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)