, Schrllhorn showed in his influential review [ 142] that most of the intercalation reactions of neutral host lattices are accompanied by redox processes; thus rather than containing neutral structural elements, the products now contain charged elements whose charges have to be compensated for by counterions, which have to be taken up in the solid. In case of the layered dichalcogenides, it has been shown by Weiss, Schrllhorn, and co-workers that the alkali metal intercalation compounds take up solvents and exchange ions, though these compounds are polyelectrolytes that have many properties in common with the clay minerals [116, 117, 198]. Because these compounds show electronic conductivity, they are conducting ion exchangers. Earlier it was shown that the intercalation processes of graphite are accompanied by redox reactions and that the carbon layers carry negative or positive charges [4, 5]. However, the high sensitivity of the carbon compounds to reaction with oxygen or water and the completely different intercalates prevents the graphite compounds from being considered as polyelectrolytes. In conclusion, the differences in the intercalation chemistry of many layered host lattices do not seem to be fundamental; the accessibility to intercalation reactions of suitable hosts and the stability of the resulting products are determined for many systems by the redox potential of the intercalation compound and the charge density on the host lattice. When the interest in electronically conducting intercalation compounds flourished, chemists rediscovered their interest in insulating host lattices and the derived compounds because of their optical transparency which facilitates the application of UV-VIS or IR spectroscopy to the elucidation of structural organization in the interlayer galleries or the study of new phenomenon like photocatalysis [144]. First, with the advanced methods of structure determination, Thomas started to investigate clay organic complexes, in which most of the alkali ions of the transition metals had been replaced [199, 200]. His research group also investigated catalytic reactions of these compounds in the interlayer space on a broader scale [199, 200]. At the same time (about 1975) Mortland, Pinnavaia, Brindley, and others found new intercalation compounds by pillaring, which allowed the preparation of mesoporous solids suitable for use as molecular sieves and catalysts [120, 121, 131, 136-138, 201,202]. Later on, new, very active catalysts (clayphen) based on clay intercalation compounds were detected [203]. In the 1980s catalytic properties were also detected in the intercalation compounds of Zr phosphate and derivatives [204] and in the so-called anionic clays--the double hydroxides [205]. During the study of these compounds old questions, surface acidity, charge distribution, and shape selectivity, received new attention. In addition, the peculiar intracrystalline surface structure and the pecularities of the Zr phosphonate compounds led to a new phenomenon, high selectivity for the uptake of molecules with special spatial arrangements [48, 206, 207]; this is a simple form of molecular recognition, well known in organic supramolecular chemistry or in biochemistry.

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2.2. Present State of Intercalation Chemistry

2.2.1. Host Lattices Table II gives an o v e r v i e w of layer structure c o m p o u n d s exhibiting intercalation reactions. It is not i n t e n d e d to give a full collection of all types of layer c o m p o u n d s that could have

Table II. Layered Solids Used as Hosts for Intercalation Reactions Solid type (i) Uncharged layers (a) Insulator hosts Clays

Examples

Formula

Ref.

kaolinite dickite pyrophyllite

AI2Si2O5 (OH)4 A12Si2Os(OH)4 AlzSi4010(OH)2

Cyanides

Hofmann-type compounds Hofmann-type compounds

Ni(CN)2 NH3 AIINi(CN)4(NH3)2; AII = Cu, Zn, Cd

[8, 210, 211]

Metal derivatives of phosphoroxyacids

phosphonates

u-MIV(RPO3)2; MTM = Ti, Zr, Sn; R = alkyl, aryl u-M Iv(HPO3)2; MTM = Ti, Zr y-Zr(PO4) (H2 PO2)

[212, 213]

phosphites Zr(IV) phosphate hypophosphite (b) Conducting layers Elements

[26-28, 208, 209]

[214] [215] [5, 6, 192-194, 196, 216-219]

graphite

Metal dichalcogenides

MX2 = Sn, Ti, Zr, Hf, V, Nb, Ta, Mo, W; X = S, Se, Te

[23, 186, 187, 220-226]

Metal phosphorous chalcogenides

MPX3 = Mg, V, Mn, Fe, Co, Ni, Zn, Cd, In; X - S, Se

[ 17, 23, 226-229]

Ta2S2C, Nb2S2C

[226, 230]

TazNiS 5 Vanadium pentoxide Molybdenum trioxide

[231]

V20 5 MoO3

[232] [23, 224, 233-236]

Metal oxyhalides

MOX; M -- Ti, V, Cr, Fe; X - C1, Br

[ 17, 23, 237, 238]

Halides

ZrNC1 PbI2 RuC13

[239-241 ] [242-244] [245]

Metal derivatives of phosphoroxyacids

VOPO4 2H20

Oxides

(ii) Charged layers (a) Positively charged hydroxides

Metal derivatives of phosphoroxyacids

Hydrotalcite Hydrotalcite-type anionic clays

[Mg6A12(OH)6]CO3 4H20

[M~IxMIII(oH)2][Ax/n]mH20

[205] [205,246]

MII -- Mg, Fe, Co, Ni, Mn, Zn; MIII = A1, Fe, Cr, Mn, V; An -- inorganic or organic anions u-Zr(NH3C2H4PO3) 2 2C1 2H20

u-Zirconium aminophosphonates

[23]

[247]

(continues)

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S U P R A M O L E C U L A R CHEMISTRY IN NANODIMENSIONS

Table II.

(Continued)

Solid type (b) Negatively charged (a) Insulators Clays

Examples

Formula

Montmorillonite Saponite Vermiculite Muscovite

Silicic acids Oxides

Transition metal dioxides Titanates Niobates Uranylvanadate

Metal derivatives of phosphoroxyacids

Nax (A12_xMgx )(Si4 O10 )(OH)2 fax / 2 (Mg3)( Alx Si4_ x O 10)(OH)2 (Na,Ca)x (Mg3_ x Lix )(Si4010)(OH)2 K(AI2)(A1Si3O10)(OH)2

[26-28 199, 208, 209]

H2Si205; H2Si14029

[248-250]

MIMIIIo2; M I = alkali metal; MIII = Ti, V, Cr, Mn, Fe, Co, Ni Na2Ti307, K2Ti409

[17,23, 251,252] [253,254] [255,256] [257, 258]

K[Ca2Nan_3NbnO3n+l] 3 < n < 7

Na(H20)n [UO2 V3 09 ]

or-Metal(IV) phosphates (arsenates) y-Metal(IV) phosphate hydrogenphosphates Uranium micas

Cyanides (/3) Conductors Silicides Chalcogenides

Ref.

ct-MIV(HXO4)2H20; M TM = Ti, Zr, Ge, Sn; X = P, As y-MIV(PO4) (H2PO 4) 2H20; M TM -- Ti, Zr VOHPO4

[204, 259, 260] [213,261]

H(H20)4[UO2XO4], X = P, As

[175, 176, 263, 264]

[23, 262]

Kx (H20 )y [Ni2+x M3+ (CN)4+ 2x ]

[89,265]

CaSi 2

[266,267]

AMS2; M -- Cr, V; A =Na, K Li2FeS 2 ACuFeS2; A = Li, Na, K K2Pt4S 6 A2M3S4; M = Pt, Pd; A = Cs

[ 187, 220] [268, 269] [270-273] [224] [224]

a potential for intercalation reactions. The table should allow the reader to gain an insight into the variety of compounds for which intercalation is really observed. In most cases the compounds listed have been well investigated; I mention others for which the potential for intercalation reactions seems to be very restricted at the moment (e.g., CaSi2 or the nickel cyanide system, Ta2NiS5 or ZrNC1). Not included are compounds of organic hosts in which the cohesion of the molecules forming the host lattices is mediated by van der Waals or ionic forces only, for example, cholic acid [274], the sodium calix[4]arene sulfonate complex, which is also called "organic clay" [ 162, 275,276], or the inorganic polyphosphates, showing one-dimensional swelling with alkylammonium ions [277]. Also not included are y-InSe, GaSe, or In2Se3; these host lattices are proposed to take up lithium or sodium only [278-280], but these systems should be considered as interstitial compounds, because the increase in layer distances is very small. The systems mentioned in the table range from elements (graphite) to very complex multinary compounds (montmorillonites, phosphates). Nearly all types of compounds, from oxides and other chalcogenides to halides or Zintl phases (CaSi2), can be found among the layered host lattices. Essential for all of these compounds is a chemical bonding system in which covalent interactions between the components building up the layers are very strong. Only one of the systems mentioned is a metal complex, the Hofmann-type compounds [210]. They consist of a sheet-like network of nickel atoms interconnected with cyanide ligands; each of the metal atoms is coordinated to four CN groups in a square.

15

LERF

Fig. 4. Structure of the Hofmann-type compound Cd(NH3)2Ni(CN)4.2C6H6. (Source: Reprinted from [211], with permission from Elsevier Science.)

Every other nickel atom carries two additional ligands directed toward the interlayer gap, extending the coordination sphere of these metals into a distorted octahedron (this is the case for those nickel atoms that are bound to the nitrogen atoms of the cyanide groups, whereas the nickel atoms coordinated to the C atoms of the cyanide groups remain in the square planar coordination). Between these staggered ligands there is enough space to occlude additional molecules like benzene [85, 86]. The nickel atoms can be replaced by a series of other metal atoms. Figure 4 shows a perspective view of such a compound in which the sixfold coordinated Ni atoms are replaced by Cd atoms. These Hofmann-type compounds are borderline cases between the intercalation compounds and the inclusion compounds because they are formed in almost all cases from solutions of the components. The layered compounds of the table are classified into to two main categories. The highest classification level is the distinction according to the charges on the host lattices: in essence there are neutral host lattices like graphite or the layered dichalcogenides or

16

SUPRAMOLECULAR CHEMISTRY IN NANODIMENSIONS

other ones carrying positive or negative charges. In the latter case the charges on the host lattices are compensated for by negative ions (mainly anions of the oxyacids) or positive ions (mainly alkali cations) in the interlayer galleries. The next important distinction is between host lattices that are electronic insulators and others that are semiconductors or metallic conductors. The type of charge and the conducting properties mainly determine the intercalation behavior of the host lattices, more than the special chemical nature of the host (more on this question in Section 2.2.2). To rank the compounds in the category of conductors, the value of the conductivity of the empty host or the mechanism of conduction is not crucial; it is only of interest that the formation of an intercalation compound accompanied by electron transfer increases the electronic conductivity. The zirconium bis(monohydrogen orthophosphate) monohydrate Zr(HPO4)2.H20 (hereafter referred to as ot-ZrP) is considered as a charged host lattice because the proton can be replaced by other cations. But the proton is bound to the phosphate group, so that the intercalation chemistry of the compound is determined at least in part by the neutral protonated form. As the type of compound varies strongly, so do the structures of the host lattices. The known structures range from monolayers of elements (cf. flat carbon layers of graphite or wrapped sheets of silicium atoms in CaSi2 [267]) to complex structural units consisting of up to seven layers of several elements, as in the case of montmorillonite (with a strongly simplified sequence of layers: O-Si-O-A1-O-Si-O). The thickest layer of a host lattice is described for the ternary oxide K[Ca2Nan-3NbnO3n+l] (3 ~< n ~< 7) consisting of up to 15 layers of oxygen and metal atoms, depending on n [255]. The structures of some more important host lattices are shown in Figures 5-11 in perspective views. The oldest known host lattice for intercalation reactions is graphite. Its structure consists of a stacking of carbon layers in which the carbon atoms are arranged in a honeycomb pattem (see Fig. 5) [217]. The approximately 20 layered dichalcogenides with undistorted structures and stoichiometric composition crystallize in essentially two different structures: a sheet of metal atoms is strongly bound to and sandwiched between two hexagonally packed layers of chalcogens [183]. Depending on the stacking of the two chalcogen layers, the metals are coordinated octahedrally, as in the case of TiS2 or 1T-TaS2, or trigonal-prismatically, as in 2H-MoS2 or 2H-TaS2 (see Fig. 6); these X-M-X slabs (X = chalcogen atoms, M = transition metal) are weakly bound to other slabs and are stacked in the crystallographic c direction in different ways, leading to different polytypes. In the temary chalcogenides NaVX2 and ACrX2 (A = Na, K; X = S, Se), the alkali metals

Fig. 5. Perspectiveview of the structure of graphite. (Source: Demonstrationexample of DIAMOND-Visuelles Informationssystemfiir Kristallstrukturen. Prof. Dr. G. Bergerhoff, Gerhard-Domagk-Strasse 1, 53121 Bonn.) See also Plate 1.

17

LERF

Fig. 6. Perspectiveview of structures of the two most important polymorphs of the layered dichalcogenides. Tantalum disulfides have been chosen as the prototype. (Source: View carried out with DIAMOND-Visuelles Informationssystem for Kristallstrukturen. Prof. Dr. G. Bergerhoff, Gerhard-Domagk-Strasse 1, 53121 Bonn. Structural data are taken from [281,282].) (a) 1T-TaS2.(b) 2H-TaS2.

are sandwiched between the MS2 layers, also showing the 1Y-YaS2 arrangement. The MO2 units of the ternary oxides AMO2 (A = Li, Na; M = 3d transition metals) with the same composition as the aforementioned ternary chalcogenides have the same structure as the isostructural TiSz-layers, but the stacking of the layers is different. The structure of the ternary neutral host YazSzC is also closely related to the structure of the dichalcogenides: a close-packed carbon layer is sandwiched between two close-packed monolayers of sulfur atoms; the metal atoms occupy all octahedral holes in this three-layer arrangement, thus forming a layer described in short by the sequence S-Ta-C-Ta-S. Furthermore, the structure of the MPX3 family can be deduced from the structure of TiS2. The X atoms form a close-packed arrangement of two sulfur monolayers. Two-thirds of the octahedral holes are occupied by the M atoms, whereas the residual one-third of the octahedral holes are

18

SUPRAMOLECULAR CHEMISTRY IN NANODIMENSIONS

Fig. 6. (Continued.)

filled with P2 pairs. The distributions of both groups are very regular, but the overall structure is slightly distorted, leading to a monoclinic, pseudo-hexagonal unit cell. The double hydroxides, also called hydrotalcite-like compounds, have positively charged layers that are built up from densely packed OH layers and the metal atoms occupying the octahedral holes, thus it is the same arrangement as in TiS2 or in the ternary oxides AMO2, but the excess positive charges are compensated for by inorganic anions inserted between the layers. The structures of most of the other host lattices are better described as a network of corner and/or edge and/or face shared polyhedra. This is the case for the conducting neutral host lattices like MoO3 (see Fig. 7) or FeOC1 (see Fig. 8), and even for the charged host lattices like the clay minerals (Fig. 9) or the ternary oxides like Na2Ti307 (Fig. 10). In these examples the surface structure of the layers is not as flat as in the case of the closepacked structures, the distances to the same atoms in the surface layers are different in the two directions parallel to the layers (MOO3 or FeOC1), and the networks are more open and have hollows in which species inserted between the layers (montmorillonite) can key or the layers are corrugated (e.g., Na2Ti3OT). The consequence of these structural features for the intercalation processes and for the structure of the intercalates will be discussed later (in Sections 2.2.2 and 3). With the exception of kaolinite and halloysite, all of these layer structures are symmetric with respect to the center of the layers; in these

19

LERF

Fig. 7. Perspective view of the structure of MoO3. (Source: View constructed with DIAMOND-Visuelles Informationssystem ftir Kristallstrukturen. Prof. Dr. G. Bergerhoff, Gerhard-Domagk-Strasse 1, 53121 Bonn. Structural data are taken from [283].) (a) Ball-and-stick representation; (b) polyhedron representation.

exceptions one side of the layer is built up from a network of corner-shared SiO4 tetrahedra, whereas the other side is a network of A1-O octahedra. Because the two layers have slightly different dimensions there is a tendency to bend the layers, which leads occasionally to cylindrical tubes [288, 289], with the layer normal perpendicular to the tube axis (such tube-like arrangements have also been observed for the layered dichalcogenides [290] and graphite [291] (cf. the carbon nanotubes); in both cases the layer asymmetry is not the reason for rolling of the layers). c~-ZrP has a layered structure in which the metal atoms lie nearly in a plane and are bridged by phosphate groups. Three oxygens of each phosphate group are bonded to three different Zr atoms arranged at the apices of a nearly equilateral triangle. The fourth oxygen

20

SUPRAMOLECULAR CHEMISTRY IN NANODIMENSIONS

Fig. 7. (Continued.)

points away from the layer and bonds to a hydrogen atom. Because of a pseudo-hexagonal stacking of adjacent layers, six-sided cavities are formed that are occupied by a water molecule (Fig. 11) [292]. y-ZrP has been recognized as a compound of slightly different composition, MIV(PO4)(H2PO4)2H20, with a more complex layer structure, shown in Figure 1 lb. Rows of metal atoms are interconnected by the PO4 groups, forming double layers of M TM and PO4 groups; all oxygen atoms of these PO4 groups are coordinated by four Zr atoms, two of them in the same row and two others in two adjacent rows. The other coordination sites of the metals are occupied by the H2PO4 groups. Two of these oxygens bridge adjacent M TM atoms; the other two are bonded to protons. These OH groups point toward the interlayer gap [158].

21

LERF

Fig. 8. Perspective view of the structure of FeOC1. (Source: View constructed with DIAMOND--Visuelles Informationssystemftir Kristallstrukturen. Prof. Dr. G. Bergerhoff, Gerhard-Domagk-Strasse 1, 53121 Bonn. Structural data are taken from [284].) Ball-and-stick representation. See also Plate 2.

2.2.2. Intercalation Reactions 2.2.2.1. Types of lntercalation Reactions The main category defining the possible intercalation reactions is the charge on the host layers: neutral or charged (cf. the center of Fig. 12). Whereas there are only a few systems in which the host layers carry positive charges (see Table II), there are a large number of host lattices with negatively charged layers; the number of the latter is even higher than the number of host lattices with zero charge. Both categories of charged host lattices (positive and negative) are accessible to ion exchange reactions and solvation reactions. Both types of reactions are closely related because the solvation of the cations is often the precursor state of an ion exchange; the interrelations of both types of reactions are shown for negatively charged host lattices in Figure 13. In this figure the expansion of the host lattices to infinity and the reverse, flocculation, are also mentioned. This type of

22

S U P R A M O L E C U L A R CHEMISTRY IN NANODIMENSIONS

Fig. 9. Perspective view of the structure of (a) 2:1 clay mineral. (Data taken from [285].) (b) 1:1 clay mineral. (Data taken from [286].) (Source: Views constructed with DIAMOND--Visuelles Informationssystem ftir Kristallstrukturen. Prof. Dr. G. Bergerhoff, Gerhard-Domagk-Strasse 1, 53121 Bonn.) Polyhedron representation. See also Plate 3.

23

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Fig. 9.

(Continued.)See also Plate 3.

24

SUPRAMOLECULAR CHEMISTRY IN NANODIMENSIONS

Fig. 10. Perspective view of the structure of Na2Ti307 . (Source: View constructed with DIAMOND-Visuelles Informationssystem ftir Kristallstrukturen. Prof. Dr. G. Bergerhoff, Gerhard-Domagk-Strasse 1, 53121 Bonn. Structural data are taken from [287].) (a) Ball-and-stick representation; (b) polyhedron representation. See also Plate 4.

reaction shows the close relationship of intercalation reactions to colloid chemistry. The ion exchange and solvation reactions can be observed for electronically insulating as well as for electronically conducting layers. If the neutral host lattices are electronically conducting, they are accessible to redox reactions, which lead to an electron withdrawal from or to an electron transfer to the host layers and an uptake of charge-compensating ions in the interlayer galleries. The only case of an oxidation reaction of a neutral host lattice known up to now is the oxidation of graphite. This host lattice, as a singular example, is susceptible to reduction and oxidation reactions. The reversal of this reaction, the oxidation (reduction) of ternary systems to neutral host lattices, is also possible. This is trivial for such cases where the charged systems have been prepared from neutral host lattices by redox reactions. However, in the case of compounds with charged host lattices prepared from elements, reduction (oxidation) has

25

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Fig. 10. (Continued.)See also Plate 4.

led to a lowering of the charge density, making the compounds susceptible to an uptake of solvent and to further intercalation reactions (e.g., K2Pt4S6). If the reaction can be carried out to the complete removal of all charges on the compound, new neutral host lattices can be prepared that are not accessible by direct synthesis at high temperatures because of metastability (e.g., VS2, CrS2). The insulating neutral host lattices undergo two reactions: the uptake of neutral molecules, which is also a sort of solvation, as in the case of the charged systems, and the so-called grafting reaction. The latter reaction results in a covalent bond formation of the intercalate and is therefore not reversible, unlike the other reactions mentioned. In this review the term "grafting" is used for covalent bond formation, regardless of the mechanism of the reaction. Grafting is not restricted to neutral host lattices. In the following, the different types of reactions shall be discussed in greater detail.

2.2.2.1.1. Ion Exchange Reactions. This reaction is widely used as a preparative method for obtaining new intercalation derivatives of charged compounds that cannot be prepared otherwise. This is the case for cations and anions of organic molecules, including biomolecules, and even for cations of metal-organic complexes or hydrated ions of the

26

SUPRAMOLECULAR CHEMISTRY IN NANODIMENSIONS

Fig. 11. Perspectiveview of the structure of both Zr phosphate modifications.(Source: View constructed with DIAMOND---Visuelles Informationssystem ftir Kristallstrukturen. Prof. Dr. G. Bergerhoff, GerhardDomagk-Strasse 1, 53121 Bonn. Structural data are taken from [112, 158, 292].) Ball-and-stick representations of (a) ct-Zr-P and (b) F-Ti phosphate (in this compound the structure of y-Zr-P was discovered first). See also Plate 5.

transition and rare earth metals. The discovery of ion exchange of organic cations into clay minerals dates back to the 1930s, when Smith [72], Gieseking [73] (see also Table I), Hendricks [293], and their co-workers observed the uptake of protonated aliphatic and aromatic amines, including purine and pyrimidine systems forming the bases of the genetic code [293]. Observation of the uptake of metal-organic species dates back to the 1950s, but it received more attention in the 1980s, when it was discovered that the intercalation compounds of photoactive metal complexes in electrically insulating host lattices can work as photocatalysts for water decomposition [ 144]. Ion exchange is known for nearly all charged host lattices and some neutral host lattices. For clay minerals only ion exchange behavior is widely studied [26]. Other systems studied in greater detail are the cation exchangers: ct-Zr-P [204] (in this compound ion exchange is only possible in strongly basic conditions due to the bonding strength of the proton to the PO4-group), ternary oxides [253,294], the

27

LERF

Fig. 11. (Continued.)See also Plate 5.

intercalation compounds of MPX3 [23, 228, 295], and the alkali metal derivatives of the layered dichalcogenides [116, 117, 198]. The only anion exchangers known up to now are the double hydroxides of the hydrotalcite-type structure [205]. The ion exchange reaction is an equilibrium process following the law of mass action. The theoretical treatment of the exchange properties is more complicated because of adsorption of the ions on the outer surface of the solid, the formation of a Gouy/Chapman electric double layer on the surface, and effects of diffusion of the ions in the solid [26]. In addition, the ion exchange capacity is not only determined by the content of exchangeable cations in the interlayer galleries, but can be increased by other processes: (a) In the case of clay minerals [26], a substitution within the lattice structure of trivalent aluminum for quadrivalent silicon in the tetrahedral sheet and of lower valent ions, particularly magnesium, for trivalent aluminum in the octahedral

28

SUPRAMOLECULAR CHEMISTRY IN NANODIMENSIONS

Fig. 12. Possible intercalation reactions of layered host lattices. The transfer of neutral host lattices to charged ones is only possible for those compounds exhibiting some electronic transport properties (at least hopping conductivity). Negativelyand positively charged host lattices of insulators. sheets, results in unbalanced charges in the structural units of some clay minerals. Sometimes such substitutions are balanced by other lattice changes (OH for O) or by filling more than two-thirds of the possible octahedral positions, but frequently they are compensated by adsorbed cations. A replacement of structural metal atoms also occurs in ion exchange reactions of some MPX3 compounds (e.g., MnPS3); these compounds take up hydrated metal atoms in the van der Waals gap, but metal atoms of the host layers are lost in the supernatant solution to keep the electric neutrality. It is very likely that at the interface between the educt and the resulting intercalation compound, a highly solvated transition state is involved: in this state MnPS3 is partially dissolved and the "intercalation compound" is reconstructed if other cationic species are present in solution that do not fit the "normal" lattice, but they lead to an increase in lattice energy of the whole system when they are taken up in the interlayer galleries [295]. (b) On the surface of the solids, broken bonds may exist, leading to unsatisfied charges, which can be balanced by adsorbed cations. They can occur on the horizontal planes and on the prism surface. This phenomenon is well studied for clay minerals [26]. The number of broken bonds and hence the exchange capacity will increase as the particle size decreases. In kaolinite and halloysite, broken bonds are very probably the major cause of exchange capacity. In illite and chlorite they are also an important cause of exchange capacity, whereas in the case of smectites and vermiculites they are responsible only for a small portion (20%) of the cation exchange capacity. In addition to the cation exchange, anion exchange, reactions can also occur. It is always a phenomenon restricted to the surface of the particles (mainly the prism surface)

29

LERF

Fig. 13. Detailedreaction scheme for negatively charged host lattices. This is an extended scheme showing all of the reactions of conducting solids. It shows that the redox reactions are reversible (at least to some extent). It shows further that the ternary compounds can be prepared out of the elements and that the obtained products can be transferred by oxidation reactions to neutral host lattices or that they can be reduced further to intercalate additional cations if empty cation sites are available.

and should therefore vary with the particle size. Two major factors are responsible for it: the exchange of phosphate (in the case of kaolinite) or fluoride ions for OH ions and the growth of the tetrahedral silica sheets by the addition of anions that have the same size and geometry as the silica tetrahedra (phosphate, arsenate, borate). This second effect can lead to a further increase of the cation exchange capacity. Perturbations of interlayer ion exchange reactions can also be expected for other host lattices, for example, perturbations due to the surface hydrolysis (intercrystalline and at outer surfaces) of chalcogenides [ 18] or the strong affinity of double hydroxides containing other interlayer anions toward CO2 or [HCO3 ] - [205,246]. Even under a given set of conditions, the various cations are not equally replaceable and do not have the same replacing power [26]. An order of replacing power will not be given because it depends on the concentrations of the ions in the exchanging solution and the nature of the host lattices. However, there are some general trends. The higher the valence, the greater is the ion's replacing power and the more difficult it is to displace when already present on the host. For ions of the same valence, replacing power tends to increase as the size of the ion increases. It has been assumed that the size of the hydrated ion, rather than the size of the nonhydrated ion, controls replacibility. Hence ions of equal valence, which are least hydrated, are the most difficult to displace when already present on the clay. For example, whereas cesium, as the largest alkali metal ion, is less hydrated than the small lithium ion and is kept stronger in the clay lattice than lithium, which is highly hydrated and has a larger size than the hydrated cesium ion. However, experimental data on the swelling, the heat of wetting, and careful dehydration cast into doubt the hypothesis

30

SUPRAMOLECULAR CHEMISTRY IN NANODIMENSIONS

that all common cations are hydrated and that hydration is the most important effect in an exchange reaction. Therefore, it has been assumed that replaceability is related to the polarization of the ion, with increasing polarization accompanied by increasing difficulty of exchange: highly polar ions are thought to be closer to the adsorbing surface. Polarization increases as the valence increases and the size of the ion decreases. (Please note that the hydration capability also increases with increasing polarization.) The influence of hydration can be clearly demonstrated by heating experiments [26]. An increase in temperature not only reduces the cation exchange capacity but also changes the relative replaceability of the cations. Heating montmorillonite to 125 ~ fixes Li + in an unreplaceable form, whereas the replaceability of Na + is not affected. At this temperature there is little or no water present between the basal layers in addition to the cations; thus the size of the ion and its geometrical fit in the structure are probably the major factors determining replaceability. Exceptions to the effect of ion size occur for those ions that have almost the correct size and coordination properties to fit in the surface structure of the host [26]. Potassium has these characteristics in the case of some clay minerals, and as a consequence it is very difficult to replace. As a consequence, when a mixture of montmorillonite and muscovite is treated with mixtures of calcium and ammonium acetate, the mica adsorbs much more of the NH + and the montmorillonite more of the Ca 2+. On the other hand, Ca 2+ in competition with equivalent concentrations of K + would be taken up preferentially by montmorillonite, whereas the opposite is the case for muscovite. The uptake of protons is also an exception. For the most part protons behave like divalent or trivalent ions in clay minerals [26]. This peculiar situation could be caused by the fact that hydrogen montmorillonite is really a hydrogen-aluminum system. Protons can pass to the octahedral layer, and in reverse, A13+ moves from the lattice to exchange positions before saturation with H + becomes complete. The movement of aluminum is facilitated by drying. As long as the sample is not dried, the amount of movement is small. Hydrogen forms can be obtained from nearly all charged host lattices by ion exchange or direct synthesis in the case of conducting solids (Table III gives a collection of such protonated host lattices). There are a few host lattices that contain protons in the state as prepared, and these protons are attached to constituents of the layers (e.g., a-ZrP, y-ZrP, or the silicic acids). Many of these solid acids can take up neutral bases very easily, leading to large number of new intercalation compounds. Extremely weak organic bases do not form complexes with clays, and large bases like codeine or brucine neutralize fewer protons than are available on clay. Hendricks [293] pointed out that the organic bases are held by van der Waals forces in addition to the Coulombic force. Hence the larger ions are more strongly adsorbed, and as a further consequence it is difficult or impossible to replace them with smaller ions. A very peculiar group of organic ions is formed by the amphiphilic derivatives of aliphatic hydrocarbons. They can be exchanged in all host lattices known, even in cases where an exchange of inorganic ions is not possible because of missing ion solvation and the accompanying reduction of ion mobility. The rate of ion exchange varies with the solid, the nature and concentration of the cations, and the nature and concentration of the anions [26]. The reaction for kaolinite is most rapid. It is slower for smectite and for attapulgite and requires an even longer time to complete in the case of illite. The exchange of alkylammonium ions in micas can take some months. The exchange on the edge of the particles, as in the case of kaolinite, can take place quickly. But penetration between the sheets of smectite or of the channels of attapulgite requires more time. The slow penetration results from the fact that ion exchange in solids is mainly a diffusion process, and its rate depends on the ion mobility. When the exchange reaction is accompanied by swelling, and the change from one stable interlayer distance to another requires a definite activation energy, hysteresis phenomena occur. The cation exchange is often accompanied with an increase in the c dimension of the unit cell,

31

LERF

Table III. HydrogenForms of Layered Host Lattices Conducting solids Oxides

Chalcogenides

Halides

HxMoO3

HxTiS2

HxZrC1

HxV308

HxVS2

HxZrBr

HxTiO2 (hexagonal)

HxNbS2

HxRuC13

c~-HCrO2 [296, 297]

HxTaS2 (1T)

HxLi0.2NbO2

HxTaS2 (2H) HxCrS2 HxMoS2 Nonconducting solids

Clays [26]

Silicic acids [248-250, 298]

Oxides [253]

Phosphates/Arsenates

H-montmorillonite

H2Si205(I-III)

HTiNbO5

a-ZrP [204]

H-vermiculite

H2Si409

HTi2NbO7.2H20

y -ZrP [213]

H2Si8O17

HTi2NbO7.H20

H2Si14029

HTi2NbO7

H(UO2PO4)4H20 [263, 264]

H2Si20041

H3Ti5NbO14-H20

H(UO2AsO4)4H20 [300]

HxTi2-x/404.H20 [299] If not otherwise stated, the compounds are taken from [14].

and this influences the rate of exchange. When an increase in the unit cell height occurs during exchange, the reactions proceed in a highly regular fashion from the edges toward the interior of a flake, because a well pronounced phase boundary is formed that can easily be followed in single crystals with a microscope. The accurate determination of cation exchange capacity is very difficult to accomplish because of the many factors controlling the process. Weiss [301 ] discussed in detail for the case of clay minerals the problems to encountered in trying achieve reproducible results and showed the wide variations in values obtained by different methods. He pointed out that quantitative determinations of all cations and anions in the exchange solution and in the solid are necessary to obtain accurate values.

2.2.2.1.2. Uptake of Neutral Molecules. The uptake of neutral molecules was observed independently for the first time by Bradley [79] and MacEwan [80] in 1945 to 1948 for the phyllosilicates (clay minerals). Today it is known that neutral molecules can be inserted in most of the charged and uncharged host lattices. Although an enormous number of different compounds have been prepared, only the intercalation compounds of the clay minerals has been studied extensively [26-28]. Thus these compounds are the leading systems for showing the underlying principles of the adsorption of neutral molecules in layered host lattices; therefore the following discussion will concentrate on these compounds, but reference will be made to corresponding compounds of other host lattices. Earlier studies had attributed a predominant role to the interaction of the adsorbed molecules with the silicate surfaces, but by applying IR [27] and NMR [302-304] spec-

32

SUPRAMOLECULAR CHEMISTRY IN NANODIMENSIONS

troscopy, the utmost relevance of the interactions with exchangeable cations has been recognized. Van der Waals attraction between molecules and the mineral substrate contributes to the adsorption forces, but its significance is secondary, except for organic compounds of large molecular weight. This explains why many more species with different chemical natures are taken up by charged than by uncharged host lattices. A medium position between these two types of host lattices is found for protonated host lattices: BrCnsted acid-base interactions determine mainly the formation of complexes with neutral molecules in this case. Water is the most essential neutral molecule that can be taken up in nearly all charged host lattices (exceptions: graphite intercalation compounds, micas, and other charged compounds with high cation density; see Section 2.2.2.2). The following discussion will concentrate on the negatively charged host lattices and the interaction of neutral molecules with cations, because the overwhelming number of charged host lattices is of this type, and the polarizing power of anions and the concomitant tendency toward solvation are much lower than those of cations. The extent of water uptake depends on the layer charge density (this effect will be discussed in greater detail in Section 2.2.2.2), the type of cation in the interlayer galleries, the water vapor pressure surrounding the sample, and in some cases the salt concentration in the supernatant solution [26, 208]. The driving force for the uptake of water is the hydration of the interlayer cation. Uncoordinated water may complete the filling of the interlayer space. The uptake of water is for host lattices with low charge density a reversible process, but for highly polarizing cations the removal of all water molecules affords drastic conditions (temperatures higher than 200 ~ If the cations fit ideally into the structure of the host layer surfaces or if the cations strongly interact with the host lattices, such "burnt out" systems do not take up water again. Much information about the coordination of water molecules around the cations, the positions of the interlayer cations, and their mobility has been gained (see Section 3.2). The properties of interlayer water differ from those of bulk water. One particular difference is the increased acidity of the interlayer water; this is especially characteristic of residual water; which can be removed from the lattice only under drastic conditions. The state of hydration is commonly expressed as the number of water layers, that is, one, two, or four, corresponding to layer expansions of about 0.25, 0.5, or 1.05 nm. These layers should not be considered to be strongly organized. This type of organization can also be found in the hydrated phases of host lattices other than clay minerals with nearly the same thickness of individual layers. Besides water, other molecules that have functional groups with free electron pairs can form coordination compounds with exchangeable cations [26, 208]. Such substances (mainly organic in nature) may be adsorbed from the vapor phase, from the pure liquid, or from solutions in water or other solvents. In either case, the uptake in the interlayer space is influenced by the state of hydration of the clay (this is even true for other host lattices). Sometimes clay samples are thoroughly dehydrated before adsorption, but more frequently they are simply air dried. When interlayer water is present, the cohesion forces of the clay are greatly reduced, and consequently penetration of the molecules to be taken up is facilitated. Many neutral molecules can be intercalated only if the interlayer space is propped open by preintercalation of other neutral species. After entering the interlayer space, the molecules compete with water for coordination sites around the cations, and depending on the relative values of solvation energies, they will (i) replace water in the first coordination sphere; or (ii) occupy sites in the second coordination sphere, being bonded to them through bridging water molecules; or (iii) accept a proton from the coordinated water or from the cation itself (e.g., NH~-). The structure and properties of the complex formed will be influenced by the electric field of the host layers and steric restrictions in the interlayer space. The interlayer space provides a special environment in which a particular chemistry occurs, and it is possible that complexes not known in solution chemistry may be obtained in this environment [208].

33

LERF

In neutral host lattices (e.g., graphite, transition metal dichalcogenides, MOO3, FeOC1) it is possible to intercalate directly solvated metal cations under completely nonaqueous conditions. Such systems could be interesting reference systems for complexes formed in the presence of water. The solvation of the most electropositive alkali and alkaline earth metal cations is restricted to polar molecules bound to the cations by ion-dipole interactions. The molecules that have been taken up are mainly mono- and polyfunctional alcohols, mono- and polyfunctional ethers (including crown ethers), ketones, amides, and other compounds (see Section 2.2.3). The uptake of amines can be accompanied by the formation of protonated forms and the release of metal cations and thus is not a pure solvation reaction. Transition metal ions with partially filled d or f orbitals form much stronger (and directed) bonds with molecules containing free electron pairs than the alkali and the alkaline earth metal ions. If these ions are intercalated in host lattices, the types of interactions switch over from solvation reactions to a coordination chemistry in restricted space. The exchange reaction of water or other species in the coordination sphere by other ones is not determined by simple ion-dipole interactions; they are true ligand exchange reactions that follow the rules of metal coordination chemistry [208]. From these considerations one can expect new intercalation compounds with a greater variety of different species than is observed for the nontransition metal ions. Metal complex formation in the interlayer space was shown for the first time by Weiss and Hofmann, who observed the formation of the Ni-diglyme complex in batavite [88]. Later on, Bodenheimer et al. [305] showed the formation of complexes with multifunctional amines. Now many intercalation compounds of very different metal complexes (Table VII) [306] are known, including those of transition metal complexes with purines, pyrimidines, amino acids (see Table XI) [27]. For the polyamine complexes of Cu, Ni, Zn, Cd, and Hg montmorillonite, it is known that their thermodynamic stability constants are two to three orders of magnitude higher than those for the same complexes in solution [208]. It has also been shown that complexes not formed in solution can be stabilized in the interlayer space of montmorillonite (e.g., the Fe-pyrocatechol complex cation). Mortland et al. have observed that Cu 2§ ions form rr-coordination compounds with arenes in montmorillonite, but it is not known whether they can do so in homogeneous solution [307, 308]. Formation of these rr-complexes and the resulting disruption of the bond resonance in the arene tings (as concluded from the variety of subsequent reaction products) suggest new reaction pathways for organic synthesis via complex formation in the interlayer space of solids [208]. The insertion of neutral molecules in clays saturated with organic cations results in interactions with the clay or with the organic cations present, or with both [208]. When the molecules intercalated are of the same species as the existing cations, hemisalt complexes are formed. Thus pyridine or ethylenediamine (EA) is adsorbed into pyridiniummontmorillonite or EA+-montmorillonite, respectively, and the corresponding hemisalts are formed in the interlayer space. On adsorption of molecules of a different species, proton transfer occurs if the molecules inserted are bases competing with the cations for the protons. Two factors were found to affect the extent to which the adsorbed molecules were protonated: the relative basicities of the two interacting compounds and the relative abundance of reactants and products in the interlayer space. Asymmetric hydrogen bonding to the organic cations occurs if the intercalated species contain functional groups capable of acting as electron donors. This has been demonstrated for the adsorption of dialkylamides and other carbonyl compounds such as aldehydes, phenyl-alkyl-diamides, and the herbicide ethyl-N,N-di-n-propyl-thiocarbamate. When the interlayer organic cations are capable of solvation, van der Waals interactions are established between the organophilic residues of the cations and the adsorbed molecules. The accommodation of additional molecules in the interlayer space will affect the orientation of the cations, so that swelling of the solid is observed. Thus adsorption of benzene or chlorobenzene in pyridinium-montmorillonite changes the disposition of the

34

SUPRAMOLECULAR CHEMISTRY IN NANODIMENSIONS

pyridinium from parallel to normal to the silicate layers, which is accompanied by an increase in the interlayer distance d (001) from 1.25 to 1.5 nm. If interlayer cations are long n-alkylammonium ions and the adsorbed species are polar n-alkyl compounds, more swelling takes place [208] (see also Section 3.4). Strong van der Waals interactions between the alkyl chains of the neutral molecules and the cations cause them to be densely packed in bimolecular layers. For short alkylammonium complexes, uptake of additional species accompanied by lattice expansion is possible only if the alkyl chain of the cation exceeds a critical length that is inversely related to the layer charge. Five or six carbon atoms are required for vermiculites, but at least 11 atoms are required for the lower charged montmorillonites. The insertion of polar molecules with branched alkyl chains or with aromatic or cyclic rings on the n-alkylammonium derivatives produces a significant layer expansion. Expansion will also occur with the di- and trialkylammonium or alkylpyridinium derivatives. The additional molecules cause first a readjustment of the orientation of the alkylammonium chains, and then they adapt themselves to the voids created in the interlayer space in the most space-saving manner, so that maximum adsorption can take place. Long-chain alkylammonium derivatives of montmorillonite can disperse in polar organic liquids, forming thixotropic gel structures with very high liquid contents. Development of organophilic properties requires that more than half of the available clay surface be covered by the hydrocarbon chains of the alkylammonium ions, and that an interlayer separation corresponding to the thickness of a flat bimolecular layer has been realized. For the complexes with the primary amines, alkyl chains of at least 12 carbon atoms are adequate to achieve that separation. Maximum swelling occurs with organic species such as nitrobenzene combining a high polarity and high organophilic character. With less polar liquids or with hydrocarbons, swelling can be enhanced if small amounts of polar additives (alcohols, esters, or aldehydes) are added. Complexes with unsymmetrical di-, tri-, or tetraalkylammonium cations with two long aliphatic chains are more organophilic because a larger part of the silicate surface is covered by the alkyl chains. They can swell with fewer polar liquids and with unsaturated hydrocarbons. The increase in organophilicity leads to a gradual reduction of the water-adsorbing properties as the montmorillonite surface is covered by alkylammonium ions. It has been shown that the larger the size of the aliphatic chain of the cation, the lower is the water content of the complex in equilibrium with atmospheres of a given humidity. However, complexes of vermiculite with short-chain alkylammonium ions swell in water or dilute solutions of the corresponding ammonium salts, forming coherent gel-like structures. In these, the layers are separated by distances of several tenths of a nanometer. Vermiculite saturated with certain amino acids in their cationic forms swells in the same manner, because these organic cations contain functional groups capable of interacting with water molecules by H-bonding. A peculiar position is taken by the protonated forms of the negatively charged host lattices. They can be formed not only for the clay minerals, but also for a great variety of other charged host lattices (see Table III). Even the neutral host lattice ot-Zr(HPO4)2 behaves to some extent as a protonated form of a negatively charged host lattice. The insertion of neutral molecules, mainly bases such as aliphatic or aromatic amines, or heterocyclic compounds acting as BrCnsted bases, is a neutralization reaction. It is a convenient method of preparation for intercalation compounds of organic cations that avoids contamination with additional cations due to incomplete ion exchange reactions. The selection of molecules to be inserted depends on the acid strength of the solid (which is not known in most cases) and the base constant of the organic molecule. The extent of intercalation is determined by the content of the protons and the size of the intercalated base. Large molecules can cover some protons; thus the number of molecules intercalated can be lower than the maximum exchange capacity [293]. The intercalation of neutral species in neutral host lattices is not as straightforward as for the charged host lattices. Because the organizing influence of the cations is no longer

35

LERF

present, the surface properties of the individual host lattices determine the type of interaction with species to be inserted. Thus, each type of host lattice has to be considered on its own. The 1:1 clay mineral halloysite, which is distinguished from kaolinite by the insertion of one water layer, takes up many more molecules than kaolinite [27, 208, 209]. The "propping open" effect of water facilitates the intercalation. Only a few molecules (urea, hydrazine, dimethyl sulfoxide (DMSO)) can open the interlayer space of pristine kaolinite. When opened by these preintercalation reactions, kaolinite is accessible to the insertion of additional species via solvent exchange reactions. Very peculiar for kaolinite is the intercalation of salts (cations + anions), which has been called intersalation. Despite several decades of study of intercalation in kaolin minerals, there is no clear understanding of which physical and chemical properties are necessary for a species to form an intercalation compound [309]. Costanzo and Giese suggest that the important factors are the surface tension of the clay layers and the liquids [309]. Rather different is the situation in the Hofmann-type compounds. During preparation, molecules like benzene and thiophene are included in the interlayer space between the staggered amine residues. These compounds decompose gradually under ambient conditions, in which the guest molecules are released; the liberation of benzene, for example, is completed by heating the specimen to 130 ~ [210]. It is not clear whether this process is reversible. Thus, this compound is more like an inclusion complex than an intercalation compound. The reaction of the hydrated or dehydrated Ni(CN)2 with long-chain alkylamines is not a BrCnsted acid-base reaction as discussed above for protonated solids; the amine is bound covalently to Ni via a water substitution or a Lewis acid-base reaction (for the dry NiCN)2) and is, therefore, more like a grafting reaction, which is discussed later in this section. Because of the long-chain alkyl residues, this reaction should have transferred nickel cyanide to an organophilic solid, which could intercalate neutral less polar substances like the long-chain ammonium derivatives of the clay minerals (see discussion above). This possibility has not been investigated up to now. A similar situation exists in the organic derivatives of the Zr phosphates, but the organic residues are packed in a nearly dense arrangement, leaving no space for the access of additional molecules [213]. Choosing special organic residues makes it possible to create voids in the structure that can be filled by other species (see later in this section and Section 3.5.2). The inorganic counterparts of these modified compounds are the Zr phosphates. These compounds show in part an intercalation like that of the neutral 1:1 clay minerals. But on the other hand, the former are much more acidic than the latter. Thus, ion exchange reactions in a strongly basic medium are possible, as is reaction with organic bases, which is found for the protonated forms of the negatively charged host lattices. The layered dichalcogenides are also known to form intercalation compounds with many neutral species. The interaction of the inserted molecules with the chalcogenide surfaces is not quite clear. Hydrogen bond formation is highly unlikely, because S-H-X bonds are very weak; the same is true for ion-dipole interactions, because the layers are symmetric with respect to the central metal layer, in contrast to the halloysite and kaolinite layers. The suggested Lewis base [20] or charge transfer [310] interactions between the lone pair of inserted molecules and empty states of the metal atoms are also very unlikely, because the distance (at least 0.4 nm) between the center of the interacting atoms is far too long for covalent bond formation. This type of interaction would also not explain the reversible nature of the compounds obtained and the high mobility of the intercalated species. Most of the intercalated compounds contain nitrogen and are acting not only as Lewis bases but also as BrCnsted bases. Considering the uptake of nearly the same compounds observed for the protonated clays or Zr(HPO4)2 (note the large number of protonated dichalcogenides given in Table III), the intercalation in the layered dichalcogenides may also be caused by a BrCnsted acid-base reaction; then the question arises, where do the protons come from? One mechanism will be discussed in the next subsection.

36

SUPRAMOLECULAR CHEMISTRY IN NANODIMENSIONS

2.2.2.1.3. Redox Reactions. the equations

Redox reactions of potential host lattices [ 142] according to

xI + + x e- + x[Host] =~ (I+)x [Host] xx I - + x[Host] =:~ (I- )x [Host] x+ + x ewill occur if 9 The metal atoms of the host lattices easily undergo changes of the oxidation state (in physical terms: the electrochemical potential E of the reducing/oxidizing agents is positioned with respect to the energy levels of the highest occupied or the lowest unoccupied states such that electrons can be taken up or withdrawn from the partially filled or empty bands of the solid). 9 There must be empty sites in the host lattices that can be occupied by the chargecompensating ions. In case of the layer host lattices, they are arranged mainly in the interlayer galleries of the empty neutral host lattices. In some charged host lattices not all available positions are occupied by the present ions. 9 The host lattices should have at least some electronic conductivity (band conduction or hopping mechanisms), so that the electrons transferred to the solid can be distributed in the bulk solid. 9 The charge-compensating counterions must have some mobility so that they can diffuse under mild conditions (room temperature or slightly above) in the bulk of the solid, otherwise the reaction will come to an end and surface redox reactions will take place. The reactions can be carried out by chemical oxidation/reduction or electrochemically. With a few exceptions (e.g., oxidation by C12) these reactions are carried out in solution (aqueous or nonaqueous). In the case of chemical oxidation reactions (the single example among layered hosts is graphite), the oxidizing agent is transferred to the anion, which can be inserted directly into the solid (C12 to C1- or Br2 to Br-; the degree of oxidation is low in many cases, and the intercalated anion is often solvated by additional species: metal halides or excess oxidizing agent, like Br2 [5]), or an excess of oxidizing agent is created in the interlayer galleries by the loss of protons (HSO4: for the graphite intercalation compound (HSO4)(H2SO4)yC24). In chemical reduction reactions, anions are the main reducing agent, and the accompanying cations are inserted in the solid [142]. Figure 14 gives a collection of reducing agents and their E values; these are compared with the experimentally determined potential regions of intercalating solids. It shows which of the reducing agents can be applied for the intercalation of some typical reducible host lattices. For the electrochemical reactions the solutions of species to be inserted in the solid must have some conductivity to work as an electrolyte. In the case of nonaqueous solvents this demand restricts the number of applicable salts and thus the number of species that can be inserted in the solid, which are mainly monovalent species. Depending on the solvation behavior of the solvents applied, the ions may be inserted in solvated or unsolvated form. If the ions (mainly cations and reducing reactions) are inserted together with the solvent, the mobility is often higher than for the naked ions, although the layer expansion by cointercalation of solvents is usually much larger than for the ions alone [ 142, 226]. Thus, the intercalation of naked cations is mainly restricted to small monovalent ions like H +, Li +, or Na + [ 142, 226]. The most powerful solvent, water, also allows intercalation of di- and trivalent cations, but only in the hydrated state [ 142, 226]. During reduction/oxidation of the solid, the electrochemical potential of the solid shifts to a more negative/positive voltage (Fig. 15). The redox intercalation reaction starts in general with a two-phase region consisting of unreacted host and a first-stage intercalation compound with a definite stoichiometry. If the solid shows the tendency to form

37

LERF

.

I

FeOCl

vs TTF

TTF

"2H-TaS2 in aqueous medium

V205 j-

__

S2/SO4 2"

__

0

s

, Iv,o,, "' IT" ]:vs "1"

pH 14 S~O,=/SO3~ _ pH>7 bzph

-1

IMoO2

nBuLi bzph

-- -2 = . . .

1T-TaS2

Tgraphite NiPS3|solvent uptak;

I

IWO2

a

H,

raphite

naph LiNH3

.._=

-3

Fig. 14. Potential regions of some intercalating solids, compared with the E values of chemically reducing agents. (Source: Extended and modified from [311,312].)

higher stage compounds, a sequence of two-phase regions may be created. The intermediate higher stage phases have the same intercalate packing density as the lowest intercalate content of the first stage phase [313]. This can be visualized most properly in voltage/time (intercalate content) diagrams monitored during an electrochemical intercalation run (Fig. 15). The flat portions with constant electrochemical potential are indicative for two-phase situations. All phases appearing in the electrochemical reaction sequence are characterized by a definite E. Two solid phases in equilibrium form a redox couple. As long as one of the two constituents of the redox couple is present in solution, the electrochemical potential stays constant. In solids there are homogeneity ranges; in them the concentration of the components may very continuously, and this leads to a continuous change in the Gibbs free energy A G of the solids and, as a consequence, to a shift in E [314]. Therefore, the region of continuous shift of the voltage during an electrochemical intercalation run indicates a single phase with a broader homogeneity range. The lowest intercalate packing density (i.e., intercalation content) of the first stage phase depends on the type of host lattice and the type of intercalate. In the case of the graphite compounds (see Fig. 15), it is on the order of x = 0.04, and in the case of the dichalcogenides it is on the order of 0.2 ~ I

N

I

~

,,,~p

re

si

II

si

N

re

C1

N

re ,,~P

I ~N si ,~,,~p

,,P !

[ PP~

re

'P

,~P

si

,,~p

[v I

si

N

N I P-.... p~

si

~

N ~

N

si

[

re

"[ P-....

e~

N II~N-

re

I

p~

P-..

Fig. 15. Schematicillustration of the symmetriesand point groups of all possible assemblies obtained from chiral transition metalbisphosphane and bis-heteroaryliodonium ligand.

stereochemical outcome via asymmetric induction upon the self-assembly process. Indeed, when chiral complexes 94 and 95 reacted with bis(3-pyridyl)iodonium triflate 98 in acetone, the result was the formation, in excellent isolated yields, of an excess of one each of the preferred diastereomers of 99 and 100, as assessed by NMR (Scheme XXVI). Liquid secondary ion (LSI) mass spectra of 99 indicate the presence of [M--OTf] + ion with an m/z ratio of 2770. For square 100, however, it was possible to detect only the doubly charged ion [M-2- OTf] 2+, with an m/z of 1398, and to unambiguously establish its charge state. These data as well as the close match of the calculated and measured isotopic patterns of these ions confirm the predicted molecular weights for both of these macrocycles (Fig. 16). Self-assembly of the all-metal chiral molecular squares was also carried out with use of the above mentioned chiral Pd(II) and Pt(II) bistriflate complexes 94 and 95 and the Czh-symmetrical diaza-ligands, 2,6-diazaanthracene (DAA) 101 and 2,6-diazaanthracene9,10-dione (DAAD) 102 [64]. When the starting bistriflates are mixed with DAA in acetone at room temperature, the formation of a single diastereomer of each of squares 103 and 104 is observed, as assessed by NMR. The singlet in the 31p NMR is indicative of the exclusive formation of only one highly symmetrical chiral product (Scheme XXVII). The absolute stereochemistry of 103 as shown was assumed based upon the known [65] X-ray structures

198

TRANSITION-METAL-MEDIATED SELF-ASSEMBLY

Fig. 16. Ball-and-stickmolecular model of a chiral hybrid molecular square 99, obtained from MM2 force-field calculations.

of chiral BINAP transition metal diaryls in combination with MM2 force-field calculations. The ball-and-stick model of molecular square 103 is presented in Figure 17. In contrast, when DAAD 102 was employed as a connector ligand (Scheme XXVIII), the reaction mixture consisted of a significant excess of one diastereomeric product, 105 and 106, respectively, along with minor amounts of other diastereomers, as demonstrated by the 31p NMR spectra. Integration of the individual expanded 31p spectra gave a diastereomeric excess of 81% for 105 and 72% for 106. The macrocyclic nature of these species is established by multinuclear NMR and confirmed by mass spectroscopic data. Thus the ESI mass spectrum of molecular square 105 showed the presence of the doubly charged [M-2-OTf] 2+ and quadruply charged [M-4-OTf] 4+ ions with m/z ratios of 2503 and 1178, respectively. These ions correspond to the cyclic tetramer with loss of two and four triflate anions, respectively, thereby proving the cyclic tetranuclear nature of these assemblies. The interesting fact that both of these types of assemblies are formed either as a single diastereomer or a significantly enriched diastereomeric mixture is attributable to the significant degree of asymmetry induced by the chiral bisphosphane complexes. In the absence of such an induction, a mixture of six isomers may be formed, as indicated in Figure 18. This mixture was indeed observed when an achiral transition metal bisphosphane complex was used instead of BINAP [64].

199

STANG AND OLENYUK

~ P h

IsPh P.M:oso cF

N

+

acetone,rt

~ P h 101

94. M=Pd 95. M=Pt

h

~

Ph2

~

~

Ph/M eph Ph'-P P-Ph

Ph2.~~'~

8" OSO2CF3

103. M=Pd,86% 104. M=Pt,84% Scheme XXVII.

2.1.6. Nanoscale-Sized Molecular Squares The synthesis of organometallic nanodimensional macrocycles was achieved by applying a different self-assembly strategy: organoplatinum linear linking unit 107 was elaborated as the sides of the square, whereas the comers were the already described modules 49 or 64, both of which possess roughly 90 ~ geometries (Scheme XXIX) [66]. Building unit 107 was prepared from 4,4-diiodobiphenyl and Pt(PPh3)4 via oxidative addition, followed by the treatment of the product with AgOTf. Modular self-assembly of both macrocyclic assemblies 108 and 109 was achieved by the addition of either 64 in acetone or 49 in dichloromethane to the linear unit 107. Both 108 and 109 were isolated in good yields and characterized by a variety of physical and spectroscopic techniques. In addition, both the matrix-assisted laser desorption/ionization (MALDI) and ESI-FTICR mass spectroscopic techniques [66] confirmed the structure of assembly 109. Both of these macrocyclic assemblies belong to the category of ultrafine particles, because their estimated dimensions are about 3.4 nm along the edge and 4.8 nm across the diagonal for assembly 108 and 3.0 nm and 4.3 nm for 109. In light of their unique structure, they may become useful in the construction of nanoscale molecular devices. Furthermore, macrocycle 109 may be of interest to material science because of its potential nonlinear

200

TRANSITION-METAL-MEDIATED SELF-ASSEMBLY

Fig. 17. Molecularmodel of chiral molecular square 103.

optical and electronic properties, due to the presence of several transition metal alkynyl units and possible conjugation within the macrocyclic frame.

2.2. Molecular Parallelograms, Binuclear Structures, Rectangles, and Triangles From both chemical and topological considerations, construction of such species must rely on the specific geometry and angles between the binding sites within each organic ligand that must be coordinated to the chosen transition metal. For example, by introducing additional tetrahedral carbons between the pyridine tings, Fujita and co-workers were able to assemble several water-soluble macrocycles that contained only two transition metals. When ligand 110 was mixed with an aqueous solution of (en)Pd dinitrate 34, they observed the formation of assembly 111 (Scheme XXX) [67-69]. Because 111 contains the perfluorinated phenylene subunit, which is electron-deficient in character, it is capable of recognizing electron-rich compounds, such as naphthalene, in water. When 1,4-bis(4-pyridylmethyl)benzene 112 was used in the self-assembly, the corresponding palladium-based bimetallic species 113 were found to be in equilibrium with its catenated dimer 114 (Scheme XXXI) [70, 71 ]. This observation may be interpreted in such way that the benzene part of the second self-assembled molecule serves as the guest for the first macrocycle that is a host unit. At room temperature, the Pd catenane is in equilibrium with its monomeric form 113, as confirmed by spectroscopic studies. At lower concentrations ( 50 mM) concentrations. With the Pt analogue 115, because

201

STANG AND OLENYUK

O

Ph isPh P.MsOSO2CF3

[~'~ i~.~..ttP~

N acetone, rt

"OSO2CF3 "H20 + O

94. M=Pd 95. M=Pt

102

Ph--P++P-Ph pht ~Mt xph

o

/

o-

o

o

P h / M Ph Ph--P P-Ph

\r

8 - OSO2CF3

105. M=Pd, 94 % 106. M=Pt, 89% Scheme XXVIII.

of the greater Pt-N bond strength, the monocyclic structure is exclusively formed at room temperature, and it is not in equilibrium with catenanes or any other species. However, by heating the reaction mixture to 100 ~ in the presence of NaNO3, the Pt-pyridine bond becomes labile and facilitates the formation of the catenated dimer 116. After this catenane is formed, the solution can be cooled to room temperature, thereby irreversibly forming the catenane. Isolation of the catenate 116 confirmed its structure by X-ray crystallographic analysis [72]. The self-assembly of molecular rectangles may be achieved by using modified organic angular subunits. When the asymmetrical angular building block 117 was mixed with (en)Pd(NO3)2 34, it formed the catenated rectangular assembly 118 (Scheme XXXII) quantitatively with remarkable stability; the dissociation of 118 into its component tings was not observed, even at low concentrations (see footnote 22 in [73]). An X-ray study of the structure of this assembly revealed two topologically chiral isomers in the solid state [73]. Fujita et al., also reported the self-assembly of a rectangular system containing three different subunits: one linear and two dissimilar angular units. When 4,4'-bipyridyl

202

/'~ z

z

9~

~,"~

~-,V ~

/~.

z

i i

Z

z

z

.-

~,---~- z : ~ : C ~ z ~

z

z

z

Z

,,,%

~~,,

z

z

z - - ~,

TRANSITION-METAL-MEDIATED SELF-ASSEMBLY

.~ z

z

z

~V ~

z

z

9~

z

203

8

0

=

o

0

~J

y

0

. ,..,~

0 o~ 0

. ,,..~ 0

r

E

0

xj 0 . ,...~

r162

r

o~

~9

PPh3 PPh3 I,+ I TfO--?~~~-'l~t+--OTf PPh3 PPh3 107 + + ["~'PPh2 Ph2P--Pt = CH2Ci2, /

[~

rt, 4 y

Ph

Ph3P

64

49

PPh2 PPh, PPh3 : ~N--I~'~I~'--N~ PPh3 PPh3 I

-OSO2CF3

~N

Ph2P"-"] :~Peh 2

i

"~,

acetone, 4h

PPh~

PPh3

PPh3

PPh3

--

t+-

Ph3P-Pt-PPh3

Ph3P-I t-PPh3

s-oso~.~

Z

Ph3P-[~-PPh3

~

Ph3P-I~t-PPh3

I~l PPh~ PPh3 PhtzP-Pt -- ~ N - - l ~ l t ~ l ~ l t ' - N ~ [.....~eeh2 Peh3 PPh3

l

t::3 9

I

PPh3

"~"

= Pt-PPh2 eh2e~...[

~~

l~N--l~t

109 Scheme XXIX.

,,h ~l~t-PPh3 108

PP,~ ~.)~I eeh3

Z ,.
380 nm

i

-2e-2H

+

+2e

+2H +

Hydrazobenzene (--NH--NH--)

Fig. 6. Dualmode of controlling the azobenzene switchingproperties by employingphoto- and electrochemistry.

230

MOLECULAR AND SUPRAMOLECULAR NANOMACHINES

(

(-)-CPL

I

~

(+)-CPL 5b

.

M

e

M

LPL

(-)-CPL Writing

Reading

UPL Erasing

Fig. 7. A chiroptical molecularswitch 5. The interconversion between the two states is accomplishedby circularly polarized light. CPL, Circularly polarized light; LPL, linearly polarized light; UPL, unpolarized light.

conrotatory electrocyclization. Upon irradiation with UV light, the colorless fulgide 6 is converted (Fig. 8) into the colored dihydronaphthalene derivative 7. Thus, a photochromic switch has been created, inasmuch as the cycle can be made reversible by irradiation of 6 with visible light. The readout procedure for the two different states is based on the differences in the absorption spectra of the two isomers. The main problem is that this detection method can interfere with the "writing" of the data. An easily accessible, nondestructive method of "reading" the two states will have to be uncovered if fulgides are to play an important role in storing data at the molecular level.

2.3.2. Diarylalkenes Irie and co-workers [28] first reported the preparation of thermally stable diarylalkenes by using furan or thiophene tings instead of phenyl tings. In this manner, the possible cis-trans isomerization of the central double bond was prevented. Upon UV irradiation at 405 nm, the yellow-colored open form 8 was converted (Fig. 9) into the brown-colored closed dihydro derivative 9: compound 8 could be regenerated by exposure of 9 to visible light ()~ = 520 nm). Based upon this system, Lehn et al. [29] have devised (Fig. 10) a dual-mode molecular switching device. The open form 10 is electrochemically inert, whereas the photocyclized hydroquinoid 11 can be oxidized reversibly at +0.72 V in MeCN. The resulting cyclic quinoid 12 is not photochemically active and cannot be reversed to the open form, that is, it is locked in the closed state. In summary, information can be "written" photochemically, and the data can be safeguarded or "locked" by oxidation to the quinoid form 12, which

~ 0

71 0 q/'~O~

L ~ R 2

X=366nm ~ ~/~ -"

R3

1ko R3 R2

O

~ > 492 nm

6

7

Fig. 8. The reversible photoinduced electrocyclization of the fulgide 6 into the dihydronaphthalene derivative 7.

231

GOMEZ-LOPEZ AND STODDART

Fig. 9. The reversible photoinduced electrocyclization of the diarylalkene 8 into the dihydro species 9.

Fig. 10. Schematic representation of an erasable optical memory system with nondestructive readout capacity based on the dual mode---electro- and photochemical---of switching of compounds 10-12.

allows for nondestructive "reading." A reduction process--back to the hydroquinoid l l - can then be used to unlock the information and permit subsequent photochemical erasing-photochemical ring opening to 10--thus rendering the cycle reversible. At the microscopic level, the system clearly behaves as a dual-mode optical-electrical molecular switching device. On the macroscopic level, the spectral and redox properties

232

MOLECULAR AND SUPRAMOLECULAR NANOMACHINES

are well suited to form the basis for a potential erasable data storage system with nondestructive readout capacitymas shown in the schematic representation on the right-hand side of Figure 10.

2.3.3. Spiropyrans The photochromic behavior of spiropyrans [30] is based on the reversibility (Fig. 11) that exists between the colorless "closed" spiropyran form 13 and the colored open merocyanine dye 14 as a result of the heterolytic cleavage of the spiro carbon-oxygen bond. On ultraviolet irradiation of the spiro form 13, the merocyanine 14 is formed. It can be made to revert, either by irradiation with visible light or thermally, to the spiro form 13. The lifetime of the zwitterionic merocyanine was increased dramatically from seconds to hours by the introduction of electron withdrawing nitro substituents. The photochromic behavior of the spiropyrans has been studied widely, and their conversion into the merocyanines have been exploited (i) to induce order into aggregated mesomorphic materials, (ii) to photocontract liquid spiropyran-merocyanine films [31 ], (iii) to assist the cross-linking of mesomorphic polymers [32], and (iv) to create organic materials with nonlinear optical responses, to cite but a few examples [33]. The most elegant use of the spiropyran-merocyanine switching cycle to date is one that combines surface chemistry, self-assembly processes, molecular recognition events, and biology. Willner and co-workers [34] have constructed (Fig. 12) a fascinating biomolecular device, in which the electron transfer communication between a cytochrome c (Cyt c) and an electrode is controlled reversibly by light. The electron transfer communication of the biomaterial Cyt c with electrodes is normally accomplished by the attachment of the pyridine substituents to the surface of the electrode, thus facilitating the recognition of the Cyt c by the pyridine substituents. The surface of the electrode can be modified by the introduction of the spiropyran component 15. The spiropyran moiety can be photoconverted into the charged merocyanine unit when electrostatic repulsions perturb the associative interactions of Cyt c with the pyridine units. Hence, the electrical communication between the Cyt c and the electrode becomes blocked. This electronic communication can be reversibly switched back on again by transforming photochemically the merocyanine unit into the neutral spiropyran form, thus restoring the molecular recognition between the pyridine units and the Cyt c. Furthermore, the Cyt c acts as an electron mediator in a series of biological pathways, such as the reduction of molecular oxygen to water by Cyt c oxidase (COX). Therefore, the biocatalyzed reduction of oxygen to water can be switched (Fig. 12) off and back on again by photochemically impeding the electronic communication of the Cyt c with the gold electrode. These results are of considerable importance because they prove that the chemist can achieve the control of intricate biological pathways in a logical manner.

Me Me

~/+Me~?e

hv 1 y

Me

hv~ or

13

A

Me 14

Fig. 11. The photochemical switchingfrom the spiropyran13 to the merocyanine 14.

233

0

GOMEZ-LOPEZ AND STODDART

Fig. 12. A photochemicallycontrolledbiomoleculardevice in whichthe reduction of molecular oxygen to water can be switched on and off reversibly by photochemical means.

2.3.4. Redox Switching of the Luminescence of a Bipyridine

Metal Complex Lehn and co-workers [35] have designed and synthesized (Fig. 13) a molecular device that combines an electroactive component with a light emitting one. Compound 16 consists of a Ru(bpy) 2+ as the photoactive center and a quinone moiety linked together by an ethylene spacer. In the case of 16, the luminescence of the Ru(bipy)~ + complex at 610 nm is very efficiently quenched by the quinone unit. Electrochemical reduction of the quinoid 16 to the hydroquinoid 17 at - 0 . 6 0 V results in a highly emitting solution, that is, the hydroquinone moiety does not quench the emission of the Ru complex. Compound 17 can be reversibly oxidized back to the quinone 16 at + 1.10 V, regenerating a nonlumiscent solution. Hence, it is possible to control electrochemically the luminescence of a bipyridine metal complex

234

MOLECULAR AND SUPRAMOLECULAR NANOMACHINES

o

N

OH

O

+2e-

+2H +

N

OH

.....

(bpy)zRu2+

2PF6-

(bpY)2Ru2+

16

17

Luminescence-OFF

Luminescence-ON

Fig. 13. Electrochemicallycontrolled switching of the luminescence of the Ru(bipy)2+.

in a reversible manner. Because both 16 and 17 are stable and isolable, they have the potential to function as an information storage device.

3. S U P R A M O L E C U L A R SYSTEMS A supramolecular system is composed of two or more subunits that come together to form an ordered superstructure because of the stereoelectronical complementarity of its components. The forces that control the formation of the superstructure are noncovalent bonding interactions, which are weak and reversible, making them ideal candidates for the construction of switching systems at the nanoscale level. Because there are many examples of supramolecular switching systems, discussing all of the examples is beyond the scope of this chapter. In our discussion, we will concentrate on more recent results, as well as on those that have emerged from within our own research group. 3.1. Crown Ethers Supramolecular chemistry came into being with the discovery of the so-called crown ethers by Pedersen [36] in 1967. It is well documented that crown ethers act as receptors for alkali metal cations and that the selectivity of this interaction depends mainly upon the size and conformation of the crown ether ring. In 1979, Shinkai and co-workers [37] described how they could modify the binding properties of crown ethers toward alkali metal cations by introducing switchable azobenzene units into their rings. The (E)-isomer of the azacrown 18 shows no complexation ability for alkali metal cations as a result of the "tight" conformation adopted by the polyether chain. On irradiation, however, the azacrown 18 is converted (Fig. 14) into its (Z)-isomer, producing a crown ether with a much bigger cavity. The (Z)-azacrown shows very high affinities toward Na +, K +, and Rb + ions. Furthermore, thermal reisomerization was prevented by the formation of the complex. The bistability in this case is total, that is, the (E)-isomer shows no binding ability, whereas the (Z)-isomer binds strongly to the alkali metal cations. Thus, they can be defined as all-or-nothing switches. Shinkai [38] also exploited the cis-trans isomerism of azobenzene and crown ether complexation in a different manner. He managed to photoregulate crown ether-metal ion complexation by competitive intramolecular ammonium ion binding. A derivative of benzo[ 18]crown[6] (19) incorporating an azobenzene unit with a primary alkylammonium ionic center at its terminus was synthesized. The (E)-isomer of crown ether 19 is able to extract alkali metal cations with no interference from the ammonium group, which is located far from the crown ether component. However, photoisomerization (Fig. 15) of

235

GOMEZ-LOPEZ AND STODDART

Fig. 14. Photochemicallyinduced isomerization in the crown ether 18. The complexation is effectively switched on and off by irradiation.

Fig. 15. Photochemicallycontrolled transport of alkali metal ions across a liquid membrane.

the (E)-isomer to the (Z)-isomer forces the ammonium ion into close proximity with the crown ether component, so that the macrocyclic polyether can bind with the ammonium ion center in an intramolecular manner, creating a "tail-biting" molecule, thus hindering the complexation of alkali metal cations. Back-isomerization to the (E)-isomer of the crown ether regenerates the original geometry, making it possible to extract alkali metal cations across a liquid membrane phase. Recently, Kimura and co-workers [39] have designed and prepared the malachite green derivative 20. This bis-crown ether is able to form strong complexes with Na + and K +

236

MOLECULAR AND SUPRAMOLECULAR NANOMACHINES

Fig. 16. Photochemicallycontrolled complexationof alkali metal cations by the crown ether 20.

ions, at least as indicated by mass spectrometric studies. When irradiated with UV light, the malachite green ionizes (Fig. 16) to its corresponding quinoid cation 21, and then, because of electrostatic repulsion, almost all of the metal ions complexed by the crown ether moiety of 20 were ejected out of the cavity. Thus, this biscrown ether can undergo clear-cut switching from a powerful cation binder in the form of 20 to the perfect cation release species in the shape of 21. This photoinduced switching behavior of cation binding is an all-or-nothing type of switch with potential device-like applications.

3.2. Fluorescent Signaling Systems A fluorescent signaling system [40] is a switch and/or a sensor in which the fluorescence of one of the components of the molecule can be switched on or off by the presence of a external chemical species that can interact with a different part of the molecule, giving rise to a supermolecule whose photophysical properties differ from those of the original molecule. A fluorescent ion signaling system is one in which the fluorescence is controlled by the presence of an ionic species. The design of such a system requires the presence of a component with fluorescent properties and an ion receptor component, which are separated by a spacer unit. The choice of the components is critical, and even the spacer unit is of crucial importance, because it has to allow electronic interactions between the fluorescent group and the receptor component of the molecule. A schematic representation of how this system works appears in Figure 17. The "fluor-spacer-receptor" system can be chosen such that its fluorescence is switched off (Fig. 17a) by a photoinduced electron transfer process (PET). The PET process can be suppressed by the entry of a cation into the receptor, thus producing an increase in the oxidation potential of the receptor. The logic of the system can easily be reversed (Fig. 17b). In this case, the PET only occurs when a cation is bound and the fluorescence is switched off in the free receptor. A very simple proton signaling system can be designed by combining an organic base (i.e., an amino function) with a common fluorescent unit (viz. anthracene), attached via a methylene spacer, as in compound 22. PET oc,~,rs (Fig. 18) in this system in so far as the fluorescence of the anthracene unit is quenched by the basic amino function. However, protonation of the amine nitrogen raises its oxidation potential to > +2.54 eV, the PET is suppressed, and a strong fluorescence is observed. Treatment with base regenerates the free amino function, resulting in the disappearance of the fluorescence and thus creating a reversible system. One of the main advantages of this system is that it can be used as a fluorimetric pH indicator. A special feature of modular systems is that their level of sophistication can be increased progressively by the designer. And so the next challenge was to extend the concept of

237

GOMEZ-LOPEZ AND STODDART

Fig. 17. Cartoonrepresentation of the design logic behind a fluorescent signaling system, a) The fluorescence of the system is switched on by the complexation of a cation by the receptor, b) The fluorescence of the system is switched off by entry of a cation into the receptor. +

H2N',.~

H3Nx

Acid

Base

22

22.H +

Fluorescence-OFF

Fluorescence-ON

Fig. 18. The pH-controUable fluorescence of the anthracene-containing compound 22.

fluorescent signaling to cations other than protons. C o m p o u n d s 2 3 - 2 6 listed in Figure 19 all behave as expected. W h e n they are free of cations, the fluorescence of the anthracene unit is q u e n c h e d by a PET process. However, in the presence of metal cations, the forma-

238

MOLECULAR AND SUPRAMOLECULAR NANOMACHINES

o

o

23

\

/

/---O

O

Me 26 CN

Fig. 19. Structuralformulas of the fluorescent signaling systems23-26.

tion of the corresponding complex inhibits the PET pathway, resulting in the generation of a fluorescent signal. Compounds 23 and 24 exhibit remarkable responses toward Na + and K + ions, in addition to showing pH-responsive fluorescence. Compound 25 exhibits very good selectivity toward Na + ions in alcoholic solutions, and compound 26 gives a maximum fluorescence emission in the presence of Rb + ions. In summary, the design of"fluor-spacer-receptor" signaling systems is simple in concept and quite general in scope and applicability. The very same concept can be applied in the construction of molecular logic gates (see Section 3.8).

3.3. Redox Switches by Ligand Exchange This supramolecular switch is based upon a receptor molecule that possesses two sets of ion binding groups, one a hard set and the other a soft set of ligating groups, both of which are anchored onto a calix[4]arene framework in an alternating fashion [41 ]. The calixarene [42] torus was chosen because it can direct the two different binding sites to the same face of the ring and allows either set to converge as a result of a conformational change. The selected "hard" binding sites were hydroxamate groups, whereas the "soft" binding sites were 2,2t-bipyridyl rings. Both of these binding sites have been attached to a calix[4]arene ring in compound 27 shown in Figure 20. In the presence of Fe nI, the hydroxamatesm the "hard" binding sites---converge to embrace the "hard" metal ion, whereas the "soft" binding sites diverge. Upon reduction to Fe n , compound 27 rearranges so that the "soft" bipyridyl binding sites engulf Fe II, whereas the hydroxamate groups separate. Subsequent oxidation reverses the process. The two states have different spectroscopic characteristics

239

GOMEZ-LOPEZ AND STODDART

Fig. 20. Electrochemicallycontrolled switchingof the modeof complexation of an iron metal cation by the calix[4]arene 27.

that enable nondestructive "reading" by UV/vis spectroscopy. Compound 27 behaves as a chromophoric switch: it changes from orange to pink upon reduction. As a result of the amphiphilicity of this switch, it is well suited for self-organization as a monolayer at airwater interfaces and for transfer into Langmuir-Blodgett films.

3.4. Translocation in Helical Complexes Based upon the principle already outlined in Section 3.3, the triply branched compound 28 shown in Figure 21, containing hydroxamate "hard" binding sites (located proximal to the core) and "soft" 2,2'-bipyridyl binding sites (at the periphery of the dendrimerlike molecule), was synthesized [43]. Addition of Fe III to 28 results in the formation of a FenI-hydroxamate complex possessing a left-handed triple-helix geometry. At this starting point, the single metal ion is located in the internal "hard" binding cavity: reduction (with ascorbic acid) of the guest ion from Fe Ill to Fe Ix induces (Fig. 21) translocation from the

240

MOLECULAR AND SUPRAMOLECULAR NANOMACHINES

Fig. 21. Electrochemicallycontrolled translocation of an iron metal cation along the triple-helical ligand 28.

internal "hard" hydroxamate binding sites to the external "soft" bipyridyl binding sites. Simultaneously with the translocation of the binding site, a change in color from light brown (FenI-hydroxamate complexes) to deep purple (FeII-bipyridyl complexes) takes place, giving the switch chromophoric properties. Subsequent oxidation by ammonium persulfate of the FeII ions regenerates Fem ions, which then move back into the internal "hard" hydroxamate binding sites. One of the challenges that still has to be met is the immobilization of this supramolecular switch on a conducting surface.

3.5. Photoswitchable Complexation of Metalloporphyrins The reversibly photocontrolled "on--off" complexation of zinc and magnesium phorphyrins with a well-designed stilbazole derivative can be induced by the cis-trans photoisomerization of the stilbazole [44]. Pyridine derivatives are well known to act as guests for metalloporphyrin hosts. Moreover, it has been reported that steric hindrance by porphyrin substituents--especially in the 2 position of the pyridine derivative--has a considerable influence on the binding constants. In the case of the zinc tetraarylmetalloporphyrin 29

241

GOMEZ-LOPEZ AND STODDART

~

J h'~

[ Steric Repulsion I hi.)' 29

Ka

29

= 279 M-1

Ka

=OM -1

Fig. 22. Photoswitchablecomplexation of the stilbazole 30 with the 4-tert-butyltetraphenyl zinc porphyrin 30. The Ka values were obtained in benzene at 23 oC.

with bulky tert-butyl substituents, the binding constant with the trans-stilbazole 30 is negligible because of the steric interactions (Fig. 22) between the phenyl ring of 30 and the tert-butyl substituents on the aryl groups of 29. However, irradiation of the mixture causes the photoisomerization of 30 from the trans-isomer into the cis one. This change in geometry results in the formation of a 1:1 complex between the porphyrin 29 and the cis-isomer of 30, the binding constant being 279 M -1 . The two states, complexed and uncomplexed, can be monitored by UV/vis and 1H NMR spectroscopies. The study of the complexation of metalloporphyrins with bases is of particular importance, because it influences the reactivity of metalloporphyrins in heme enzymes. 3.6. Dendritic Boxes: Ships in a Bottle

Dendrimers can be defined as monodisperse, highly branched macromolecules with welldefined constitutions [5]. One of the main potential applications of dendrimers is their ability to encapsulate guest molecules within their globular structures. Meijer and coworkers [45] have recently reported that it is possible to imprison guest molecules in a molecular dendritic container with a diameter of 5 nmmthe so-called dendritic box. These dendritic boxes are constructed from a flexible poly(propylene imine) dendrimer with 64 amino functions as end groups. These end groups can be capped with a t-BOC-protectedL-phenylalanine derivative, producing a 64 L-Phe box with a highly dense hydrogenbonded shell that confers upon the dendritic box a solid-state character, as demonstrated by 13C NMR relaxation data. The guest molecules present in solution, 3-carboxyproxyl, TCNQ, and Rose Bengal, are captured (Fig. 23) within the internal cavities of the globular dendritic boxes like ships in a bottle. When the t-BOC groups are hydrolyzed by formic acid, the guest molecules residing in the cavity of the dendritic box are released back into solution again. Furthermore, it has been possible more recently to achieve the shape-selective liberation of guest molecules from the dendritic boxes [46]. Thus, Rose Bengal and p-nitrobenzoic acid were encapsulated within the dendritic box. Hydrolysis, followed by dialysis (5% water in acetone) resulted in the liberation of the guest p-nitrobenzoic acid molecules, whereas the Rose Bengal molecules remained in the cavities of the dendritic box. However, hydrolysis of the outer L-Phe shell (12 N HC1), followed by dialysis (100% water), brought about the liberation of the Rose Bengal molecules and the recovery of the starting poly(propylene imine) dendrimer in 50-70% yield.

242

MOLECULAR AND SUPRAMOLECULAR NANOMACHINES

Fig. 23. Cartoonrepresentationof the encapsulationand release of chemical speciesby a poly(propylene imine) dendrimeroperating as a dendritic box.

In summary, a chemically driven supramolecular switch has been created. The fact that the shape-selective liberation of guests can be easily accomplished in a two-step process indicates that the fine-tuning of dendrimers is possible and opens up new opportunities for research in host-guest chemistry.

3.7. Complexation/Decomplexation of Pseudorotaxanes Much effort has been invested in recent years within our research group in exploring the donor-acceptor interactions between re-systems. In the mid-1980s, it was discovered [47] that the crown ether bis-p-phenylene-34-crown-10 (BPP34C10) binds strongly (Ka = 720 M -1) with the herbicide Paraquat in acetone solution. The solid state crystal structure reveals the formation of a 1:1 complex with a pseudorotaxane-like geometry in which the Paraquat dication threads itself through the cavity of the crown ether. Closer inspection of this X-ray crystal structure shows that the driving forces for the formation of the complex are the noncovalent bonding interactions associated with [C-H...O] hydrogen bonding interactions involving both the methyl and ct-bipyridinium methine hydrogen atoms on the Paraquat dication and the central oxygen atoms of the two polyether loops in BPP34C10, and re-re stacking, including charge transfer interactions between the re-electron deficient bipyridinium unit and the re-electron rich hydroquinone tings incorporated within the macrocyclic polyether. With these recognition features established, the design logic was inverted and the Paraquat units were incorporated [48] into a macroring in the shape of the tetracationic cyclophane, cyclobis(paraquat-p-phenylene). This compound, as its hexafluorophosphate salt, binds strongly with re-electron-rich aromatic substrates, such as 1,3- and 1,4-dioxybenzene [49], and 1,5-, 1,6-, 2,6-, and 2,7dioxynaphthalene [50] derivatives in both acetone and acetonitrile solutions. The corresponding tetrachloride salt has been shown to bind biologically significant compounds, such as amino acids and neurotransmitters (e.g., phenylalanine, tryptophan, serotonin, etc.), in water [51 ]. Cyclobis(paraquat-p-phenylene) complexes the re-electron-rich template 1,4-bis-2-(2(2-hydroxy)ethoxy)ethoxy)benzene. The solid-state structure of this 1:1 complex shows a familiar pseudorotaxane-like arrangement, with stabilization provided by cooperative noncovalent bonding interactions [52]. The oxygen atoms associated with the hydroxyl groups at the termini of the polyether chains of the linear compound are involved in [C-H...O] hydrogen bonds with two of the ct-bipyridinium hydrogen atoms on the tetracationic cyclophane. This additional hydrogen bonding is reflected in a dramatic increase in the binding constant, relative to that observed for 1,4-dimethoxybenzene. In addition to this source of

243

GOMEZ-LOPEZ AND STODDART

stabilization, [C-H... re ] interactions between two of the the aromatic hydrogen atoms of the hydroquinone ring of the diol and the re-cloud of the p-xylyl spacers in the tetracationic cyclophane also play a significant role in adding to the stability and defining the geometry of the complex. Against this background of knowledge it became possible to construct large and ordered molecular assemblies and supramolecular arrays. The structures and superstructures of these compounds and complexes depend upon the nature of the noncovalent bonding interactions and the fact that small changes in the stereoelectronic characteristics of the subunits allow for extensive changes in the binding constants. The reversible nature of the noncovalent bonding interactions provides the framework for the self-assembly of various supramolecular switching systems with pseudorotaxane-like geometries.

3. 7.1. A PhotochemicaUy Driven Supramolecular Machine The self-assembly of the receptor 31.4C1 and the naphthalene-containing substrate 32, which gives rise to the pseudorotaxane 32.31.4C1 (Fig. 24), is a result of donor-acceptor interactions between the re-electron-rich 1,5-dioxynaphthalene moiety of 32 and the re-electron-deficient bipyridinium units of 31.4C1, as well as of [C-H. 9.O] hydrogen bonding and [C-H... re] interactions. When 32 is added to an aqueous solution of 31.4C1, the substrate threads spontaneously through the center of the receptor to produce the 1:1 complex with a pseudorotaxane-like geometry. The threading process is supported by absorption and emission spectroscopic data in addition to 1H NMR spectroscopy. In a 6 • 10 -5 M aqueous solution of 32 and 31.4C1, a charge transfer band (~max = 520 nm), appears and the intensity of the naphthalene fluorescence ( ~ . m a x " - 345 nm) of 32 is quenched. It is well known that intermolecular redox reactions can be driven with light by means of suitable photosensitizers. A deoxygenated solution containing 9-anthracenecarboxylic acid (33), [Ered(33+/33 *) = - - 0 . 8 8 V vs. SCE], the complex 32.31.4C1, and a sufficient amount of a sacrificial reductant, triethanolamine, so that the oxidized 33 + species can be rapidly scavenged, was irradiated (Fig. 25) with 365-nm light to cause the reduction of the re-electron acceptor bipyridinium unit (Ered = --0.35 V for the "alongside" bipyridinium unit of an analogous [2]catenane). On photoreduction, dethreading takes place [53]. Proof of the occurrence of the dethreading process is the increase in the fluorescence of the 1,5-dioxynaphthalene moiety, which can only originate from free 32. After dethreading has occurred, if oxygen is allowed to enter the solution, the reduced cyclophane is promptly reoxidized, and 32 threads

m

+N

00

/---k/~k

OH

~

N + 4(31

~

+

~

~I

t~)

+ 4CI

31.4CI .o

o

o

32

H20

r--'X~"--- 32-31.4CI HO

0

k~/k__../

Fig. 24. The formation of the [2]pseudorotaxane 32.31.4C1.

244

0

MOLECULAR AND SUPRAMOLECULAR NANOMACHINES

Products Red hv

3 + N/~~N

+

33 +

+

313+

r--< N §

HO~__/Ox~/O [32"31] 4+

33

'

02

Red

HO~__/k_...../ O O

32

N~ O H

? OH

Fig. 25. A photochemicallydriven supramolecularmachine. The dethreading of the [2]pseudorotaxane 32.31.4C1 occurs after the photoinduced reduction of one of the bipyridiniun units in 31.4C1.

through it again, as shown by the decrease in the intensity of the fluorescence band and the recovery of the initial absorption spectrum. Thus, a simple supramolecular system, where complexation can be switched on and off photochemically in a reversible fashion, can be constructed rather easily.

3. 7.2. An Optically Responsive Supramolecular Switch It is possible to self-assemble [2]pseudorotaxanes from cyclobis(paraquat-p-phenylene) 314+ as the ring with dioxy-disubstituted arenes beating macrocyclic polyethers at their termini as the linear thread-like components. These [2]pseudorotaxanes can be used [54] to trigger an optical response on metal binding. The 18-crown-6 derivative 34, containing a 1,5-dioxynaphthalene ring system, can act both as a host toward alkali metal cations and as a guest toward the tetracationic cyclophane 31.4PF6. The binding of the Jr-electron-rich substrate 34 by 31.4PF6 can be impaired significantly by the addition of alkali metal cations, such as K +, which form complexes with 18-crown-6 derivatives. The resulting electrostatic repulsive forces induce dethreading of 34, leaving the tetracationic cyclophane 31.4PF6 free to act as a receptor for the :r-electron-rich cosubstrate 35, which lacks a crown ether terminus. Mixing equimolar proportions of 34, 35, and 31.4PF6 in MeCN results in a deep purple color arising from a charge transfer band at 518 nm, indicating that the tetracationic cyclophane resides mainly around the 1,5-dioxynaphthalene residue of 34. Upon the addition of KPF6 to the solution, the purple color fades and the UV/vis spectrum reveals a new (red) charge transfer band at 475 nm, which is consistent with the 1,4-dioxybenzene ring of 35 residing within the cavity of the tetracationic cyclophane. It may be concluded that when KPF6 is added to the solution, an unstable complex 34.K.31.5PF6 is formed (Fig. 26) in which electrostatic

245

/--k

r~o% 0 0.~

mo Oq~o

o.

/---k

r"~O/~xOH ~ / - - ~ ~ ~ + O #I.4PF~,

~'0

4PF6-

o

+ /_

r~o~

O

O

O~ o

O)

~o.J

~---, +

(/'.,O/--kOH

O

N

+

34

34-31.4PF6 + +~__.

_/

PURPLE 9

l

MeCN

N 9 N

~o~ -

PF6 C O

~

0~0~ ~) 0

r,.,~o/-koH

O

~N

0

+ 4PF6 -

9

5PF6-~ I''~Ov'J

"--~N-+ ~ / ] Electrostatic ( ~~ " IRepulsions C ~ ~

+

K,34.pg6 --/N K.34.31.5PF 6

RED Fig. 26. The chemically controlled complexation of the linear threads 34 and 35 by the tetracationic cyclophane 31.4PF6. The change of complexation is accompanied by a change of color, rendering the system a chromophoric supramolecular switch.

9 >

MOLECULAR AND SUPRAMOLECULARNANOMACHINES

repulsions between the bound K + ion within the 18-crown-6 complement of 34 and the tetracationic cyclophane 31.4PF6 force the disassembly of the complex 34.K.31.5PF6, producing the metalated derivative 34.K.PF6 and the free tetracationic cyclophane 31.4PF6, which can now form a complex with the neutral cosubstrate 35. The development of selfassembling systems such as this one could lead to functioning supramolecular entities that can be switched by chemical stimuli to give optical responses.

3.7.3. An Electrochemically Driven Supramolecular Machine Tetrathiafulvalene (TTF) 36 is a n-electron-rich building block widely used in supramolecular and materials chemistry [55]. Being a n-donating unit, TTF is complexed [56] by the tetracationic cyclophane 31.4PF6, forming a 1:1 complex in which TTF is threaded through the cavity of 31.4PF6. One attractive feature of TTF is that it is readily oxidized--in two, reversible, single-electron processes--to form sequentially the cation radical and dicationic species. An equimolar mixture of TTF and the tetracationic cyclophane in Me2CO resuits [57] in the formation of a dark green solution, and the UV/vis spectrum reveals a charge transfer band at )~max 854 nm associated with a 1:1 complex with a Ka value of 2600 M -1. Electrochemical oxidation of the TTF unit produces (Fig. 27) the positively charged TTF radical cation (TTF ~ which is ejected from the cavity of the tetracationic cyclophane 31.4PF6 as a result of repulsive electrostatic interactions. This process can be monitored by UV/vis spectroscopy and by cyclic voltammetry. Electrochemical reduction back to the neutral TTF n-electron-rich unit regenerates the 1:1 complex 36.31.4PF6 with its associated charge transfer band, rendering the cycle reversible. This process leads to a distinct color change from dark green (when a complex is present) to pale brown (when the system is uncomplexed). Hence, this supramolecular system behaves as a chromophoric switch.

3. 7.4. A Chemically Driven Supramolecular Machine In the case of the [2]pseudorotaxane discussed in this section, we will be inverting the molecular recognition pattern employed in the last three examples. The n-electrondeficient 2,7-dibenzyldiazapyrenium salt 37.2PF6 will be the linear threadlike component, and 1,5-dinaphtho-38-crown-101/5-DN38C10 (38), containing n-electron-rich 1,5dioxynaphthalene ring systems, will be acting as the ring component. When 37.2PF6 is added to a solution of 38 in MeCN, the dication threads itself through the center of the macrocyclic polyether ring, giving rise to the 1:1 complex 37-38.2PF6 with a pseudorotaxane-like geometry and with a reported [58] Ka value of 3 • 105 M -1. The dication 372+ also forms adducts with aliphatic amines, presumably as a consequence of charge transfer interactions between the electron-accepting dication and the electrondonating amines. Thus, advantage can be taken of the chemical affinity of 372+ for

+ N~

Q

k,,w_/

~N+ 4PF 6

+N ~ N

-

Q

+~L~jI~

+

9

9

+ 4PF6-

+e

o+ 36-31.4PF 6

Fig. 27.

31.4PF6

36

Electrochemically controlled complexation of TTF by the tetracationic cyclophane 31.4PF 6.

247

GOMEZ-LOPEZ AND STODDART

~/--o~~, 2PF6-o ~,,,,~_/'~ o

Lo--

2PF 6-

_

o)

TFA

NH2

d

37.38.2PF6

38

392.37.2PF6

Fig. 28. The chemically controlledcomplexation of the salt 37.2PF6 by the 1/5-DN38C10macrocyclic polyether.

aliphatic amines, such as hexylamine (39), to induce (Fig. 28) the unthreading of the ring and threadlike components of the [2]pseudorotaxane 37-38.2PF6. Upon the addition of 39, large spectral changes occur with the appearance of an absorption band, which can be assigned to a charge transfer band in the 392.37.2PF6 adduct, along with the recovery of the emission band for the naphthalene tings in 38, this emission having been quenched when 38 is complexed by 37.2PF6. The unthreading process can be reversed quantitatively by the addition of TFA to the solution. Protonation of the nitrogen atom in 39 disrupts the 392.37.2PF6 adduct and liberates 37.2PF6, and the [2]pseudorotaxane 37-38.2PF6 is formed once again. This system represents a prototype at the supramolecular level for the design and construction of a simple nanoscale machine in which the changes in the relationships between the components can be followed by differences in the absorption and luminescence spectra.

3.7.5. pH-ControUableSupramolecular Switching Recently, it has been discovered [59] that secondary dialkylammonium cations form pseudorotaxane-like 1:1 complexes with suitably constituted crown ethers, such as dibenzo-24crown-8 (DB24C8). When dibenzylammonium hexafluorophosphate is mixed in apolar solvents (e.g., CHC13 and CH2C12) with DB24C8, a strong 1:1 complex is formed that can be isolated in a crystalline form. X-ray crystallography reveals that the NH + center resides in the center of the cavity of the crown ether. The main noncovalent bonding interactions that stabilize this complex are [N+-H .. .O] hydrogen bonds between the two hydrogen atoms on the nitrogen atom and some of the oxygen atoms in the polyether chains of the crown ether. They are augmented by weaker [C-H...O] hydrogen bonds involving some of the benzylic methylene hydrogen atoms in the cation and oxygen atoms in the crown ethers and zr-zr stacking interactions between one of the cation's phenyl groups and one of the catechol tings in the crown ethers. When dibenzylammonium hexafluorophosphate is cocrystallized with a crown ether possessing a bigger cavity, such as bisparaphenylene-34crown-10 (BPP34C10), a 2:1 pseudorotaxane-like complex is formed in which two cations are threaded simultaneously through the cavity of the crown ether [60]. The secondary dialkylammonium salt 40-H.PF6 containing an anthracenylmethyl unit as one of its substituent groups [61] has been used as a photochemical probe in the complexation-decomplexation processes by Balzani's group in Bologna [62]. When one equivalent of DB24C8 is added to 40-H.PF6, a 1:1 pseudorotaxane-like complex is formed between the two species. The [2]pseudorotaxane formation can be monitored by photophysical studies as a result of the presence of the anthracene ring system. If DB24C8 and 40-H.PF6 are brought together in close proximity to each other, the luminescence properties of the catechol tings in DB24C8 are quenched by energy transfer (ET) to the anthracene. However, after the addition of a suitable base---diisopropylethylaminemto the [40-H]-[DB24CS].PF6 complex, deprotonation of the NH + center occurs, disrupting the

248

MOLECULAR AND SUPRAMOLECULAR NANOMACHINES

40-H-41 .PF6

40

41

Fig. 29. The pH-controllable complexation of the linear secondarydialkylammoniumsalt 40-H.PF6 by the DB24C8 macrocycle.

noncovalent bonding interactions responsible for the complex formation, such that unthreading of the cation from the crown ether takes place (Fig. 29). This process can be monitored by luminescence studies because the anthracene ring system and DB24C8 are no longer in close proximity, with the consequence that the emission of the catechol rings in DB24C8 is no longer quenched--the ET pathway is not operative--and can be observed. Unthreading can be reversed upon the addition of TFA to the solution. Protonation of the amino function takes place, regenerating the NH~- center and reforming the 1"1 complex.

3. 7.6. Electrochemically Controlled Complexation in Cyclodextrins Cyclodextrins (CDs) are among the building blocks most widely used for the self-assembly of molecular and supramolecular entities [63]. They constitute a series of naturally occurring cyclic oligosaccharides, consisting of six or more c~-1,4-1inked D-glucopyranose rings. Their rigid hydrophobic cavities give rise to high binding affinities for guests of all types in aqueous solutions. The binding interactions in CD-guest complexes are most likely a summation of several relatively weak forces and effects--for example, van der Waals interactions, hydrophobic binding, and the release of high energy water. Kaifer et al. [64] have studied the complexation of water-soluble viologen derivatives, such as 41.2C1, with/~-CD and its heptakis(2,6- O-dimethyl) analogue DM-/3-CD in aqueous solution. It was found that the interaction between the fully oxidized viologen and the CD is negligible, that is, it is too weak to be observed experimentally. However, cyclic voltammetric experiments indicate (Fig. 30) that, upon reduction of the viologen unit, its hydrophobic character is enhanced, thus increasing the stability of its CD inclusion complex. The neutral fully reduced viologen derivative is a much better guest, particularly for /3-CD. This system constitutes an excellent example of redox control of the strengths of host-guest interactions. Furthermore, the researchers were able to discern the mechanism of the electron transfer process. The viologen guests do not engage directly in heterogeneous electron transfer reactions when they are included inside the cavities of CDs acting as hosts.

3.8. Logic Gates Logic gates are switches whose output states (0 or 1) depends on the input conditions (0 or 1). The design and construction of molecular systems capable of performing complex logic functions is of considerable fundamental scientific interest, because it introduces new concepts into the field of chemistry [65]. YES and NOT single-input gates are the simplest logic devices. A YES gate operates without changing the input bits (input: 1, output: 1;

249

GOMEZ-LOPEZ AND STODDART

)

' HO

~

0

OH

No Binding

412+

-e-yl

~-CD +e

-i-

.o

o

or

o

OH

Weak Binding -e

HO

--Yl -+e

0

Strong Binding I Fig. 30. Electrochemicallycontrolled complexation of the viologen derivative 41.2PF6 by/3-CD. Table I. The Truth Table for an AND Logic Gate X

Y

O

0

0

0

0

1

0

1

0

0

1

1

1

The output (O) peformed is a function of two chemical inputs (X and Y).

input: 0, output: 0). On the other hand, a NOT gate inverts the input data (input: 1, output: 0; input: 0, output: 1). More complex logic gates--AND, OR, and XOR--are those whose operations occur under the influence of two chemical inputs (X and Y). An AND gate performs (Table I) the logic product between the inputsmthat is, the output signal is 1, provided all inputs are 1. An OR gate performs (Table II) the logic sum between inputs-i.e., the output is 1, provided at least one of the inputs is 1. An XOR gate (Table III) is a more complicated situation in which the truth table is the same as for the OR logic gate, except that the output is 0 if both of the inputs are 1. The design and synthesis of molecules and supermolecules capable of performing multiple logic functions represents a major challenge to chemists. In this section, we will describe how the challenge is being met using the principles of supramolecular chemistry.

250

MOLECULAR AND SUPRAMOLECULAR NANOMACHINES

Table II. The Truth Table for an OR Logic Gate ,

X

Y

0

0

0

0

0

1

1

1

0

1

1

1

1

The output (O) peformed is a function of two chemical inputs (X and Y). Table III. The Truth Table for a XOR Logic Gate X

Y

O

0

0

0

0

1

1

1

0

1

1

1

0

The output (O) peformed is a function of two chemical inputs (X and Y).

3.8.1. Photonic AND Logic Gates The logic gate that will be discussed here is based upon receptors of the type described in Section 3.2. De Silva and co-workers [66] showed that, by exploiting photoinduced electron transfer (PET), it was possible to develop chemical sensors based on fluorescent signaling. Compound 42 is a receptor that operates as a logic device with two input channels, that is, the fluorescence signal depends on the binding of the molecule with protons, Na + ions, or both. The receptor is an anthracene derivative, linked to a tertiary amine and a benzo crown ether. It is well known that anthracene derivatives undergo PET processes from both free tertiary amine nitrogen atoms and benzo crown ethers, hence switching off the fluorescence of the anthracene ring system. The PET process can be suppressed by the addition of protons and Na + ions simultaneously, causing the switching on of the fluorescence. The successful operation of 42 as an AND logic gate depends on the fact that tertiary amines and benzo crown ethers are very selective for protons and Na + ions, respectively. This selectivity allows the molecule to self-select its input ionic signals into the appropriate site. The fluorescence of 42 increases by a factor of 1.1 when only 10 -2 M of Na + ions are present and by a factor of 1.7 when only 10 -2 M of protons are present. On the other hand, when both inputs are simultaneously applied, the fluorescence output increases (Fig. 31) by a factor of 6.0. In conclusion, the fluorescent signaling is only high when both inputs, Na + ions and protons, are coincident in their occupation of 42 and remains low for the other three possible input signal conditions. Receptor 42 not only acts as a photonic molecular device--a logic gate--but it also allows direct fluorescence monitoring of situations where two (or more) chemical species must come together to cause a vital process. A constitutionally similar AND logic gate 43 has been reported [67] recently by the Belfast group. The main advantage of this system over the one described previously is that the "off" states are virtually nonfluorescent and the fluorescence efficiency in the "on"

251

GOMEZ-LOPEZ AND STODDART

Fig. 31. The fluorescent signaling system 42, behaving as a photonic AND logic gate. Note that the anthracene fluorescence is only observed in the presence of Na+ and protons.

state is very high indeed. The fluorescence of 43 is unobservable unless both H + and Na + are present (Fig. 32) in suffuciently high concentrations, and when this happens a large fluorescence enhancement factor of > 37 is observed. Another remarkable feature of these photoionic gates is that they operate in a wireless mode and are able to self-select the two ionic inputs with negligible cross-talk.

3.8.2. A Photonic OR Logic Gate The design principle [68] behind the photonic OR logic gate 44 containing a fluorescent anthracene unit, which is attached via a methylene linker to London's receptor, relies upon the lack of selectivity of London's receptor toward Mg 2+ and Ca 2+ ions. The fluorescence of the anthracene unit in 44 is quenched by a PET from the 1-amino-2-alkoxybenzene unit. The binding of Ca 2+ and Mg 2+ ions to the receptor 44 causes an increase in its oxidation potential which is translated into a suppression of the PET process, resulting in fluorescence emission. For 44, the fluorescent signal enhancement caused by Ca 2+ and Mg 2+ ions is very similar, and hence it behaves as a two-input photonic OR logic gate. Both Mg 2+ and Ca 2+ ions cause the amine electron pair to be directed orthogonally with respect to the plane of the :r-orbitals on the aromatic ring upon complexation. Thus, fluorescence recovery (Fig. 33) by PET suppression is equally efficient for the two ion inputs. This situation represents, in chemical terms, a good quality truth table for the OR logic function and another triumph for de Silva's research group.

3.8.3. A XOR Gate Based upon Pseudorotaxane Formation Attention has already been drawn to the fact that the 2,7-diazapyrenium unit is a good electron acceptor, capable of forming pseudorotaxane-like complexes with aromatic crown ethers. The :r-electron accepting 2,7-dibenzyldiazapyrenium dication 372+ forms a pseudorotaxane-like complex with the crown ether 45 (which contains two 2,3-dioxynaphthalene zr-electron donating units) in which the diazapyrenium unit is sandwiched between the naphthalene tings [69]. Because of the donor-acceptor interactions, there

252

MOLECULAR AND SUPRAMOLECULAR NANOMACHINES

Fig. 32. The improved molecular AND logic gate 43 with greater fluorescence enhancement.

Fig. 33. The fluorescent signaling system 44, behaving as a photonic OR logic gate. The fluorescence of the anthracene unit is observed when either Ca2+ or Mg2+ metal ions are present.

is a charge transfer band at ~-max around 400 nm. This charge transfer interaction is responsible for the disappearance of the strong fluorescence exhibited by the two separated c o m p o n e n t s - - a )~max at 432 nm for 37.2PF6 and a ~-max at 343 n m for 45. Upon the addition of tributylamine (46), a 1:2 complex is formed (Fig. 34) between the dication 372+ and

253

~o~o~o~o ~o o__o,j

(Bu)3N=

CF3SO3H

(Bu)3N |

o3 o.1

9

(Bu)aN =

o~j 2PF6-

[4612.37.2PF6

2PF6-

N

t9 N

o

4~

9

4 9

.2PF CF3SO3H

Fig. 34.

45.37.2PF6

0

~o o__/o~ 45.H+ ~+f / - ~ ~ 2PF6N'~N~7.2

(Bu)3N= 46

PF6

A XOR logic gate based upon the complexation of the dication 37.2PF 6 with the macrocyclic crown ether 45 and the amine 46.

MOLECULAR AND SUPRAMOLECULAR NANOMACHINES

the amine 46, with the consequent unthreading of the pseudorotaxane. This process causes spectral changes associated for the most part with the recovery of the emission of the free 45 and the appearance of a broad absorption band characteristic of the [4612.37.2PF6 complex. Subsequent addition of a stoichiometric amount of trifluoromethanesulfonic acid unlocks 37.2PF6 and allows for rethreading of 37.2PF6 through the cavity of crown ether 45. The unthreading-rethreading cycle can also be performed (Fig. 34) by reversing the order of two inputs. The addition of trifluoromethanesulfonic acid causes protonation of the crown ether 45, with the subsequent unthreading of the pseudorotaxane, a process that is accompanied by large spectral changes, including the appearance of an emission band for 45-H + (which is identical to that of 45), the recovery of the emission band for 37.2PF6, and the disappearance of a CT band between 37.2PF6 and 45. The addition of a stoichiometric amount of tributyl amine deprotonates the crown ether and permits the rethreading of 37.2PF6 through the cavity of 45. Both processes cause a strong increase in emission intensity at 343 nm, and when both inputs (acid and base) are present, the fluorescence output is switched off altogether. This supramolecular system exhibits the input-output relationship associated with the truth table of a XOR logic gate. The fluorescence at 343 nm only occurs when either amine 46 or H + are present: on the other hand, the fluorescent signal is absent when none or both of the inputs are present.

4. INTERLOCKED M O L E C U L A R SYSTEMS Once the noncovalent bonding interactions, which control the formation of pseudorotaxane-like complexes, have been established, efficient template-directed syntheses of novel interlocked molecular compounds become a reality. The main families of interlocked molecular compounds that have been self-assembled so far include the so-called catenanes and rotaxanes.

4.1. Switching Properties in Catenanes Catenanes are composed of two or more interlocked rings that are joined together, not by covalent bonds, but rather by mechanical bonds. The first catenane, which exploits the molecular recognition between :r-electron rich and -deficient aromatic units, was self-assembled by our research group, which at the time (1989) was located in Sheffield [70]. The crown ether BPP34C10 (47) was used as a template for the cyclization of cyclobis(paraquat-p-phenylene) around the zr-electron rich hydroquinone tings of BBP34C10. This reaction produced (Fig. 35) the [2]catenane 48.4PF6 in 70% yield when one molar equivalent of the salt 49.2PF6 was reacted with 1,4-bis(bromomethyl)benzene in the presence of three molar equivalents of BPP34C10. This yield is remarkable when one considers that three molecules are being brought together in the self-assembly steps to form the [2]catenane 48.4PF6. As a result of this observation, it became possible to construct a large new family of molecular assemblies. The next challenge was to proceed to the construction of higher order [n]catenanes. To address this goal, the macrocyclic polyether and tetracationic cyclophane components were enlarged, and hence the multistep self-assembly of a [5]catenane [71 ] via a key [3]catenane intermediate became possible. This [5]catenane was baptized "Olympiadane" because of its topological similarity to the logo used by the Olympics movement. The next challenge lies in the production of polycatenated compounds, which may possess interesting properties as novel polymeric materials. A vital feature for mechanical switching properties of the [2]catenanes is that they possess [52] dynamic properties associated with the circumrotation of the two macrocyclic components with respect to one another (Fig. 36). In the case of a desymmetrized [2]catenane, this relative motion gives rise to two different so-called translational isomers [72] (if

255

GOMEZ-LOPEZ AND STODDART

Fig. 35. The self-assembly in 70% yield of the [2]catenane 48.4PF6.

Fig. 36. Cartoonrepresentation of the four possible isomers in a desymmetrized [2]catenane.

only one of the interlocked rings is desymmetrized) or four different translational isomers (if both ring components are desymmetrized). Recently the term "coconformation" [73] was coined to describe the different relative spatial arrangements of the components in molecular assemblies and the building blocks in supramolecular arrays. (Strictly speaking,

256

MOLECULAR AND SUPRAMOLECULAR NANOMACHINES

the term "conformation" refers to those arrangements of atoms in space that differ only as a result of rotation about a single bond in a discrete molecular species. The term "coconformation" is used to designate the relative three-dimensional spatial arrangements of (i) the constituent parts (e.g., host and guest) in supramolecular systems, such as precatenanes and pseudorotaxanes, and of (ii) the components of interlocked molecular systems, such as catenanes and rotaxanes. See [73].) If the movement of the tings can be controlled by an appropiate external stimulus and the different states can be easily addressed by spectroscopic techniques, then this translational isomerism is certainly a phenomenon that can be exploited in the fabrication of molecular compounds with switching properties.

4.1.1. A Solvent.Dependent [2]Catenane The unsymmetrical [2]catenane 50.4PF6 comprises [74] two different :r-electron-rich units in its crown ether component--that is, a hydroquinone ring and a 1,5-dioxynaphthalene ring system (Fig. 37). In the supramolecular context, the cyclobis(paraquat-p-phenylene) exhibits a much larger binding affinity toward 1,5-dioxynaphthalene derivatives than toward 1,4-dioxybenzene derivatives. However, in many cases--and this one is no exception--it is not possible to extrapolate from the supramolecular world into the molecular one. 1H NMR spectroscopic studies reveal that, in CD3 SOCD3, the tetracationic cyclophane component encircles the 1,5-dioxynaphthalene unit preferentially in 50.4PF6. The ratio between the two translational isomers is 70:30 in favor of translational isomer 2. On the contrary, when the [2]catenane 50.4PF6 is dissolved in CD3COCD3, the cyclobis(paraquatp-phenylene) tetracation encircles the hydroquinone ring preferentially--the isomer ratio being 70:30 in favor of translational isomer 1 this time (Fig. 37). This behavior can be explained in the following way. In solvents with low dielectric constants, such as CD3COCD3, the need for the 1,5-dioxynaphthalene ring system to act as a shield "alongside" the positively charged bipyridinium units is more important than the fact that the tetracationic cyclophane possesses a much higher binding affinity for the 1,5-dioxynaphthalene ring system located "inside" than for the hydroquinone ring in the analogous pseudorotaxane-like complexes. In more polar solvents, such as CD3SOCD3, the 1,5-dioxynaphthalene unit is not required to act as a shield, because the bipyridinium unit is solvated by the highly polar solvent molecules and is therefore able to reside "inside" the cavity of the cyclobis(paraquat-p-phenylene) tetracation. In summary, the position of the tetracationic cyclophane component can be controlled by the polarity of the

/---~/---~/---~/---~ o

o

o

o

+N/~ ~ N + 9

o

4PF6-

4PF 6

CD3SOCD3

@ CD3COCD 3

I

~

2, /0

I

0\ ,

/0\

/0\

/0 \

50.4PF 6 Translational Isomer 2

Translational Isomer 1

Fig. 37. The solvent-dependent translational isomerismin the [2]catenane 50.4PF6.

257

/0

GOMEZ-LOPEZ AND STODDART

solvent, that is, the equilibrium proportions of the translational isomers are highly solvent dependent.

4.1.2. An Electrochemically Controlled [2]Catenane Another way to exercise control over translational isomerism in [2]catenanes is by using zr-extended viologen units as building blocks in the construction of the interlocked tetracationic cyclophane component. The [2]catenane 51.4PF6, in which the macrocyclic polyether component BPP34C10 is encircled (Fig. 38) by an unsymmetrical tetracationic cyclophane containing one bipyridinium unit and one bis(pyridinium)ethylene unit, has been self-assembled [75]. 1H NMR spectroscopic studies in CD3COCD3 at - 6 0 ~ revealed that the isomer in which the bipyridinium unit resides in the center of the neutral component becomes favored (Fig. 38) to the extent of 98:2. This selectivity is a consequence of the lower r-electron accepting ability of the zr-extended viologen unit relative to that of a bipyridinium unit. The [2]catenane 51.4PF6 shows four single-electron reduction waves [76]. The first reduction occurs at the bipyridinium unit with a potential very similar to that of the first reduction potential of the parent symmetrical [2]catenane 48.4PF6. This observation indicates that the bipyridinium unit resides "inside" the cavity of the crown ether component, as demonstrated by 1H NMR spectroscopy. Next, there are two single-electron reductions that occur at the extended viologen unit--the bis(pyridinium)ethylene unit--before the final one reduces the bipyridinium radical cation. The first reduction wave associated with the extended viologen unit is very close to that observed in the analogous [2]catenane with two bis(bipyridinium)ethylene units present in its tetracationic cyclophane component. This result implies that, after a single-electron reduction, the translational isomerism is inverted in favor of the less zr-electron deficient unit. The molecule is therefore switchable electrochemically. At the outset, the predominant isomer in solution is the one in which the bipyridinium unit is located within the cavity of the macrocyclic polyether. The first reduction occurs at the "inside" bipyridinium unit because of its lower reduction potential, converting it (Fig. 39) to a radical cation. After reduction, the "inside" radical cation is no longer a good zr-electron acceptor, and so circumrotation of the cyclophane takes

0

/---k /--k /---k /---k 0 0 0 0

0

4PF 6

/---k /--k /--k /--k 0 0 0 0

PF6 CD3COCD3 9

+

I

51.4PF 6 Translational Isomer 1

I

Translational Isomer 2

I

Fig. 38. The two translational isomersin the extended viologen-containing [2]rotaxane 51.4PF6.

258

MOLECULAR AND SUPRAMOLECULAR NANOMACHINES

o

I 4PF6

m

~F6 m

+e y

-e

51.4PF 6

O

k~/ Ok__/Ok__/Ok__/O

Fig. 39. Electrochemical switching properties of the [2]rotaxane 51.4PF6.

place (Fig. 39) to locate the extended viologen bis(pyridinium)ethylene unit "inside" the crown ether component. The predominant species is now related to translational isomer 2. The process is reversible. Electrochemical oxidation regenerates the bipyridinium unit and induces circumrotation of the tetractionic cyclophane to relocate the bipyridinium unit "inside" the neutral crown ether component. It may be concluded that, in this unsymmetrical [2]catenane, the components can be controlled electrochemically in a reversible fashion, conferring upon the [2]catenane 51.4PF6 molecular switching properties.

4.1.3. A Solvent-Dependent Amphiphilic [2]Catenane The use of complementary hydrogen bonding interactions between benzylic amides to afford a new family of [2]catenanes was first described by Hunter [77]. This approach to catenane formation has been extended considerably by V6gtle [78] and Leigh [79] in recent years. Leigh et al. [80] have reported the solvent-dependent coconformational behavior of some amphiphilic benzylic amide [2]catenanes (Fig. 40). The homo[2]catenane 52 is composed of two identical interlocked rings that have a lipophilic linear alkyl chain portion and a benzylic diamide portion. In CDC13, the lipophilic sebacoyl chains are located on the surface of the molecule, and the hydrogen bonding groups are buried in the middle of the molecular structure and are involved in inter-ring intramolecular hydrogen bonding, a feature that causes a downfield shift in the signal for the amide protons by 1.5 ppm. The network of hydrogen bonds locks the aromatic tings in close proximity to each other (see translational isomer 1). On the other hand, in CD3SOCD3, a hydrogen-bond-accepting

_ 5-o \

/

~

~"

//~_~x~ . . . . . 0 N H'" ,,

',

\

o

07/0.=.

x.._(,

~ l

CD3SOCD3-~-N~/H'

,~----o

_p--N,

o

Translational Isomer 1

--U,,.

~2Z-~

O;'

/--~\

/

2/--

d 52

Translational Isomer 2

Fig. 40. The solvent-dependent translational isomerismin the [2]catenane 52.

259

N-H

O

/

o

GOMEZ-LOPEZ AND STODDART

solvent, the 1H NMR spectrum suggests that the aromatic rings spend very little time close to each other. Moreover, the fact that the protons on the sebacoyl chain are heavily shielded is consistent with a structure in which the lipophilic chains are buried in the center of the catenane, whereas the amide groups are exposed so that they interact with the polar solvent, that is, translational isomer 2 is the predominant isomer in CD3 SOCD3 solution.

4.1.4. Electrochemically Controlled Circumrotation of a [2]Catenane Sauvage and his group [81] were first to achieve the efficient synthesis of a [2]catenate by exploiting the tetrahedral coordination of Cu + with 1,10-phenanthroline ligands. Using this approach, the Strasbourg group has managed to construct an impressive series of catenanes, polycatenanes, and rotaxanes, as well as a topologically fascinating molecular trefoil knot [82]. The dissymmetric [2]catenane 53.PF6 consists [83] of a transition metal (Cu) complex whose organic components consist of two interlocked coordinating rings. The interconversion between the two forms of the complex can be triggered electrochemically and corresponds to a sliding motion of one ring with respect to the other ring. The fundamental reason for the process is the difference in coordination number (CN) for the two different redox states of the metal: CN -- 4 for Cu(I) and CN = 5 for Cu(II). The organic backbone of the [2]catenane 53.PF6 has a 2,9-diphenyl- 1,10-phenanthroline (dpp) bidentate chelate located in one ring, which is interlocked with another ring containing two different subunits--a dpp moiety and a tridentate ligand 2,2',6,2"-terpyridine (terpy). Depending on the relative positions of the interlocked rings, the central metal atom can be tetrahedrally complexed (two dpps), or it can be 5-coordinated (dpp + terpy). The interconversion between these two states, which results from the circumrotation of one ring with respect to the other, can be induced by an external stimulus. At the outset, Cu(I) is 4-coordinate (two dpps), electrochemical oxidation to Cu(II) leads (Fig. 41) to an unstable 4-coordinate Cu(II) complex, which then rearranges to the more stable 5-coordinate state (dpp + terpy). The process can be reversed by reducing Cu(II) back to Cu(I). The reduction gives rise to a transient 5-coordinate Cu(I) species, before circumrotation of the tings takes place with regeneration of the 4-coordinate Cu(I). The switching process can be monitored by UV/vis spectroscopy, because all of the four possible species have different spectroscopic properties. Therefore, by exploiting the coordination properties of two different redox states of a transition metal within a catenate environment, a reversible switching system has been constructed.

4.1.5. A Switchable Hybrid [2]Catenane A novel hybrid [2]catenane 54.5PF6, in which the cation complexing abilities of the dpp ligand and the noncovalent bonding interactions between Jr-electron-rich and -deficient aromatic units are combined, has been synthesized [84]. This hybrid interlocked molecular compound has two different modes of interaction that govern the relative geometries of the component macrocycles. These different modes can be interchanged by the inclusion or exclusion of a cation that is chelated by the catenane. If the self-assembly of the [2]catenate takes place in the presence of Cu(I)---employed as a metal ion template--the topology of 54.5PF6 is the one shown in Figure 42, in which the Cu(I) ion is complexed tetrahedrally between the two dpp units. However, upon the addition of KCN, the Cu(I) ion is released and circumrotation of the rings in 54.4PF6 induces a change in topology with the Jr-electron-rich 1,5-dioxynaphthalene unit sandwiched between the two bipyridinium units of the other ring. The topology of the molecule is now controlled by the noncovalent bonding interactions between the 1,5-dioxynaphthalene unit and the bipyridinium units. Addition of LiBF4 to the solution causes the disappearance of the charge transfer band associated with the noncovalent bonding interactions between the n-electron-rich and

260

MOLECULAR AND SUPRAMOLECULAR NANOMACHINES

Fig. 41. The electrochemically driven circumrotationin the Cu(I)-containing [2]catenane 53.PF6.

-deficient aromatic units. The Li + ion can form a tetrahedral complex with the dpp ligands, inducing a coconformational change within the [2]catenane. Unfortunately, the Li + ion could not be removed from the catenane. Hence, although it was possible to switch from the zr-electron donor-acceptor mode of complexation to the metal ion mode, the reverse . process is not easy to control in this case. Despite this failure, the behavior of catenane 54.4PF6 was studied in acidic and basic media. In the beginning, 54.4PF6 possesses a topology in which the zr-electron donoracceptor interactions dominate (Fig. 43). The addition of TFA to a MeCN solution induces large changes in the 1H NMR spectrum, which are consistent with the disappearance of the zr-electron donor-acceptor mode of complexation, which is accompanied by the suppression of the charge transfer band. The topology of the catenane corresponds now to one in which an H + ion is surrounded by the two dpp ligands. In this respect, the H + ion is functioning in a manner very similar to that of a transition metal ion. Upon the addition of a base, such as pyridine, the original 1H NMR and UV/vis spectra are reconstructed, indicating complete reversion (Fig. 43) to the r-electron donor-acceptor mode of complexation. It is clear that the [2]catenane 54.4PF6, which was first synthesized by a metal

261

GOMEZ-LOPEZ AND STODDART

i ,xM+=

Cu + or Li +

X= PF 6- or BF 4-

54.5PF 6

LiBF4

KCN

,,,/~f

~

4PF6-

54.4PF 6 Fig. 42. The chemicallyinduced change of geometry in the hybrid [2]catenane 54.4PF6.

ion templated strategy, behaves as a pH-dependent molecular switch in which the system changes from a proton catenate to a zr-electron donor-acceptor mode of complexation in the [2]catenate.

4.1.6. A Chemically and Electrochemically-Switchable [2]Catenane The [2]catenane 55.4PF6 is composed of a crown ether component comprising two :relectron-rich unitsman isomeric cis-trans mixture of tetrathiafulvalene (TTF) and a 1,5-, dioxynaphthalene ring system--and the :r-electron deficient cyclobis(paraquat-p-phenylene) cyclophane tetracation. X-ray crystallography in solid state and NMR spectroscopy and UV/vis spectroscopy in solution revealed that the TTF unit is positioned (Fig. 44) "inside" the cavity of the tetracationic cyclophane, with the 1,5-dioxynaphthalene ring system lying "alongside" one of the bipyridinium units. Chemical oxidation of the TTF unit with Fe(C104)3 causes dramatic changes in both the 1H NMR and UV/vis spectra. After oxidation, the resonances of the H-4 and H-8 protons of the 1,5-dioxynaphthalene ring are shifted to higher fields (3 2.45), indicating that the 1,5-dioxynaphthalene moiety is now encircled by the tetracationic cyclophane. Reduction with Na2S205 regenerated the original NMR spectrum, thus rendering the cycle reversible. Similarly, UV/vis experiments show a dramatic shift in the maximum of absorbance of the charge transfer band from

262

MOLECULAR AND SUPRAMOLECULAR NANOMACHINES

4PF 6-

54.4PF 6

C5H5N I

_~TFA

v

F6-

"".::H+_. ---N 9"

.,,

..

0

oJ 54.5PF 6 Fig. 43.

A pH-controllable molecular switch.

/ - k /----k /---k / ~ k 0 N

0

].:~

0

0

/---k / - k / ~ k F-k

0

Fe(Cl04)3

N

I

\

554+

o

/\,

0

0

-e- (- 2e-) I

o

0

|

/0\

/0\

0

0

+ (2+) s, "s

+e-(+ 2e-)

/0 [ Na2S205/H2O I

DarkGreen

0\

/0\

555+(556+ )

/0\

/o\

/o

Maroon

Fig. 44. The TTF-containing [2]catenane 55.4PF 6. Note that it behaves as a chemically and electrochemically driven molecular switch.

263

GOMEZ-LOPEZ AND STODDART

835 nm (when the TTF unit is located inside the cyclophane) to ~.max - - 515 nm (when the 1,5-dioxynaphthalene ring system is located inside the cyclophane). The switching can also be achieved by electrochemical means. One-electron electrochemical oxidation of the TTF unit forces the positively charged TTF +~ unit out of the cavity of the cyclophane, compelling the circumrotation of the macrocyclic polyether with respect to the tetracationic cyclophane so that the 1,5-dioxynaphthalene ring is located inside the cyclophane. This process can be monitored by cyclic voltammetry, and it can be made reversible.

~.max - -

4.2. An Electrochemically Controlled Self-Complexing Macrocycle Recently we self-assembled [85] a series of molecules that display self-complexing geometries. These types of molecules consist of a linear component comprising a n-electron-rich unit--that is, 1,5-dioxynaphthalene, which is linked covalently to the n-electron-deficient tetracationic cyclophane by means of an ester linkage. The n-electron-rich aromatic unit lies inside the cavity of the cyclophane, giving rise to a molecule that exhibits an exotic self-complexing topology. Oneexample of this type of molecule is the self-complexing macrocycle 56.4PF6, which is also a molecular analogue of the supramolecular system already discussed in Section 3.8.1. Therefore, one can expect 56.4PF6 to behave as a compound that exhibits switching properties at the molecular level. A photochemical experiment similar to that performed on 32-31.4PF6 was carried out on 56.4PF6. However, after photoinduced reduction of the bipyridinium units, no luminescence could be observed emanating from the free 1,5-dioxynaphthalene ring system. This lack of emission does not rule out the possibility that decomplexation has occurred. It is well known that the emission from a 1,5-dioxynaphthalene ring system can be quenched by the presence of a nearby bipyridinium unit. In the case of the supramolecular system 32.31.4PF6, once decomplexation has taken place, the 1,5-dioxynaphthalene-containing thread 32 can diffuse away from the bipyridinium-containing tetracationic cyclophane. On the other hand, such a motion is not possible in 56.4PF6 because the 1,5-dioxynaphthaleneand the bipyridinium-containing components are linked together covalently. Nevertheless, the self-complexing macrocycle 56.4PF6 acts as an electrochemically driven molecular machine. After the first two-electron reduction of 56.4PF6 to the corresponding diradical dication, the noncovalent bonding interactions responsible for the self-complexing topology are disrupted, and the 1,5-dioxynaphthalene moiety is ejected (Fig. 45) from within the cavity of the cyclophane. This fact is supported by the value of the second two-electron reduction potential of the bipyridinium units in 56.4PF6, which is

/--k/--k o +

o

o

e uctioo + 2e0

+

N

"-o..../

Oxidation

564*

OMe

N

+ ~

+

562*

1/5-Dioxynaphthalene "outside"

1/5-Dioxynaphthalene "inside"

Fig. 45. Electrochemicallycontrolled self-complexation in the self-complexing macrocycle56.4PF6.

264

MOLECULAR AND SUPRAMOLECULAR NANOMACHINES

the same as that for the last reduction potential for the "empty" parent tetracationic cyclophane 31.4PF6, indicating that, in this instance, the 1,5-dioxynaphthalene does not reside inside the cavity of the cyclophane. The process can be reversed by electrochemical or chemical oxidation to the tetracationic cyclophane. 4.3. Rotaxanes: From Molecular Shuttles to Molecular Switches

Another class of mechanically interlocked molecules, which may be self-assembled by employing the molecular recognition that exists between the :r-electron-rich and -deficient components, are the so-called rotaxanes [86]. A rotaxane consists of a ring component (Fig. 46), which can be clipped, slipped, or threaded onto a dumbbell-shaped component-and a rod with large stoppers at both its termini that prevent the ring component from slipping off the dumbbell-shaped component. In many cases, this component is a linear polyether chain interrupted by :r-electron-rich aromatic units, and the ring component is the cyclobis(paraquat-p-phenylene) tetracation. Just like the catenanes, rotaxanes also exhibit translational isomerism. Not surprisingly perhaps, rotaxanes, as a result of their abacus-like geometries, have become one of the most popular starting points in the search for molecular switches. 4.3.1. A Molecular Shuttle

In 1991, the first molecular shuttle, 57.4PF6, was reported [87]. It is a [2]rotaxane (Fig. 47) consisting of a dumbbell-shaped component possessing two hydroquinone tings separated by polyether chains (a linear analogue of BPP34C10) and terminated by two bulky triisopropylsilyl groups as stoppers and encircled by the cyclobis(paraquat-p-phenylene) tetracation. Dynamic 1H NMR spectroscopic studies in CD3COCD3 revealed that the tetracationic cyclophane component shuttles back and forth (Fig. 47) between the two degenerated hydroquinone tings approximately 500 times a second at room temperature. Because the movement of the cyclic component cannot be controlled, the molecular shuttle 57.4PF6 does not possess molecular switching properties. However, it prepares the way for the construction of abacus-like controllable molecular shuttles (Fig. 48). By providing two different nondegenerate, :r-electron-rich recognition sites on the dumbbellshaped component in such a manner that they can be addressed selectively by an external stimulus, which can be chemical, electrochemical, or photochemical in nature, the resulting translational isomerism can be exploited in a molecular switching sense.

Fig. 46. Cartoonrepresentation of the different modes of self-assembling a [2]rotaxane.

265

GOMEZ-LOPEZ AND STODDART

Fig. 47. The original molecular shuttle, 57.4PF6.

Fig. 48. A cartoon representation of the design logic for a desymmetrized [2]rotaxane with binary switching properties.

4.3.2. Nondegenerate Molecular Shuttles A series of desymmetrized molecular shuttles were designed and self-assembled that comprise two nondegenerate Jr-electron rich recognition sites--one always being a hydroquinone ring--in the dumbbell-shaped component. The [2]rotaxane 58.4PF6 possesses [88] a p-xylene unit and a hydroquinone ring as its recognition sites in the dumbbell-shaped component. The 1H NMR spectrum of the molecular shuttle 58.4PF6 in CD3COCD3 reveals (Fig. 49) that the tetracationic cyclophane component distributes itself between the two recognition sites with 70% occupancy

266

MOLECULAR AND SUPRAMOLECULAR NANOMACHINES

Fig. 49. The desymmetrized molecular shuttle 58.4PF6 comprising two nondegenerate stations, a hydroquinone ring and a p-xylene moiety.

Fig. 50. The desymmetrized[2]rotaxane59.4PF6 comprisingtwo nondegenerate stations, an indolering and a hydroquinonemoiety.The tetracationic cyclophaneresides exclusivelyon the hydroquinonestation.

at the more zr-electron-donating hydroquinone ring and 30% occupancy at the less zrelectron-donating p-xylene unit. The [2]rotaxane 59.4PF6 comprises [89] (Fig. 50) an indole residue and a hydroquinone ring as its recognition sites in the dumbbell-shaped component. However, in this case, the design logic failed and 1H NMR spectroscopy showed that the tetracationic cyclophane component is located exclusively at one recognition sitemnamely, the hydroquinone ringmand so it is unable to exhibit molecular shuttling properties. Although the indole residue is more 7r-electron-rich than the hydroquinone ring, its inclusion inside the cavity of the cyclophane is much more sterically demanding. Thus, the hydroquinone ring is included preferentially within the cavity of the tetracationic cyclophane.

4.3.3. A Solvent.Controllable [2]Rotaxane Another molecular shuttle that was investigated by us [90] is the [2]rotaxane 60.4PF6. It comprises (Fig. 51) two degenerate hydroquinone tings and a tetrathiafulvalene (TTF) unit as the rr-electron-rich recognition sites present in the dumbbell-shaped component. This [2]rotaxane adopts different coconformations, depending on the nature of the solvent. 1H NMR spectroscopic studies show that, in CD3COCD3, the tetracationic cyclophane

267

GOMEZ-LOPEZ AND STODDART

Fig. 51. The desymmetrizedmolecular shuttle 60.4PF6 containing a TTF unit sandwichedby two hydroquinone stations. This molecularshuttle possessessolvent-dependentswitchingproperties.

occupies exclusively the two degenerate hydroquinone rings, whereas, in CD3SOCD3, the cyclophane is located exclusively on the TI'F unit. In principle, the proportions of the translational isomers populated in 60.4PF6 can be controlled by changing the nature of the solvent. However, none of the [2]rotaxanes described in this section have the potential of becoming useful as materials that will exhibit molecular switching properties, because the external stimulus that might control the translational isomerism is a change of solvent, which implies evaporation of one solvent followed by the addition of another one.

4.3.4. A Chemically and Electrochemically Controlled Molecular Shuttle In view of the less than satisfactory results obtained with the [2]rotaxanes 58-60.4PF6, the design logic was changed [91] to produce 61.4PF6, which has turned out to be the most successful rr-acceptor-donor rotaxane so far in terms of its molecular switching properties. The dumbbell-shaped component in 61.4PF6 consists (Fig. 52) of two non-degenerate rr-electron-rich recognition sites: a benzidine unit and a biphenol one. Dynamic 1H NMR spectroscopic studies in CD3CN show that the tetracationic cyclophane resides predominantly on the more rr-electron-rich benzidine residue. Nonetheless, this preference can be addressed (Fig. 52) by one of two external stimuli as follows: (i) The benzidine ring can be oxidized electrochemically and reversibly to the corresponding radical cation, whereupon the positively charged tetracationic cyclophane is forced to migrate to the neutral 7r-electron-rich biphenol ring system as a result of the repulsive electrostatic interactions from the benzidine radical cation. When the benzidine radical cation is reduced back to the neutral benzidine unit, the tetracationic cyclophane forsakes the biphenol ring system to occupy the more yr-electron-donating benzidine unit once again, rendering the cycle reversible. (ii) Alternatively, the basic nitrogen atoms of the benzidine unit can be protonated by treatment with acid, resulting in the expulsion of the tetracationic cyclophane from the fully protonated benzidine unit, thus obliging the cyclophane to reside on the biphenol unit. Because, treatment with base regenerates the neutral zr-electron-donating benzidine unit, the molecular switching process is reversible. It may be concluded that the [2]rotaxane 61.4PF6 behaves as a prototype binary molecular switch. This step represents the first in

268

MOLECULAR AND SUPRAMOLECULAR NANOMACHINES

+

+N-r"f~ +

5X-

.

.

Y

,--,~,.-.,

)--.Si-O

" ,,)X

O

,~

~

~

~

,~

,---.. , . - ,

O HN--( ~)------(())---NH O

O

7,

~

~

',-.'1/

O--((-'))~((]))~O

..--, , - - , ~ . .

O

>-Y-o~o%%'~+}-.~o~o~o- J

0

,o.~.,.-Oo; .---o..~j

.

o

l. C-~ ~

~.^ ("-u

L. ~

0

OR OR

.."

O - ~ .N~ H O tr ~ ".)

RO

RO

RO,~o 0=~0

%~

~ I

OR RO 0 - - O

\+o 0~O

oo HN

.,,I~ O RO

~

H'~O "I HO oN.N.

RO.~ O"~ N

~

I'" ~. i /

"'.

)'=N

0

=

(- o - J ' ~ N - ~ . o-, 0,,

/~k

.N~_

OO

~""" OR

N,.,~ 0 " - - " ~ OR

,/N-'~

RO_~o ( o o~

"Lyo g-

OR

.o

R O . , ~ O-- N~'O [ _/-~H ~ 0 t O P /

0

=o

1"

J

OJ O~ -u

o,,.j 1

/

.

.o'7~

.

.

.

~"--o - >,-oR,o-{,-- oJ ?

k 0

O

=o

\o

u

,oX=

\

/

0

\

dg"o

0

-

OR

OR

'

\

Moo

0.~

L_,.o

7{

O

oR

o.

0

RO

O~N O . , ~ OROR H'~---~

~0 ~0 ' I

0

OR

OR

OR

Fig. 10. Dendrylationof a ruthenium-bipyridine complexresults in new properties. The shielding effect of the dendryl substituents renders the metal center less prone to quenching with solventmolecules and dissolved oxygen.

who connected aryl-nickel complexes to a carbosilane skeleton and were able to show that the catalysts are as effective as their unbound counterparts in the Kharash addition of tetrachloromethane to methyl methacrylate. Unlike the latter, however, dendrimer-bound catalysts could be separated easily from the reaction mixture and would allow reactions to be conducted homogeneously--an advantage over catalysts attached to a solid polymer support. For arrays that consist of catalytic sites attached to a dendrimer, we propose the specific term "dendralysts," because we think that this aspect will become important in the near future. Reetz et al. [41 ] recently demonstrated that, in fact, dendritic catalysts can be held back by membrane techniques in the case of a metal phosphine catalyst linked to a polyamine dendrimer. Asymmetric catalysis can be achieved with the dendritic poly-TADDOL ( = or, c~, c~', ot'-l,3-dioxolane-4,5-dimethanol) compounds of Seebach et al. [42] (Fig. 12). The latter are similarly effective catalysts as their monomeric counterparts [43]. Combinatorial chemistry is a very active field of organic chemistry today [44]. Kim et al. [45] have taken advantage of the specific properties of dendrimers for the construction of a combinatorial peptide library (Fig. 13). A major obstacle to the versatility of combinatorial syntheses is the use of solid supports that limit the scope of synthesis methods available and often force the researcher to perform conversions heterogeneously. The problems that accompany solid (polymer) supports, can be circumvented as described by Kim

342

Br I (H3C)2~1 ? N(CH3)2 B~NitN~OH3)2

04H

(H3C)2N~ (H3C)2N~ B~_~( ]

2 "~'3 "

"-k_

N N ~ N(CH3)2

/0 \

INH o~'o L ~L~

(H30)2N~NH

(H30)2N.~N(Br

"

J

~,' )

, ,.,

O~r~ ~.o

N(CH ) r'~ ~2 ~N[---ur 0~-.N~ N ( O H 3 ) '

5

,.,",,v H3c---S,i--CH3,.Si--CH3/ - - - '

--~o

Y'/'~,

% J.~c,, , , o - - -

u ^ ~si

n3t"-" ~ ,CH31\ CH3"~~ I ,---/k.__, .s~J ' , - ~ C/H3 / a3 C~-si ~ S i , h

L

.Si

CH-

3 CH"'OH ' r I ~ 0 / - - ? l , 5;2 /--~--O../V..O.X.N._Z=3,_g~_Br ~kS,~ ~CH 3 H '~M_N~(CH3)2 /~ ") k'''k ,,.si.- CH3 ,._O/ \ O H J ( ~ ~Si7n~c~H~'O~.... H3C--s!,,/ C"Si"CH3 / NO ~' ~ 0 / I ~3 I CH3 l 0-4 H N(CH3)2 T 9Ni''Br ..11 (, 0~/0 u ~/ 1" ',,_N(CH3) L_.. 2 o

(H3C)2N-'~ 1.~ H e~-N,~N..r (H30)21~_.J-- 0

H (CH3)2N~ ar /Ni"\

N/••O

II

--

Si~ ~

~

F

HN~NT~N(CH3)2

(CH3)2 Ni.~ /. . Br N(CH3)2

r~ ~

(CH3)2N \Br

(CH3)2N--Ni--N(CH3)2 I Br Fig. 11.

The dendralyst introduced in the literature by Knapen et al.

Ph HO__V.-Ph

Ph

Ph-4__OH

pHO, )'-0

O--'(

0 Ph HO__~PH

OHh

0

~0

HO, /L.O Ph~ph"~O~~JL~

Ph Ph--~--OH

Me+

~

o

' 'O J~'' ~'hO:h

o

0

0

Ph ~ Ph Ph~'OHOH Xph

Ph_ ~ .Ph phX OHOH /~Ph

Fig. 12. A dendralyst for asymmetric syntheses based on TADDOL residues appended to a dendritic skeleton.

343

ARCHUT AND VOGTLE

| (i) Dendrimer

(ll

|

(ill)

Fig. 13. Dendrimersas soluble supports in combinatorialchemistry.

et al. be using dendrimers instead. Dendrimers, like commonly used solid supports, can be held back by ultrafiltration methods or by gel-permeation/size-exclusion chromatography, but they allow syntheses to be performed homogeneously due to their usually good solubility.

2.2. Dendrimers and Chirality Among functionalized dendrimers, those species containing chiral groups have become particularly important. Peerlings and Meijer [46] published a systematic approach to dendrimers and chirality. Seebach et al. [47] suggested a classification system of chiral dendrimers based on the position of the chiral information within the molecule. Chiral dendrimers can be subdivided into those beating chiral centers in either the core, the branches, the periphery, or any combination of the latter. The first chiral dendrimers, reported by Denkewalter et al. [4], were lysine-based dendrimers. An all-peptide dendrimer consisting of lysine units was reported by Zhang and Tam [48]. Such molecules are interesting as biologically reactive species. One of the first dendrimer-carrying chiral groups in the periphery was an amino-acid-substituted arborol reported by Newkome et al. [49] (Fig. 14). For this molecule, no generation-numberdependent change of the optical rotation per end group was found. Ashton et al. [50] made similar observations with saccharide-capped poly(propylene imine) dendrimers. In contrast, Meijer's investigations on the chirality of "dendritic boxes" (vide infra)m a poly(propylene imine) dendrimer with 64-point chiral dipeptide groups in the peripherym showed decreasing optical activity with increasing generation number~an effect that is not yet fully explained. Peerlings and Meijer [46] attributed these observations ("hidden chirality") to the solvent dependence of the optical rotation of the phenylalanine units and to the dense packing of the substituents in the higher-generation dendrimers. No generation dependence of the optical activity was found for poly(propylene imine) dendrimers equipped with planar-chiral peripheral units (Issberner et al. [51 ]; Fig. 15). A dendrimer with a chiral

344

t~

i

0"0

0"o

,i

0"0

/

lftf

Z

S]

i

Z

7

Z

tf

|

9

9

O

r

O

t

;.,..

?

!

>.

0"0

"r

O

O

O

9-r

Z

T

z.U.....~

o

o

0

I

z

"-

z -r

Oo-4

~, z -1T..'-'.-~ ~

O

O

J

"T

o

.O

'-A O '''~

"O

z

O

T

u

z

\

f

z

o ~o

o

o---...M~

O O

z

~

"~o

o.

7 ~

o

-r

zT

ARCHUT AND VOGTLE

NO2 02N ~

NO2

o

NO 2

02N ~

NO2

~0 R

0

HN

o

NH

02N,,,~O NO2 Fig. 16. Dendrimerwith a chiral core, an example of interesting model compounds for the investigation of dendritic chirality.

carbon atom serving as the core unit was equipped with four different dendritic residues by Kremers and Meijer [52]. All attempts so far to separate the racemic mixture of this dendrimer into the enantiomers have failed. A smaller species, which bears a first- and a second-generation aryl ether wedge, a hydrogen atom, and a benzyl ether group on the central carbon atom, could be obtained enantiomerically pure [46], and this species does not show optical activity; for this reason, it is referred to as "cryptochiral" [53]. Seebach et al. met the challenge of synthesizing chiral dendrimers to investigate the influence of chiral building blocks on the chirality of the whole molecule and to determine whether enantioselective complexation was possible [54, 55]. They achieved dendrimers with a chiral nucleus as well as dendrimers with additional chiral branches (Fig. 16). The optical activity of dendrimers with only a chiral nucleus decreases with increasing size of the dendrimer, whereas the optical activity of dendrimers that are "fully chiral" corresponds to the optical activity of the nucleus. These dendrimers also form quite stable clathrates.

2.3. Glycodendrimers A special chapter of the chemistry of dendrimers deals with those containing sugar units. Such dendritic glycoconjugates have attracted great interest as a novel approach to artificial sugar clusters and to structures that mimic cell surfaces. The attachment of natural products or drugs to a dendritic skeleton is a promising concept. Multiplication of specific sugar epitopes in one molecule results in highly increased avidities in adhesion processes and is called the cluster effect [56]. (Whereas the word affinity describes the strength of a reaction of a monovalent antigen (haptene) with a monovalent antibody (antigen docking unit), the word avidity is used to describe the total tendency of an antibody to bind an antigen, particularly that of antibodies with several docking units and antigens with several epitopes [57].) This is of importance where carbohydrate-protein interactions are

346

DENDRITIC MOLECULES--HISTORIC DEVELOPMENT AND FUTURE APPLICATIONS

HO. HI~ HO. H(~ " '

HO'--..-..~ HO" "

H0 HO hO.:...,,~J HO'", ~

oH ~'~ ~

Oh OHoH HO.:IQ ''j

0 vn " ~

; 0 OH

OH OH :~" ..... P

HO . . . . . . .

H

HoH% H6 "~ Q~ HO'~"[/~HO""L~H~)HO"-~ :~ HO .~" O,, ...OHOH HO,..:~) Hn HO~.~,.,O H0..~ O &u ,N,N~onUHo...~,,l..jvn HO...(,,~,.~.#,OH HO,~,

HO

za HN%., "~,

,.~ y C~NY

U.~,,,,,~" ()H r,

HO,..>.~.,,HO,.~HO:'"~ /O

OH ..... [/--D H~.,, ~,1.t y HD'~, H O, " ~ . c.~ ~ N 5a : HO'--. OH N ,.r N ~J"-.o .... o HO'" ~. ( -O "~ / OH .-..~',,,,~ ,, ~ N HO ::i " N n Z_ HO H HO--"~,.-n H0"~" OH ~'~,~. / -~ HO ......( "~.:.O:~:. ( ~I _,,~r,#,,~ N N~ ~. .~ ~:~'~ N~s'~'r HO OH HO OH H H01"/

OH

,1

__,,,~,rN~N

HO"~~]W'O'N..'"0,;,.;.,~/OH C'~N ,v'uvv'v~ ~ OUO'~':~OH ~_~. :""OH "Nvv.~_ '~ \ -;: ~OH Y"qu'~'~ II~ "~ i~j-./~OH OH ~ ~ ~,~ HN HoHO~.. '"0.:..y,,~....,OH N :~ "~OH ca~,... '~ ~"~H O'~.:." OH . ~ . "~OH

X X

N,~"

/\

OH

~O~-'~" HO HO U'~r'"NH e Y (7~ NH I:~'~;" ~,. U::~,.,..~ HO".~.:--OH f'J'X.~...OH, ... 0..~H _~ H 0=~..... .OH~.::.OH HO (~,,"" H[J" H~3 HO o 'OH ~ ) ....~ O" o~ 1o. ~ ~'~. OH ,~. ....OH ;: r"~.-... ~--/." HO "" :: OH /'-"?'~ .....OH HO i~ " ( ~ " O H ~. Q ~-."OH HO .~, ~" H() 0 HO ! .::.OH .~ HO H0 .,:..~1~.... OH O ~ ...-OH (~.:. '~CIHOH [ N-"a:~ I I ,,.>.,,,,.;/'-.OH OH OH

OH u~

Fig. 17. Lactose-and maltose-appendedPAMAMdendrimerscalled sugarballs.

under investigation. Sugar units were multiply built into polymers via copolymerization or telomerization to give glucomimetica. Dendrimers are used more and more as core building blocks of tailormade cluster glucosides. Aoi et al. [58] prepared PAMAM dendrimers equipped with lactose and maltose residues ("sugar balls"; Fig. 17) and investigated their recognition ability with concanavaline A (Con A) and peanut agglutinine. Roy and coworkers [59-61], Lindhorst and co-workers [62-64], and Ashton et al. [65] reported new glycodendrimers. Jayaraman et al. [66] described a synthetic route toward dendrimers that consist exclusively of carbohydrates. In another study, Zanini et al. [59] prepared a secondgeneration polylysine dendrimer functionalized with disaccharides. Preliminary tests with the influenza A virus indicate that the dendrimer depicted in Figure 18 is a strong inhibitor of erythrocyte hemaggluttination. Similar systems among the star polymers were synthesized with peptide residues. Even nucleic acids can be constructed in a dendritic way, as Hudson and Damha [67] have shown. In an automated procedure, the nucleic acid chains were first prepared and then divergently connected to give a cascade molecule containing 87 nucleic acid residues and having an approximate molecular weight of 25,000. It was necessary to use longer branches for the inner core of the dendrimer than for the periphery. Rao and Tam [68] proved that peptides can be connected in a dendritic manner. An octameric peptide dendrimer, which could be useful as a synthetic protein, was prepared and characterized by laser-desorption mass spectrometry.

347

ARCHUT AND VOGTLE

HO

HO"~~CO2H

Ho

~"e~ N

AcHN~

C02H

0 N

N

~n OHoH C02H ,, 0 ,, ' '"'~N~.-'~'' O~L.S.,.~ ~v.,I.LN.,,~ ~ ~CHNHo"kJ 0 " 0

O

0

0 H NH ~ 0 N~ ~v..LLN/~/C02 H H NH H o.J

~

.oc

/

o O NH

H O ~

~L-N'J"'l

AoHN~o

H _/---. Z

< O: C~ ..-] r"

"/

H,c

-

>

DENDRITIC MOLECULES--HISTORIC DEVELOPMENT AND FUTURE APPLICATIONS

20r~ Ru

~Ru

N_k==/N_ Ru N%_.~

d

Ru

N-N--~~~N Ru NN~l~/k=/ _

-

NRu

where M = Ru2G Qnd L =

Fig. 23. Variousmetal-polypyridine dendrimers with interesting electrochemical properties.

and Aida [99] investigated the dioxygen-binding ability of an iron-porphyrin equipped with aryl ether dendrons and found that these molecules form stable, long-lived dioxygen adducts. Jin et al. [ 100] were the first to describe a dendrimer with a metal-porphyrin as its core (Fig. 24). The convergent synthesis method of Fr6chet was used to prepare a dendrimer in which the photoactive metal-porphyrin center was sterically shielded, resulting in a size-dependent accessibility of quencher molecules. Dandliker et al. [ 101 ] investigated the influence of surface groups on the electrochemical behavior of metal-porphyrins. Following a divergent synthesis devised by Newkome et al., they prepared a third-generation porphyrin dendrimer that has a molecular weight of over 19,000. Its redox chemistry strongly contrasts with that of nondendritic zinc-porphyrins. The porphyrin nucleus is shielded by a core of electronegative oxygen atoms such that reduction by electrons from the outside is hindered. Similar dendritic molecules with phthalocyanine cores have been reported as well [102]. Dandliker et al. [103] prepared dendrimers with a zinc-porphyrin core and Newkometype poly(ether amide) branches with the aim of tuning and controlling the redox potential of the chromophore (Fig. 25). Cyclovoltammograms of these dendrimers showed that the first reduction potential of the zinc-porphyrins decreases with increasing dendrimer generation, and the authors rationalize that this observation is the result of the increasingly

353

ARCHUT AND VOGTLE

.. "o

t,

~.~ 0 O---Ar -

%~Ar

L. o

\o_ IO-,o -,, ~ -o\ ~o/A%

o,,,/

\

o\

~7 /

~0

Ar

Xo__ /o

L. ~

--

\ ,,o

r"~ r -

o

~

o

/"-u

I

I Ar

,p -- ArJ " A r I

--

F

I ~o F ~ /o'-~

-O'o

/ /~

/0--/

Ar,

Ar

J

L Ar / --o

o - - Ar _ A~J

,

"0~ O--

_./ " O A A r x o A

O

_o /

/o--

0

I

Ar

I ~~__o~

j

O\ArAo/Ar k.._0 0/ ~O~Ar / vO~. --O ..ArvO\Ar F ~0\

o,,o

)

0 ~r-" Ar--- 0 Ar-~o/ oF o -J 01

x0




0/At O-) O / ~ ,Ar
o-" ;~, "-o i

/

~

\

I

t"Ar

/ Ar\ O /O~ Ar "-~ O v Ar''O v \ O Ar / \ ~ O-N 0.. O~ Ar/ ~ \oAr "ON.--Ar "-'0\ 1 0- 7

^,-o,

Ar~o ~

07 L Ar'~O~O" ?r_ok / \ \

--

Fig. 24. A porphyrin dendrimer, which is a model compound for heme-containing proteins.

electron-rich microenvironment created by the dendritic branches. The dendryl substituents "shield" the porphyrin center and hence hinder the addition of electrons to it. Similar effects were found for iron-porphyrin dendrimers in organic and aqueous solutions [ 104]. Bhyrappa et al. [ 105] equipped metal-porphyrins with poly(aryl ester) dendrons. The manganese(III) species have been found to be more regioselective oxidation catalysts than the nondendritic parent catalyst. Vacus and Simon [102] reported a dendritic metallo-phthalocyanine. The dendritic wedges on the metal-complex core resulted in good solubility of the molecule and, in addition, provided enough shielding so that luminescence could be detected and measured in aqueous solution.

2.5.4. Other Metal-Containing Dendrimers In addition to ferrocene and ruthenium-ligand-type dendrimers, there have been reports on many other metal-containing cascade molecules in the literature. Moors and V6gtle [ 106] introduced cobalt to polyamine dendrimers capped with salicylidene moieties. Figure 26 shows the cobalt complex of a hexasalen dendrimer derived from TREN (tris(aminoethyl) amine). Cobalt also has been complexed into dendrimers with acetylene units in the branches by Newkome et al. [107] via the addition of dicobaltoctacarbonyl. Such cobalt-acetylene complexes are known to catalyze cyclopentenone cyclization reactions [ 108], and the dendritic species have been termed Cobaltomicellane TM (Fig. 27) [ 109].

354

DENDRITIC MOLECULES--HISTORIC DEVELOPMENT AND FUTURE APPLICATIONS

R

R

-R

/R .R

......./R

~-Co

o

o. ~~

o

o

0-3-

'~&',N~O d ~ H ~"0"-"~o

~~~~o o~L~ ~_jd o, , _ , ~. .~ .JIY 1 0 2 -E~

R

H

)H

0

0

0

0

R R"

R/

RR

R

R

R=

C02CH 3

Fig. 25. Dendrylated zinc porphyrin.

o, ,,

/

",,, \~

.~

Nod

,,,, "",.,. f

,.

/"

l/ /

/##

/

/

Fig. 26. Cobalt complex of a hexasalen dendrimer.

355

ARCHUT AND VOGTLE

R

R

R

R

L3C~

R~ J r

r~

R

R

% ~ ~--~CoL3

R

R

"~

f

R

J

L

R

CoL3 L .~

v-

L-, L3C~~" /, L3Co

CoL3 ~~~.CoL3

7,CoL3 \

R

R

"R

R

R = CH2OCH2Ph

L=CO Fig. 27. Newkome's"Cobaltomicellane."

Complexes of gadolinium(III) salts are interesting contrasting agents for magnetic resonance imaging [110, 111] because they are paramagnetic species with a great number of unpaired electrons, a high magnetic moment, and a long electron relaxation time. Wiener et al. [112] attached suitable ligands for the complexation of Gd(III) ions to PAMAM dendrimers of second and sixth generation to form the corresponding gadolinium complexes (Fig. 28) and then measured their relaxativity. Particularly high relaxativities were observed in the case of the sixth generation gadolinium dendrimer that were attributed to the surface properties and the rigidity of this species. Achar and Puddephatt [113-115] developed several organoplatinum dendrimers by a convergent approach with up to 28 metal centers (Fig. 29). The work of van Koten et al. on catalytically active nickel-containing dendrimers has already been described [26, 27]. 2.6. P h o t o a c t i v e A z o b e n z e n e D e n d r i m e r s

Light is useful to manipulate molecular systems because its effect is fast, mild, and often reversible. Azobenzene derivatives have been used to construct photoswitchable devices

356

DENDRITIC MOLECULES--HISTORIC DEVELOPMENT AND FUTURE APPLICATIONS

~2 ~

,,~

U~,, I

t"N~CO2e

~02C v N

., 002C~N

E)02C~

H,,N

e

_ B

. o

S

' ~

.\.

.

N,,

LN~

F

? o4

H H '~A"2 c

~N.~N ~ ..,.J H 0.~..i~

,,

,,~ HN 0

N"II"!"~- NH H / H 0~/~_ N N o ~ N ' ~ o

N'H

;" H--N

D

N. ~

$~"i I~

-)'-Me

ANI.~N [

O02CvN'

-L

....(~ ,,"~'~ I~NI~NI /

,.,~_~ ~-"~ /

O

~;02(::

/ N,,~,S eO,)C: H / "1

N-~

BON>2C~ i I

C(~

-v2~"

0 FIN.. O , II "1 ~ N--'~v J~--~ -N" ~" N"~k'N I I ''~ H H H H~ O

) k,

Lco~

N"'ll",I ~ I i H H

_T

L N...~.. ~ N F

~-

~

CX)z

?

o,~,.

~

~--C02''~'

()

H -N

_

OO2C~ N"J I ~

_/N--~

02C

H

i..N.~N . ~ NvC02 " 'W'N"~ H. _ ~ Me .,,J I H r-" b"~_ N O2C O0_e " ~ S .N-~ (J -- "I I~,~I~ N,,JI~Nr--~ 0 k.NH ,

0

S ~ N'H

L,~

I ' ~ N"II"N_ I I

,-.

~"Me

H~N"I

(N ~ " . ""r" vCO2 z

,--', ~

,.,,~_E)

~,.N~C02~

~ F'N"I v 02Clde..,,~NA C02~ 02C

Me,_.,l

N

M.,.i,3 ~02C v N~C020

Fig. 28. Dendriticgadolinium complex. Such complexes are of interest as contrasting agents for magnetic resonance imaging.

(Fig. 30) for many years [116, 117]. Azobenzene-type compounds, when they are not strongly sterically hindered, do not show any appreciable fluorescence or phosphorescence, but they can be easily and reversibly photoisomerized. The thermodynamically stable E isomer can be photochemically converted to the Z isomer, which is converted back to the E isomer by light excitation and thermal change in the dark [118, 119]. Azobenzene moieties have, therefore, been applied to construct photoresponsive molecular and supramolecular systems like molecular tweezers [ 120], liquid-crystal films [ 121 ], concave dyes [ 122], photoresponsive polymers [ 119], donor-acceptor complexes [ 123], switchable receptor molecules [ 124, 125], and others. Recently, Junge and McGrath [126] reported the synthesis of a two-directional dendrimer with an azobenzene group in the center, and they investigated its E/Z isomerization induced by ultraviolet light (Fig. 31). Although the steric effect of the isomerization of the chromophore is probably minor, the work has prompted speculation on whether such molecules could be used to "grab" molecules upon irradiation. Freemantle [127] stated that to obtain such an effect there would have to be more switchable moieties present in the molecule. Such molecules are now available (vide infra).

357

ARCHUT AND VOGTLE

Br


.

> 2~

9

r"

m


472 2 1 0 0 0

I 50

,

I ~

i,

~

100 150 C r y s t a l size / nm

200

Fig. 30. Relationship between excitonic absorption peak positions and the crystal size of perylene nanocrystals. The crystal size was measured by DLS.

A

400

450 500 550 Wavelength / nm

600

Fig. 31. Emission spectra of perylene nanocrystals with sizes of (A) 50 nm and (B) 200 nm, and (C) bulk crystals. The excitation wavelength was 350 nm.

perylene crystals emit two kinds of fluorescence: one kind from the free (F) exciton level and the other kind from the self-trapped (S) exciton state. In the bulk crystals, only the luminescence from the S-exciton state was observed at 560 nm [57, 58], because the S-exciton state is more stable than the F-exciton state, and the energy difference between them is large. However, for perylene microcrystals, very strong luminescence was observed near 480 nm at room temperature that is from the F-exciton state in the microcrystals [57]. Furthermore, crystal size dependence also was observed for the emission peak position of the F-exciton state. The luminescence peak wavelengths of microcrystals with sizes of 50 and 200 nm were 470 and 482 nm, respectively. From these results, the potential curves of perylene microcrystals and bulk crystals can be illustrated as in Figure 32. In accordance with the experimental data, the potential curves of both the F-exciton and S-exciton states in the microcrystals are shifted to the higher-

464

SPECTROSCOPIC CHARACTERIZATIONOF ORGANIC NANOCRYSTALS

s

Bulk crystal

Microcrystal

Fig. 32. The energy diagrams of perylene in bulk crystal and nanocrystal forms. F, free exciton state; S, self-trapped exciton state; G, ground state.

energy side relative to those of the bulk crystal, but the shift for the S-exciton state is larger than that for the F-exciton state. As a result, the energy difference between the F-exciton and S-exciton states is smaller than that of bulk crystals. Therefore, strong luminescence from the F-exciton state was observed.

7.4. C60 Nanocrystals Nanocrystals of C60 have been prepared [59]. Photophysical and photochemical properties of C60 nanocrystals were examined by nanosecond laser flash photolysis. When C60 solution is purple, the dispersion of C60 nanocrystals is light brown, similar to the crystalline color of C60. The absorption spectrum of C60 nanocrystals dispersed in ethanol showed an absorption peak at 350 nm, accompanying shoulders around 450 and 620 nm. Triplet-triplet annihilation due to migration of the triplet state within C60 nanocrystals was observed. Photoexcitation of C60 nanocrystals in the presence of an electron donor resulted in photoinduced electron transfer. The reaction rate was 1 order of magnitude smaller than that in solution, suggesting interfacial electron transfer.

7.5. Comparison of Optical Properties with Other Low-Dimensional Systems Table VI summarizes the size dependence of optical absorption properties among organic superlattice, PDA, perylene, and semiconductor microcrystals [20, 31-33, 22, 54, 60-62]. Size effects in organic superlattices as well as semiconductor microcrystals appear when the size is reduced to less than 10 nm; these effects has been explained in terms of quantum confinement. However, interestingly, in the case of organic microcrystals, such as PDA and perylene, high-energy shifts in excitonic absorption were observed even though the crystal size was much larger than about 100 nm. Although the reason for this peculiar phenomenon is not clear, two factors are presumed to be the cause of the size effect in organic microcrystals. One factor is the change of lattice state. Because the lattice softens by microcrystallization, the Coulombic interaction energies between molecules get smaller. As a result, the optical absorption properties of the molecules change in the microcrystals. The other factor is the electric field effect of the surrounding media with varying dielectric constants.

465

KASAI ET AL.

Table VI. The Size Dependence of Excitonic Absorption Peak Positions (Xmax and v) and the Energy Shift from Bulk Crystal (AE) of Various Nanocrystals

Inorganics

Organics

Crystal size

Xmax

v

AE

Materials

(nm)

(nm)

( c m - 1)

( c m - 1)

Measurement

CuC1a

Bulk 3.3 2.1

386 384 382

(25,900) (26,000) (26,200)

0 100 300

77 K

CdSea

Bulk 12 1.8

674 664 507

(14,800) (15,100) (19,700)

0 300 4900

2K

NTCDA/ PTCDAb

Bulk 4g 1g

560 558 555

(17,860) (17,900) (19,000)

0 40 160

Room temp.

PPy/PBTc

Bulk 9 3

(16,130) (16,210) (116,390)

0 80 260

Room temp.

Perylened

Bulk 200 50

480 470 450

(20,800) (21,300) (22,200)

0 80 260

Room temp.

PDAe (DCHD)

Bulk 150 50

665 652 635

(15,000) (15,300) (15,700)

0 300 700

Room temp.

VOPcR4f

Bulk 140 40

681 665

(14,680) (15,000)

0 320

temperature

Room temp.

a Reference [ 16].

bNTCDA = (3,4,9,10-perylene-tetracarboxylic dianhydride); PTCDA = (3,4,7,8-naphthalene-tetracarboxylic dianhydride) [62]. Cppy = (polypyrrole); PBT = (polybithiophene). These data were measured by photoluminescence [60]. dReferences [20] and [54]. eReferences [21] and [22]. f Reference [24] [VOPcR4 = VOPc(SC6H13)4]. g Superlattice.

8. NONLINEAR OPTICAL PROPERTIES OF NANOCRYSTALS Third-order nonlinear optical properties have been investigated for many kinds of reconjugated molecular and polymeric materials that include dyes, fullerenes, chargetransfer complexes, conjugated polymers, organometallics, biomaterials, liquid crystals, and nanocomposites [35, 45]. For example, third-order N L O susceptibility X (3) values on the order of 10 -6 esu in the resonant wavelength region around 0.65 lzm [63] and 10 -9 esu in the nonresonant region above 1 # m up to 1.6 /zm were reported for single crystals of polydiacetylenes [64]. The fast response time of about 2 ps was reported to be due to the self-trapped exciton [65]. These interesting third-order N L O properties result from zr-electron delocalization in one-dimensional conjugated systems such as polyacetylenes, polydiacetylenes, polythiophenes, poly(p-phenylene)s, poly(p-phenylene vinylene)s, polyazines, polyazomethines, polyacenes, poly(quinoline)s, polyanilines, heteroaromatic ladder polymers, etc. [35, 66]. Cyanine dyes including two-dimensional

466

SPECTROSCOPIC CHARACTERIZATION OF ORGANIC NANOCRYSTALS

zr-conjugated systems such as metallophthalocyanine also exhibit very large X (3) and optical quantum yields. The NLO properties of several kinds of cyanine dyes have been estimated by different measurements to evaluate their potential for future photonic technologies [67, 68]. For NLO device applications, it is very important to prepare large crystals or homogeneous thin films of zr-conjugated compounds with good optical quality. Several preparative methods for organic thin single crystals have been investigated and a few successful techniques have been reported for the evaluation of the NLO properties. However, uniform large area thin single crystal formation is often difficult, and the strong thermal conductivity anisotropy encountered causes difficulty for optical device applications. Several trials of optical devices using spin-coated thin films or Langmuir-Blodgett films have been carfled out [69]. The NLO properties of PDA thin films become smaller than those of crystals because the stereoregularity of the 7r-conjugated main chain is distorted. The materials are required to satisfy the following conditions: (i) high optical transparency, (ii) large NLO susceptibilities, and (iii) ultrafast response. To achieve little light scattering while keeping the structure uniform, nanometer sized crystals have been considered to be suitable for optical device application. Some interesting physical properties like the electron confinement effect could be expected in quantum-dot systems. The nonlinear refractive indices and nonlinear absorption measured on nanocrystals of PDAs and cyanine dyes in the film state or as dispersed liquids have been discussed. The third-order NLO properties of organic nanocrystals were measured by third harmonic generation (THG), Z scan, optical Kerr shutters (OKS), and degenerate four-wave mixing (DFWM). The samples were prepared by the reprecipitation method and were measured as dispersion liquids or thin films. Third-order NLO properties of amphiphilic merocyanine dye (MCSe-C 18) nanocrystals in a polymer matrix were measured by third harmonic generation [70]. The nanocrystals of MCSe-C 18 dispersed in water were converted to J-aggregated form. The dispersion of the modulus and phase of X (3) as a function of the measurement wavelength are shown with the absorption coefficient in Figure 33. A three-photon resonant effect can be observed clearly at the absorption peak of 630 nm, where only the imaginary part of X (3) contributes to the NLO process. The X (3) of the J-state microcrystals (10 wt%) in a polymer matrix was found to be 20 times larger than that of non-J-state microcrystals (10 wt%). At thirdharmonic wavelengths slightly longer than that at the absorption peak, the modulus of X (3)

3

T 250

A2.5

8 v

200 2 && uml

A

&

k

1 5 0 ~*...,

IA

E

o m M

X 1.5 A

8

m

100 ~.

0.5

II

750

i

. . ;A. .&. : &

&

700

&

3

n

;-,-" 650

;--o 600

.... 550

..,0

-0

500

Wavelength (nm)

Fig. 33. Modulusand phase of X(3) as a function of the third-harmonic wavelength on the film of Jformed merocyaninenanocrystals, n, modulus of X(3). s, phase of X(3); solid line, absorbance.

467

KASAI ET AL.

6 E =

4

5

o N ~

'o

4

3

X

E :t

3

2

1

nnnu|nnmm

n

u

9

9

0

0 760

700

650

600

650

500

Wavelength (rim)

Fig. 34. Figureof merit (IX(3)j/c~)as a function of the third-harmonicwavelength.

increased, while the phase remained small. This shows that the real part of X (3) increases at the band edge due to the resonant contribution. To clarify the resonance contribution, the figure of merit Ix(3)l/c~ is plotted as a function of the third-harmonic wavelength in Figure 34. The figure of merit shows a maximum value of 5.7 • 10 -12 esu # m at 670 nm. This figure of merit was found to be 1.5 and 20 times larger than that of the nonresonant value at 720 nm and the excitonic peak at 630-nm wavelengths, respectively. Such an enhancement of the figure of merit can be observed because of the sharp band edge of exitonic absorption due to the formation of J-aggregate state. At the band edge, the optical absorption decreases rapidly away from resonance, while the real part of the X (3) is still large due to the resonance effect. These results demonstrate that by sharpening the absorption peak and using a wavelength near the band edge, a significant enhancement of third-order nonlinear optical properties can be achieved. The NLO properties of DCHD microcrystals in a gelatin film also were evaluated by the Z-scan method [71 ]. The X (3) nonlinear refraction n2, and nonlinear absorption fl around the exciton peak were obtained by using a tunable picosecond laser, and the results are shown in Table VII. The signs of the measured values are positive/negative at wavelengths shorter/longer than the exciton peak, and strong saturability where/3 is negative is estimated around the peak. From these results and theoretical calculations, it was concluded that the observed optical nonlinearity is based on the one-dimensional re-conjugated main chain of the DCHD microcrystals. The values of X (3) at near resonant wavelength reached an order of magnitude comparable to polydiacetylene single crystals [64]. On the other hand, the OKS response of organic microcrystals was investigated by using dispersed liquid [72, 73]. The compounds used were MCSe-C18 and polydiacetylenes. Measured X (3) values ranged from 10 -13 to 10 -12 esu and the largest X (3) was 2.2 x 10 -12 esu for poly(DCHD) even in the nonresonant range. This is slightly less than the maximum X (3) so far reported for organic dyes in solution. However, the X (3) values normalized by the concentration for the dispersion system are 10 .9 esu M -1 , which is about 2 orders of magnitude larger than those for any other solution systems. These results suggest that microcrystal dispersion systems of large X (3) are applicable for OKS materials when the concentration increases without increasing scattering loss. Although a size effect on absorption maximum has been observed for poly(DCHD) microcrystals, clear differences between X (3) values on these samples were not observed. Another virtue expected for microcrystal dispersion systems is ultrafast response because molecular orientation effects seem to be negligible due to the larger mass of microcrystals compared to molecules.

468

SPECTROSCOPIC CHARACTERIZATION OF ORGANIC NANOCRYSTALS

Table VII. The n2, Re X(3),/3, and Im X(3) of Poly(DCHD) Nanocrystals (2.4 wt%) in Gelatin [71]

(nm)

n2 (10-2 cm2 GW-I)

Re X(3) (10-9 esu)

/3 (102 cm GW-1)

Im X(3) (10-9 esu)

550

+0.68

0.41

-4.2

-0.11

570

+0.82

0.50

-7.0

-0.19

580

+0.94

0.57

-9.3

-0.26

590

+1.00

0.61

- 11.0

-0.32

600

+0.63

0.39

- 10.0

-0.29

620

+ 1.00

0.61

-9.2

-0.28

630

+1.70

1.0

-17.0

-0.53

640

+2.4

1.4

-39.0

-0.95

650

a

-47.0

- 1.50

660

-2.20

- 1.3

-26.0

-0.84

670

- 1.40

-0.88

-5.2

-0.17

680

b

+3.4

+0.11

740

b

+2.3

+0.084

750

b

+ 1.9

+0.068

a The data cannot be analyzed because the Z-scan closed aperture profile was strongly deformed. bThe Z-scan signal was too small compared with the noise level.

However, it was impossible to measure the ultrafast response, because the pulse width of the laser was on the order of 10 -9 s. Yanagawa [74] reported the ultrafast response of phthalocyanine microcrystals dispersed in water by D F W M measurements using an optical parametric oscillator as an incoherent light source. The 7'1 = 200 fs for the absorption level was observed. Organic microcrystals are considered to be useful for future optical materials. The data for N L O measurements on nano/microcrystals are summarized in Table VIII. If the nanocrystal size reaches several nanometers, quantum confinement effects, which have been observed in inorganic semiconductors, may appear even in organic materials.

9. SUMMARY We have discussed an effective and simple method for preparing a variety of organic microcrystals in water. The solid-state polymerization of 4 - B C M U microcrystals was estimated to proceed from one end to the other end. The possibility of preparing PDAs with controlled molecular weight was qualitatively demonstrated. In the case of microcrystals of 14-8ADA, size-dependent conversion was found and can be explained by the looseness or thermal vibrations of the crystal lattice. Regarding the optical properties, size was found clearly to affect the absorption m a x i m a of PDA microcrystals. Organic microcrystal dispersions are applicable for OKS devices, where X (3) values and X (3) values normalized by concentration for PDA dispersions are 10-13"~10 -12 esu and 10 -9 e s u M -1, respectively. Further efforts to increase dispersion

469

KASAI ET AL.

Table VIII. Third-Order NLO Susceptibility Data for Organic Nano/Microcrystals

Materials

Sample condition

Crystal size (nm)

Measurement technique a

~. (nm)

X(3) (10-12 esu) 2.52

X(3)/C (10 -9 esu M -1)

MCSe-C 18

PVA film (10 wt%)

20

THG

640

14-8ADA

PVA film (34 wt%)

300

THG

657

22.0

DCHD

Gelatin film (2.4 wt%)

100

Z-scan

660

33.6

VOPcR4b

Water dispersion (2.0 x 10-4 M)

40

Z-scan

680

23.0

80

Z-scan

633

8.20

20

OKS (NR)

813

1.10

1.80

20

OKS

813

0.20

1.00

MCSe-C18

Water dispersion (6.2 x 10-4 M) (2.0 x 10-4 M)

14-8ADA

Water dispersion (1.0 x 10-3 M)

300

OKS (NR)

813

0.86

0.86

DCHD

Water dispersion (2.3 x 10-3M) (2.3 x 10.3 M) (1.6 x 10.3 M)

70

OKS (NR)

813

1.40

0.61

100 150

OKS OKS

813 813

2.20 1.60

0.93 1.00

aNR denotes nonresonant. bVOPcR4 = VOPc(SC6H13)4.

c o n c e n t r a t i o n will e s t a b l i s h n a n o c r y s t a l l i z a t i o n as a n e w t e c h n i q u e for i n c o r p o r a t i n g crystalline c o m p o u n d s into large isotropic m e d i a . In addition, m i c r o c r y s t a l s c o m p o s e d o f single c h a i n s o f c o n j u g a t e d p o l y m e r s f r o m o n e e n d to the o t h e r c o u l d be u s e f u l for m a k i n g m o l e c u l a r d e v i c e s as well.

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SPECTROSCOPIC CHARACTERIZATION OF ORGANIC NANOCRYSTALS

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KASAI ET AL.

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Chem. Soc. 108, 2100 (1986). 28. E M. Gallagher, M. E Coffey, V. J. Krukonis, and N. Klasutis, Am. Chem. Soc. Symp. Ser. 406, 334 (1989). 29. H. Kasai, Y. Yoshikawa, T. Seko, S. Okada, H. Oikawa, H. Matsuda, A. Watanabe, O. Ito, H. Toyotama, and H. Nakanishi, Mol. Cryst., Liq. Cryst. 294, 173 (1997). 30. K. Yase, T. Hanada, H. Kasai, T. Sato, S. Okada, H. Oikawa, and H. Nakanishi, Mol. Cryst., Liq. Cryst. 294, 71 (1997). 31. K. Yase, T. Hanada, H. Kasai, S. Okada, H. Oikawa, and H. Nakanishi, J. Electron. Microsc., in press. 32. H. Katagi, H. Kasai, S. Okada, H. Oikawa, H. Matsuda, Z. Liu, and H. Nakanishi, Jpn. J. Appl. Phys. 35, L1364 (1996). 33. H. Katagi, H. Kasai, S. Okada, H. Oikawa, H. Matsuda, and H. Nakanishi, J. Macromol. Sci., A 34, 2013 (1997). 34. (a) D. Bloor and R. R. Chance (eds.), "Polydiacetylenes: Synthesis, Structure and Electronic Properties." Nijhoff, Dordrecht, 1985; (b) V. Enkelmann, Adv. Polym. Sci. 63, 91 (1984). 35. (a) H. S. Nalwa, in "Nonlinear Optics of Organic Molecules and Polymers" (H. S. Nalwa and S. Miyata, eds.), Chap. 11, pp. 611-797. CRC Press, Boca Raton, FL, 1997; (b) H. S. Nalwa, Adv. Mater. 5,341 (1993). 36. S. Etemad, G. L. Baker, and Z. G. Soos, in "Molecular Nonlinear Optics" (J. Zyss, ed.), p. 433. Academic Press, San Diego, 1994. 37. S. Molyneux, H. Matsuda, A. K. Kar, B. S. Wherret, S. Okada, and H. Nakanishi, Nonlinear Opt. 4, 299 (1993). 38. E Kajzar and E Messier, Polym. J. 19, 275 (1987). 39. H. Nakanishi, H. Matsuda, S. Okada, and M. Kato, Polym. Adv. Technol. 1, 75 (1990). 40. G. Wegner, Z Naturforsch. 24b, 824 (1969). 41. C. Sauteret, J. E Hermann, R. Frey, E Pradere, J. Ducuing, R. H. Baughman, and R. R. Chance, Phys. Rev. Lett. 36, 956 (1976). 42. R. Iida, H. Kamatani, H. Kasai, S. Okada, H. Oikawa, H. Matsuda, A. Kakuta, and H. Nakanishi, Mol. Cryst., Liq. Cryst. 267, 95 (1995). 43. H. Oshikiri, H. Katagi, H. Kasai, S. Okada, H. Oikawa, and H. Nakanishi, Mol. Cryst. Liq. Cryst., in press. 44. H. Kasai, H. Oikawa, S. Okada, and H. Nakanishi, Bull Chem. Soc. Jpn. 71, 2597 (1998). 45. (a) H. S. Nalwa and J. S. Shirk, in "Phthalocyanines: Properties and Applications" (C. C. Leznoff and A. B. E Lever, eds.), Vol. 4, Chap. 3, pp. 79-81. VCH Publishers, New York, 1996; (b) H. S. Nalwa, Appl. Organometal. Chem. 5, 349 (1991); (c) Z. Z. Ho, C. Y. Ju, and W. M. Hetherrington, III, J. Appl. Phys. 62, 716 (1987); (d) N. Q. Wang, Y. M. Cai, J. R. Helfin, and A. E Garito, Mol. Cryst., Liq. Cryst. 189, 39 (1990); (e) J. S. Shirk, J. R. Lindle, E J. Bartoli, C. A. Hoffman, Z. H. Kafafi, and A. W. Snow, Appl. Phys. Lett. 55, 1287 (1989); (f) J. S. Shirk, J. R. Lindle, E J. Bartoli, and M. E Boyle, J. Phys. Chem. 96, 5847 (1992); (g) H. Matsuda, S. Okada, A. Masaki, H. Nakanishi, Y. Suda, K. Shigehara, and A. Yamada, SPIE Proc. 1337, 105 (1990); (h) R. A. Norwood and J. R. Sounik, Appl. Phys. Lett. 60, 295 (1992); (i) A. Grund, A. Kaltbeitzel, A. Mathy, R. Schwarz, C. Bubeck, P. Vermehren, and M. Hanack, J. Phys. Chem. 96, 7450 (1992); (j) H. S. Nalwa, A. Kakuta, and A. Mukoh, J. Phys. Chem. 97, 1097 (1993); (k) H. S. Nalwa and A. Kakuta, Thin Solid Films 254, 218 (1995); (1) H. S. Nalwa, T. Sato, A. Kakuta, and T. Iwayanagi, J. Phys. Chem. 97, 10515 (1993); (m) H. S. Nalwa and S. Kobayashi, J. Porphyrins Phthalocyanines 2, 21 (1998).

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46. (a) G. Decher, Science 277, 1232 (1997); (b) X. Wang, S. Balasubramanian, L. Li, X. Jiang, D. J. Sandman, M. E Rubner, J. Kumar, and S. K. Tripathy, Macromol. Rapid. Commun. 18, 451 (1997). 47. S.L. Clark, M. E Montague, and P. T. Hammond, Supramol. Sci. 4, 141 (1997). 48. S. K. Tripathy, H. Katagi, H. Kasai, S. Balasubramanian, H. Oshikiri, J. Kumar, H. Oikawa, S. Okada, and H. Nakanishi, Jpn. J. Appl. Phys. 37, L343 (1998). 49. R. Iida, H. Kamatani, H. Kasai, S. Okada, H. Oikawa, H. Matsuda, A. Kakuta, and H. Nakanishi, Mol. Cryst., Liq. Cryst. 267, 95 (1995). 50. H.S. Nalwa, H. Kasai, S. Okada, H. Matsuda, H. Oikawa, N. Minami, A. Kakuta, A. Mukoh, and H. Nakanishi, "Proceedings of the 9th Miyazaki International Symposium on Electrical and Optical Properties of Organic Materials," Tokyo, Japan, 1992, p. B 121. 51. B. Tieke, D. Bloor, and R. J. Young, J. Mater Sci. 17, 1156 (1982). 52. H. Katagi, H. Oikawa, S. Okada, H. Kasai, A. Watanabe, O. Ito, Y. Nozue, and H. Nakanishi, Mol. Cryst., Liq. Cryst., to appear. 53. T. Asahi, K. Kibisako, H. Masuhara, H. Kasai, H. Katagi, H. Oikawa, and H. Nakanishi, Mol. Cryst., Liq. Cryst., to appear. 54. H. Kasai, H. Kamatani, S. Okada, H. Oikawa, H. Matsuda, and H. Nakanishi, Jpn. J. Appl. Phys. 35, L221 (1996). 55. H. Kasai, Y. Yoshikawa, T. Seko, S. Okada, H. Oikawa, A. Watanabe, O. Ito, H. Toyotama, and H. Nakanishi, Mol. Cryst., Liq. Cryst. 294, 173 (1997). 56. H. Kasai, H. Kamatani,Y. Yoshikawa, S. Okada, H. Oikawa, A. Watanabe, O. Ito, and H. Nakanishi, Chem. Lett. 1181 (1997). 57. H. Nishimura, T. Yamaoka, K. Mizuno, M. Iemura, and A. Matsui, J. Phys. Soc. Jpn. 53, 3999 (1984). 58. H. Auweter, D. Ramer, B. Kunze, and H. C. Wolf, Chem. Phys. Lett. 85, 325 (1982). 59. M. Fujitsuka, H. Kasai, A. Masuhara, S. Okada, H. Oikawa, H. Nakanishi, A. Watanabe, and O. Ito, Chem. Lett. 1211 (1997). 60. M. Fujitsuka, R. Nakahara, T. Iyoda, T. Shimidzu, and H. Tsuchiya, J. Appl. Phys. 74, 1283 (1993). 61. T. Tokizaki, H. Akiyama, M. Tanaka, and A. Nakamura, J. Cryst. Growth 117, 603 (1992). 62. F.F. So, S. R. Forrest, Y. Q. Shi, and W. H. Steier, Appl. Phys. Lett. 56, 674 (1990). 63. S. Molymeux, H. Matsuda, A. K. Kar, B. S. Wherrett, S. Okada, and H. Nakanishi, Nonlinear Opt. 4, 299 (1993). 64. G. Stegeman, B. Lawrence, M. Cha, W. Torruellas, S. Etemad, G. BakerSome, G. Baker, and J. Meth, "Technical Digest of the 4th Iketani Conference" 1994, p. 58. 65. T. Kobayashi, "Organic Materials for Non-linear Opticals, III" (G. J. Ashwell and D. Bloor, eds.). Royal Society of Chemistry, Cambridge, UK, 1993. 66. H.S. Nalwa and S. Miyata (eds.), "Nonlinear Optics of Organic Molecules and Polymers." CRC Press, Boca Raton, FL, 1997. 67. S. Kobayashi and F. Sasaki, Nonlinear Opt. 4, 305 (1993). 68. H. Tomiyama, H. Matsuda, S. Okada, and H. Nakanishi, "Nonlinear Optics, Fundmentals, Materials and Devices" (S. Miyata, ed.), p. 305. Elsevier Science Pub., Amsterdam, 1992. 69. P.D. Townsend, J. L. Jackel, G. L. Baker, J. A. Shelburne, and S. Etemad, Appl. Phys. Lett. 55, 1829 (1989). 70. H. Mastuda, E. Van Keuren, A. Masaki, K. Yase, A. Mito, C. Takahashi, H. Kasai, H. Kamatani, S. Okada, and H. Nakanishi, Nonlinear Opt. 10, 123 (1995). 71. H. Mastuda, S. Yamada, E. Van Keuren, H. Katagi, H. Kasai, S. Okada, H. Oikawa, H. Nakanishi, S. C. Smith, A. K. Kar, and S. Wherrett, SPIE Proc. 2998, 241 (1997). 72. H. Kasai, H. Kanbara, R. Iida, S. Okada, H. Matsuda, H. Oikawa, and H. Nakanishi, Jpn. J. Appl. Phys. 34, L 1208 (1995). 73. H. Kasai, R. Iida, H. Kanbara, S. Okada, H. Matsuda, H. Oikawa, T. Kaino, and H. Nakanishi, Nonlin. Opt. 15,263 (1996). 74. T. Yanagawa, Y. Kurokawa, H. Kasai, and H. Nakanishi, Opt. Commun. 137, 103 (1997).

473

Chapter 9 POLYMERIC NANOSTRUCTURES Guojun Liu Department of Chemistry, University of Calgary, Calgary, Alberta, Canada T2N 1N4

Contents 1. 2. 3.

4.

5.

6.

7.

8.

9.

10.

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Polymer Synthesis and Characterization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Star Polymers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1. Example Preparation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2. Robustness of This Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3. Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Hairy Nanospheres . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1. Example Preparation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2. Properties of the Nanospheres and Potential Applications . . . . . . . . . . . . . . . . . . . . . Tadpole Molecules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1. Example Preparation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2. Some Future Prospects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Hollow Nanospheres . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1. Example Preparation of Hairy Hollow Nanospheres . . . . . . . . . . . . . . . . . . . . . . . . 6.2. Example Preparation of Semi- and Fully-Shaved Hollow Nanospheres . . . . . . . . . . . . . . 6.3. Potential Applications and Some Future Prospects . . . . . . . . . . . . . . . . . . . . . . . . . 6.4. Related Chemistry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Polymer Brushes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.1. Example Preparation of Cross-Linked PS-b-PCEMA Brushes . . . . . . . . . . . . . . . . . . 7.2. Layered Structure of PS-b-PCEMA Brushes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.3. Properties and Potential Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Block Copolymer Nanofibers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.1. Example Preparation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.2. Potential Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Nanochannels in Thin Films . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.1. Example Membrane Preparation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.2. Chemical Valving Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.3. Potential Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

475 477 478 479 479 480 481 481 482 484 484 484 485 485 485 487 488 488 489 489 490 490 492 494 495 495 495 497 497 498 498

1. INTRODUCTION A n a n o s t r u c t u r e h a s its s m a l l e s t d i m e n s i o n in t h e 1 - 1 0 0 - n m

s i z e r a n g e [1]. A l t h o u g h t h e

s i z e o f a p o l y m e r c o i l in d i l u t e s o l u t i o n f a l l s i n t o t h i s r a n g e , p o l y m e r c o i l s a r e n o t c o n s i d e r e d to b e n a n o s t r u c t u r e s b e c a u s e t h e y a r e s t r u c t u r a l l y n o t s t a b l e ( t h e y u n d e r g o l a r g e - s c a l e

Handbook of NanostructuredMaterials and Nanotechnology, edited by H.S. Nalwa Volume 5: Organics, Polymers, and Biological Materials Copyright 9 2000 by Academic Press All rights of reproduction in any form reserved.

ISBN 0-12-513765-6/$30.00

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structural fluctuation with time). The radii of surfactant or polymer micelles also fall into the nanometer range. They are not included in the nanostructure category in this chapter because they are not permanent structures either. Micelles form in one solvent and may disintegrate in another. Even in a solvent in which the micelles form, chains are constantly exchanged between micelles and the unimer pool or between different micelles. Polymeric nanostructures in this chapter refer to cross-linked nanometer-sized structures prepared from polymers and, in particular, block copolymers. A major driving force for the booming activities in the nanoscience and nanotechnology field has been the demand for ever smaller electronic devices [1 ]. Also, nanometer-sized semiconductors are interesting for their unique properties derived from the quantum size effect. Further interest derives from the expectation that composites made from nanoparticles may be useful as high performance construction materials and that nanoengineered materials may imitate the functions of proteins and enzymes in molecular recognition. As is evident from this handbook, nanostructures are typically prepared from inorganic or organic precursors. Other than nanosphere preparation from microemulsion [2] or precipitation [3] polymerization, no systematic work has been reported before ours on synthesizing different nanostructures from polymers. For this reason, this chapter will essentially review our work in the past 3-4 years. Results of other groups will be referenced in the sections that discuss the preparation of individual nanostructures. The scarcity of activities in polymeric nanostructure preparation and study is not in line with the potentially important role polymeric nanostructures may play in future nanometersized or molecular electronic devices. A thin polymer film with nanochannels may, for example, be an ideal matrix for semiconductor or metal nanocomponent embedment for preparing nanoelectronic devices just like the use of plastic cards to hold integrated circuits. Also, nanochannels with precisely controlled size and size distribution in thin polymer films can be used as templates for preparing nanomaterials [4] or can be used in separating chemicals with minor size or functionality differences, a function enzyme or protein chemists try to mimic. In the membrane application, the obvious advantage of using a polymer is that one can easily obtain large continuous films. Although hexagonally packed uniform nanochannels can be prepared in individual zeolite particle [5], their preparation in thin films with the channels permeating the whole film thickness is difficult [6]. We prepare nanostructures mostly from block copolymers. A copolymer is a macromolecule that contains two or more types of basic units or monomers. A block copolymer is a linear copolymer in which the different monomers occur in long sequences or blocks. The simplest block copolymer is diblock copolymer (A)n(B)m, which consists essentially of two linear polymer chains with n units of A and m units of B joined together head to tail. Some diblock copolymers we first synthesized and used in nanostructure fabrication are polystyrene-block-poly(2-cinnamoylethyl methacrylate) (PS-b-PCEMA), poly(2-cinnamoylethyl methacrylate)-block-poly(acrylic acid) (PCEMA-b-PAA), poly(t-butyl acrylate)-block-poly(2-cinnamoylethyl methacrylate) (PtBA-b-PCEMA), and polyisoprene-block-poly(2-cinnamoylethyl methacrylate) (PI-b-PCEMA):

CH3CH2(CH3)CH-~CH 2--

CH 2 -

C

~_CH2--C ---t H /CO 0

PS-~PCEMA

476

~OOCCH_C?

POLYMERIC NANOSTRUCTURES

These block copolymers are unique in that PCEMA is photocross-linkable. Then, the t-butyl groups of PtBA are easily hydrolyzable and the PI block can be degraded by ozonolysis. Block copolymers self-assemble under appropriate conditions to form mesophasic structures both in bulk and in solution. In this chapter, a mesophasic structure refers to an uncross-linked precursor to a nanostructure. In a block-selective solvent, a diblock copolymer may, for example, form spherical micelles, where the insoluble block makes up the core and the soluble block forms the corona that stretches into the solution phase [7, 8]. If the PCEMA block of the preceding diblocks forms the core, photolysis of such micelles would yield "permanent" structures, which we refer to as star polymers or hairy nanospheres for micelles with relatively thick or thin corona, respectively. Using the simple strategy of "locking in" mesophasic structure, we prepared a range of nanostructures including star polymers, nanospheres, "tadpole molecules," cross-linked polymer brushes (monolayers), and nanofibers. The nanospheres can be subdivided further into hairy nanospheres (cross-linked nanospheres with polymer chains on their surfaces), shaved nanospheres, nanospheres with cross-linked shells, and hollow nanospheres. In a hairy hollow nanosphere, long hair grows from both the outer and inner surfaces of the solid shell. The hair can be long relative to the size of the inner cavity, but its volume fraction in the cavity should be ~ 10%. Hairy nanospheres are different from those with crosslinked shells in which the caged chains are densely packed. More sophisticated nanostructures, such as nanochannels in thin films and semi- and fully-shaved hollow nanospheres, were obtained by combining cross-linking with degradation. Semi- and fully-shaved hollow nanospheres were obtained by shaving the outer polymer chains and all of the chains off hairy nanospheres, respectively. The next section describes the preparation and characteristics of diblocks. The subsequent sections are devoted to discussion of properties and applications of individual nanostructures before some conclusions are drawn in Section 10.

2. POLYMER SYNTHESIS AND CHARACTERIZATION

The precursors to the diblocks containing PCEMA were synthesized by anionic polymerization. To prepare PS-b-PCEMA, styrene was polymerized at - 7 8 ~ in tetrahydrofuran (THF) using sec-butyl lithium as the initiator [9, 10]. Then 1,1-diphenyl ethylene (DPE) and lithium chloride, both at 3 molar equivalents to sec-butyl lithium, were added. DPE reacted with polystyryl (PS) anions to convert them into the sterically more hindered PS-DPE anions. Lithium chloride improved the polydispersity of the second block. The second block was prepared by initiating the polymerization of trimethylsiloxyethyl methacrylate (HEMA-TMS) with PS-DPE anions. The trimethylsilyl protecting groups were removed by hydrochloric acid-catalyzed hydrolysis of PS-b-P(HEMA-TMS) in a THF/methanol mixture to produce polystyrene-block-poly(2-hydroxylethyl methacrylate) (PS-b-PHEMA). PS-b-PHEMA was then reacted with cinnamoyl chloride in pyridine to attach the cinnamoyl groups. To synthesize PCEMA-b-PAA, HEMA-TMS and t-butyl acrylate (tBA) were polymerized sequentially with fluorenyl lithium at - 7 8 ~ in THF to yield P(HEMA-TMS)-bPtBA [ 11 ]. P(HEMA-TMS)-b-PtBA was then hydrolyzed in acidic methanol at room temperature to yield PHEMA-b-PtBA. After cinnamation of PHEMA in pyridine, the t-butyl groups of PtBA were removed following the procedure of Jung and Lyster [ 12]. PtBA-b-P(HEMA-TMS) was prepared by reversing the polymerization order of HEMA-TMS and tBA used for preparing P(HEMA-TMS)-b-PtBA [13]. To prepare PI-b-PCEMA, isoprene was polymerized in a minimal amount of hexane at room temperature for 2 days using sec-butyl lithium as the initiator [ 14]. After the addition

477

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Table I. Important Characteristics of the Polymers Used [19] Laboratory code

(n / m) by NMR

Mw/Mn by

GPC

10-4 Mw by GPC

10-4 Mw by LS

10-2n

10-2m

PS-b-PCEMA $813-C59

13.8

1.17

9.6

10.0

8.1

0.59

$267-C22

12.0

1.10

2.9

3.4

2.7

0.22

$342-C34

10.1

1.14

3.8

4.4

3.4

0.34

S122-C12

9.9

1.13

1.5

1.6

1.22

0.12

$204-C22

9.6

1.09

2.5

2.7

2.04

0.22

S 1640-C182

9.0

1.10

21.8

21.8

16.4

1.82

S 1209-C152

7.9

1.10

14.8

16.5

12.1

1.52

$750-C107

7.0

1.12

10.0

10.6

7.5

1.07

$859-C268

3.2

1.09

9.7

15.9

8.6

2.7

S 1077-C1158

0.93

1.10

24.4

29.6

10.8

11.6

22.1

3.8

6.4

PtBA-b-PCEMA t 380-C640

0.59

1.18 PCEMA-b-PAA

C460-A187

0.41

1.09a

5.5a

13.3

4.6

1.87

C360-A560

0.65

1.07a

6.9a

16.6

3.6

5.6

PI-b-PCEMA I88-C231

0.38

1.19

2.7

6.6

0.88

2.3

I346-C 179

1.94

1.11

2.9

7.0

3.5

1.8

aResults obtained for PCEMA-b-PtBA, precursor to PCEMA-b-PAA.

of freshly distilled DPE, T H F was introduced into the polymerization flask by cryodistillation. H E M A - T M S was p o l y m e r i z e d at - 7 8 ~ for 2 h before the polymerization was terminated by methanol. The p o l y m e r s synthesized were characterized by gel permeation c h r o m a t o g r a p h y (GPC), proton nuclear magnetic resonance (1H NMR), and light scattering (LS). The important characteristics of the p o l y m e r s used to prepare the nanostructures described in this chapter are summarized in Table I. For G P C molar mass m e a s u r e m e n t in THF, the columns were calibrated with monodisperse PS standards.

3. STAR P O L Y M E R S A star p o l y m e r is a m a c r o m o l e c u l e that consists of three or more linear p o l y m e r chains of approximately equal length joined together at one end to a core. The core of a star p o l y m e r should be small relative to the size of each arm or constituent p o l y m e r chain. A hairy nanosphere consists of a relatively large cross-linked spherical core with a thin corona. Star p o l y m e r s and hairy nanospheres (see Fig. 1) were prepared by us from essentially the same m e t h o d by cross-linking the core block of diblock c o p o l y m e r micelles in a block-

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POLYMERIC NANOSTRUCTURES

Star Polymer

Hairy Nanosphere

Fig. 1. A star polymerand a hairy nanosphere. (Source: Reprinted with permissionfrom [19]. 9 1996 American ChemicalSociety.)

selective solvent. The difference lies in the use of diblocks with different relative block lengths. Several groups achieved diblock micelle cross-linking before us. Thermal [ 15] or photoinitiators [ 16, 17] were used in these studies to effect the cross-linking of the core block of the diblock micelles. These strategies worked well in the solid state in which the rate of domain fixation was much faster than that of micelle chain exchange [ 18]. In solution, insoluble products were sometimes obtained due to micelle fusion during core cross-linking [ 15]. PCEMA photocross-linked without additives such as an initiator. Using diblocks containing PCEMA, soluble star polymers [19, 20] and hairy nanospheres [11, 19] were always prepared.

3.1. Example Preparation Micelles were prepared by refluxing $813-C59 (Table I, i.e., a PS-b-PCEMA sample with 8.1 • 102 units of styrene and 59 units of CEMA) in cyclopentane (CP; 95%, Aldrich) for 2 days. The sample was then photolyzed with UV light from a 500-W mercury lamp that had passed through a 260-nm cutoff filter to achieve a CEMA conversion of 40%. The sample was then collected by precipitation into methanol. Illustrated in Figure 2 is a transmission electron microscope (TEM) image of the star polymer prepared from $813-C59. Because the sample was stained by OSO4, which selectively reacted with the residual aliphatic double bonds in PCEMA, the PCEMA region appears dark. Figure 2 clearly shows that PCEMA makes up the core and PS constitutes the relatively thick gray shell of the micelles, as expected. Also, the star polymer appears to have a relatively narrow size distribution, as confirmed by both GPC and dynamic light scattering results. Molar mass determination showed that this polymer had 115 arms. $813-C59 had a n/m value of 13.8. It should be possible to increase the n/m value to minimize the relative CEMA content in the cross-linked micelles. At even larger n/m values, the cross-linked micelles are essentially star polymers.

3.2. Robustness of This Method There are several traditional methods for star polymer preparation [21]. Our method is unique for its robustness in producing star polymers with a large number of arms. For example, with this method we prepared a star polymer with 2.0 x 103 arms and a molar mass of 9.0 • 108 g/mol [22]. Also, the PS and PCEMA blocks were found to phase-segregate well in the star polymers, and the star polymers prepared generally had narrow size distributions. Determination of the size and molar mass of PS-b-PCEMA micelles in cyclopentane before and after UV irradiation indicated that the photocross-linking locked in only the micellar structure and did not change the aggregation number of the micelles [20].

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Fig. 2. TEM image of cross-linked $813-C59 micelles. (Source: Reprinted with permission from [20]. 9 1997 American Chemical Society.)

3.3. Applications Star polymers are useful in industry as melt strength improvers. We carried out some fundamental studies of PS-b-PCEMA micelles by taking advantage of the "locking in" feature of the micelle photocross-linking process. Assuming the star (thick corona and small core) and crew-cut (large core and thin corona) micelle models, Halperin [23] and de Gennes [24] derived the scaling relationship for aggregation number, f , of diblock micelles formed in a block-selective solvent, f

~ m ~

(1)

where m is the number of repeat units in the insoluble block. For star micelles, a = 0.80. This value increases to 1 for crewcut micelles. Aggregation numbers, f , were reported as a function of m for several systems [25-32]. Except in one system [32], the m dependence of f did not follow Eq. (1) at all. The reason for the discrepancy between the theory and experimental results varied from system to system. In some cases, abrupt increases in f with m were observed, probably due to the formation of cylindrical or vesicular micelles instead of spherical micelles as m changed. Other systems probably never reached thermodynamic equilibrium. We examined the m dependence of f for micelles prepared from the first six PS-bPCEMA diblocks in Table I [20]. The diblocks were refluxed in cyclopentane for 2-3 days to ensure micellar structure equilibrium before they were photolyzed at 50 ~ to yield star polymers. TEM was used to confirm the spherical shape of the micelles. Taking advantage of the "permanent" nature of the star polymers, we separated unimers from the star polymers by GPC fractionation. The molar masses of the stars were determined in toluene at room temperature by light scattering. Plotted in Figure 3 is In f vs. ln m for the six star polymers. The slope obtained from linear regression was ct - 0.92 with a correlation coefficient of 0.975 [20]. Although the data quality as judged from the correlation coeffi-

480

POLYMERIC NANOSTRUCTURES

7.0 5.6 4.2 2.8 1.4 0.0

0

I

I

2

4

6

Inm Fig. 3. Plotof In f vs. Inm for six PS-b-PCEMAstar polymers. The plus sign represents the $267-C22 datum that overlaps with that of $267-C22.

cient is still poor, it represents a great improvement over the correlation coefficient of 0.86 obtained by Khougaz et al. [32] for another system. Also, the ot value is between those predicted by Halperin [23] and by de Gennes [24]. Thus, the scaling results appear correct. As to which model is more appropriate, a further study involving samples with a larger m range is being carried out. The advantages offered by micelle cross-linking in this study are twofold. First, the f value can be determined more accurately because of the separation of the star polymers from the unimers. Then, light scattering studies of the star polymers can be carried out at room temperature in toluene or any other good solvents for PS instead of at 50 ~ in cyclopentane in which the micelles were prepared. It was inconvenient to use cyclopentane for light scattering measurements because the purest commercial cyclopentane is only 95% pure. To determine the specific refractive index increment (required for molar mass evaluation) in a mixed solvent, one has to dialyze a polymer solution against the solvent. This is a tedious process.

4. HAIRY NANOSPHERES 4.1. Example Preparation We prepared hairy nanospheres from PS-b-PCEMA with short PS and long PCEMA blocks [ 19]. The preparation of nanospheres from PCEMA-b-PAA is described here because these nanospheres are water soluble and may be more useful. C460-A187 (PCEMAb-PAA with 4.6 x 102 units of CEMA, 187 units of acrylic acid, and a PAA weight fraction of 10%) was dissolved in dimethylformamide (DMF) [ 11 ]. Water was added dropwise until it reached a volume fraction of 80%. The mixture was then dialyzed against distilled water for 4 days to remove DME Permanent PCEMA nanospheres were obtained after UV irradiation of the crewcut micelles. A TEM photograph of some nanospheres prepared from this polymer is shown in Figure 4. The cross-linked micelles are spherical and have a narrow size distribution around a mean diameter of --~25 nm. These probably represent cross-linked spheres of this size with the narrowest size distribution, because microemulsion polymerization has been known not to work well in producing spheres with diameters smaller than 100 nm with narrow size distributions [2].

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Fig. 4. TEM image of C460-A187 nanospheres.

Although also stained with OsO4, the nanospheres do not show a distinctive PAA layer. This is in agreement with the hairy nanosphere picture in which the corona is thin relative to the core. More recently, C360-A560 was used to prepare nanospheres [33, 34]. Whereas the PAA block is relatively long in this diblock, which makes the polymer directly soluble in warm water, the use of DMF and the dialysis step were thus unnecessary.

4.2. Properties of the Nanospheres and Potential Applications PCEMA-b-PAA nanospheres possess hydrophobic PCEMA cores and a hydrophilic PAA corona. The core can uptake a lot of organic compound from water. The hydrodynamic radius, Rh, of 48 nm for the C460-A187 nanospheres in water, for example, increased to 62 nm in water/DMSO (dimethyl sulfoxide) with 2.5% DMSO by volume [12]. This represents a nanosphere volume increase of 116% due to DMSO uptake. The nanospheres can also uptake solid organic compounds from water [33, 34]. In one experiment, solid perylene was stirred with 4.00 mL of a C360-A560 nanosphere solution at 6.8 x 10 -2 mg/mL for 3 weeks. The excess solid perylene was then filtered out and the amount of perylene incorporated into the nanospheres was analyzed by monitoring the fluorescence intensity from the supernatant. Plotted in Figure 5 is the increase in the perylene fluorescence intensity as a function of the amount of solid perylene, mpE, added initially to the aqueous nanosphere solution. The fluorescence intensity initially increases steeply with mpE. The rate of perylene fluorescence intensity increase with mpE decreases at greater mpE values and the intensity value eventually levels off. The initial fluorescence intensity increase with mpE is expected because the amount of perylene solubilized into the nanosphere cores (perylene solubility in water is very low) increases with mpE. The leveling off of the fluorescence intensity at high mpE is reasonable as well. The nanospheres have only a certain capacity. Once saturated, they cannot uptake more perylene, regardless of how much perylene is added. The excess perylene in

482

POLYMERIC NANOSTRUCTURES

3.0 [ st

o| ,~

,//

1.0 0.0-

0.0

l

i

i

0.8

1.6

2.4

,3.2

mJiJg Fig. 5.

Increase in perylene fluorescence intensity as a function of the amount of perylene added, mPE,

to 4.00 mL of a C360-A560 nanosphere solution at a concentration of 6.8 x 10 - 2 mg/mL.

2.00 .4.,,,1

=

1.50

" ;>

1.00

---, (D

0.50 0.00 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 440 460 480 500

520

Wavelength/nm Fig. 6. Comparisonof the perylene fluorescence spectra of a 2.50-mL perylene-saturated C360-A560 nanosphere solution at a concentration of 6.8 x 10 - 2 mg/mL (m), after the addition of 80 #L of a 0.100-M CaC12 solution (---), and after the addition 120/~L of a 0.100-M EDTAsolution (. . . . ).

the form of microcrystals in the water was removed by filtration and did not contribute to further fluorescence intensity increase. At the intermediate stage, the fluorescence intensity increased more slowly with mpE, possibly for two reasons. First, the uptake of many perylene molecules by the same nanosphere may decrease perylene fluorescence quantum yield due to "concentration quenching" or excimer formation. Second, the partition coefficient K of the nanospheres may decrease at higher perylene loadings. Also illustrated in Figure 5 is our method for determining the capacity of the nanospheres. The maximal amount of perylene the nanospheres can uptake is determined to be 0.77/zg from the crossing point between the straight lines describing intensity vs. mr,E data at high and low perylene loadings. Because the total amount of nanospheres used was 0.272 mg, the capacity of the nanospheres is 2.83 mg/g. This trapping capacity is disappointingly low. The value was increased to ~-300 mg/g by stirring an aqueous nanosphere solution with perylene in the presence of some acetone. Acetone helped increase the trapping capacity, probably because acetone swelled the PCEMA core, which facilitated the penetration of the core by perylene, a molecule with five fused benzene rings. We then demonstrated that the perylene-loaded nanospheres could be precipitated out by the addition of CaC12 to the calcium concentration of ~2.0 x 10 -3 M (Fig. 6). Ca 2+

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caused the precipitation of the nanospheres, probably by the bonding of each Ca 2+ cation with two AA units from different nanospheres. The precipitated nanospheres were then extracted with an organic solvent such as THF to remove the perylene. Once perylene was removed, the nanospheres could be redispersed in water by adding sodium carbonate to precipitate Ca 2+ or by adding ethylenediamine tetraacetate (EDTA) to complex with Ca 2+ (Fig. 6). Based on these observations, we believe that the nanospheres should be useful in cleaning up tailings ponds left behind by the oil and gas industry. In such ponds, the relatively low molar mass hydrocarbons should function to plasticize the core of the nanospheres. The plasticized nanospheres should be able to uptake a large amount of high molar mass components such as asphalt. In addition, the nanospheres may be useful as drug carriers in controlled drug release. Other than the trapping capacity study, we also determined the coefficient of perylene partition between water and PCEMA-b-PAA nanosphere cores to be 3.3 • 105 by using a fluorescence method. This figure suggests that perylene is 3.3 • 105 times more likely to reside inside the nanosphere cores than in water at an equal nanosphere core and water volume. We also studied perylene uptake kinetics. In all cases, the perylene partition equilibrium was established within 2 days [33, 34].

5. TADPOLE MOLECULES So far, the photocross-linking of micelles to produce star polymers and nanospheres has been discussed. Coexisting with micelles are some unimers or unimolecular micelles. In a unimer, the insoluble block should cluster together like a globule and the soluble block should assume the normal random coil conformation, as first hypothesized by Sadron [35]. An indirect way to verify the unimer shape is to show that a diblock shrinks in size in a block-selective solvent. This verification has been difficult, because the critical micelle concentration of a diblock is normally too low to allow the use of scattering techniques to determine the unimer size in a block-selective solvent. This difficulty was circumvented by using PS-b-PCEMA. When photolyzed in a blockselective solvent, not only micelle but also unimer structures are locked in. An intramolecularly cross-linked unimer should have a globular PCEMA head and a PS tail, and structurally resembles a tadpole. The structurally stable tadpole molecules and cross-linked micelles then can be separated by fractionation precipitation or GPC. Light scattering studies of the tadpoles can be performed in any solvents in which the tadpoles are soluble.

5.1. Example Preparation $859-C268 was dissolved in THF [36]. Cyclopentane (CP) was added to a CP volume fraction of 60%. Such a solution was photolyzed to give a CEMA conversion of 26%. The tadpole molecules were then separated from the cross-linked micelles by GPC fractionation. Light scattering studies of the tadpoles in toluene gave a radius of gyration of 14.2 i 1.0 nm and a molar mass of (1.59 4- 0.22) x 105 g/mol; those for the diblock were 19.1 • 0.7 nm and (1.65 -+- 0.07) x 105 g/mol. Although the tadpole molecules have the same molar mass as the diblock within experimental error, the decrease in size suggests the tadpole shape of the intramolecularly cross-linked unimers and the retention of the tadpole shape in toluene.

5.2. Some Future Prospects This study represents the first preparation and isolation of diblock tadpole molecules. They may have unique diffusional properties. It remains to be seen how the properties of the

484

POLYMERIC NANOSTRUCTURES

cross-linked block of the tadpoles differ from those of the molecular globules prepared from intracross-linking linear homopolymers at high dilutions [37].

6. HOLLOW NANOSPHERES Other than spherical micelles, block copolymers also can form vesicular [ 14, 38, 39], cylindrical [20, 38-40], and donut-shaped micelles [39] in block-selective solvents. The exact morphology of the micelles formed depends on the n/m value of the diblock and the composition of the binary mixture used as the solvent [38, 39]. In general, diblocks with a short soluble and long insoluble block tend to form vesicles, cylinders, or donuts. Increasing the content of the block-selective solvent relative to the mutual solvent for both blocks may induce vesicle, cylinder, or donut formation in a binary solvent mixture. A block-selective solvent and mutual solvent for PS-b-PCEMA are, for example, CP and THF, respectively. Copolymer I88-C231 has a low PI weight fraction and formed vesicles in THF/hexanes (HX) with HX volume fractions greater than 50%. In such a vesicle, the insoluble PCEMA block makes up the essentially solvent-free shell. The soluble PI block stretches into the solution phase from both the inner and outer surfaces of the shell. Hairy hollow nanospheres were prepared by photocross-linking the PCEMA shell. Because isoprene was polymerized in hexane using sec-butyl lithium as the initiator, 93% of the isoprene units were incorporated into the polymer by 4,1-addition [14]. The double bonds in the backbone of PI were decomposed by ozonolysis to cause PI degradation. Semishaved hollow nanospheres were obtained by selectively cleaving off the outer PI chains. Fully-shaved nanospheres were obtained by removing all the PI chains.

6.1. Example Preparation of Hairy Hollow Nanospheres I88-C231 was dissolved in THF/HX with 35% HX by volume. The solution was then slowly added into an equal volume of THF/HX with 85% HX to induce vesicle formation. The vesicle solution in THF/HX with 60% HX was stirred for 1-2 weeks before an equal volume of HX was added to yield a vesicle solution at a concentration of ~ 1.0 mg/mL in THF/HX with 80% HX. The solution was irradiated immediately to obtain a PCEMA conversion of 40%. The vesicles initially were equilibrated in THF/HX with 60% HX, because the vesicles were found to have the narrowest size distribution at this solvent composition. More HX was added just before irradiation. This supposedly increased the rigidity of the PCEMA shell (due to the reduced PCEMA swelling by THF) and should have decreased intervesicle fusion during the cross-linking process. Illustrated in Figure 7 is a TEM image of the cross-linked I88-C231 vesicles or hairy nanospheres [41 ]. The light circle in the center of each particle corresponds to the location of the cavity. The dark ring separating the shell from the cavity represents the inner PI chains, which should have collapsed upon solvent evaporation. The outer PI layer is not evident here because it might be too thin.

6.2. Example Preparation of Semi- and Fully-Shaved Hollow Nanospheres Hairy hollow nanospheres of I88-C231 were dissolved in methylene chloride and chilled to - 4 0 ~ Ozone was bubbled through this solution for 89 or 10 min, depending on whether semi- or fully-shaved hollow nanospheres were prepared. The ozonides formed were then reduced with P(OCH3)3. Illustrated in Figure 8 is a TEM image of hairy hollow nanospheres treated with 03 for 89min. Compared to vesicles of Figure 7, the outer boundaries of the vesicles here are not as sharp, which suggests the degradation of the outer PI layer. The remnants of dark rings at the cavity and shell interfaces indicate the

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Fig. 7.

TEM image of cross-linked I88-C231 vesicles prepared in THF/hexanes with 80% hexanes.

Fig. 8.

TEM image of cross-linked I88-C231 vesicles treated with ozone for 0.5 min.

486

POLYMERIC NANOSTRUCTURES

Fig. 9. TEM image of cross-linked I88-C231 vesicles treated with ozonefor 10 min.

integrity of the inner PI layer. These conclusions were further substantiated by Fourier transform infrared (FTIR) spectroscopy and light scattering results. Our FTIR results indicated that approximately half of the PI double bonds disappeared after the ozonolysis treatment. A dynamic light scattering study witnessed an 11-nm decrease in the vesicle hydrodynamic radius in THF after the ozonolysis [41 ]. Illustrated in Figure 9 is a TEM image of some hairy nanospheres treated with ozone for 10 min. The dark ring between the shell and the cavity is absent for the vesicles in Figure 9. This clearly suggests the decomposition of the inner PI layer. This conclusion was confirmed by our FTIR result [41 ].

6.3. Potential Applications and Some Future Prospects Semi- and fully-shaved hollow nanospheres were stably dispersed in CH2C12 after their preparation. Once precipitated and dried, semishaved hollow nanospheres are barely soluble in any organic solvent. The solubility of fully-shaved hollow nanospheres decreases even further. Due to the cavity present in each nanosphere and the voids between different nanospheres in the solid state, these nanospheres may be useful as macroporous resins. Although selective PI chain degradation was used to demonstrate the superior control in nanoengineering in this study, different chemistry can, in principle, be performed on the inner and outer PI chains to create useful hollow nanospheres. The double bonds of the PI chains on the outer surfaces can, for example, be selectively converted to hydroxyl groups, while the inner PI chains are left intact. If successful, this will yield water-soluble nanospheres with cavities partially filled with PI chains. Whereas the cavities are large (~28 nm in diameter), these species may function as high-capacity absorbents for organic compounds from water. By tailor-making the diblocks, the vesicles also may be used in controlled drug delivery.

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6.4. R e l a t e d C h e m i s t r y

Due to the relatively long PI block, I346-C 179 formed spherical micelles in THF/HX with HX contents between ~60 and ~95%. Hairy nanospheres were prepared from this diblock by photocross-linking the PCEMA cores. After ozonolysis, the PI block was degraded to yield cross-linked PCEMA nanospheres with immediately attached carbonyl or ketone groups [42]. We have demonstrated that the carbonyl or ketone groups react with a range of reagents such as cyclopentadiene [42] and 2,5-bis(trifluoromethyl)aniline [43]. Although the carbonyl- or ketone-covered nanospheres were not soluble in any organic solvent tested, the nanospheres surface-modified by reaction with cyclopentadiene and 2,5-bis(trifluoromethyl)aniline dissolved in solvents such as hot DMSO. These shaved nanospheres are potentially useful as catalyst supports or as solid lubricants.

7. P O L Y M E R B R U S H E S

So far, the preparation of various nanostructures in solution has been discussed. Next, the preparation of diblock brushes or monolayers at the solution and solid interface will be reviewed. In a block-selective solvent, a diblock copolymer may also be deposited from the solvent and self-assemble to form a polymeric monolayer on a substrate being contacted. If the interaction between the insoluble block and the substrate is favorable, a dense monolayer called a polymer "brush" may form in which the insoluble block spreads on the solid substrate like a melt and the soluble block stretches into the solution phase like bristles of a brush as illustrated in Figure 10 [44--46]. Polymer brushes have been traditionally used to help disperse latex and pigment particles in paint [47]. Due to its industrial relevance, there have been many studies of polymer brushes in the past decade [44--46]. In most previous studies, dilute block copolymer solutions ( 0. According to this diagram, PS-b-PI in the weakly phase-segregated regime (20 < NX < 30) is in a disordered state at low PI volume fractions, fpI, or the PI and PS chains are miscible. The PI domains (white regions) may subsequently assume the spherical (S), cylindrical (C), gyroidal (G), and lamellar shape as fPI gradually increases to ~50%. For higher molar mass samples (N larger) or at lower temperatures (X larger), the gyroidal morphology of the sample may be replaced by a perforated layer morphology. To prepare PS-b-PCEMA

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nanofibers, the PS-b-PCEMA sample we used had a PCEMA weight fraction of 24%, and PCEMA existed as cylinders dispersed in the PS matrix. Photolysis of such a solid sample cross-linked the PCEMA cylinders. Separating different cylindrical domains by dissolving the PS chains yielded nanofibers.

8.1. Example Preparation Solvent evaporated from a 5-mL $750-C107 solution in toluene, at ~ 10% by volume, in a polyethylene bottle over a 3-4-day period. The resultant $750-C107 film was dried and annealed under 30-cm Hg pressure at 65 + 5 ~ for 3 days and 105 ~ for 2-3 weeks. The film was then irradiated with light from a 500-W mercury lamp that had passed through a 310-nm cutoff filter to obtain a CEMA conversion of ,-~30%. Dissolution of the resultant film in THF yielded nanofibers as illustrated in the TEM image shown in Figure 14. The nanofibers have a diameter of ~ 5 0 nm and length of ~ 2 0 #m. The expected PCEMA core and PS shell structure is seen in Figure 15. The formation of PCEMA cylinders in bulk $750-C107 is evident from Figure 16. This picture was taken of a microtomed and OsO4-stained specimen before UV irradiation. The dark circles represent PCEMA cylinders pointing out of the picture. The cylinders are packed with the expected hexagonal symmetry. Other than locking in the cylindrical domains of a bulk sample to produce nanofibers, we observed cylindrical micelle formation from $750-C107 in cyclopentane [20]. The photocross-linking of the PCEMA cores led to the preparation of nanofibers in solution. Fibers prepared this way were, however, not as long as those derived by cross-linking a solid sample. Also, spherical micelles were found to coexist with the cylindrical micelles.

Fig. 14. TEM image of $750-C107 nanofibers. The TEM sample was prepared by transferring a thin film, formed after dispensing a drop of a THF nanofiber solution on a water surface, onto a copper grid. (Source: Reprinted with permission from [73]. 9 1996American Chemical Society.)

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POLYMERIC NANOSTRUCTURES

Fig. 15. Core-shell structure of $750-C107 nanofibers. The TEM sample was prepared by freeze-drying a benzene solution of nanofibers on a copper grid. (Source: Reprinted with permission from [73]. 9 1996 American Chemical Society.)

Fig. 16. Ordered domain structure of $750-C107 in bulk. The dark regions represent PCEMA cylinders pointing out of the picture.

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8.2. Potential Applications Since microdomain formation occurs in most block copolymers, it represents a general method for preparing uniform nanofibers from polymers with various diameters. We expect this method to be useful in producing precursor fibers that can be pyrolyzed to yield carbon or metal carbide nanofibers. Alternatively, this method can be modified to make nanowires by replacing the core block with a conductive polymer. In such a case, the outer block will function as an insulating plastic layer. The $750-C107 nanofibers were found to be soluble in bromoform at all mixing ratios. Illustrated in Figure 17 is a polarized optical microscopic image of a trace left in a 42.5%, by weight, $750-C107 nanofiber solution in bromoform, after a spatula stroke through the solution [77]. The birefringence suggests alignment of the fibers along the scratching direction. As the relative position between the polarizers and the sample stage changed, the bright regions in the image turned dark and vice versa, as expected. Although such nanofibers, particularly water-soluble nanofibers, may be useful as "environmentally friendly" liquid crystals, their sluggish response to changes in electric fields may ultimately limit their application in liquid crystal display applications. This remains to be established with a more detailed study. The liquid crystalline properties of the nanofibers would certainly facilitate the preparation of macroscopic ropes consisting of well aligned nanofibers or nanofilaments.

Fig. 17. Opticalmicroscopic imagesof a trace left after a spatula stroke across a 42.5% by weight $750C107 nanofiber solution in bromoform.The top picture was taken at a position with the shearing direction parallel to the analyzing polarizer axis. The bottom picture was taken after the sample stage was rotated by 45~ The width of each frame is about 5 mm.

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POLYMERIC NANOSTRUCTURES

9. NANOCHANNELS IN THIN FILMS Individual nanotubes have been prepared from carbon [68, 78], peptides [79], and silica gel [80]. When the tubes are dispersed in a matrix, they are referred to as nanochannels. Nanochannels with a narrow size distribution but no regular packing were prepared in polymer films by the track-etch method [81-83]. More recently, methods have been developed for the formation of hexagonally packed nanochannels with narrow size distributions in metals [84, 85], glasses [86], zeolite particles [5], zeolite films [87], and even in a diblock solid [88]. No evaluation of thin films containing hexagonally packed nanochannels as membranes has been reported, however. In this section, a brief review of nanochannel preparation from one diblock copolymer and the performance of the thin film prepared as membranes [ 13, 89] will be given.

9.1. Example Membrane Preparation The general procedure for membrane preparation from a diblock copolymer involves (1) synthesis of a diblock copolymer (A)n(B)m with the A block degradable and the B block cross-linkable; (2) preparation of (A)n(B)m solid with A forming the regularly packed cylinders dispersed in the continuous B matrix; (3) obtaining thin films of the diblock from microtomy; (4) cross-linking the continuous B phase; (5) full or partial degradation of the A cylinders [ 13]. We first prepared thin films with nanochannels from t380-C640 (PtBA-b-PCEMA with 3.8 x 102 units of tBA and 6.4 x 102 units of CEMA). At n/m = 0.59, PtBA formed cylinders dispersed in the PCEMA matrix. Slices with thickness between 0.050 and 2 tzm were obtained by ultramicrotomy and irradiated with UV light that had passed through a 310-nm cutoff filter to obtain a PCEMA conversion of ~38%. The films were then supported on gold TEM grids and soaked in a 0.050-M (CH3)3SiI solution in CH2C12 for 2 weeks to perform the following reaction in the PtBA cylinders:

(CH3)3Sil

,,~ --~H2--CH l-L-n

+ (0H3)30-1

CO0-Si(CH3) 3

C O O - C(CH3)3

The trimethylsilyl groups were subsequently cleaved by hydrolysis in a water/methanol (v/v = 5/95) mixture. Upon drying, the poly(acrylic acid) chains should collapse to the PCEMA walls to yield thin films that contain nanochannels partially filled with PAA chains. Illustrated in Figure 18 is a TEM image of a small area of a 50-nm-thick film, where the light circles represent channels normal to the picture. Because the contrast between the light cylindrical domains and the dark PCEMA phase was obtained without chemical staining, the lighter regions should have lower polymer mass densities, as expected, due to the removal of the t-butyl groups [13]. The hexagonally packed channels in this case have a diameter of ~ 17 nm and a density of ~5 • 1ol~ 2.

9.2. Chemical Valving Effect To test water permeation, a 2-#m-thick PS-b-PAA film was sandwiched between two polyethylene films (~30 # m thick) with paraffin linings (,-~10 # m thick), where both the polyethylene films and paraffin linings had a 1-mm hole in the center. The softer paraffin linings were used to obtain a seal between the polyethylene films and the membrane. After the membrane was sandwiched, the composite film was lightly pressed between two glass plates and mounted between two arms of a U-tube with a ground interface and a circular opening of ~ 1.5 mm. The two sides were held together by a clamp [89].

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Fig. 18. TEM image of a small area of a 50-nm thick t380-C640 film. The PCEMA region of the film has been cross-linked and the t-butyl groups of the PtBA cylinders have been removed. (Source: Reprinted with permission from [ 17]. 9 1997 American Chemical Society.)

6

3

0

2

4

6

8

10

t/hour Fig. 19. Variation in the water height difference h between the two arms of a U-tube as a function of time t. The water transport rate was slowest at pH 3.0 (0), but increased at pH 1.0 (o) and pH 13.0 (11).

Water flowed f r o m one a r m of a U - t u b e to the other due to a height difference of h b e t w e e n the two arms. Illustrated in F i g u r e 19 is the variation in h with time t for a q u e o u s solutions at three different pHs. T h e data were fitted with the equation h = h0 e x p ( - t / r )

(2)

w h e r e h0 is the initial height difference and 1 / z is proportional to the m e m b r a n e p e r m e a b i lity constant P [90]. Plotted in Figure 20 is the variation in z with pH (adjusted by adding

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POLYMERIC NANOSTRUCTURES

1000

0

0

100

0

c3

0

10 0 0 1

0

0 I

I

I

I

I

I

2

4

6

8

10

12

14

0H Fig. 20. Variationin r as a function of pH.

different amounts of hydrochloric acid) for a membrane. The enormous variation in r with pH demonstrates the tremendous potential of the nanochannels as "chemical valves" [89]. Water transportation rate is the lowest at pH -~ 3, because the PAA chains take up little water and form a gel inside a nanochannel at this pH due to hydrogen bonding between different AA units [90]. As pH is decreased, the hydrogen bonds are broken by protons, which increases P. The P value increased at high pHs, because the AA groups are converted into sodium acrylate, which does not form hydrogen bonds easily. Also, ionized carboxyl groups take up more water molecules for solvation. We also examined the effect of ionic strength on ~.. At pH 6.0, the r values were 29 and 10 h, respectively, in water and in an aqueous 0.100-M NaC1 solution. The effect of the divalent cation was demonstrated with the use of a 1.0-M CaC12 solution. When such a solution was used, the water height difference between the two sides of a U-tube remained at 7.6 cm after 28 h. This suggests the complete blockage of these nanochannels to water transportation. This closure was probably caused by Ca2+-induced network formation from PAA because each Ca 2+ ion may bind to two AA units of different PAA chains.

9.3. Potential Applications The methodology used for PCEMA-b-PAA membrane preparation is general and can be used to prepare membranes from other diblocks. Like traditional membranes, membranes produced this way should have a wide range of applications. The potential advantage of membranes produced from this method may lie in their improved selectivity toward different permeates due to uniform pore size. These membranes also should work well as templates for further metal or semiconductor nanostructure fabrication. The particular PCEMA-b-PAA films prepared should be useful in sensing devices and controlled drug delivery, because the PAA channels close and open depending on their chemical environments. Also, the membranes should be useful in studying polymer chain reptation across nanochannels.

10. CONCLUDING REMARKS The range of nanostructures we prepared is diversified. The underlying principle is, however, straightforward and involves (a) diblock self-assembly, (b) locking in the mesophasic structure by cross-linking one block, and possibly (c) the degradation of the other block.

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T h e b l o c k c o p o l y m e r n a n o s t r u c t u r e s p r e p a r e d m a y have applications not only in the general area of n a n o s i z e d electronic device m a n u f a c t u r i n g , but also in fields such as catalysts, c o n t r o l l e d drug delivery, water r e c l a m a t i o n , separation science, n a n o c o m p o s i t e preparation, etc. A l t h o u g h our w o r k so far has b e e n restricted to the use of diblock c o p o l y m e r s , the use of triblock c o p o l y m e r s in the future will further e x p a n d the repertoire of functional p o l y m e r i c nanostructures.

Acknowledgment M a n y p o s t d o c t o r a l fellows and students contributed to the w o r k r e v i e w e d herein. T h e i r contributions have b e e n a c k n o w l e d g e d by citing their publications. T h e Natural Sciences and E n g i n e e r i n g R e s e a r c h C o u n c i l of C a n a d a is t h a n k e d for research grants, e q u i p m e n t grants, and an industrial oriented research grant to G. L i u as well as a strategic grant to V. I. Birss and G. Liu. T h e g e n e r o u s support p r o v i d e d by the E n v i r o n m e n t a l Sciences and T e c h n o l o g y A l l i a n c e of C a n a d a and V X Optronics to G. Liu is also gratefully acknowledged.

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Chapter 10 CONDUCTIVE POLYMERS AS ORGANIC NANOMETALS Bemhard Wessling Ormecon Chemie GmbH and Co., D-22949 Ammersbek, Germany

Contents 1. OrganicMetals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1. Metallic Character and Nanostructure of Conductive Polymers . . . . . . . . . . . . . . . . . . . 1.2. Nanotechnology with Nanometals? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2. ConductivePolymer/Solvent Systems: Solutions or Dispersions? . . . . . . . . . . . . . . . . . . . . . 2.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2. ThermodynamicConsiderations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3. SurfaceTension of Polyaniline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4. Discussingthe "Solution Hypothesis" Again . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5. What Experimental Evidence Do We Have for the "Dispersion Hypothesis"? . . . . . . . . . . . 2.6. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3. Applications of Organic Metals Emerging from Basic Science: Macro-Effects of Nanoparticles . . . . 3.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2. PAniDispersion and Blend Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3. FinalRemarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

501 502 524 525 526 530 538 542 546 553 554 554 558 572 572

1. O R G A N I C M E T A L S The broad potentials and both scientific and technological possibilities with organic metals are widely unknown. A recent interesting publication in Nature shows how scientists are oriented toward nanotechnology with conventional metals, even if the approach is more complicated. In their research work, Erez Braun et al. [1] placed a D N A double strand between the two electrodes to be contacted and then deposited about 3 0 - 5 0 - n m silver particles by reduction of a Ag + solution on the D N A (Fig. 1). W h e n producing only 1 0 - 2 0 - n m particles, they did not make successful electrical contact. In contrast, the existence of organic metals and their character as true metals, though "nanometals," is widely unknown, so that people do not consider their use as shown above. "Conductive polymers," in contrast, is a well-known term [2]. Polyacetylene, polyaniline (PAni), polypyrrole, polythiophene, and many others have been synthesized and studied, but under the heading "conductive polymers" the possibilities of studying nanoscale phen o m e n a are not broadly considered, as those groups in the scientific c o m m u n i t y focusing on their polymeric character are trying to treat them primarily like other polymers (though

Handbook of Nanostructured Materials and Nanotechnology, edited by H.S. Nalwa Volume 5: Organics, Polymers, and Biological Materials Copyright 9 2000 by Academic Press ISBN 0-12-513765-6/$30.00 All rights of reproduction in any form reserved.

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Fig. 1. Preparationof a nanosized silver wire, using DNA as a reaction template. (Source: Reprinted with permission from [1]. 9 1998 Macmillan Magazines Limited.)

conductive) and relate their properties to the individual chains (Fig. 2), instead of looking at them primarily as metals, organic metals, or synthetic nanometals. The difference in the understanding is centered around the question of whether the primary structural and functional unit for "conductive polymers" is the single (eventually oriented) chain and the main transport mechanism is the transport of polarons, or the primary unit of the "organic metal" is a nanoparticle of ~ 10 nm and the transport mechanism is metallic plus tunneling (from particle to particle). Here again, it is very interesting to see, that even in reviews under the heading of "Metal Clusters and Colloids," [3] organic metals and their colloidal and nanostructural properties are not mentioned. We will therefore discuss the metallic character and the nanoparticle structure and dynamics, the precondition for these properties and for eventual nanotechnology, the principal insolubility of organic metals (or: conductive polymers), and some actual technical applications ultimately based on their nanocharacter and on dispersion and the macrotechnology, with dramatic effects in the nanoscale.

1.1. Metallic Character and Nanostructure of Conductive Polymers The deciding hint for explaining the basic electron transport mechanism in conductive polymers came from basic studies with nanoparticles of conventional metals like indium, silver, or copper. Nimtz and his group [4] found in 1989 that metallic particles, if pre-

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CONDUCTIVE POLYMERS AS ORGANIC NANOMETALS

Fig. 1. (Continued.)

pared on the nanoscale below 1/zm down to 10 nm, show some distinct deviations from macroscopic metals (Fig. 3). For the first time, Nimtz succeeded to prove experimentally that the conductivity of regular metals, if they are present as "mesoscopic metals" (i.e., in a size between macro- and microscopic; hence "nanometals"), differs basically from that of macroscopic metals. Not only does the absolute conductivity decrease exponentially with decreasing particle size; the conductivity dependence on temperature is no longer purely metallic, but decreases with decreasing temperature. Normally the metallic conduction band is extended over macroscopic distances and allows electrons (the electron gas) to move freely, only interacting with phonons (lattice vibrations). With decreasing temperature, the vibrations lose intensity, and hence the electrons can move even better, which is the basis for the increasing conductivity of metals with decreasing temperature. In nanometals, however, the conduction band has a size in the same range as the electron wavelengths. Therefore, only certain wavelengths are allowed, that is, those that have a node plane at the boundaries of the three-dimensional conduction band. Therefore, the conductivity is

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Fig. 2. (a) Present understanding of conductivity between metallic "islands" (or metallic fibrils, connected by amorphous individual chain(s). (Source: Reprinted from [27], with permission from Elsevier Science.) (b) Comparison of two different interpretations of polyacetylene fibrils: flat platelets spherical globules. (Source: Reprinted from [6], with permission from Hiathig and Wepf Publishers, Zug, Switzerland.)

10 8

bulk 10

6 ~--~~dass,cal d3

-

quantum

G

(Qm) -I

10 z /

~0 o

~

/ /

/

10 "1 10-a

Indium ( T : 30OK) i

10-7

10.6

10 -s

d{m)

Fig. 3. Principal behavior of size-dependent conductivity according to classical or quantum theoretical interpretation, compared with experiment. (Source: Reprinted from [5], with permission from Elsevier Science.)

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CONDUCTIVE POLYMERS AS ORGANIC NANOMETALS

limitedJmore correctly, it is "quantum size limited." We observe the quantum effects of conductivity. These results motivated us to work together with the Cologne group and to find out if there are similarities between mesoscopic metals and organic metals [5].

1.1.1. Nanoparticulate Morphology and Dispersion The background of this idea was our finding in previous work that conductive polymers are composed of more or less globular primary particles (Fig. 4). We first found [6] that polyacetylene, even though apparently in a fibrillar morphology (as concluded from transmission electron microscopy), clearly showed a particle substructure with a particle size of 100 nm (Fig. 5). Yet at this early time, we saw some fine structure below 100 nm, but we had not yet been able to conclude that the particle size was even finer. But even at a 100-nm size, one would have to consider conductive polymers as being made up of nanoparticles. We will see below that these (secondary) particles play an important role in the dispersion process in polymeric media. We drew a model (Fig. 2a) according to which the fibrillar morphology, which was seen by many researchers, is due to an oriented arrangement of these particles in a chainlike structure. We found later [7] by membrane filtration that the basic primary particle in all conductive polymers is --~10 nm in size. Subsequently, in ever deeper studies, using various techniques like scanning tunneling microscopy (STM) [8] and photon correlation spectroscopy [9], and routinely via laser Doppler measurements [ 10] (Fig. 6), we confirmed a primary particle size of "~ 10 nm. Independent of our research, STM studies [ 11 ] on the morphology of oriented polyacetylene with very high conductivity (so-called N-PAc [ 12]) revealed particular subunits in the "fibrillar" structure, very densely aggregated and with maximum contact area between them (Fig. 7). Their form deviated somewhat from a globular shape, resembling more a square with round edges and side planes. With the first insight into the particulate morphological substructure, our very early idea of processing conductive polymers via dispersion was supported for the first time. We decided to polymerize powders, preferably with very well-displayed globular morphology, and we were successful in our first dispersion (Fig. 8). At that time, it was rather unclear how and at which concentration a dispersed conductive polymer would conduct when dispersed in a (polymeric) matrix. With our first patent application [13], we had published that doped PAc, after dispersion, caused a conductivity breakthrough for the whole system at a critical volume concentration around 10%. Based on the picture of fibrillar morphology in which chains oriented in the fibril direction are the structural basis for solitonic or polaronic electron transport mechanism, such a result would only be understandable if the fibrils were arranged in the matrix in a stretched, unoriented, nonparallel form, which was definitely not the case. In contrast, instead of fibrils, below the critical volume concentration we found particles isolated from each other, in a size and a form that are detected as the (secondary) morphological units of the raw powder (see Fig. 8). But this does not explain how a conductivity would arise at a certain critical concentration or why this happens (with a drastic jump of many orders of magnitude) at a certain concentration (and not gradually). Carbon black or metal powder containing polymer compounds show a similar behavior when dispersed in a matrix above certain different critical concentrations, and to explain this, percolation theory is thought to be the best tool [ 14]. It is believed that metal powder, having a globular particle shape, is distributed in a statistically even manner and will make contacts, governed by statistical laws (probability) whenever enough particles are present and close enough to finally form the first continuous conductive pathways. The critical volume concentration of metal powders is within the range of what is predicted by the percolation theory (45-64 vol%). For carbon black, however, the theory

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Fig. 4. Scanning electron microscopic evidence for globular or spherical subunits in fibrils detected by TEM. Reprinted from B. Wessling, Makromol. Chem. 185, 1265 (1984) with permission. 9 1984 Htithig and Wepf, Zug, Switzerland.

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CONDUCTIVE POLYMERS AS ORGANIC NANOMETALS

Fig. 4. (Continued.)

Fig. 5. TEM of flocculated polyaniline in polymer matrix, showing further fine structure in the about 100 nm big secondary particles. Reprinted from B. Wessling, in "Handbook of Organic Conductive Molecules and Polymers" (H. S. Nalwa, ed.), Vol. 3, pp. 497-632 with permission. 9 1997 John Wiley and Sons.

cannot explain the rather low critical concentrations, between 25 and 10 vol%. Percolation theorists assume that carbon black particles are highly structured, with a high length-todiameter ratio of their "arms," and therefore have a bigger chance of contacting each other.

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Fig. 6. LaserDoppler measurement of primary particles of organic solvent dispersion.

Fig. 7. Primaryparticles in stretch aligned, highly conducting polyacetylene. (Source: Reprinted with permission from [11]. 9 1989 Springer-Verlag.)

This, again, is based on correct oberservations according to which carbon fibers (with a l:d ratio of 10 or higher), if distributed in a nonoriented way and if no shear during flow orients the particles, show rather low breakthrough concentration values down to 1% (e.g., in thermosetting resins). It was also correctly observed that carbon black as a raw powder may occur in a highly structured form. However, it was never shown that the carbon black particles, highly structured in raw form, were also structured the same way in the matrix after the dispersion process. Figure 9 shows carbon black structured particles, but the samples were prepared by dissolving the polymer matrix and evaporating the solvents depositing these structured particles; the authors did not mention that the structures found may (and certainly will) have formed only because of the preparation method. We evaluated the morphology in the compounds in great detail, as we could not imagine how the complex and brittle structure of a carbon black particle could be retained during processing in mostly very viscous matrices.

508

CONDUCTIVE POLYMERS AS ORGANIC NANOMETALS

Fig. 8. Secondaryparticles of polyacetylene (a) the powderas synthesized, before being dispersed in a polymermatrix at 0.1% (b). Reprinted from B. Wesslingand H. Volk,Synth. Met. 15, 183 (1986) with permission. 9 1986Elsevier Science.

And indeed, we did not find any structures of the carbon black in the matrix after dispersion below the critical volume concentration, but we did find very clearly expressed globular particles of the same size as we had found with PAc [15]. Moreover, the carbon black grade used in this study (Ketjenblack EC and Printex XE-2) was not structured in raw powder form, although this was claimed by the suppliers. At and above the critical concentration (in the case described in the figures at 7% in polystyrene), a sudden change in the arrangement of the particles occurs: the previously well-dispersed and well-separated particles form complex networks. We found that dispersion led to a rather complex arrangement of phases, adsorbed layers, and finally even more complex flocculation structures in the form of networks. Within the networks (Fig. 10), the particles can touch and at least contact the nearest neighbors. The threedimensional connectivity of the two-dimensional networks is provided by further complex three-dimensional arrangements and structures of the dispersion and flocculation layers.

509

WESSLING

Fig. 9. Structure of primary particles and assumed superstructures in polymer matrix of conductive carbon black. Reprinted from A. I. Medalia, in "Carbon Black-Polymer Composites" (E. K. Sichel, ed.), pp. 1-49 with permission. 9 1982 Marcel Dekker.

510

CONDUCTIVE POLYMERS AS ORGANIC NANOMETALS

Fig. 10. SEM studies on dispersed and flocculated conductive phases and mechanical interpretation model for the flocculation process. Part a is reprinted from B. Wessling, Polym. Eng. Sci. 31(16), 1200 (1991) with permission. 9 1991 Polymer Science and Engineering. Part b is reprinted from B. Wessling, Synth. Met. 45, 119 (1991) with permission. 9 1991 Elsevier Science.

Dispersion, although it is a process pushed by macroscopic tools and processes, results in very fine and precisely expressed nanostructures: in polymeric matrix, a m o n o m o l e c u l a r layer of ~ 15 n m thickness is forced to adsorb on the particles, becoming dispersed down to a particle size of 5 0 - 2 5 0 nm (depending on matrix nature, process efficiency, etc.). These

511

WESSLING

Fig. 10. (Continued.)

particles (with their adsorbed layer) phase separate to monolayers (with a thickness of 80-280 nm), wherein flocculation and network formation occur at and above the critical volume concentration, with branching roughly every 10 nanoparticles, building a network size comprising --~30-50 particles (in one network element).

512

CONDUCTIVE POLYMERS AS ORGANIC NANOMETALS

Fig. 10. (Continued.)

Such structures, although chaotic and based on nonequilibrium thermodynamics [ 16], are nonetheless reproducibly formed. "Reproducibly" meaning that the properties in nanoscale leading to properties in macroscale can be reproducibly achieved, although the responsible nanostructures differ widely and are never "identical." Their formation is purely a process of "self-organization" [ 17]. And although the resulting exact structures are never the same, it is the inherent nature of the self-organization process on the nanoscale that allows stability and reproducibility. In an analogous way, dispersion in nonpolymeric media (solvents) can be understood. The first difference is that we can now disperse down to the primary particle size, ~ 10 nm (cf. particle size analysis with laser Doppler, Fig. 6). Furthermore, an adsorbed layer (however, now composed of solvent molecules) on the surface of the particles being dispersed is caused to form. Interestingly, at very low concentrations such dispersions suddenly gel, probably because the dispersed particles arrange into very fine chains and filaments, or even more complex three-dimensional branched tubes (Fig. 1 l c), which is the reason for the photon correlation peak around 250 nm (Fig. lib). Again, this is a self-organization process of nanoparticles under nonequilibrium conditions.

1.1.2. Metallic Properties and Conduction Mechanism of the Organic Nanometal Now that we know about the particulate morphology and the complex dynamics under which the particles become dispersed and self-organize to continuous complex networks and filaments, it remains to discuss how conductivity is achieved in a dispersion (above the critical concentration) (Fig. 12). We will start with the observations. At the critical concentration conductivity jumps over several orders of magnitude, and the flocculated network structures can be observed under the electron microscope. Many theories have been developed (involving solitons, excitons, polarons, bipolarons) [ 18] to explain the conductivity phenomenon under the assumption that the chains of conductive polymers are arranged and at least somewhat oriented in fibrils. But now it

513

WESSLING

Fig. 11. Photon correlation spectroscopy of primary particle dispersions of neutral and doped polyaniline; cf. Fig. 6, where laser Doppler only shows the true particle diameter, whereby photon correlation spectroscopy also shows superstructures (b). Reprinted from B. Wessling, Adv. Mater. 5(4), 300 (1993) with permission. 9 1993 Wiley-VCH Verlag GmbH.

514

CONDUCTIVE POLYMERS AS ORGANIC NANOMETALS

E 1E+2 / ..9. ~ _~ PAni PMMA ~ >, ~ #900210 (1995) ~ . ~ .~ 1E+0 _.~f~ O 1 .~"f'f~"-/~ "O 9 A o 1E-2

--" 9

09

,-

. "

.

.~

PAni #172 i i988) .~.~--'--'~'PAn, (1986)

1E-4 1E-6 1E-8 1E-10 1E-12 10

20

30

40 50 concentration Vol.%

Fig. 12. Criticalconcentration for various generations of organic metal dispersibility between 1986 and 1995. Reprinted fromB. Wessling,in "Handbookof Organic ConductiveMolecules and Polymers"(H. S. Nalwa, ed.), Vol. 3, pp. 497-632 with permission. 9 1997John Wiley and Sons.

must be explained why our dispersed (and later flocculated) polymers showed mainly the same transport properties as the "fibrillar" conductive polymers, as can be concluded from conductivity versus temperature and thermopower measurements. The thermopower measurements themselves (to be compared with those of other conductive materials) show that dispersed conductive polymers have essentially the same thermopower behavior as metals: it is small (semiconductors show a high S) and decreases practically linearly with decreasing temperature [19]. These properties were known to us from our own previous measurements [20], which showed the linear temperature dependence for a range of ~ 100 K, not enough for thermopower experts, but enough for us to assume that the primary transport mechanism is metallic but obviously influenced by a barrier mechanism, which to be overcome a temperature-activated transport process had to be active as well. Our cooperation with Guenther Nimtz of Cologne University showed very quickly [5] that the conductive polymer (in the first experiments deposited from dispersions onto PC films) behaves principally in the same way as Nimtz's mesoscopic metals, which he had purposely prepared by vapor deposition in oil to form a colloidal dispersion of finest metal droplets in oil. But whereas conventional metals are hard to prepare in a small particle size, and their quantum size effect is hard to observe, the conductive polymers only occur (at least according to our results and conclusions) in nanoparticulate morphology. (This is due to their extremely high surface tension, to be discussed in Section 2.) So we should see their quantum size-limited conductivity rather easily, and this is indeed the case. Rolf Pelster in Nimtz's group studied the quantum effects in close cooperation with us in various dispersions and in the raw poly(phenyleneamine) [21 ]. We found that the primary metallic unit is "-,8 nm in size, surrounded by a nonmetallic (amorphous) layer of the same composition but with a less optimal structure (so that a particle size of 9.6 nm was determined, very close to the 10-nm value we had found before by other techniques). This and the dielectric between the contacting particles are the

515

WESSLING

Fig. 13. Modelof electron wave density distribution, barrier heights, and crystalline core in the primary particles, and visualization of the limitation of electron wave length in the nanometallic primary particles to such values that have a node plane at the particle walls. Reprinted from B. Wessling, in "Handbook of Organic Conductive Molecules and Polymers" (H. S. Nalwa, ed.), Vol. 3, pp. 497-632 with permission. 9 1997 John Wiley and Sons.

barriers through which the electron wave (thermally activated) will eventually tunnel to reach neighbor particles (Fig. 13). These results forced us to conclude that the conductive polymers are in fact "organic metals" or they are "nanometals," and two different transport mechanisms contribute to the conduction mechanism: (a) a purely metallic part within each particle and (b) a thermally activated part from one particle to another (Fig. 13b). This explained why there was no principal difference between the raw poly(phenyleneamine) (doped) and its dispersions, in whatever medium. The differences to be observed were only gradual or quantitative, not of any qualitative nature, at least not in the direction that was expected by most of those who still favor the "fibril" hypothesis. They believe that the chain is the primary active unit, which could also be dissolved and is believed to have conductive properties, even as a single chain. If that were the case, a dispersed (i.e., mechanically separated, and in the case of assumed fibrillar morphology, even destroyed) conductive polymer would not have the same conductivity in the dispersion medium above the critical volume concentration.

516

CONDUCTIVE POLYMERS AS ORGANIC NANOMETALS

1.2

PAniblends 1a

60%

0.8100% PAni 03

~"

#-

0.6

60% PETG

0.4

O.2] o

,oo

'

2o0

300

'

T (K)

(a) 10

67% PMMA ." 60*/,

8 -

9999 ooOe~ pe:, ,@.~

ee ~

.~o~

6 -

T >

4;

o e~

9

PETG blends

ee

.-~

4 -

~

co

2

t_

=

===awl= o

,..

9 ....

o o o =o=

PAni

II o Oil

-

0 O0 0 9 9

=%%.=,,J

"2

I

0

I

'

!

100

' I

200

!

"

300

T (K)

(b) Fig. 14. Transformationof a pure premetallic organic metal (100% PAni) to a truly metallic polyaniline in blends after dispersions. Reprinted from C. K. Subramaniam, A. B. Kaiser, P. W. Gilberd, C.-J. Liu, and B. Wessling, Solid State Commun. 97(3), 235 (1996) with permission. 9 1996 Elsevier Science.

Such results (i.e., lower conductivity in blends and at maximum concentrations, compared to the pure conductive polymer) can often be found in the literature [22]. Our results showed the contrary (Fig. 14): the lowest conductivity at room temperature we get at concentrations between 25% and 40% (i.e., --~18-30 vol% only) was in the range of the conductivity of the undispersed raw material: 5-10 S/cm [23]. In the best dispersions at 40%, we find around 50-100 S/cm, 10 times more than the undispersed pure raw material. At any temperature lower than ambient, the blends were several orders of magnitude more conductive than the pressed powder. This shows that the metallic contribution to the conductivity is the same in the raw undispersed organic metal; the temperature activated tunneling process, however, is easier in the dispersion---or, better, after dispersion!

517

WESSLING

C) @ @ I

J

,

,

i

.+

I

@ Fig. 15. Model for the anisotropic location of the counterions in the metallic core. Reprinted from B. Wessling, in "Handbook of Organic Conductive Molecules and Polymers" (H. S. Nalwa, ed.), Vol. 3, pp. 497632 with permission. (~) 1997 John Wiley and Sons.

In contrast to the expectations of most scientists, dispersion does not lead to a deterioration of the conductivity properties (by, e.g., new barriers from the dispersion matrix), but to an improvement! This implies that during the dispersion process, barriers must have been reduced, and possibly the arrangement of the particles in relation to each other (in the flocculated network) is optimized with regard to the tunneling process. So it was only a relative surprise when we found a ~ 10 times higher conductivity (between 20 and 100 S/cm) at 40% organic metal content in a thermoplastic polyacrylic dispersion. Furthermore, for the first 70 K temperature decrease, conductivity increased, as is the case for conventional metals (Fig. 14) [24]. A new effect had been discovered: the raw organic metal powder, undispersed and pressed to a pellet, has the normal conductivity of 5 S/cm and a nonmetallic temperature dependence of conductivity (but a metallic thermopower). When dispersed (and even at lower concentrations, such as 30 vol%), it has an absolutely higher conductivity at ambient temperature, a partially metallic conductivity/temperature dependence and the conductivity at 10 K only decreased to ~ 5 - 1 0 S/cm, where the starting raw material has a conductivity of "~ 10 -1~ S/cm (cf. Fig. 14a) [24]. Further proof (in the worst case) for the unchanged or even improved metallic character of the organic metal after dispersion and in dispersion came from ESR and magnetoconductivity measurements [25]. First studies, performed on polyaniline-polyester blends (the same as used in [23]), showed a much higher Pauli susceptibility and a much higher density of states at the Fermi level than even the relatively highly conducting "polyanilinecamphersulfonic acid" as doped in m-cresol [26]. Up to then it was common opinion that

518

CONDUCTIVE POLYMERS AS ORGANIC NANOMETALS

only solution processes (also often called secondary doping [27]) could be improved in conductivity, and these effects were related to better orientation of the chains. The scientific community did not yet recognize the importance of these results for the understanding of the conductive polymers as organic metals. Further studies [25] showed that according to the reduced activation energy, W vs. T log-log plot between 300 K and 300 mK, unblended PANI is on the insulator side of the Metal-Insulator (MI) transition. For PAni-PMMA blends, W decreases as the temperature is decreased below 1 K and the systems are found to be on the metallic side of the MI transition. This was the first time that such a material was truly metallic; comparable (CSAdoped) materials were metallic only under pressure. In the vicinity of the MI transition, localization and electron-electron interactions both play an important role in determining conductivity. The results of temperature dependence of paramagnetic susceptibility of PAni and PAni-PMMA blends between room temperature and 2 K further confirm our position. The results are discussed in terms of weak electron-electron interactions in a disordered metal near the MI transition (Fig. 16). Our commercially available polyaniline powder, Ormecon, was used for preparing the PAni-PMMA blends. The blends were prepared by using melt dispersion techniques used for the production of commercially available products. The magnetic susceptibility of unblended PAni and PAni-PMMA blends was measured using a commercial SQUID magnetometer in the temperature range 2.0-300 K in an applied magnetic field of 100 milliTesla. A nonmagnetic quartz tube was used as the sample holder. The magnetic susceptibility of the sample holder was measured separately in the same temperature range and magnetic field range. The total magnetic susceptibility, Xtot, is expressed as a sum of the core diamagnetic susceptibility, Xfore, and the paramagnetic susceptibility, XPara: Xtot -" XCore + XPara

(1)

The dopant is p-toluene sulfonic acid (p-TsA), and the core value of PAni-p-TsA (y = 0.5) is calculated to be - 2 0 6 • 10 -6 emu/mol-2ring. The core susceptibilities of PAni-PMMA and PAni-PMMA are calculated by using a core value of PMMA of

_

_

,

_

,

.

.

.

.

.

.

.

.

.

.

-

,~I f

C

II

PANI(40oY o ) - ~ 6 0 oN zx PANI(33%)-PMM~67%) o UNBLENDED PANI

0.1

lr

=

9

lrl

|

1

',

'

,'

-

t

'

9

,

',

,'~"

10.

zx

~

'

'-,

,

~'

',

,

,~ 9

|

"

9

:

-

100

Fig. 16. Log-Logplot of W(T) vs. temperaturefor PAni-PMMAblends in the metallicregime.

519

WESSLING

Table I. The Density of States at the Fermi Level (N(EF)) for PAni and Its Blends, in Comparison with Other Work

PAni (wt. %)

S. n o

PMMA XPauli (wt. %) (emu/mol;2 rings)

C N(EF) ( e m u / m o l ; States/eV/2-rings 2 rings/K) (+0.2)

NS (• 1020)

8.17

91.83

0.00024

0.00016

7.8

2.6

13.30

86.70

0.00019

0.00018

6.4

2.9

16.87

83.13

0.00026

0.00037

8.6

5.9

21.39

78.61

0.00007

0.00045

2.2

7.1

27.03

72.61

0.000080

0.00048

2.6

7.7

33.61

66.39

0.000076

0.00060

2.5

9.6

41.56

58.44

0.000082

0.00090

2.7

14.0

22.8

70.0

100.00

--

0.000690

0.00435

ES I HC1 (see footnote 4 in text)

100.00

--

m

~

0.26

ES II HC1

100.00

--

--

--

0.083

PAni-CSA m-cresol [43]

100.00

--

0.00002

--

0.7

PAni(HC1) [171

100.00

--

--

--

1.4

[39] 4

- 6 2 . 8 2 x 10 -6 emu/mol. The calculated core values of P A n i - P M M A blends are shown in Table I. After subtracting the core value from the experimental values, the total paramagnetic susceptibility of PAni and its blends is plotted as a function of temperature. The data are shown in Figures 16 and 17. All samples show a nearly temperature-independent magnetic susceptibility down to 50 K. Below 50 K a temperature-dependent Curie-like susceptibility is observed. The total paramagnetic susceptibility, XPara -- XPauli -Jr-C / T

(2)

XPauli- 2 / z 2 N ( E F )

(3)

where C is a constant and

where N ( E F ) is the density of the states at the Fermi energy. Figure 17 shows the X vs. 1/ T plots for unblended PAni and PAni-PMMA blends. The temperature-independent Pauli susceptibility is calculated from the above plot, and the density of the states at the Fermi energy is calculated using Eq. (3). These values are shown in Table I. The values of N ( E F ) of PAni (Ormecon) and its blends are much higher than that reported for the PAni-CSA system [26], that is, in the range of 2 - 7 0 • 10 2~ whereby PAni-CSA [28] shows only 0 . 7 4 emu/eV/2-ring. The general formula for the static spin susceptibility in the Anderson localized regime was derived by K a m i m u r a [28] and is given by X = 2/3# 2 Z {

2 + e x p [ ( # - ec~ - Uc~)] + e x p [ - f ( #

a

520

- 8or)] } -1

(4)

CONDUCTIVE POLYMERS AS ORGANIC NANOMETALS

Fig. 17. Paulisusceptibility.

where/3 - 1/ kB T , / z m is the chemical potential, e~ are the energies of the localized states labeled by ct, and U~ - U (e~) - U is the average intrastate electron-electron Coulomb interaction energy. The numerical solution of Eq. (4) shows that at low temperatures when kBT is less than U, the states near the Fermi energy become singly occupied, and the spin susceptibility obeys the Curie law,

x(T)- ~Us

(5)

kBT where Ns is the number of singly occupied states. Because a finite density of states is observed at the Fermi energy, the Curie-type behavior of the spin susceptibility arises from single occupancy of localized states near EF. Ns values are calculated from the slope of X vs. 1 / T for PAni and PAni-PMMA blends for T < 50 K. These values are also shown in Table I. For unblended PAni, Ns is equal to 7 • 1021 emu/mol-2rings/K. The conclusion is clear: without any secondary doping and just by dispersion, PAniPMMA blends show a temperature-independent Pauli susceptibility down to 50 K, and below 50 K a Curie-like behavior is observed. A finite density of states at the Fermi energy implies that PAni and its blends form a "Fermi glass." The Curie-like behavior arises from the single occupancy of localized states at the Fermi energy. We conclude that, without any solvent, recrystallization, or secondary doping, dispersion alone, if done properly, can improve the conductivity significantly and enhances the paramagnetic susceptibility in these systems. The results can also be understood with the understanding of PAni as an organic nanometal, that is, a metal with quantum size-limited metallic space, where the electron wave eventually tunnels from particle to particle. However, these results do not yet explain why PAni in the dispersion-processed blend crossed the MI transition to the metallic side, as both raw material/on the insulator side, and dispersed product/on the metallic side have a much higher density of states than any other comparable material. Obviously, this is only one precondition.

521

WESSLING

Table II. d-Spacings d(A) Pulver

(010)

(100)

(110)

(111)

(020)

cr (.102 S/m)

549

5.87

4.65

3.52

3.38

3.06

5.5

604

5.97

4.37

3.52

3.36

3.02

13

380

5.98

4.37

3.54

3.36

3.03

13

610-12

5.99

4.39

3.52

3.36

3.04

18

578-10

5.92

4.43

3.53

3.36

3.00

37

610-10

5.97

4.46

3.54

3.36

3.01

42

604-pd45

5.91

4.54

3.53

3.37

3.02

45

a (t~)

b (A)

c (/~)

V (]t 3)

6 (o)

549

4.7

5.9

10.6

294

146

604

4.4

6.0

11.0

290

166

13

380

4.4

6.0

10.9

288

159

13

610-12

4.4

6.0

10.8

285

154

18

578-10

4.4

6.0

10.7

282

149

37

610-10

4.5

6.0

10.4

280

140

42

604-pd45

4.6

5.9

10.2

277

134

45

5.5

Recently we were able to propose a first reliable structural analysis of the metallic core [29]. For this purpose, we examined 7 different PAni powder lots that showed different conductivities and different dispersibilities. They were all prepared by principally the same procedure (water solution of aniline-p-toluene sulfonate, which is oxidized by potassium peroxodisulfate), with identical m o n o m e r - o x i d a n t ratios, but slightly differing reaction parameters. 1 A calculation of representative spectra leads to lattice plane distances and indexes of the reflexes. A recalculation of the spectra for the different lots showed slightly different d-spacings, as shown in Table II with the elemental cell, as in Figure 18a. (There are further details in the original publication (in preparation). For direct access to the data, see [30].) The cell volume developed as shown in Figure 18b. It is very interesting, if not surprising, that the cell volume decreases with increasing conductivity, mainly because of a tendency toward decreasing c, which is due to a decreasing angle 8 of C6-N-C6. To our surprise, it is not the flatter but the more bent arrangement of the chain that makes PAni more conductive. It seems that with this conformational change, the packing of the chains leads to a better orbital overlap for forming conduction bands. With a C6-N-C6 angle of < 140 ~ it crosses the border of the IM transition and becomes truly metallic [25d]. Moreover, the higher order (greater size) of the crystalline regions plays an important role, as it seems from the evaluation of the half-width of the reflexions. This shows again that only via dispersion can dramatic changes influencing the crystalline structure and then 1 The different lots were taken from an internal computer-controlled study to evaluate the process window of our polymerisation procedure and to make sure that every lot will be reproducibly the same. We have achieved this necessary reproducibility, which is following the parameters of lot 604, and we are using a computer-controlled reactor with no default results.

522

o

S~

F-

o

~

l___,

03 c~

cl

C)

4~ 0

I~0 O-

.

I~ o')

,

I

I

,

I

I

I

I

~

I~ *',,I f31

I~ ",.,I 0

,

"-

I

,

I

-

I I

I

I~ oo o

,

--

I I

,

v[A3]

I

I

"--

I

I

I~ Oo fjrl

,

I

.,, m

,

I

m m

I

I

I~ co 0

,

,

I

I

"-

I

I~ co f3*l

I I

,

,

II 0 ._i.

D~

I;> 13"

I I

I

O" r

I

f,~ 0 0

,

,

I

o rjrl

~00 i

~

~

M=,=~

~

4:~

~

t~

~

~-~

~-~

i,~ ~ Lj bo L~ ~

(~

b i~ "~ ~ ~ ~' b

--4

t~

4~

s

,---

..

~

X

X

X

X

Z 0

,z

Cl > Z

0

>

r~

t-l-I

0

> 0 and I - T A S I < AH. Therefore, the energy necessary to form the interfaces also has to be pumped in by process energy; solvents are (only) capable of lowering the interfacial energy when interacting with insoluble materials, as are detergents.

2.3. Surface Tension of Polyaniline Let us assume that conductive polymers and, more specifically, polyaniline are just dispersible but not soluble (we will discuss the other option again later). Then the solvents would act as described above: they would lower the surface tension of PAni (Fig. 26). The only measurement of surface tension of polyaniline or any intrinsically conductive polymer (in "doped" form) that I am aware of is our own measurement on layers of pure PAni-HC1 deposited from dispersion [7] (Figs. 27 and 28). We found a surface tension of 69.4 mN/m. As this is the only experimental determination of it until now, we will deal with it carefully, but one should not just discard the value and state if the value seems too high, without measuring, as was done before [33]. Such a value could be translated into a solubility parameter of ,~45 (j/m3) 1/2 if we were allowed to use this relation, even though the protonated form of PAni (ES) is a salt. This is

>,, .~ ~o t,..., c'~

100

->"

.m O~

90-, 80-

100

I

c

90 -~

E

8O

"-

~

i

70

70

60

60 -j

50

5O

40

40 J

I

I '

i

i

rl

30 20 10 0

i

,

1

30

i

20

i

10

i

r 10

0 ' 1O0 1000 10000 particle diameter (nm)

100

particle diameter (nm)

Fig. 26. Photoncorrelation spectrum of a PAni dispersion in organic solvents.

538

C O N D U C T I V E P O L Y M E R S AS O R G A N I C N A N O M E T A L S

Fig. 27.

SEM of a thin PAni layer deposited from a pure PAni dispersion.

Fig. 28.

STM taken from the same sample as in Figure 27.

539

WESSLING

close enough to make the reasonable assumption that water, with a solubility parameter of 47.9, should be able to dissolve polyaniline. But this is not the case, and everyone accepts this as factual. Now, according to the majority, solvents with a much lower solubility parameter should be able to dissolve polyaniline. How is this possible? This would be in basic contradiction to solution thermodynamics as discussed above. Let us compare our value for polyaniline with surface tension values of some solvents (in mN/m):

Aniline 42.9

Morpholine Pyrrolidone DMSO m-Cresol NMP 23.5

47.7

24

32.5

25

DMF

p-Xylene

25

28.4

These solvents were considered to be "single solvents for polyaniline tosylate" [33]. We consider some of them to be efficient dispersion media for polyaniline, in accordance with our assumptions for this discussion paragraph. This means that these solvents would reduce the surface tension of PAni. But what is the real surface tension of PAni? Shacklette deduced from his "dissolution" experiments a value of 49.6 mN/m for PAni-tosylate. We had found 69.4 mN/m experimentally for PAni-HC1. Any solvent--especially one miscible with water, but not limited to this---could reduce the surface tension found by us to any lower value. So, Shacklette's "solvents" would act as a dispersion medium. This is still in accordance with a value of 69.4. If pure polyaniline tosylate is not soluble, but dispersible, and if it has a rather high surface tension, it would adsorb other materials to reduce its surface tension. What would be adsorbed? I propose: preferentially water. Polyaniline tosylate is polymerized in water medium, is washed with water; when dried very carefully, it takes up water very easily (about 1-2%), so it is highly probable that water is adsorbed on the polyaniline particle surface. Let's look at the surface tension of water, 72.9 mN/m. Considering the arguments above, water would first reduce the surface tension of polyaniline, so that we [21] measured only the surface tension of a material that had water adsorbed (which dissolves some electrolytes like HC1 or tosylate)mso we measure the surface tension of the modified water surface! And PAni might have a surface tension from 200 mN/m (like salts) to 2000 mN/m (like metals). This would explain another fact: It is not so easy to prepare dispersions of polyaniline in water. Why? If water is adsorbed preferentially, leading to a surface tension of 69.4 mN/m, 5 then water would not be able to disperse this material, as it can no longer reduce its surface tension. 6 Recently, Chemini et al. [44] reported a study using inverse gas chromatography (IGC) to evaluate the dispersive (or: London) contribution to the surface energy of polypyrrole (PPy) and its time-dependent variation. They included PAni-HC1 (however, a only type resulting from a crude synthetic procedure), as a comparative conductive polymer in their evaluation. Even earlier, Vincent et al. [49] had determined the Hamaker constant (A) for colloidal PPy particles. A is related to the surface tension by Ys - A/24FID 2 (where Do, the intermolecular distance, is taken to be --~0.165 nm for organic materials). 5 And analogously for PAni and counterions other than HC1,provided that the monomer/counterion relation is 0.5, so that no shell of detergent-like counterions forms, as is the case with DBSA, CSA and others. 6 In the meantime we have succeeded in preparing several different types of stable water dispersions of polyaniline, but only by using a nonconventional approach (cf. data sheet by Ormecon Chemie).

540

CONDUCTIVE POLYMERS AS ORGANIC NANOMETALS

They found values that were much higher than for any other conventional polymer, matching those of metals. It should be mentioned that the following Ys values are only the dispersion (London) contribution to the complete surface (surface interactions via pure dispersive, i.e., London/van der Waals forces) energy ys, with

ys-

+ ys + ys"

17)

where ysP is the "polar contribution" (surface interactions via polar forces), and ysH is the hydrogen contribution bonding. Chemini et al. studied the pure London/van der Waals forces by measuring the free energy of adsorption for alkanes with different numbers of C atoms. First, ysd of PPy and PAni showed decreasing values with increasing temperature, a classical behavior. Extrapolated to room temperature, ysd was (in mJ/m 2 (mN/m)) ~130 for PPy-HC1 close to 90 for PPy-TsOH, ~ 100 for PAni-HC1, and 43 for PMMA. These results are in good agreement with our considerations, and they lead us to conclude that the whole surface tension (including polar and hydrogen bonding contributions) is much higher, as outlined above. Second, Chemini et al. found that fresh PPy had much higher surface energy, like 150 mJ/m 2 (at 57 ~ Aged PPy went down to a ysd of 70 (cf. our result with PAni, which was also not fresh and probably reflects the adsorbed water; see above). Fresh PPy decreased in surface tension over the days to reach a certain stable value (between 60 and 90). The authors did not come to a final conclusion about the reasons for this decay, but they suspected that (besides instability of PPy) it probably reflects a time-dependent (irreversible) adsorption of low-surface-energy materials on the very high-surface-energy PPy. The authors made the observation that PAni did not share this behavior with PPy. We suggest that PAni does, but much more quickly (the first measurement was made after 1 day, PAni or PPy, respectively, in a 60 ~ oven). This means that PAni probably has an even higher surface energy, lowered directly from its formation by adsorbed water. Wherever such further conclusions lead, it is evident that conductive polymers have an extremely high surface tension and hence cannot be soluble. But as we know, PAni is not soluble in water, but showed a surface tension very close to that of water (72.9 mN/m). If pure polyaniline tosylate is not soluble, but dispersible, and if it has a rather high surface tension, then it would adsorb other materials to reduce its surface tension, preferentially w a t e r . Polyaniline tosylate is polymerized in water medium, washed with water, and dried; a completely dry powder takes up water very easily (,~ 12%), so it is highly probable that water is adsorbed on the polyaniline particle surface. Polyaniline prepared in other media, like 2-butoxyethanol [45], would adsorb 2-butoxyethanol, not water, preferentially. Such a polyaniline type would be dispersible in other media, and, in fact, it is. The company claimed [46] that their polyaniline is "soluble" in xylene (surface tension 28-29 mN/m), butylacetate (-~24 mN/m), methylene chloride (~26.5 raN/m), and toluene (~27.5 mN/m). 2-Butoxyethanol has a surface tension of "-~27 mN/m. The surface tension of the PAni particles polymerized in this medium will probably be somewhat higher because of the influence of water and electrolytes present. The a.m. solvents are then capable of lowering the surface tension of this material, which has a different adsorbed layer and hence a lower surface tension compared with polyaniline prepared in water media (cf. Fig. 32). Polyaniline doped with other "dopants" like dodecylbenzenesulfonic acid (DBSA) are showing a different behavior: they are said [47] to be soluble in unpolar solvents like xylene. This would be rather surprising if we were to find true solutions. In the context of this section, we suggest that dopants like DBSA or camphersulfonic acid (CSA) (which also changes the "solubility" characteristics drastically [48]) are partially located at the particle surface with their unpolar tail directed to the outside. If this

541

WESSLING

model is correct, then several appropriate solvents would wet these surface types better than others, which are better suited for polyaniline tosylate particles. m-Cresol acts slightly differently in our dispersion picture: first it protonates EB, then it disperses the formed ES. It then acts by reducing the increased surface tension of the resuiting ES PAni-cresolate. m-Cresol cannot dissolve or disperse other PAni types. J. Frommers' first observation of "dissolution" of PPS-AsF5 in AsF3 (cf. Section 2.4.1) is to be understood in the same way.

2.4. Discussing the "Solution Hypothesis" Again 2.4.1. What Indicates That the Systems Could Be True Solutions? I will now try to consider the option that such polyaniline-solvent systems are real solutions, even though the consequences from Sections 2.2.1 and 2.2.2 do not allow this. What is the experimental background provided by the scientific community for the conclusion or hypothesis of "solution"? To be candid, there are only a few weak arguments. For most people in the field it is sufficient to state that a solvent/polyaniline system is "clear" (green). But as there are many absolutely transparent, crystal clear dispersions (beginning with Faraday's gold sol, up to microdispersions of oil/water/selected detergents [49] that are clear and stable!), this observation is not at all convincing. The first publication with the message "conducting polymer solutions are feasible" came from J. Frommer [50], who claimed to dissolve poly(phenylene sulfide) in AsF3 during "doping" with AsFs. It was mentioned as being important that the "doping" is performed in the solvent. If doping is made first and if only a few seconds later after this the product is brought into contact with the solvent, this "results in incomplete dissolution." This observation was attributed to cross-linking. Later emeraldine base (EB), the base form of polyaniline, was treated similarly when liquids capable of both "doping" and "dissolving," H2SO4 [41] and m-cresol [48], were used. In the first case the authors also presented viscosity curves [51 ]7 and stated that the viscosity dropped over tie.e (when the solution was allowed to sit), which was attributed to a decrease in molecular weight. No consideration was given to the possibility that (in case they were dealing with a dispersion) the particle size could be changed over time (here: increased by aggregation). Such a process would also decrease the viscosity significantly. We do not currently see any indication of a real dissolution effect of these doping solvents. One should have to look for other experiments that could prove this assumption and disprove my proposal that the solvent is first "doping" and then wetting the particle surface. Is it not reasonable to assume that a liquid that is able to react with EB in the form of an acid-base reaction or in the form of an oxidation (like m-cresol, or AsF4, which could be the active species when AsF3 is in AsFs) is also able to wet the resulting particles? There are two publications in which some serious arguments supporting the "solution hypothesis" have been developed from extensive experimental studies.

2.4.1.1. Dynamic Light Scattering of PAni-CSA Heeger et al. [52] have published a "solution characterization of surfactant-solubilized polyaniline." We might first ask what the term "surfactant-solubilized" might have as a meaning, as "surfactants" are generally active at a surface, reducing their surface tension. But the authors are claiming a "solubilization," and hence there is no surface to be treated! But from the text it becomes clear that they believe that "PAni-CSA exists as single chains in solution at low concentrations in m-cresol." The dynamic light scattering study was performed by comparing the results with those for polyelectrolytes. But here, the ions are quasi-infinitely separated, which, as we know However,from this presentation at the ICSM G6teborg, the author only published the abstract and not the viscosity data presented at the conference.

7

542

CONDUCTIVE POLYMERS AS ORGANIC NANOMETALS

from Section 2.2.3, cannot be done with polyaniline. Also the authors admit that "the previous work on polyelectrolyte-surfactant solutions will give insights into the solution properties of PAni-CSA," but they are nevertheless using equations derived for such systems to interpret their measurement results. One aspect that is clearly different between the polyelectrolyte solutions and the PAni systems investigated is that PAni is insoluble without the addition of what they call a "surfactant," whereby the polyelectrolyte is soluble without a "surfactant." The group reports first on the preparation procedure. It should be asked why it was necessary to "sonicate" (i.e., treating the PAni/CSA mixture in m-cresol at very low concentrations like 0.01% under ultrasound) for 5 h? The use of ultrasound is a widely used technique for the preparation of colloids, 8 where the colloidal particles are hard to disperse. We have described this technique for the dispersion of conductive polymers as early as 1984 (cf. [31, examples 1, 3, 4]). Despite this very high energy input, the "solution" had to be filtered through millipore filters. And even then there was evidence of a certain degree of aggregation, as was detected from the slower of two relaxation effects. This relaxation was attributed to large particles convecting through the laser beam. A particle diameter was not given. The faster relaxation was attributed to "single chain polymer diffusion." It remains unknown how the authors concluded that they were observing "single chains," inasmuch as they had shown that the particles that were detected did not show behavior characteristic of extended (more rigid) rods, which one would expect from solvated PAni chains. What was clearly observed by the authors was (1) a hydrodynamic radius of between 10 and 50 nm, (2) an increase in the radius with decreasing PAni concentration, (3) an increase in the radius with an increasing amount of water in m-cresol, and (4) no "chains" or "particles" with a significant difference between the length and the diameter (hence the particles or chains were more or less globular). Their interpretation of these findings was that the PAni is completely dissolved (although they mentioned "some degree of aggregation"), and the PAni chain is present as a more random coil, not as a rigid rod. They concluded this from the difference in the hydrodynamic radius in the different concentrations of PAni. This behavior was analogous to phenomena found for polyelectrolytes. But it remains unclear whether one can deduce anything valuable from this apparent analogy. From the difference in hydrodynamic radius they concluded a varying persistence length of the chain ranging from 0.5 nm (!?) to 9 nm (so over a factor of 20), depending on a concentration difference between 0.01% and 0.001%. In other words, it was claimed that the random PAni coil is completely folded at 0.01% and completely unfolded (and more stretched) at 0.001%. This seems at least questionable, if the conclusions are compelling. In contrast, the observations can also be interpreted by assuming dispersed particles. This can be seen when taking into account the following: 9 the necessity of sonicating 9 the presence of bigger particles, even at such low concentrations 9 the general observation that dispersion by ultrasound is more efficient when the medium has a higher viscosity (i.e., at the higher concentration of 0.01%, the shear rate induced by the sonotrodes is higher, leading to a better dispersion; cf. [16b]) 9 that this accounts for the dependence of particle size from concentration 9 the presence of water (becoming adsorbed on the PAni particles) decreasing the dispersion ability of m-cresol, which leads to bigger particles (cf. Section 3). 9 8 Becauseit provides a high shear stress, which is necessary for dispersion, as was theoretically shown [16b]. It should be noted that the authors mentioned the following: "In our experiments, we did not observe any measurable effects on the size of the polymer radius until considerably higher water/aniline fractions (about 1000); even at these concentrations the size of the radius was reduced only by a factor of 2." This is in accordance with the consideration, that water is soluble in m-cresol and only a portion is being adsorbed on the PAni particles. 9

543

WESSLING

It also seems unreasonable that PAni, dissolved in a single chain, should be present as a random coil and not as a rigid rod. But even more, it must be asked if the persistence length can vary so drastically at such relatively low concentrations. It must be stressed that a direct confirmation of single solvated chains has not been given in this publication.

2.4.1.2. Liquid Crystalline "Solutions" Another very interesting observation was published by Cao and Smith [53]: liquid crystalline "solutions" (as they claimed) of electrically conducting polyaniline. Again they studied PAni-CSA in m-cresol and found liquid crystalline behavior, in contrast to emeraldine base in m-cresol. First it must be known that birefringeance and other characteristics of liquid crystalline systems are not limited to solutions. In fact, these phenomena are widely known and described for many colloidal systems; everywhere that a high shear (which was obviously applied by sonicating) is induced in viscous media of colloidal particles, which are anisodimensional, the inner friction of the systems leads to an orientation leading to liquid crystalline behavior. In contradiction to the (later) findings of the same group from dynamic light scattering, Cao and Smith claimed: "Apparently, complete protonation by strong acids was essential for transforming the polyaniline chains from flexible coils (in emeraldine base) to more rigid entities and, consequently, for the formation of liquid-crystalline solutions of polyaniline." But when looking at our model for colloidal systems of PAni, we had deducted a certain anisotropy from other experiments [ 16a] and hypothesized a structure for the adsorbed solvent layer on the PAni particles, leading to their orientation in dispersions and gels (Fig. 29b). In fact, the assumption of real solutions of intrinsically conductive polymers has not yet been well supported by experimental results, and only a very few attempts have been made in this direction, probably because researchers did not realize the importance of this question. 2.4.2. What Experiments Would We Need to Prove the Existence

of Solutions? Scientists who prefer the opinion that such systems are real solutions should consider conducting several key experiments to prove their position. Comparing the results with reasonable predictions--and with the results of experiments directed at proving the "dispersion hypothesis"--would lead us to a clearer picture. The following experiments could be useful: 1. Melt point depression: To evaluate how many moles of solvated monomer units are "dissolved" in relation to the expected number. 2. Measuring the swelling degree induced by the preferred solvents: Such experiments would be in accordance with two aspects: first, people say that the increasing problems in dissolving OMs and polyaniline in particular when using very dry material is due to cross-linkingmthis is exactly where swelling degree measurements are always made. Second, for determination of solubility parameters, the soluble polymers are purposely cross-linked to measure the swelling alone (without dissolution), so a potential cross-linking would have happened automatically as an advantage in such experiments. Prediction: No swelling can be observed; PAni is not cross-linked but is very hard to disperse. 3. Recrystallization: I would be excited if someone were to recrystallize polyaniline, for example, because single crystals would be an extremely helpful object

544

CONDUCTIVE POLYMERS AS ORGANIC NANOMETALS

...-.,. tt} 13.. v Cn O

-2,40 -2,42 -2,44

-

-2,46 -2,48 -2,50 -

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-2,52 -2,54 -2,56 -2,58 -2,60 -2,62 -2,64 -2,66 -2,68 -j -2,70

I

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(b) Fig. 29. (a) Viscosity of PAni in DMSO dispersion. (b) Hypothetic structure of the colloidal particles in dispersion.

for studying and improving PAni and other OMs. 1~ Polymers generally tend to increase their crystallinity in solution, especially with careful cooling and subsequent precipitation. I have made this proposal many times in public without any positive feedback. If we were really dealing with true solutions, I am convinced 10

Compare our theory of the mesoscopic metallic character of polyaniline and ICPs in general [21].

545

WESSLING

that there would be a doctorate fellow somewhere in the world who is capable of overcoming potential experimental problems and will recrystallize polyaniline as people did in earlier days with proteins and DNA. It is very hard to crystallize-but only if we are dealing with true solutions? I am afraid that single crystals must be prepared by other techniques, as recrystallization from solution will not occur. 4. Dielectric absorption [54]: It should be possible to determine the difference in such relaxation experiments by comparing a system that is a "solution" according to the assumptions of the experimentalist with another systems that he agrees are "dispersions." At frequencies above 1 MHz, characteristic dielectric absorption peaks should be detectable that are due to dipole relaxations. These could be assigned to motions in the polymer backbone, but this is only feasible when the polymers are dissolved. Even a stiff molecule will have some additional degrees of freedom in comparison to the chains in a (colloidal) bulk particle. Furthermore, rodlike molecules exhibit a different dielectric response in solution compared to their behavior in bulk. Prediction: There will be no difference found in OM-solvent systems, whether one measures a "solution" or a "dispersion." 5. Comparison of the primary particle size in bulk and in "solution" (see next section).

2.5. What Experimental Evidence Do We Have for the "Dispersion Hypothesis"? What I am claiming should not be surprising to the readermthere are many experimental hints supporting this hypothesis, and there are certainly many more for than against. But I would like to point out again that the purpose of this discussion should be to learn more about conductive polymers and organic metals, about polyaniline and the others. The presentation of those experimental results or observations that led me to promote the "dispersion hypothesis" should encourage those preferring the other options to conduct new and improved experiments to finally find out the "truth."

2.5.1. Our Experimental Studies The following experimental results have been found by us or in cooperation with others.

2.5.1.1. Particle Size (Morphologically) We have determined the particle size of PAni in different states, as a pure material or in dispersion, and in thermoplastic polymers, paints (coatings), pure (organic) liquid dispersions, and thin coatings prepared therefrom (for more details, see [55]). We found 9 ~ 100 nm in thermoplastic polymers, with a tendency toward smaller particles with better dispersion, which leads to lower critical volume concentration 11 and higher saturation conductivity 9 ~ 5 0 nm in paints, connected with even lower critical volume concentration 9 a fine structure in TEM pictures of such systems, pointing to smaller primary particles as the building blocks of the particles found in polymeric dispersing media 12 9 particles ~ 10 nm in size in pure (organic) solvent dispersions (by membrane filtration and photon correlation spectroscopy) (see Fig. 7) and laser Doppler The concentration at which a log (conductivity) vs. concentration plot has its curve inflection point. From our nonequilibrium theory of dispersion in heterogeneous polymer systems it is understandable, that smaller particles are not possible in polymeric media, as the polymer matrix has to wet the particles being dispersed, which cannot be performed on a surface with such a small radius such as, for example, 10-nm particles would have. 11

12

546

CONDUCTIVE POLYMERS AS ORGANIC NANOMETALS

9 --~100 nm (secondary) particles in pure layers of PAni deposited from such dispersions (see Fig. 8), consisting of 9 ~ 10-nm primary particles, a fine structure that we resolved by STM (see Fig. 9) It is most important for our debate that the particles' diameters are not at all different from the state in solvent systems (liquid dispersions), as it can be found in solid-state/solid dispersions, where the 10-nm particles are the building blocks of the secondary particles. Maybe the reader would agree that our results from photon correlation or laser Doppler spectroscopy show the correct particle size range: how can such particles consist of 90% solvents (or even more), as they would have to if they were solvated (cf. Section 2.1.1). And how can we understand the finding (using microwave absorption of polyaniline blends) of a primary particle size of 9.6 nm (with a metallic core of 8 nm), which is the size we find in the solvent system? How else should we conclude rather than assume that the particle (size) has not (principally) been changed by the interaction with the solvent? We call this a dispersion process, the particles have just been wetted by it, and the result is a "dispersion," a sol.

2.5.1.2. Particle Size (Electronically) During our research with Pelster et al. [21], we found that the metallic core is a (spherical) body 8 nm in diameter, surrounded by an (amorphous) nonmetallic shell that is less conductive, of "~0.8-nm thickness, so that an overall diameter of 9.6 nm results. This is in surprisingly good accordance with all conclusions we had drawn earlier from various particle size determinations. From Sections 2.5.1.1 and 2.5.1.2 it should be apparent that we are dealing with a material consisting of 10-nm particles as primary building units, which cannot be altered principally by actions of solvents or other dispersing media, which do not change shape and size during interaction with solvents, and which are also the basic unit for the metallic (although quantum-size limited) conductivity.

2.5.1.3. Viscosity and Gelation We had determined the viscosity of pure PAni dispersions in an organic solvent system and had found a good correlation that gives validation for dispersions (see Fig. 29a). However, one could also have concluded that deviations are not far from a behavior of true solutions, even though we showed that these systems had 10-nm particles as the dispersed phase. Furthermore, we had reported a sudden increase in viscosity to infinity at a certain critical point, when our dispersion exceeded a certain concentration (at 2.4%; in other experiments around 0.5 %). Other authors also observed this behavior, but often at much higher concentrations (which we assign to a greater particle size), which they interpreted as "cross-linking." But why should PAni cross-link suddenly (within seconds?) just above 0.5%, whereas we can store a 0.5% or less concentrated dispersion "forever"? Gelation of dispersion is the result of a process of structure formation, induced by long-range interparticle attraction forces. The particles form long chains (filaments) of aggregating particles (instead of big particles precipitating) that penetrate the whole solvent volume, and as soon as it forms a complete network, the system can no longer flow.

2.5.2. Other Experimental Results There are even more hints to be found in the literature, even though the authors might not come to the same conclusions as I do.

547

WESSLING

2.5.2.1. OM Morphology/Particle Size/Coherence Length The debate we are engaged in is not limited to the topic of "solution or dispersion." It starts with the question: Are OMs of a fibrillar 13 or a globular 14 morphology? It is still not yet accepted that even the very highly conducting polyacetylene (called N-PAc) consists of very fine globular (altho~,gh in this case elliptical) primary particles, as Theophilou found out later by STM [ 11 ]. They were ~ 2 0 nm in length in the stretching direction. Even more convincing is the fact that the coherence length generally accepted in the field ranges from 5 to 10 nm [57]. All determinations of the coherence length or the "metallic islands" in conductive polymers not depending on its chemical nature lead to values between 3 and 7.5 nm, not far from the value determined by us (8 nm plus 1.6 nm amorphous shell; cf. Section 2.5.1.2).

2.5.2.2. Concave Viscosity Curves K. Levon et al. reported a viscosity study of PAni (EB) in NMP and NMP with LiC1 [58]. They found concave reduced viscosity curves (Fig. 30). In dispersions, viscosity curves of all shapes including concave forms, can be found. The form is only dependent on the microscopic structure of the dispersion; that is, if superstructures are formed, if the particles flocculate or deflocculate, or if phase transitions (from, e.g., bicontinous to normal twophase structures with one continuous phase) occur at various concentrations. However, Levon et al. interpreted their findings without going into further detail by saying that "aggregation of polyaniline chains in dilute solution was observed." Was it really what they observed? Would it not have been more correct to state that a concave reduced viscosity curve was observed, which can be interpreted by assuming something? At least the authors admit that "aggregates still exist in solution as shown by light scattering. It may be that aggregates larger than dipolymers were not dissociated completely into the isolated chains but into small aggregates." This is what colloidal scientists call "dispersions."

2.5.2.3. "Solubilization" of PAni in Water by Interpolymer Complexation Liao and Levon [59] claim to have made a dilute solution of PAni (EB) with LiC1 in either poly(4-styrenesulfonic acid) or its monomer in NMP, which could be transferred into water without precipitation. However, the reduced viscosity curves (Fig. 31) show almost no dependence on concentration. This was attributed by the authors to a "dissolution by complexation" (of the PAni chains by the PSSA or SSA) without further explanation. However, if that were the case, the viscosity must increase with concentration of dissolved PAni chains (PAni-PSSA complex), which is not the case. I would interprete the reported results with a rather poor and irreproducible dispersion of PAni in NMP, with PSSA at the interface, which forms a very complex (and probably dramatically changing) micelle structure in water. Such systems would be an exciting object to be studied in colloidal science, another type of microemulsion: a sol (PAni-PSSA in NMP) forming an emulsion in water (probably with PSSA at the NMP-water interface).

2.5.2.4. Wormlike Micelles Dai and White reported "aggregation in conducting polymer solutions" [60]. The objects of the study were polyacetylene-polyisoprene block copolymers and mixtures of these with 13 A summary of arguments for this opinion that are still actively proposed can be found in [56] and in other articles in the same issue. 14 I started this debate by publishing the first comparison of a TEM showing fibrillar polyacetylene and a SEM taken from the same sample, showinga globular morphology(cf. [6]).

548

CONDUCTIVE POLYMERS AS ORGANIC NANOMETALS

~3 .J

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549

WESSLING

.... crystallinemetallic core, with surrounding anaorphous shell: surface tension >200 mN/m (1.500?) ...... adsorbedwater monolayer: reduction of surface tension to about 70 mN/m adsorbed dispersion medium (e.g. m-cresol): reduction of surface tension to about 30 mN/m Fig. 32. Double-adsorbedlayer model for PAni in colloidal state.

different PAc-PI block contents in toluene. In viscosity measurements they observed nonideal behavior and attributed it (correctly) to intermolecular interactions. The temperature dependence of viscosity was also studied, and it was shown that in contrast to different mixtures of comparable pure PI-polymer mixtures, the deviations came from interactions between the PAc blocks. From viscosity measurements with polymers containing different amounts of PAc blocks, they derived the Huggin's constant k', a measure for the solvent strength (degree of solution) in polymer solutions. The constant found was much higher (up to 1.1 with higher PAc content) than normal values for true solutions (0.3-0.4), which is a sign of intermolecular interactions and association/aggregation. Their structure hypothesis of the polymer-solvent system is a "wormlike micelle" form. By measuring the surface tension of their systems, they determined the critical micelle concentration (i.e., the concentration above which the surface tension no longer decreases, or: below which the surface tension increases). From small-angle X-ray scattering (SAXS) measurements they derived the statement that the systems contain a mixture of particles with different scattering length densities or multicomponent particles. They derived an aggregate size of 12-14 nm for undoped PAc blocks and close to 4-5 nm for the J2-doped lower values. They concluded that the undoped block copolymer forms wormlike micelles, the doped one a lamellar structure in the solvent systems due to aggregation of the PAc blocks.

2.5.2.5. Soaplike Structures Garrin et al. [61 ] reported on another PAc block copolymer, the one made with polystyrene. Their study was focused on small-angle neutron scattering (SANS) experiments in tetrahydrofuran (THF) "solution," from which they derived clear evidence for aggregation (micelle formation) and, to their surprise, a demixing upon heating, where the copolymer formed a film at the solvent-gas interface. A layer structure was found earlier by Aldissi et al. [62] for a similar Pac block copolymer. The authors complained that it was difficult to explain why the copolymer formed a film at the solvent-gas interface, "even at a qualitative level." They did not consider that the copolymer was not truly soluble (but was dispersed like a soap) and therefore has to

550

CONDUCTIVE POLYMERS AS ORGANIC NANOMETALS

form micelles, when dispersed throughout the solvent, or will form a separate phase at the solvent surface, like soap.

2.5.2.6. Aggregation of Poly(3-octylthiophene) Heffner and Pearson studied "solution processing of a doped conducting polymer" [63] (poly-3-octyl-thiophene, P3OT, FeC13, or nitrosylhexafluorophosphate doped, in toluene). Beware: the dopants were not soluble in toluene, so that they were introduced to the polymer as an acetonitrile solution, which is miscible with toluenembut in the resulting system, it will play a complex role, probably at the interfaces! Upon introduction of the doping solution to the (undoped) polymer solution, some "aggregation" (as they called it) of the resulting doped solution "invariably occurred." 15 They continue: "Although the spectral change which occurs in the sol phase upon doping indicates that some doped polymer must remain dissolved [from what did they conclude this?], aggregates were still clearly visible in doped solutions with polymer concentrations as low as 0.01c* (c*: critical micelle concentration). 16 [...] The degree of aggregation ranged from tiny clusters suspended in clear solution to the entire sample forming a cohesive gel. 17 [...] We have found the gelation to be a reversible process" (cf. Section 2.5.1.3). The authors are still convinced they deal with solutions (which only by mistake show some aggregates) and so tried to improve the solution (prevent aggregation) by adding some organic salts (tetrabutylammonium-p-toluenesulfonate) "to screen the interaction and reduce the degree of aggregation, as is observed in the 'salting in' of aqueous protein solutions. [...] However, rather than creating a deaggregated doped solution as we hoped, interactions between the charged ions caused a complete dedoping of the solution." As an interpretation of this phenomenon I suggest that the original system is again a complex microemulsion consisting of doped phases, surrounded by the octyl side chains arranged as a shell (micelles) in toluene with some complex phase structure mediated by acetonitrile. The addition of the salt might have changed the phase structure in such a way that acetonitrile can no any longer facilitate this microemulsion and the micelle formation, but can facilitate a phase separation between toluene/P3OT (undoped) and acetonitrile/doping/salt, leading to a microemulsion of this composition.

2.5.2.7. Viscoelasticity Gregory presented [64] fascinating results from his viscosity studies of PAni (EB) in NMP "solutions." He showed convincing evidence that these solvent systems are viscoelastic, a property directly linked to their colloidal character. Most colloidal systems do not show Newtonian behavior of the viscosity upon shear stress, and time-dependent phenomena (relaxation) are often observed. These are due to dynamic structure formation and restructuring processes based on reversible long-range interaction between the particles.

2.5.2.8. Gel Permeation Chromatography: Changes upon Salt or Cosolvent Addition M. Angelopoulos reported in the same conference some "magic" change of, as she interpreted, "the molecular weight of PAni (EB)." When comparing the retention time in GPC using NMP or NMP/5% LiC1, the "high molecular weight fraction" (at a retention 15 Elsenbaumer[32] and Shacklette [33 and personal communication] alwaysobserved"insoluble" portions and precipitates independent of the concentration range they workedin. 16 Whichmeans nothing more than there is no dilution effect resulting in a more complete dissolution. In other words: this is not a true solution, but a nice dispersion! 17 Whichmeans no more than they had submicronparticlesmnot visible by eye or microscope--responsible for the colorless "solution" and bigger particles that were visible; when the particle size was small enough, then the critical gelation concentration was very low (cf. Section 2.5.1.3).

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WESSLING

time of 25 min) vanished, and the peak at 30-min retention time ("low molecular weight") increased. When 10% m-cresol was added to a EB "solution" in DMPU, again the peak of the "high molecular weight fraction" vanished, whereby the "low molecular weight" peak increased. Her interpretation was that the salt and the cosolvent were "breaking up the high MW fraction." I would like to ask how LiC1 or m-cresol would be able to cut the chemical bonds in the PAni (EB) chains, which are supposed to occur fully solvated in the NMP. This is virtually impossible. An alternative interpretation would be that GPC of NMP-PAni (EB or ES) systems just tells us about the retention time (adsorption-desorption process) of NMP-dispersed PAni particles in the GPC column, whereby the "high molecular weight fraction" would be the bigger particles (here: secondary particles, i.e., aggregates of primary particles), and the "low molecular weight fraction" peak (higher retention time) represents the fraction of the smaller (primary?) particles. Upon the addition of LiC1 or m-cresol, we happen to desaggregate (-- disperse) the bigger particles, the equivalent peak disappears, and the peak representing the smaller particle fraction becomes the only and increased peak.

2.5.2.9. Magnetic Susceptibility of Polyaniline in "Solution" Cao and Heeger reported [65] electron spin resonance measurements of the protonated form of polyaniline (protonated with campher sulfonic acid and dodecyl sulfonic acid). First we note that the room temperature magnetic susceptibility is more or less equal for PAni-CSA in m-cresol or -DBSA in xylene, in cast films, or in polyblends with PMMA (around 3-4 x 10 -5 emu/mol). In free-standing films there is a small temperature dependence, in the solvent systems there is none. The peak-to-peak linewidths of the electron spin resonance (ESR) signals, somewhat smaller for the PAni-CSA compound compared with the -DBSA, both show no temperature dependence. In the solvents (m-cresol, xylene) the respective compounds show the same magnetic susceptibility as in the free-standing film, but now show no temperature dependence at all. The ESR signal linewidths sharpened somewhat, but not significantly. The magnetic susceptibility of PAni-CSA in m-cresol is independent of the PAni concentration (concentration values between ~ 10 -4 and 10 -1 weight%). The linewidth of the ESR signal sharpens with increasing concentration. Also in polyblends with PMMA, the susceptibility is independent of PAni concentration, even though a conductivity breakthrough is observed at a critical concentration of 1% because of dissipative structure formation (cf. [16, 31 b, 43]). The results are virtually independent of the solvents used. Even such different solvents as m-cresol, formic acid, and xylene do not produce significantly different values. Because of the stability of the metallic state in the solvents, the authors themselves suspect "that the 'solution' [quotation marks by Cao and Heeger] might actually consist of micro-aggregates." However, based on the observation that the magnetic susceptibility in "solution" is constant over a wide concentration range, they concluded that "micelle formation" seemed unreasonable, but without giving further reasoning. The first important conclusion to be drawn from these results is that as there is no difference at all in the magnetic susceptibility of PAni in solvents, as 100% pure film, or in a polyblend, there is no difference in the structure or size of the metallic unit, irrespective whether we call it a "metallic island" or a "metallic core"; hence there is no change in the intrachain electronic interactions when PAni is transformed from the solid state into a solvent. This means that the solvent does not interact with PAni between the chains, where they form a metal. The coherence length is not changed. The solvent does not change the chain state from being incorporated in a metallic primary particle to a truly dissolved, solvated chain (e.g., becoming a random coil). Here, we note an important contradiction between this clear conclusion and the conclusions made by the same group on the basis of light scattering (cf. Section 2.4.1.1 and [52]).

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CONDUCTIVE POLYMERS AS ORGANIC NANOMETALS

In light of the "dispersion hypothesis," these observations are easy to understand: PAni consists of primary particles close to 10 nm in diameter containing a metallic core ~ 8 - 9 nm in size. These particles are unchanged as such, they are only separated from each other more or less completely by solvents or PMMA matrix, when transferred into media other than air. Solvents are acting principally in the same way as the polyblend matrix PMMA: PAni is dispersed in the medium and its surface is wetted by the solvent (or PMMA). These conclusions are further supported by the fact that solvents as different as m-cresol and decalin do not change the magnetic susceptibility. The only change one can observe is some sharpening of the linewidths, which one would have to assign to different interaction possibilities between the particles: if they cannot interact at all (too great an interparticle distance at low concentrations), the linewidth is broader; if there are interparticle contacts (in the pure film, at higher concentrations in blends and the same in the dispersing solvents), then the linewidth becomes somewhat sharper. The particle size itself does not change, only the flocculation degree. Note: Also in solvents, dispersed particles produce complex structures (flocculates), which may be elongated chains or complex three-dimensional structures (cf. [3 lb]). Furthermore, the observation of temperature dependence in the pure film in contrast to no temperature dependence in solvents can be explained by the same fact: in the pure film, one measures the temperature-activated tunneling, which is absent when no tunneling can occur.

The work by Cao and Heeger is an important contribution to the understanding of polyaniline in solvents. It is a further clear hint that such systems are colloidal in nature, where the metallic properties do not change between the solid state and the dispersed state in solvents or blends (cf. also [26]). 2.6. Conclusions It was the purpose of this section to present a complete description of all arguments supporting the following conclusions: 9 Conductive polymers (organic metals) form dispersions (sols) with suitable solvents. And the opposite hypothesis: 9 Conductive polymers can build true solutions with appropriate solvents. Thermodynamic considerations---especially when looking at the enthalpic term in the free energy of solutionmshow that the necessary introduction of the melt enthalpy as well as the lattice energy that must be overcome will prevent any possibility of making true solutions. The lack of direct experimental evidence for effectively solvated single chains is in accordance with these considerations. On the other side, numerous experimental hints support the "dispersion hypothesis." Thermodynamic aspects show conclusively that the surface tension of conductive polymers (organic metals) is very high because of very strong intramolecular forces, so that their primary and secondary particles will have solvents (water or others) adsorbed on their surface, reducing surface energy. Dispersed systems of OMs/OM in solvents can be made as soon as the solvent is capable of reducing the previous surface energy. Metallic conductivity and insolubility of organic metals (conductive polymers, which are polymeric salts) go together and are linked together, because they are based on the same intramolecular electronic interactions and hence on very strong intramolecular forces. The principal insolubility and the feasibility of nanoparticulate colloidal dispersions are the crucial precondition for the industrial application of organic metals.

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WESSLING

3. APPLICATIONS OF ORGANIC METALS EMERGING FROM BASIC SCIENCE: MACRO-EFFECTS OF NANOPARTICLES 3.1. Introduction Practical applications of organic metals (or: conductive polymers) like polyaniline (PAni) have been thought of since the very beginning of the research in this field. But what had originally begun with a kind of euphoria, reaching even daily newspapers all over the world, has gone through a deep valley of disappointments since 1989. The strongest motivation for the previously broad support of basic and applied research by the industry and by public funding was the hope of developing "polymeric" accumulators and batteries using OMs. As this hope vanished (because of the--at best---only equivalent charge storage capacity compared to conventional inorganic systems), most bigger companies stopped their work. Earlier attempts by Bridgestone-Seiko in 1987 at marketing a battery [66, refs. 10 and 33] were stopped in 1992. Now a new concept is attracting a lot of interest: "plastic LEDs" and "plastic lasers" [67], which are based on neutral, not conductive conjugated polymers. Other applications, although at least as challenging and interesting as batteries or LEDs and even much further advanced in the market, have not yet found any comparable attention by the science community or the broader public. So most of our dispersion-oriented researchl8--both fundamental as well as application-oriented--is still widely unknown. No application would ever be realized if OMs could not be processed from an appropriate polymerization over intermediate process steps up to the final product. This problem was far from being trivial, as OMs are insoluble and unmoldable. Moreover, this problem was also not unproductive scientifically: as we managed to find out why they are insoluble and unmoldable, we learned a lot about important basic properties of the OMs, and we even could overcome these drawbacks, or, as I would say, have learned to live with insolubility and unmoldability with the help of dispersion. Both areas, batteries and LEDs, require the OM (or undoped conjugated polymer, respectively) in a pure unblended form, as the active material. For batteries, the idea was to polymerize directly into the form of the later electrode. No processing research was thought to be necessary. This was why most scientists active in OM research did not realize the importance of basic research devoted to materials science and processing aspects. With the end of battery research, the need for processing became evident, as new ideas connected with LEDs emerged. 19 These demanded a kind of solvent-based processing technique. Based on work by Elsenbaumer et al. [32], a variety of "soluble" conductive polymers and solvents, even for "doped" polyaniline, have been proposed. This question was discussed in detail in Section 2. Here, only conductive polymers will be discussed. Most other applications or potential applications require a raw material form that can be processed further into an end product. In the meantime, our very early concepts [68] of preparing polymer blends between OMs and various insulating polymeric matrices have been followed by several groups, often using a somewhat different technical approach, but without changing the basic concept: blends are always dispersions of the OM in a matrix polymer, and conductivity above a certain critical volume concentration is possible only due to very complex self-organized structures [16, 69]. There are several techniques available for preparing polymer blends (often called "composites," which is not the correct term) composed of OMs and an insulating polymer matrix. For an overview,see [24b]. Otherproduct concepts like electrolytic capacitors, as have been realised with TNCQ salts [66, ref. 30], are often approached by polymerizingpolypyrrole or polyaniline directly on the substrate; such a mostly unreproducible and "dirty"procedure can be replaced by using solvent-born colloidal systems(dispersions). 18

19

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CONDUCTIVE POLYMERS AS ORGANIC NANOMETALS

3.1.1. OM Dispersions and Polymer Blends: Comparative Preparations and Benefits 1. Direct dispersion of a (fully polymerized, washed, and dried) OM powder (e.g., polyacetylene, polypyrrole, polyaniline, etc., today exclusively practiced with PAni) in a polymer matrix. The first realization of this concept was published by us in 1984 [68]; improvements based on a new technology for the polymerization of dispersible OM powders were realized in 1987 [70]. The technology described in [68] and [70] and in further improvement patents is independent of whether one is preparing a nanoparticulate dispersion in a polymer matrix or in a solvent, or with the help of solvents in a polymer matrix. 2. The technique most widely used in university laboratories is (or has been) polymerization in situ in the matrix polymer (cf. as one of the earliest examples, polyacetylene in LDPE [71 ]). The disadvantage is that the monomer must be able to diffuse into the matrix, and so must the polymerization agent. Furthermore, there is no possibility of purifying the resulting product, either the resulting polymer or the blend. Finally, such blends are not processable afterward without losing conductivity. 3. Another (better) option is to polymerize the OM directly on a latex (in fact, S. Jasne from Polaroid had proposed this route in the mid-1980s [72], without practical success, and it was again recently proposed by the Intch Company DSM [73]) or in a sterically stabilized colloidal form [74]. Both concepts are based on the idea that an OM polymer blend should be a dispersed system, but that unquestionably one could get around the very complicated dispersion task by starting with colloidal particles. This is not basically wrong; however, it was not taken into account that (a) Conductivity in a blend is not only a question of the presence of a colloidally dispersed conductive phase, but also of its interfacial structure. (b) The dispersed phase has to have the capability of self-organizing to flocculates, which is only possible with a very specific mechanism, 2~ first described in [69] (cf. also [15]). (c) The restrictions of the usability in various polymer blends are caused by the colloidal matrix system (most lattices are water bomemwhich might be an advantage if water-based blends are the only goalmhence most other water-free matrix polymers are not accessible). (d) There were problems with the recovery of the latex or (even more) the sterically stabilized colloidal system before the next process step was begun. We therefore had decided very early, before the first proposals of this kind became public, not to follow this route, but to strictly polymerize and recover a dry (dispersible) OM powder, even if the dispersion process itself proved to be the toughest technical and scientific question of all in this whole context. 4. A variation of this concept is to disperse (which is the precise term, in contrast to "dissolve") the OM (PAni) in a solvent, preferably with the help of ultrasound to create fully dispersed nanoparticles, and to mix this with a dissolved matrix polymer. Such an approach was described by us in the early dispersion patents [68]. Other groups have confirmed the principal feasibility of this approach by "counter-ion induced processability" [75] or by dispersing the neutral emeraldine base in a suitable solvent like NMP and mixing this dispersion with a solution of the matrix polymer (e.g., PVP, PMMA, etc.), leading to blends, 20 The delamination of the adsorbed matrix polymer monolayerand the formationof a joint layer surrounding all flocculatingparticles in the complexnetwork structure.

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WESSLING

which had to be post-doped to show conductivity (cf. [76] as one of the more recent examples). It should be noted that in contrast to the opinion expressed by these authors, such blends should never be considered "compatible," as the phase size of PAni will be around 50-100 nm, which is not resolvable by light microscope. This is confirmed by [75b], in which the authors show comparable network structures of aggregated submicron particles, as we have shown earlier [15] for blends resulting from "dry" dispersion techniques. This also means that solvent ("solution")-made and processed blends are in fact dispersions. Such blends do not principally differ from other OM blends that are considered nonequilibrium two-phase systems [ 16], in which the conductive phase is the dispersed (and above the critical concentration: flocculated to a dissipative structure network) phase. This has also been supported by the principally equal conductivity and transport properties, as can be seen by comparing the results in [75b] and [23b and 24a]. 5. A further variation was proposed by the Finnish company Neste Oy, which attempted to prepare a "melt-processable polyaniline" [77]. 21 It still remains a matter of debate what the melt behavior they observed resulted from, but it was evident that the resulting blend again is a two-phase system with nanosized network structures formed by the dispersed PAni phase. Up to now, none of alternative approaches 2-5 (for a review, cf. [78b], a review of processing techniques for conductive polymers) found any practical application, and they do not seem to offer an advantage over the dispersion concept favored by us. Although our own research has outlined a complete new theoretical concept, there is still a great need to invest further research into the fundamentals of blend technology, such as dispersion, interfacial phenomena, conductivity breakthrough at the critical concentration, electron transport phenomena in blends, and others. It is not the purpose of this section to review these aspects in greater depth than in Sections 1 and 2. In the context of this handbook, it should be sufficient to summarize them as follows: the basis of any successful OM (PAni) blend with another (insulating and moldable or otherwise processable) polymer is a dispersion of OM (here PAni, which is present as the dispersed phase) and a complex dissipative structure formation under nonequilibrium thermodynamic conditions (for an overview, see [67]; for the thermodynamic theory itself, see [ 16]; for detailed discussions, cf. [79]). Dispersion itself leads to a drastic insulator-to-metal transition by changing the crystal structure in the nanoparticles (see Section 1). It is surprising that dispersion-generated polymer blends with PAni show a typical metallic behavior (see [21], [23b], [24a], and [68]), and some even exhibit an increasing conductivity with decreasing temperature (for the first 50--70 K below room temperature) (see [23b] and [24a]), in contrast to the raw PAni used, and at any temperature conductivity a several orders higher compared to the raw PAni (measured as pressed plate). But our dispersion theory is able to explain this phenomenon [79a, e.g., pp. 566-567], and the new findings (Ph-N-Ph angle < 140 ~ for metallic PAni) are a further support for the theses. The macroscopic dispersion step is a tool for very reproducible and crucial processes at the nanoscale. And if properly understood, these are the basis for important macroscopic applications based on nanostructures. Many proposals have been made in which OM (mainly PAni) blends could be used. Some of them are visionary and creative, like roofs coated with photovoltaic cells, wallpaper with electrical heating capability, heated textiles, dust filters, and many more [78]. Often the expectation that such blends would have properties superior to those of carbon black-filled ones, in conductivity or in mechanical or color aspects, guided the 21 It was introduced at the international plastics show "K 95" in DiJsseldorfas Neste Conductive Polymer NCP (as a trial product; this is not available in a commercial scale) and withdrawn shortly after.

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CONDUCTIVE POLYMERS AS ORGANIC NANOMETALS

vision. Whereas PAni blends can deliver actually somewhat higher conductivity values (up to 50 S/cm, the best value for laboratory samples (see [23b] and [24a]), 5 S/cm for technical scale [80]) compared to those of carbon black compounds (best values around 0.5 S/cm), 22 the other presumed advantages are not there. Nor are mechanical or processing properties, electrochemical stability under applied voltage and current (like for heating devices), or the color aspects of PAni blend any better than with carbon black compounds. There is also often a misunderstanding in the scientific community that carbon black compounds are a relatively bad compromise. This is not the case, as many highly performing compounds have been developed and have been in commercial use for many years (cf. [79b, Section 11 ]). Both systems, however, the PAni blends and the carbon black compounds, are based on the same structural principle: the conductive phase is the dispersed phase in nanoscale, which suddenly self-organizes into complex networks above the critical concentration [ 15]. This is the reason for all properties, including mechanical or rheological, and for abrasion. But most of the poorer products have been replaced by products based on subtle and successful developmental work (cf. [79b, Section 11 ]). As a consequence, the market does not ask for replacements of carbon black compounds, which provide more or less comparable properties, and this at a higher price. (Neste Oy offered PP and PE blends with PAni as a replacement for carbon black compounds in 1995 and stopped the program in 1996.)

3.1.2. PAni and PAni/Polymer Blends: Some Key Advantages A new material, like OMs, and blends based on them, will only find a way to those markets, in which either a drastic cost reduction (which is not to be expected) or new useful properties or new useful combinations of properties can be offered. PAni and its blends are new in the following respects: 9 Their conductivity is metallic (more precisely: comparable with mesoscopic metals [ 108], or in other words, "nanometals.") 9 In the galvanic series, PAni and its blends are positioned fight below silver. 9 Thin layers (3-50 #m) are transparent, although green, with conductivity values between 10 -9 and 10 -1 S/cm. At higher conductivity, only very thin layers (less than 3/zm) are semitransparent. 9 PAni and its blends are electro- and chemochromic (i.e., they change color upon application of a certain voltage or appropriate chemicals); they also change their conductivity together with these chemical changes: green/metallic; blue/neutral base/insulating; colorless/reduced state/insulating. 9 The three accessible oxidation states reproducibly connected with three colors (cf. Fig. 38) can also be accessed in blends and can serve as different states of PAni in catalytic processes. Applications like corrosion protection by ennobling and passivation and manufacture of printed circuit board surfaces composed of the organic metal polyaniline (Ormecon) are based exclusively on this unique set of properties and use most of the properties in parallel. Here this new materials class is able to offer a penormance that cannot be matched by any other material or by another conductive polymer. To realize this performance, commercial products are actually being introduced into the market. A review by J. Miller [81] is still relatively accurate, except for significant technical and market progress in transparent coatings (3.2.1), corrosion protection (3.2.2), and printed circuit board production applications (3.2.3). More applications like EMI Zippefling Kessler, technical data sheet product 400266, now produced and sold by Clariant Masterbatch GmbHfor the commercialuse as electrode material in the zinc-brominebattery of PowerCell, Austria.

22

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WESSLING

shielding (3.2.4) or "smart windows" (3.2.5) and others are still under development and demand further improvements of the basic PAni properties.

3.2. PAni Dispersion and Blend Applications

3.2.1. Transparent Coatings It is not possible using carbon black compounds to achieve any kind of (semi-)transparent and still antistatic or conductive products or coatings. For electronic products packaging and handling purposes, however, this is important for preventing electrostatic discharges while still maintaining a capacity for optical inspections. The industry has met this demand by vacuum metallization or humidity dependent antistats. Indium-tin-oxide (ITO) ceramic powders and other comparable inorganic (transparent) conductors have also been proposed as fillers for transparent coatings or as pure thin layers prepared by deposition methods. These techniques show several technical disadvantages, like 9 brittleness 9 humidity dependence (i.e., they do not function in all climates) 9 poor long-term performance. At least in some areas, OM coatings have been shown and in the future will prove even more to be a well-performing alternative. PAni blend coatings are made commercially by an extreme dispersion of PAni powder in suitable coating systems [82]. The dispersed phase is ~70 nm; the critical volume concentration, where sudden conductivity breakthrough occurs, is around 1%. These are the preconditions under which coatings with a layer thickness of 1-20 # m are transparent (with a transparency of up to 95%). The coatings are green, hence they absorb at ~350 nm and, beginning with ,-~650 nm, in the near-infrared. Depending on product type and coating thickness, conductivity values between 10 -9 and 10 -1 S/cm are achievable (in resistance values 109 tO 102 ~1[-]) (cf. Table for a PMMA coating).

Layer thickness (#m)

Resistance(~)

Transparency(%)

0.4

107-109

95

0.6

106

90

0.8

104-106

85

1

103

75

Coating systems for spray, dip, drawbar, gravure, and roller coating techniques, as well as for screen or flexo printing on a variet2y of substrates (like plastics including polyolefines, or glass, paper, cardboard, and others) have been developed and are in practical use. The various products also offer different hardnesses, ranging from 2B to 4H. UV and EB curable systems are also available. Most of the products are actually solvent-borne (mainly isopropanol, butanol, toluene, or xylene-based), but water-borne systems are also becoming available. Comparable systems could be designed for more than just two properties (conductivity + transparency). Electrochromic, indicator, and sensor functions could also be envisioned for coatings based on blends.

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CONDUCTIVE POLYMERS AS ORGANIC NANOMETALS

Another transparent (and in this case even colorless) coating system based on ethylenedioxy-thiophene (EDT) is offered by Bayer AG. The monomer is polymerized directly on the substrate, an Agfa film, to serve as an antistatic layer for photographic films that is virtually colorless. Up to now, this coating application is limited to relatively low conductivity levels, but has its unquestionable value due to the very weak absorption in the visible range. The costs of the monomer and the need for polymerization on the substrate to be coated are additional limitations. Bayer intends to offer a latex with a prepolymerized PEDT coating on the latex particles. (The monomer is also coming to be used as a polymerizable agent in a through-hole-plating process for printed circuit board production, which was previously performed using pyrrole.) 3.2.2. Corrosion Protection

About 10 years ago, deBerry [83] found that a reduction of the corrosion rate could be achieved by electrochemical coating of prepassivated steel (in passivating environment) with polyaniline (from aniline monomer). He supposed that the preformed passive state of the metal was maintained by the PAni layer. Troch-Nagels et al. [84], however, concluded that PAni, unlike polypyrrole, after electrochemical deposition under comparable conditions, did not offer any corrosion protection. Starting in 1986, we tried to coat steel that was not prepassivated, under nonelectrochemical conditions, but with a paint containing dispersed polyaniline. We wondered if some kind of corrosion protection--by whatever mechanism--could be created by an interaction between a dispersion paint and a normal metal surface. This would be, in contrast to previous approaches, a nonelectrochemically applied PAni on a nonprepassivated metal surface. 1987, we achieved the first promising results [85]. Subsequent work (also published in various patents) 23 confirmed the previous findings, but did not show an exciting "quantum leap" in corrosion protection. Moreover, it was hardly reproducible and did not convince any paint manufacturer. It was only in 1992-1993 that we finally found out, after an in-depth evaluation of the interactions between various metal surfaces and coatings of polyaniline (applied as pure dispersion or as dispersion paints), that a remarkable corrosion potential shift ("ennobling") and an iron oxide layer formation ("passivation") together lead to a significant anticorrosion effect [86, 93]. In a study with Elsenbaumer et al. [87], we found out that the corrosion rate was reduced by a factor of up to 10,000! The iron oxide that formed between the metal surface and the polyaniline primer coating was determined to be Fe203, later confirmed with even clearer X-ray photoelectron spectra (XPS) [24b]. In the meantime, we have evaluated the reaction mechanism by which polyaniline as a redox catalyst mediats the reaction between iron (or in an analogous way, other metals) and oxygen/water to form the passivating oxide layer [88] (see Fig. 33). Parallel product development towards commercially useful and competitive anticorrosion coating systems has led to various products that have been successfully tested under practical and various laboratory conditions [89] and found their place in the market in the meantime. It also became evident that the conclusions that were drawn from the basic research on dispersion and the corrosion prevention mechanism of polyaniline have led to superior performance compared to other systems, which have been proposed as alternative techniques [90]. This is probably due to the fact that the alternative methods do not fulfill all chemical, physical, and technical requirements that a corrosion prevention technology based on polyaniline in technical scale has to. The technique proposed by the NASA/Los Alamos group [90a] 24 is not only not practical for the general coatings industry, but also does not 23 For example, PCT/US93/00543, by Zipperling Kesslerand Allied Signal, priorityJanuary 1992. 24 A pure neutral PAnilayer deposited from "solution" (dispersion), postdoped, and coated with a top coat.

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EB

J4 H + J

~

ES + 4 H +

"--'------'-"'~e, 0.5 O2 ~2H+

z2

H-

~- L E

H20 2 Fe

2 F e 2+

0 2 -I-

9 2 F e 3+

2 H20

~ Fe20 3

, 4 OH

Fig. 33. Reaction scheme. Reprinted from B. Wessling, Synth. Met. 93, 143 (1998) with permission. 9 1998Elsevier Science.

meet industrial requirements in terms of adhesion or reproducibility and did not prove to have a superior performance compared with high-performing coating systems. The Monsanto variation [90b] 25 has not yet proved its applicability and performance under practical conditions. The DSM concept [90c] 26 is actually only a form of polypyrrole that is potentially useful as a paint additive, but to our knowledge has not yet demonstrated any anticorrosion performance in real paints. We conclude from our basic chemical, physical, and theoretical evaluations of the polyaniline interactions with metal surfaces leading to corrosion prevention, and from our practical experience with the development, testing, and marketing of various PAnicontaining anticorrosion paints (primers) in numerous applications, in widely differing corrosion environments, and summarizing the advantages and disadvantages known up to now, that the following requirements have to be fulfilled by a PAni-containing coating for principally successful (and commercially attractive) applications: 9 The paints must contain well-dispersed (maximum 70-100-nm particle size) PAni. 9 They must be conductive (emeraldine base-containing paints have no ennobling or passivation, but a nice "inhibition" effect, leading to an anticorrosion efficiency many orders of magnitude lower compared to the conductive form) and metallic; hence they must be a nanometal. 9 The PAni coating (regardless if pure or dispersed in paints) must adhere well to the metal surface, especially under the corrosion conditions? 9 The paints must exhibit metallic properties to ennoble the metal surface. 9 They must offer chemical reactivity (catalytical activity for the reaction path, as shown in Fig. 1) throughout the whole primer volume. 9 The primer and the complete coating system must be chemically and mechanically stable, also with regard to (interfacial) adhesion (Ormecon polyaniline and their Corrpassiv paints are practically "infinitely" stable; polypyrrole is not stable, even under ambient conditions). 9 Complete systems have to be designed for each application field and technique, 27 because a PAni primer itself does not work properly enough alone or under all practical applications. A "soluble" polyaniline, presented as "PANDA."CompareMonsanto technical information. A water-borne latex, presented as "ConQuest" (cf. DSM technical information). Ormecon Chemie developed and produces specially designed coating systems (Corrpassiv) for steel, aluminum, galvanized steel, and other metals; for general industrial or very aggressive(chemical) corrosionenvironments; for maritime corrosion; and for various application techniques, like brush or spray coating, roller coating, dip and spin coating, coil coating and others.

25 26 27

560

CONDUCTIVE POLYMERS AS ORGANIC NANOMETALS

The design and production of PAni-containing coating systems with commercial applicability asks for much more than just the application of PAni to a metal surface by whatever method. It requires a full and deep understanding of corrosion prevention chemistry and physics itself, of the interfacial interactions between the PAni primer and the metal surface as well as those between the different coating layers, and especially of the science of OM dispersion. In essence, only 1% of OM in the paint, which has to form a 20-#m primer layer containing a nanosized complex OM particle network, provides a drastic change in the metal surface behavior: it stops corroding. This can be measured, for example, by scanning the voltage potential and by impedance spectroscopy [91 ]. Here, the nanostructures cause the following macroscopic consequences: 9 a reduction in the delamination velocity from 30 to 60 # m to close to zero (3 ~zm/h) 9 an increase in the overall coating resistance by many orders of magnitude These elements are the basic of several exciting applications [92] that have been achieved with polyaniline anticorrosion coatings. One of the products has been designed as a coating for boats and ships (Skippers Corrpassiv [92]). It consists of three coating layers, a polyaniline dispersion primer, an interprimer, and a top coat, in different compositions, depending on whether it is to be applied above or below the water line. In comparison to well-performing coatings of the previous state of the art (barrier coatings), the new coatings offer a lifetime about five times longer for the coated vessel. Many hundred boat owners, several shipyards, and bigger container vessels are using the product in real life under commercial conditions. A continuous test in an Icelandic harbor shows its superior performance over that of previous leading anticorrosion coatings. Another heavy corrosion environment is waste water management. A two-layer coating comprising a polyaniline dispersion primer and an epoxy top coat (Corrpassiv 4900) are being used and specified for suburban hydraulic waste water management system, allowing the replacement of stainless steel hydraulic cylinders with ordinary steel, with an improvement in corrosion performance. Furthermore, in a hydraulic system being used in Airbus manufacture at Airbus Industries, Hamburg, stainless steel has been replaced by general steel coated with the same product. Variations of this product (for outdoor exposure and for application on prerusted surfaces) have been designed and used in the first real applications in biofilters, waste water treatment facilities, on several industrial sites, bridges, and a pipeline. 28 A further advantage of polyaniline dispersion coatings and complete coating systems including interlayers and top coats is its applicability to metal substrates other than steel. Aluminum is subject to so-called filiform corrosion, which can be effectively beaten by suitable products, in this case Corrpassiv 4901 (a different kind of primer and top coat); the performance was tested by an independent institute (see footnote 28). The same primer was also successfully tested in the meantime in various applications on magnesium. 3.2.3. Printed Circuit Boards

After 3 years of development, including 2 years of practical testing in the industry up to commercial scale, we can report (text written 1998) an interesting new application: the preparation of the surface finish of printed circuit boards. The places where the diodes, resistors, etc. have to be mounted and connected to copper-based printed circuits have to be solderable for a period of at least 1 year in all climates. This is tested in the industry by >4 h at 155 ~ followed by a complex solderability testing procedure. 28 Corrpassiv test report on filiform corrosion by Forschungsinstitut ftir Pigmente und Lacke, FPL, Stuttgart, July 1996.

561

WESSLING

Current density - potential curves of copper uncoated/coated with Organic M e t a l

20 Cu uncoated

18 16 14 12 10

8

Cu coated with ORMECON|

6

E o

4

E

2

=9

0

==

"ID

-2"'

-----t~

,2

t

-1

-0,8

--

I

-0,6

I

t

-0,4 ~

-

-

0 0,2

0,4

0,6

I

"1

t

I

0,8

1

1,2

1,4

---

t

1,6

' --t

1,8

t

I

2

2,2

2,4

-6 -8

-10 -12 -14 -16 -18 -20

potential U-Hz IV]

Fig. 34. Potential curves of copper. Reprinted from B. Wessling, Synth. Met. 93, 143 (1998) with permission. 9 1998 Elsevier Science.

Copper alone does not meet this requirement at all, whether it is coated with organic coatings (like benzo-triazoles) or chemically deposited tin. Only gold (with a Ni interlayer), palladium, or a thick layer (10-17 #m) of solder tin (applied by a melt and then a hot air leveling process) do the job. We have found that a very thin (80 nm in average) coating of PAni deposited from a water dispersion, 29 followed by a special chemical tin deposition of only 0.5-1 # m thickness, allows us to achieve solderability stability for more than 4 h at 155 ~ plus a full industrial soldering process. Here, PAni's function is fourfold: (1) it passivates the copper (see Figs. 34 [93, Fig. 1] and 35); (2) it catalyzes the tin deposition, so that also with the increased Cu concentration used tin deposition baths, only pure tin is deposited (see Fig. 36); (3) the interdiffusion of Sn and Cu is inhibited; (4) the oxidation of the final tin surface is decreased. This application is based on the most advanced dispersion technology for PAni in water. In contrast to other approaches, nonfunctionalized polyaniline has been used as the raw material. This makes it possible to start with a generally commercially available polyaniline powder (Ormecon) instead of special polyaniline derivatives for different applications 29 This is the first commercial dispersion of PAni in water (cf. Ormecon Chemie data sheet Ormecon CSN, PCB 7000).

562

CONDUCTIVE POLYMERS AS ORGANIC NANOMETALS

Fig. 35. Copperpassivated by Ormecon. It becomes golden with tempering. Reprinted from B. Wessling, Synth. Met. 93, 143 (1998) with permission. (g) 1998 Elsevier Science. See also Plate 7.

or dispersion media. It shows, furthermore, the generally applicable dispersion concept. The application on printed circuit boards is a long-term and high-end application and is specified on the basis of the long term stability of our product. 3.2.4. E M I Shielding

The metallic properties of OM, an uncomplicated processing technology in the form of coatings, and the potential of direct thermoplastic processing into electrically conductive plastic housings suggest the possibility of using OMs as a material for shielding against electromagnetic fields. All present techniques using conventional plastics (filled with conductive fillers) or zinc flame spray coating are commercially unattractive and technically insufficient, especially in view of the increasing demand for EMI shielding efficiency in our modem world. This has

563

WESSLING

Monochromated

Ai Kcr

LMM l,d~llll,, /

=

!

5~..t r~/

LMM 560

[

3p

I

. . . . . . . . .

570

f " ~ ' - ~ Cu ~ + Cu l+ 2pvt =I 932.8 eV

580

3s

[I

" 930

0

I

200

~ " '940 . . . . ''

I

I

I

I

400

600

800

1000

950 I

1200

Binding Energy ! eV

Photoelektronenspektrum von Kupfer (15 ~tm Leiterplattenmaterial) (c) Fig. 35.

(Continued.)S e e

564

a l s o P l a t e 7.

CONDUCTIVE POLYMERS AS ORGANIC NANOMETALS

Monochromated A! Keg Cu" Cu' I I

-~.~

\

Cu" and Cu'

5

-580

::222., ............ , . . . . . . . . 930 940 950

-

-

0

I

i

1

200

400

600

1

800

I

1000

1200

Binding Energy / eV Photoelektronenspektrum von Kupfer nach Eintauchen in O R M E C O N | PCB 7000 (d) (Continued.)

F i g . 35.

induced a trend back to metal housings in recent years, at least for medium- and high-level EMI shielding specifications. Several single exceptions do not contradict this statement. A (thermoplastic) polymer blend with OMs or a powerful OM coating, in principle, would meet all demands, as the conductivity could be even throughout the whole mass, in contrast to metal fiber or flake-filled plastic compounds (problems in comers and small tips). Highly conductive polymer blends using polyaniline have been developed by us for EMI shielding purposes [94]. By dispersing polyaniline in a matrix polymer like PVC, PMMA, or polyester, conductivity of ~20 S/cm, and in some cases up to 100 S/cm, can be achieved. Such values, which are higher than has been achieved so far by incorporating carbon black in polymers, promise a very high standard of EMI shielding. The shielding effect is up to 25 dB higher than with carbon black compounds and lies, depending on the frequency of the electromagnetic interference, in the region of 40-75 dB for both near and far field. But a considerable improvement in mechanical values is still needed, however, preferably conductivity levels that are higher by 1-2 orders of magnitude, as shown below. This is why we are actually not offering such blends for commercial purposes. Together with Shacklette et al., we had systematically investigated the extent to which the shielding effect depends on conductivity and coating thickness [79b, Section 5.4, ref. 15]. In general the shielding effectiveness (SE) of a material is defined as the ratio of the transmitted energy (P0) to the arriving radiation energy (Pi): SE -- 10 l o g/I, - ~pi - , --20 l o g ( E i ~ [dB]

\ Po]

565

(18)

WESSLING

previous generation immersion tin without ORMECON

0,20 Cu-increase 0,15

i,,-,,,i m ===

o 0,10 E

=-._i

0,05

Tinned Cu-Surface [m=/I]

0,00

,

0 , 0

9

,

'1

,

,

0,2

,

i

,'

9

0,4

,

=

0,6

9

'

, "

,

|

,

0,8

,

,

1,0

/\

/\ Solderability OK Cu:Sn ~ 1:1

unstable /~ Solderability

Solderability /~ NOK

steadily increasing Cu:Sn ~

Cu:Sn 2.5:1

(a) Fig. 36. Lineartin deposit on copper after ORMECONpretreatment. Reprinted from B. Wessling,Synth. Met. 93, 143 (1998) with permission. 9 1998 Elsevier Science.

Useful shielding effectiveness values for commercial applications in electronic housings are in excess of 40 dB at frequencies of 1 GHz. For military applications and for near-field shielding requirements, even better performance in the region of 80-100 dB is required. As long as the conductive component is uniformly and well dispersed in the polymer matrix, the shielding effectiveness proves in theory and in practice (Fig. 37) to be a function of conductivity and thickness. Shacklette and Colaneri [79b, Section 5.4, ref. 15] have developed a correlation function describing this dependence. For near-field shielding, just as for far-field shielding, it is possible to approximate a general expression by means of the limits of the electrically thin and electrically thick samples. At the limit of an electrically thick shielding (d/d >> 1 or w >> Wc), near-field shielding effectiveness can be approximated as S E - 10log

c2o" ) d 16e0w3r2 +20-~log(e) [dB]

(19)

The first term on the fight-hand side of the equation is interpreted as the shielding due to reflection, and the second as the shielding due to absorption. It is expected that the

566

CONDUCTIVE POLYMERS AS ORGANIC NANOMETALS

modern generation immersion tin C S N

7001 with ORMECON

0,20

Cu-increase 0,15

m m

o

E

0,10

=___1

0,05 Sn-decrease

Tinned Cu-Surface

0,00 0,0

0,2

0,4

0,6

0,8

1,0

continuous solderability up to 1.2 m= Cu:Sn continuously 2.2:1

(b) Fig. 36. (Continued.)

shielding due to reflection will decrease by ~,30 dB per decade of frequency increase (steps of 10). The entire near-field shielding will naturally never be smaller than the far-field shielding. As the wavelength decreases, the near-field shielding zone approaches the farfield shielding. Here, too, we find a difference in frequency dependence for electrically thick and electrically thin samples. The approximation d/d k T, ~k is large and the layers are flat over macroscopic distances. The transition occurs through a lamellar phase. The interest in microemulsions lies in their ability to solubilize simultaneously large amounts of oil and water and in the attainment of very low interfacial tensions (y 10 -3 raN.m- 1). Microemulsions can also coexist in equilibrium with various phases, the most widely studied being the so-called Winsor phase equilibria. Winsor I is a globular oil-in-water

582

BIOPOLYMER AND POLYMER NANOPARTICLES

Fig. 6. Schematicrepresentation of the phase equilibria coexistingin multicomponentsystems.(Source: Reprinted withpermissionfromE Candau, in "Polymerisationin OrganizedMedia" (C. M. Paleos, ed.), Chap. 4, p. 215. Gordonand Breach, New York, 1992 [56].)

microemulsion in equilibrium with excess oil, Winsor II is a globular w/o microemulsion in equilibrium with excess water, and Winsor III is a middle-phase bicontinuous microemulsion in equilibrium with both oil and water phases [49] (Fig. 6). The determination of the different domains in the phase diagram is a tedious and time-consuming study. In particular, bicontinuous and globular microemulsions are both transparent and isotropic, have a low viscosity, and therefore are hardly distinguishable. Clear evidence of the bicontinuous structure may be provided by transmission electron microscopy (TEM) [50].

2.1.3. Main Polymerization Processes The above structures may be polymerized to create small particles with different properties. These organized surfactant polymeric structures may be used in a wide range of applications, such as drug carriers, solar energy conversion, catalysis [26, 51, 52], etc. In this section, we present these polymerizations and their applications.

2.1.3.1. Polymerization of Surfactants in Aqueous Micelles Organized assemblies such as micelles, vesicles, and microemulsions are extensively used in high added value applications, most notably in the formulation of drugs and cosmetics and in the delivery of drugs. An important problem with these applications is the stability of the systems owing to the dynamic nature of surfactant assemblies. It has recently been proposed to decrease the dynamic character of these rather labile organized assemblies by polymerizing them. This can be achieved by the use of polymerizable surfactants. Much work has been performed in the field of polymerization of vesicles, monolayers, and multilayers [53, 54] (see below). In contrast, there have been only a few reports on the polymerization of micelle-forming monomers in the micellar state. This is probably due to the fact that vesicles are characterized by lifetimes much longer than those of micelles (weeks or months as opposed to 10 -3 to 1 s), which permits their topochemical polymerization, that is, with the preservation of the initial vesicle structure. In fact, the organized

583

NAKACHE ET AL.

structure should have a lifetime longer than the characteristic time for the polymerization (related to the reciprocal of the rate constant) to remain identical during the reaction. This case is observed with vesicles. In contrast, micelles may exhibit lifetimes that are fairly short, as compared to the polymerization time scale, leading to final materials strongly different from the starting structures. The lifetime of surfactant organized assemblies is mainly governed by parameters such as the alkyl chain length, the temperature, the ionic strength, etc., whereas the polymerization rate mainly depends on the nature of the polymerizable group. On the other hand, three main effects closely related to micelle formation may affect the polymerization kinetics and the structure of the final polymer [55, 56]. These are 1. Intramicellar concentration of the polymerizable groups. This value is close to that of bulk (~5 M) and is independent of the overall concentration in the solution. As a consequence, the polymerization rate is much higher in a micellar polymerization than in homogeneous solution. 2. The medium effect, which arises from the fact that the polymerizable groups are in a different microenvironment, depending upon whether the surfactants are in a micellar state or are molecularly dispersed in solution. This environment will also affect the polymerization rate, as well as the structure and properties of the final polymers. 3. The topochemical effect, which is the consequence of the organization of surfactant molecules induced by the micellar state. Many polymerizable surfactants have been synthesized [57-69], with all possible combinations of the various types (ionic, nonionic, and zwitterionic) and of classical polymerizable groups (acrylate, methacrylate, acrylamido, vinyl, allyl, diallyl, etc.). The polymerizable group can be located at different parts of the surfactant molecule, most often near the polar head or at the end of the hydrophobic tail, or even in the counterion (Fig. 7). The structure and properties of the resulting polymers are expected to depend a great deal on this structural feature. Most studies of polymerization in the micellar state have been performed in aqueous solutions. These micellar systems were characterized prior to polymerization by their critical micellar concentration (CMC) and their aggregation number, NA, by means of classical techniques such as electrical conductivity, fluorescence intensity, and the time-resolved fluorescence quenching method (TRFQ). The knowledge of these quantities is essential, as it will allow the selection of the experimental conditions under which the polymerization is performed (above CMC). Furthermore, some understanding of the polymerization mechanism can be gained from a comparison of the values of the micelle aggregation number and the degree of polymerization (DP) of the polymer formed. As a rule, the measured CMCs are close to those for the nonpolymerizable homologues [59]. The introduction of a terminal double bond increases the CMC by a factor of ~ 2 (equivalent to decreasing the carbon number by one unit) [70, 71 ]. As for conventional surfactants, the CMC of series of homologous polymerizable surfactants varies with the carbon number n of the surfactant alkyl chain according to the following equation [59, 71]: In

CMC

= A-

Bn

(2)

where A and B are two constants. The free radical polymerization can be initiated thermally, photochemically (UV), or under y radiolysis. The kinetic studies have shown the major role played by the micellar organization in the parameters that control the reaction. Thus, surfactants of low reactivity, such as sodium undecenoate [56, 58, 61, 72, 73] or allyldimethyldodecylammonium bromide [74] polymerize only above their CMC. This can be explained by high local concentration effects

584

BIOPOLYMER AND POLYMER NANOPARTICLES

OPolar head

eri;

H-Type Polymer

neriz~

T-Type Polymer Fig. 7. Schematicideal representation of head and tail monomeric and polymeric micelles. (Reprinted with permission [55].)

(close to that of bulk) and by the monomer orientation (strong hydrophobic interactions). On the other hand, surfactants with polymerization groups of sufficient reactivity (acrylate, vinyl, acrylamido, etc.) can polymerize both above and below [59, 60] their CMC (micellar state) or in apolar solvent (molecularly dispersed state) [75-77]. However, the polymerization rate is much greater above the CMC than in the molecularly dispersed state for the reasons discussed above. As for the molecular weights of the polymers, the results can be classified into two classes: (i) The surfactants with a reactive polymerizable group (acrylamide, styryle, acrylate) lead after polymerization to high-molecular-weight polymers (M > 106) [57, 59, 65, 75, 77, 78]. This excludes the possibility of intramicellar polymerization and implies micellar exchange during the reaction process. (ii) The surfactants with a polymerizable group of low reactivity (allyl type) yields after reaction low-molecular-weight polymers with a DP close to the micelle aggregation number before polymerization [56, 62, 73, 74]. However, several mechanisms other than a topochemical polymerization can account for such a result: transfer reactions to monomer, specific effects related to the nature of the initiator, or incomplete characterization of the system. For example, a degree of polymerization as measured by fluorescence probing corresponds indeed to the aggregation number of the microdomains where the probe is located,

585

NAKACHE ET AL.

but not necessarily to the DP of the macromolecule. These considerations stress the necessity of complementary techniques to a thorough characterization of the systems.

2.1.3.1.1. Polymerization Mechanism. The polymerization mechanisms can be listed according to surfactant CMC value, that is, the alkyl chain length [60]. (1) Case of low CMC surfactants (long alkyl chain). In the concentration range usually investigated (0.02-0.1 M, that is, C >> CMC), the monomer is essentially in the micellar state and the initiation starts within a micelle. The propagation mode will depend on the lifetime of the initial micelles, TM, which, in turn, is a function of the alkyl chain length. In general, TM is high (>>5 • 10 -2 s for C16 surfactants [60]). Because the time required for the addition of a reactive monomer to a growing radical is 10 -3 s [65], an oligomeric radical containing 20-200 units (that is, all of the monomers constituting the micelle) may be formed after a time close to TM. Such a radical will considerably stabilize the micelle and will keep growing to give rise to a polymer of high DE by being fed by monomeric surfactants coming from unnucleated micelles. This mechanism is quite reminiscent of emulsion or microemulsion polymerization. If the monomer reactivity is low, the oligomeric radical formed in a micelle after a time TM will be very short and will not prevent the micelle disintegration. This brings the radical into the aqueous phase and leads to low molecular weight polymers. (2) High-CMC surfactants (short alkyl chain). In the range of surfactant concentration used, close to the CMC (0.1-0.2 M), the fractions of free and micellized surfactants are comparable [60]. It results that homogeneous nucleation can effectively compete with micellar nucleation. The growth phase is complex because the lifetime of high-CMC surfactants is much shorter (TM < 10 -3 s for C8 surfactants), allowing at most the formation of a radical IM ~ by the addition of a monomer M to an initiator radical I ~ before micelle breakdown. IM ~ will propagate in the aqueous phase or acts as a germ for the formation of a micelle. Repetition of these processes can lead to high-DP polymers only if the reactivity of IM ~ is high enough. If not, low-DP polymers are obtained. In conclusion, whatever the reactivity of the surfactant monomer and its alkyl chain length, which determines the CMC and the micelle lifetime, the polymerization cannot be topochemical [60, 64]. The structure of the polymerized systems is also directly related to the alkyl chain length of surfactants [59, 60]. Ionic surfactants with long alkyl chains (C16) exhibit after polymerization a structure similar to that of a polysoap, that is, a flexible cylinder made up of hydrophobic microdomains of ~50 repeat units covalently linked and connected by short polymer segments. Ionic surfactants with short chains (C8-C 12) behave like classical polyelectrolytes. This difference in structure is the direct result of the competing hydrophobic attractions between alkyl chains and repulsive electrostatic interactions and the steric effect due to the covalent binding of the monomers. The relevant parameters are the alkyl chain length and the density of alkyl chains on the polymer backbone [79]. The polysoap structure, which consists of covalently linked hydrophobic microdomains, is quite attractive for many types of medical and pharmaceutical applications. Studies cover drug carriers and controlled release, and immunological adjuvants used to fix or stabilize enzymes or antibodies, and to lower the toxicity of polysoap-bound drugs [80]. The very small or zero CMC of aggregates of oligomers and polysoaps provides solubilization capacity, even at very low content of polymerized surfactant (microencapsulation).

586

BIOPOLYMER AND POLYMER NANOPARTICLES

2.1.3.2. Polymerization of Surfactants in Vesicles Polymerization of monomeric to polymeric vesicles was performed to stabilize relatively unstable monomeric vesicles [26, 32, 36, 81-90]. These polymeric vesicles have been the object of intensive researches because of their potential applications as energy conversion system, as drug carriers in medicine, or as media for the performance of biomimetic reactions [30, 82]. Polymerized vesicles are formed not only under topochemical conditions (i.e., from their monomer organized into monomeric vesicles), but also by sonication of polymeric surfactants, the homogeneous polymerization of appropriate vesicle-forming monomers, or by polymerization of polymerizable counterions, leading to vesicles covered by protective polymer [30]. Five synthetic approaches may lead to polymeric vesicles.

2.1.3.2.1. Addition Polymerization. The polymerization of vesicle-forming monomers (i.e., vesicles functionalized by an appropriate group, such as vinyl, acrylate, or methacrylate) leads to the formation of polymerized vesicles. Szoka and Papahadjopoulos [91 ] have reviewed the different methods for the formation of vesicles. They have shown that, depending on the method and conditions of preparation, multilamellar or unilameilar vesicles may be obtained. Polymerization of monomeric vesicles is accomplished by conventional methods, that is, with radical initiators, UV light, or y-rays [26]. Polymerization may be followed by NMR spectroscopy or by absorption spectroscopy. Depending on the location of the polymerizable group, polymerized vesicles can be linked at the polar head, at the middle, or at the end of the lipophilic chains. Headgroup mobility is preserved when the monomers are linked at the end of the long aliphatic chain and is lost otherwise [92]. The polymeric structures that may be obtained from a monomeric surfactant are shown in Figure 8 [82]. In the case of diacetylene monomer, polymerization leads to extremely rigid structures without the phase transition characteristic of their monomeric counterparts. In the case of diene monomer, more flexible polymeric backbones are formed. 2.1.3.2.2. Redox Reactions. The synthesis of such monomers is accomplished by the functionalization of vesicle-forming molecules, either with a disulfide group or with two thiol groups. The resulting monomer forms bilayer structures, which are then polymerized or, rather, "switched on" by oxidation. They may be depolymerized or "switched off" by reduction and used as membrane models. Otherwise, they may be polymerized in the vesicular phase by ring-opening polymerization initiated by a catalytic amount of dithiothreitol [93]. In all cases, polymerization results in improved vesicle shelf life. 2.1.3.2.3. Vesiclesfrom Amphiphilic Amino Acids. Functionalization of amino acids with long alkyl chains leads to the formation of vesicle-forming molecules. If a condensation reaction occurs between the amino acids, this results in the formation of polypeptide vesicles [94]. In this case again, these vesicles are stable but susceptible to biodegradation. 2.1.3.2.4. Vesiclesfrom lonene Polymers. Ionene polymers are formed by the interaction between a long chain dibromide and a ditertiary amine of the same chain length. After sonication of this polymer, vesicles are formed [95]. It should be noted that ionene polymers of alkyl chains of different lengths do not form membrane structures. 2.1.3.2.5. Vesicles from Preformed Polymers. Polymers prepared under homogeneous conditions from monomers form polymerized vesicles under the usual conditions [40]. A characteristic of these polymers is the introduction of a hydrophilic spacer between the polymerizable group and the amphiphilic moiety. The fluidity of the polymerized vesicles

587

NAKACHE ET AL.

AIBN ou hv

[I

[[

n

Fig. 8. Differentstructures of polymerized vesicles according to Fendler [26]. The surfactant vesicle polymerization induced by UV light irradiation or by an initiator (such as azo-bis-isobutyronitrile, AIBN) leads to the disappearance of the double bonds. Depending on the position of the double bond, vesicles may be linked either by their bilayers or by their polar heads.

due to the spacers is preserved, and this results in membrane structures mimicking biological membranes. However, it has been reported that spacers are not essential for preserving the "monomer-like" packing behavior of polymeric surfactants. Preformed copolymers were also tested for their ability to form bilayers of vesicles. 9 Different types of polymerized structures. Such vesicles exhibit improved stability while maintaining the monomeric state of the amphiphile within the bilayer. Four classes of polymerized vesicles may be distinguished (Fig. 9A-D) [32], according to the polymeric backbone location in the center of the bilayer (Fig. 9A), in the lipid chains of inner and outer monolayers (Fig. 9B), in the polar headgroups of each monolayer (Fig. 9C), or in a monolayer lipid membrane (Fig. 9D). Regen et al. [32] proposed a fifth type of structure with dioctadecyldimethylammonium methacrylate (DODAM) molecules. When polymerized, this structure corresponds to a lipid bilayer ionically encased within two concentric polymeric monolayers (Fig. 9E) [96]. Its size range is "~300-600 A.

9 Kinetics of photopolymerization in the vesicular phase [30, 82]. Among organized surfactant assembly polymerizations, the vesicular polymerization mechanism is not yet well understood, even though there have been some photopolymerization studies [31 ].

588

BIOPOLYMER AND POLYMER NANOPARTICLES

Fig. 9. Differenttypes of polymerized vesicles according to the polymericbackbone location. (Source: Reprinted with permission from [32]. 9 1984American Chemical Society.) Mechanistic studies have been performed for styrene-bearing quaternary ammonium surfactants at the end of the apolar tail or on the polar head, and the polymerization has been monitored by absorption spectroscopy. Continuous UV irradiation or irradiation by laser pulses decreases the styrene absorbance according to a first-order process. Calculated rate constants were found to be independent of the vesicle concentration but increase linearly with increasing intensity of the laser pulses. In isotropic ethanol solution, rates were slower compared to the vesicular medium and were found to be dependent on monomer concentration. This finding and the fact that the size remained unchanged suggest that polymerization occurs intravesicularly on the surface. The steps of the photopolymerization may be described as follows. The absorption of a photon h v excites the surfactant monomer, which then reaches the singlet excited state 1M*. Most of 1M* decays back to the ground state (via fluorescence or thermal deexcitation), another part goes to the triplet state 3M*. A part of 3M* decays to the ground state (via phosphorescence), and the remaining part interacts with another monomer or water to form a free radical M ~ The formation of a free radical via the singlet state is less probable. When the free radical is formed, it may tie successively to other monomers and may propagate to form the polymer chain. It may also be deactivated and return to the ground state, or it may react with oxygen or impurities. There are other possibilities that will not be detailed here. As a first approximation, a polymerization model is described by a vesicular surface assumed to be hexagonally packed, with each monomer surrounded by six other monomers. The photoinitiated free radical can react with any one of its neighbors to initiate polymerization, to disproportionate, or to form nonpolymeric products. Alternatively, the free radical may return to the ground state or react with oxygen impurities or the wall of the reaction container. The morphological consequence of this polymerization is a two-dimensional shrinkage that pulls together some of the aromatic tings and causes a cleft in the vesicle surface. 9 Characterization. Researchers have mainly focused on the characterization and applications of the resulting structures [54, 92]. The interest in polymeric structures is twofold: not only do polymerized vesicles retain the structure of their monomeric counterparts; their stability in ethanol is also improved [33, 51, 84, 88, 89, 97].

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NAKACHE ET AL.

Polymerization of surfactants bearing a vinyl group both on their bilayer and their headgroup may lead to different structures, depending on the polymerization method. It was found that whereas UV irradiation provokes the complete loss of vinyl protons, evidence of the cross-linking of both the inner and outer surfaces, the addition of AgO-bis-tiobutyronitrile (AIBN) and subsequent heating cause incomplete loss of the vinyl protons. In the latter case, the polymerization only concerns the external surface of vesicles. Polymerization of diacetylene surfactants organized in vesicular form has also been the subject of numerous studies, because they present the advantage of color chang during the course of the polymerization, which makes the polymerization easy to follow. Whatever the chosen surfactant, all polymeric vesicles show enhanced stability in alcohol compared to their nonpolymeric counterparts. Their shelf lives are enhanced and the size is unchanged. Their fluidity depends on the nature of the surfactant [98]: polydiacetylene vesicles are rigid without thermotropic phase transitions, whereas vinyl and styrene vesicles show temperature dependent phase transitions. An improvement of the synthetic vesicle stability may be expected after the coating of the vesicular surface with polypeptides or polysaccharides [99]. In contrast to the previous method for which the polymerization of the polymerizable groups leads to a modification of the membrane (polymerization of the alkyl chain leads to a reduction of the membrane mobility, whereas polymerization of the polar headgroups yields membrane with a polymeric headgroup), no modification of membrane properties is observed. In this approach, the vesicle is surrounded by a polymeric network without any covalent linkage between the vesicle and the polymer. Polymers are attached to vesicular surface by ionic interactions, hydrophobic anchor groups, or polymerization of charged watersoluble monomers. These ionic monomers are attached to a vesicular surface either through the neutralization of appropriate polymerizable heterocyclic amines or by the introduction of polymerizable counterions. In the latter case, vesicles encased within two concentric polymeric monolayers are formed. Retention of the structure after coating with a polymer is confirmed by electron microscopy. There are four possible coatings (Fig. 10): 9 adsorption of polymer molecules at the liposomal surface by hydrophilic or ionic forces 9 fixation of polymer molecules by hydrophobic anchor groups, embedded in the lipid matrix 9 fixation of polymerizable, water-soluble molecules to the liposomal surface via salt formation, followed by an initiated or spontaneous polymerization 9 preparation of liposomes from amphiphiles with a polymerizable group linked to the polar headgroup by a cleavable headgroup, followed by the cleavage of the spacer after polymerization

2.1.4. Applications of Polymerized Vesicles They may be used in several areas.

2.1.4.1. Membrane Modeling Polymerized vesicles may constitute membrane models that can be useful for obtaining information on lipid-lipid and lipid-protein interactions in biological membranes [30, 52, 100-105].

2.1.4.2. Drug Carrier and Molecular Recognition Polymeric vesicles, because of their higher stability compared to unpolymerized vesicles may be explored as potential drug carriers [26, 51, 81, 100, 106-109]. Experiments showed that they were able to retain molecules, such as glucose, longer than their nonpolymeric

590

BIOPOLYMER AND POLYMER NANOPARTICLES

Fig. 10. Differentpossibilities of coating. (Source: Reprinted from [99], with permissionfrom Htithig and Wepf,Zug, Switzerland.)

counterparts. Gros et al. [97] have suggested potential applications in cancer chemotherapy. They envisaged cell specific recognition and tumor cell destruction by the incorporation of membrane destroying agents into polymeric vesicles. An example of an application that has already been tested is the use of ATP-synthetase loaded polymeric vesicles [26]. ATP-synthetase is an enzyme made up of a hydrophobic and a hydrophilic part, which may respectively incorporate into the bilayer and the aqueous compartment of the polymeric vesicles. This isolated enzyme has no activity. If it is bound to polymeric vesicles, it is reactivated. Differential scanning calorimetry studies revealed the presence of monomeric domains, thus providing the site for ATP-synthetase incorporation.

2.1.4.3. Photoconductivity-Microlithography Polymeric multilayers have been developed for submicron microlithography [ 110-112]. In conventional systems, the resolution is limited to ~ 1 nm by the thickness of the resin and the required minimum electron energy. Using polymeric multilayers, thinner (30-1000 ,&), stronger, and more uniform films can be prepared. Doped monolayers and bilayers can photoconduct current. Stable photoconductors find applications in solar energy [26, 51,100] and photoelectrochemistry [26].

2.1.4.4. Artificial Photosynthesis: Solar Energy Conversion The aim of artificial photosynthesis is economically viable catalytic photosensitized water splitting. During natural photosynthesis, visible light is captured by two pigments systems, PS I and PS II, and transformed into chemical energy, which is then utilized for carbon dioxyde reduction [26]. In artificial photosynthesis, PS I and PS II are replaced by simple sensitizers S and electron relays R in surfactant vesicles.

591

NAKACHE ET AL.

Ideally, S and R should be thermodynamically able to generate hydrogen and oxygen from water [113-117]. They are expected to bring favorable energy and to prevent backtransfer of electrons between the reduced relay R- and the oxidized sensitizer S +. R - and S + are supposed to generate hydrogen and oxygen according to the following equations: 2R- + 2H20 ~

2R + 2OH- + H2

4S + + 2H20 --+ 4S + 4H + + O2

2.1.4.5. Reactivity Control In polymeric vesicles, molecules may be located in four sites. Hydrophobic molecules can be distributed among the hydrocarbon bilayers of the vesicles or anchored by a long chain ending in a polar headgroup [26]. Hydrophilic molecules, particularly those that are electrostatically repelled from the inner surface of the vesicles, may move about relatively freely in the water pools trapped in the vesicles, may be associated with or bound to the inner and outer surfaces of vesicles, or can also be anchored to the vesicle surface by a long hydrocarbon tail. Polymerization allows a large variety of reactivity control (catalysis, product separation) by localizing the substrate in different parts of the vesicles. One example is given by organic esters. These molecules may enter the vesicles and their hydrolysis may occur in the matrix of these polymeric vesicles. The final product is then expelled into the bulk solution. 2.2. Polymerization of a Monomer in Colloids

Most of the methods for preparing nanoparticles based on the polymerization reaction of a monomer are related to the methods of latex manufacture developed in polymer chemistry [ 118]. 2.2.1. Emulsion Polymerization

Emulsion polymerization [ 118] is one of the best known processes of organized surfactant assembly polymerization. It leads to the formation of nanospheres or lattices [ 16].

2.2.1.1. Oil-in-Water Emulsion Polymerization In this classical free radical emulsion polymerization, the initial reaction medium contains water, monomer, emulsifier, and initiator, the two latter are water-soluble. Most of the monomer is located in large droplets, some is solubilized within micelles (d = 5-10 nm), and some is dissolved in the water. It is generally assumed that the polymerization starts in water, the greater the monomer solubility in water, the larger the efficiency. Oligoradicals form, which become waterinsoluble as soon as they reach a critical size. Then, either they precipitate to form a polymer particle (homogeneous nucleation), or they are captured by micelles to become a polymer particle (micellar nucleation).

2.2.1.1.1. Micellar Nucleation Theory. The first coherent description of emulsion polymerization was given by Harkins in 1947 [119]. A more quantitative model was then developped by Smith and Ewart [ 120]. The Harkins model applies to the case of highly water insoluble monomers (styrene) and high surfactant concentration (>CMC). The course of the reaction can be described in terms of three intervals (Fig. 11). According to Harkins, water-borne free radicals enter monomer-swollen micelles to form monomer-swollen polymer particle nuclei. The nuclei grow by the addition of monomer, which is supplied from the monomer droplets by diffusion through the aqueous phase. The growing polymer particles are stabilized by surfactant supplied by inactive

592

BIOPOLYMER AND POLYMER NANOPARTICLES

conversion IX

m

~

m

ili

'~ Time Fig. 11. Differentsteps of emulsion polymerization. For the details on the please see text. micelles. By the end of the particle nucleation stage (interval I, conversion 2-15%), all of the surfactant has been adsorbed by the polymer particles, and no more micelles are present. During interval II, the number of polymer particles remains constant, and the polymerization proceeds in polymer particles that grow in size as the monomer droplets decrease. Interval II ends with the disappearance of the monomer droplets. Overall monomer conversion at the beginning of intervall III depends strongly on the monomer; it is typically at 40-50% for styrene and butadiene and at 15% for vinylacetate (more water soluble). The polymerization rate decreases steadily as the monomer concentration in the polymer particles decreases. Quantitative conversions can be achieved. The final particles size are around 100-400 nm, and are intermediate between those of the initial micelles and monomer droplets. The polymer rate Rp and the average degree of polymerization DP are proportional to the number of polymer particles (N) [ 120]: Rp = kp Nh [M]p/NA DP =

2kpNft[M]p/Ri

where kp is the propagation constant, t7 is the average number of radicals per particle, Ri is the rate of radical generation, [M]p is the monomer concentration in the particles, and NA is Avogadro's number. Three limiting cases may be distinguished according to Smith-Ewart theory: Case 1: h > 0.5 applies to systems with large particle size or a low termination rate constant.

2.2.1.1.2. HomogeneousNucleation. This mechanism was first proposed by Fitch [121] and applies to highly water-soluble monomers (vinylacetate, acrylonitrile, methylmethacrylate) and low surfactant concentration (> CMC). It involves the formation in the aqueous phase of soluble oligomeric radicals. When these radicals reach a critical size, they

593

NAKACHE ET AL.

become insoluble and precipitate on themselves. The precipitated species are stabilized by absorbing surfactant and form primary particles that grow by propagation of monomer. Primary particles may also grow by coagulation with themselves or by capture of oligomers, which will limit the final number. The number of particles and the particle size distribution are controlled by the parameters that affect colloidal stability; in particular, the nature and concentration of the surfactant and the surface charge density are critical.

2.2.1.1.3. Coagulative Nucleation. The coagulative nucleation theory proposed by Napper et al. [122] is a straightforward extension of the homogeneous nucleation theory. It postulates first the formation of "precursor" particles by precipitation (d = 6 nm), which are colloidally unstable. The "precursor" particles may grow by polymerization at a reduced rate because of their small swelling by monomer. The second step is the formation of "mature" particles by coagulation of "precursor" particles until colloidal stability is reached. Precursor particles grow faster by coagulation than by propagation. The result is that the rate of production of mature particles will initially increase with time, then decline toward the end of the nucleation period. This mechanism accounts well for the positive skewness of the particle size distribution observed for styrene emulsion polymerization; this indicates that most of the "mature" particles are produced late in the nucleation period. 2.2.1.1.4. Applications. By means of this method, many kinds of nanospheres were synthesized for controlled release [ 10, 123-125]. Polyalkylcyanoacrylate nanoparticles [ 126-129]: The main advantage of cyanoacrylate over other acrylic derivates is the polymerization step and their capacity for biodegradation. Indeed, alkyl cyanoacrylate may be polymerized without any energy input, which could affect the potential drugs to be incorporated. The polymerization mechanism is an anionic process. The resulting nanospheres in the range of 150 nm are biodegradable by a surface erosion process, according to Couvreur et al. [ 15], which makes them adequate for drug vectorization. By increasing the concentration of the surfactant in the polymerization medium, it is possible to decrease the size of the nanoparticles to ~30 nm. When observed by freeze fracture microscopy, the internal structures of these nanospheres show a matrix made up of a dense polymeric network. Drugs may be incorporated after dissolution in the medium, either before the introduction of the monomer or after polymerization. These nanospheres are more specifically applicable to the treatment of cancer and intracellular infections [ 10]. As an application to cancer chemotherapy, dactinomycin-loaded polymethylcyanoacrylate nanoparticles were developed and tested for their activity against an experimental solid tumor of the rat. It was observed that tumor growth inhibition was more marked with these loaded nanoparticles than with free dactinomycin [ 130]. As for intracellular infections, ampicillin-loaded nanoparticles were tested in the treatment of experimental Listeria monocytogenes. Therapeutic activity of ampicillin after adsorption onto nanoparticles was observed to be improved compared to the free drug [131 ]. Others: Other nanospheres were synthesized by emulsion polymerization: 9 poly(methyl methacrylate) nanoparticles that result from a radical emulsion polymerization mechanism, used as adjuvants for vaccines [132, 133] 9 acrylic copolymer nanoparticles (methylmethacrylate (MMA), acrylamide, etc.) whose initiation may be achieved either chemically or by y-irradiation [134, 135] 9 other types (polystyrene [136], polyacroleine [137], polyglutaraldehyde [138], polyvinyl pyridine [ 139]) used as immunosorbents. Nevertheless, these particles were not developed as much as the others because of their lack of biodegradability.

2.2.1.2. Water-in-Oil Emulsion Polymerization Polymerization of water-soluble monomers in hydrocarbon fluids has attracted a renewed interest over the past two decades, owing to the suitability of the process for producing high

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BIOPOLYMER AND POLYMER NANOPARTICLES

no monomor-p

gmer

pcrh'cle

,,o ,-o ,,-0 so

R- R--2R"

micet(e d.-150 ~-100,~1

M +

H20

o-,

o~

CP?

d-c2oo-5oooi

Fig. 12. Schematicrepresentation of polymerization in inverse emulsion. (Source: Reprinted with permission from [141].)

molecular weight polymers at high reaction rates. In this process, a hydrophilic monomer (usually in aqueous solution) is emulsified in a continuous oil medium with a water-in-oil emulsifier. Polymerization can be initiated with either oil-soluble or water-soluble initiators (Fig. 12). The product is a dispersion of fine particles of an aqueous high-polymer solution that can be easily inverted into water, so that the water-swollen polymer particles dissolve rapidly, in contrast to solid-powder polymer, which forms gels or aggregates when added to water. These high viscosity polymer solutions find applications in water treatment, flocculation of colloidal suspensions, tertiary oil recovery as pushing fluids, fine retention in paper manufacturing, etc. [ 140]. Inverse (or water-in-oil) emulsion polymerization has been investigated far less than conventional (i.e., aqueous) emulsion polymerization. At first glance, a water-in-oil polymerization can be considered as a replica of the conventional emulsion polymerization (oilin-water), in which the water is replaced by the oil and the hydrophobic monomer by an aqueous solution of hydrophilic monomer. In fact, understanding the water-in-oil polymerization phenomenon is more difficult than understanding the corresponding oil-in-water process. In the latter, the continuous phase is exclusively water, and the particle stabilization is electrostatic and/or steric. In the former, aromatic or aliphatic continuous phases are commonly used, and the stabilization is essentially steric in origin [ 141,142a, 142b]. These factors, among others, will control the structure of the dispersion, as well as the mechanism and kinetics of the polymerization, which complicates considerably the generality of the phenomena. This complexity might account for the paucity of fundamental studies published in the literature despite an abundant number of patents in relation to the numerous applications of water-soluble polymers. The basis for the kinetic mechanisms of inverse emulsion polymerization can be found in the seminal work of Vanderhoff et al. published in 1962, which dealt with the polymerization of sodium p-vinylbenzene sulfonate in xylene [143]. There was then a gap of almost two decades before new fundamental studies were reported, mainly motivated mainly by the novel applications developed in the field of oil recovery processes. However, the results are in many respects contradictory and diversely interpreted, and a full comprehensive picture of the kinetic mechanism occurring in these systems has not yet emerged. The major difficulty here comes from the fact that, contrary to conventional emulsion polymerization, the kinetic laws depend on a number of variables such as the nature of the initiator, the type and concentration of emulsifier used, and the nature of the organic phase (aliphatic or aromatic). Moreover, the temperature, the ionic strength, the stirrer speed, the reactor design, and operating procedures all affect the kinetic mechanisms. In any heterophase polymerization, the nature of the kinetics may be discerned by calculating the average number of radicals per particle h during any stage of the polymerization (Smith-Ewart cases 1, 2, 3) [120] and by the locus of nucleation prevailing in the reaction, for example, monomer droplets, micelles, or homogeneous processes. In an

595

NAKACHE ET AL.

inverse emulsion, the distinction between the monomer droplets and monomer-swollen micelles is rather semantic, because of the larger emulsifier levels needed to stabilize the systems (2-5% of the total mass) [141,143]. It follows that all dispersed entities are possible sources of particle nucleation. The kinetics of inverse emulsion polymerization can be classified more or less arbitrarily into two subclasses according to the solubility of the initiator. When water-soluble initiators are used, most of the authors conclude that acrylamide polymerization proceeds within the monomer droplets, irrespective of the nature of the organic phase (aromatic or aliphatic) [ 144-148]. Both monomer and initiator reside in the dispersed droplets, and each particle acts as a small batch reactor. In the case of oil-soluble initiators, only a few attempts have been made to apply the Smith-Ewart theory [143, 149-151]. The determination of h is difficult here because of the ill-defined stages of the reaction, the unusual kinetics, and the broad particle size distribution. The kinetic studies of Vanderhoff et al. [143, 152] and Visioli [150] are examples of applying the Smith-Ewart theory to the polymerization of acrylamide and p-vinylbenzenesulfonate in xylene initiated with benzoyl peroxide. The data unexpectedly followed Smith-Ewart case 1 (h 4 765

1. I N T R O D U C T I O N B i o m i m e t i c s is defined as "the study of b i o l o g i c a l structures, their functions and their synthetic p a t h w a y s in order to stimulate new ideas and to d e v e l o p these ideas into synthetic s y s t e m s similar to those f o u n d in b i o l o g i c a l s y s t e m s " [1]. It is a strategy for d e s i g n i n g c o m p l e x , m u l t i f u n c t i o n a l materials with a capacity for s u p r a m o l e c u l a r s e l f - a s s e m b l y and c o n v e r s i o n b e t w e e n chemical, thermal, m e c h a n i c a l , e l e c t r o m a g n e t i c , and electrical e n e r g y and the ability to sense and adapt to the e n v i r o n m e n t [2, 3]. Synthetic materials with these characteristics are called " s m a r t materials" [4]. B i o l o g i c a l s y s t e m s and materials have hierarchical organization. In the context of materials science, Di M a r z i o defines hierarchical

Handbook of Nanostructured Materials and Nanotechnology, edited by H.S. Nalwa Volume 5: Organics, Polymers, and Biological Materials Copyright 9 2000 by Academic Press All rights of reproduction in any form reserved.

ISBN 0-12-513765-6/$30.00

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structure as an "assemblage of assemblages" that include scale, interaction between assemblages, and architecture [5]. Hierarchical systems abound in biology. A survey of common systems and their relation to the design of new materials has been described in a recent monograph [6]. An example given is the tendon, in which the levels of structural hierarchy and fiber diameter are collagen polypeptide (0.5 nm) ~ triple helix (1.5 nm) ~ microfibril (3.5 nm) --+ subfibril (10-20 nm) --+ fibril (50-500 nm) ~ fascicle (50-300/zm) --+ tendon (0.1-0.5 ram). Other examples given include wood and a diarthroidial joint, each with six levels of structural hierarchy. Many of the components of a biological system have the capacity to undergo self-assembly. Self-assembly is "self-organization of many identical, or nearly identical subunits" [5]. Phase transitions leading to self-assembled systems include the helix-to-coil transition, adsorption onto a surface, liquid crystal transitions, and membrane formation. This chapter gives examples of multilayers in self-assembly (Section 2.1), biology (Section 3.1), and the biomineralization process (Section 3.2). Biomimetics can be applied to the development of unique thin films. A novel film formation technique has been described that mimics aspects of the sequential adsorption of materials onto a surface observed in biomineralization. Several review articles have recently been published describing sequential adsorption and related thin film preparation techniques [7-11]. Films prepared by this technique are given many names in the literature focusing on the completed film or the film preparation process, including fuzzy nanoassemblies [7], polyion multilayers [ 12], alternate polyelectrolyte thin films [13], alternate assembly [ 14], alternate adsorption [ 15], molecular deposition films [16], alternate layer-by-layer assembly [ 17], layer-by-layer deposition [ 18], bolaform amphile multilayers [ 19], alternating multilayer films [20], polymer self-assembly solution adsorption [21 ], multilayers of polyelectrolytes [22], multilayer films [23], layered composite films [24], self-assembled alternating multilayers [25], layer-by-layer self-assembly [26], molecular deposition [27], reactive self-assembly [28], self-assembled polymer thin films [29], molecular self-assembly [30], molecular beaker epitaxy [31], nanoparticle heterostructures [32], polycation/polyanion self-assembly [33], sequential adsorption [34], stepwise assembly [35], ultrathin polyelectrolyte films [36], ultrathin film based on electrostatic interaction [37], and electrostatic self-assembly [38]. In this chapter the film-forming process will be called sequential adsorption (SA). A polyion-containing film prepared by SA will be called polyion multilayerfilm (PMF). This chapter reviews the literature on PMFs prepared by the SA technique published prior to August 1997. Films containing polymers, dyes, amphiphiles, inorganic compounds, colloids, and proteins are described, guidance on the preparation and characterization of PMFs is given. 2. EXAMPLES OF SUPRAMOLECULAR COMPLEXES IN BIOLOGY AND POLYMER SCIENCE 2.1. Thermodynamics and Kinetics of Self-Assembly

Formation of biological thin films includes self-assembly of macromolecular complexes. Certain macromolecules have the ability to spontaneously form complex structures. Examples of these processes in thin film formation include coil-to-helix formation upon adsorption to a surface [38], formation of the biotin-streptavidin complex [39], and antigenantibody interactions [20]. S layer proteins are an example of a protein forming an ordered two-dimensional array on a surface [40]. A simple model of linear assembly processes leading to filaments has been described by Engel [41]. In the first step, two monomers dimerize: A + A ~ A2

(1)

Polymerization to a linear aggregate occurs by addition of monomer to the flament: Ai-1 + A = Ai

712

(2)

BIOMIMETIC THIN FILMS

By analogy to the helix-to-coil transition, the initial dimerization step is a nucleation process with subsequent propagation steps with equilibrium constants" K2 = cr K Ki = K

(nucleation)

(3)

(i >~ 3) (propagation)

(4)

The cooperativity parameter o- is small (or > 1). The model predicts that the monomer concentration cl will always be smaller than a critical concentration Ccrit- K -1. When a selfassembly experiment is performed, the total (monomer + aggregate) concentration co is varied. Below Ccrit, monomer concentration increases with co. Aggregate formation only occurs above Ccrit. Engel gives an example of "all or nothing" behavior in the association of actin. The cooperativity parameter ~r is 2 • 10 -7, and the equilibrium constant for the propagation step is K - 1.7 • 105 M -1. Filaments form only above Ccrit - 5.88/zM. In a similar manner, the kinetics of self-assembly follow a mechanism involving slow dimer formation as a nucleation step followed by faster propagation steps. In his review article, Engel describes the kinetics of polysheath formation. The kinetics follow a sigmoidal growth curve, with a slow bimolecular nucleation rate constant of kN -- 10 -2 M-1 s-1 and a rapid propagation bimolecular rate constant of k - 105 M- 1 s- 1.

2.2. Examples of Self-Assembly in Protein and Polymer Systems Tropomyosin provides a well-understood example of a protein that undergoes selfassembly processes (Fig. 1) [42]. Having a coiled-coil conformation, it belongs to the K-M-E-F (keratin, myosin, epidermin, fibrin) class of proteins. Its amino acid sequence has a sevenfold repeat pattern abcdefg, in which amino acids in positions a and d tend to have hydrophobic side chains, and those in positions b, c, e, f, and g tend to be hydrophilic [43]. Because the amino acids tend to be helix formers, the polypeptide chain self-assembles into an or-helix. Upon the formation of an or-helical conformation, a new, higher order structure forms on the surface of the helix. The hydrophobic amino acids in positions a and d form a hydrophobic band on the surface of the helix. The remainder of the surface contains the hydrophilic amino acids. Two tropomyosin monomers self-assemble into a coiled-coil dimer. The coiled-coil dimer forms numerous higher order structures, including filaments resulting from head-to-tail interactions and complex formation with its natural partner troponin [44, 45]. The tropomyosin-troponin complex aggregates with actin and myosin, forming muscle fibers. Recent work has demonstrated self-assembly in synthetic polymer systems that mimic processes seen in proteins. Synthesis of a two-dimensional (2D) polymer shaped like a molecular sheet has been described [46, 47]. The molecular precursor of the 2D polymers contains three subunits that contribute to the final morphology (Scheme 1).

3

Scheme 1 Fragment 1 is a alkyl biphenyl smectogen that promotes layer formation. Fragment 2 contains a chiral center with a strongly polar cyano group. Molecular recognition between the

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Fig. 1. Exampleof self-assembly in tropomyosin. I: Three heptets of the tropomyosin amino acid sequence [43]. Amino acids in a heptet are labeled abcdefg. II: Polypeptide chain self-assembles into an ct-helix. III: Self-assembly into u-helix causes formation of hydrophobic regions in heptet positions a and d, and hydrophilic regions at heptet positions b, c, e, f, and g. IV: Two tropomyosin helices self-assemble into coiled-coil.

chiral units is possible. Upon heating, the cyano groups polymerize to form imine bonds and the acrylates form poly(acrylate). Fragment 3 contains an acrylate group that can also polymerize with its neighbors. When only one of the functionalities is present, the oligomer polymerizes into a comb polymer. When both functionalities are present, the oligomer selfassembles into a layered structure in which the cyano and the acrylate groups polymerize in different layers. The 2D polymer has a molecular mass on the order of 106 Da and a monodisperse thickness of 5 nm. Electron micrographs of the 2D polymer shows self assembly of the sheets into stacks of sheets. Another example from the same research group is the rodcoil [48, 49] (Scheme 2).

Coil Diblock

Rod Block

Scheme 2

714

BIOMIMETIC THIN FILMS

The oligomer precursors have three blocks. The first block consists of a styrene monomer polymerized with an average length of 9 monomer units. A second block with the same degree of polymerization contains isoprene units. The third block contains three biphenyl units. The oligomer behaves like a rod diblock linked to a coil block. When thin films of the triblock molecules are cast, arrays of nearly identical mushroom-shaped nanoaggregates form, with approximately 100 molecules in each nanostructure. Contact angle and nonlinear optical measurements suggest that the nanoaggregates stack in a noncentrosymmetric fashion.

2.3. Interpolyelectrolyte Complexes Investigations of interpolyelectrolyte complexes (IPECs) give insight into the properties of structures held together by electrostatic forces. Kabanov has written a review of their properties [50]. The review article describes several Russian studies that give insight into the fundamental mechanism of multilayer deposition. When two aqueous solutions, one containing a polycation, the other a polyanion, are mixed, a complex forms: (A-b+)n + (B+a-)m ~ (A-B+)x + (A-b+)n_x + (B+a-)m_x + x a - + xb + The conversion ratio 0 = x / m when n ~> m and 0 = x / n when n < m. The ratio 0 is a function of pH and ionic strength. The ratio Z = m/n. When Z < 1, the IPEC will have a negative charge. When Z > 1, the complex will have a positive charge. When Z -- 1, the complex will have no charge and will be insoluble. Fluorescence quenching experiments were performed using pyrenyl-labeled polymethacrylate (PMA*) anions containing one label per 350-1500 monomer units and (1-ethyl-4-vinylpyridinium)-vinylpyridine copolymer cations (PVPC) the 1-ethyl-4-vinylpyridinium units quench the fluorescence of the pyrenyl labels (Schemes 3 and 4).

(CH~)i+~? (CH~)fi--

(

~ ~

02H5 PVPC

PMA*

Scheme 3

Scheme 4

Through the use of stopped flow kinetics measurements, the fundamental complexation reaction is probably diffusion limited. The polyion exchange reaction has also been investigated: (PMA/PVPC) + PMA* ~ (PMA*/PVPC) + PMA In this experiment the bimolecular rate constant is on the order of 104 to 106 1/mol-s, three to five orders of magnitude smaller than the diffusion rate constant. The result suggests that the exchange reaction occurs through the formation of a temary complex PMA*-PVPCPMA, resulting from the interpenetration of PMA-PVPC coils and the PMA* coil. The rate constant increases dramatically with ionic strength, showing that counterion charge shielding stabilizes the ternary complex. Enzymes have been placed in IPECs. Kabanov gives kinetic parameters of the enzyme penicillinamidase under various conditions. When bound to a PMA/PVPC IPEC, enzyme activity is nearly identical to that of the native preparation.

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When bound to celluose triacetate fibers or polyacrylamide gel, enzyme activity decreases 50-fold.

3. EXAMPLES OF MULTILAYER THIN FILMS IN B I O L O G Y

3.1. Biological Structural Colors There are numerous examples of optical thin films in biology that show a variety of optical phenomena. Structural colors in insects have been investigated for many years [51 ]. Original light microscope studies [52-54] drew a distinction between structural and pigment colors. Structural colors could be altered by physical means like pressure, swelling, or shrinking or the addition of an index-matching solvent. For example, iridescent wing membranes undergo a reversible color change upon the addition of a swelling agent. These phenomena result from thin film optical interference. The white color seen in insect wings results from light scattering. In contrast, pigment colors are extractable by solvents. Recent electron microscopy investigations give details about the source of the optical phenomena in insect wings. Structural colors appear in butterfly and moth scales and serve as thin film interference filters [55]. Each scale is a flattened stack with two surfaces, the upper and lower laminae, with a stalk attached to a socket on the wing (Fig. 2). The upper lamina contains a grid consisting of raised longitudinal ridges regularly joined by cross-fibs. The ridges and cross-fibs form a series of windows opening into the scale interior. In the scale interior are pillars that serve as spacers between the lower and upper laminae. Pigment granules are found in the interior of the scale. In ridge-iridescent scales, the ridges contain microribs that form the reflective elements. The ridge structure is an alternating stack of high- and low-refractive index layers. Each ridge acts as a quarter-wave thin film interference mirror with a phase change upon reflection. The optical thickness (nt) of a dielectric stack layer composed of alternating thicknesses tl and t2 and indices n l and n2 is given by the relation nit1 =n2t2

(5a)

Fig. 2. Imageof a portion of an ultraviolet-reflecting scale of the male Eurema lisa. The laminate ridges projecting upward have ultraviolet reflecting capability. Ellipsoidal structures projecting downwardare pigment granules, giving a yellow color to the scale. Pillar-like trabeculae join the upper and lower lamina. Scale bar: 0.5 tzm. (Source: Reprinted with permission from [57]. 9 1972 American Association for the Advancement of Science.)

716

B IOMIMETIC THIN FILMS

and nlq

4- n 2 t 2 = n t

(5b)

where n t is the optical thickness of one bilayer composed of a high-index and a low-index component. Upon normal incidence, the wavelength of maximum reflection is given by = 4nltl

-- 4n2t2

(6a)

An alternative formulation is )~ = 2 n t

(6b)

For example, certain butterflies have ultraviolet-reflecting scales with an index of refraction n - 1.60 and microribs with 510/~ thickness with an 848-/k air space between them [56, 57]. If the system behaves as a quarter wavelength reflection filter, the layers should reflect light with a constructive interference maximum at 343 nm. Reflection spectroscopy measurements of scales show ultraviolet reflection with a maximum at 348 nm. The structures also change color when the scale tilts. The wavelength of maximum constructive interference varies from 320 to 348 nm over a wing tilt from 0 ~ to 50 ~ How are these structures formed? Ghiradella studied the development of iridescent scales from two lycaenid butterflies [58]. The two types of internal reflective structures are closely related developmentally. The diffraction lattice appears to form within the scale cell boundaries through the assistance of a convoluted series of membranes (Fig. 3). The cell produces membrane-cuticle units that are continuous with the invaginations of the plasma membrane. The units aggregate, forming "crystallites that grow toward each other by accretion until the adult morphology arises." Formation of the thin film interference laminae "results from the condensation of a network of filaments and tubes secreted outside boundaries of the cell." Ghiradella hypothesizes that the lattice may form by a process within

Fig. 3. Sketchof developing scale of the butterfly M. grynea. The smooth endoplasmic reticulum (ER) buds off into the rough ER into a regular framework, around which the membrane cuticle (MC) units form themselves into a reflective lattice. (Source: Reprinted by permission from [58]. 9 1989 Wiley-Liss, Inc., a subsidiary of John Wiley and Sons, Inc.)

717

COOPER

the scale cell in which the cell produces a material that self-assembles into a face-centered cubic lattice. The thin film laminae then form by stretching the lattice. Structural colors have been found in plants. Iridescence in leaves has been observed in understory plants growing in shady areas of tropical rain forests [59-61 ]. For example, the leaf reflectance spectrum from Lindsaea lucida has a blue-green reflection band at 538 nm. The outermost cell wall of the adaxial epidermis contains helicoidal nests of arcs arranged in ranks separated by lamellae with a lamellar spacing (t) of 192 nm. Assuming a refractive index n = 1.45 and a bilayer optical thickness of 278 nm, a reflectance maximum of 557 nm is calculated. Iridescent blue fruits of Elaeocarpus angustifolius have a reflection band at 439 nm [62]. Electron microscopy reveals a multilayer structure within the epidermis consisting of a parallel network of strands 78 nm thick. Thin film interference theory, assuming n -- 1.40, predicts an optical thickness of 109 nm and a calculated reflectance maximum of 436 nm.

3.2. Biomineralization Detailed information about the mechanism of biomineralization in molluscs has been obtained through investigations of "flat pearls" [63]. By placing a glass substrate between the mantle and the inner surface of the mollusc shell, the process of biomineralization can be monitored in vivo. A schematic cross section of the outer edge of the shell of a red abalone is given in Figure 4. Epithelial tissue lining the inner surface of the shell secretes shell precursors into the extrapallial space, a thin compartment between the mantle and inner shell surface. The shell structure contains multiple organic, calcite, and aragonite layers. Growth of a fiat pearl showed that biomineralization begins with the deposition of an organic sheet on the substrate, followed by growth of a calcite layer and an abrupt transiton to an aragonite layer. The biomineralization process was shown to be sensitive to substrate. Implantation of roughened glass coverslips or a hydrophobic substrate caused deposition of regions of disorder in the calcite layer and deposition of an organic sheet associated with reinitiation of the biomineralization process. Soluble mollusc shell proteins have been found that control the crystal phase during nacre formation [64]. These proteins contain a high proportion of aspartate, glycine, glutamate, and serine residues with a (asp-Y)n, where Y is primarly glycine [65]. Proteins were isolated from the aragonitic or the calcitic portions of the red abalone shell. Denaturing gel electrophoresis showed that the aragonitic com-

Fig. 4. Schematicof a vertical section of the outer edge of the shell and mantle of a red abalone (Haliotis rufescens). The figure is not drawn to scale. (Source: Adapted with permission from [63]. 9 1996 American Chemical Society.)

718

BIOMIMETIC THIN FILMS

posite contains three proteins, whereas the calcitic portion contained six proteins. Calcium carbonate crystals were grown in the presence of these proteins. Crystals grown in the absence of soluble protein exhibited the rhombohedral calcite morphology. Crystals grown in the presence of the calcitic protein fraction had the spherulitic calcite morphology, whereas those grown in the presence of the aragonitic fraction formed aragonite needles in the plane of the nucleation layer. The addition of mineral-specific proteins induced the abrupt calciteto-aragonite transition seen in abalone shell. Rhombohedral calcite crystals were exposed to a crystal growth medium containing the proteins. The addition of aragonitic polyanionic proteins caused aragonite needle growth, and the addition of calcitic proteins caused calcite overgrowth. Sequential transition of calcite to aragonite and back to calcite was caused when soluble aragonite proteins were depleted, causing formation of calcite. In a related study, glycoproteins were isolated from mollusc shells, and in vitro studies of the nucleation of calcium carbonate in the presence of the glycoproteins, chitin, and silk fibrin demonstrated similar behavior [66]. Insight into the mechanism of aragonite tablet growth has been obtained through a recent atomic force microscopy (AFM) study [67]. Flat pearls were demineralized, leaving an iridescent patch of organic material. AFM and scanning ion conductance microscopy revealed that the organic sheets had pores 5-50 nm in diameter. The results support a model in which nacre formation occurs when mineral bridges form through the pores in the organic layers between the aragonite tablets. Crystal synthesis analogous to the biomineralization process has been demonstrated [68]. CdS has been synthesized in PEO thin films. The synthetic factors emphasized included strong binding by the matrix to the inorganic reagents, solubility of the reagents in the polymer matrix, and an ordered, regular environment to induce nucleation. The CdS crystals prepared had uniform size, phase, and crystallographic orientation. The crystals were in the "rock salt" morphology, a phase normally appearing at high temperatures.

4. BIOMIMETIC THIN FILMS PREPARED BY THE SEQUENTIAL ADSORPTION TECHNIQUE

The composition, morphology, and mechanism of formation of the structures that result in insect iridescence and plant structural colors are poorly understood. Because of the development of the flat pearl model system, the mechanism of mollusc shell biomineralization is beginning to be clarified. Biomineralization in mollusc shells involves sequential laying down of organic layers that serve as templates for the growth of specific calcium carbonate polymorphs above the layers and through the pores in the organic sheets. By changing the protein secreted by the secretory epithelium in the mantle, the crystal morphology can be altered in a controlled manner. Aspects of the process of biomineralization can be mimicked for the synthesis of multilayer thin films. Iler described the process in the 1960s [69, 70]. He gives several examples of multilayer formation, including albumin/silica, silica/alumina, treatment of fabrics, multilayers on metal, and mica. The process is depicted in Figure 5. A charged substrate is placed in a solution containing an oppositely charged polyelectrolyte. The polyelectrolyte adsorbs to the surface. Following a rinsing and drying step, the film is placed in another polyelectrolyte solution. The resulting film contains a multilayer with alternating oppositely charged monolayers. To the knowledge of the author, there was no activity on this method until the early 1990s. An example of nomenclature used in this chapter follows. S + (A/B)n + (C/D)m represents a substrate (S) upon which n A/B bilayers and m C/D bilayers have been placed. The order of adsorption is from left to right, with the charge of subsequent layers determined by the charge of the substrate. When the substrate is not specified, it is implied in the text.

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Fig. 5. Schematicof SA process. A positively charged substrate is dipped into an aqueous solution containing a negatively chargedpolyelectrolyte (1). The negativelychargedpolyelectrolyte adsorbs to the surface. After rinsing and drying, the filmis dipped into a solution containing a positively chargedpolyelectrolyte (2). This process can be repeated indefinitely with multiple electrolyte solutions.

4.1. Procedure for Preparing Polyion Multilayer Films

4.1.1. Substrate Preparation 4.1.1.1. Substrate Cleaning Successful film formation requires clean substrates. Glass slides are cleaned with a boiling solution of a 7:3 mixture of concentrated H2SO4 and 30% H202 (Piranha solution) while stirring. The slides are then rinsed with a stream of deionized water and dried with N2. The slides are then hydroxylated by dipping in a 10:3:3 solution of deionized water, 30% H202, and concentrated NH4OH at room temperature for 2-3 days. The slides are then dipped in a deionized water bath, rinsed with CH3OH, and dried with N2 [38]. Gold coupons are cleaned with Piranha solution, followed with a 20-rain sonication with distilled water [71 ]. (Warning: These mixtures are corrosive and can cause severe burns. They react violently with many organic materials and should not be stored. Perform the cleaning procedure under a fume hood while wearing suitable personal protective equipment.)

4.1.1.2. Glass and Quartz Although films can be prepared on an untreated surface [38], efficient film formation requires modification of the surface with charged groups. The following procedures have been used successfully, but details about kinetics and surface density of charged groups are not known. Positively charged surfaces have been made by letting a 5% solution of N-[3(trimethyloxysilyl)propyl]ethylenediamine solution sit for 5 min to ensure silanol formation. The slides are then silanized for 10 min, followed by an ethanol rinse, a deionized water rinse, N2 drying, and a 10-min cure in a vacuum oven [38]. Another example of the use of this agent involves a 12-h silanization in a 5% solution, followed by a 10-min toluene rinse, a 10-min 1:1 methanol/toluene rinse, a 10-min methanol rinse, and a water rinse. Silanizations with 3-aminopropyltrimethoxysilane have been performed under a dry N2 atmosphere to prevent oxidation to poly(dimethyoxysilane) [72]. Quartz plates washed in alkaline aqueous alcohol with sonication have negative charges resulting from partial hydrolysis of the surface [73]. A hydrophobic surface can be prepared by exposing glass slides to 1,1,1,3,3,3-hexamethyldisilazane at reduced atmospheric pressure (200 torr) for 36 h [74].

720

BIOMIMETIC THIN FILMS

4.1.1.3. Gold Gold surfaces have been used as substrates for PMFs [75]. Caruso exposes the gold surface to 1 mM 3-mercaptopropionic acid-ethanol solution for 24 h, followed by a deionized water rinse and nitrogen drying. The carboxyl groups on the gold surface are ionized at pH 8. He advises careful choice of film deposition time, as exposure of the coated gold substrate causes deterioration of the gold surface. Sulfonic acid groups have been added to a gold surface by dipping gold foil into a 1 mM solution of MPS solution in ethanol for 12 h, followed by rinsing in pure ethanol [71 ]. Negatively charged groups have been placed on a gold surface by immersing the surface in a 0.5 mM solution of 11-mercapto-undecanoic acid in acetonitrile for 30 min, followed by rinsing with acetonitrile and drying with a stream of warm air [76].

4.1.1.4. Other Surfaces PET has been used as a substrate for PMF film [18]. Hydrolysis in 1 M NaOH for 16 min gives a surface containing carboxylic acid and alcohol functional groups and is negatively charged at high pH. When a PAH solution is applied to the surface at high pH, amide linkages form between the carboxylate groups and some of the PAH amino groups. At lower pH, only electrostatic interactions occur. Single crystal silicon wafers are cleaned for 20 min at 60 ~ in a solution containing one part 28% NH4OH, one part 29% H202, and five parts deionized water, followed by a deionized water rinse [77].

4.1.1.5. Charging the Surface Dipping silanized slides into a 1 N HC1 acid solution gives them a net positive charge [38]. Freshly cleaved mica, silicon wafers, or glass or quartz slides can be given a positive charge by coveting with a layer of PEI. To charge the surface, the wafers are immersed in a PEI solution for 30 min [77]. A oriented crystal silicon wafer cleaned with Piranha solution gives a hydroxylated surface that forms positively charged monolayers when dipped into a 5% solution of PDDA [78]. It has been demonstrated that a plasma treatment yields a charged surface to adsorb polyelectrolyte layers [79]. To ensure linear film buildup, a precursor film (PSS/PAH)2 should be placed on the substrate surface.

4.1.2. Dip Time, Electrolyte Concentration, and Ionic Strength 4.1.2.1. Dip Time A basic question associated with PMFs is determination of dip time for monolayer formation. Dip times yielding successful multilayer formation include 5-10 s [78], 1 min [38], 5-10 min [74], 20 min [73, 80, 81], 30 min [82, 83] and 24 h [84]. In all cases the citations give data showing a linear increase in thickness with number of dip cycles. Proper determination of dip time requires an understanding of the mechanism of monolayer formation. Monolayer formation includes at least two steps: diffusion of the ion to the surface and binding to the surface. A calculation of film formation based on diffusion alone gives rates 100 times faster than observed rates [85]. Transition states similar to those seen in IPEC ion exchange studies (Section 2.3) may form at the film-solution interface. QCM investigations of monolayer formation reveal first-order kinetics with lifetimes of 5 min for proteins [81 ] and similar lifetimes for adsorption of dyes to the multilayer surface. Figure 6 gives examples of deposition kinetics measured by QCM [73]. Figure 6A gives data for the CR/PDDA system. The polymeric PDDA has adsorption kinetics comparable to that of the dye CR; both saturate within 20 min. In contrast, the TPPS/PDDA system shows significant differences between dye and polymer behavior. In this case PDDA adsorbs completely within 5 min, whereas the porphyrin dye TPPS has not saturated after 20 min. Furthermore, the adsorption half-lives for PDDA were different for a CR surface (1.5 min) vs. a TPPS

721

COOPER

A ----o--- C R - - D - - - PDDA

-5 g~

-10 -150

1L

DDDDn

-200-250

, ,

~ ,

0 0

o , , , , I

5

I I

,

,

Timel(0min)

,

t

I I

,

,

,

,

15

I I

20

B

o

-200 -400

.~

-600

o-.- T P P S

-800-

=-1000k -1200-1400

ww

' ' ' '

9

I'

5

''

'

t

. . . .

Timl~min)

I' . . . .

15

i'

20

Fig. 6. Adsorption kinetics monitored by QCM. A: CR/PDDA film. Adsorption half-life was calculated to be CR: 2.5 min, PDDA: 1.5 min. B" TPPS/PDDA film. Adsorption half-life was calculated to be TPPS: 6.3 min, PDDA: 0.39 min. Adapted with permission from [72]. 9 1997 American Chemical Society.

surface (0.39 min). Because of the variation in kinetics, measurement of the rate of monolayer formation by the QCM technique will make possible a choice of dip times. As a rule of thumb, a 20-min dip time will usually give good results. A commercially available automated slide stainer can be used to prepare PMFs [91 ]. 4.1.2.2. Concentration

The relation between electrolyte concentration and film properties has not been explored in detail. Successful film formation has been demonstrated for electrolyte (monomer unit or individual molecule) concentrations ranging from 0.1 mM to 35 mM in deionized water [38, 73, 81, 86-90]. A systematic measurement of the effect of electrolyte concentration suggests no strong electrolyte concentration dependence [73]. Table I shows QCM data for the CR/PDDA system [73]. There are no major differences in the amount of material deposited when either the CR or PDDA concentrations were varied. In general, good results can be obtained with polyelectrolyte monomer concentrations of 0.01 M, corresponding to a weight concentration of 1-3 mg/ml.

722

B IOMIMETIC THIN FILMS

Table I. FrequencyChanges upon Adsorption of CR or PDDA* [CR]t

- AF :~

[PDDA]w

1.0

84 • 7

10

73 + 12

1.9

43 + 23

1.0

77 • 13

1.9

60 4- 15

0.1

74 + 9

1.9

50 + 15

0.01

78 4- 10

1.9

46 + 8

19

- AF :I: 42 • 12

*Reprinted in part with permission from [73]. 9 1996 American Chemical Society. t Dye concentration (mM) in water. Dip time was 20 min with water washing between adsorption steps. ~tFrequency decrease (Hz) per dye or polycation adsorption step measured from QCM. w concentration (mM). Dip time was 20 min with water washing between adsorption steps.

4.1.2.3. Rinsing and Drying A rinsing step is usually included in published film preparation procedures. Hoogeveen [22] describes the effect of rinsing on the kinetics of monolayer formation. Film deposition is monitored by measuring reflectance. During rinsing, no major changes in film reflectance were observed. During the subsequent adsorption step, significantly more material adsorbs to the film surface. Rinsing appears to cause changes in film morphology that facilitate the adsorption of a new layer. A 2-min rinse will usually give good results. Drying the film with a nitrogen stream is necessary when analytical measurements are to be performed. However, drying may affect film morphology. The effect of drying-induced manipulation of the film surface at regular intervals has been investigated in (PSS/PAH)n films [92]. Instead of keeping the film wet throughout all deposition cycles, the films were dried at regular intervals during alternating deposition of a PSS polyanion or PAH polycation. For example, when the films were dried after every sixth layer, X-ray reflectance measurements showed the appearance of higher order Bragg peaks, suggesting reorganization of film structure to form unit cells larger than the bilayer thickness [92]. Drying procedure effects on thickness were shown in (Pre-PPV/PVS)12 films [93]. When the films were dried after four adsorption cycles and there was no salt present in the dipping solution, the thickness per bilayer was 47 A. The bilayer thickness increased to 90 ,~ when the films were dried after each adsorption cycle. The difference became negligible under high salt conditions.

4.1.2.4. Ionic Strength Ionic strength has been found to have a major effect on deposition kinetics and the amount of material deposited on the surface. The presence of counterions shields the electrolyte charges and increases the rate of adsorption [ 14]. A detailed investigation of ionic strength effects on colloidal silica particle adsorption has been performed [94]. At ionic strengths below 200 mM, the mass uptake per layer was directly proportional to ionic strength. At higher ionic strength, the mass uptake increased with the square root of ionic strength. An investigation of (SiO2/PDDA)n films revealed a strong dependence of ionic strength on mass uptake [95]. When the ionic strength was 0 M, the film mass was 8.1/zg; increasing the ionic strength to 0.25 M caused the film mass to increase to 47/zg.

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104-~..___

10 3_

-,.\

/~-,-~.

-

--"-,_

6

~, 10 2\

x,

.--.,

10 :t_

10 ~ 0.5

/

I

1

I

I

1.5

2 20(deg)

I

2.5

I

3

I

3.5

Fig. 7. X-rayreflectivity data for PSS/PAH adsorbed on optical waveguides precoated with boladication. Data shown are for 4, 6, 8, and 10 monolayers (2, 3, 4, and 5 bilayers). (Source: Adapted from [85], with permission from Elsevier Science.)

4.2. Methods for Characterizing Polyion Multilayer Films

4.2.1. X-Ray Small-Angle Reflectometry Method A powerful method for measuring film thickness is small-angle X-ray reflectance (SAXR) [96]. X-ray reflection from a uniform film on a substrate with a thickness L exhibits interference between waves reflected at the air-film interface. A plot of reflectance vs. incident angle yields Kiessig fringes whose minima or maxima show a regular spacing A0, and film thickness can be estimated from L=

2A0

(7)

where ~. is the X-ray wavelength. An example of X-ray reflectivity data is shown in Figure 7. Electron density and film roughness can be measured by fitting experimental data to a suitable theoretical model.

4.2.2. Optical Spectroscopy 4.2.2.1. UV/Vis Spectroscopy If the PMF has a chromophore, UV/Vis spectra of PMFs show a linear buildup of absorbance [9, 38, 73, 86, 90]. Kinetics of film deposition can be monitored by UV/Vis. By monitoring the absorbance at 420 nm, the kinetics of deposition of a single monolayer of PTAA onto a PAH layer has been monitored [97]. Multilayers of positively and negatively charged colloidal particles like silica and alumina exhibit interference colors that exhibit maxima and minima in their reflection bands from which thickness can be determined [69].

4.2.2.2. Ellipsometry Ellipsometry is another technique for measuring film thickness [98]. Spectroscopic ellipsometry involves measurement of the phase and amplitude change upon reflection of s or p polarized light. The basic equation of ellipsometry is p = tan(qJ)e i•

(8)

where p is the ratio of complex reflectances between s or p polarized light, A represents the relative phase shift between the s and p components, and qJ represents the change in

724

BIOMIMETIC THIN FILMS

1.8-~-

A

1.7"~ 1 . 6-::

& 1.>: 1.4-:'

o

.~

0

0 0

210

410 '

610

810

1 O0

Number of Bilayers Fig. 8. Real (A) and imaginary (B) refractive index components calculated from ellipsometric data for (PLL/Cu-PTSA)n films. (Source: Reprinted with permission from [38]. 9 1995 American Chemical Society.)

intensity. A and q~ are functions of film thickness and refractive index. At any wavelength two equations (A and qJ) are a function of three variables: film thickness (d) and the real (n) and imaginary (k) index components. When k = 0, n and d can be solved for a given film model. When k -r 0, two variables can be obtained by fixing the third. An example of refractive indices obtained from ellipsometric data is given in Figure 8. The data show calculated n and k for a series of (PLL/Cu-PTSA)n films. By fixing d, n and k were calculated. The trends in n and k reflected changes in film roughness and homogeneity. The calculated imaginary component k became independent of thickness with optical density greater than 1 [99]. It was then possible to use a simple expression for film thickness obtained from the absorbance (A) and k [38]: L=

2.303AX 4n-k

(9)

With this approach, film thickness can be measured. Real-time ellipsometry has also been used to monitor deposition kinetics of the amphiphilic PAM on a self-assembled mercaptoalkanoic acid monolayer on gold [100] (Scheme 5).

H21~ / ~ /~ NH2 + /~\ /)--O(CH2)sO~\ I}'--~ + H2N ,c_._v ~ NH2 PAM Scheme 5

725

COOPER

4.2.2.3. Reflectance Hoogeveen [22] describes reflectance measurements of PMFs. For small reflectances, the reflectometer signal is given by r =

1 AS

As So

(10)

where As is the sensitivity factor proportional to the refractive index increment of the polymer. Caruso used reflectance measurements on gold substrate PMFs, as gold is highly absorbing [75]. His reflectance measurements were referenced to the substrate, so reflectance data could be converted to absorbance using A -- - l o g

(11)

where A is the absorbance, R is the reflectance from the gold plate with adsorbed multilayer, and R0 is the reflectance from the gold plate. PMFs have been characterized by total internal reflection fluorescence (TIRF) spectroscopy [36, 101]. The technique requires a fluorescent species to be present in the film. An argon ion laser beam couples into the glass substrate through glass prisms. The evanescent field at the substrate surface excites the fluorescent dye in the film. The fluorescent light is collected by an optical system and analyzed by an optical multichannel analyzer. To investigate different experimental conditions, the substrate serves as the top of a flow cell flushed by a pump.

4.2.2.4. Surface Plasmon Resonance Surface plasmon resonance spectroscopy has been used to measure PMF thickness and deposition kinetics. The technique involves production of a surface plasmon, a transverse magnetic electromagnetic wave traveling along the interface between two media [102]. The experimental apparatus consists of a prism on which a 70-nm gold film has been deposited. The surface plasmon mode can be excited by the evanescent field arising from total internal reflection inside the prism. By measuring the intensity of the reflected light as a function of incident angle into the prism, a resonance angle can be found that gives maximum production of the evanescent field. Deposition of a thin film on the gold layer causes the resonance angle to vary. The reflectivities can be fit to the Fresnel equations for the system, from which refractive index and film thickness can be obtained. Examples of surface plasmon resonance measurements on PMF systems include polymer [21, 75, 103], nanoparticle [8], and protein [20] systems.

4.2.2.5. IR Spectroscopy IR spectroscopy has been used to monitor material deposition [34]. Albumin, adsorbed to a germanium crystal, can be monitored with infrared multiple internal reflection spectroscopy. Deposition kinetics have been measured from the albumin absorbance at 1549 cm -1 . Deposition of heparin on an albumin monolayer has been monitored from the absorbance at 1030 cm- 1.

4.2.3. Atomic Force Microscopy~Scanning Tunnelling Microscopy Atomic force microscopy (AFM) and scanning tunneling microscopy (STM) are kindred microscopy techniques that give resolution down to the atomic level [ 104-106]. STM measures the electrical tunneling current that flows between two conductors (the STM tip and the analyzed surface) separated by distances on the order of Angstroms. Factors influencing the current include the distance between the two conductors and their electron band structure. The technique has been particularly succesful in imaging molecules containing aromatic groups. The more popular AFM technique does not require electrically

726

BIOMIMETIC THIN FILMS

conducting surfaces, but rather measures forces between the scanning tip and the surface, including electrostatic, magnetic and van der Waals forces. Another variation on these techniques is friction force microscopy [104], in which both horizontal and vertical forces between the tip and the surface are investigated. Although these techniques make it possible to image molecular and atomic scale objects, the microscopy saying "Believing is seeing" applies. Sources of artifacts include room vibrations, electrical noise, confusing step edges in the substrate or the substrate itself with adsorbed molecules and monolayers, and scratches on the surface formed by the AFM tip. In addition to the creation of images, AFM has been used to measure film roughness, defined as the RMS difference between peak and valley height. A recent variation on the technique is chemical force microscopy. By chemically modifying the cantilever tip with specific groups (hydrogen bond donors, hydrophobic groups, etc.), it is possible to image a surface in terms of specific intermolecular forces [ 107]. AFM has been used to characterize PMFs and give insight into the mechanism of film formation. Multilayers composed of a cationic polyelectrolyte and individual sheets of the mineral hectorite have been prepared [78]. Individual hectorite sheets 25-30 nm in dimension were imaged by AFM. A common observation with PMFs is increased surface roughness and poor deposition of material with less than five monolayers. Direct AFM observations of PSS monolayers showed nonuniform deposition at the earliest stages [108]. At short deposition times (1 min), the charged macromolecules adsorbed to surface defects, forming islands and retaining their coil conformation. At longer deposition times (10 min), homogeneous monolayers composed of flattened polymer chains formed. AFM has been used to study the adsorption of charged latex particles on mica [ 109]. Because latex particles are large and easy to image, AFM was a useful tool for probing the mechanism of monolayer formation in PMFs. Surface coverage, determined by analysis of AFM images, was measured as a function of adsorption time and ionic strength. From analysis of the images, the initial kinetics are diffusion limited, converting to random sequential adsorption at long times. For each ionic strength, surface coverage rose rapidly during the early stages of adsorption, then leveled off. The total surface coverage increased dramatically with increasing ionic strength. At low ionic strength, long-range repulsions between latex particles limited the extent of adsorption. At higher ionic strength, interparticle repulsions decreased because of double layer screening. In situ images of adsorbed layers differed from those of dried samples, showing rearrangement of the particle packing upon evaporation.

4.2.4. Quartz Microbalance The quartz crystal microbalance (QCM) technique allows for real-time monitoring of rate and amount of monolayer deposition during PMF monolayer formation. The QCM is a piezoelectric device capable of measuring mass changes on the order of nanograms. The Sauerbrey equation describes changes in the resonant frequency of a quartz crystal with the change of mass of material loaded onto the crystal [110]" Af =

-2Amf 2 (Po#o)l/2A

(12)

where f0 is the fundamental frequency, P0 is the density, and #0 is the shear modulus of the unloaded quartz crystal. When a mass Am is deposited on a crystal of area A, the resonant frequency decreases by Af. For a 9-MHz quartz resonator, the relationship between adsorbed mass (g) and frequency shift (Hz) is A F = - 1 . 8 3 x 108M A

(13)

For a resonator area of 0.16 cm e, a 1-Hz frequency change corresponds to a 0.9-ng mass increase. The technique can be used to measure the mass of a dried film. After the sample is dried in a nitrogen stream, the resonance frequency can be measured and the Sauerbrey equation used to calculate the adsorbed mass. Figure 9 shows a plot of frequency

727

COOPER

--

1000

A 8111) 600 m I

40O -

200 --]

0

.

. . . . . . . .

E

5

10

0 Number

of Adsorption

'

'

'

I

15

Cycles

Fig. 9. Frequency decrease (-AF) measured by QCM upon dye-polyion film adsorption. A: Oddnumbered steps represent adsorption of 1 mM CR. Even-numbered steps represent adsorption of 1.9 mM (in monomer) PDDA. B: Odd-numberedsteps represent adsorption/desorptionof 10 mM CR. Even-numberedsteps represent adsorptionof 35 mM (in monomer)PEI. (Source: Adapted with permission from [73]. 9 1997 American Chemical Society.)

decrease as a function of the number of adsorption steps for (CR/PDDA)n and (CR/PEI)n. In (CR/PDDA)n (Fig. 9A), the frequency decrease represents monotonic adsorption of dye and polymer. In the second case, (CR/PEI)n (Fig. 9B), the frequency increases in the presence of PEI, showing partial dye desorption. The QCM technique can also be used to measure film thickness [81 ]. For example, in (GOx/PEI)n films, a plot of A f vs. number of adsorption cycles underwent a linear decrease in frequency past five films. The frequency change per cycle had two components: - 2 1 5 0 Hz for GOx and - 5 0 Hz for PEI. By making assumptions about film density, a "rule of thumb" equation of thickness on both sides of a 0.16 cm 2 electrode is L (,~) " ~ - 0 . 1 6 A f (Hz)

(14)

giving a bilayer thickness of 350 ok. The technique can also be used for adsorption kinetics measurements. By placing one side of the resonator in permanent contact with the solution, real time measurements of the resonance frequency can be obtained. To prevent a short circuit, the upper contact wire is convered with silicon paint to insulate it from the solution. Alternatively, there are commercially available beakers with resonators mounted so that only one side is exposed to the sulution. An example of QCM kinetics data is given above (Fig. 6).

4.2.5. Contact Angle Measurements Contact angle measurements have been used to characterize PMFs. Unless it wets the surface, a liquid placed on a solid will form a drop with a contact angle between the liquid and solid phases. The contact angle is given by Young's equation [ 111 ]" YLVCOS0 -- YSV -- YSL

(15)

where 0 is the contact angle and FLV, YSV, and YSL are the surface energies for the liquidvapor, surface-vapor, and surface-liquid interfaces, respectively. When 0 = 0 ~ the liquid wets the surface. When 0 = 180 ~ a spherical droplet forms on the surface. Tables of contact angles for various surfaces have been prepared [ 111 ]. Hydrophobic surfaces have contact angles around 110 ~ whereas hydrophilic surfaces approach 0 ~ Methods for measurement of the contact angle have been described by Murray [ 112] and Adamson [111 ]. For accurate measurements, Murray recommends making multiple measurements on the same

728

BIOMIMETIC THIN FILMS

40 30

.< 2o ~

lO

r,,) .

.

.

.

.

.

.

.

t ........

t ........

0 5 10 15 20 25 N u m b e r of Layers of TIO2/PSS Films

30

Fig. 10. Advancingcontact angles of TiO2/PSS multilayerfilms as a function of the numberof deposited monolayers. Adapted with permission from [113]. (g) 1997 American Chemical Society.

drop and having an awareness of the effect of surface roughness and heterogeneity on the contact angle. The technique involves measurement of the shape of a liquid drop deposited on a surface or the contact angle of the meniscus during dipping or withdrawal from the liquid. Liu [113] gives advancing water contact angle measurements of a TiO2/PSS multilayer (Fig. 10). Glass treated with N-2-(2-aminoethyl)-3-aminopropyltrimethoxysilane gave a contact angle of 18 ~ Anionic PSS adsorbing on this surface increased the contact angle to 37 ~ The increased contact angle resulted from adsorption of PSS with polar sulfate groups interacting with the positively charged surface and the nonpolar hydrocarbon chains oriented toward the surface. When cationic TiO2 adsorbed to a PSS surface, the contact angle decreased to 22 ~ The lower contact angle reflects the hydrophilic nature of cationic TiO2. The contact angle oscillated between these two values as the multilayer built up. Chen describes similar oscillations in a PSS/PAH multilayer prepared on a PET substrate [ 18]. These results illustrate the utility of contact angle measurements for characterizing PMF films, as the film surface energy significantly changes with the adsorption of different materials.

4.2.6. X-Ray Photoelectron Spectroscopy X-ray photoelectron spectroscopy (XPS) has been used to measure the element composition of the surface of PMF films [ 114]. A thin film is irradiated with soft X-rays and photoelectrons are emitted. The photoelectrons are collected by a lens system, and an analyzer counts the number of electrons at a given kinetic energy. The data are presented as a plot of counts per second vs. binding energy, given by B . E . - h v - K.E. - 4~

(16)

where h v is the X-ray energy, 4~ is the sample work function, K.E. is the kinetic energy of the photoelectron, and B.E. is the binding energy. The binding energies derive from the atomic core Is level from which the photoelectron was emitted and can therefore be used for analysis of the elemental composition of the surface. The surface sensitivity of XPS results from the distance an electron of a certain kinetic energy can travel through a material before undergoing an inelastic collision. The attenuation of photoelectron intensity as a function of sampling depth is given by N = N o e -t/~" cos0

(17)

where No is the number of photoelectrons that originate at depth t, N is the number of photoelectrons that have not inelastically scattered, )~ is the mean free path of the electron, and

729

COOPER

Ols

Cls

1 0----

_

6t "415 _

.m

410

41)5

41)0

395

4_ .

0 2b0 1:~00 1t~00 860 660 460 Binding Energy(eV) ,

,

.

.

.

.

.

.

.

.

.

.

I

,

,

~

1

6

Fig. 11. Exampleof XPS data. Data collected from chitosan + (sulfonated C60/tetrapyridiniumporphyrin)10 film. The inset gives high-resolution data collected in the vicinity of 400 eV. Data are courtesy of Dr. Hao Jiang, Anteon Corporation, Dayton, OH.

0 is the takeoff angle. The sampling depth, the depth that gives 95 % of the signal intensity, is 3kcos0. Munro lists mean free paths ranging from 7 to 15/k. By varying 0, different depths of the sample can be probed. Delcorte gives an extensive study of PMF films, containing correlations of XPS data with ToF-SIMS, SAXR, and AFM [13]. An example of XPS data from a PMF film is given in Figure 11. The XPS spectrum was obtained from a (sulfonated C60/TMPyP)10 film that had been placed on a chitosan-treated glass slide. High resolution XPS data (inset to Fig. 11) showed fine structure associated with nitrogen. The satellite peak at 407 eV resulted from charge transfer interactions between sulfonated C60 and the porphyrin.

4.3. Polymer/Polymer Films 4.3.1. PSS/PAH PMFs composed of PSS/PAH bilayers have been investigated in detail and serve as a model system (Schemes 6 and 7). An early study demonstrated the formation of thin films composed of up to 50 PSS/PAH bilayers [80]. The absorbance and film thickness determined by SAXR increased linearly. Thin films containing PAH/PSS bilayers have been successfully grown on gold surfaces [75]. Regular film buildup was observed after two PAH/PSS precursor bilayers were placed on the gold surface. PAH/PSS multilayers have also been prepared on a PET substrate [18].

SO3 PSS

PAH

Scheme 6

Scheme7

4.3.1.1. Structure and Composition The structure of films composed of PSS/PAH bilayers have been probed by X-ray scattering, neutron reflectivity, and optical waveguiding experiments. To prove that multilayer

730

BIOMIMETIC THIN FILMS

organization exists in PMFs, films with the composition (PSS/PAH + PAZO/PAH)n were made [92] (Scheme 8).

NH I

N~"N

[ ~CO0OH

PAZO Scheme 8 A Bragg peak in X-ray reflectivity gave a spacing of 93.4 ,~ corresponding to the four-layer repeat unit. Combined neutron reflectivity and SAXR measurements were performed on partially perdeuterated PSS/PAH films [83]. The film [PSS-hT/PAH + PSS-hT/PAH + PSSdT/PAH]8 had one perdeuterated layer every six layers. The layers were deposited from high ionic strength solutions. A schematic of a PSS/PAH bilayer is depicted in Figure 12. The authors analyzed the film in terms of its constituents: polyelectrolyte, water, and counterions. Film thickness measured by SAXR and neutron reflection agree, giving a bilayer thickness of ~ 5 0 ,~. The large monolayer/monolayer roughness (19 ,~) reflected considerable chain-chain interdigitation. Film composition data suggested a high water (four water molecules per monomeric PSS unit) and estimated counterion content (0.5-0.8 anions/cations per polyelectrolyte repeat unit), as well as a nonstoichiometric NpAH/Npss = 1.5. The monomer ratio agreed with XPS data obtained from PSS/PAH multilayers adsorbed on PET. In that study the ratio of nitrogen to sulfur ranged from 1.3 to 2 [18]. Evidence for the presence of water in PMF films was obtained from a thermal stability study of PSS/PAH films [39]. A (PSS/PAH)20 was annealed at 190~ for 3 h. Comparison of FTIR spectra before and after annealing showed a decrease in absorbance at 3450 cm -1 , corresponding to water loss.

Fig. 12. Schematicof PAH/PSS bilayer, using data from [83]. The bilayer is composedof a PSS layer, a PAH layer, and a 12-/~thickness interdigitation region.

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COOPER

The structure of a PSS/PAH multilayer has been probed through the use of optical waveguide experiments [85]. The PSS dipping solution contained 0.5 M MnC12, and the PAH dipping solution contained 2 M NaBr. The thin film had three refractive index tensor components: two equal no components parallel to the substrate and one component ne perpendicular to the substrate. As the number of layers increased, no decreased and ne increased, giving a positive birefrengence ne - no. The birefringence increased from 0.036 in a two-bilayer film to 0.081 in a five bilayer film. The birefringence data suggested that the polymers tended to lay parallel to the substrate surface when there were a few bilayers and formed polymer loops and chains oriented perpendicular to the substrate where there were more bilayers.

4.3.1.2. Ionic Strength Effects As well as polymer concentration, dip time, and substrate properties, dipping solution ionic strength has a significant effect on film thickness. Table II lists the results of several studies focusing on ionic strength effects. By changing the ionic strength of the anionic electrolyte solution while keeping the cationic electrolyte solution at low ionic strength, bilayer thickness could be varied by a factor of 2 [9, 115]. With both the PAH and PSS solutions at high ionic strength, the bilayer thickness increased by another factor of 2 ([9] and other references cited in Table II). When the films prepared from high ionic solutions were placed in water, the salts did not leave the film. Instead the films swelled 6-10% over 15 days. The increased thickness remained upon drying [9]. A PSS/PAH film prepared from low-ionicstrength solutions showed similar swelling/drying behavior but was four times thinner. The salt effect resulted from ionic strength effects on polyelectrolyte conformation. Early investigations of polyelectrolyte adsorption on surfaces revealed that the polymer had a "fiat" conformation on a highly charged surface in the presence of a low-ionic-strength medium [116]. With increased ionic strength, intersegmental electrostatic repulsion was suppressed, and the polyelectrolyte chain assumed an extended conformation (Fig. 13). Advancing contact angle measurements provided another probe of the effect of dipping

Table II. The Effect of Ionic Strength on Bilayer Thickness in PSS/PAH Multilayers

PAH solution*

Bilayer thickness(/~)

PSS solutiont

Reference

0.0

0.0

10.7

[9]

0.0

0.5

14.0

[91

0.0

1.0

17.2

[91

0.0

1.5

19.4

[9]

0.0

2.0

24.0

[9]

2.0

2.0 & 1.5

51.0I:

[9, 79, 80, 83, 85, 92, 169, 170]

0

3.0

100

[751

*Ionic strength of low-molecular-weight electrolyte (NaC1or NaBr) added to PAH solution. t Ionic strength of low-molecular-weight electrolyte (NaC1,NaBr or MnC12)added to PSS solution. ~Bilayer thickness is average of estimates given in the references.

732

BIOMIMETIC THIN FILMS

Fig. 13. Schematicof polymer monolayer under conditions of low and high ionic strength. High ionic strength lessens electrostatic repulsion, promoting formation of loops, trains, and tails.

solution ionic strength on film properties [ 18]. In a series of PSS/PAH multilayers having PAH as the outermost layers, the advancing contact angle was 70 ~ when 1.0 M MnCI2 was in both dipping solutions. When MnCI2 was only in the PSS solution, the angle decreased to 60 ~ When no MnCI2 was used, the angle decreased to 46 ~ When the PSS layer was the outermost layer, the ionic strength effect was smaller: the contact angle was 45 ~ in both experiments using MnCI2 and increased to 53 ~ when no MnCI2 was present. The PSS layer tended to be more wettable than the PAH layer, possibly reflecting the tendency of the sulfate groups orienting near the surface facing the dipping solution and the aromatic tings orienting away from the surface. When PAH was on the surface, the films became less wettable with increasing ionic strength of the dipping solution. To a lesser degree the opposite trend occurred with films that have PSS on the surface. The trends reflect dipping solution ionic strength effects on the relative proportion of film surface hydrophobic and hydrophilic groups. Increasing ionic strength also caused reversible thickness changes in previously prepared PMFs [77]. A series of PSS/PAH multilayers were prepared and immersed in salt solutions of varying ionic strengths. After the salt solution was removed, film thickness was measured by SAXR. Film thickness changes up to 18% were complete after 1-2 h of immersion time. By immersing the films in deionized water, the film swelling could be reversed within experimental error. Moreover, the films became smoother after several cycles of dipping into salt solutions and deionized water. Measurement of film thickness changes as a function of salt concentration revealed a small range of salt concentrations (0.02-0.1 M) in which swelling occurred. When the concentration was below 0.02 M, no swelling occurred. Furthermore, no further swelling occurred with concentrations greater than 0.1 M. Changes in the proportion of loops, trains, tails, intralayer entanglements, the width of the polyanion/polycation interface, and salt bridges could contribute to the observed swelling changes, although the exact structural changes are unknown.

4.3.1.3. Electrostatic Properties The electrostatic properties of a PSS/PAH multilayer have been probed through the use of a pH-sensitive fluorescent dye [36]. PAH was derivatized with fluorescein isothiocyanate to form FITC-PAH. Initially, a 140-~ precursor film containing layers of PEI, PSS, and PAH was placed on the substrate (Schemes 9 and 10).

"~

NI-I~+ ) PEI Scheme 9

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COOPER

I

NH

I

~COOH O~OH FITC-PAH Scheme 10 After the last PSS layer of the precursor film, a monolayer of FITC-PAH was placed on the film. Then varying numbers of PSS and PAH layers were placed on the FITC-PAH layer. The dye fluorescence was measured by the TIRF technique under conditions of varying external pH. Shifts in the pH titration curve monitored by fluorescence gave information about the proton concentration gradient in the multilayer. The authors considered three parameters: film thickness, charge on the film surface, and ion concentration of the buffer solution. The nature of the group on the surface of the film had a significant effect on the pKa of the FITC-PAH. The pKa of FITC-PAH in solution was 4.6. For all films with PAH as the outermost layer, the pKa was 5.9. In contrast, films with PSS on the surface had a pKa of 7.5 for the thinnest films, decreasing to 5.8 for the film (PSS/PAH)8 + PSS. The pH effect on fluorescence intensity decreased with increasing film thickness, with no effect beyond a 100-,~ thickness above the FITC-PAH layer. When in the presence of divalent cations, the portion of the titration curve that could be measured for films with a PSS surface layer shifted to a lower pKa. The divalent cations neutralized the sulfonate charge, thereby decreasing proton affinity. In the presence of buffered high salt concentration, films with a PSS surface layer had increased fluoresence intensity, whereas films with a PAH surface layer showed decreased intensity. The results for films with a PAH surface were not reversible, reflecting salt-induced morphology changes. The salt effect was negligible in thick films. The ionic strength effect on fluorescence intensity was attributed to ionic strength effects on pKa. When PAH was on the surface, the pKa increased, whereas it decreased with PSS on the surface. The Gouy-Chapman-Stern model was used to describe the ion distribution inside the film. The electrical potential decayed exponentially, where decay length was a function of surface charge and ionic strength. A more recent study uses similar strategies to measure transport through a PMF [ 101 ]. A series of fluorescent films containing a FITC-PAH layer was prepared as above. A rhodamine solution was added to the outer aqueous phase, and diffusion of the dye into the multilayer was measured by energy transfer between the dyes that quenched FITC-PAH fluorescence. A depth-dependent diffusion coefficient of 10 -15 cm 2 s -1 was measured for the rhodamine dye. The smaller paramagnetic quencher 2,2,6,6-tetramethyl-4-piperidinol1-oxide had a diffusion coefficient at least two orders of magnitude larger.

4.3.1.4. Gas Transport Stroeve describes the gas permeation properties of PSS/PAH multilayers [ 117]. Multilayers were placed on silicone membranes and gas permeability was measured. A polyion film adsorbed to a silicone membrane gives significantly reduced gas permeability compared to an untreated membrane. Because of incompatibilities in mechanical properties, microcracks appear in the multilayers, forming leaks and increasing gas permeability. The polyion coated membrane gives increased CO2/N2 selectivity, so the multilayer films have

734

BIOMIMETIC THIN FILMS

a possible application as a gas separation membrane. In a related study, Lavasalmi prepared PSS/PAH films on a surface oxidized poly(4-methyl-1-pentene) substrate with the goal of developing an asymmetric gas separation membrane [ 118]. The PSS/PAH multilayer has a gas permeability to N2 18,000 times lower than that of the substrate alone. 4.3.2. OtherPolymer~PolymerSystems

Thin films composed of bilayers PVS/PAH have been prepared [88] (Scheme 11).

SO3 PVS Scheme 11 Unlike PSS/PAH films described above, film buildup could not be followed spectrophotometrically, but rather was followed from SAXR. Like the systems described above, increased ionic strength caused the bilayer thickness to increase from 13 ,~ to 34 ,~. The film thickness of a 24-bilayer PVS/PAH film was measured as a function of temperature. From room temperature to 50 ~ the film thickness remained constant. From 60 ~ to 120 ~ the film thickness decreased 6%. The film thickness remained constant to 150~ When the film cooled, the high temperature thickness remained constant. After 2 weeks, the film thickness nearly retumed to its initial value. A likely explanation for the thickness changes is the removal/addition of water. The SA technique has been used extensively to prepare multilayers of conjugated polymers, thereby providing a means of assembling thin films with novel electrical and optical properties. PMFs containing the conjugated polymers SPAn, polyimide precursor, and PTAA have been investigated for potential electrooptic applications [97, 119] (Schemes 12-14). O

(HN

.0 .

PTAA

"OOC" ~

O NH

)

NH

"COO"

Polyimide Precursor

~NOaSPAn

Schemes 12-14 For both SPAn/PAH and PTAA/PAH films, the amount deposited was directly proportional to the number of bilayers. During short deposition times, adsorption kinetics followed a diffusion-controlled adsorption process, slowing thereafter. In the pH range 4.86.4, adsorption of PTAA to a charged surface was dependent upon pH. The equilibrium amount of PTAA adsorbed increased with increasing pH. The pKa of PTAA was near 4.6, so protonation of ionized acetate groups enhanced adsorption by decreasing electrostatic repulsion. In the pH range 2.0-4.0, films containing SPAn showed less dependence of deposition on pH with the amount adsorbed increasing with decreasing pH. In this case, NH groups in SPAn were protonated, decreasing the net charge and electrostatic repulsion. The more complex film (SPAn/PAH/FI'AA/PAH)20 has also been prepared. The UV/Vis data showed a linear increase in the amount of both polymers deposited with increasing number of bilayers. Light-emitting diodes have been prepared by the SA technique [120]. Multilayers containing the negatively charged polymers PSS or PMA and the positively charged p-phen-

735

COOPER

ylene vinylene precursor (pre-PPV) were prepared using a programmable slide stainer (HMS programmable slide stainer; Zeiss).

pre-PPV Scheme 15 After the slides were dried overnight under a vacuum, pre-PPV was converted to PPV by heating at 210 ~ under vacuum for 11 h, followed by 4-h cooling period. After film preparation, an A1 layer was depositied by thermal evaporation on the film. The intensities of both the absorption spectra and photoluminescence spectra of the films were directly proportional to the number of bilayers. Another example consists of SPAn/pre-PPV multilayers that have been thermally converted into electroluminescent films [121] and PVS/pre-PPV [93]. More complex heterostructures have been fabricated as light-emitting diodes [122]. Onitsuka fabricated a series of PPV-containing thin films and measured the voltage/current/light intensity relationship. He found the nature of the anion layers had a significant effect on the electrical properties of the films. He compared the weak carboxylic acid functional group of PMA with the strong sulfonic acid group of PSS (Scheme 16).

PMA Scheme 16 Devices based on PMA/PPV had consistently higher light levels than PSS/PPV, possibly because of p-type doping taking place between the acidic sulfonic PSS groups and PPV's conjugated backbone, creating polarons and bipolarons that quenched luminescence. However, there was efficient hole transport from SPS/PPV films into PMA/ PPV bilayers. To use this property advantageously, a heterostructure of the type ITO + (PSS/PPV)5 + (PMA/PPV)15 + A1 was made. Compared to devices fabricated with only PMA/PPV bilayers, an order of magnitude luminescence increase occurred. Film performance was a strong function of the nature of the heterostructure. For example, they prepared a series of heterstructure devices ITO + (PMMPPV)20 + (PSS/PPV)n + A1, with n varying from 1 to 20. A single PSS/PPV bilayer dramatically decreased the output of the device. When n = 5, the device had negligible output. The opposite performance was observed in the devices ITO + (PSS/PPV)n + (PMA/PPV)20 + A1. Up to n = 10, the luminescence intensity increased with the number of PSS/PPV bilayers. This behavior resulted from the ability of the PSS/PPV bilayer to increase the electron injection barrier at the A1 electrode or trap electrons injected from this electrode. Both behaviors can be controlled by preparing a suitable heterostructure. A related system was prepared from multilayers consisting of Bu-PHPyV/PSS bilayers [29] (Scheme 17).

H

Bu-PHPyV Scheme 17

736

BIOMIMETIC THIN FILMS

A multilayer assembly of redox polyelectrolytes has been prepared [71 ]. CV of multilayers with the composition (PBV/PSS)n showed a linear increase in peak current with n (Scheme 18).

PBV Scheme 18 The result suggested that all electroactive material in the film underwent oxidation and reduction, thus requiting an electron-hopping mechanism between bilayers. A strong influence of distance between PBV layers and the electrode was observed. A series of multilayers Au + MPS + (PAH/PSS)n q- PBV/PSS was prepared. For n = 1-3, the CV was similar to the results described above, except that the slower electron transfer caused a greater cathodic/anodic peak separation. When n -- 4 or greater, no current was detected. Extensive interpenetration between layers was shown by variable-angle XPS, which revealed a 1:1 stoichiometry between charges in the multilayers. No salt ions were detected. Tsukruk describes multilayer films prepared from dendrimers [ 123]. He used PAMAM dendrimers with surface amine groups from generations 4, 6, and 10 as the positively charged polymers and dendrimers with carboxylate surface groups from generations 3.5, 5.5, and 9.5. All even generations formed homogeneous, stable monolayers on a silicon surface. Monolayer thickness was much smaller than the diameter of hypothetical spherical dendrimers, implying compression of the dendrimers into oblate spheroids with axial ratios ranging from 1:3 to 1:6. Multilayers with the composition (Gn/Gn-o.5) were successfully prepared, with thicknesses ranging from 1.8 to 5.6 nm/monolayer and 100-fold variation in dendrimer molecular weight. Nonlinear optical effects have been demonstrated in PMF films [124]. Lvov et al. prepared films with an azobenzene-containing polyanion, PAZO. (PEI/PSS)2 + (PDDA/ PAZO)n multilayers showed generation of second harmonic radiation at 532 nm upon irradiation at 1064 nm (Scheme 19).

PDDA Scheme 19 Measurement of the angular dependence of second harmonic intensity while the film was rotated gave Maker fringes, behavior expected for a noncentrosymmetric film (Fig. 14). When n was varied, maximum SHG was observed for n = 4, with the signal decreasing thereafter. The result implied that substrate surface effects promoted noncentrosymmetric morphology in the films, with the effect decreasing with larger numbers of bilayers. When the films were heated, the SHG signal decreased to the signal seen for n = 1, showing that chromophore orientation was retained in the first layer. A detailed investigation of the mechanism of SA has been made by Stuart and his research group [22]. They measured the if-potential of monodisperse colloidal silica particles in the presence of charged polymers. Colloidal silica particles had a net negative charge and ~'-potential. They formed the multilayer (PVI/PAA)2 on the silica particle, with measurement of the ~'-potential and hydrodynamic radius at each step (Fig. 15). With the addition

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COOPER

300

----

250 -

-- -- -IIPPs-pI 200e~

150 100500

....

0

I ....

10

I ....

I ....

t ....

20 30 40 Incident Angle(deg)

I*'

,J

I

60

50

Fig. 14. Exampleof Maker fringes in (PDDA/PAZO)4 film. (Source: Adapted from [124], with permission from Elsevier Science.)

J

0-

0-

~,

20-

re

O-

PVI +

f

-20-~ I / ' i ~ l l 0

PAA

-40-60-80

"0 .....

0

', ....

J ....

t ....

I ....

0.1 0.2 0.3 0.4 0.5 D e g r e e of Q u a t e r n i z a t i o n

1

0.6

Fig. 15. (-potentials of silica particles after addition of PVI+ (open squares), PAA (filled squares), PVI+ (open circles), and PAA (filled circles). The abscissa is the degree of quaternization of cationic PVI+, a measurement of the proportion of charged groups. (Source: Adapted with permission from [22]. 9 1996 American Chemical Society.)

of highly charged PVI, the (-potential became positive. With the addition of PAA, the (-potential became negative (Schemes 20 and 21).

CH3 PVI

PAA

Schemes 20 and 21 The changes were the same with subsequent bilayer formation. The results demonstrated that addition of the oppositely charged polyelectrolyte caused strong overcompensation of the surface charge. The overcompensation of charge is a fundamental reason why polyion multilayer films can be prepared. Multilayer formation on a silica or titania substrate was monitored by reflectance measurements. By systematically varying the charge on PVI, the

738

BIOMIMETIC THIN FILMS

effect of charge on adsorption was determined. The ~'-potential of colloidal silica was a function of counterion charge. No adsorption on a PAA monolayer was observed when the PVI's average charge/monomer dq = 0. Significant adsorption occurred when dq = 0.5. Similar behavior was observed in the PAMA/PMA system when the charge was varied with increasing pH, causing deprotonation of the cationic PAMA (Schemes 22 and 23).

H3C~N"CH3

~

PAMA

+-CH3

PVP

Schemes 22 and 23 From reflectance measurements, the stoichiometry of multilayer formation was determined (Table III). In the PVP/PSS system the ratio between cationic and anionic charges was --,3. This value was independent of ionic strength and pH, although the amount of both polymers adsorbed increased with ionic strength. In contrast, the PAMA/PSS system had a stoichiometry of ~ 1. From these results, it appears that the type of polymer influences the stoichiometry. For PAMA and PSS, the charge resides farther from the backbone than PVP, suggesting that steric factors may influence stoichiometry. For electroneutrality, the rest of the charge must be compensated for by small ions. Hammond describes polymer microstructure formation by the deposition of PDDA/PSS multilayers on a monolayer template [ 12]. She used the technique of microcontact printing to prepare a template. The technique involves a poly(dimethylsiloxane) stamp molded from a photolithographic master to transfer 2.5-#m lines of hexadecanethiol or 16-mercaptohexadecanoic acid to a surface separated by 3.5-/zm spaces. To prevent adsorption of the ionic polymers to regions of bare gold, the gold substrates were then dipped into a 5 mM solution of an oligo (ethylene glycol)-terminated alkanethiol to cover the remaining gold regions. As the gold substrate was patterned with C O O - regions, selective adsorption of polycations occurred in these areas. Polymer ridging reflecting the patterning was observed in films containing high-molecular-weight polymers.

Table III. IonicStrength Effects on (PSS/PVP)n and (PSS/PAMA)n films* System

It

F+ ~

F_ w

Stoichiometry82

(PSS/PVP)n

0.005

0.56

0.35

2.7

(PSS/PVP)n

0.1

2.18

1.13

3.2

(PSS/PAMA)n

0.005

0.26

0.34

1.0

(PSS/PAMA)n

0.1

0.80

0.94

1.1

*Reprinted in part with permission from [22]. 9 1996 American Chemical Society. t Ionic strength of KNO3 in all solutions. ~tAdsorbed amount per layer of polycation (mg/m2). wAdsorbed amount per layer of polyanion (mg/m2). 82 between the number of cationic and anionic charges on the polymers in the multilayer.

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4.4. Systems Containing Dyes and Amphiphiles

4.4.1. Amphiphiles Decher and Hong have prepared multilayers containing boladikation and boladianion [ 125, 126] (Schemes 24 and 25).

Boladikation Scheme 24

"03S0C11H22--0~0--C~

1H220SO3 -

Boladianion Scheme 25 Both of these molecules contain rigid biphenyl cores and long alkyl side chains with charged groups on the end. From UV/Vis measurements, linear buildup of material was shown. They demonstrated the assembly of a 39-bilayer film composed of a monolayer of polymer PSS and 38 alternating layers of polycation PVDA and boladianion (Scheme 26).

H5c'N~c2H5 __ +.C2H 5

PVDA Scheme 26 Boladianion has a length of 44.6 ,~ in its extended conformation. Assuming that it orients perpendicular to the surface, 19 monolayers of boladianion have a thickness 847 ,~,. The calculated polymer layer thickness, 33 A, is in the range observed for other polymer systems. The bolaform amphiphile DIPY08 and the anionic polyelectrolyte PAMPSA have been investigated by AFM [19] (Schemes 27 and 28).

H

CN~(CH2)800~ /r--COO(CH2)8-N~

SO 3

PAMPSA

DIPY08 Schemes 27 and 28

The amphiphile was photopolymerizable by UV radiation. It took less than 5 min to dissolve a film in chloroform. After photopolymerization, immersion of the film in chloroform

740

BIOMIMETIC THIN FILMS

for 2 h caused only partial film removal. The diacetylene-containing amphiphile DCDS was photopolymerized after being placed in an PMF film [25, 72] (Scheme 29). -0390C9H1 u

--

---,..C9H180903-

DCDS Scheme 29 After UV irradiation, the film turned red, and a broad absorption band appeared in the visible range at 536 nm, indicating formation of a conjugated polymer backbone. Azobenzenecontaining polymeric thin films containing the bolamphiphile PyC6BPC6Py showed pH effects on film morphology [16, 127] (Scheme 30).

~~/N+--(CH2)6Q~~~'-O(CH2)~0N+ PYC6BPC6PY Scheme 30 The polymer contained both sulfonic acid and carboxylic acid groups. When the pH was 4, the carboxylate groups were protonated, and only the sulfonate groups contributed to the binding. When the pH of the bolamphiphile solution was 10, both the carboxylate groups and the sulfonate groups on the polymer surface had a negative charge, so the positively charged bolamphiphile bound to both groups. X-ray diffraction measurements gave evidence for pH-dependent morphology changes. The bolamphiphile PyC6BPC6Py has been used to prepare multilyers consisting of negatively charged porphyrins (TPPS) and phthalocyanines (Cu-PTSA) [128]. To prepare a chemically modified electrode, a multilayer consisting of Co-PTSA and the bolamphiphile PyC6BPC6Py adsorbed to a 3-mercaptopropionic acid modified electrode was prepared [ 129]. CV data demonstrated that the phthalocyanine deposited on the electrode could catalyze the oxidation of glucose. For one to five bilayers and a fixed glucose concentration, the anodic peak current was proportional to the number of bilayers, with the signal leveling off at six bilayers. The proportionality reflected increased availability of sites for catalytic oxidation of gluose. Thicker films inhibited the diffusion of glucose into sites near the electrode. The anodic peak current was directly proportional to glucose concentration in the range 1-5 mM and to the square root of the scan rate, showing that the electrode process involved glucose diffusion. Under flow injection conditions, the detection limit for glucose was 150 pmol. A closely related system for the detection of copper(II) ions involved multilayers containing Cu-PTSA; the bolamphophile PyC6BPC6Py has been described [ 130].

4.4.2. Dye Systems Multilayers containing up to 30 porphyrin bilayers CuTPPS/ZnTPyBBCR have been prepared [86] (Scheme 31).

R

/~ //~

'~

"IN-

R =

C .P~'/'~,_ . ' ~

- - ~

R

R

PyBBCR Scheme 31

741

COOPER

CV measurements on electrodes modified with these films gave a reversible 0.94-Vwave and had the ability to photocatalytically reduce 02. The photoaction spectra of the films showed a photocurrent profile mirroring the film absorption spectrum. Under backside illumination, the phtocurrent intensities increased with thickness. Action spectra obtained under frontside illumination did not show the proportionality, showing that the photoactivity was confined to layers next to the ITO/film interface. Films composed of dyes/polypeptide multilayers have been prepared [38]. The plateshaped dye Cu-PTSA and the rod-shaped dye CR (Schemes 32 and 33)

-o3s.,l =N

"03Sx

, ~

v

~

/=~

NH2

-SO3_

S03"

NH2

so3-

Cu-PTSA

CR Schemes 32 and 33

formed multilayers with the polypeptide PLL. Films composed of up to 100 bilayers of Cu-PTSA and PLL had dye aggregation changing with increasing number of bilayers. The UV/Vis spectra can be used to probe chromophore complexation. Figure 16 shows UV/Vis spectra of (Cu-PTSA/PLL)n films. The shape of the Q band of the absorption spectrum changed with increasing number of bilayers. The spectral changes resulted from variations in Cu-PTSA monomer and dimer proportions with increasing number of bilayers. Figure 17 shows plots of mole fraction monomer as a function of the number of bilayers for phthalocyanine-containing films. In all systems the monomer content decreased with increasing number of adsorption cycles. The monomer mole fraction varied with the nature of the oppositely charged species. The highest fraction of monomer appeared in Cu-PTSA monolayers, with decreasing proportion when bound to PLL and the lowest proportion when bound to the positively charged phthalocyanine alcian blue. The phthalocyanine layers had increased monomer content near the substrate, reflecting deposition of less material with only a few deposition cycles. Similar observations were made with multilayers corn-

10 o_-

[ l

~ //.~*---~.~\1

/ / / / / / . ~ .... " ~ //// ~!

A 0 ~

One BilayerI 20 Bilavers I 40Bilayersl

•

6o ,,.,.;..r.

I

, 80BUaversl IX lOOBilayersl

10.1_

z ..z

10 ' . . . . ', . . . . . . . . I .... I . . . . . . . . t ' ' ' 450 500 550 600 650 700 750 800 Wavelength(nm)

Fig. 16. Absorptionspectra of (CuPTSA/PLL)n films adsorbed to a silanized glass substrate. (Source: Reprinted with permissionfrom [38]. 9 1995AmericanChemical Society.)

742

BIOMIMETIC THIN FILMS

9,

AB (AB, CPTA )

0.4

q

:

-

0.35

CPTA -• -

A

0.3-

t!

~

(Poly(K),CPTA)

,,

A

• o 0

0.25 -

" -.

0.2

x" " ->