Recent Advances in Dielectric Materials [1 ed.] 9781616682705, 9781606922668

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Copyright © 2009. Nova Science Publishers, Incorporated. All rights reserved. Recent Advances in Dielectric Materials, Nova Science Publishers, Incorporated, 2009. ProQuest Ebook Central,

Copyright © 2009. Nova Science Publishers, Incorporated. All rights reserved. Recent Advances in Dielectric Materials, Nova Science Publishers, Incorporated, 2009. ProQuest Ebook Central,

Copyright © 2009. Nova Science Publishers, Incorporated. All rights reserved.

RECENT ADVANCES IN DIELECTRIC MATERIALS

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Copyright © 2009. Nova Science Publishers, Incorporated. All rights reserved. Recent Advances in Dielectric Materials, Nova Science Publishers, Incorporated, 2009. ProQuest Ebook Central,

RECENT ADVANCES IN DIELECTRIC MATERIALS

AI HUANG

Copyright © 2009. Nova Science Publishers, Incorporated. All rights reserved.

EDITOR

Nova Science Publishers, Inc. New York

Recent Advances in Dielectric Materials, Nova Science Publishers, Incorporated, 2009. ProQuest Ebook Central,

Copyright © 2009 by Nova Science Publishers, Inc. All rights reserved. No part of this book may be reproduced, stored in a retrieval system or transmitted in any form or by any means: electronic, electrostatic, magnetic, tape, mechanical photocopying, recording or otherwise without the written permission of the Publisher. For permission to use material from this book please contact us: Telephone 631-231-7269; Fax 631-231-8175 Web Site: http://www novapublishers.com NOTICE TO THE READER The Publisher has taken reasonable care in the preparation of this book, but makes no expressed or implied warranty of any kind and assumes no responsibility for any errors or omissions. No liability is assumed for incidental or consequential damages in connection with or arising out of information contained in this book. The Publisher shall not be liable for any special, consequential, or exemplary damages resulting, in whole or in part, from the readers’ use of, or reliance upon, this material. Any parts of this book based on government reports are so indicated and copyright is claimed for those parts to the extent applicable to compilations of such works.

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Independent verification should be sought for any data, advice or recommendations contained in this book. In addition, no responsibility is assumed by the publisher for any injury and/or damage to persons or property arising from any methods, products, instructions, ideas or otherwise contained in this publication. This publication is designed to provide accurate and authoritative information with regard to the subject matter covered herein. It is sold with the clear understanding that the Publisher is not engaged in rendering legal or any other professional services. If legal or any other expert assistance is required, the services of a competent person should be sought. FROM A DECLARATION OF PARTICIPANTS JOINTLY ADOPTED BY A COMMITTEE OF THE AMERICAN BAR ASSOCIATION AND A COMMITTEE OF PUBLISHERS. LIBRARY OF CONGRESS CATALOGING-IN-PUBLICATION DATA Huang, Ai, 1965Recent advances in dielectric materials / Ai Huang. p. cm. Includes index. ISBN 978-1-61668-270-5 (e-Book) 1. Dielectrics. 2. Interconnects (Integrated circuit technology) I. Title. TK453.H83 2009 537'.24--dc22 2008047491

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CONTENTS

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Preface

vii

Chapter 1

Low-k Nanoporous Interdielectrics: Materials, Thin Film Fabrications, Structures and Properties Moonhor Ree, Jinhwan Yoon and Kyuyoung Heo

Chapter 2

Dielectric Materials: Introduction, Research and Applications R.N.P. Choudhary and S. K. Patri

Chapter 3

Understanding the Impact of High-K Gate and Spacer Dielectrics on the Device and Circuit Performance of Nanoscale MOSFETs C.R. Manoj, Angada Sachid and V. Ramgopal Rao

167

Chapter 4

Orientation Selectivity Control by Surface Potential Modification in Oxide Thin Film Epitaxial Growth Tomoyasu Inoue

197

Chapter 5

Unusual Dielectric Properties of CaCu3Ti4O12 W. Kobayashi and I. Terasaki

231

Chapter 6

Dielectric Response Methods for Diagnostics of Power Transformers Issouf Fofana, Zié Yéo and Masoud Farzaneh

249

Chapter 7

Symmetry-Induced Resonant Transmission of Electromagnetic Waves in Non-periodic Dielectric Microstructures Ru-Wen Peng

301

Chapter 8

Polymer Dielectric Materials Xiong-yan Zhao, Hong-jie Liu and Ming-zhu Wang

323

Chapter 9

Effective Permittivity, Tunability, Loss and Commutation Quality of High Contrast Composites A.A. Kolpakov, A.G. Kolpakov and S.I. Rakin

369

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vi

Contents

Chapter 10

Dielectric Materials for Electrohydrodynamic Actuators Dedicated to Aerodynamic Flow Control Pierre Magnier, BinJie Dong, Dunpin Hong, Vincent Boucinha, Annie Leroy-Chesneau and Regine Weber

421

Chapter 11

Time-Domain Methods for the Simulation of Dielectric Nanophotonic Structures Wolfram H.P. Pernice

435

Chapter 12

Dielectric Relaxation in Dilute Solutions of Polar Molecules in Non-polar Solvents Kamal N. Abd-El Nour and S.L. Abd- El-Messieh

469

Chapter 13

Design and Development of Multiferroic Relaxors and Layered Nanostructured Thin Films Ashok Kumar, Margarita Correa, N. Ortega and Ram S. Katiyar

493

Chapter 14

Modification in Dielectric Tunable Properties of Ferroelectrics for Microwave Device Applications L.B. Kong and J.W. Zhai

521

Chapter 15

Dielectric Properties of Barium Titanate Filled Mullite Composites in the Low Frequency Region (10Hz –1MHz) Alex See, Jumiah Hassan, Mansor Hashim and W. Mohd. Daud Wan Yusoff

553

Chapter 16

Modal Dispersion Curves of an Optical Waveguide Having Unconventional Core Cross Section Using Weak Guidance Approximation H.P. Singh, Vivek Singh and V.P.Arora

565

Chapter 17

Recent Advances in the Characterization of Composite Dielectric Structures Stefano Giordano and Pier Luca Palla

573

Chapter 18

Polymeric Materials for Some Electrical Applications S.L. Abd-El-Messieh and K.N. Abd-El-Nour

629

Chapter 19

Dielectric and Magnetic Properties of Ferrite Composites and Ferrite Ceramics for Potential Applications in Antenna Miniaturizations L.B. Kong, Z.W. Li and G.Q. Lin

675

Index

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761

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PREFACE This book describes various dielectric material properties, used in many kinds of research, and its industrial applications. A dielectric is a nonconducting substance and a poor conductor of electricity. They are often used in the construction of radio-frequency transmission lines. Most dielectric materials are solid (i.e., porcelain, glass, plastics). An important property of a dielectric is its ability to support an electrostatic field while dissipating minimal energy in the form of heat. The use of low dielectric constant (low-k) interdielectrics, which can lower line-to-line noise in interconnects, are described in this book. The preparation techniques, chemical structure and related properties of polymer dielectric materials are also discussed. The impact of high-K dielectric integration as a gateand space-materials for nano scale MOSFETs are described, as well as the impact of high-k devices on the circuit performance. This book also explains the resonant transmission of electromagnetic waves through aperiodic dielectric microstructures. New technology, such as the orientation selective epitaxy (OSE) which enables epitaxial growth artificially choosing growth orientation on cerium dioxide is reviewed. In addition, the development of ElectroHydroDynamic (EHD), which establishes non-thermal plasmas on a dielectric surface, is also discussed. This book describes recent advances in the simulation techniques of dielectric photonic structures. In addition, how to obtain measurements of dielectric relaxation in dilute solutions of polar molecules in non-polar solvents are explained. The practical applications of oxides, obtained by modifying the dielectric constant, is described, as well as ways to form better dielectric composite materials. The use of low dielectric constant (low-k) interdielectrics in multilevel structure integrated circuits (ICs) can lower line-to-line noise in interconnects and alleviate power dissipation issues by reducing the capacitance between the interconnect conductor lines. Because of these merits, low-k interdielectric materials are currently in high demand in the development of advanced ICs. One important approach to obtaining low-k values is the incorporation of nanopores into dielectrics. The development of advanced ICs requires a method for producing low-k dielectric materials with uniform distributions of unconnected, closed, individual pores with dimensions considerably smaller than the circuit feature size. Thus the control of both pore size and pore size distribution is crucial to the development of nanoporous low-k dielectrics. Chapter 1 reviews recent developments in the imprinting of closed nanopores into spin-on materials to produce low-k nanoporous interdielectrics for the

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production of advanced ICs. This review further provides an overview of the methodologies and characterization techniques used for investigating low-k nanoporous interdielectrics. The research and development on dielectric materials in the form of crystals, ceramics (bulk and nano), and thin films have been closely related to industrial applications i.e., electrical, radio technology, telecommunications, computing, defense, aerospace, microelectronics, laser technology, microwave applications and devices (e.g., transducer, actuators, computer memory, electro-optical modulator, light valves, nonlinear optical devices etc). The scale of studies has grown and the experimental techniques available have been broadened, together with the sphere of practical application. The most intense studies within this field include the phenomena of polarization, dielectric loss, ionic conductivity, breakdown, etc. of polar and non-polar dielectrics. Dielectric ceramic materials have been studied for decades due to both their application in important technologies and the fundamental interesting relationships among their crystal chemistry, crystal structures, and physical properties. Hence, research in dielectrics is mostly focused on the study and application of ferroelectrics, antiferroelectrics, piezoelectric, pyroelectric and multiferroic materials. Detailed studies on H-bonded, oxides and complex systems of different structural family in the form of single crystal, ceramics and thin film have triggered to develop new materials for device applications. It has been observed that the properties and structure of these materials can be tailored by substitution, replacement and doping of suitable elements at different atomic sites. In view of the importance of the dielectric materials for technological applications, several synthesis methods (i.e., high temperature solid-state reaction, highenergy ball-milling, different chemical methods, pulsed laser deposition etc.) have been used for material preparation. Present work mainly gives emphasis on the preparation techniques, characterization and optimization of different physical properties (i.e., structural, microstructural, electrical, thermal and magnetic) using a number of advanced and/ standard techniques. In this regard, the authors shall discuss some of the important results of some Hbonded materials, oxides like BaTiO3, PbTiO3, PbZrTiO3, advanced oxide ferroelectrics (e.g., tungsten bronze, layered perovskites, spinel structures) and multiferroics of different structural families. Most recent work on multifunctional materials, which has been coined for materials having two or all three ferroic orders; ferroelectrics, ferromagnetics, and ferroelastics in the same phase will be given more emphasis. Recent discovery of ferromagnetoelectricity in BiFeO3 at high temperature (Tc = 1100K and TN= 630K) has attracted much attention of researchers to design and develop (single crystals, thin films and ceramics) modified BiFeO3 and/or the search of new materials with high magnetoelectric coefficient above room temperature useful for multifunctional devices. In view of the above, the authors have also designed and developed (ceramics and composites) a few Pb/Bi based ferromagnetoelectrics for better understanding and enhancement of the ferroelectric/ferromagnetic and coupling properties of materials for possible devices. The authors have been monitoring and solving the challenges in multiferroics to combine and couple ferroelectric-ferromagnetic order, reduce the leakage current, enhance the coupling coefficient and provide materials to show multiferroicity at room temperature and above. In Chapter 2, emphasis will be given on the design, development and applications of various dielctric and multiferroic materials. There are reports published recently which show that use of high-k as a spacer material is also an interesting option from the device scaling point of view. Chapter 3 reviews the impact

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of high-K dielectric integration as a gate- and spacer-material for nano scale MOSFETs and discusses the impact of high-k devices on the circuit performance. In hetero-epitaxy of oxide layers on silicon substrates, it is well known that epitaxial relations vary in accordance with the overlaying layer materials. The factors determining the growth orientation have been discussed mainly in terms of thermodynamics, but surface polarity of the nuclei is also a very important factor. In Chapter 4 the authors describe a new technology of orientation selective epitaxy (OSE), which enables epitaxial growth artificially choosing growth orientation, on the specific material of cerium dioxide (CeO2). CeO2 has strong tendency of (111) nucleation due to minimum surface energy, which leads to epitaxial growth of CeO2 (111)/Si(111) at very low temperature as low as room temperature. On the other hand, for most important substrates of Si(100), CeO2layers usually grow with (110) orientation on Si(100) substrates, which is thought to be due to themodynamical properties and non-existence of Coulombic interaction between neutral CeO2 (110) and substrate surfaces. The key parameter determining the nucleus orientation is thought to be competition of surface energy minimization and electrostatic interaction between nuclei and substrate surfaces. Since CeO2(100) surfaces have polarity, CeO2(100) nuclei are hard to adsorb on neutral surface and coalesce together due to electrostatic repulsion. There are two ways to grow CeO2(100) layers on Si(100) substrates overcoming the surface polarity effect. One is application of substrate bias and the other is charged particle beam irradiation during the epitaxial growth process, both of which are based on the surface potential modification for screening the nuclei surface polarity effect. By the control of substrate bias or charged particle beam irradiation, the authors can realize OSE growth of CeO2(100) or CeO2(110). Details of the two are described; the substrate bias method and an electron beam irradiation method. These are fundamentally applicable widely to most of materials having both polar and non-polar surfaces. The A-site ordered perovskite CaCu3Ti4O12 has been extensively studied since the discovery of the huge dielectric constant by Subramanian and the coworkers. This material is clearly different from conventional ferroelectrics, because the dielectric constant comes from neither structure phase transitions nor soft phonons. The huge value is thus most likely to be extrinsic, and can be explained by a barrier layer capacitor model. An important feature is that the dielectric constant is well controlled in the forms of solid solutions and composites. In Chapter 5, the authors will review various aspects of CaCu3Ti4O12 such as the basic physical properties, the impurity effects, and the composites with other dielectrics to show how unusual they are. The authors further introduce some related oxides that have unconventional physical properties originated from the peculiar crystal structure of AA03B4O12. In these last decades, increasing requirements for appropriate techniques to diagnose power transformer insulation non-destructively and reliably in the field drive the development of diagnostic tools based on changes of the dielectric properties of the insulation. Among these non-destructive monitoring techniques Polarisation/Depolarisation Current (PDC) measurement, Return Voltage Measurement (RVM) and Frequency Domain dielectric Spectroscopy (FDS) are gaining exceptional importance to the utility professionals. These methods, which became recently available as a user-friendly method, offer promising alternatives for an off-line, insulation condition assessment of power equipments and its predictive maintenance non-destructively and reliably in the field. In Chapter 6, after a short review of commonly used chemical and electrical diagnostic techniques, a description of the state of art of the theories, analyses and interpretation of

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dielectric spectroscopic techniques for transformer insulation condition assessment along with the future research trends are presented. Because, results from these techniques are highly operating conditions dependant, practical measurements issues that need to be considered are addressed. In Chapter 7, the authors review resonant transmission of electromagnetic waves through some aperiodic dielectric microstructures. First, a theoretical analysis is given to show a generic feature that the internal symmetry in dielectric systems can induce the resonant transmission of electromagnetic waves. It is shown that resonant transmission originates from the positional correlation in the system. In the second, resonant transmission is experimentally observed in symmetric Finonacci dielectric multilayers, which characterized by multiple perfect transmission peaks. Thirdly, resonant transmission is found in Thue-Morse dielectric multilayers, which possesses the mirror symmetry or inversely symmetry. The frequency trifurcation feature of resonant modes is experimentally demonstrated. Finally, some dielectric microstructures with internal symmetry are designed and fabricated to achieve selectable-frequency and tunable quality-factor perfect transmission. The results presented here may achieve the potential applications in optoelectric devices such as the wavelength division multiplexing system. Chapter 8 focuses on the polymer dielectric materials with low dielectric constants. The preparation techniques, chemical structure and related properties of these polymers will be discussed. A brief introduction about the history of the polymer dielectric materials will be the first portion of the chapter. Then the new polymer dielectric materials reported in recent years will be reviewed, include polycyanate esters, polynitriles, heteroaromatic polymers, polyaniline, poly(N-methyl pyrrole), polythiophene, poly(quinoline)s, poly (binaphthylene ether), polysiloxanes, fluorinated polyimides, fluorinated epoxy resin, fluorinated poly(benzoxazine), poly(aryl ether)s, porous polymers etc..The corresponding deposition methods of dielectric thin films including solution-based deposition, plasma polymerization deposition, plasma-enhanced chemical vapor deposition (PECVD), templating, sol-gel processing, and thermal induced phase separation will be also reviewed within their respective sections. In summarizing the chapter, the development, potential applications and future directions of polymer dielectric materials will be discussed, especially the film properties required for applications in integrated circuit manufacturing. The problem of computation the effective characteristics of composite materials has a long history. A classical (linear) problem of computation of the effective characteristics of composite material turns to Maxwell’s [28] consideration of electric field in a periodic array of bodies. Later, the problem was investigated by numerous authors, see, e.g., [12, 15, 35, 38], and it is the problem of interest at the present time, see [2, 7, 9, 18, 29, 32, 33, 42, 43, 56]. Most of the modern problems represent the nonlinear version of the classical problem [31, 37, 44, 45, 53]. In Chapter 9 the authors consider composite materials formed by components with strongly different characteristics - so called high contrast composites. In the general case, effective characteristics of composite materials can be computed using the homogenization theory [3, 6]. Computational procedures of the homogenization method does not work well for high-contrast composites as well as for composites with thin layers, holes etc. The authors develop a modification of the homogenization method for high contrast composites and carried out detailed analysis of nonlinear characteristics of composite: effective tunability, effective loss and commutation quality factor for composites of periodic structure. The

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assumption of the periodicity of structure is not a strong restriction because arbitrary composite material can be approximated by material of periodic structure by using the idea of representative volume [10, 42]. The authors pay main attention to the mathematical and computational aspects of the problem. Dielectric material properties are used for many research and industrial applications. Recent applications deal with the development of ElectroHydroDynamic (EHD) actuators. Their principle consists in establishing non-thermal plasmas between two metallic electrodes on a dielectric surface. Ions are generated by the strong electric field and move in the vicinity of the dielectric material surface. The movement of charged particles involves the movement of neutral molecules of the surrounding gas by momentum transfer, inducing the so-called “ionic wind”. This mechanical property of plasma is used for aerodynamic applications. In Chapter 10, the authors first present our EHD actuator configuration which consisted in a Dielectric Barrier Discharge supplied by a sine high voltage. The influence of dielectric materials on plasma properties was analysed in terms of dissipated power and ionic wind velocity. Various thicknesses and sorts of materials were studied for different amplitudes and frequencies. An empirical law of dissipated power in plasma was deduced from experimental measurements. The dissipated power in dielectric materials was also determined. Then the ionic wind induced by the EHD actuator in an initial still air was characterized by pressure probe measurements. Finally, an example of EHD actuator application in aerodynamic flow is presented. The induced flow in the vicinity of the dielectric surface involves modifications of the flow boundary layer. This effect was used to modify separated flows around an airfoil in a subsonic wind tunnel. Time-domain simulations are the method of choice when spectral information of a device is required. In particular dispersive and non-linear characteristics of dielectric structures are easily accessible when the device is studied in the time domain. In Chapter 11 the authors describe recent advances in the simulation techniques of dielectric photonic structures and consider different methods for large scale simulations. Material equations for dispersive behavior are described and it is shown how they can be incorporated in a time-domain framework. A multi-pole Drude-Lorentzian expansion is used to model the dispersive properties of materials in the optical and near-infrared wavelength regime. The expansion is included in the time-domain framework by using an auxiliary differential equation (ADE) technique. The authors address stability issues arising from the ADE approach and show how the Courant stability limit can be preserved by proper discretization of the ADEs. As a first time-domain simulation method, the finite-difference time-domain method is described and a memory efficient formulation is presented. Alternatively, the authors apply spectral time domain methods to the simulation of phase characteristics. They introduce a multi-domain spectral method for the simulation of curved objects and furthermore a Fourier spectral method. It is shown, that in terms of convergence and memory management the spectral approach performs superior to the FDTD method. In Chapter 12, the writers summarize their research work in the field of dielectric relaxation in dilute solutions of polar molecules in non-polar solvents through the measurements of dielectric loss at microwave frequency region In the last decade, multiferroics have been extensively investigated due to their higher degree of functionality compare to the parent materials i.e. ferroelectrics, ferromagnetics and

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ferroelastics. The search for new single phase and artificially designed multiferroic materials is driven by the prospect of controlling charges by applied magnetic fields and spins by applied voltages and using this to construct new forms of multifunctional devices. Besides the potential applications, the fundamental physics of multiferroic materials are rich and fascinating. Magnetoelctric multiferroics can be roughly divided into four classes: First, rare earth magnetite, i.e. TbMnO3, in which electric polarization is present in only the magnetically ordered state (strong magnetic field dependent). Second, single-phase materials like BiFeO3 (BFO) and PbFe1/2Nb1/2O3 (PFN), in which magnetic spin order at low temperatures produces only a weak effect on dielectric properties. Third, artificially designed multilayer structures showed higher magnetoelectric coupling and slow switching behavior but good for magnetic field sensors. Fourth, single-phase multiferroic relaxor i.e. PbFe2/3W1/3 (PFW)-PbTiO3 (PT), PSc1/3Nb2/3O3 (PSN)-PbFe1/2Nb1/2O3 (PFN) solid solutions, in which the electric dipole and the magnetic spin order are above room temperature, so that the coupled ferroelectric and ferromagnetic properties coexist at room temperature. Chapter 13 consists of two parts, first one emphasizes the synthesis and characterization of the single phase PFW, PFW-PT thin films by chemical solution deposition techniques on Pt/TiO2/SiO2/Si(100) substrates and PbSc0 50Nb0 25Ta0 25O3 (PSNT) and PFN epitaxial thin films on oriented substrate over a wide range of temperature (100-600 K) and frequency (100Hz to 1MHz). Pb(Fe0 66W0 33)0 80Ti0 20O3 (PFWT20) showed relaxor behavior up to 50 kHz frequency and almost linear dielectric constant for higher frequency at ambient temperature. Capacitance variation as function of applied field showed perfect “butterfly loops” for frequency (>10 kHZ) at room temperature and for a full range of experimental frequencies near the freezing temperature (~ 240K). Magnetization vs. applied magnetic field of PFWT20 showed weak ferromagnetic properties. The microstructure of PSNT films revealed compressive strain which is capable for producing the relaxor behavior. The wellbehaved hysteresis loops were observed in a broad temperature range for PSNT thin films indicating relaxor ferroelectric. PFN films showed high dielectric constant near the Curie temperature (Tc~380K) with spin-phonon coupling at Neel temperature. Multiferroic properties of PFN and PSN-PFN thin films will be discussed. The Second part consists of the fabrication of polycrystalline and epitaxially Pb(Zr,Ti)O3–CoFe2O4 (PZT-CFO) layered nanostructures with 3, 5, and 9 layers by pulsed laser deposition technique. The films were deposited on the polycrystalline Pt/TiO2/SiO2/Si(100) substrates, (001) oriented lattice matched LaSr0 5Co0 5O3/SrTiO3 (LSCO/STO) substrates and oriented LSCO/MgO substrates. X-ray diffraction and Raman analysis revealed that PZT and CFO were in the perovskite and spinel phases respectively in the layered nanostructure, having high quality crystallinity. The TEM and STEM line scan of the multilayer thin films showed that the layered structure was maintained. All the layered nanostructures showed well saturated both ferroelectric and ferromagnetic hysteresis loops at room temperature. The temperature dependence of magnetization, polarization, and magnetoelectric coupling will be discussed. High dielectric tenability, low dielectric loss tangent and appropriate dielectric constant, are basic requirements for microwave device applications, such as tunable oscillators, phase shifters and varactors. Ferroelectric materials, for example, barium strontium titanate (Ba1xSrxTiO3 or BST), are known to be the most promising candidates for such applications. A critical issue for practical device application of ferroelectric materials is the reduction of the dielectric losses, because the dielectric loss tangents of BST ferroelectric materials are

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relatively high. Recently, many efforts have been made in order to reduce the dielectric losses of BST based ferroelectrics. It has been found that doping of oxides, such as MgO, ZrO2 and Al2O3, TiO2, LaAlO3, and Bi1 5ZnNb1 5O7 and so on, with low dielectric losses into ferroelectric materials is an effective way to reduce the dielectric losses. In addition to the reduction in dielectric losses, the introduction of oxides would also be able to modify the dielectric constant to be suitable for practical applications. Chapter 14 reviews the recent progress in tunable properties of ferroelectrics modified for microwave device applications. Chapter 15 was designed to form better dielectric composite material using one steady state dielectric (Kaolinite) with a good dielectric material (Barium Titanate). Distinct dielectric composite were successfully produced using locally sourced kaolinite clay. The samples were made using kaolinite as the base matrix and barium titanate (BT) added in varying ratios. Barium Titanate were synthesized via solid-state reaction using barium carbonate and rutile titanium (IV) oxide sintered at 1300°C. Local white kaolinite was used to fuse the barium titanate material in varying weight ratios. The powders were dry-mixed and made into pellets for calcination at 1000°C. The dielectric measurements were carried out using the HP 4291B Impedance Analyzer dielectric setup in the frequency range of 10Hz to 1MHz. Six samples were prepared, namely BT 0%, BT 10%, BT 20%, BT 30%, BT 40% and BT 50%. The dielectric measurements were carried out in a controlled LT furnace for 30°C 400°C. Measurements showed distinct varying interfacial and dipolar relaxation for all composite samples. In Chapter 16, using Goell’s point matching method under the weak guidance condition, modal characteristic equations have been derived for two lightguides with proposed core cross section. In one case both of the boundaries ate taken as conducting and in other case, we consider only one side as conducting. In the both cases dispersion curves are obtained and compared. The central problem in predicting the dielectric behavior of heterogeneous materials (like, e.g., composite or nanostructured systems, powders or mixtures) consists in the evaluation of their effective macroscopic properties, still taking into account the actual microscale material features. This leads to the concept of homogenization, a coarse graining approach addressed to determine the relationship between the microstructure and the effective behavior: the prediction of the effective electromagnetic properties of a composite material from those of its constituent material phases is the major objective of various homogenization models. The resulting effective properties can be observed at the macroscale, where the refined effects of the morphology cannot be directly measured. Dispersions of particles (inclusions with a given shape and a given volume) in a host homogeneous matrix are the most studied heterogeneous structures. From the historical point of view, early mixture theories generally work well when the volumetric proportion of the inclusion phase is small and when the contrast between the electromagnetic properties of the two material phases is not large. More recently, refined and improved models have been developed in order to yield better predictions, also in these critical situations. Recent increases in activity in the field are, at least, partially caused by the interest in selective absorbers of solar and infrared radiation, by an increasing number of applications in astronomy and atmospheric physics, by several applications in the design of novel materials in optics and in material science, and by the indications that the electromagnetic behavior of the composite system may be very different from the behavior of individual components.

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These approaches can be applied not only to the static (d.c.) electric and magnetic properties, but also to the case of wave propagation in low frequency (l.f.) or high frequency (h.f.) regime. It is in fact well known that when any form of energy propagates through a medium containing scatterers (particles), the entrained energy will be either redistributed in various directions by scattering or absorbed by intrinsic absorption mechanisms. The standard homogenization theories can be applied also in such cases provided that the wavelength of the propagating field is much larger than the average size of the particles. Recently, these methodologies have been applied to light scattering from coatings, to heat transfer in powder insulators, to chemical and nuclear reactors, to cryogenic insulation and, finally, to microwave or laser coatings. In all heterogeneous or composite materials, the nonlinear regime and the anisotropic character have not yet been investigated thoroughly. Nevertheless, both the nonlinear and the anisotropic features are relevant in many materials science problems (crystal optics, optical bistability and optical devices). Therefore, we devote Chapter 17 to the development of some analytical models able to take into account the refined effects of the nonlinearity and the anisotropy of the constituents. Electrical application of polymers requires special precautions due to overheating problems. Thus to be useful in this field, the polymeric materials should have good electric insulation characteristics, in addition to flame resistance properties. Chapter 18 will include some information about conducting polymers which becomes important because of their application in solid state polymer batteries and fuel cells. The polymer films that can be used in electrochemical devices should be mechanically and chemically stable as well as highly ionically conducting This chapter deals with the modifications of polymeric materials to be used for such purposes. This study will also extended to thorow light on the problem of waste polymeric materials to be used for insulation purposes. It is well known that reduction of antenna size has always been a challenge to the designer, especially for HF (3-30 MHz) and VHF (30-90 and 100-300 MHz) bands where conventional antennas have rather large physical sizes. For practical reasons, the physical dimensions of an antenna should be compatible with the radiation performance, which requires materials for antenna applications to have specific magneto-dielectric properties. These properties include high refractive index ( n =

μ ' ε ' , where μ ' and ε ' are real parts

of permeability and permittivity, respectively) and impedance-matched to free space ( Z = η0

μ ' ε ' = η 0 , with ε ' = μ ' , where Z and ηo are impedances of the materials and

free space, respectively), together with sufficiently low dielectric and magnetic loss tangents, over the frequency bands of interest. Chapter 19 summarizes the recent progress in fabrication and characterization of magneto-dielectric materials. It is found such materials can be obtained with ferrite composites and ferrite ceramics. Ni-Zn-Co ferrite composites have almost equal permeability and permittivity of ~7, while MgFe2O4 and Li0 50Fe2 50O4 ceramics have refraction index of 6-15, over 3-30 MHz. Ni-Zn-Co ferrite ceramics can be made to have matching permeability and permittivity of 8-12 over 30-90 MHz. Focus will be on the characterization and explanation of dielectric and magnetic properties of the magnetodielectric materials as a function of processing parameters, such as types of sintering aids, concentration of sintering aids and sintering temperature.

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Chapter 1

LOW-K NANOPOROUS INTERDIELECTRICS: MATERIALS, THIN FILM FABRICATIONS, STRUCTURES AND PROPERTIES Moonhor Ree*, Jinhwan Yoon and Kyuyoung Heo Department of Chemistry, National Research Laboratory for Polymer Synthesis & Physics, Pohang Accelerator Laboratory, Center for Integrated Molecular Systems, and BK school of Molecular Science, Pohang University of Science and Technology, Pohang 790-784, Republic of Korea

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Abstract The use of low dielectric constant (low-k) interdielectrics in multilevel structure integrated circuits (ICs) can lower line-to-line noise in interconnects and alleviate power dissipation issues by reducing the capacitance between the interconnect conductor lines. Because of these merits, low-k interdielectric materials are currently in high demand in the development of advanced ICs. One important approach to obtaining low-k values is the incorporation of nanopores into dielectrics. The development of advanced ICs requires a method for producing low-k dielectric materials with uniform distributions of unconnected, closed, individual pores with dimensions considerably smaller than the circuit feature size. Thus the control of both pore size and pore size distribution is crucial to the development of nanoporous low-k dielectrics. This article reviews recent developments in the imprinting of closed nanopores into spin-on materials to produce low-k nanoporous interdielectrics for the production of advanced ICs. This review further provides an overview of the methodologies and characterization techniques used for investigating low-k nanoporous interdielectrics.

I. Introduction Continuous improvements in device density and performance have been achieved through feature size reduction and the scaling down of device dimensions to the deep submicrometer *

E-mail address: [email protected]. Tel: +82-54-279-2120. Fax: +82-54-279-3399. To whom correspondence should be addressed.

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level. The coupling of the intermetal capacitance effect with line resistivity is now a limiting factor for the ultra-large-scale integration of electric circuits. To reduce this problem, low-k interdielectrics have received significant attention from the microelectronics industry and end users because their use in integrated circuits (ICs) with multilayer structures can lower lineto-line noise in interconnects and alleviate power dissipation issues by reducing the capacitance between the interconnect conductor lines.[1-8] Further, low-k interdielectrics have advantages over low-resistivity metal conductors such as copper and silver, because in addition to providing device speed improvements they also provide lower resistancecapacitance delay.[1-7, 9, 10] Thus there is a strong demand for such materials (k>100 nm are generated depending on the porogen loading. New hyperbranched polymer porogens based on aliphatic polyethers have recently been prepared and tested as porogens in a copolymer of PMSSQ precursor,

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poly(methylsilsequioxane-co-1,4-bis(ethylsilsesquioxane)-benzene) (PMSSQ-BESSQB), which exhibits better properties than PMSSQ dielectrics.[86] The new porogens are hyperbranched polyglycidol (PG) and its ketalized derivative (K-PG) (Figure 7), which were synthesized via a new polymerization pathway of glycidol. In particular, K-PG has good solubility in common solvents and good miscibility with the PMSSQ-BESSQB precursor. Moreover, K-PG exhibits sacrificial thermal decomposition characteristics that make it suitable for use as a porogen in the fabrication of porous PMSSQ-BESSQB dielectric films. K-PG can be loaded into the PMSSQ-BESSQB precursor at concentrations up to 40 wt%. A GIXS study of the porous thin films prepared from PMSSQ-BESSQB/K-PG composite films with various compositions found that the average size of the pores in the porous dielectric films varies from 6.7 to 18.5 nm (i.e., a radius of 3.4 to 9.3 nm) as the initial loading of the KPG porogen is increased from 10 to 40 wt%. These pores are spherical and have a sharp interface with the dielectric matrix. As the initial loading of the K-PG porogen is increased up to 40 wt%, the porosities of the PMSSQ-BESSQB films increase almost linearly to 37 vol% and the refractive indices n decrease almost linearly from 1.450 to 1.270. The presence of the imprinted pores reduces the k values of the PMSSQ-BESSQB films almost linearly as the initial loading of the K-PG porogen increases.

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II.5. Crosslinked Polymer Nanoparticles In recent years nanoparticles have attracted significant attention because of their potential applications in the nanotechnology field.[87-93] In particular, thermally labile organic particles in the nanometer range are very attractive because of their potential use as porogens in the production of low-k nanoporous dielectrics. One approach to fabricating organic nanoparticles is through the self-crosslinking reaction of a crosslinkable polymer.[91-94] This approach relies on the controlled intramolecular crosslinking of a functionalized polymer chain. The shape of the nanoparticle is controlled by the crosslinking chemistry, polymer type, functionality, and architecture. Examples are crosslinked poly(styrene-co-methacroyloxyethyl methacrylate), poly(εcaprolactone-co-acryloyloxycaprolactone), and poly(methyl methacrylate-comethacroyloxyethyl methacrylate) nanoparticles (Figure 8).[94] The syntheses of these crosslinked polymeric nanoparticles consist of two steps. The first step involves the preparation of the potentially crosslinkable macromolecules. In the second step, the nanoparticles are prepared via the self-crosslinking reactions of the crosslinkable macromolecules in ultra-dilute solutions using a radical initiator. The resulting nanoparticles have a hydrodynamic radius of 3.8−13.1 nm; the particle size increases with the molecular weight of the crosslinkable polymer. It was found that polymer nanoparticles could be used to imprint nanopores in cured PMSSQ dielectric films by their sacrificial degradation through heat treatment up to 450°C. This approach depends on the solubility of the nanoparticles and the uniform dispersion of the nanoparticles with minimal aggregation in the dielectric matrix. The best results have been achieved with crosslinked poly(methyl methacrylate-co-methacroyloxyethyl methacrylate) nanoparticles. This nanoparticle has a hydrodynamic radius of 6.5 nm and has been found to generate nanopores with a radius of 7.2 nm in cured PMSSQ dielectric films. Nanoporous films imprinted with 20−30 wt% loadings of these nanoparticles were shown to exhibit

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refractive indices n of 1.31−1.28. The k value of a PMSSQ film with 20% porosity was found to be 2.1, which is a significant reduction below that of the PMSSQ film.

Figure 8. Nanoparticle porogens: a crosslinked polymer nanoparticle and its preparation scheme (e.g., crosslinked poly(ε-carprolactone-co-acryloyloxycarprolactone)) (top); a core-corona nanopoarticle (e.g., a nanoparticle based on a core consisting of polynorbornene blocks and a corona composed of poly(ethylene oxide) blocks) (bottom).

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II.6. Core-corona Polymer Nanoparticles Core-corona polymers have recently been introduced for use as porogens, particularly norbornene-ethylene oxide copolymers (Figure 8).[95] As shown in Figure 5b, these polymers actually consist of a hyperbranched polymer with norbornene polymer inner parts and ethylene oxide polymer outer parts. The inner parts are insoluble and bulky, and can act a core in solution as well as in a dielectric matrix. The outer parts are polar and soluble, and can act as a corona to favorably interact with the solvent as well as with the dielectric matrix. The outer corona renders the insoluble core compatible with the dielectric matrix and suppresses aggregation and precipitation of the insoluble interior. Core-corona polymers have been synthesized with diameters of 10−20 nm, depending on the sizes and fractions of the core and corona parts. They are dissolved in a solution with the PMSSQ precursor and the resulting solution is spun onto substrates and thermally treated at 450°C to produce porous PMSSQ dielectric films. A TEM study has found that pores are generated with a size of 10−20 nm in the dielectric films, depending on the porogens and their initial loadings; the imprinted pores are comparable in size to the core-corona polymer nanoparticles. The k value of the resulting dielectric film has been found to decrease from 2.8 to 1.7 with increases in the porogen loading up to 50 wt%. Other core-corona molecules is octa(2,4-dinitrophenyl)-silssesquioxane (ODNPSQ), which consists of one cubic Si8O12 core covered by eight dinitrophenyl groups as corona. Due

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to the lipophilic character of 2,4-dinitrophenyl group, this porogen show good miscibility with polyphenylsilsesquioxane (PPSQ), resulting porous spin-on thin film after sacrificial thermal degradation at 450 oC. With the 40% of porogen loading, porous film show low water absorption of 0.45% and low dielectric cnstant of 1.93.[96]

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II.7. Linear Polymers Various linear aliphatic homo- and co-polymers have been investigated as porogens for producing nanoporous dielectrics: linear homopolymers,[97, 98] random copolymers,[99103] amphiphilic diblock copolymers,[104, 105] and triblock copolymers.[106-108] Representative homopolymer porogens are poly(alkylene ether)s (e.g., poly(ethylene oxide) (PEO) and poly(propylene oxide) (PPO)) and polyesters (e.g., poly(ε-caprolactone) (PCL) and poly(lactic acid) (PLA)).[97, 98] However, these polymers exhibit very limited miscibility with PASSQ precursors, which results in severe phase separation depending on their loading levels, and in large, interconnected pores in cured PASSQ dielectrics. One example of a random copolymer porogen is poly(methyl methacrylate-codimethylaminoethyl methacrylate) (P(MMA-co-DMAEMA)), which was synthesized via the radical copolymerization of methyl methacrylate and N,N-dimethylamino ethyl methacrylate.[99, 101, 102] The tertiary amino group in the DMAEMA component of the copolymer favorably interacts with the functional groups (i.e., hydroxysilyl groups) of the PASSQ precursor via strong hydrogen bonding, and thus its presence results good miscibility with the precursor, but it also catalyzes the polycondensation (i.e., sol-gel reaction) of the precursor even at room temperature, causing phase separation and precipitation of the precursor. Because of this dual functionality, the incorporation of the DMAEMA component is restricted to loadings less than 15 mol%, which produces a copolymer miscible with the PASSQ precursor (e.g., PMSSQ precursor) and ultimately generates small pores in cured dielectrics by sacrificial degradation through thermal treatment at 400−450°C. At a porogen loading of 40 wt%, the k value of the resulting porous dielectric film is decreased to 1.95, which is less than that of PMSSQ dielectrics (k=2.70).[99] Small angle X-ray scattering (SAXS) and prism coupling measurements on the resulting porous dielectric films showed that for initial porogen loadings in the range 5−50 wt%, the pore sizes range from 2 to 10 nm, the porosities range from 5 to 50 %, and the refractive indices at 633 nm range from 1.35 to 1.21.[99, 101] However, with increases in the porosity, the pore size increases and the pore size distribution broadens, indicating that the generated pores change from closed-cell structures to interconnected bicontinuous structures, which is attributed to changes in the phase separation of the blends of the porogen and matrix components with changes in the blend composition.[101] The pore size and size distribution are also found to be affected by the numbers of hydroxylsilyl and alkoxysilyl groups in the PMSSQ precursor. Moreover, neutron reflectivity measurements on these porous films found localized higher porosities at the interface between the porous films and their silicon substrates.[102] Poly(styrene-b-2-vinylpyridine) (PS-b-P2VP) is an example of an amphiphilic diblock copolymer porogen; the P2VP block fraction ranges from 26 to 65 mol%.[105] As for P(MMA-co-DMAEMA), PS-b-P2VP porogens exhibit good miscibility with PMSSQ precursor via hydrogen bonding interactions between the pyridine rings of the P2VP block in the porogen and the hydroxysilyl groups of the precursor, and can be used to produce small

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pores in cured dielectric films. As the initial loading of the diblock copolymers is increased up to 60 wt%, the refractive indices n of the resulting porous PMSSQ films decrease almost linearly from 1.361 to 1.139. SAXS analysis found that nanopores with an average size of 11.6 nm were generated in PMSSQ films imprinted with 30 wt% porogen loading. Poly(ethylene oxide-b-propylene oxide-b-ethylene oxide) (PEO-b-PPO-b-PEO) has been tested as an amphiphilic triblock copolymer nanopore template in PMSSQ dielectrics.[106, 108] Positronium annihilation lifetime spectroscopy (PALS) measurements on the resulting porous dielectric films found that closed pores are generated at porogen loadings ≤20 wt% but that interconnected pores are imprinted for porogen loadings >20 wt%. Small angle neutron scattering (SANS) and PALS observations showed that nanopores with sizes in the range 2.2−5.2 nm were generated, depending on the initial porogen loading. The k value was reduced to 1.5 and the porosity increased to 53% as the initial porogen loading was increased to 50 wt%. Poly(styrene-b-3-trimethoxysilylpropyl methacrylate) (PS-b-PMSMA: the numbers of repeat units are 118 for the PS block and 12 for the PMSMA block) was synthesized as a reactive linear block copolymer porogen and then tested in a PMSSQ precursor.[104] For initial porogen loadings up to 50 wt-%, the PMSSQ film’s k value was found to decrease to 1.84, down from k = 2.70, and the refractive index n at a wavelength of 633 nm was found to decrease to 1.226, down from 1.354. Atomic force microscopy (AFM) and TEM observations found that for 10−50 wt% porogen loadings, pores 5.2−12.7 nm in size were generated in the dielectric films. These pores are smaller than those (5.4−20.4 nm) imprinted with the same loading of poly(styrene-b-acrylic acid) (PS-b-PAA: the numbers of repeat units are 30 for the PS block and 58 for the PAA block). However, the reduction in pore size achieved by using this reactive block copolymer is not significant.

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II.8. Cage Supramolecules Cyclodextrins (CDs) are cyclic oligosaccharides consisting of at least six glucopyranose units joined together by an α-linkage: α-cyclodextrin (α-CD) (6 glucose units), β-cyclodextrin (βCD) (7 glucose units), and γ-cyclodextrin (γ-CD) (8 glucose units) (Figure 9).[109-112] They are composed of a hydrophobic interior and a hydrophilic exterior; in particular, the hydrophilic exterior may produce favorable interactions with dielectric materials with polar characteristics. These aliphatic compounds are thermally labile cage supramolecules with a maximum diameter of 1.5−2.0 nm. Due to their molecular sizes and characteristics, CDs are potentially useful as porogens. CDs are capable of generating pores in silicate dielectrics prepared via the sol-gel reaction of tetramethoxysilane.[110] However, a TEM study found that these CDs imprinted wormlike pores 1.5 nm in diameter and tens of nanometers long in the silicate dielectrics, which was attributed to their aggregation in a stacking manner in one direction.[110] To improve their miscibility with dielectric materials, the hydroxyl groups of CDs have been modified.[111, 112] Some modified CDs are prepared: methyl-β-CD, methyl-β-CD, ethyl-β-CD, acetyl-β-CD, propanoyl-β-CD, and benzoyl-β-CD.

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Figure 9. β-Cyclodextrin (β-CD), a cage supramolecular porogen.

PALS analysis found that methyl-β-CD can be used to imprint 1.6−2.2 nm nanopores in cured cyclic silsesquioxane (CSSQ) dielectrics by sacrificial thermal degradation at 420°C, depending on its initial loading in the range 10−40 wt%; the porosities ranged from 9.4 to 25.9%.[111] For initial porogen loadings up to 40 wt-%, the nanoporous films’ k value was 1.90, down from 2.51, and the refractive index n at a wavelength of 633 nm was 1.335, down from 1.433. As mentioned earlier, PMSSQ dielectric films have n = 1.3936 and k = 2.70. This suggests that all the k values reported for the porous CSSQ films imprinted with methyl-β-CD were under-estimated. However, methyl-β-CD loadings of ≥50 wt% were also found to generate wormlike and interconnected pores, as observed for the porous silicates imprinted with CDs without any modifications. Furthermore, the other modified CDs (ethyl-β-CD, acetyl-β-CD, propanoyl-β-CD, and benzoyl-β-CD) are also found to create such interconnected pores in cured CSSQ and modified CSSQ dielectric films.[111, 112] The lengths of the interconncted pores were found to vary in the range 30−160 nm, depending on the modified functional groups in the β-CD and their loading levels. Thus the affinity between β-CD molecules with different functional groups is crucial to reducing the pore size and pore interconnectivity of porous dielectric films generated with this method. Furthermore, β-CDs have been modified with chemically reactive triethoxysilyl group. Triehoxysilyl cyclodextrin (TESCD) was synthesized by allylation and hydrosilylation reaction using triethoxysilane. The porosity linearly increased with increase of TESCD loading to poly(methyl trimethoxy silane-co-bistriethoxysilyl ethane) matrix, indicating no pore collapes occurred during pore generation. TESCD porogen resulted in higher mechanical strengths than PCL porogen, and k values reached down to 2.2 at 40% of porogen loading.[113]

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II.9. High Boiling Point Molecules

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Soluble PASSQ precursors are known to undergo curing reactions (i.e., secondary polycondensation) in their dried films over the temperature range 75−360°C in heating runs under a nitrogen atmosphere or in vacuum.[3-5, 79, 80] The curing of PASSQ precursors can even be carried out at room temperature with the aid of catalysts such as primary, secondary, and tertiary amines.[3, 99] Because of these curing characteristics of PASSQ precursors, a solvent with a high boiling point and low vapor pressure can be used to create pores in cured PASSQ dielectric films by carrying out its thermal evaporation after the dielectric precursor film solidifies, as long as the chain extension and crosslinking reactions of the hydroxysilyl and alkoxysilyl groups occur to a certain extent below the boiling point of the solvent.[114, 115] Several organic solvents with high boiling points and low vapor pressures were tested with the aid of ammonia catalyst as porogens in polyhydrogensilsesquioxane (PHSSQ) dielectrics: laurone, hexadecylhexadecanoate, squalane, didecylphthalate, triaconene, and triaconene.[114, 115] In this approach, the soluble PHSSQ precursor is deposited with a high boiling-point solvent that is insoluble with the PHSSQ precursor solution but compatible with the precursor; the high boiling-point solvent is then present in small domains within the precursor matrix. This deposited film is treated with wet ammonia to create gel state PHSSQ. During curing at 470°C in a nitrogen atmosphere, the PHSSQ precursor molecules form a network structure and nanopores are generated by boiling out the solvent from the precursor matrix. Average pore sizes range from 2.6 to 5.3 nm depending on which high boiling point solvent is used as the porogen. Among the high boiling point solvents studied so far, laurone yields the smallest pore size, 2.6 nm. A k value of 2.2 was achieved, which is a reduction from that (3.0−3.2) of the PHSSQ dielectric film. However, most of the generated nanopores were found to be open and interconnected rather than closed.

II.10. Hybrid Copolymers Hybrid organic-inorganic copolymers composed of thermally labile organic parts that produce pores and thermally curable inorganic or organosilicate precursor parts that become dielectric matrix can be used in another approach to introducing porosity into dielectric materials.[115117] A PHSSQ precursor containing –OC20H41 groups covalently linked to the precursor backbone was synthesized.[115] Films of this organic-inorganic copolymer were prepared by solution casting and subsequent drying, and then subjected to thermal processing at 450°C in a nitrogen atmosphere, resulting in nanoporous dielectric films.[115] This approach was found to produce dielectric films with 2.2 nm size nanopores and a low k value of 1.8. However, it was confirmed with PALS measurements that interconnected rather than closed pores were formed. Other hybrid copolymers are poly(methyl-co-trifluoropropyl)-silsesquioxanes (P(M-coTFP)SSQs), which can be synthesized from methyltrimethoxysilane and trifluoropropyltrimethoxysilane.[118] Curing of films of this copolymer at 420°C produces dielectric films with k = 2.2 and n = 1.348; these relatively low k and n values are attributed to the porosity

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generated by the thermal degradation of the trifluoropropyl groups. However, for this dielectric film the reduction in the k value is not significant. PMSSQ precursors chemically linked with poly(methyl methacrylate) (PMMA) thermally labile branch chains have been described.[119] In these hybrid organic-inorganic block copolymers, the PMSSQ fractions range from 18 to 70 mol%. The weight average molecular weights range from 7,700 to 100,000; hybrid block copolymers with higher PMSSQ fractions can be synthesized with lower molecular weights. These hybrid block copolymers can be used as porogens in cured PMSSQ and its copolymer dielectrics. In the case of a 18 mol% PMSSQ block porogen hybrid, nanopores with a size of 1.7−2.4 nm were generated in cured PMSSQ-based dielectric films by thermal treatment at 430°C with increases in the initial porogen loading up to 30 wt%. The porous films imprinted with 30 wt% loading of the porogen have a k value of 2.2. Other hybrid copolymers system prepared with covalently bonded adamantylphenol to PMSSQ. The adamantylphenol groups were grafted or bridged to PMSSQ through propyl linkers and thermal decomposition of such groups occurred through the cleavage of covalent bonds during thermal curing. This organic-inorganic hybrid copolymer was prepared by hydrosilylation between trimethoxylsilane and (allyloxyphenyl)adamantane and then copolymerized with methyltrimethoxysilane (MTMS). Curing of films of this copolymer at 250°C produces dielectric films with k = 2.3 and elastic modulus of 5.5 GPa.[117]

Figure 10. Polymethylsilsesquioxane-four-armed poly(ε-caprolacone) (PMSSQ-PCL4) hybrid system: PMSSQ, dielectric precursor part; PCL4, thermally labile porogen part.

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Another organic-inorganic hybrid system consists of soluble PMSSQ precursors chemically linked with PCL4 porogens (Figure 10).[116] These hybrid star-block copolymers are synthesized via the sol-gel reactions of triethoxysilyl-terminated PCL4 (mPCL4)[79, 80] and PMSSQ prepolymer in various compositions; in these sol-gel reactions the amount of mPCL4 was adjusted to 10, 20, and 30 wt% relative to the PMSSQ prepolymer, which has a weight-average molecular weight of 3800. Porous PMSSQ dielectric films derived from the hybrid star-block copolymers were prepared with curing at 400°C. In the resulting porous films, nanopores with a size of 5.0 nm were found to be generated. Porous films prepared from a hybrid star-blocked copolymer containing 30 wt% PCL4 segments were found to exhibit a refractive index of 1.320, down from that of PMSSQ dielectrics (n=1.396). In addition to the low-k nanoporous PASSQ dielectrics described above, there have been attempts to prepare low-k nanoporous organic polymer dielectrics based on high temperature polymers such as polyimides[120-125] and polyphenylquinoxalines.[126] These organic polymer dielectrics have high glass transition temperatures Tg and thermal stabilities up to around 500°C. These high temperature polymers are modified in the syntheses to have thermally labile organic polymer blocks in their polymer backbones or as side chains (Figure 11); the labile blocks are PPO,[120-123] polystyrene,[124, 125] PCL,[126] poly(δvalerolactone),[126] PMMA,[127-129] poly(acrylamide),[123] and poly(ethylene glycol-comethyl ether methacrylate).[130] These syntheses have been extended to produce fluorinated polyimides.[131-133]

Figure 11. Organic-organic hybrid systems: triblock copolymer (top); grafting copolymer (bottom).

The labile polymer blocks undergo thermolysis below the degradation temperatures of the polyimide dielectric blocks or the poly(phenylquinoxaline) dielectric blocks, producing porous organic polymer dielectrics. The resulting porous dielectric films have porosities of 25−30%. Low k values have been achieved with these porous films. However, the generated pores were found to collapse slowly or rapidly through thermal cycles associated with IC fabrication processes. Such pore collapses are more severe when thermal cycles are conducted above the Tg of the organic polymer dielectric. Pore collapse phenomena are mainly driven by the build-up of capillary pressure inside the pore as well as by the high molecular mobility of the organic polymer dielectrics induced by thermal cycles. Pore collapse is the major drawback of this approach to producing porous organic polymer diele ctrics.

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III. Characterization of Pore Structures The pore structure of nanoporous organosilicates is as important for their use as low-k dielectrics as their electrical, mechanical, and chemical properties[2, 6, 7, 11 3-5, 40, 42, 7073, 82, 101, 102, 108, 134, 135]. This use requires that porous low-k materials have a uniform distribution of closed pores with no interconnections between pores, and with dimensions considerably smaller than the circuit feature size in order to avoid circuit defects[2, 6, 7, 11 35, 40, 42, 70-73, 82, 101, 102, 108, 134, 135]. Accordingly, the accurate evaluation of the properties of the introduced pores is required for the successful introduction of nanoporous thin films as low-k dielectrics. As a result, much techniques have been developed for characterizing the pore structures of nanoporous low-k dielectrics, such as grazing-incidence X-ray scattering (GIXS), transmission neutron/X-ray scattering (TNS/TXS) combined with specular X-ray reflectivity (SXR), transmission electron microscopy (TEM), high resolution transmission electron microscopy (HRTEM), scanning electron microscopy (SEM), field emission scanning electron microscopy (FESEM), scanning tunneling microscopy (STM), atomic force microscopy (AFM), adsorption porosimetry, ellipsometric porosimetry, positron annihilation lifetime spectroscopy (PALS). They are classified into transmission radiation scattering, microscopy, porosimetry, and spectroscopy. However, accurate measurements are difficult, because these film thickness continuously decreases (several hundred nanometers or fewer) with increasing integration and reducing feature sizes, and precise correlations between these techniques have not yet established. These problems make the selection of the appropriate method for characterization of pore structures more difficult and delay research into porogen design and pore generation methods. In this chapter, one can learn about the analytical techniques used to characterize the pore structures of nanoporous dielectric thin films and identify the strengths and weaknesses of these techniques. Especially, GIXS comes into the spotlight due to its powerful, quantitative method for the charaterization of pore structure in nanoporous low-k thin film.

III.1. GIXS In general, TXS/TNS techniques have been used to get the information for pore structure in nanoporous materials. However, these techniques are hard to apply to pore characterization of low-k materials, which are applied as form of thin film with thicknesses of several hundreds of nanometres. Recently, grazing-incidence X-ray scattering (GIXS) can be used to overcome the limitations of conventional transmission scattering techniques with respect to extremely small scattering volumes, in particular for the characterisation of the pore sizes and pore size distributions of porous thin films as well as of the thin films' properties.[5, 46, 47, 136-139] GIXS has several important advantages over TNS and TXS: (i) a highly intense scattering pattern with high statistical significance is always obtained, even for films of nanoscale thickness; because the X-ray beam path length through the film plane is sufficiently long; (ii) there is no unfavourable scattering from the substrate on which the film is deposited; (iii) sample preparation is easy, and no additional sample treatment is required.[5, 46, 47, 140] The GIXS technique is very versatile and quantitative method to chracaterize the pore structure of nanoporous thin films. Besides the pore size, size distribution, and shape, the

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GIXS technique provides average electron density and relative porosity of film like a SXR technique.[5, 46, 47, 141, 142]

Figure 12. (a) Geometry of GIXS and schematic structural diagram of nanoporous thin film deposited onto silicon substrate: medium 1 = vacuum; medium 2 = nanoporous film; medium 3 = silicon substrate; d = thickness of medium 2 (i.e. nanoporous film). (b) Geometry of TXS. αi is the incident angle at which the X-ray beam impinges on the film surface; αf and 2θf are the exit angles of the X-ray beam with respect to the film surface and to the plane of incidence, respectively, φ is the azimuthal angle, and qx, qy, and qz are the components of the scattering vector q.

Figure 12a shows a typical GIXS geometry, here the incident X-ray beam impinges onto surface of the tin film at an angle αi, and the scattered pattern is recorded on a twodimensional charge-coupled detector (2D CCD); αf is the exit angle with respect to the film surface, and 2θf is the scattering angle with respect to the plane of incidence. Porous films are

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generally found to have a surface roughness of a few angstroms[5], which is much smaller than a typical nanoporous film thickness, i.e. less than 800 nm, so that volumes of the interfaces with air and the silicon substrate are much smaller than that of the porous film. Thus the perturbation of the scattering due to interfacial roughness is small for porous films coated on silicon substrates.

Figure 13. (a) 2D GIXS pattern measured at αi = 0.20° for a 100 nm thick nanoporous low-k thin film derived from a PMSSQ precursor loaded with 30 wt% 4-armed star-shaped porogen. (b) Pattern calculated for porous film in a using GIXS formula.[79] Pores were assumed to have log-normal size distribution (r0 = 4.46 nm and σ = 0.439: r0 and σ are pore radius corresponding to peak maximum and width in radius distribution, respectively), and electron densities of porous film and silicon substrate are 273 and 699.5 nm-3, respectively. The film thickness is 123 nm.

Contrary to transmission scattering, the analytical solution of GIXS bases on distorted wave Born approximation (DWBA) which describes the complicated reflection and refraction effects of nanoporous thin film coated onto a substrate (Figure 12a).[5, 139, 140, 143-145] Taking into consideration the negligible scattering contribution from the film surface, a novel GIXS formula with DWBA was derived to analyze quantitatively GIXS data obtained from nanoporous low-k thin films[5, 46, 47, 141, 142, 146] and from thin films with other

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structures[140, 147-150]. The GIXS formula derivation[5, 46, 47] and its application in scattering data analyses[140-142, 146-151] have been used to show that scattering from scatterers (i.e. pores or structural elements) buried in a film coated onto a substrate results in four main types of process: (a) the incident beam scatters without reflection; (b) the scattered beam is reflected at the interface between the film and the substrate; (c) the reflected beam scatters; (d) the scattered, reflected beam is reflected once more.

Figure 14. (a) In-plane GIXS profiles extracted along the qy direction at αf = 0.18° from the 2D GIXS patterns measured for nanoporous PMSSQ films. (b) Out-of-plane GIXS profiles extracted at 2θf = 0.24° from the 2D GIXS patterns of nanoporous PMSSQ films imprinted with the 4-armed star-shaped porogen. The symbols represent the measured data, and the solid lines were obtained by fitting the data with the GIXS formula.

A representative 2D GIXS pattern is shown in Figure 13a; it was obtained at αi = 0.20° for a 108 nm thick nanoporous PMSSQ film imprinted with a 30wt% loading of a 4-armed star-shape poly(ε-caprolactone) porogen.[142] Similar GIXS patterns were obtained for nanoporous films prepared with other porogen loadings (data not shown). PMSSQ is an excellent dielectric material because its dielectric constant (2.7–2.9) is lower than those (3.9– 4.3) of silicon dioxide materials; it also has thermal stability up to 500°C, a low moisture uptake and good mechanical strength.[5, 46, 47, 86, 152] As can be seen in Figure 13a, bright striped patterns appear along the qy direction at several exit angles (αf) between the critical angles of the film and the silicon substrate (αc,f and αc,s), which arise from intense scattering due to a type of standing-wave phenomenon and total reflection at the interface between the film and the substrate. One-dimensional (1D) in-plane GIXS profiles were extracted from the measured 2D GIXS patterns along the qy direction at αf = 0.18° (which is an exit angle between αc,f and αc,s) and are plotted in Figure 14a. These scattering profiles were quantitatively analysed with the GIXS formula (IGIXS) in the following[5]:

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⎡ T T 2 I (q , Re(q )) + ⎤ 1, z ⎢ i f 1 || ⎥ 2 ⎢ ⎥ 1 1 − e − 2 Im(q z )⋅d ⎢ Ti R f I 1 (q|| , Re(q 2, z )) + ⎥ ⋅ ⋅ I GISAXS (α f ,2θ f ) ≅ 2 Im(q z ) ⎢ T R 2 I (q , Re(q )) + ⎥ 16π 2 ⎢ f i 1 || ⎥ 3, z ⎢ ⎥ 2 ⎢⎣ Ri R f I 1 (q|| , Re(q 4, z )) ⎥⎦

(1)

where Im(qz) = |Im(kz,f)| + |Im(kz,i)|, Re(x) is the real part of x, d is the film thickness, Ri and Ti are the reflected and transmitted amplitudes of the incoming X-ray beam respectively, Rf and Tf are the reflected and transmitted amplitudes of the outgoing X-ray beam respectively. In addition,

q1, z = k z , f − k z ,i ,

q2 , z = − k z , f − k z , i ,

q3, z = k z , f + k z ,i ,

q4, z = − k z , f + k z ,i , and q|| = qx2 + q y2 ; here, k z,i is the z-component of the wave vector of the incoming X-ray beam, which is given by k z ,i = k o nR − cos 2

2

α i , and k z, f is the z-

component of the wave vector of the outgoing X-ray beam, which is given by

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k z , f = k o nR2 − cos 2 α f , where k o = −2π / λ , λ is the wavelength of the X-ray beam, and nR is the refractive index of the film given by nR = 1 – δ + iβ with a dispersion δ and an absorption β, αi is the out-of-plane grazing incidence angle of the incoming X-ray beam, and αf is the our-of-plane exit angle of the out-going X-ray beam. I1 is the scattering intensity of the porogens or pores in the film, which can be calculated kinematically. To analyze the scattering profiles using the above GISAXS formula, all scattering models (sphere, ellipsoid, cylinder and so on) for the I1 term have to be examined. In this case, a sphere model is the most suitable for the structures in the films (i.e., nanopores): ∞

I 1 = c ∫ n(r )υ 2 (r ) | F (qr ) | 2 S (qr )dr 0

(2)

where c is a constant, υ(r) is the volume of each pore, F(qr) is the spherical form factor, and S(qr) is the structure factor for the monodisperse hard sphere model[153]. n(r) is the lognormal size distribution function of the pores:

n( r ) =

− ln( r / ro ) 2

1 2π roσeσ

2

/2

e

2σ 2

(3)

where r is the pore radius, and r0 and σ are the pore radius corresponding to the peak maximum and the width of the pore radius distribution, respectively. In these fittings, all possible packing structures were further considered for the structure factor S(qr) in eq. (2), and then only a randomly packed structure of spheres fits the scattering data well. Therefore

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the fitting results indicate that, in the porous films imprinted with 10–40wt% porogen, the spherical pores having a sharp interface with the dielectric matrix are randomly dispersed. This data analysis found that the film imprinted with a 10wt% loading of porogen has pores with an average pore radius r of 3.13 nm and a relatively narrow pore size distribution (σ = 0.395) (Fig. 4). This pore size is larger than that (1.26 nm) of a single porogen molecule. As he porogen loading was increased to 40wt%, it was found that pores of larger size ( r = 6.89 nm) and broader distribution (σ = 0.450) were generated in the PMSSQ films. Collectively, these scattering data analysis results confirm that the porogen molecules have a tendency to aggregate in the PMSSQ matrix, a tendency that is enhanced as the porogen loading is increased. Figure 14b shows the out-of-plane GIXS profiles for porous PMSSQ films prepared with porogen.[142] The out-of-plane scattering profiles of the films imprinted with 10–40wt% porogen loadings were successfully fitted with the GIXS formula and the pore parameters obtained from the analysis of the in-plane GIXS profiles, and it was confirmed that the pore size and pore size distribution are isotropic in the films. As can be seen in Figure 14b, the profiles consist of oscillations between the critical angle of the film and that of the substrate, which are related to the film thickness. The critical angle of the film αc,f clearly decreases with initial porogen loading, whereas that of the silicon substrate αc,s is insensitive to porogen loading. αc,f is directly dependent on the film electron

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density ρe;

ρ e = πα c,f2 re λ 2 , where re is the classical radius (2.818 × 10-15 m) of the electron,

and λ is the wavelength of the X-ray beam used in the GIXS measurements. Thus film porosity with respect to that of a PMSSQ film prepared in the absence of porogen can be estimated from the film’s electron density. The nanoporous low-k films were found to have electron densities in the range 364–237 nm-3, depending on the porogen loading. Thus, the porosity of nanoporous low-k films were found to have porosities in the range 8.1–40.2%, which were called relative porosity estimated from the electron density of the film with respect to the electron density of PMSSQ (396 nm-3). From the parameters determined with this procedure, 2D GIXS patterns can be generated using the GIXS formula. One of these patterns, shown in Figure 13b, was calculated for the porous film imprinted with 30wt% porogen loading. This calculated pattern is in good agreement with the measured pattern (Figure 13a). For the porous films imprinted with 10, 20, and 30 wt% porogen loading, the calculated patterns were also found to be in good agreement with the measured patterns (data not shown). As discussed above, the star-shape porogen was found to aggregate in the PMSSQ [47]films, ultimately imprinting nanopores that were larger than the individual molecular size. Such unfavourable aggregation of star-shape porogen molecules can be prevented partially or completely by the use of more arms in porogen molecule. One good example is the use of 6armed star-shape poly(ε-caprolactone) porogen.[47] More arms were found significantly to suppress aggregation in the PMSSQ throughout thin film processing.[47] Another good example is the globular ethyl acrylation of the end groups of the dendritic polypropyleneimine porogen.[46] The dendritic porogen was found to exhibit excellent miscibility with the PMSSQ precursor and was used to imprint very small nanopores with a size comparable with that of individual porogen molecules, approximately 2 nm in diameter.[46]

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Thus the 2D GIXS technique is a very powerful tool for characterising the pore shape, size, size distribution, electron density, and porosity of nanoporous low-k thin films of nanoscale thickness. Moreover, GIXS measurements can be conducted in-situ as a function of thin film processing parameters (e.g. time, temperature etc.). This in situ GIXS technique can make it possible to determine the mechanism of pore generation within a thin film. One example is discussed here. For blend films of PMSSQ precursor and 4-armed star-shape porogen, in-situ GIXS measurements were performed during both heating up to 400 °C and subsequent cooling to room temperature.[142] Of the GIXS data obtained as a function of temperature and time, some representative 2D scattering patterns and 1D in-plane and out-of-plane scattering profiles are presented in Figure 15. As can be seen in Figure 15a, b, and c, all the 1D scattering profiles were well fitted with the GIXS formula for hard spherical particles with a lognormal size distribution. The pore sizes of the porogen and the imprinted nanopores are plotted in Figure 16a as a function of the temperature during the heating run as well as of the initial porogen loading. Among them, for the PMSSQ dielectric film loaded with 30 wt% 4armed star-shaped porogen, pore radii and their radius distributions determined from the GIXS analysis of the in-plane scattering profile data for in Figures 15a and b are plotted in Figure 16b.

Figure 15. (a), (b) In-plane GIXS profiles at αf = 0.18° of 2D GIXS patterns measured during heating (2.0 °C min−1) of a PMSSQ precursor film loaded with 30 wt% 4-armed star-shaped porogen under vacuum. 2D GIXS pattern measured during heating (2.0 °C min−1) of a PMSSQ precursor film: (c) 400 °C; (d) 300 °C; (e) 200 °C; (f) 50 °C. (g) Out-of-plane GIXS profiles at 2θf = 0.24° of 2D GIXS patterns measured during heating (2.0 °C min−1) of a PMSSQ precursor film loaded with 30 wt% 4armed star-shaped porogen under vacuum. αf indicates the critical angle of the composite film.

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This in situ GIXS study obtained the following results. Heating of the porogen-loaded PMSSQ precursor matrix produces a curing reaction in the precursor matrix component, resulting in the phase separation of the porogen component. On heating, limited aggregations of the porogen, however, took place in only a small temperature range of 100–140 °C as a result of phase separation induced by the competition of the curing and hybridization reactions of the dielectric precursor and porogen (Figure 16); higher porogen loading resulted in relatively large porogen aggregates and a greater size distribution. The developed porogen aggregates underwent thermal firing above 300 °C without further growth and movement, and ultimately left their individual footprints in the film as spherical nanopores. Figure 15g shows representative out-of-plane scattering profiles, which were extracted from the 2D GISAXS patterns measured during the heating of a PMSSQ precursor composite film with a 30 wt% porogen loading. Here, a variation in the critical angle of the composite film, αc,f, with increasing temperature is clearly evident. The αc,f value of 0.186° (ρe = 401 nm3 ) at 50 °C shows a very slow shift towards the low-angle region as the temperature draws closer to 300 °C. This is due to the removal of the water and ethyl alcohol byproducts, formed in the composite film during the curing of the precursor matrix component. Above 300 ◦C, the αc,f shows a dramatic shift towards the low-angle region as the temperature is increased, achieving a final value of 0.152° (ρe = 237 nm-3) at 400 °C. This drastic shift in αc,f towards the low-angle region is attributed primarily to the electron density of the film, which is lowered when pores are generated in the film through the thermal degradation of the porogen aggregates, and partly lowered following removal of the water and ethyl alcohol byproducts from the hybrid film. Similar trends in the αc,f variation with temperature were observed in the out-of-plane scattering profiles of the other hybrid films (data not shown).

Figure 16. (a) Average radii of porogens and pores in the PMSSQ films determined from the GIXS analysis of the in-plane scattering profile data obtained for the films loaded with 10-40 wt% 4-armed star-shaped porogen. (b) Porogen and pore radii and their radius distributions determined from the GIXS analysis of the in-plane scattering profile data for the PMSSQ dielectric film loaded with 30 wt% 4-armed star-shaped porogen in Figures 15a and b.

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III.2. Transmission Radiation Scattering

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Transmission neutron and X-ray scattering (TNS and TXS) are widely used in conjunction with specular X-ray reflectivity (SXR) to obtain the average pore sizes and size distributions of porous materials (Figure 12b).[135, 154-158] In TNS, neutron beams are scattered when they travel through media with varying neutron scattering length densities (SLDs). The key parameter determining the scattering intensity is contrast, which is the difference between the SLDs of the pores and the matrix. The scattering intensity is mostly interpreted by the correlation length approach with the random two-phase model of Debye.[156, 159, 160] However, it is difficult to obtain pore structure information with such methods when there is a lack of contrast between the pores and the matrix, which is always attributed to the very thin film thicknesses of ≤ 800 nm, because a significant contrast term is crucial to obtaining sufficient scattering intensity. One method for overcoming the lack of contrast to some extent in such measurements is to employ a stack of several tens of thin films deposited on thin silicon wafers, which have low attenuation.[156, 158] A TXS investigation of porous polymethylsilsesquioxane (PMSSQ) thin films has been reported in which the TXS data were analysed with a hard sphere model.[5, 50, 141] In this case, the scattering contrast between the pores and the MSSQ matrix was sufficient. This approach has also been used to characterise the three-dimensional disordered morphologies of isotropic two-phase materials, and to study the transition from closed pores to interconnected pores or to a bicontinuous morphology that arises with increases in the content of the pore generator (so-called 'porogen').[161] TXS provides information about the mean pore size and size distribution and can be carried out with various models (e.g. sphere, core shell, disc and rod etc.).

Figure 17. (a) A representative specular X-ray reflectivity curve measured from a thin nanoporous PMSSQ low-k film. αc,f and αc,s are the critical angles of the film and the silicon substrate, respectively. The inset shows a magnification of the region around the two critical angles.

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Along with transmission scattering technique, SXR can give detailed structural information about the low-k dielectric thin films in terms of porosity, electron density/or mass density, density distribution, thickness, out-of-plane coefficient of thermal expansion (CTE), roughness of surface and interface.[70, 146, 154-156, 162] Using SXR, the electron density (ρe) of a thin film can be determined independently from the film thickness. Figure 17 diaplays a representative SXR profile, which was measured for a nanoporous PMSSQ low-k film. The two critical angles, which are attributed to the film (αc,f) and the substrate (αc,s), respectively, can be clearly observed in the measured data. The critical angle is directly related to the average electron density of the corresponding fillm by

α c,f = λ ( ρe re / π ) , where λ represents the wavelength of radiation and re is the classical 12

electron radius.[143, 144] Thus the average electron densities of the film and the substrate are directly determined by the two critical angles, and they can be transformed into mass densities if the chemical compositions of the materials are known. The electron density is directly proportional to the mass density. In general, the porosity, so-called relative porosity, can be obtained by comparing the average film density to an assumed density of the non-porous film. However, for low scattering volumes, such as those of thin films, TXS is no longer applicable owing to its low sensitivity and resolution. Further, it requires an intense, highenergy (approximately 15 keV) X-ray beam to produce an acceptable scattering signal, as the X-rays must pass through both the film and the much thicker substrate on which the film is deposited.[5] In addition, for TXS to be effective, the substrate should be free of crystal domain boundaries, as these can give rise to unfavourable X-ray scattering and reflection.[5]

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III.3. Microscopy Several microscopy techniques, such as such as TEM, HRTEM, SEM, FESEM, STM, and AFM are are used to characterise pore structures.[49, 50, 135, 163-166] The spherical structure and the randomly dispersed pores in porous PMSSQ dielectric film is shown in Figure 18. This TEM image clearly shows that the pores generated in the dielectric film by the sacrificial thermal degradation of the porogen are spherical in shape.[47, 141] Recently, High-resolution electron microscopy has recently been used to produce images with atomic resolution.[167] These techniques are widely used for the direct characterisation of pore structures because of their powerful visualisation features, which can provide topographical and structural information in plan or cross-sectional views. Further, qualitative analysis is possible with these techniques, even with specimens of limited area. However, they are insensitive and complicated to use in quantitative analysis, because of the overlapping of pores in crosssectional views, and have profound analytic resolution limitations. Moreover, TEM and SEM techniques require intensive and exacting specimen preparation processes, typically under high vacuum conditions and with highly focused ion beams. Nevertheless, they will continue to be widely used in conjunction with other techniques.

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Figure 18. TEM image of a nanoporous PMSSQ dielectric prepared from a PMSSQ precursor sample loaded with 10 wt% 4-armed star-shaped porogen.

III.4. Porosimetry Adsorption porosimetry has been widely used to determine pore size distribution and porosity; this method determines the adsorption–desorption isotherm of nitrogen vapor for the sample by weighing the sample.[168, 169] However, there are some problems in the adaptation of this technique to the requirements of industry. First, most current research is focused on materialising the nanoporous materials as thin films with thicknesses of several hundreds of nanometres. However, thin films have insufficient mass for adequate measurements with the traditional nitrogen adsorption technique, because it is based on the use of a microbalance, which is only suitable for samples with relatively high mass. Secondly, it is only applicable to open pores, not to closed pores. Thirdly, it is destructive, because the sample must be grind into a powder to be weighed with the microbalance. However, for accurate results to be obtained, the thin film sample must retain the same structural features that it had when it was produced. Finally, adsorption porosimetric measurements are usually performed near the boiling point of nitrogen vapour (~77.4 K). These unfavourable conditions act as crack-driving forces. In an attempt to investigate thin film specimens non-destructively at room temperature, and thus to avoid severe stress conditions, the use of quartz crystal microbalance (QCM)[168, 170, 171]and surface acoustic wave (SAW) methods[172] has been suggested. However, these methods cannot be used for sensing the adsorption of vapor

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onto a silicon wafer or other substrate, because QCM and SAW require that the sample be deposited directly onto the sensor. To overcome the significant drawbacks of gas adsorption porosimetry, ellipsometric porosimetry, which opens up a new genre of adsorption porosimetry, has been introduced.[173, 174] This technique is similar to gas adsorption porosimetry in that the sample is exposed to an adsorptive gas or probe liquid (e.g. toluene, heptane etc.). The change in the refractive index of the sample is then employed for the determination of the mass of the adsorptive that is condensed and/or adsorbed into pores, instead of the direct weighing used in adsorption porosimetry. The full porosity, open pore volume and pore interconnectivity can be calculated from the changes in the refractive index and the thickness of the film.[175, 176] It is also possible, with this method, to characterise a film's surface roughness (which includes open pores at the surface)[177, 178] The reliability of pore size distribution analysis with ellipsometric porosimetry using various organic adsorptives has been demonstrated by Baklanov et al.[173] Although the use of ellipsometric porosimetry can provide impressive physical and structural details, this technique can only be used for open pores, as is the case for nitrogen porosimetry. Further, this approach assumes that the refractive index of liquid condensed and/or adsorbed in nanoscale pores is identical to that of the bulk liquid. This assumption is only reasonable when the pore size approaches that of a few adsorptive molecules. Lastly, this technique cannot take into account the swelling of the thin film by the probe liquid, which results in an overestimate of the gas uptake and thus of the pore size.

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III.5. Spectroscopy Positron annihilation lifetime spectroscopy (PALS) is applicable to the determination of free volume at the atomic or molecular level and is based on the annihilation lifetime of positronium (Ps, positron-electron bound state) through collisions with the electrons of the pores' inner surfaces (Figure 19).[179-181] Unlike adsorption techniques, this method can be used for both closed pores and open pores. Gidley et al. have sucessfully demonstrated that pore structure (pore size, size distribtuion, and interconnectivity) of both isolated pores and highly interconnected open pores, in the latter case, thin capping layer such as Al on film surface is necessary to Keep Ps escaping into vacuum (on the right side of Figure 19).[182185] Moreover, the PALS can be applied a multilevel thin film which the film is capped with a diffusion barrier (e.g. Ta, TaN or TiN) or sacrificial layer such as silicon oxide layer prepared from tetraethoxysilane (TEOS).[174] These features resolve the major problems of porosimetry methods. Further, the possibility of analysis of capped systems enables the use of this method on practical multilevel integrated circuits with various layers such as an etch stop layer, a capping layer and a copper conductor with a barrier/metal seed layer.[185] The most powerful feature of PALS is its sensitivity to much smaller pores (down to a few angstroms) than those detectable with TEM, TNS and TXS (down to a few nanometres). Recently, the complete depth-dependent pore structure of a nanoporous thin film was characterised using depth-profiled PALS.[182-185] This technique is suitable to monitor any variations in the depth-dependent pore structure in the fabrication of a nanoporous low-k thin film.[175, 178] To calculate the pore size distribution from the lifetime spectra, a calibration curve is required that connects the Ps lifetime with the pore size.[135]

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Figure 19. Annihilation of positron in two types of nanoporous low-k thin film: (left) closed pores; (right) interconnected open pores. e+s are positrons and they form Ps (positron –electron bound state) within pores.

The PALS method does have some limitations.[183, 186-188] First, if the pores in the film system under investigation are open and highly interconnected, the highly mobile Ps diffuses out of the film and escapes into the vacuum, resulting in a lifetime the same as that in a vacuum (about 142 ns), and then information about pore size cannot be obtained. This problem with open, interconnected pores can be solved by a capping layer being deposited onto the thin film layer to prevent the Ps escaping from the film layer into the vacuum. Secondly, in some materials (e.g. polyimides), Ps formation is suppressed because of an abundance of free radicals that scavenge electrons during the Ps formation process. Thirdly, the Ps formed within the thin film must be able to diffuse into the pores; otherwise PALS probes only molecular voids (i.e. molecular-free volumes) in the bulk film part rather than the pores of interest in the nanoporous film. Finally, commercial positron beams are not readily available.

III.6. Comparitive Studies of Characterization of Pore Structure As mentioned above, various methods have been utilized for characterising pore structure of nanoporous low-k thin films: microscopy (TEM, HRTEM, SEM, FESEM, STM, and AFM), porosimetry (adsorption porosimetry and ellipsometric porosimetry), spectroscopy (PALS), and radiation scattering (TXS, TNS, SXR, and GIXS). It is difficult to select which technique is the best tool for the characterisation of nanoporous low-k thin films, because all methods have strength and weakness according to their lights based on physicochemical principles and methodologies. Furthermore, all the techniques except for the microscopy methods, the pore size and pore size distribution of nanoporous thin films are not directly obtained from raw data. Information about the pore size and size distribution of a thin film can only be obtained from the raw data by formulation of a model that takes into account the pore structure and the pore–probe (e.g. laser, positron, X-ray, and neutron) interaction. This strong dependence on the assumed model may lead to differences between the results of the various techniques.

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Thus, one need to be careful in the selection of technique but also to optimise the selected technique for the specific task. Further more, comparative studies are required to establish criteria for characterization of nanoporous low-k thin film. Several comparative studies of various techniques have been reported.[138, 154, 156, 160, 166, 175, 183, 189-191] These comparative studies found that the pore sizes obtained with the various techniques were in reasonable agreement. However, detailed correlations between the pore sizes and size distributions obtained with the various methods were not given.

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IV. Conclusions As reviewed above, there are two principal methods for producing low-k spin-on dielectric materials containing closed nanopores, which are the most promising interdielectric layers for the production of advanced ICs by the semiconductor industry. The first approach is to prepare thermally and dimensionally stable hollow closed nanoparticles with a low k value and disperse them uniformly throughout the dielectric film volume, producing nanoporous low-k thin films. In this case, avoiding or minimizing the aggregation of hollow nanoparticles within the dielectric film is preferred but not absolutely required because the hollow particles are thermally and dimensionally stable, and thus stand alone individually. Moreover, due to their high thermal and dimensional stability, there are a wide variety of dielectric matrices that can be used with these hollow nanoparticles, including curable and noncurable dielectrics and precursors as well as inorganic and organic dielectrics. However, the fabrication of hollow nanoparticles of the desired size and miscibility with dielectric matrices remains a significant challenge. The second approach is based on the addition to the dielectric precursor of nanoscale porogens with tailored thermal stabilities. The stability of these porogens must be such that they are not affected by the coating and drying steps in the dielectric film formation process; they are removed by sacrificial thermal degradation during the final heat treatment of the dielectric films at temperatures typically in the range 300–400 °C. Their volume distribution in the film is the template for the formation of residual closed nanopores in the dielectric film. The porous fraction of the film is in principle directly related to the fraction of porogen with respect to the total solids in the dielectric precursor solution, and the size of the sacrificial porogens is directly related to the final pore size. However, there are some practical requirements if these relationships between the sacrificial porogens, imprinted pores and porosity are to be maintained. Firstly, the sacrificial porogen should be compatible with the dielectric matrix material in order to avoid porogen aggregation. Secondly, the sacrificial porogens should be uniformly distributed throughout the film volume in order to avoid the coalescence or interconnection of the pores. There are two ways in which the sacrificial porogens can be introduced into the dielectric precursor solution. One method is the dispersion of porogens in the solution. The second is chemically linking the sacrificial porogens to the network polymers as block components of the backbone or through grafting. This second method enables control of the volume distribution of the porogens in the dielectric film. Finally, the porogen template approach requires that the dielectric matrix film has a higher degree of cross-linking so that it is dimensionally stable when the pores are created. The porous structure is therefore less affected by any further processes associated with the resulting nanoporous dielectric film; this is why silicate and organosilicate precursors

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(e.g., PASSQ precursors) and their cured dielectrics are appropriate for the porogen template approach to producing low-k nanoporous dielectrics. Otherwise the pores in the dielectric film may collapse during post-processing of the film, including thermal cycles, which arises because of high capillary pressure and the molecular mobility of the film induced by thermal processing; this is why non-curable organic polymers (e.g., polyimides and polyphenylquinoxalines) are not appropriate for the porogen template approach. In addition, closed nanoporosity can be obtained, within certain boundary conditions related to the nature and total load of the porogen. The closed pores in a porous low-k dielectric layer film must be 5–10 times smaller than the smallest device feature; the minimum metal feature size is nowadays approaching 50 nm and may reach 25 nm in the near future. Nanoporous materials for low-k application need control of pore size and size uniformity to nanometer scale. Because the mechanical stability of nanoporous materials for integration to multilavel semiconductor are close related to the pore structures. Therefore, the pore structures of nanoporous materials are very important for their use as low-k dielectrics as their electrical, mechanical, and chemical properties, and the accurate evaluation of the properties of the introduced pores is required for the successful introduction of nanoporous thin films as low-k dielectrics. However, the pore size and film thickness of interlayer dielectrics (ILDs) continue to be reduced in the pursuit of increased integration and reduced feature sizes. Thus the characterization of pore structure becomes more and more difficult. For this reason, various advanced techniques for the characterisation of pore structures have recently been developed: GIXS, TNS/TXS combined SXR, various kinds of microscopy, adsorption porosimetry, ellipsometric porosimetry, and PALS. In this book, usefulness of these techniques in the precise, and quantitative characterization of the pore shapes, size and size distribution of nanoporous low-k thin film were mentioned. Characterization of structures with dimensions approaching those of atoms is required. However, no all-encompassing technique is currently available. Thus a synergistic approach, i.e. the application in combination of various analytical techniques to obtain results superior to those obtained with each individual technique, is necessary. In conclusion, considering the Semiconductor Industry Association’s International Technology Roadmap for Semiconductors, significant challenges remain in the fabrication and production of high performance low-k dielectric materials consisting of closed nanopores of 4 nm or less that meet the requirements of the production of advanced ICs in the microelectronics industry. Moreover, suitable characterization technique for precise and quantitative evaluation of pore structures is necessary to advance the development of nanoporous low-k materials with porogen and pore generation method points of view.

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[133] Wang, W. C.; Vora, R. H.; Kang, E. T.; Neoh, K. G.; Ong, C. K.; Chen, L. F. Adv. Mater. 2004, 16, (1), 54-57. [134] Oh, W.; Shin, T. J.; Ree, M.; Jin, M. Y.; Char, K. Macromol. Chem. Phys. 2002, 203, (5-6), 801-811. [135] Rajagopalan, T.; Lahlouh, B.; Lubguban, J. A.; Biswas, N.; Gangopadhyay, S.; Sun, J.; Huang, D. H.; Simon, S. L.; Mallikarjunan, A.; Kim, H. C.; Volksen, W.; Toney, M. F.; Huang, E.; Rice, P. M.; Delenia, E.; Miller, R. D. Appl. Phys. Lett. 2003, 82, (24), 4328-4330. [136] Lee, B.; Oh, W.; Yoon, J.; Hwang, Y.; Kim, J.; Landes, B. G.; Quintana, J. P.; Ree, M. Macromolecules 2005, 38, (22), 8991-8995. [137] Hsu, C.-H.; Jeng, U.-S.; Lee, H.-Y.; Huang, C.-M.; Liang, K. S.; Windover, D.; Lu, T.M.; Jin, C. Thin Solid Films 2005, 472, 323– 327. [138] Jousseaume, V.; Rolland, G.; Babonneau, D.; Simon, J.-P. Appl. Surf. Sci. 2007, 254, 473–479. [139] Omote, K.; Ito, Y.; Kawamura, S. Appl. Phys. Lett. 2003, 82, 544-546. [140] Lee, B.; Park, I.; Yoon, J.; Park, S.; Kim, J.; Kim, K. W.; Chang, T.; Ree, M. Macromolecules 2005, 38, (10), 4311-4323. [141] Heo, K.; Jin, K. S.; Oh, W.; Yoon, J.; Jin, S.; Ree, M. J. Phys. Chem. B 2006, 110, 15887-15895. [142] Yoon, J.; Heo, K.; Oh, W.; Jin, K. S.; Jin, S.; Kim, J.; Kim, K.-W.; Chang, T.; Ree, M. Nanotechnology 2006, 17, 3490-3498. [143] Tolan, M., X-Ray Scattering form Soft-Matter Thin Films. Springer: New York, 1998. [144] Holy, V.; Pietsch, U.; Baumbach, T., High-Resolution X-ray Scattering from Thin Films and Multilayers. Springer: New York, 1999. [145] Lazzari, R. J. Appl. Crystallogr. 2002, 35, (4), 406-421. [146] Heo, K.; Park, S.-G.; Yoon, J.; Jin, K. S.; Jin, S.; Rhee, S.-W.; Ree, M. J. Phys. Chem. C 2007, 111, 10848-10854. [147] Heo, K.; Yoon, J.; Jin, S.; Kim, J.; Kim, K.-W.; Shin, T. J.; Chung, B.; Chang, T.; Ree, M. J. Appl. Crystallogr. 2008, 41, 281-291. [148] Jin, S.; Yoon, J.; Heo, K.; Park, H.-W.; Shin, T. J.; Chang, T.; Ree, M. J. Appl. Crystallogr. 2007, 40, 950-958. [149] Yoon, J.; Choi, S. C.; Jin, S.; Jin, K. S.; Heo, K.; Ree, M. J. Appl. Crystallogr. 2007, 40, s669-s674. [150] Yoon, J.; Yang, S. Y.; Heo, K.; Lee, B.; Joo, W.; Kim, J. K.; Ree, M. J. Appl. Crystallogr. 2007, 40, 305-312. [151] Harmer, M. A.; Farneth, W. E.; Sun, Q. J. Am. Chem. Soc. 1996, 118, (33), 7708-7715. [152] Kim, S.; Toivola, Y.; Cook, R. F.; Char, K.; Chu, S.-H.; Lee, J.-K.; Yoon, D. Y.; Rhee, H.-W. J. Electrochem. Soc. 2004, 151, (3), F37-F44. [153] Pedersen, J. S. J. Appl. Crystallogr. 1994, 27, 595-608. [154] Lin, E. K.; Lee, H. J.; Lynn, G. W.; Wu, W. L.; O'Neill, M. L. Appl. Phys. Lett. 2002, 81, (4), 607. [155] Lee, H.-J.; Lin, E. K.; Bauer, B. J.; Wu, W.-l.; Hwang, B. K.; Gray, W. D. Appl. Phys. Lett. 2003, 82, 1084-1086. [156] Lee, H. J.; Lin, E. K.; Wang, H.; Wu, W. L.; Chen, W.; Moyer, E. S. Chem. Mater. 2002, 14, (4), 1845-1852.

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[157] Huang, Q. R.; Volksen, W.; Hunag, E.; Toney, M.; Frank, C. W.; Miller, R. D. Chem. Mater. 2002, 14, 3676-3685. [158] Hedden, R. C.; Lee, H. J.; Soles, C. L.; Bauer, B. J. Langmuir 2004, 20, (16), 66586667. [159] Wu, W. L.; Wallace, W. E.; Lin, E. K.; Lynn, G. W.; Glinka, C. J.; Ryan, E. T.; Ho, H. M. J. Appl. Phys. 2000, 87, (3), 1193-1200. [160] Yang, S.; Mirau, P. A.; Pai, C. S.; Naiamasu, O.; Reichmanis, E.; Lin, E. K.; Lee, H. J.; Gidley, D. W.; Sun, J. Chem. Mater. 2001, 13, (9), 2762-2764. [161] Chamard, V.; Bastie, P.; Le Bolloch, D.; Dolino, G.; Elkaim, E.; Ferrero, C.; Lauriat, J. P.; Rieutord, F.; Thiaudie?re, D. Phys. Rev. B - Condens. Matt. Mater. Phys. 2001, 64, (24), 2454161-2454164. [162] Hedden, R. C.; Waldfried, C.; Lee, H.-J.; Escorcia, O. J. Electrochem. Soc. 2004, 151, (8), F178-F181. [163] Hatton, B. D.; Landskron, K.; Whitnall, W.; Perovic, D. D.; Ozin, G. A. Adv. Funct. Mater. 2005, 15, (5), 823-829. [164] Mori, H.; Lanzendorfer, M. G.; Muller, A. H. E. Macromolecules 2004, 37, 5228-5238. [165] Toivola, Y.; Kim, S.; Cook, R. F.; Char, K.; Lee, J.-K.; Yoon, D. Y.; Rhee, H.-W.; Kim, S. Y.; Jin, M. Y. J. Electrochem. Soc. 2004, 151, (3), F45-F53. [166] Silverstein, M. S.; Shach-Caplan, M.; Bauer, B. J.; Hedden, R. C.; Lee, H.-J.; Landes, B. G. Macromolecules 2005, 38, 4301-4310. [167] Li, G.; Zhou, H.; Honma, I. Nat. Mater 2004, 3, 65-72. [168] Gregg, S. J.; Sing, K. S. W. Adsorption, Surface Area and Porosity 1982. [169] Baklanov, M. R.; Dultsev, F. N.; Repinsky, S. M. Poverkhnost 1988, 11, 145-146. [170] Baklanov, M. R.; Vasilyeva, L. L.; Gavrilova, T. A.; Dultsev, F. N.; Mogilnikov, K. P.; Nenasheva, L. A. Thin Solid Films 1989, 171, (1), 43-52. [171] Baklanov, M. R.; Vasilyeva, L. L.; Gavrilova, T. A.; Dultsev, F. N.; Mogilnikov, K. P.; Nenasheva, L. A. Thin Solid Films 1989, 171, 43-52. [172] Ramsay, J. D. F. MRS Bulletin 1999, 24, (3), 36-40. [173] Baklanov, M. R.; Mogilnikov, K. P.; Polovinkin, V. G.; Dultsev, F. N. J. Vac. Sci. Technol. B 2000, 18, (3), 1385-1391. [174] Dultsev, F. N.; Baklanov, M. R. Electrochem. Solid-State Lett. 1999, 2, (2-4), 192-194. [175] Baklanov, M. R.; Mogilnikov, K. P. Microelectronic Engineering 2002, 64, (1-4), 335349. [176] Othman, M. T.; Lubguban, J. A.; Lubguban, A. A.; Gangopadhyay, S.; Miller, R. D.; Volksen, W.; Kim, H.-C. J. Appl. Phys. 2006, 99, 083503-1-7. [177] Shamiryan, D.; Baklanov, M. R.; Maex, K. J. Vac. Sci. Technol. B 2003, 21, (1 SPEC.), 220-226. [178] Shamiryan, D.; Baklanov, M. R.; Maex, K. J. Vac. Sci. Technol. B 2003, 21, (1), 220226. [179] Petkov, M. P.; Weber, M. H.; Lynn, K. G.; Rodbell, K. P.; Cohen, S. A. Appl. Phys. Lett. 1999, 74, 2146-2148. [180] Gidley, D. W.; Frieze, W. E.; Dull, T. L.; Sun, J.; Yee, A. F.; Nguyen, C. V.; Yoon, D. Y. Appl. Phys. Lett. 2000, 76, 1282-1284. [181] Petkov, M. P.; Weber, M. H.; Lynn, K. G.; Rodbell, K. P. Appl. Phys. Lett. 2000, 77, 2470-2472.

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[182] Sun, J. N.; Hu, Y. F.; Frieze, W. E.; Gidley, D. W. Radiat. Phys. Chem. 2003, 68, 345349. [183] Dull, T. L.; Frieze, W. E.; Gidley, D. W.; Sun, J. N.; Yee, A. F. J. Phys. Chem. B 2001, 105, (20), 4657-4662. [184] Sun, J. N.; Hu, Y.; Frieze, W. E.; Chen, W.; Gidley, D. W. J. Electrochem. Soc. 2003, 150, (5). [185] Sun, J. N.; Gidley, D. W.; Dull, T. L.; Frieze, W. E.; Yee, A. F.; Ryan, E. T.; Lin, S.; Wetzel, J. J. Appl. Phys. 2001, 89, (9), 5138-5144. [186] Gidley, D. W.; Frieze, W. E.; Dull, T. L.; Yee, A. F.; Ryan, E. T.; Ho, H. M. Phys. Rev. B - Condens. Matt. Mater. Phys. 1999, 60, (8). [187] Sun, J. N.; Gidley, D. W.; Hu, Y.; Frieze, W. E.; Ryan, E. T. Appl. Phys. Lett. 2002, 81, (8), 1447. [188] Peng, H. G.; Frieze, W. E.; Vallery, R. S.; Gidley, D. W.; Moore, D. L.; Carter, R. J. Appl. Phys. Lett. 2005, 86, (12), 1-3. [189] Tian, D.; Blacher, S.; Pirard, J. P.; Je ro?me, R. Langmuir 1998, 14, (7), 1905-1910. [190] Grill, A.; Patel, V.; Rodbell, K. P.; Huang, E.; Baklanov, M. R.; Mogilnikov, K. P.; Toney, M.; Kim, H. C. J. Appl. Phys. 2003, 94, (5), 3427-3435. [191] Yu, S.; Wong, T. K. S.; Hu, X.; Pita, K. J. Electrochem. Soc. 2003, 150, (5), F116F121.

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In: Recent Advances in Dielectric Materials Editor: Ai Huang, pp. 45-166

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Chapter 2

DIELECTRIC MATERIALS: INTRODUCTION, RESEARCH AND APPLICATIONS R.N.P. Choudhary and S.K. Patri Department of Physics and Meteorology, Indian Institute of Technology, Kharagpur - 721 302, India

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Abstract The research and development on dielectric materials in the form of crystals, ceramics (bulk and nano), and thin films have been closely related to industrial applications i.e., electrical, radio technology, telecommunications, computing, defense, aerospace, microelectronics, laser technology, microwave applications and devices (e.g., transducer, actuators, computer memory, electro-optical modulator, light valves, nonlinear optical devices etc). The scale of studies has grown and the experimental techniques available have been broadened, together with the sphere of practical application. The most intense studies within this field include the phenomena of polarization, dielectric loss, ionic conductivity, breakdown, etc. of polar and non-polar dielectrics. Dielectric ceramic materials have been studied for decades due to both their application in important technologies and the fundamental interesting relationships among their crystal chemistry, crystal structures, and physical properties. Hence, research in dielectrics is mostly focused on the study and application of ferroelectrics, antiferroelectrics, piezoelectric, pyroelectric and multiferroic materials. Detailed studies on H-bonded, oxides and complex systems of different structural family in the form of single crystal, ceramics and thin film have triggered to develop new materials for device applications. It has been observed that the properties and structure of these materials can be tailored by substitution, replacement and doping of suitable elements at different atomic sites. In view of the importance of the dielectric materials for technological applications, several synthesis methods (i.e., high temperature solid-state reaction, highenergy ball-milling, different chemical methods, pulsed laser deposition etc.) have been used for material preparation. Present work mainly gives emphasis on the preparation techniques, characterization and optimization of different physical properties (i.e., structural, microstructural, electrical, thermal and magnetic) using a number of advanced and/ standard techniques. In this regard, we shall discuss some of the important results of some H-bonded materials, oxides like BaTiO3, PbTiO3, PbZrTiO3, advanced oxide ferroelectrics (e.g., tungsten bronze, layered perovskites, spinel structures) and multiferroics of different structural families. Most recent work on multifunctional materials, which has been coined for materials having two or all three ferroic orders; ferroelectrics, ferromagnetics, and ferroelastics in the

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R.N.P. Choudhary and S.K. Patri same phase will be given more emphasis. Recent discovery of ferromagnetoelectricity in BiFeO3 at high temperature (Tc = 1100K and TN= 630K) has attracted much attention of researchers to design and develop (single crystals, thin films and ceramics) modified BiFeO3 and/or the search of new materials with high magnetoelectric coefficient above room temperature useful for multifunctional devices. In view of the above, we have also designed and developed (ceramics and composites) a few Pb/Bi based ferromagnetoelectrics for better understanding and enhancement of the ferroelectric/ferromagnetic and coupling properties of materials for possible devices. We have been monitoring and solving the challenges in multiferroics to combine and couple ferroelectric-ferromagnetic order, reduce the leakage current, enhance the coupling coefficient and provide materials to show multiferroicity at room temperature and above. In this paper, emphasis will be given on the design, development and applications of various dielctric and multiferroic materials.

1. Introduction A dielectric material is a poor conductor of electricity, but an efficient supporter of electrostatic fields. Dielectric substances do not have free electrons but their behavior is changed by the application of electric field. Dielectrics is the study of dielectric materials and involve physical models to describe how an electric field interacts with an atom and behave inside a material. The science of dielectrics, which has been pursued for well over one hundred years, is one of the oldest branches of physics and has close links to chemistry, materials and electrical engineering. The term dielectric was first coined by Faraday to suggest that there is something analogous to current flow through a capacitor structure during the charging process when current is introduced at one plate (usually a metal) flows through the insulator to charge another plate (usually a metal). Dielectric materials can be solids, liquids, or gases. Some examples are given as follows:

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•

• •

•

•

Some ionic crystal and polymer dielectrics exhibit a spontaneous dipole moment which can be reversed by an externally applied electric field. This behavior is called the ferroelectric effect. These materials are analogous to the way ferromagnetic materials behave within an externally applied magnetic field. Ferroelectric materials often have very high dielectric constants, making them quite useful for capacitors. Industrial coatings such as parylene provide a dielectric barrier between the substrate and its environment. The surface of a dielectric may retain stranded excess electrical charges, when the dielectric is rubbed (the triboelectric effect). This can be useful, as in a Van de Graaff generator or electrophorus, or it can be potentially destructive as in the case of electrostatic discharge. Mineral oil is used extensively inside electrical transformers as a fluid dielectric. Dielectric fluids with higher dielectric constants, such as electrical grade castor oil, are often used in high voltage capacitors. Specially processed dielectrics, called electrets may retain excess internal charge or frozen in polarization. Electrets have a semipermanent external electric field, and are the electrostatic equivalent to magnets. Electrets have numerous practical applications in the home and industry.

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Piezoelectric materials are another class of very useful dielectrics. Such type of dielectrics can generate a potential difference when subjected to mechanical stress, or change its dimension if an external voltage is applied across the material.

Solid dielectrics are perhaps the most commonly used dielectrics in electrical engineering, and many solids are very good insulators. As we know, solids may be classified according to various criteria: (i) structure (as crystalline and non-crystalline solids); (ii) electrical conductivity (conductors, semiconductors and insulators); (iii) the existence of some basic properties (e.g. materials that allow current to flow; magnetic materials that possess some magnetic order and dielectric materials which may acquire spontaneous or induced electric polarization) [1]. Dielectric materials can be divided into 32 crystal classes or point groups. A study of these thirty-two crystal classes (point groups) reveals that; eleven of them are characterized by the existence of a center of symmetry; called as centrosymmetric. A centrosymmetric crystal can of course possess no polar properties. The remaining twentyone crystal classes do not have a center of symmetry; they are non-centrosymmetric. The absence of a center of symmetry makes it possible for crystals in these classes to have one or more polar axes, and thus show vectorial or tensorial properties. With one exception, all classes devoid a center of symmetry, exhibit piezoelectric effect. The single exception is the cubic class 432 which although without a center of symmetry; nevertheless has other symmetry elements that combine to exclude the piezoelectric activity. Out of the twenty piezoelectric classes which have the property that a polarization can also be induced by an applied mechanical stress, ten are characterized by the fact that they have a unique polar axis, i.e., an axis which shows properties at one end different from those at the other. Crystals of this class are called polar because they are spontaneously polarized. When the polarization is dependent upon temperature, then that class belongs to pyroelectricity. Finally ferroelectric crystals are the subclass of pyroelectric crystals with reversible polarization in presence of electric field. In all of these classes a polarization of dipole moment can be induced by an applied electric field. Half of the piezoelectric classes of materials, i.e., ten of the original dielectric classes (which may be a polar or non-polar material), exhibit the very important property that a finite and permanent value of polarization, known as spontaneous polarization, exists in the absence of an applied electric field or stress. Such dielectrics are termed as polar materials. The spontaneous polarization of a polar material results from an inherent asymmetry within the basic crystal cell. But in non-polar dielectrics the polarization occurs due to the induced effect. [2]. Depending upon the response of the dielectric materials with external stimuli, they may be ferroelectric, pyroelectric, piezoelectric or multiferroic. Multiferroics are the multifunctional materials having the multiple (charge, spin) order parameters; offer an exciting way of coupling between electronic and magnetic ordering [3]. Multiferroic compounds are the source of magnetoelectric (ME) effects that are strong enough to induce magnetic or electric phase transitions, thus exerting ME phase control. Due to their interesting physical, chemical, and mechanical properties, these materials have been used to realize a vast number of devices ranging from giant devices like electrical transformers to tiny devices like sensors, used in integrated circuits or as storage devices. Furthermore, these materials are likely to offer new kinds of devices and functionality, because of their size-dependent physical and chemical properties, which have motivated a lot of current research activity in the area of ferroelectric and magnetic materials. In particular, advances in atomic and nanoscale growth and characterization techniques have led to the

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production of modern ferroelectromagnetic materials that reveal a range of fascinating phenomena. These phenomena derived from the fact that electrons have spin as well as charge, giving an extra level of complexity to the physics, and an extra degree of freedom in device design. Multiferroics may be in the form of single-phase exhibiting mulitferroicity generally at low temperatures and in a composite form as a product property of a composite phase consisting of a magnetostrictive and a piezoelectric material. Recently, the search continues for new single-phase and composite multiferroic materials that exhibit high ordering temperatures, high coupling constant, low dielectric loss and low leakage current. Study of electrical properties of polymers become an interdisciplinary subject. The development of intrinsically conductive polymers has benefited immensely from the contributions of synthetic chemists. Research on this topic has demonstrated the feasibility of obtaining materials with entirely novel sets of properties have opened up new areas of application for polymers. The emergence of semiconducting polymers in 1950s and the discovery of polymers having metallic levels of conductivity in 1970s onwards have been leading to the fundamental and applied research on numerous conductive polymers. In polymers, polarization resulting from distortion and alignment of molecules under the influence of an applied field. In conductive polymers; the presence of charge carriers produces pronounced local deformation of the molecular framework and here electronphonon and electron-electron interactions play vital role. Thus, such materials have long-term potential gain to drive research for practical applications. The dielectric properties of polymeric substances have interest from both practical and fundamental point of view. The low electrical conductivity and low dielectric losses of many polymers make them very useful for electronic packaging market, bottles, semiconductor devices, electrical insulation and encapsulation. Polymeric materials have been utilized extensively due to their low cost, ease of processing, chemical inertness, and attractive electrical properties. Specific applications, to name only a few, are for capacitors, interconnection insulation, component potting, and encapsulation. From a more basic standpoint, the dielectric properties of polymers offer a tool for studying their molecular structure. Now, we focus our attention on liquid crystal (the fourth state of matter). The design and development of liquid crystals at molecular level are the most important attempts for device application. Their unusual shapes and exotic behavior have not only spawned a new electronic technology but have also given us a better understanding of the way matter behaves.The technological application of liquid crystals is growing steadily. Liquid crystals are liquids with long-range orientational ordering (anisotropic fluids), which combine the fluidity of ordinary liquids with the interesting electrical and optical properties of crystalline solids. They are observed as thermodynamically stable phases between the crystalline solid and ordinary isotropic liquid states (thermotropic liquid crystals). Dielectric property of liquid crystal is dependent on temperature, frequency, pressure, sample thickness and bias electric field. Ferroelectric properties in liquid crystals are found in tilted smectic (SmC) phase due to the presence of chiral molecules in these systems. Apart from their well known uses in display technology and in thermography, the unique properties of liquid crystalline phases now being utilized in the production of ultra high strength – high modulus fibers. In the following discussions, we outline the main features of different dielectric materials; general introduction, theory and possible applications.

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2. Classification of Dielectrics Dielectric materials may be classified into two major categories: (a) non-ferroelectric (or normal dielectric or para-electric) materials and (b) ferroelectric materials.

A. Non-ferroelectric Materials The non-ferroelectric materials may be divided into three classes according to the prevailing polarization mechanism as: (i) non-polar dielectrics, (ii) polar dielectrics, (iii) dipolar dielectrics. The non-polar dielectric substances consist of one type of atoms. These types of dielectric substances become polarized in an external electric field due to the relative displacement of electronic charge with respect to the nucleus. Examples of such substances are gases, liquids and mono-atomic solids. For these materials, the appreciable absorption occurs at the resonance frequency ω0, which is in the visible-to-ultraviolet region. For frequencies lower than the resonance frequency, the dielectric constant is independent of frequency and equal to the static dielectric constant (εo). According to Maxwell’s relation, the refractive index of such materials can be written as n = (εo)1/2

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and the total polarizability (α) is equal to electronic polarizability (αe), i.e., α = αe

(2.1)

The polar dielectric substances made up of molecules without permanent dipole moment. Besides electronic polarization, there exists an induced polarization (ionic polarization) by the modification of the relative positions of ions in the external field. Among the materials in this class, there are the ionic crystals (halides, oxides), paraffins, benzene, carbon tetrachioride etc. The appreciable absorption occurs at two resonant frequencies: one in the optical frequency region (corresponding to electronic polarization) and the other in the lower resonance frequency region (the infrared region corresponding to ionic polarization). In this case, the total polarizability can be written as: α = αe + αi

(2.2)

where αi is the ionic polarizability. The dipolar dielectrics include substances whose molecules possess a permanent dipole moment. Polarization in an external field is caused by the partial reorientation of permanent dipoles. The materials of this class have all three fundamental polarizations: electronic, ionic, and orientational [4]. Thus, the total polarizability is α = αe + αi + αo where αo is the orientational polarizability.

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(2.3)

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R.N.P. Choudhary and S.K. Patri

The dielectric materials are not nonconductive and always involve charge carriers as electrons, holes or both, injected from electrical contacts. Therefore, in this case, the total polarizability should include the space charge polarizability (αd) [5] expressed mathematically as: α = αe + αi + αo + αd,

(2.4)

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B. Ferroelectric Materials A ferroelectric material is normally in single crystalline, thin film or polycrystalline form, and possesses a reversible spontaneous polarization over a certain temperature range. There is a critical temperature (usually referred as the Curie or transition temperature), which marks the transition from an ordered to a disordered state. The phase transition induces a mechanical strain, tending to change not only the volume and the shape of the material body, but also the refractive index of the material. Thus ferroelectric materials exhibit piezoelectric, pyroelectric, and electro-optic properties in addition to the ferroelectric property, which can be used for many technological applications. In modern physics of dielectrics, we deal with the study of ferroelectric, antiferroelectric, piezoelectric and pyroelectric materials. All ferroelectrics are piezoelectric and pyroelectric, but they additionally possess a reversible, non-volatile macroscopic spontaneous electric dipole moment in the absence of an external electric field. In simple words, ferroelectric crystals can be seen as an assembly of batteries with a particular orientation, which remains stable unless an external electric field is applied to change its direction. Their polar state is a consequence of the structural transition from a high-temperature (highsymmetry) para-electric phase to a low-temperature (low-symmetry) ferroelectric phase. These materials also behave as high dielectric-constant insulators useful for the development of capacitors and energy storage materials [6]. Further, the ferroelectric materials can be categorized as normal and relaxor type. Normal ferroelectrics have sharp first or second order transition at Curie point (Tc). They are weakly dependent on frequency. Above transition temperature, it follows Curie-Weiss law. This type of ferroelectrics is strongly anisotropy to light. Barium titanate, BaTiO3 (BT) is the most commonly studied normal ferroelectric material, while the distinction between hysteresis losses and low field losses in ferroelectrics is normally blurred only quite close to transition temperature. There is a group of materials where such conditions persist over a wide temperature range. This group is made up of mixed oxides of perovskite or related structure, and is usually called “relaxor ferroelectrics”. The relaxor ferroelectrics may be distinguished from normal ferroelectrics by three distinct properties: (i) broad diffused phase transition is observed in relaxor ferroelectric over a large temperature range where transition temperature of relaxor ferroelectrics shifts in a large temperature range with frequency along with diffused phase transition, (ii) the spontaneous polarization of relaxor ferroelectrics is not lost at Tc of a first or second order transition but decays gradually to zero, (iii) most astonishing behavior of relaxor ferroelectrics is that to longer coherence length probing radiations, where samples cooled to very low temperature, show no evidence of optical anisotropy or of the X-ray line splitting. Relaxor ferroelctrics have extensive use in the fabrication of multilayer capacitors, electrostrictive and piezoelectric devices, high sensitivity

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pressure gauges, ultrasonic humidifier transducer, ceramic resonator used for automatic vehicle identification systems and bi-stable optic devices etc [7-13]. The ferro- and antiferroelectric, pyroelectric and piezoelectric properties are related directly to the arrangement of the ions/atoms in the unit cell of the crystal and the modification of lattice symmetry is caused by the distortions of structural units. Therefore, any explanation of the phenomena, that takes place in dielectrics, requires knowledge of crystal lattice structure and of structural transformation mechanisms.

3. History 3.1. Ferroelectricity Ferroelectricity was discovered in 1920 by Valasek [14] in Rochelle salt (potassium sodium tartrate) which was originally produced in France in 1665 by Pierre Seignette [15]. Historically, ferroeletricity was first discovered (after piezoelectricity and pyroelectricity) in BaTiO3 (barium titanate) by Wul [16] and Goldman [17]. This discovery triggered considerable efforts in search of additional ferroelectrics having the same structure. A significant progress in applications was made possible after the discovery of ferroelectricity in lead zirconate titanate - Pb(Zr, Ti)O3 (PZT) with a very strong piezoelectric response, and a large remanent (ferroelectric) polarization. Since then lead-based materials have become the dominant compounds in this field.

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3.2. Pyroelectricity Pyroelectricty was probably first observed in tourmaline by ancient Greeks, but quantitatively investigated only in the eighteenth century, during the early studies of electrostatics. Sir David Brewster [18] was the first to use the term pyro (fire) electricity in 1824. Pyroelectric materials have a spontaneous polarization whose amplitude changes under the influence of temperature gradients. The discovery of PZT triggered many applications based on this phenomenon, such as infrared detection, thermal imaging (absorption of energy resulting in polarization changes) and dielectric bolometers. The spontaneous polarization appears (or disappears) at the temperatures of ferroelectric phase transitions and pyroelectric effect is the strongest at these temperatures. It is also strong at temperatures corresponding to transition from one ferroelectric modification to another.

3.3. Piezoelectricity Piezoelectricity was discovered later, around 1880, by Pierre and Jacques Curie [18] who was the first to demonstrate the generation of electricity (surface charges) on well prepared crystals of quartz as a result of mechanical pressure. Inversely, when a voltage is applied across a piezoelectric material, it can undergo a mechanical distortion in response. The beginning of the twentieth century gave birth to most of the classic applications of piezoelectrics, such as quartz resonators, accelerometers and those already mentioned above. After World War II and following the discovery of PZT, the advances made in materials

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science allowed the development of numerous applications based on tailored piezoelectric properties.

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3.4. Multiferroicity To achieve rich functionality; one of the very promising approaches to create novel materials is to combine different physical properties in a single material. Two independent events mark the birth of the magnetoelectric (ME) effect: (i) in 1888 R¨ontgen discovered that a moving dielectric became magnetized when placed in an electric field [19], which was followed by observation of the reverse polarization effect of a moving dielectric in a magnetic field [20], and (ii) in 1894 Curie pointed out that it would be possible for an asymmetric molecular body to polarize directionally under the influence of a magnetic field [21]. The term ‘magnetoelectric’ was coined for the first time by Debye [22], a few years after the first (unsuccessful) attempt to demonstrate the static ME effect experimentally [23, 24]. In spite of Curie’s early recognition of symmetry being a key issue in the search for ME behavior, many decades passed until it was realized that the ME response is only allowed in time-asymmetric media [25]. Such violation of time-reversal symmetry can extrinsically occur through application of an external magnetic field or movement as in the historic experiment conducted by R¨ontgen, or intrinsically in the form of long-range magnetic ordering. Dzyaloshinskii [26] was the first to show violation of time-reversal symmetry explicitly for a particular system (antiferromagnetic Cr2O3), which was soon followed by experimental confirmation of an electric field-induced magnetization [27] and a magnetic field- induced polarization [28, 29] in Cr2O3. The search for ferromagnetism-ferroelectricity in the same material began in Russia in the 1950s, with the replacement of some of the do B cations in ferroelectric perovskite oxides of a general formula ABO3 (A = mono-tri, B = tri-hexavalent elements) by magnetic dn cations [30, 31]. Later, Landau and Lifshitz [32] showed from symmetry considerations that a linear ME effect can occur in magnetically ordered crystals. On the basis of theoretical analysis by Dzyaloshinskii [33], the existence of the ME effect in antiferromagnetic Cr2O3 was predicted. This was confirmed by Astrov [34] by measuring the electric field induced magnetization and later by Rado and Folen [28, 35] by detection of the magnetic fieldinduced polarization. Smolenskii and Loffe [36] in 1958 synthesized the antiferromagneticferroelectric perovskite ceramic Pb(Fe1/2Nb1/2)O3 (PFN). The first synthetic ferromagnetic ferroelectric material, (1−x)Pb(Fe2/3W1/3)O3 − x Pb(Mg1/2W1/2)O3 (x = concentration) was produced in the early 1960s. Other examples include (a) B-site ordered in Pb2(CoW)O6 which is ferroelectric and ferromagnetic and (b) B-site disordering in Pb2(FeTa)O6 [37] which is ferroelectric and antiferromagnetic [38, 39]. Because of dilution of the magnetic ions, these materials have rather low Curie or N´eel temperatures. The attempts to combine both the (ferro) magnetic and ferroelectric (FE) properties in one system was started in 1960’s predominantly by two groups in then the Soviet Union: (i) the group of Smolenskii in St.Petersburg (then Leningrad) [40, 41] and (ii) by Venevtsev in Moscow [42]. Materials combining these different “ferroic” [43] properties were later on called as “multiferroics” [44]. Since then the probability of new techniques has been realized for such novel materials for very promising applications in diverse fields [45-48]. In composite materials, the ME effect is realized by using the concept of product properties introduced by Van Suchetelene

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[49]. In 1978, Boomgaard [50] outlined the conceptual points inherent to the ME effect in composites. These can be summarized as follows: (i) two individual phases should be in equilibrium, (ii) mismatching between grains should not be present, (iii) magnitude of the magnetostriction coefficient of piezomagnetic or magnetostrictive phase and magnitude of the piezoelectric coefficient of the piezoelectric phase must be greater, (iv) accumulated charge must not leak through the piezomagnetic or magnetostrictive phase and (v) deterministic strategy for poling of the composites. The basic ideas underlying composite electroceramics can be classified into three categories: (i) sum properties, (ii) product properties, and (iii) combination properties [49-53]. On the basis of point group symmetry, Aizu et al. [54] have enlisted a number of possible species of ferroic crystals, their number of orientation states, and their relationships to ferromagnetism, ferroelctricity, and ferroelasticity. In 1980, Ismailzade et al. [55] reported the presence of linear ME effect in BiFeO3, a compound with antiferromagnetic-feroelctric nature. Its combination with bismuth titanate and barium titanate forms a family with Aurrivilius structure (Bi4Bim-3Ti3Fem-3O3m+3) showing coexistence of ferroelectric and magnetic nature up to high temperatures [56]. Schmid [57] has worked on boracites belonging to the large crystal structure family with a general formula M3B7O13X, where M stands for a bivalent cation of Mg2+, Cr2+, Mn2+, Fe2+, Co2+, Ni2+, Cu2+, Zn2+, etc. and X stands for a monovalent anion like OH-, F-, Cl-, Br-, I- or NO3-.

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4. Dielectric Response of Materials Two of the most important dielectric concepts have been developed by concerning the induced and orientational polarization in external electric fields. The first treatment of the static response by Clausius and Mossotti [58] in the 1870’s represents one of the earliest attempts to approach a many-body situation. The other decisive development came in the early years of this century with Debye’s theory of dynamic dielectric response of freely floating dipoles, found in dipolar liquids. This opened up a new era of investigations of the frequency- and time-dependence of the dielectric response of materials where two separate tendencies became evident as time went on. The dielectric response of many materials has been of immediate interest to scientists and technologists for a long time. The most intense studies within this field have been of the phenomena of polarization, dielectric loss, ionic conductivity, breakdown, relaxation etc. An important property of a dielectric is its ability to support an electrostatic field while dissipating minimal energy in the form of heat. The lower the dielectric loss (the proportion of energy lost as heat), the more effective is a dielectric material. Another consideration is the dielectric constant, the extent up to which a substance concentrates the electrostatic lines of flux. Substances with a low dielectric constant include a perfect vacuum, dry air, and most pure, dry gases such as helium and nitrogen. Materials with moderate dielectric constants include ceramics, distilled water, paper, mica, polyethylene, and glass. Metal oxides, in general, have high dielectric constant. The prime asset of high-dielectric-constant substances, such as aluminum oxide, is the fact that they make the manufacturing of possible high-value capacitors with small physical volume. But these materials are generally not able to withstand electrostatic fields as intense as low-dielectric-constant substances such as air. If the voltage across a dielectric material becomes too large (if the electrostatic field becomes too intense), the material will suddenly begin to conduct current. This phenomenon is called dielectric breakdown. In components

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that use gases or liquids as the dielectric medium, this condition reverses itself if the voltage decreases below the critical point. But in components containing solid dielectrics, dielectric breakdown usually results in permanent damage. The nature of dielectric response may be static electric field response or time-dependent dielectric response. One of the important electrical properties of dielectric materials is permittivity (which is generally referred as the dielectric constant) which directly relates to the polarization phenomena. A dielectric material is made up of atoms or molecules that possess one or more of five basic types of electric polarization: 1. Electronic polarization: due to the opposite displacement of positive nuclei and negative electrons within the same atom. 2. Atomic or ionic polarization: due to the opposite displacement of positive and negative ions in the substance. 3. Dipolar polarization: results from permanent dipoles of complex ions or molecules. 4. Spontaneous polarization: this type of polarization is observed even in the absence of an external electric field. 5. Interface or space charge polarization: this type of polarization is associated with mobile and trapped charges. The absolute complex permittivity of a material is represented by the symbol ε*, where

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ε*= ε′- j ε′′

(4.1)

It is also frequency dependent, although ε′ and ε′′ (real and imaginary component of complex permittivity) cannot vary independently with frequency, since their frequency variations are connected through the Kramers–Krönig relationship [59, 60]. The relative permittivity (εr) is directly related to the electronic, atomic and orientational polarization of the material. The electronic and atomic polarization induced by the applied field, and is caused by displacement of the electrons within the atom, and atoms within the molecule, respectively. The orientational polarization only exists in polar materials. Electronic and atomic polarization are temperature independent where as orientational polarization, very much dependent on the extent to which the applied field can order the permanent dipoles against the disordering effect of the thermal energy of their environment, varies inversely with absolute temperature. All of these polarization mechanisms can only operate up to a limiting frequency, after which a further frequency increase will result in their disappearance. Because of the spring-like nature of the forces involved, this is accompanied by absorption of the resonance type for electronic and atomic polarization, but for orientational polarization the disappearance, accompanied by a broader peak in the loss factor due to the relaxation mechanism, and may involve a broad distribution of relaxation times. The frequency at which these mechanisms drop out is related to the inertia of the moving entities involved. Typically, electronic polarization persists until a frequency of about 1016 Hz, atomic polarization until about 1013 Hz, while the dispersion for orientational polarization may lie anywhere within a wide frequency range (i.e.,102–1010 Hz), depending on the material and its temperature. In addition to these polarization mechanisms, the existence of interfacial effects such as macroscopic discontinuities in the material, or blocking at the electrodes, causes the trapping

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of charge carriers, and such phenomena, as well as the inclusion in the dielectric of impurities giving rise to conducting regions, result in behavior classified under the general heading of Maxwell–Wagner effects. When orientational polarization is operative, it is usually the dominant polarization mechanism present. The classical theory of this mechanism is due to Debye (1954). For a single relaxation time τ, the variation of εr with angular frequency ω is given by the Debye equation,

ε r − ε ∞ 1 − jωπ = ε s − ε ∞ 1 + ϖ 2τ 2

(4.2)

where εs and ε∞ are the relative permittivity at frequencies much lower and much higher (but not high enough to involve any reduction in atomic or electronic polarizations) respectively than the anomalous dispersion region. Equating real and imaginary parts gives:

ε '−ε ∞ 1 = ε s − ε 1 + ϖ 2τ 2

(4.3)

ε '' ϖτ = ε s − ε ∞ 1 + ϖ 2τ 2

(4.4)

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and

If ε′′ is plotted against ε′, the Cole–Cole plots results. This is a semicircle if the Debye equation is obeyed. In general the experimental results yield a circular arc, rather than a semicircle, with its centre below the abscissa. Such behavior can be expressed as a suitable distribution of relaxation times, though no satisfactory physical reason for doing so has yet been established. There is a variety of other shapes obtained in practice, such as the skewed arc in which the high frequency end of the arc approximates to a straight line. Anything other than a perfect semi-circle is now taken as evidence of co-operative effects within the dielectric. The permittivity of many substances changes not only with frequency and temperature, but also with specimen age and history. Two specimens of nominally the same material may have significantly different permittivity because of different manufacturing processes, different amounts of oxidation, and different inclusions, some of which might have been deliberately introduced, e.g. anti-oxidants. For such reasons, tables of values should be used as an indication of the magnitudes to be expected, and not as a source of precise data which can be repeated by accurate measurements on particular test specimens, except in cases in which the physical and chemical state of both the reference material and the test specimen are very closely specified. The properties of ferroelectric materials depend on so many factors that it is inappropriate to include them in tables of data. Generally, they have permittivity of the order of a thousand, strongly dependent on applied voltage and temperature, and exhibit considerable power loss [61- 65].

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5. Dielectric Spectroscopy Dielectric information may be presented in a number of equivalent ways and it is impor -tant to use the most appropriate form of presentation to suit particular requirements. The following principal dielectric functions may be defined as (a) The complex susceptibility is given by χ* = [ε*- ε∞] / ε0 = χ´(ω)- iχ´´ (ω) (b) The dielectric modulus, M*= 1/ ε*= M´(ω) + iM´´ (ω) =

ε ' (ω ) + iε ' ' (ω ) [ε ' (ω )]2 + [ε ' ' (ω )]2

(5.1)

(5.2)

(c) The complex capacitance, C*= (A/d) ε*

(5.3)

and the corresponding susceptance, Χ*(ω) = C*(ω)-C∞

(5.4)

Y*(ω) = iωC*(ω)

(5.5)

Z*(ω) =1/ Y*

(5.6)

(d) The admittance is given by

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(e) The impedance is,

When a dielectric is placed in an alternating electric field, a temporary phase shift is found to occur between the driving fields and resulting polarization, consequently a loss current component appears giving rise to the dielectric loss of the sample. The polarization Pe varies periodically with time as well as electric displacement D. In general, Pe and D may lag behind in phase relative to electric field E, so that; D = D0 cos(ωt - δ) = D1cosωt + D2sinωt

(5.7)

where δ is the phase angle and slightly less than 90 degree D1= D0cosδ and D2 = D0sinδ. The ratio of displacement vector to electric field (D0/E0) is generally frequency dependent. To describe the situation one may thus introduce two-frequency dependent dielectric constant: ε' (ω) = (D0/E0) cosδ,

ε′′ (ω) = (D0/E0) sinδ

where ε' (ω) and ε′′(ω) are real and imaginary complex dielectric constant respectively. These two parameters can be expressed in term of single complex dielectric constants, Recent Advances in Dielectric Materials, Nova Science Publishers, Incorporated, 2009. ProQuest Ebook Central,

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ε* = ε' - j ε′′. The applied voltage (V) varies periodically with time as follows: V = V0ejωt The total current, IT =

dQ d (CV ) = = jCωV = jεC 0ωV dt dt

(5.8)

where C and C0 are the capacitance in the dielectric medium and vacuum respectively. Therefore, IT = jωC0V (ε'-j ε′′) = ωε′′C0V + jωC0Vε' = Il + IC

(5.9)

The capacitor can be resolved into two components, a charging current (IC) in quadrature The dielectric or tangent loss is given by tanδ =

I L ε '' = . IC ε '

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The vector resolution of current is shown in Figure 5.1. For a parallel plate capacitor sinusoidal applied voltage, the charging current is given by IC = jωC0ε' V and loss current IL = ωC0ε′′ V = σV, where σ = ωεε0tanδ is defined as the effective conductivity. The vector resolution of ac current in a capacitor depends upon frequency, and is always greater than dc conductivity. The loss factor is the primary criterion for the usefulness of a dielectric as an insulator material. The dielectric constant and loss tangent are usually obtained as a function of temperature and frequency using the following experimental techniques.

Figure 5.1. Vector resolution of current.

• • •

RF method- lumped circuit method Microwave method (distributed circuit method) Impedance method

The value of capacitance of the sample is measured using impedance bridges like Schering Bridge, Transformer Bridge, etc. The values of the dielectric constant and loss tangent are calculated from the measured values of the capacitance and loss factor. The dielectric measurements are carried out using impedance meter in a wide range of frequency. So, for some applications where high capacitance in the smallest physical space is required,

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materials with high dielectric constant and low dissipation factor (tanδ) must be used. The dielectric properties of ferroelectrics depend on the field strength at which it is measured; this is a consequence of non-linear relation between polarization and the electric field. The dielectric constant obeys Curie-Weiss law above the transition temperature. Dielectric spectroscopy is a technique used for a complete study of ferroelectric or structural phase transition, relaxation phenomena etc. Dielectric spectroscopy enables one to determine independently both real and imaginary parts of the response function (i.e., complex permittivity) and it can compare the soft mode contribution with the static value of permittivity. Some common dielectric processes investigated by dielectric spectroscopy include: • • • • •

small-molecule rotation in liquids - chemical and physical diagnostics large-molecule reorientation in polymers - physical diagnostics bulk conduction in solids and liquids and separation of electrode effects surface conduction and grain - boundary charge in porous materials interstitial ion effects in various solids

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5.1. Phase Transition Phase transition is the transformation of a material from one thermodynamic phase to another, which is accompanied by an abrupt/slow change of certain physical properties of the substance on continuous change of external parameters (temperature, pressure, or some other physical quantities). The crystal structure of many dielectric materials changes with temperature (i.e., they undergo a phase transition). The phase transitions in crystals are due to the change in the forces of interaction between atoms in crystals. This change may produce various new properties in the crystal. The phase transition that produces or alters the spontaneous polarization is called ferroelectric phase transition. By changing temperature or pressure, the atomic arrangements in the crystals may be changed without any change in chemical compositions. The difference in crystal structure on either side of transition temperature (Tc) may be large or small. The following are the main classification of phase transition: 1) Reconstructive transition: no orientational relationship. Complete fragments of single crystal. 2) Substitutional order-disorder transition: close orientational relationship. 3) Martensite transition: coarse orientational relationship with large change of shape but no diffusion. 4) Reversible transition: close orientational relationship, change is reversible in single crystal, small change in atomic positions. a) pure displacive: no breaking of atomic bonding, only small displacement of atom with respect to others. b) hydrogen hopping: order-disorder change in hydrogen atom in hydrogen bonds. c) orientational contribution: order-disorder change of orientation of small groups of atoms with small displacement.

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Usually phase transition can be classified into two categories, first and second order. In the first order phase transition, entropy, volume, polarization and structural parameters of a crystal or material (i.e., atomic position, thermal vibration and lattice constants etc.) change discontinuously at the transition point. In the second order transition, these parameters do not change continuously at the transition point, whereas the temperature derivatives of the above parameters show discontinuity. Ehrenfest [66] first defined the kind (order) of transition (T1) and according to his definition, an nth order transition is a transition where the (n-1)th derivative of Gibbs free energy G is continuous while the nth derivative shows discontinuity at the transition temperature. Landau [67] explained the ferroelectric phase transition by means of thermodynamical theory. This theory is known as Landau theory of phase transition. A thermodynamical theory explaining the behavior of a ferroelectric crystal can be obtained by considering the form of the expansion of the free energy as a function of the polarization P. We assume that the Landau free energy F (in one dimension) can be written as F(P,T) = (1/2)α Ps2 + (1/4)β Ps4 + (1/6)γ Ps6 + …

(5.10)

∂F/∂Ps = E = α Ps + β Ps3 + γ Ps5

(5.11)

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The coefficients α, β, γ depend, in general, on the temperature. The series does not contain terms in odd powers of Ps (spontaneous polarization) because the free energy of the crystal will not change with polarization reversal (Ps>-Ps). The phenomenological formulation should be applied for the whole temperature range over which the material is in the paraelectric and ferroelectric states. To obtain the ferroelectric state, the coefficient of Ps2 term must be negative for the polarized state to be stable, while in the paraelectric state it must be positive passing through zero at some temperature To (usually called as Curie-Weiss temperature): α = (T – To)/εoC

(5.12)

where C is taken as a positive constant called the Curie-Weiss constant. The value of To may be equal to or lower than the actual transition temperature Tc (Curie temperature). The first or second order phase transition can also be explained with the help of the order parameter η. In first order phase change, η changes from a finite value to zero abruptly at the transition temperature. If η approaches to zero from some finite value over a small range of temperature around Tc, the transition is of second order. Depending on the temperature variation of dielectric constant or the Curie constant C, ferroelectric materials are broadly divided into two groups: 1) soft ferroelectrics (KDP-type) 2) hard ferroelectrics (BaTiO3 –type) The phase transition in soft (H-bonded) ferroelectrics is of order–disorder type while for hard ones (i.e., BaTiO3) it is of displacive type. The ferroelectric phase transition of barium titanate was also discovered independently in the year 1946 [68].

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The nature of phase change (i.e., order-disorder/displacive) can be understood on the basis of the structural investigations. In some cases, however, this information is already available from the results of dielectric investigations. On the basis of temperature dependence of dielectric constant, and the value of the Curie constant, it is observed that ferroelectrics are further classified into two groups; (i) compounds having the Curie constant in the order of 103 belong to the order-disorder type and (ii) for those which undergo displacive type of transition, with Curie constant in the order of 105 [69]. The phase transition in soft ferroelectrics involves not only the ordering of the disordered hydrogen atoms, but also the deformation of the atomic groups like SO4-2, SeO4-2 and PO4-3. In case of displacive-type of transition, a small atomic displacement of some of the atoms is mainly responsible for the phase transition, which has been observed in some of the perovskites. However, the difference between displacive and order-disorder type of transition becomes uncertain when the separation of relevant disorder become comparable to the mean thermal amplitude of those atoms. The characteristic of ferroelectrics is represented in terms of the dynamics of the phase transition. Though a large number of theories have been proposed in the past, Cochran [70] suggested the most general and important theory of ferroelectrics phase transitions based on Lyddane-Sachs-Teller (LST) relation [71].

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ω2LO/ω2TO = ε (0) / ε (∞)

(5.13)

where ωTO and ωLO are the frequencies of transverse and longitudinal optic modes respectively and ε (∞) and ε (0) are the high frequency and static dielectric constants respectively. This LST relation predicts an anomaly in the lattice vibration spectrum of ferroelectrics at the transition temperature [72]. In a ferroelectric crystal, if the value of ε (0) is high, corresponding ωTO become very low. In case of second order phase transition, ε (0) follows the Curie-Weiss law. The ferroelectric phase transition could be regarded as instability of the crystals for a particular normal mode of vibration, often referred as soft mode. But in case of first order phase transition, ωTO is not zero at the transition temperature.

5.2. Diffuse Phase Transition The transition temperature in many macroscopic homogeneous materials is not quite sharply defined. The transition is smeared over a certain temperature interval known as Curie range, resulting in the gradual change of physical properties. The width of the Curie region depends on compositional fluctuation and sensitivity of the Curie temperature to composition change. This type of phase transition is generally known as diffuse phase transition (DPT). Though this phenomenon is observed in several types of materials [73], the most remarkable example of DPT was found in ferroelectric materials [74]. Ferroelectricity with diffuse phase transitions (FDPT) was first reported in 1951 [75] and their extensive studies were carried out on different systems. Some of the characteristics of ferroelectric diffuse phase transition are: • •

broadened maxima in the permittivity-temperature curve gradual decrease of spontaneous polarization with rise in temperature

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no Curie–Weiss behavior in a certain temperature interval above the transition temperature relaxation behavior of dielectric properties in transition region and transition temperatures obtained by different techniques do not coincide.

The diffuseness of the phase transition is assumed to be due to the occurrence of fluctuation in a relatively large temperature interval around the transition. Usually, two kinds of fluctuations are considered: (a) compositional fluctuation and (b) structural (polarization) fluctuation. From the thermodynamic point of view, it is clear that the compositional fluctuation is present in ferroelectric solid-solutions, and polarization fluctuation is due to the small energy difference between high and low temperature phase around the transition. Kanzig [76] observed (from X-ray diffraction) that in a narrow temperature range (around the transition) BaTiO3 single crystal splits up into ferroelectric (FE) and paraelectric (PE) micro-regions. According to Fritsberg [77], substances of less stability are expected to have a more diffuse phase transition. For relaxor as well as other FDPT (ferroelectric diffuse phase transition) the width of the transition region is mainly important for practical applications. Smolenskii [78] and Rolov [79] introduced a model based on Gaussian distribution to calculate diffusivity of DPT (due to compositional and polarization fluctuations).

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5.3. Dielectric Relaxation Dielectric relaxation in solids is one of the most intensely studied research topics. Relaxation consists in the recovery of strain on removal of stress and it is time dependent, typically under sudden removal or sudden application of a steady stress [80]. The subject of relaxation covers all types of stress relief in solids (in dielectric, mechanical, photoconductive, chemical process and so on). It is not expected that all these different forms of relaxation should obey the same laws, but it is possible to observe a common behavior [81]. A wide range of relaxation phenomena are associated with interfacial processes in metal–insulator, semiconductor–insulator, electrode–electrolyte and similar systems.

6. Synthesis of Different Dielectric Materials There are different methods to be adopted for the synthesis of dielectric materials (single crystals, polycrystalline materials, polymers, thin films). Most of the works on ferroelectric and related compounds are carried out with crystals grown from different methods like solution growth; melt growth, etc. [82, 83]. The natural growth habit of a single crystal does not always lend itself readily to a specific crystallographic cut. Therefore, single crystals require particular care in their preparation, cutting and polishing to make them suitable for device applications [84-86].

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6.1. Single Crystal Single crystal is a crystalline solid with no boundaries i.e., ideally single crystals are free from internal boundaries. The crystal lattice of the entire sample is continuous and unbroken to the edges of the sample. Single crystals often have a well-defined form which reflects the symmetry of the unit cell. In general the physical properties of single crystals are anisotropic in nature. As the properties associated with a single crystal are structure-sensitive (crystal defects, mobility, dislocations etc.), single crystals of meaningful size are exceedingly rare in nature, and can also be difficult to produce in the laboratory under controlled conditions. Ferroelectric crystals have ferroelectric domains. The demarcation between two domains is called a domain wall. Although by definition, a single crystal does not contain more than one grain, but it may contain more than one domain [87]. There is an increasing number of application in which it is necessary or desirable to have single crystal ceramics because of special optical, electrical, magnetic, or strength requirements [88]. The driving force for crystallization during crystal growth comes from the lowering of the potential energy of the atoms or molecules when they form bonds to each other [89]. Most of the electric devices are made of artificially grown single crystals such as semiconductors. The control of crystal growth is responsible for the development of many properties of metallic and ceramic materials [90]. Crystallization is a chemical solid-liquid separation technique, in which mass transfer of a solute from the liquid solution to a pure solid crystalline phase occurs. Crystallization is the (natural or artificial) process of formation of solid crystal precipitation from a uniform solution or melt. The crystallization process consists of two major events: nucleation and crystal growth. Nucleation is the step where the solute molecules dispersed in the solvent start to gather into clusters. These stable clusters constitute the nuclei. It is at the stage of nucleation that the atoms arrange in a defined and periodic manner that defines the crystal structure. The crystal growth is the subsequent growth of the nuclei that succeed in achieving the critical cluster size. Nucleation and growth continue to occur simultaneously while the super-saturation exists. Super-saturation is the driving force of the crystallization; hence the rate of nucleation and growth is driven by the existing super-saturation in the solution. Depending upon the conditions, either nucleation or growth may be predominant over the other, and as a result, crystals with different sizes and shapes are obtained (control of crystal size and shape constitutes one of the main challenges in industrial manufacturing, such as for pharmaceuticals). Once the super-saturation is exhausted, the solid-liquid system reaches equilibrium and the crystallization is complete, unless the operating conditions are modified from equilibrium so as to supersaturate the solution again. Factors affecting crystallization are: •

•

Solvent- moderate solubility is best for crystallization, because super-saturation leads to sudden precipitation and smaller crystal size. Presence of benzene in solvent can help crystallization. Highly volatile solvents and long chain alkyl solvents should be avoided. Nucleation- crystal formation initiates via nucleation, as a crystal can grow after being nucleated. Fewer nucleation sites are better for crystal growth, because too many nucleation sites lower the average crystal sites.

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Mechanics- crystals grow by the ordered deposition of the solute molecules onto the surface of a preexisting crystal. Crystal growth is facilitated by the environmental changing slowly over time. Mechanical disturbances are undesirable during growth process. Time- good quality crystals can grow over time under equilibrium conditions. The longer the time, the better the crystals. Faster crystallization is not good as slower one, as there is a chance of getting lower quality crystal in faster crystallization.

Several atoms or molecules in a supersaturated vapor or liquid start forming clusters; the bulk free energy of the cluster is less than that of the vapor or liquid. The total free energy of the cluster is increased by the surface energy (surface tension), however, this is significant only when the cluster is small. A cluster of radius smaller than a critical radius r* will evaporate (or dissolve in the solution) and a cluster of radius greater than r* will become stable will increase its size by the addition of other atoms and is thus growing. Assuming a spherical shape for the nucleus, the free energy of its formation is: DG = 4πr2s + ((4/3)πr3)GV

(6.1)

where DG is the total free energy; r is the radius of cluster; s is the surface tension; DGV is the free energy change per unit volume forming the stable solidification from vapor or liquid. The total free energy DG goes through a maximum DG* at a critical radius r* which can be obtained by derivation of total free energy as given above with respect to radius and by solving, we get:

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(dDG*/dr) = 0

(6.2)

where DG* is the free energy of a critical nucleus. There are an increasing number of applications to have single crystal ceramics in optical, electrical, magnetic, or strength requirements. Different techniques are used for growing single crystals, which are discussed below: •

•

Melt growth technique: this technique is most common in industry. It is suitable for highest yield of single crystals in a definite time, because it can be preceded by heat, which is the easiest parameter to control, and it is easier to apply to large-scale operations. In this technique, crucibles of high melting temperature materials and inactive to the melt should be used. To grow metal/alloy, inter-metallic compounds, sulfide, halide and semiconductor crystals, ceramic series crucibles made of oxide, nitride and graphite are used. In this technique relatively larger and highly perfect crystals can be grown in a short time. Czochralski (CZ) technique: crystal pulling or the CZ technique [91] is a popular technique for producing large, dislocation free crystals in a short space of crystals are grown from the melt directly by pulling up the seed crystal. The size and diameter of the crystal can be controlled while it is growing. In this technique, the material to be grown is melted in a crucible. A seed crystal is dipped into the melt, to be rotated in order to attain thermal symmetry and stirred the melt. To grow good crystals the pull

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and rotation rates should be smooth and the temperature of the melt should be accurately controlled. The materials suitable for growing by the CZ method would have the properties [92] such as: (a) congruent melting point, (b) no destructive phase changes, (c) low vapor pressure, (d) low viscosity, (e) suitable growth habit, and (f) no destructive cleavage. Kyropolos technique: this technique is similar to CZ technique. The technical progress of this technique is slow in comparison to CZ technique. Materials that do not melt congruently, and have a high volatile nature, or a high melting temperature, have been tried for growth using a modified Kyropolos technique [93-96]. Bridgman technique: is a pulling technique, which enables the crystal growth by cooling and solidifying the melt in a crucible. The molten material is put into a crucible, often of silica, which has a cylindrical shape with a conical lower end. Heaters maintain the molten state. As the crucible is slowly lowered into a cooler region, a crystal starts growing in the conical tip. The rate of moving the crucible depends on the temperature and the material. When done successfully, the entire molten material in the crucible grows into a single large crystal. Solution growth technique: it is a method to achieve crystal growth at lower temperatures with a solvent. This technique is preferable to grow crystals that melt incongruently. The crystals are obtained from deposits in the solution in which the raw material is dissolved. Water and organic solvents are the proper solvents chosen in this technique. The solution growth technique is further divided into the solvent evaporation technique and the slow cooling technique. Hydrothermal technique: crystals like quartz are used to synthesize by this technique. This is also a kind of solution growth technique where crystals are deposited on a seed crystal (a small piece of single crystal which can be put in a saturated or supersaturated solution to grow a large crystal from the solution under high temperature and high pressure). Epitaxy: is the technique of growing a crystal layer by layer, on the atomically flat surface of another crystal. In homo-epitaxy, a crystal is grown on a substrate of the same material and in hetero-epitaxy; a crystal is grown on the substrate of another. Different semiconductor crystals can be grown on silicon, such as gallium arsenide, germanium, cadmium telluride (CdTe), and lead telluride (PbTe). Any flat substrate can be used for epitaxy, and insulators such as rock salt (NaCl) and magnesium oxide (MgO) are also used. Molecular-beam epitaxy commonly abbreviated as MBE, is a form of vapor growth. The amount of gas molecules can be controlled to grow just one layer, or just two, or any desired amount. This method is slow, since molecular beams have low densities of atoms. Chemical vapor deposition (CVD) is another form of epitaxy that makes use of the vapor growth technique also known as vaporphase epitaxy (VPE). VPE is much faster than MBE since the atoms are delivered in a flowing gas rather than in a molecular beam. Liquid-phase epitaxy (LPE) uses the solution method to grow crystals on a substrate. The substrate is placed in a solution with a saturated concentration of solute. This technique is used to grow many crystals employed in modern electronics and optoelectronic devices, such as gallium arsenide, gallium aluminum arsenide, and gallium phosphide.

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In addition to the above techniques to grow single crystals, a number of techniques and concepts have been developed for the characterization of single crystals. For the identification and evaluation of purity of materials, the following major techniques are employed: (i) conventional chemical methods, (ii) spectro-chemical methods including spectro-chemical emission analysis, atomic absorption spectrometry and infrared absorption spectroscopy, (iii) X-ray powder diffractometry, (iv) flourescence analysis methods in which the radiation used to excite fluorescence could be ultraviolet radiation, X-rays, gamma rays or accelerated particles including electrons.

6.2. Ceramics Polycrystalline ceramics have the added advantages over single crystals as they can be fabricated easily, and also are cost effective. The positive aspects of ceramic processing in comparison to single crystals are: • •

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Ceramics are usually easier to fabricate into different shapes and sizes. Ceramics have their additional structural – the microstructural features (i.e., grain shape, size and porosity, etc). These microstructural features can be exploited in the design of the electro-ceramic materials for particular devices. The presence of grain boundaries give rise to additional effect, which is not present in single crystals, but actually plays an important role in practice. Ceramics have the added advantages of thermal, chemical and mechanical stability.

Ceramic processing is a sequence of operations like mixing, calcination, sintering etc. that intentionally and systematically changes the chemical and physical properties of the material. The growing applications of ceramics have received increasing interest in the multidisciplinary approach to their synthesis. There are several methods for the preparation of ceramics materials. There are possibly two approaches for synthesis. One is the chemists’ approach (i.e., chemical processes) and the other is the physicists’ approach (i.e., mechanical alloying, sputtering, plasma pyrolysis etc.). For convenience, the powder preparation methods are divided into two categories:

1. Mechanical Methods •

Mixed oxide process (MOP) or solid-state reaction process: this is a conventional method in which mostly oxides and carbonates are used. These chemicals have to meet a certain application dependent specification with respect to their purity and grain distribution. Using this method, ceramics are produced under high temperature by mixing their constituent ingredients in a suitable ratio. The completeness of the reaction and uniformity of the product depend on particle size, homogeneity of the mixture, thermal schedule, and even on the atmosphere during calcination. In this method, high temperature and heating for prolonged time makes the particles coarse and as a result high energy destruction (break down) force is required to get fine powders.

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High energy ball milling: during high energy ball milling the powder particles are repeatedly flattened, cold welded, fractured and rewelded. Possible mechanisms that may contribute to material transfer during milling of brittle components may include plastic deformation, which is made possible by (a) local temperature rise, (b) microdeformation in defect-free volumes, (c) surface deformation, and (d) hydrostatic stress state in the powder during milling. Besides producing the required particle size distribution, ball milling can also produce a very active powder that is easier to densify in later process steps. However, there is a chance of contamination, and also the mill walls and media are wearing while the particle size is decreasing. Screening: this can be conducted with dry or with the particles suspended in a slurry. It is a shorting method of particle size. Depending on the screen openings or mesh sizes, one can assume the particle size. Some limitations of screening are: the screens used in this process should not have any damage otherwise the particle size will not be homogeneous, and for agglomerated particles, a group of particles acts as a single particle resulting to inaccurate screening. Elutriation: is a general term referring to the separation of particle size based on the settling rate. So, the particles with large or high specific-gravity settle more rapidly from a suspension than the particles of small or low specific-gravity. A major problem with elutriation is that the fine particles must be extracted from the fluid before they can be used, which can be done by evaporating the fluid or by filtration. Unless the elutriation and liquid removal are conducted in a closed system, chances for contamination are high. Air classification: it is used to separate coarse and fine fractions of dry ceramic powders. The equipment used is known as an air classifier in which separation is achieved by control of horizontal centrifugal force and vertical air currents. Air classifier is linked with milling, crushing, grinding, or other comminution equipment in a closed circuit. It is an efficient and high volume approach for separating coarse particles from fine particles and producing controlled size ranges. However, it is limited in its efficiency and accuracy in producing controlled sizing of particles below 10μm. Attrition milling: similar to a ball mill since it is cylindrical and contains balls or grinding media, but rather than the cylinder rotating, the small balls are rotated by a series of stirring arms mounted to an axial shaft. Attrition milling can easily be conducted in dry, wet, vacuum and inert gas atmosphere. The problem with this type is the amount of contamination and difficulty of separating the powder from the media. Vibratory milling: it is different from ball milling or attrition-milling. The energy for milling is supplied through vibration rather than tumbling or mechanical stirring. Vibratory milling is relatively fast and efficient and yields a finer powder than usually achieved by ball milling. To minimize contamination, the mill chamber is typically lined with polyurethane or rubber. Vibratory mills are not exclusively used for powder processing, but are used extensively for deburring and cleaning of metal parts. Fluid energy milling: the particle size reduction is achieved in a high-velocity fluid. The fluid may be compressed air, carbon dioxide, nitrogen, superheated steam, water,

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or any other gas or liquid compatible to the equipment. It can achieve controlled particle size with minimum contamination. The disadvantage in this type of milling is collecting the powder. Hammer milling: generally the hammer mills contain rapidly rotating rigid bar or plate. The particles are dropped in the path of this bar or plate and fragmented by the impact and further fragmentation occurs when the batted particles strike the walls of the mill. Roll crushing: provides a coarse crushing alternative to hammer milling. The ceramic chunks are crushed in between two hard faced rollers that rotate in opposite directions.

2. Chemical Methods •

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Co-precipitation method: it is used to prepare multicomponent ceramic oxides through formation of intermediate precipitates usually hydrous oxides or oxalates to form an intimate mixture of components during precipitation. The chemical homogeneity is maintained on calcination. Washing and drying procedures such as water washing, solvent washing, azeotropic distillation etc. are used for coprecipitated oxides that can have a drastic effect on the mechanical properties of a sintered powder. Sol-gel process: preparation of a powder by a sol-gel approach involves the following steps: (i) form a stable dispersion (sol) of particles of very small size in a liquid, (ii) by change in concentration, aging, addition of suitable electrolyte to occur throughout the sol to form a gel, (iii) evaporate the remaining liquid from the gel, (iv) increase the temperature to convert the dehydrated gel to the ceramic composition. The versatility of sol-gel processing is illustrated by its use for the fabrication of ceramic shapes other than powders. Hydrothermal preparation: hydrothermal synthesis offers a low-temperature, direct route to sub-micrometer, oxide powders with a narrow size distribution avoiding the calcination step required in sol–gel processing. When applied to ceramic powders hydrothermal techniques often involve heating metal salts, oxides or hydroxides as a solution or suspension in a liquid at elevated temperature and pressure up to about 300°C and 100 MPa. It involves crystallization of a composition in hot, pressurized water. The feedstock can be oxides, hydroxides, salts, gels, organics, acids, and bases. The conditions can be oxidizing or reducing. In this process a wide variety of pure, fine particle ceramic compositions can be synthesized. The Pechini and Glycine Nitrate methods: in the Pechini method [97], polybasic chelates are formed between a-hydroxy carboxylic acids containing at least one hydroxyl group. The glycin-nitrate process adds amino acid glycine which performs two functions: (i) it forms complexes with the metal cations and increases their solubility. This seems to prevent selective precipitation and segregation during evaporation, (ii) the glycine act as a fuel during charring. The metal nitrates are combined with glycin in water and evaporated until a homogeneous viscous liquid forms.

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Nonaqueous liquid reaction: this reaction take place in a non-aqueous solvent which may be inert or one of the reactants. This method basically associated with the synthesis of non-oxide powders, particularly Si3N4. Low temperature decomposition is an advantage of non-aqueous reactions that have been extended to oxides and include condensation between metal chlorides and metal alkoxides. Emulsion combustion method: this method is classified into liquid phase syntheses but it also has the features of gas phase syntheses. The emulsion combustion process is characterized by (i) an isolated small reaction field in which constituent metal ions are mixed homogeneously in the aqueous phase, (ii) a short reaction period achieved by the combustion of the thin kerosene film surrounding each aqueous droplet, (iii) a continuous fabrication procedure which contributes to lower production costs. Spray pyrolysis method: is used for synthesis of high-purity metal oxides. A solution of a metal chloride in water is sprayed into a heated ceramic-lined chamber. The resulting oxide powder consists of crystallites of approximately 0.2 to 0.4 μm in diameter agglomerated into hollow spheres 100 to 200 μm in diameter.

For a large-scale production the mechanical methods are generally used, as the production costs are very high for the chemical methods. In these days both the processes are used, for example, mixed oxide method for the cost conscious applications and chemical methods for more stringent applications. This method, although successful for a large-scale production of bulk ceramic powders at its low cost and easy adaptability, has several limitations in the production of fine ceramics [98]. In conventional solid-state method, high temperature heating for prolonged time makes the particles coarse, and as a result high energy destruction (break down) force is required to get fine powders [99]. Several authors [100-102] studied the fabrication and properties of the ceramics prepared by a solid-state reaction technique. Using this method ceramics are produced under high temperature by mixing their constituent ingredient. The completion of the reaction and uniformity of the product depend on particle size, homogeneity of the mixture, thermal schedule, and even on the atmosphere during calcination. On the other hand, ceramic powders prepared by certain non-conventional chemical methods have shown improved characteristics with respect to purity, homogeneity, stoichiometry, and reactivity as well as particle size, shape, surface, and agglomeration behavior [103-105]. Both methods have their own inherent advantages. Ball milling is a well established technology in which it can provide more uniform powders on reducing the chance of agglomeration. In high-energy planetary ball milling; powders suffer severe high-energy impacts between balls or between wall and balls during milling, due to which fragmentation occurs vigorously. Further addition of wetting agent during milling makes grinding faster, break down surface tensions of aggregated particles and can also absorb excess heat produced. There are some disadvantages in the traditional solid state reaction. However, there are undesirable features such as nonstoichiometry, compositional fluctuation and poor microstructure because of the high temperature processes. Therefore, it is necessary to process the materials at as low a sintering temperature as possible. Low firing temperature processing in ceramic fabrication demands fine precursor powders of high homogeneity of components mixing. Chemical methods such as co-precipitation and alkoxide sol-gel processes are employed nowadays to synthesize it [106-109]. Semi-chemical methods [110-

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113] can be used as well. It was based on simultaneous oxide milling and one component precipitation.

6.3. Thin Film Thin films are thin material layers ranging from fractions of a nanometer to several micrometers in thickness. Electronic semiconductor devices and optical coatings are the main applications benefiting from thin film fabrication. Ceramic thin films are also in wide use. The relatively high hardness and inertness of ceramic materials make this type of thin coating of interest for protection of substrate materials against corrosion, oxidation and wear. In particular, the use of such coatings on cutting tools may extend the life of these items by several orders of magnitude [100]. Thin-film ferroelectrics are an exciting new field with applications in microwave circuits, semiconductor devices, and optical systems. There are different deposition techniques for thin film preparation as: (i) the chemical deposition technique and (ii) the physical deposition technique. In chemical deposition technique, a fluid precursor undergoes a chemical change at a solid surface, leaving a solid layer. Chemical deposition is further categorized as: •

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Plating: here a solution of water with a salt of the metal to be deposited. It can be used for chemical-mechanical polishing techniques. Thin-film deposition in CSD (chemical solution deposition) method: it is one of the most common processes used as a fabrication method for thin films. This process can be widely used for optical, electrical, magnetic, mechanical and catalyst applications. Notable advantages of the chemical solution process are high purity, good homogeneity, lower processing temperatures, precise composition control for the preparation of multicomponent compounds, versatile shaping, and preparation with simple and cheap apparatus, compared with other methods. However, the more the number of elements, the more complicated the solution chemistry, leading to difficult problems in obtaining the desired crystalline phase. In the CSD process, the starting raw materials are not only mixed at a molecular level in the solution, but also reacted to cause an appropriate chemical modification of the metallo-organic complexes, leading to the development of new molecular engineering. The chemically designed new precursors allow chemical solution preparation of the desired materials in the form of fine powders, fibers or films. This is a relatively inexpensive, simple thin film process that is able to produce stoichiometrically accurate crystalline phases. Chemical vapor deposition: chemical vapor deposition (CVD) of thin films involves the chemical reactions of gaseous reactants i.e., generally uses a gas-phase precursor, often a halide or hydride of the element to be deposited.on or near the vicinity of a heated substrate surface. Moreover, it can produce single layer, multilayer, composite, nano-structured, and functionally graded coating materials with wellcontrolled dimension and unique structure at low processing temperatures.

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Plasma enhanced chemical vapor deposition (PECVD): uses an ionized vapor, or plasma as a precursor. Atomic layer deposition (ALD): ALD films are deposited by a repetitive process of single layer deposition sequences. Each sequence consists of several gas– surface interactions that are all self-limiting. The self-limiting nature of the sequences is the foundation of ALD. ALD offers the ultimate control over film thickness and uniformity.

The physical deposition technique produces thin films of solid by using mechanical or thermodynamic means. Physical deposition [114] is further categorized into the following:

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Physical vapor deposition (PVD): Physical vapor deposition (PVD) is a technology where a material is evaporated and condensed to form a thin film coating over an object (substrate). In general, coatings consist of metals or ceramics; usually nitrides, carbides and oxides. With this highly flexible method, thicknesses of the coatings can be varied from a few atomic layers up to approximately 10 µm. With a wide range of coating materials and thicknesses, coatings can be optimized for various characteristics, such as electrical, mechanical, optical and decorative. In PVD, the substrate does not need to be metallic or electrical conductive, thus making it possible to coat non metallic isolators, plastic and ceramic objects. Further the possibility of maintaining low process temperatures, below 100 ºC increases the number of applications of PVD. Today, PVD is used industrially in a wide spectrum of industrial applications. The most common are semiconductors, CD/DVD-media, tools, mechanical components, automotive components, sensors, biomedical, optics, etc. The use of PVD is also increasing rapidly in other industries to replace less environment-friendly chemical and galvanic methods. Evaporation in PVD can be done by the following methods. − −

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Thermal evaporation: it uses an electric resistance heater to melt the material and raise its vapor pressure to a useful range, which can be done in a high vacuum. Electron beam deposition: in this technique, an electron beam evaporator fires a high-energy beam from an electron gun to boil a small spot of material. Since the heating is not uniform, lower vapor pressure materials can be deposited. Sputtering: it is especially useful for compounds or mixtures, where different components would otherwise tend to evaporate at different rates. Sputtering involves the ejection of material from a solid or liquid surface following the impact of energetic ions, atoms, or molecules. Pulsed laser deposition (PLD): PLD systems work by an ablation (i.e., the removal of material from the surface of an object by vaporization, chipping, or other erosive processes) process. Pulses of focused laser light vaporize the surface of the target material and convert it to plasma; this plasma usually reverts to a gas before it reaches the substrate. Cathodic arc deposition: here an electrical arc is created that blasts ions from the cathode. If a reactive gas is introduced during the evaporation process; dissociation, ionization and excitation can occur during interaction with the ion flux and thus a compound film will be deposited.

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Molecular beam epitaxy (MBE): It is a technique for epitaxial growth via the interaction of one or several molecular or atomic beams that occurs on a surface of a heated crystalline substrate. The beam of material can be generated either by a furnace or by a chemical reaction. Spin coating: In this method; an excess amount of a solution is placed on the substrate, which is then rotated at high speed in order to spread the fluid by centrifugal force, which leads to the formation of a uniform thin film on a flat surface. The machine used for this technique is known as a spin coater or spinner. Electrodeposition: In electrodeposition technique, the deposition of a substance to be done on an electrode by the action of electricity. Metallo-organic decomposition (MOD): In this method, a solution comprising the materials of certain volume percent is deposited onto a substrate.

Single layer surface mount capacitors have been developed on the basis of thin film technologies for cellular networks, satellite telecommunications systems and high frequency applications. Various thin-film dielectric materials are used for making capacitive elements in microelectronics circuitry.

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6.4. Polymers Polymers, special class of materials, consist of long macromolecular chains. The polymer chain is formed by reiteration of an identical structural unit, known as monomer. Some polymers, such as proteins, cellulose, and silk are found in nature, while some others, including polystyrene, polyethylene, and nylon are produced synthetically. The birth of polymer science may be traced back to the mid-nineteenth century. In 1830s, Charles Goodyear [115] developed the vulcanization process that transformed the sticky latex of natural rubber to an elastomer. In 1847, Schonbein [116] tested the reaction of cellulose with nitric acid to produce cellulose nitrate. This was used in the 1860s as the first man-made thermoplastic celluloid [117]. Thus, gradually the discovery of synthetic polymers with a number of high-performance have been developed to date. Polymers can be classified on the basis of polymerization mechanisms and their structure: •

•

All polymers can be divided into two major groups based on their thermal processing behavior as thermoplastics and thermosets. The polymers that can be heat-softened in order to process into a desired form are called thermoplastics and thermosets whose individual chains have been chemically linked by covalent bonds during polymerization or by subsequent chemical or thermal treatment during fabrication. Based on the polymerization technique, the polymers may be either addition or condensation type. Polystyrene (polymerized by a sequential addition of styrene monomers), polyethylene, polyoxymethylene are a few examples of addition-type of polymers. The condensation polymers are obtained by the random reaction of two molecules. A molecule participating in a poly-condensation reaction may be a monomer, oligomer, or higher-molecular-weight intermediate each having complementary functional end units, such as carboxylic acid or hydroxyl groups.

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Polyamidation of nylon-6, 6 and polymerization of bisphenol-a-polycarbonate are some other examples of condensation polymers. polymers may also be grouped based upon the chemical structure of their backbones.

Polymers having all carbon atoms along their backbone are important examples of homochain polymers. They may further be classified depending upon whether there are single, double, or triple bonds along their backbone. Carbon-chain polymers with single bonds along the back bone are known as polyalkylenes, with double bonds are called polyalkenylenes, and with triple bonds are polyalkynylenes. Polymers having more than one atom type in their backbone are grouped according to the type of atoms and chemical groups (e.g., carbonyl, amide, or ester) located along the backbone. Some of the important organic hetero-chain polymers are: carbon-oxygen polymers (polyethers, polysters of carboxylic acids, polycarbonates), carbon-sulfur polymers (polythioethers, polysulfones), carbon-nitrogen polymers (polyamines, polyimines, polyamides, polyureas). Bulk properties can be varied by chemical modification of polymers in solution or melt. The chemical modification has been investigated as a means of optimization of essentially every physical property of polymers. Surface properties are often easily dealt with by reaction of the solid polymer surface, as well as bulk modification.

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6.4.1. Electrical Properties of Polymers The electrical properties of polymers are a subject which is inherently interdisciplinary in nature. The development of intrinsically conductive polymers has benefited immensely from the contributions of synthetic chemists. The atoms, which form the backbone of organic polymers, are predominantly carbon atoms, sometimes in combination with oxygen and/or nitrogen. The nature of the chemical bonding in the polymer directly influences the electrical properties. The occurrence of dielectric properties in polymeric substances has long attracted the attention of researchers and scientists in science, technology and engineering from both a practical and a fundamental point of view. The low electrical conductivity and low dielectric losses of some polymers make them very useful for electrical insulation, encapsulation, capacitors, interconnection insulation, component potting etc. From more basic standpoints, the dielectric properties of polymers offer a tool for studying their molecular structure. The choice of polymer dielectric for a particular electronic packaging application is mainly based on the inherent physical properties of that material. These properties affect the performance of the package in several key areas: signal speed, power consumption, thermal stability, interaction with other materials, and wiring density. The ease with which polymers can be tailored to display certain electrical, mechanical, and thermal characteristics, and their ease of processing have made them ideal materials for use in electronic packaging. Dielectric constant (εr) is a critical electrical parameter for microelectronic polymer dielectrics. The magnitude of εr depends on the amount of mobile (polarizable) electrical charges and the degree of mobility of these charges in the material. Because the charge mobility depends on temperature, εr is temperature dependent, and since polarization of the material requires a finite amount of time, the frequency of the electric field also influences the measured dielectric constant.

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6.4.2. Different Types of Dielectric Polymers

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(i) After the discovery of ferroelectricity in polyvinylidene fluoride (PVDF) type polymers in 1980 [118-120], the materials have received particular attention for many reasons. One of the most important features is that the polymers can be easily produced in the form of large thin flexible sheets and in a variety of shapes. The low dielectric permittivity and elastic stiffness of PVDF-type polymer films at room temperature, resulting in high voltage sensitivity and low acoustic impedance make them attractive for application in electromechanical transducers [121, 122]. As the permittivity and dielectric losses are involved in figures of merit of pyroelectric sensors, PVDF-type polymers with high pyroelectric coefficient and low ε and tan δ values are used in pyroelectric applications [123]. The dielectric response in low-temperature range is the characteristic of segmental motions of the polymer, i.e., freezing of dipolar motions in the amorphous phase of the semi-crystalline polymer. The process is strongly dependent on temperature and frequency. Torsional and rotational motions of dipoles attached to the main chains are responsible for the peculiar dielectric (i.e., anomaly). The characteristic of the ferroelectric-paraelectric transition is observed just before dynamical melting of the polymer where a minimum in the permittivity appears [124]. The Curie point anomaly appears in PVDF at temperatures ~ 150 K higher than the dynamic glass transition but the Curie point can be shifted downward by loading the planar zigzag chains with units having the dipole moment different from that of VDF [125, 126] or by introducing random field in form of radiation-induced defects [127, 128], which may be related to a decrease in the density of ferroelectrically active dipoles and random field (defects) result in rounding and decrease of the Curie point anomaly. The relaxor-like dielectric response of this material with a single broad and dispersive anomaly appears in semi-crystalline ferroelectric polymers as a result of defect-induced merging of the Curie point anomaly with the response of the amorphous phase. (ii) The systematic study of very thin polymer films for their dielectric properties reflects the history of bulk polymers. A thin polymer (dielectric film) is a solid layer of more or less homogeneous composition which is less than 3μ thick, uniform in thickness, coherent in structure and adherent upon a supporting surface. Polymer insulating films are generally prepared by the interaction of a monomeric or low molecular weight polymeric species, usually in gaseous form, with a solid surface in the presence of some form of energy. The energy is often supplied by the thermal energy of the substrate or by radiation; in some cases, it arises from a catalytic reaction involving the surface or resides in the monomer itself. In almost all practical applications, it is desirable or even mandatory that some methods for defining the geometric area of the film be available. The resolution required will depend largely on the specific application. Slight modification of the structure of the monomer could give rise to polymer films with various optical absorption properties, and hence various colored films could be obtained. Various Mechanisms of polymer film formation are: • •

Addition polymerization: the formation of long chain molecules by the addition of a monomer unit to an already existing polymer molecule. Ionic polymerization: the reaction of an ionic species with another ionic or neutral species or molecular site.

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Recombination polymerization: the production of a solid polymer film of amorphous structure by the creation of numerous reactive species. Condensation: process such as a gas discharge. It refers to the condensation on a surface of a polymer species to form a film which is basically a low molecular weight, low vapor pressure material.

(iii) Polymer-based composites with high dielectric permittivity have potential application in microwave communication devices [129], artificial muscles [130] and embedded capacitors for micro-electromechanical systems [131, 132] due to weight, shapeflexibility, cost effectiveness and good processability of the materials. The most common process for enhancing the dielectric permittivity of a polymer is to disperse a high dielectric permittivity insulating ceramic powder such as barium titanate (BaTiO3) [133, 134] and lead titanate (PbTiO3) [135] into the polymers to form composites. The dielectric permittivity of the polymers significantly increases by dispersing conductive particles, e.g., carbon nanofibers, silver particles and copper phthalocyanine oligomers [136-138] into a polymer matrix. The increased dielectric permittivity observed in such composites arises from conducting particles isolated by very thin dielectric layers to form micro-capacitors [139].

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6.5. Liquid Crystals A liquid crystal (LC) is a substance that flows like a liquid but maintains some of the ordered structure characteristic of crystals. The liquid crystal “phase'' exists between the solid and the liquid phase. Liquid crystal phases are formed by materials from the whole spectrum of chemical classes: organic, organometallic, and biological molecules. The molecules in liquid crystal do not exhibit any positional order, but they do possess a certain degree of orientational order. The structures are easily affected by changes in mechanical stress, electromagnetic fields, temperature, and chemical environment. Basically liquid crystal is divided into: thermotropic, lyotropic and metallotropic type.

Thermotropic LCs Thermotropic LCs exhibit a phase transition into the LC phase as temperature is changed. The thermotropic LCs further classified as: nematic, smectic, chiral, blue phase, discotic. Nematics have long range orientational ordering (i.e., the molecules tend to align parallel to each other) and such molecules can not be distinguishable from their mirror image. Cholestrics are the twisted nematic phases and have its structure twisted about the helical axis lying perpendicular to the orientation of molecules. An external field applied to the cholestric fluid can change the pitch of the helix, converting the fluid to the nematic type. Smectic liquid crystals are ordered liquid crystal phases having a layer structure. The molecules align themselves in parallel layers gliding one relative to the other, thereby promoting fluidity. There are variety of smectic phases such as SmA, SmB, SmC, SmD, SmE, SmF, SmG, SmH, SmI, SmJ, SmK and chiral Sm. In the smectic-A (SmA) phase, the director is perpendicular to smectic layer plane and there is no particular position order in the layer. Similarly, the smectic-B (SmB) phase orients with the director perpendicular to the smectic plane, but the molecules are arranged into a network of hexagons within the layer. In the smectic-C (SmC)

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phase, molecules are arranged as in the SmA phase, but the director is inclined at a constant tilt angle with the layer normal. As in the nematic phase, the SmC phase has a chiral state designated C*. The director of the SmC phase is neither parallel nor perpendicular to the layers. In the smectic- C* (Sm C*) phase, it rotates from one layer to the next. Blue Phases are special types of liquid crystal phases that appear in the temperature range between a chiral nematic phase and an isotropic liquid phase, and are of interest for fast light modulators or tunable photonic crystals. Many chiral compounds with sufficiently high twist will appear in three distinct blue phases (BPI, BPII and BPIII). Discotic nematic phase have disk-shaped mesogens that can orient themselves in a layer-like fashion. If the disks pack into stacks, the phase is called a discotic columnar. The columns themselves may be organized into rectangular or hexagonal arrays. Chiral discotic phases, similar to the chiral nematic phase.

Lyotropic Lyotropic LCs exhibit phase transitions as a function of concentration of the mesogen (i.e., the fundamental unit of LC that induces structural order in the crystals) in a solvent (typically water) as well as temperature. Such types of LCs are the mixtures or solutions of unlike molecules in which one is a nonmesogenic liquid. The lyotropic liquid crystal phases are formed by the dissolution of amphiphilic molecules (containing a large organic cation or anion which possesses a long unbranched hydrocarbon chain) of a material in a suitable solvent. Amphotropic materials are able to form thermotropic as well as lyotropic mesophases.

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Metallotropic The metallotropic LCs based on low-melting inorganic phases like ZnCl2. The addition of long chain soap like molecules leads to a series of new phases that show a variety of liquid crystalline behavior both as a function of the inorganic-organic composition ratio and of temperature [140]. Liquid crystals are also derived from certain macromolecules (polymers) usually in solution but sometimes even in the pure state. They are known as liquid crystal polymers (LCPs) [141]. The phase classification in liquid crystal can be done on the basis of its structure, microscopic structure, miscibility rules etc. The structural characterization can be carried out by X-rays supported by some other methods like nuclear magnetic resonance, neutron scattering, infrared and Raman spectroscopy to characterize the arrangement and the confirmation of the molecules and intermolecular interactions. The textures are observed microscopically in polarized light. They are characterized by defects of the phase structure. Details of texture analysis give the idea about the classification of the meso-phases [142-144]. The miscibility rule states that the liquid crystals are of same type, if they are miscible in all proportions.

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6.5.1. Ferroelectric Liquid Crystals Based on the ferroelectric properties of liquid crystals, they are specifically categorized as non-ferroelectric phases, ferroelectric smectic phases, anti-ferroelectric and ferrielectric phases. •

•

•

Non-ferroelectric phase: the twisted nematic or chiral nematic phases cannot be ferroelectric because of symmetry properties. Due to the twisted or helical structure this phase possess special optical properties, useful for practical applications. Ferroelectric smectic phases: all the tilted chiral smctic phases are ferroelectric liquid crystals. Due to their low symmetry, they possess spontaneous polarization and piezoelectric properties. Presence of permanent dipoles in asymmetric molecules lead to alter the nature of the interactions between the molecules themselves and with any cell wall or applied electric field. The spontaneous polarization in ferroelectric liquid crystals is about 100 to 1000 times smaller than that of solid ferroelectrics [145]. Antiferroelectric and ferrielectric phases: the molecular layers of antiferroelectric smectic C* phase are arranged in such a way that the polarization directions in adjacent layers point in opposite directions which results in an average of the spontaneous polarization equal to zero, whereas in a ferrielectric smectic phase, the layers are stacked in such a way that the net spontaneous polarization can be measured.

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6.5.2. Dielectric Spectroscopy of Liquid Crystal Dielectric spectroscopy is a powerful method for the investigation of liquid crystals [146, 147], and enables the dielectric anisotropy properties of such compounds to be determined. Dielectric anisotropy (Δε) is one of the most important physical properties of liquid crystalline compounds, which in essence determines the lower threshold voltages of liquid crystal displays (LCDs) [148, 149]. In recent years, ferroelectric properties of the chiral smectic C (SmC*) phase have gained considerable interest due to their peculiar physical properties and potential applications in fast switching electro-optic liquid crystal display devices. The dielectric spectroscopy of SmC* liquid crystal gives useful information about the static and dynamic properties of these compounds. When a liquid crystal exhibiting Sm C* phase is placed between two electrodes, then weak electric field breaks the symmetric distribution of all dipoles on microscopic and macroscopic scales, thus inducing a macroscopic polarization Pind which has a contribution from all electronic, atomic, ionic and orientational polarizations. The dielectric permittivity ε can be written as: ε0 ε =

lim

∑ E →0

( Pind ) i + ε0 E

(6.3)

where the sum is made over all contributions, ε0 is permittivity in free space and E is applied electric field. When it is away from equilibrium, the system becomes dissipative, and the induced polarization lags behind the field is out of phase. Mathematically, this phase Recent Advances in Dielectric Materials, Nova Science Publishers, Incorporated, 2009. ProQuest Ebook Central,

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difference between the field and induced polarization is expressed in the imaginary part ε'' of a complex permittivity ε* which may be written as: ε* = ε΄-i ε''. Dielectric response of LCs mainly consists of four modes. Out of these four modes, two are due to the fluctuations of the polarization order parameters having relaxation frequencies of the order of 500 MHz [150]. Other two modes are connected to the director fluctuations known as Goldstone mode (GM) and soft mode (SM) [151]. The dielectric behavior of the SmA and SmC* phases and its dependence on temperature, frequency [152], pressure, sample thickness [153] and bias electric field has been studied by several groups during the last few years [154, 155].

7. Characterization Techniques 7.1. Thermal Analysis

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Thermal analysis involves a physical measurement and not, strictly speaking, a chemical analysis. There are a number of different thermo-analytical methods such as calorimetry, i.e., differential scanning calorimetry (DSC), differential thermal analysis (DTA), thermogravimetry (TG), thermal mechanical analysis (TMA, DMTA), thermal optical analysis (TOA) and dielectric thermal analysis (DETA) available to characterize different type of materials such as ceramics, polymer, glass etc [156]. Thermal characterization techniques are standard and established methods to study phase transition, thermodynamics and kinetics of the reaction. Most of the substances when heated undergo thermal reaction because of dehydration, oxidation, destruction of lattice structure, and change in crystalline phase etc. The thermal reaction temperature, intensity and general behavior of a substance provide main criteria for its identification by thermal methods.

7.1.1. Differential Thermal Analysis (DTA) DTA is used to study high temperature phase changes or reactions. Even thermal reactions of very low intensity can be utilized in the method if they begin abruptly and are completed in a short temperature interval. This technique is based on measurement of the difference in the temperature of the material sample (usually alumina) as a function of temperature or time. The sample and the inert reference material are contained with the same heating block to maintain the same heat input for both. The mass of the material taken is kept in close proximity to that of the thermal mass of the reference material. Since the sample and the reference undergo controlled heating or cooling varying linearly with time during thermal event, the temperature of the sample will differ from that of the reference. Usually linear heating rate is maintained during experiment. The difference of temperature given by ∆T when plotted as a function of time results the DTA curve. Any phase transformation of the sample upon thermal cycling is accompanied either by absorption (endothermic) or release of heat (exothermic). The results are recorded generally in the form of a continuous curve on which endothermic reactions are deflected downwards and exothermic reactions deflected upward from the base line. The enthalpy change either exothermic or endothermic are caused by various phase transition, dehydration, decomposition and crystallization [157 - 159].

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R.N.P. Choudhary and S.K. Patri • •

•

If ∆T =0, it indicates that no physical or chemical change takes place. If ∆T = -ve, then it shows that absorption of heat takes place due to thermal energy being used up in promoting the phase transformation. This transformation is accompanied by the relative cooling of the sample with respect to the difference, and is indicated by the appearance of an endothermic peak in the DTA pattern. The endotherm may be sharp or broad depending upon the nature of the physical changes. If ∆T = +ve, it shows that heat is released in phase transformation such as crystallization of a solid from glassy state and is indicated by the appearance of an exothermic peak.

For ferroelectric materials, DTA technique has its utility because of the specific heat anomaly of these materials at transition or Curie temperature. The difference between specific heat Cp=T(dS/dT)P where dS (change in entropy) is the main cause for phase transition in ferroelectrics. The abrupt change of spontaneous polarization in these materials is associated with latent heat and anomalous behavior of specific heat [33].

7.1.2. Thermo Gravimetric Analysis (TGA) In this technique change in weight of a material is recorded as a function of temperature. It is useful strictly for transformations involving the absorption or evolution of gases from a specimen consisting of a condensed phase. When the sample is heated dynamically in a programmed manner, a change in mass (mass loss) with temperature is observed in a definite pattern giving a TGA curve. The curve provides the following information regarding the sample.

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• •

•

TG curve is basically quantitative in nature and gives an estimate of the material stoichometry at any given temperature. The horizontal portion (slope) on the thermo-gram indicates weight loss, which provides an understanding of chemical nature of the material coupled with the analysis of volatiles and residues. It enables us to obtain a differential TG curve (DTG) when the rate of change of weight with time (i.e., dw/dt) is plotted with temperature. The peak indicates the temperature at which mass loss is maximum corresponding to dw/dt=0. On the other hand, minimum is the plot characterized by the inflection (i.e., change in slope in TGA curve) corresponding to dw/dt ≠ 0 represents the situation of weight loss followed by formation of an intermediate product.

7.3. Structural and Microstructural Analysis The properties of materials are highly structure dependent. Structure is in turn determined by composition, heat treatment, and processing. Thus it is necessary to characterize both composition and microstructure at the highest possible resolution in order to understand material behavior, and to facilitate the design of new or improved materials. Such characterization requires advanced and sophisticated methods of analysis using diffraction, microscopic, and spectrographic techniques.

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7.3.1. X-ray Diffraction Study (XRD) X-ray diffraction (XRD) technique is a powerful tool for material characterization as well as detailed structural analysis. In polycrystalline materials, the randomness of crystallite orientation always allow a fraction of the sample to be suitably oriented with respect to the incident beam, which in turn enables an arbitrary diffraction line to be observed. The X-ray diffraction profile is used to determine the atomic arrangements in the structure of the materials because the interplanar spacing (d-spacing) of the diffracting planes is of the order of X-ray wavelength λ. For a crystal of given d-spacing and wavelength λ, the various orders n of reflection occurs only at the precise values of angle θ, which satisfies the Bragg condition: 2d sinθ = nλ

(7.1)

The accurate determination of interplanar spacing, lattice parameters etc. provide important basis in understanding various properties of materials by XRD. The advantage of X-ray powder diffraction method can be described as follows: • •

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• •

The powder diffraction pattern is the characteristic of a substance. Each substance in a mixture produces its own diffraction pattern independent of the others. It describes the state of chemical combination of elements in the material. The method is competent in developing quantitative and qualitative analysis of a substance.

The accurate determination of interplanar spacing (d) of a plane (hkl) and lattice parameters (a, b, c, α, β and γ) provide important basis in understanding various properties of a material. The calculation of lattice constants from the line or peak positions or d spacing can be done using a general formula [160-161]. The most commonly and widely used powder diffraction techniques is the photographic and counter techniques [162]. The factors upon which the intensity depends are: (a) Structure factor: Structure factor signifies the nature of the constituent atoms and their arrangements in the unit cell. It is given by N

F (hkl) =

∑

fj exp 2π (hxj + kyj + lzj)

(7.2)

j =1

where xj, yj and zj are the fractional co-ordinates and fj is the atomic scattering factor for the jth atom in the unit cell, N being the total number of atoms in the cell. (b) Polarization factor: Unpolarized rays emanating from the X-ray tube get polarized due to the scattering of X-rays from electrons. The extent of the polarization is a function of the angle through which the beams get scattered. The intensity of the scattered beam depends on the angle of scatter and is given by

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R.N.P. Choudhary and S.K. Patri

I = Io

(

2 k 1 + cos 2θ 2 r2

)

(7.3)

where Io = Intensity of the incident beam and k is a constant. The term

(1 + cos 2

2

2θ

) is known as the polarization factor (P).

(c) Lorentz – Polarization factor: For powder specimens, Lorentz-polarization factor can be expressed as

1 + cos 2 2θ L= sin 2 θ cosθ

(7.4)

This factor reaches its maximum value when θ approaches 0o and 90o and minimum value when θ becomes 45o. Therefore, this factor becomes prominent at very low and very high angle. In case of line profile analysis, this factor is negligible. (d) Scale factor: The superposition of reflected beams enhances the intensity of a line from a single plane. In order to account for this increased intensity, a factor J, called scale factor is introduced for determining the relative intensity. In powder diffraction technique, the value of J depends on the symmetry of the crystalline material.

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(e) Temperature factor: A crystal consists of atoms, located at fixed points in the lattice. Actually the atoms have thermal vibration about their mean positions even at absolute zero temperature, and the amplitude of this vibration increases as the temperature increases. Thus the temperature factor is taken into consideration. (f) Instrumental factors. The instrumental factors which influence the broadening of the profile are: x-ray source profile, divergence of the beam, absorption of the beam by sample, width of the receiving slits and misalignment of the apparatus. Table 7.1. Comparison of lattice parameters (Å) with estimated standard deviation (in parenthesis), particle size (nm) and tolerance factor (t) of tetragonal crystal structures of (Bi1−xPbx ) (Fe1−xZr0.6xTi0.4x ) O3 for x = 0.15, 0.25, 0.40, 0.50 x

a

c

c/a

V

P

t

0.15

3.9398 (84)

3.9744 (84)

1.0088

61.69

32

0.847

0.25

3.9709 (48)

3.9895 (48)

1.0047

62.91

35

0.852

0.40

3.9967 (41)

3.9706 (41)

0.9935

63.43

40

0.858

0.50

4.0286 (12)

4.0163 (12)

0.9970

65.18

32

0.863

Ref. 164.

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Ref. 163.

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Figure 7.1. Room temperature XRD pattern of Na1/2La1/2TiO3 with an orthorhombic crystal structure of lattice parameters: a = 3.8545Å, b = 3.8716Å and c = 3.8642Å.

Ref. 164.

Figure 7.2. Comparison of XRD patterns of (Bi1−xPbx )(Fe1−xZr0.6xTi0.4x )O3 for x = 0.15, 0.25, 0.40, 0.50.

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Table 7.2. Comparison of lattice parameters a (Å) and α (◦) (estimated standard deviation in parenthesis) with rhombohedral crystal structure, unit cell volume V (Å3) and average grain size P (μm) of Pb0 92(La1−zFez)0.08] [Zr0.65Ti0.35]0 98 O3 ceramics z

a

α

V

P

0.0

4.0715 (1)

89.933 (1)

67.49

2

0.3

4.0874 (3)

89.796 (3)

68.29

3

0.6

4.0873 (3)

89.772 (4)

68.28

5

0.9

4.0873 (4)

89.921 (3)

68.28

6

1.0

4.1435 (3)

89.934 (3)

71.1300

8

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Ref. 165.

Ref. 165.

Figure 7.3. Room temperature XRD pattern of [Pb0.92(La1−zFez)0.08][Zr0.65Ti0.35]0.98O3 for z = 0.0, 0.3, 0.6, 0.9, 1.0.

The above figures (Figure 7.1-7.3) and tables (Table 7.1-7.2) depict some typical XRD patterns of ferroelectric materials.

7.3.2. Scanning Electron Microscopy (SEM) The scanning electron microscopy (SEM) can produce high-resolution images of a sample surface, and hence it is frequently used to study microstructure of materials. Large depth of focus and no restriction of shape and size of bulk sample are the main advantages of SEM. SEM produces the image of the object/particle with marked three-dimensional appearance, and is useful for judging the surface structure of the sample. It produces micrographs by scanning the surface of the specimen with a small electron probe (a beam of electrons)

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synchronous with an electron beam from a source. The contrast is due to the topographical variation and atomic number differences in the specimen. SEM can reveal topographical details of a surface with clarity; examine void content, particle agglomeration as well as phase differences within a material, which cannot be obtained by other means. Image formation in SEM occurs in the following manner: The secondary electrons emitted from a point on the bombarded specimen are collected and converted into a minute current that is amplified to produce a signal voltage, this signal is passed on to a cathode ray–tube (CRT) where it determines the potential of the regulating or modulating electrode which controls the current in the cathode-ray tube. As a result, a point on the screen of the CRT is formed whose brightness is controlled by the current reaching the collector. The basic units of SEM are: • • •

electron-optical columns together with appropriate electronics the vacuum system, which includes the specimen chamber and stage signal detection and display system

The following figures (Figure 7.5-7.6) show some room temperature SEM of typical ferroelectric materials. The interaction of high-energy electrons with specimen leads to the excitation of a variety of signals, which can be used for characterization of microstructure, crystallography, etc. Grain size of the samples is estimated by measuring more than 100 grains of different regions in each sample and taking their root mean squares diameter. The following figures show some room temperature SEM of typical materials.

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7.3.3. Transmission Electron Microscopy (TEM) TEM is used to determine the internal structure of the materials in nanoscale order. It gives the following information • •

•

Morphology: The size, shape and arrangement of particles, which make up the specimen as well as their relationship to each other on the scale of atomic diameters Crystallographic information: The arrangement of atoms in the specimen and their degree of order, detection of atomic scale defects in areas of a few nanometers in diameter. Compositional information: The elements by which the sample is composed and their relative ratios in areas of a few nanometers in diameter.

The selected area electron diffraction (SAED) patterns can be used to make a direct correlation between the morphological and crystallographic information of very small areas. This technique is of particular importance, when more than one phase is present in the specimen. The figures (Figure 7.6-7.8) show TEM and SAED patterns of some typical dielectrics.

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Ref. 166.

Figure 7.4. SEM of Pr doped PZT (60/40) ceramics.

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Ref. 163.

Figure 7.5. SEM of Na1/2La1/2TiO3

Ref. 167.

Figure 7.6. TEM and SAED pattern of PbSn0 15Ti0 85O3.

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Ref. 168.

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Figure 7.7. TEM and corresponding SAED pattern of Pb0 97Ca0 03Zr0 05Ti0 95O3.

Ref. 169.

Figure 7.8. TEM and corresponding SAED pattern of (Pb0 92La0 08) (Zr0 60Ti0 40)0 98O3.

7.3.4. FTIR Spectroscopy Spectroscopy is conventionally defined as the science of the interaction between the radiation and matter, and deals with both experimental and theoretical aspects of these interactions Fourier transform infrared (FTIR) spectroscopy is a simple mathematical technique to resolve a complex wave into its frequency components. The infrared (IR) region corresponds to the energies of the vibrations and rotations of molecules. If a molecule is subjected to IR radiation whose frequency is equal to that of one of its oscillators, this oscillator will resonate and absorb a part of the radiation. Absorption in the infrared region results in changes in vibrational and rotational status of the molecules. The absorption (emission) intensity is given by the transition probability between the ground and excited states. The intensity of the infrared band is proportional to the square of the change in dipole moment. The transitions corresponding to vibrations with variation in dipole moment are active in infrared spectroscopy. The absorption frequency depends on the vibrational frequency of the

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molecules, whereas the absorption intensity depends on how effectively the infrared photon energy can be transferred to the molecule, and this depends on the change in the dipole moment that occurs as a result of molecular vibration. Therefore, a molecule will absorb infrared light only if the absorption causes a change in the dipole moment. Thus, all compounds except for elemental diatomic gases such as N2, H2 and O2, have infrared spectra. FTIR analysis is faster and has a better signal to noise ratio. In an FTIR instrument, an interferometer (usually of Michelson type) is present. A beam of radiation is divided into two beams by means of a beam splitter and a path difference between the beams is introduced. When the beams are allowed to recombine, interference between the beams is obtained and the intensity of the output beam from the interferometer can be obtained as a function of path difference using an appropriate detector [170]. FTIR techniques have made significant impact on rapid scanning, signal to noise ratio, high sensitivity, high resolution and data processing [171].

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7.3.5. Raman Spectroscopy Raman spectroscopy is the measurement of the wavelength and intensity of inelastically scattered light from molecules. It is one of the spectroscopic techniques used in condensed matter physics and chemistry to study vibrational, rotational, and other low-frequency modes in a system [172]. The Raman scattered light occurs at wavelengths that are shifted from the incident light by the energies of molecular vibrations. The shift in energy gives information about the phonon modes in the system. The mechanism of Raman scattering is different from that of infrared absorption, and Raman and IR spectra provide complementary information. Typical applications are in vibrational information for the chemical bonds in molecules, molecular structure determination, multicomponent qualitative analysis, quantitative analysis, sample temperature, and strain from analysis of the material specific phonon mode energies [173]. Raman spectroscopy is very much useful in polymers. The polymer related problems, which can be solved by spectroscopy, are many and varied. They may be concerned with chemical aspects and chain structure (i.e., tacticity, ‘mer’ sequence distribution, chain branching or structure of radicals). They may also concern physical aspects (i.e., chain orientation, crystallinity, and chain conformation or chain dynamics) [174-176]. Raman spectroscopy is based on the absorption of photons of a specific frequency followed by scattering at a higher or lower frequency. The modification of the scattered photons occurs from the incident photons either gaining energy from or losing energy to the vibrational and rotational motion of the molecule. Quantitatively, a sample (solid, liquid, or gas) is irradiated with a source. When a molecule is placed in an electric field (E), polarization (P) takes place, given by P=αE, where α is the polarizability (a tensor with nine components) of the molecule. If f0 is the frequency of incident radiation on molecules, each molecule experiences a varying electric field, E=Eocos (2π fot)

(7.5)

Let us consider the vibrational motion of the molecule and x is the normal coordinate associated with a particular mode of vibrational frequency fm of the molecule. Now, in the harmonic expression, x can be expressed as x = x0 cos (2π fmt) Recent Advances in Dielectric Materials, Nova Science Publishers, Incorporated, 2009. ProQuest Ebook Central,

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Using Taylor’s series, the polarizability can be expressed as

⎛ ∂α ⎞ ⎟ x + ........ ⎝ ∂x ⎠ 0

α = α0 + ⎜

(7.6)

On neglecting the higher order term, we get the polarization as

⎡ ⎤ ⎛ ∂α ⎞ P = ⎢α 0 + ⎜ ⎟ x0 cos(2πf m t ) ⎥ E 0 cos(2πf 0 t ) ⎝ ∂x ⎠ 0 ⎣ ⎦ ⎛ ∂α ⎞ =α 0 E 0 cos(2πf 0 t ) + ⎜ ⎟ x0 E 0 cos(2πf 0 t ) cos(2πf m t ) ⎝ ∂x ⎠ 0

(7.7)

Using the relation, 2cosθ cosΦ = cos(θ+Φ) + cos(θ-Φ) in the above equation, we get

1 ⎛ ∂α ⎞ P = αE 0 cos(2πf 0 t ) + ⎜ ⎟ x0 E 0 [cos{2π ( f 0 + f m )t} + cos{2π ( f 0 − f m )t}] (7.8) 2 ⎝ ∂x ⎠ 0

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Hence, it is evident that, when (∂α/∂x0) is zero, no Raman line will be observed. Therefore, we get a Raman active molecular vibration only if it causes a change in a component of polarizability. Thus, the induced polarization contains three distinct frequency components • • •

f = fo Rayleigh line f = fo-fm Raman Stokes line f = fo+fm Raman anti-Stokes line

From the above relations, we could know that there will be both elastic scattering (Rayleigh scattering) involving no change in frequency of the scattered light, and inelastic scattering (Raman scattering) [171]. Only a few photons (one in 108) can undergo Raman scattering. The energy is lost to vibrations (normal modes), and hence the change in frequency is equal to the frequency of the normal modes. The strongest inelastic scattering (Stokes-Raman scattering) has a frequency, which is lower than the frequency of the incoming light. Inelastic scattering with a higher frequency than the incoming light is called anti-stokes-Raman scattering. Not all the normal modes are Raman active. The entire requirement for Raman scattering to occur is a change in polarizability accompanying the vibration. It is necessary to illuminate the sample under investigation with highly monochromatic (laser) light to detect the Raman scattering. Otherwise, the weak Ramanscattered light is lost in the spectrum of the elastically scattered light. The Raman shift in frequency corresponds to many cases with the IR absorption spectrum. For a molecule with n atoms, there are 3n-6 vibrational degrees of freedom.. However, some vibrational modes appearing only in IR absorption originates from highly polar groups. The Raman scattering arises from highly non-polar groups. The presence of absorption bands in certain frequency region suggests the presence of certain groups in the sample.

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7.4. Dielectric Study

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Dielectric characteristics of ceramic materials are of increasing importance due to their various applications in the field of solid-state electronics. The main applications of ceramic dielectrics are as capacitive elements in electronic circuits and as electrical insulator. The dielectric constant, loss tangent and dielectric strength are the important characteristics of the dielectrics relevant to their suitability for application purpose. The advantages of ceramics are: (a) they have superior electrical properties, (b) absence of deformation under stress at room temperature and (c) greater resistance to environmental changes. The dielectric properties of ferroelectrics depend on the field strength at which it is measured; this is a consequence of non-linear relation between polarization and the electric field. The dielectric constant obeys Curie-Weiss law above the transition temperature.

Figure 7.9. A typical hysteresis loop illustrating the coercive field Ec, spontaneous polarization Ps and remanent polarization Pr

7.4.1. Spontaneous Polarization Study The primary feature of distinguishing ferroelectrics from other pyroelectrics is that the spontaneous polarization can be reserved with the application of electric field. The first demonstration of polarization reversal/dielectric hysteresis was made by Valasek [177]. At low and very high electric field, ferroelectrics behave like an ordinary dielectric (usually with a high dielectric constant). At a coercive field Ec, polarization reversal occurs giving a large dielectric non-linearity. The hysteresis (Figure 7.9) arises from the energy needed to reverse the metastable dipoles during each cycle of the applied field. The area of the loop represents the energy dissipated inside the sample in the form of heat during each cycle. In general, the hysteresis loop is measured with ac fields at low frequencies to avoid heating of sample. At zero field, the electric displacement within a single domain (saturated value of the displacement) has two values corresponding to the opposite orientations of the spontaneous polarization. In a multi-domain [178] crystal, the average zero field displacement can have any value between these two extremes.

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Some typical hysteresis loops (7.10-7.11) of some materials are shown below.

Ref. 166.

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Figure 7.10. Room temperature P-E hysteresis loop of (Pb1-zPrz)(Zr0 60Ti0:40)1-z/4O3 for (a) z = 0:07 and (b) z = 0.08.

Ref. 165.

Figure 7.11. Room temperature hysteresis loop of [Pb0.92(La1−zFez)0.08] [Zr0.65Ti0.35]0.98O3 for z = 0.0, 0.3, 0.6, 0.9, 1.0. Recent Advances in Dielectric Materials, Nova Science Publishers, Incorporated, 2009. ProQuest Ebook Central,

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In principle, the spontaneous polarization is equal to the saturation value of the electric displacement extrapolated to zero fields. The remanent polarization Pr (the displacement at zero field) may be different from the spontaneous polarization Ps, if reverse nucleation occurs before the applied field reversal. This can happen either in the presence of internal or external stress or if the free charges below the crystal surfaces cannot reach their new equilibrium distribution during each half-cycle of the loop. Cycling the loop at very low frequencies can minimize this effect. The area within the loop is the measure of the energy loss per cycle. If the temperature is increased, the area of the loop decreases and ultimately becomes a straight line. The temperature at which the loop becomes a straight line is called the ferroelectric Curie temperature (Tc), which is associated with the ferroelectric to paraelectric phase transition.

7.4.2. Pyroelectric Studies Pyroelectric detectors have been discussed by various authors, and the advantages of fast response at room temperature have already been reported [179-180]. A change in temperature alters the lattice spacing of a non-symmetrically located ion which varies the spontaneous polarization of the pyroelectric crystal. The variation of spontaneous polarization produces a displacement current, I parallel to the polar axis described by I = Ap (T )

p(T ) =

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where

dT dt

dp (T ) dt

(7.9)

(7.10)

is the pyroelectric coefficient evaluated at temperature T and A is the surface area normal to the polar axis. The pyroelectric coefficient is given by

p(T ) =

Therefore, when

I A

dT / dt

(7.11)

dT is constant over a large temperature range, a measurement of the dt

current I gives a direct plot of p (T) over that temperature range. Prior to the pyroelectric measurements, the poling of the samples to be done for some time. The pyroelectric current can be measured with a nano or picometer in the desired temperature range.

7.4.3. Piezoelectric Study Piezoelectric materials produce a charge proportional to an applied stress, as first discovered in 1880 by Jacques and Pierre Curie, and are natural sensor and electrical materials. The

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converse piezoelectric effect, as utilized in actuator applications, describes the deformation of the material in response to an applied electric field. An elastic body exhibits numerous resonances on excitation. The most pronounced are those where bodies can just accommodate one half wavelength of a standing elastic wave. In poled ceramics, such elastic waves can be excited and the interaction of mechanical resonance with electrical behavior can be observed. If a piezoelectric crystal is considered equivalent to an LCR circuit, impedance will be low at resonance. The frequency of minimum impedance is called resonance frequency (fr) and the frequency of maximum impedance is called antiresonance frequency (fa). Today there are a myriad of piezoelectric compositions and material variants in front of an application engineer. By altering the electromechanical properties, materials can easily be tailored to operate at a desired voltage, frequency or stress, etc. Piezoelectric properties of various practical devices using the piezoelectric effect have been the main subject of many researchers. The selection of materials for device applications depends on the properties of piezo-ceramics. The basis for evaluating the piezoelectric properties of a ferroelectric material is its electromechanical coupling coefficient or planar coupling constant (kp) and mechanical quality factor (Qm). Further, piezoelectric strain coefficients namely, charge coefficient d33 and voltage coefficient g33 are important parameters to be considered for this purpose. In case of ceramic materials consisting of a multitude of tiny piezoelectric crystallites at random orientation, it is essential to provide some means to reorient the crystallites (i.e., polarize) in order to detect the piezoelectric properties. Poling is commonly employed in the case of ceramic crystallites, which are both piezoelectric as well as ferroelectric. The wide spread applications of the piezoelectric effect based on ferroelectric ceramic materials can be attributed to three main facts: • • •

the piezoelectric effect is particularly large in ferroelectrics, ceramics can be produced cost effectively. Most of these materials are either impossible or the best difficult to produce in single crystal form. ceramic materials offer a high degree of variation concerning geometrical shape on the one hand and physical properties on the other hand by virtue of composite and creation of different grain structure and interaction of various ferroelectric or nonferroelectric phases.

For piezoelectric measurements, poled samples are used. The piezoelectric strain coefficient d33 of the samples can be measured using Piezometers such as piezo-test, model: PM 200, UK (as shown in Figure 4.28) at 110 Hz under a dynamic force of 0.05N at room temperature. The system (PM 200) works by clamping the sample, and subjecting it to a low frequency force. The processing of the electrical signals from the sample and comparison with a built-in reference enable the system to give a direct reading of d33; one of the most useful piezo-coefficients (parameters) in evaluating the material. In some of the ferroelectric materials, we observe very low piezoelectric coefficient, which may be may be due to high disorderness and low dielectric constant of the materials. However, even with smaller remanent polarization and piezo-coefficient d33, the existence of ferroelectric properties can be concluded.

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7.5. Electrical Property

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7.5.1. Complex Impedance Spectroscopy Complex Impedance Spectroscopy (CIS) is an experimental tool for the characterization of electrical properties of materials [181]. The technique is based on analyzing the a. c. response of a system to a sinusoidal perturbation and subsequent calculation of the impedance as a function of the frequency of the perturbation .The technique enables us to evaluate and separate the contribution to the over all electrical properties in frequency domain due to electrode reactions at the electrode/material interface and the migration of charge carriers (ions) through the grains and across the grain boundaries within the specimen sample. In impedance spectroscopy technique, a sinusoidal signal of low amplitude is applied across a sample and the impedance (Z) and phase shift (θ) are measured directly at the output. The impedance, being a complex quantity, can be represented in vector diagram in the form of its real (Z′) and imaginary (Z′′) components. So, the impedance of a sample is known as the “complex impedance”. Impedance analysis basically involves the display of the impedance data in different formalism and provides us the maximum possible information about the materials. The display of impedance data in the complex plane appears in the form of a succession of semicircles attributed to relaxation phenomena with different time constants due to the contribution of grain (bulk), grain boundary and interface/polarization in a polycrystalline material (Figure 7.12). Hence the contribution to the overall electrical property by various components in the material is separated out easily. In case of a solid crystalline material, the physicochemical process and polarization events leading to the formation of double layer capacitors at the electrode-material interface take place in such a way that this phenomenon can be represented in terms of equivalent circuit representations by a series combination of parallel RC units (Figure 7.13). Cole-Cole [182] utilized both complex plane plots and frequency explicit plots to explain the dielectric behavior and electrical conductivity of a wide range of solid-state materials. One of the main advantages of frequency dependent measurements is that the contributions of the bulk material, the grain boundaries and electrode effects can easily be separated, if the time constants are different enough to allow separation [183]. The complex plane plots result in different semicircles, intercepting along x-axis (Z'-axis) at different region. The intercept of the first semicircle (of the high frequency region) is due to grains; the second one (of intermediate frequency) due to grain-boundaries and the third one (of the low frequency region) due to material-electrode interface. The resistance of the materials, obeying Arrhenius behavior, is evaluated in terms of bulk resistance (Rb) and conductivity (σ) is expressed as,

⎛ − Ea ⎞ ⎟ ⎝ kT ⎠

σ = σ 0 exp⎜

(7.12)

where σ0 = pre-exponential factor, Ea = Activation energy, k = Boltzmann constant, T = absolute temperature. The peak of the semicircle in the complex plane plot enables us to evaluate the relaxation frequency (fmax) of the (bulk) material in accordance with the relation,

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Figure 7.12. Relationship between microstructure-electrical properties.

Figure 7.13. An electrical equivalent circuit in complex impedance plane.

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ω maxτ = ω max Rb C b = 2πf max Rb C b = 1 , f max =

1 1 andτ = 2πRb C b 2πf max

where Cb = bulk capacitance and τ = relaxation time. The impedance data also enable us to investigate the information on relaxing dipoles in the material (dielectric relaxation spectroscopy) in terms of the real and imaginary parts of the complex dielectric constant ε = ε '− jε " through the relations:

ε'= −

Z" ωC 0 ( Z ' 2 + Z "2 )

(7.13)

ε"= −

Z' ωC 0 ( Z ' 2 + Z " 2 )

(7.14)

and

The real and imaginary parts of complex electric modulus are represented as:

M ' = ωC 0 Z " and M " = ωC 0 Z ' , tan δ =

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ε" M" = ε' M'

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R.N.P. Choudhary and S.K. Patri

where Z ' , ε ' , M ' and Z " , ε " , M " have their usual meaning, frequency and C 0 =

ε0 A l

ω = 2πf is the angular

= geometrical capacitance of the sample.

7.5.2. Electrical Conductivity Study Electrical conduction in dielectrics is caused due to ordered motion of weakly bound charged particles under the influence of electric field. When an alternating emf, V is applied across a capacitor, an alternating current I (i.e. I = jωεC0V) will flow through it [184]. In general, however, an in phase component of current will appear corresponding to a resistive current between the condenser plates. The conduction process is always dominated by the type of charge carriers like electrons/holes or cations/anions. The most commonly used dielectric materials including all polymers, glasses and ceramics do not show any evidence of free charge carriers that would give rise to higher level of dc conductivity than actually observed. In all ferroelectrics, the study of electrical conductivity (order and nature) is very important, since the associated properties like piezoelectric, pyroelectrics, etc depend on it. The variation of electrical conductivity (σ) with temperature can be described by the equation

σ = A exp(− E a / kT ) + B exp(− E a / kT )

(7.15)

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where Ea and Eb are the activation energy for the intrinsic and extrinsic conduction process respectively and A and B are constants. At higher temperatures the intrinsic conduction process dominates, and hence the above expression reduces to σ = A exp(− E a / kT ) . From the CIS technique, both ac and dc conductivity can be obtained which helps in the characterization of the interfacial, grain boundary and bulk grain effects. The electrical conductivity in dielectric materials can be explained in terms of ac and dc conductivities. ac Conductivity The ac electrical conductivity (σac) can be calculated using the dielectric data and an empirical relation; σac = ωεrε0tanδ

(7.16)

where ε0 permittivity in free space, and ω angular frequency. In order to have an idea of frequency dependent electrical behavior of materials, ac conductivity measurement is often made by using Jonscher [185] law (below) to explain the behavior of ac conductivity:

σ Τ (ω ) = σ 0 + σ 1 (ω )

(7.17)

σ Τ (ω ) = σ 0 + aω n

(7.18)

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where σ (0) is the frequency independent term giving dc conductivity and σ1(ω) is the pure dispersive component of ac conductivity having a characteristic of power law behavior in terms of frequency ω. The exponent n can have a value in the range of 0 to 1. This parameter is frequency independent but temperature and material dependent.

dc Conductivity The value of the bulk conductivity (σb) determined from the complex impedance plots can be considered as the true value conductivity, because of the negligibly small thickness of the grain boundary layer in the sample. The apparent grain boundary conductivity (σgb) cannot give insight for the grain boundary effect since the grain boundary area parallel to the current flow is much smaller compared to that of lattice [186]. The calculation of the (true) grain boundary conductivity σgb requires different geometrical parameters. In terms of the blocking model proposed by Wang and Nowick [187] the true grain boundary conductivity can be defined as; σgb=(d/l)(σgb)

(7.18)

where d is the thickness of the grain boundary layer and l is the average grain size. Therefore, the bulk conductivity of a compound is evaluated from the impedance data using a relation;

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σ dc =

t Rb A

(7.19)

where Rb is the bulk resistance, t is the thickness and A is the area of the electrode deposited on the sample. The value of bulk resistance (Rb) is obtained from the low frequency intercept of the semicircle on the real axis (Z′) in the complex impedance plot. The dc conductivity also follows the Arrhenius law σ = σ0 exp (-Ea/kBT) and the activation energy Ea is calculated from the slope of the linear portion of the plot (σ versus 103/T graph).

8. Research on Some Dielectric Materials A large number of materials (starting from the hydrogen-bonded phosphates to the multiferroic composites) in different form were studied for the crystal structure, phase transitions and characterization of different physical properties mentioned above. Basically this article has been emphasized on solid dielectrics having properties like ferroelectricity, piezoelectricity, pyroelectricity, and multiferroicity with related phenomena. Starting from ferroelectricity we shall conclude the recent fast growing multiferroic properties of the materials.

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8.1. Hydrogen-Bonded Materials Ferroelectric properties have been discovered in a considerable number of hydrogen-bonded compounds. There are two main reasons for ferroelectricity in this type of compounds [188]: (i) an ordering of the dipolar hydrogen bonds in a pyroelectric class of crystal may result in a spontaneous polarization, (ii) sometimes; the polarization reversal is associated simply with a movement of hydrogen atoms from one side of the hydrogen bond to the other which can be found in KH2PO4 Since the discovery of ferroelectricity in KH2PO4, a considerable amount of theoretical and experimental work has been done on the dihydrozen phosphate family for the understanding of the phase transition mechanism. The phase transition in ferroelectric crystals involves not only the ordering of the disordered hydrogen atoms [189] but also the deformation of the atomic groups of type SO4-2, SeO4-2 and PO4-3.

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8.1.1. KH2PO4 Potassium dihydrogen phosphate (KDP) is non-linear optical material; specifically known for its large non-linear coefficients, wide transparency range, and high optical damage threshold [190]. The main applications of KDP crystal are: SHG, THG and 4HG of Nd: laser, SHG of dye laser, shutter for high speed photography, electro-optical modulators and Q-switches [191-192]. KDP crystallizes in a tetragonal structure above 123K and orthorhombic ferroelectric phase exists below Tc The spontaneous polarization occurs mainly due to the displacement of K, P, O ions in the direction of the polar c-axis [193]. However, the transition temperatures Tc for KDP crystal were not conclusive and the nature of transition mechanism was not consistent. Lee [194] suggested that the anomaly found in this type of crystal is due to thermal decomposition instead of a structural phase transition. Busch et al. [195] showed that KDP exhibits a phase transition at low temperature. It was shown that a strong anharmcnicity is present and acts on Raman modes in the transition from the ferroelectric to the paraelectric phases [196-197]. Melo et al. [198] have reported the occurrence of a phase transition in KDP taking place at temperatures near 60 K by Raman spectra and polarization measurements, which was also supported by pyroelectric curves in the same temperature region. Chen et al. [199] have reported that the crystal of KDP is thermally decomposed on heating at temperature above 195 °C. They studied the dielectric properties of the sample and found that the electrical conductivity increases with increasing temperature and frequency. The distinguishing feature of ferroelectric crystals of KDP family is the high mobility of domain walls that manifests itself particularly in the large values of low frequency dielectric constant. NH4H2PO4, NH4H2AsO4, KH2AsO4, RbH2AsO4, CsH2AsO4, RbH2PO4 etc. belong to KDP family [200]. These compounds have been extensively studied for their technological importance due to their specific properties such as piezo-electric, electro-optic, and optical properties [201-205].

8.1.2. PbHPO4 A neutron diffraction structural study of PbHPO4 of the ferroelectric phase at room temperature shows partial onset of order in agreement with the observed half-saturation of Pr, at this temperature [206]. PbHPO4 and PbDPO4 are interesting materials, because:

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the transition mechanism is of KH2PO4 type, involving ordering of the H (or D) and hence a large isotope effect on Tc. the one-dimensional chains formed by small unit cell and H (or D) bonds linking are known for such transitions. second-order transition and spontaneous polarization saturates slowly over a range from Tc. the paraelectric phase appears to be centrosymmetric [207].

8.1.3. CsH2PO4 CsH2PO4 is one of the interesting H-bonded materials due to its ferroelectric phase transition with a very deuteration-dependent transition temperature. The dielectric property of this compound was studied by Levstik et al. [208]. They found the transition temperature of CsH2PO4 is 153.5 K. Single-crystal neutron-diffraction structural study has located the hydrogen atom position in the paraelectric phase of CsH2PO4 at room temperature. Choudhary et al. [209] have found hydrogen sites: one (H1) in a special position on the mirror plane and the other (H2) in a general position with a site occupancy of 0.5. The hydrogen bonds O1-H1 …O2 in the mirror planes link PO4 groups into chains along the a-axis. These chains are then cross-linked to similar parallel chains by O3-H2-H2-O3 bonds, which have a centre of symmetry at their mid-points; the H2-H2 distance is 0.49 Å. This disordered hydrogen bond is of particular interest in relation to the ferroelectric phase transition. In view of the large isotope effect on Tc, it seems probable that the transition involves an ordering of the H2 atoms. [208], however the hydrogen atoms are disordered in high temperature paraelectric phase [210].

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8.2. Oxide Ferroelectrics Oxygen octahedral type ferroelectrics have been the subject of investigations for their structural diversity, tailoring properties and ample application in various fields. The family of oxygen octahedral consisting of one or more component oxides and have four basic structures, namely: (i) perovskite, (ii) tungsten-bronze, (iii) layer structure oxides and complex compounds, and (iv) pyrochlore type. A common feature of all these materials is the BO6 octahedral building block, although the materials may have different crystal structures, electrical and mechanical properties, Curie temperature and polarization.

8.2.1. Perovskite Structures A general chemical formula of this family of compounds is ABO3, where A is a mono-or divalent ion and B is tri-hexavalent ions. It is cubic with A atoms at the corners, B atoms at the body centre and the oxygen atoms at the face centers. A large number of perovskite can be prepared by doping different ions at the A and B sites. The complex perovskite structure has a general formula (A1………An) (B1……….Bn)O3 and that can be only prepared if they satisfy the following basic conditions [211]

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(a) Charge Neutrality j

k

∑ i =1

XAi nAi +

∑

XBi nBi = 6

(7.20)

i =1

where j

k

∑

XAi = 1; 0 ≤ XAi ≤ 1,

i =1

∑

XBi = 1; 0 ≤ XBi ≤ 1

i =1

and nAi = 1, 2, 3; nBi = 2, 3, 4, 5, 6

(b) Goldschmidt Tolerance Factor

tL =

rA + ro

(

2 rB + ro

)

, rA = average ionic radius of A-site atoms, rB = average ionic

radius of B-site atoms, r0 = ionic radius of O2-. For usual perovskites 0.8 ≤ tL ≤ 1.05 For ideal cubic perovskite structure the value of tL is equal to 1.0. In practice, those structures whose tolerance factor tL is about 0.95-1.0 are cubic, those with lower values are slightly distorted and non-ferroelectric, and those slightly over 1.0 tend to be ferroelectric [212-214]. Some perovskite structures are discussed below:

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•

BaTiO3: Though this compound was known since 1938, it was brought to lime-light by Von Hippel and co-workers [215-216] in 1944 for its promising dielectric properties. The sensitivity of its properties to minor impurities has been recognized in early 1950s [217]. The positive temperature coefficient of resistance (PTCR) anomaly in semiconducting BaTiO3 was first reported by Haaijman et al. [218] and later by Sauer and Flaschen [219] in 1956. Semiconductivity in BaTiO3 was described as the controlled valence effect due to the replacement of Ba2+ by M3+ and Ti4+ by M5+ by Verwey and others [220]. Harman [221] observed the effect with Sm2O3 as the dopant, and suggested some studies on the effects of various 4f- and 5fseries rare-earth additives on different ferroelectric and antiferroelectric materials. The variation of resistivity jump of about 4 orders of magnitude in the temperature range of 120-150oC was achieved by introducing 0.1 mol% of Ce in it. Nowadays, by introducing some magnetically ordered compound into BaTiO3, we can get some interesting multiferroic properties. Hence it can be seen that ferroelectric ceramic BaTiO3 is an interesting and sensitive material. Its dielectric and piezoelectric properties can be affected by its own stoichiometry and microstructure, and by the effect of a host of ions that can enter into solid solution. A given ion can have radically different effects on the nature of dielectric and piezoelectric properties, depending on its concentration and effect of stoichiometry. When BaTiO3 is used as a capacitor, different groups of additives are used, as it is desired to suppress the

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•

•

99

ferroelectric and piezoelectric properties. Usually two types of modifiers are used: Tc shifters and Tc depressors. The Tc shifters as well as the depressors are added in small quantities to the parent compound to lower or depress the sharpness of the dielectric constant-temperature profile. The net results of these efforts are to produce ceramic capacitors with dielectric constant up to 3000, loss tangent of 1% or less and temperature stability ±15% [222]. As it turned out, that BaTiO3 can not be used as transducers in the form of pure individual compounds. In 1950, lead titanate was reported to be a ferroelectric on the basis of the structural analogy with BaTiO3, and the discovery of a high temperature transition around 500oC [223-224]. Many isovalent solid solutions prepared to tailor the property and structure of PbTiO3 for various application like substitution of Ca+2, Sr+2, Ba+2, Cd+2 etc., which converts the original system into a new system with different concentration. SrTiO3: During the dielectric spectroscopy analysis, the distribution and contribution of different type of polarization with respect to frequency and temperature can be observed. Choudhary et al. in 1989 [225] studied the effect of laser excitation and γray irradiation on the dielectric properties of quenched SrTiO3 single crystals. SrTiO3 has a large dielectric constant at room temperature which increases considerably with lowering of temperature. The electrical transport properties, the oxygen self-diffusion and kinetics of SrTiO3 have been well investigated [226]. Excess oxygen as impurity is found to have considerable influence on the electrical conductivity of SrTiO3. The results of the study carried out over moderately large regions of frequency (100Hz1MHz) and temperature (30-350°C) on SrTiO3 subjected to treatments like quenching, laser excitation or γ-ray irradiation (or a combination of them), which is expected to produce lattice defects subsequently influencing the dielectric properties significantly. PZT: Pb(Zr1-xTix)O3, (PZT) perovskite is an excellent material for device applications. In the past, a considerable amount of work has been done to study the effects of various dopants in varying concentrations (x) at the A and B sites of PZT and to modify the properties of the material for different piezoelectric devices. The majority of the dopants were isovalent, supervalent and subvalent. On double doping with different alkali ions at Pb sites (A site) on structural and dielectric properties has been done on Pb0 93(La1-xKx)0 07(Zr0 65Ti0 35)O3, x=0.0, 0.1, 0.3, 0.5 and 0.7 [227-234]. Similarly on substituting Na+ in place of K+, we observed a diffused phase transition and showed relaxor behavior which can be good candidates for device application. [235-238]. (Pb1-xCax)(Li1/4La1/4Mo1/2)O3: In 1959, Smolenskii et al. [30] proposed that a wide range of oxygenous complex perovskite compounds of a general formula (A1,……..,Am) (B1,………..,Bn)O3 can be prepared by keeping in mind the condition of electrical charge neutrality, the properties of a given structure, the affinity of ions to a given co-ordination number and tolerance factor [208]. Thus, (Pb1-xCax) (Li1/4La1/4Mo1/2)O3, x=0.0, 0.03, 0.07, 0.1 were prepared [239] and their dielectric behavior was studied. Ca2+ doped at Pb site makes a large effect on their electrical properties and phase transition in them. These compounds show diffuse phase transition (Figure 8.1). The dc resistivity increases with concentration of Ca2+ ion at a fixed biasing field. This is because of the decrease in ionic conduction through the

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solid which is controlled by the concentration of Ca2+ ion. The temperature dependence of dc resistivity of (Pb1-xCax)(Li1/4La1/4Mo1/2)O3, x=0.0, 0.03, 0.07, 0.1 at a constant biasing electric field (8.5 kV/m) (Figure 8.2) show the decrease in resistivity with increasing temperature owing to the addition of thermal energy, electrons could be set free from O2- ion, which results in unstable valance states and decrease in resistivity. This type of resistive behavior was found in many semiconductors and is usually called negative temperature coefficient (NTC) resistor. Above 373 K the compounds behave as NTC thermistors.

Ref 239.

Figure 8.1. Variation of dielectric constant (ε) of (Pb1-xCax) (Li1/4La1/4Mo1/2)O3 as a function of temperature at 10 kHz.

•

Alkali metal oxides: The perovskite type alkali tantalates and niobates constitute an important group of oxides with broad ranges of dielectric, piezoelectric, ferroelectric and optoelectronic properties [240]. Among these compounds, sodium potassium niobates (Na1-xKxNbO3) and sodium potassium tantalate (Na1-xKxTaO3) have attracted considerable attention. Solid solutions of these mixed oxides can be formed over the whole composition range (x = 0 to 1). For low x values these systems appear to exhibit true phase transitions and the dielectric properties can be understood in terms of soft optic phonons [241-244]. Na1-xKxNbO3 ceramics, with perovskite structures, are widely used for transducer applications [245]. The low dielectric constant coupled with fine structure and improved piezoelectric activity, especially near the equimolar composition of Na and K, make these materials desirable for

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certain solid ultrasonic delay line applications, which require the use of thin-section transducers [246]. The interesting aspects of this system are that its end compounds, i.e., NaNbO3 and KNbO3, are antiferroelectric and ferroelectric, respectively, at room temperature. NaNbO3 is antiferroelectric in the temperature range -200 to 643oC and shows many structural phase transitions in this range, but when mixed with small amount of potassium (~ 2 mole %) at A site [247], it becomes ferroelectric and shows structural transition behavior of KNbO3, i.e., showing cubic to tetragonal transition at 420oC and tetragonal to orthorhombic at 210oC [248-250]. Similar to Na1-xKxNbO3 system, the Na1-xKxTaO3 system has also interesting end members, i.e., NaTaO3 is ferroelectric and KTaO3 is paraelectric at room temperature [251]. The variation of dielectric constant with temperature (Figure 8.1) and resistivity with temperature (Figure 8.2) of a typical ferroelectric oxide are shown below.

Ref 239.

Figure 8.2. Variation of dc resistivity of (Pb1-xCax)(Li1/4La1/4Mo1/2)O3 as a function of temperature at constant biasing field 8.5 kV/m.

8.2.2. Tungsten Bronze Structure Tungsten bronze (TB) structures are found to be very important because of their various physical properties suitable for fabrication of many devices. The largest crystal family of oxygen octahedra ferroelectrics with structure closely related to the tetragonal tungsten bronze KxWO3 and NaxWO3 were described by Magneli [252]. The TB-structure consists of a skeletal framework of BO6 octahedra sharing corners to form three different types of tunnels parallel to the c-axis in the unit cell having a general formula [(A1)2(A2)4C4][(B1)2(B2)8]O30, where A-type cations (mono or divalent) can be accommodated in any or all three different

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type of interstitials A1, A2 and C while B-type cations (tri or pentavalent) are substituted at octahedral site B1 and B2 [253]. The A-type cations enter into the structure in the interstitial tunnels in a variety of ways depending on the particular composition. The interest in tungsten bronze ferroelectrics is renewed in 1960’s because of the large optical non-linearities of the materials.

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•

Barium sodium rare earth niobate (BNN): Barium-sodium niobate crystals have been considered as an outstanding electro-optic material [254, 255] for many industrial applications. BNN containing rare-earth ions has been found to be more interesting and important from the chemical structure point of view due to its broad or diffuse phase transitions [256]. Some preliminary work on the ferroelectric properties of some members of this family, such as Ba2Na3RNbl0030 (R = La, Eu, Gd, Dy or Y), were reported by Iwaski [257]. The effect of Gd and Ce on the ferroelectric properties and lattice parameters of BNN have been studied. It is interesting to observe relaxation phenomena in some compounds of this family. Ba2Na3RNbl0030 (R = rare earth ions) belongs to TB type structures. The structure consists of NbO6 octahedral units joined at their corners, enclosing 9-, 12- and 15-co-ordinated cation sites, usually called γ, α, and β (i.e., C, A and B) sites respectively [257]. In the TB niobates/tantalates, B1 and B2 are filled by Nb5+/Ta5+, and A1, A2 and C by alkali, alkaline earth metals and rare-earth ions. When a wide variety of cations are substituted at these A, B and C sites, many interesting physical properties, such as electro-optical, non-linear [258], elasto-optical, etc. are obtained.

The temperature variation of dielectric constant of Ba2Na3LaNblO30 and Ba2Na3SmNbl0O30 is shown in Figures 8.3(a) and 8.3(b) respectively. The transition temperature (Tc) of the La and Sm containing compounds were found to be -50.5 and 180°C respectively. It was also found that at the transition temperature, the dielectric peak is not very sharp for Ba2Na3LaNblO30 , which suggests a diffuse phase transition for it. This broadening of the phase transition has been considered to be due to the structural disorder and the compositional fluctuation at micro/nano scale in the solid solution [260]. Also, the external field has a much larger effect on the position of the dielectric constant maxima, and affects the magnitude of the dielectric constant over a much wider temperature range than in normal ferroelectrics. The broadening in the dielectric peak in Ba2Na3LaNblO30 was not observed. The structural disorder arises due to the presence of voids and impurities [259]. The diffusivity in the dielectric peak in Ba2Na3LaNblO30 is much more than that in Ba2Na3SmNblO30 Dielectric properties and diffusivity (in the peak) of Ba2Na3RNbl0O30 (R = La, Y, Gd, Eu and Dy) [261], K2LaNb5O15 [262], Bal/xR2x/3Nb2O6 [263] and Ba4NaNb10O30 [264] have also been reported.

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Ref 259.

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Figure 8.3. Variation in dielectric constant (K) of (a) Ba2Na3LaNb10O30 and (b) Ba2Na3SmNb10O30 as a function of temperature at 1 kHz.

(a)

(b)

Ref 265.

Figure 8.4. Variation of (a) dielectric constant and (b) loss tangent of Ba5NdTi3Nb7O30 (A), Ba5EuTi3Nb7O30 (B), Ba5GdTi3Nb7O30 (C) with temperature.

In 1999 Choudhary et al. [265] have reported dielectric properties and phase transition in a new compounds of this family, Ba5RTi3Nb7O30 (R = rare-earth ions = Nd, Eu, Gd). Further, it was observed that the size of the substituted ions has significant effect on the disorderness of the structure [260] and diffuseness of the phase transition in this family. Figure 8.4 (a) shows the variation of dielectric constant with temperature at two different frequencies, 103

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Hz and 104 Hz. It has been observed that all the compounds have dielectric anomaly. For Eu containing compound (i.e., B), there is a large difference in the values of ε at low frequencies. There is an increase in dielectric constant above 310°C for Nd containing compound (i.e., A), which may be due to the presence of space charge polarization in high-temperature region. The region around the dielectric peak was found broadened in all three cases. The broadening of the dielectric peak may be considered due to the disorder in the arrangements of rare earth and other atoms leading to a microscopic heterogeneity in the composition, and thus a distribution of different local Curie points results [265]. Anomaly in tanδ was observed in these compounds (Figure 8.4. (b)). The high value of loss tangent in each material is due to transport of ions at higher thermal energy.

8.2.3. Layered Structure Oxides and Complex Compounds The perovskite structures lead to the building of complex superstructures like: RuddlesdenPopper structures, Aurivillius structures, etc. The Ruddlesden-Popper structures usually represented by Sr2TiO4, Sr3Ti2O7, and Sr4Ti3O10 [266]. These can be described as SrO. nSrTiO3, and consist of sequences of n perovskite blocks separated by a NaCl-structure block. The other one is the Aurrivillius phase [267] in which Bi4Ti3O12 is the prototype. Again the complex structure is composed of perovskite units but separated by Bi2O2 layers. These layers consist of sheets of BiO4 edge-sharing pyramids. The garnets are another class of complex oxides having a common formula A3VIIB2VIC3IVO12. Because of the availability of three coordinate sites, the garnet structure accepts a great variety of ionic substitutions.

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Bi9Fe5Ti3O27: Bi9Fe5Ti3O27 is a bismuth layered Aurivillius compound with a general formula Am−1Bi2BmO3m+3 (m=8), where A is mono-trivalent elements (Bi, Ca, Ba, Sr, Pb, K or Na) allowing dodecahedral coordination and B is tri-pentavalent transition elements ( i.e., Fe, Ti, Nb, Ta, Mo or W) allowing octahedral coordination and m represents the number of perovskite layers. The microstructure and physical properties of these materials significantly depend upon number of perovskite layers (m). Further, some of the Fe containing compounds of this family show simultaneous ferroelectric and ferromagnetic properties, and hence exhibit magnetoelectric (ME) effect under the influence of an external magnetic/electric field [268]. Because of the existence of ME effect, anisotropic electronic, dielectric, optical and ionic properties, these materials have a wide range of multifunctional applications in spintronics, information storage devices such as multi-state nonvolatile memories, sensors, phase shifters, amplitude modulators and electro-optic devices etc [269]. It has been reported earlier that the eight-layered compound (i.e., Bi9Fe5Ti3O27) has an orthorhombic crystal structure at room temperature [270]. Investigations of magnetic properties showed that this compound is antiferromagnetic (TN=130°C) with a weak ferromagnetism. The compound Bi9Fe5Ti3O27 first behaves like a superparamagnet, and then transformed to an antiferromagnetic state around 400 K [271, 272]. In recent years, there has been a growing interest in magnetoelectric materials because of their potential applications for both magnetic and ferroelectric devices. Also, the ability to couple the charge and spin order parameters of these materials provides an additional degree of freedom for designing multifunctional devices. Besides their potential applications, study of the fundamental physics of magnetoelectric materials

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is also fascinating. Patri et al. [273] have synthesized Bi9Fe5Ti3O27 by solid state reaction method, and found in an orthorhombic crystal structure with lattice parameters: a=5.5045 Å, b=5.6104 Å, and c=76.3727 Å. They studied the electrical properties of this material and found the ferroelectric phase transition at about 291oC (Figure 8.5), which in fact lower than that of the earlier reported value. This feature may be attributed due to (1) change of the state of electronic system of the crystal, and (2) origination of lattice strain during the thermal reduction [274]. Anomaly near the vicinity of Tc has been observed in the loss tangent versus temperature plot (Figure 8.5). The value of dielectric constant decreases with increase in frequency. It indicates the presence of all types of polarizations (i.e., ionic, dipole, atomic, electronic etc.) in the material at lower frequencies.

Ref 273.

Figure 8.5. Variation of dielectric constant (ɛr) and dielectric loss (tanδ) of Bi9Fe5Ti3O27 with temperature at different frequencies.

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Y3/2Bi3/2Fe5O12: Yttrium iron garnet (YIG) is a well-known ferrimagentic material of the family (i.e., A3Fe5O12, where A = Y, Bi, Ca), which is very much useful for microwave applications [275]. A lot of work has been carried out in the past on YIG, by partially/fully replacing yttrium by rare earths and other ions [276-281]. Recently, bismuth iron garnet (BIG) based materials are emerging as promising candidates for magnetoelectric, magneto-optical and multifunctional devices [282-285]. It has been reported that the crystallization temperature of YIG decreases on inclusion of Bi3+ ions at the Y3+ site [286]. Jawahar et al. [287] have studied structural and dielectric properties of a new composition of YIG (i.e., Y3/2Bi3/2Fe5O12). A diffused type dielectric anomaly was observed at 325°C (Figure 8.6 (a)). The broadening of dielectric peak may be attributed to the disorder and defects present in the system. It may be considered as antiferrodistortive structural phase transition [288]. This phase

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R.N.P. Choudhary and S.K. Patri transition may also be correlated to the structural distortion of the material. The preparation of BIG in its bulk form is thermodynamically unstable [289]. But the inclusion of Y3+ ions at the Bi site improves the structural stability with some distortion. The loss tangent (Figure 8.6 (b)) increases slowly with rise in temperature and attains a maximum value at the temperature close to transition temperature and then decreases. The low values of tanδ at higher frequencies suggest the application of this material for microwave filters/IR detectors.

Ref 287.

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Figure 8.6. Variation of dielectric constant (a) ɛr and (b) tanδ of Y3/2Bi3/2Fe5O12 with temperature.

8.2.4. Pyrochlore Oxides The pyrochlore group of compounds includes many oxides, halides, and oxyhalides of different compositions [290]. The general formula of pyrochlores is A2B2X6Y, where X can be O, S, F. In oxide pyrochlores A2B2O6Y, the B-site elements are from periodic group III, IV, V and VI, Y can be O, OH, F and H2O. The A atom ranges from Na, K, Rb, Cs, Tl, Ag, H (valence I) to Ca, Sr, Ba, Sn, Pb, Cd, Hg (valence II), In, Tl, Bi, Sc, Ln (valence III), Pb (valence IV). The electrical nature of the pyrochlores varies from highly insulating through semiconducting to metallic behavior with a few compounds exhibiting a semiconductor-tometal transition. Many phases where the A and B elements are present in the maximum possible oxidation state exhibit interesting dielectric, piezo- and ferroelectric behavior [291292]. Normal pyrochlores contain an array of stoichiometry (A2Y)n units. The chemical bond between the rigid framework (BX3)n and that lose array may be more or less weak, according to the chemical composition, but is critical in determining the chemical and physical properties. In fact because of the weakness of that interaction, atom A and Y may be partly or completely missing giving rise to defect pyrocholores [293]. Defect pyrochlores have a B2X6 network similar to regular pyrocholores but with vacancies introduced in the A2Y array. Thus these compounds are generally formulated as AB2X6 or 2B2X6A (: vacancy) depending

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on the size of A cation. It is found that the compounds of defect pyrochlore family, having ferroelectric property along with fast ion conduction in high temperature (paraelectric) phase are very promising. [294]. Materials of the pyrochlore structure type exhibit a variety of potentially useful properties, which include catalysis, ferroelectricity, ferromagnetism, luminescence, and ionic conductivity [295-300]. Many defect (vacancy containing) pyrochlores do possess very good cationic conductivity and can be considered to be solid electrolytes. Synthesis, characterization and measurement of physical properties of the substituted stoichiometric and defect pyrochlores are areas receiving wide attention at the present time.

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NaTaXO6 (X= W, Mo): Some molybdate and tungstate compounds (e.g., TiNbWO6, RbNbWO6) of a general formula ABXO6 (A are alkali ions, B are Nb, Ta, X are W, Mo) with defect pyrochlore structure have not only ferroelectric–paraelectric like phase transition [301–303] but also have strongly temperature dependent resistive properties and behave as superionic conductor in elevated or high temperature region. This defect structure has a stable three-dimensional BXO6 network, which is a favorable structure for ion transport [304].

(a)

(b)

Ref 306.

Figure 8.7. Variation of (a) dielectric constant (εr) and (b) loss tangent (tanδ) of NaTaWO6 and NaTaMoO6 as function of temperature at different frequencies.

Superionic/fast ion conducting ceramics find extensive applications in various electrochemical devices [305]. Kar et al. [306] have extensively studied the structural, dielectric and electrical properties of the compounds. Figure 8.7. (a) and (b) show the variation of dielectric constant (εr) and loss tangent (tanδ) of NaTaWO6 and NaTaMoO6 as function of temperature at different frequencies. Both the compounds have no dielectric anomaly in the measured temperature range (i.e., 290–600 K). In both the cases, tanδ starts increasing with temperature and varies in the manner shown in the Figure 8.7. The rapid

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increase of εr and tanδ at temperatures greater than 400 K may be because of the highly conducting nature of the compounds in the said temperature region [301]. Addition of thermal energy enhances the movement of cations (i.e., Na1+, Ta5+, W6+, Mo6+ ions) in the main skeleton of the compounds [307].

8.2.4. Other Dielectrics

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LiNbO3: The increasing demand for internet access, telecommunications, and broadband service has led to the search for a greater light wave transmission capacity and compactness. In order to combine excellent electro-optical, acousto-optical and non linear optical properties; lithium niobate (LiNbO3) becomes an attractive host material for application in integrated optics. A number of prominent (pyroelectric, piezoelectric, electro optical etc.) properties of the lithium niobate have opened up numerous practical applications for this crystal. It is also useful in the field of electro-optic modulators, parametric oscillators, harmonic generators, etc. Lithium niobate (LiNbO3) is an extremely versatile nonlinear crystal material. Its electrooptic and nonlinear optical coefficients are used for various photonic applications. Although LiNbO3 do not have perovskite structure but they are ABO3 lattices with oxygen octahedral. At room temperature, LiNbO3 is a slightly nonstoichiometric, typically Li-deficient crystal [260]. The crystal structure of lithium niobate in the ferroelectric room temperature phase is characterized by distorted oxygen octahedra. During ferroelectric polarization, Nb and Li ions are displaced from the exact center positions along the ferroelectric c-axis. Off-center displacement and distortion of the octahedra cause various different bond lengths for the Nb–O and Li–O bonds, respectively. A large variety of dopants ranging from the +1 to +3 valent state cations can be introduced into the crystal structure frame of lithium niobate crystals. Most are known to occupy Li sites [308] that can be understood from the defect structure of Li-deficient lithium niobate [309-310]. From the synthetic chemistry viewpoint, the dopant usually prefers to occupy the vacant lattice site in the host. Even excess Nb in nonstoichiometric lithium niobate occupies vacant Li sites. Any changes in the crystal composition will finally affect all physical properties of the crystal, such as the linear dielectric response, i.e., the refractive index, and the second-order nonlinear optical susceptibility. Li-deficient lithium niobate shows that replacing Li cations has a considerably stronger effect on the dielectric properties. In LiNbO3, the dielectric study applied for characterization of cation vacancies as well the dielectric constant was shown to decrease with growth of lithium vacancies concentration [311]. It should be noted that a large concentration of lithium vacancies can also affect the transition temperature. Here it is relevant to discuss briefly two possible mechanisms of the decrease in Tc, due to (i) change of the state of electronic system of the crystal, and (ii) origination of lattice strain during the thermal reduction. While in the stoichiometric pure crystals, the Curie temperature Tc = 1210 oC, variation of Li/Nb ratio can shift Tc. The decrease of this ratio can lower the transition temperature to some ten degrees, and the increase of this ratio slightly raises Tc [312]. It is assumed that lithium sites are the more sensitive lattice sites affecting the dielectric properties of lithium niobate. Therefore, the dielectric properties should be modified more strongly by introducing dopants into lithium sites [313].

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Pb5Ge3O11: Lead germanate is an important ferroelectric material, which has attracted a considerable interest due to its several applications in ferroelectric, pyroelectric, piezoelectric and optoelectronic devices. Some interesting physical properties of this material are its high pyroelectric coefficient, a large electro-optic coefficient [314] and a small dielectric constant etc. Perhaps it is the only material whose Curie constant (~ 104) lies between the Curie constants of displacive (= 105) and order-disorder (~ 103) type transition [315]. Its Curie temperature can be changed by suitable substitution in Pb5Ge3O11 It has been found that the apatite nasonite structure of Pb5Ge3O11 is a good host material for ionic substitution, and hence the isomorphous compounds of lead germanate can be obtained by suitable substitutions at lead or/and germanium sites. It has been observed that such substitution in some cases allowed the tailoring of the material properties, which is useful for device applications. Misra et al. [316] have studied the structural and dielectric properties on substituting the divalent Ca2+ ions at Pb2+ site i.e., Pb4 8Ca0 2Ge3O11 for better understanding of its phase transition ( shown in Figure 8.8), Similar interesting results can be obtained by the substitution of tetrahedrally coordinated ions. Thus incorporation of Zr4+ at Ge4+ site i.e., Pb5Ge2ZrO11, keeps the cell parameters same without distorting the basic structure of Pb5Ge3O11. It has been observed that Zr4+ substitution lowers the dielectric constant and phase transition temperature as shown in Figure 8.9 which can be useful for the fabrication of IR detector [317].

Ref 316.

Figure 8.8. Variation of dielectric permittivity and loss with temperature of Pb4 8Ca0 2Ge3O11

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Ref 317.

Figure 8.9. Variation of dielectric constant (εr) of Pb5Ge2ZrO11 with temperature at frequencies 1, 10, 100 and 1MHz.

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PFW-BFO: The discovery of ferroelectricity in PbTiO3 perovskite with high dielectric constant, low loss tangent, first order phase transition at high temperature, etc. has attracted much attention of researchers to carry out some work on related materials and its composites. In particular, Pb-based complex perovskites (i.e., (PbB′1-xB″x); B′ = smaller ionic radius, B″= larger ionic radius, and x = composition) with Fe3+ at the B′ site were found to be more interesting because of their unique properties, such as relaxor (frequency-temperature dependent dielectric dispersion) [318-319] and magnetoelectric (i.e., coexistence of at least two of charge, spin, and strain ordering in the same phase) [320-321] useful for multilayer capacitor and multifunctional devices (electrically and magnetically controlled). Nowadays, attempts are being made to work with more environmental friendly materials (i.e., free from Pb or reduced Pb) with smaller particle size (i.e., nanoscale) for multifunctional applications. A recent discovery of multiferroicity in Pb-free compounds, BiFeO3 (BFO) at high temperature (TN=650 K, Tc=1103 K) [322] has attracted much attention to work on it. Unfortunately, this material also suffers from the above problems, and hence it becomes a challenge to get suitable compound or composition of BFO for device applications. There are some contradictory reports on the existence of ferroelectricity and relaxor behavior of one of the compounds of perovkites such as Pb(Fe2/3W1/3)O3 (PFW) [323-326]. Further, synthesis of single-phase relaxors and multiferroics is a difficult task, even with different chemical and solid-state routes. Recently, mechanical activation

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(alloying) by high-energy ball milling route has been found more suitable for fabrication of nanosized materials [327]. The polycrystalline samples of (1−x) Pb(Fe2/3W1/3)O3 + xBiFeO3 ( x=0.0, 0.1, 0.15, 0.2) (PBFW) were prepared by a four-step synthesis method (i.e., (i) mechanical mixing, (ii) mechanical activation by high-energy ball mill, (iii) high-temperature calcinations (1125 K, 4 h), and (iv) high-temperature sintering (1200 K, 4 h)) [338]. Figure 8.10 (a) and (b) show the effect of temperature and frequency on the relative dielectric constant and loss tangent of the PBFW composites. In the low temperature region, εr of PFW increases significantly on decreasing temperature but no dielectric peak was observed even up to 85 K. It is interesting to observe a strong frequency dependent dielectric dispersion with diffuse phase transition near 150 K with maximum εr usually referred as εmax at a particular temperature for 10% substitution of BFO in the PBFW composites. For x=0.15, no dielectric anomaly or relaxor behavior was observed. It is clear that 10% substitution of BFO in PFW induces relaxor properties in PBFW. Again, no dielectric anomaly was observed for x = 0.20. These results suggest that the critical concentration of BFO (x=0.10) can generate relaxor properties in PFW below room temperature. Above 300 K, εr of all the samples increases drastically as in other multiferroics with rise in temperature and exhibits the presence of high leakage current, high dielectric loss, and high electrical conductivity of composites (in the high-temperature region). The induction of relaxor characteristics in PBFW may be considered due to the presence of isovalent and nonisovalent mixed valence cations i.e., Bi3+, Pb2+, Fe3+, and W3+ at the A/B sites. The presence of microscopic polarization and anisotropy at temperatures below Tm (dielectric maxima temperature) due to valence and compositional disordering created at the A/B sites in the complex PBFW may be the main reasons for creation of relaxor characteristic and diffuse phase transition in it. The sharp increase in εr in the high temperature (paraelectric) region seems to be an inherent characteristic of Fe-containing perovskites and is observed in most of the relaxors of this family such as PFN and PFT. Thus, induction of relaxor behavior in complex PBFW composite/complex system may be considered due to (i) microscopic compositional fluctuations, (ii) merging of micro/nanopolar regions into molecular region, (iii) coupling of electric and magnetic order parameters, (iv) creation of local disordering by local system, and (v) randomly distributed electric/magnetic field in a mixed oxide system. PVDF: polyvinylidene fluoride (PVDF), the toughest of the fluoroplastic resins belongs to the fluoropolymer family. This high-molecular-weight homopolymer has excellent resistance to stress, fatigue, abrasion, and to cold flow. PVDF and its copolymers have widely been studied and used because of their interesting piezoelectric, pyroelectric, and dielectric properties [329-334]. A special feature that distinguishes PVDF from other polymers is its polymorphism, i.e., it may present at least in five crystalline phases, namely α, β, γ, δ, and ε [335]. It is an extremely hard material, may be used at temperatures from –62 °C to 149 °C. No oxidation or thermal degradation occurs during continuous exposure up to 149 °C. Its properties will not be affected much even with long-term exposure to sun light, ultra-violet radiation, and other sources of radiations. It also retains its properties in high vacuum and gamma radiation. PVDF can be used with halogens, acids, bases, and strong

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R.N.P. Choudhary and S.K. Patri oxidizing agents [336-337], but it is not recommended for use in contact with ketones, esters, amines, and some organic acids. Depending upon the variation in their behavior, plastics can be classified as polar and non-polar. The polar plastics do not have a fully covalent bond and the dipoles are created by an imbalance in the distribution of electrons. In the presence of an electric field, all the dipoles will be aligned with the field. This will create dipolar polarization of the material which is time dependent. Examples of polar plastics are PMMA, PVC, PA (Nylon), PC, and these materials tend to be only moderately good as insulators. As the polar dipoles take time for alignment, the alternating current with a suitable frequency plays a vital role for high dielectric constant. At very low frequencies, the dipoles have sufficient time to align with the field before it changes direction and the dielectric constant. At very high frequencies the dipoles do not have time to align before the field changes direction, and hence the dielectric constant becomes low. At intermediate frequencies the dipoles move but have not completed their movement before the field changes direction and they must realign with the changed field. The electrical properties of plastics may also be changed quite dramatically by the environmental conditions, such as moisture and/or temperature, and this is particularly true for polar plastics. The polar plastics have a tendency to absorb moisture from the atmosphere and can often contain a significant amount of water at normal room temperature. For these materials, the presence of water generally raises the dielectric constant and lowers both the volume and surface resistivity. Raising the temperature of a polar plastic allows faster movement of the polymer chains and faster alignment of the dipoles, which is particularly true if the temperature is raised above glass transition temperature,Tg (because above Tg, much more molecular movement is possible). Rise in temperature inevitably raises the dielectric constant of polar plastics. The non-polar plastics are truly covalent and generally have symmetrical molecules. In these materials there are no polar dipoles present and the application of an electric field does not try to align any dipoles. The electric field does, however, move the electrons slightly in the direction of the electric field to create electronic polarization. Examples of non-polar plastics are PTFE (and many other fluoropolymers), PE, PP and PS and these materials tend to have high resistivities and low dielectric constants. For non-polar plastics, the dielectric constant is independent of the alternating current and frequency because the electronic polarization is effectively instantaneous. Non-polar plastics always have dielectric constants less than 3. Non-polar plastics, such as the fluoropolymers are not as affected by water because they do not absorb water, and hence temperature effects are not generally too much severe because increased temperature does not affect the electronic polarization. Although electrical properties of PVDF are not as good as those of other fluoroplastics, it is widely used in insulating wire and cable in computers as well as in other electrical and electronic equipments. Heat-shrinkable tubing of PVDF is used as a protective cover on resistors and diodes as an encapsulant over soldered joints. Valves, piping, and other solid and lined components are typical applications of PVDF in chemical-processing equipments [338-342]. It is the only fluoroplastic available in rigid pipe form. Woven cloth made from PVDF monofilament is used for

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chemical filtration applications. A significant application area of PVDF materials is as a protective coating for metal panels used in outdoor service. Blended with pigments, the resin is applied, usually by coil-coating equipment, to aluminum or galvanized steel. The coil is subsequently formed into panels for industrial and commercial buildings. A recently developed capability of PVDF film is based on the unique piezoelectric characteristics of the film in its so-called beta phase [343]. Betaphase PVDF is produced from ultrapure film by stretching it as it emerges from the extruder. Both surfaces are then metallized, and the material is subjected to a high voltage to polarize the atomic structure. When compressed or stretched, polarized PVDF generates a voltage from one metallized surface to the other, proportional to the induced strain. Infrared light on one of the surfaces has the same effect. Conversely, a voltage applied between metallized surfaces expands or contracts the material, depending on the polarity of the voltage. PVDF has a very high dielectric permittivity among polymer materials [344] and high dc dielectric strength, which make PVDF, a very promising dielectric material for use in energy storage capacitors. In addition to the high dc dielectric strength of PVDF itself, it has also been demonstrated that the dielectric strength of other polymer films can be enhanced after coating with PVDF films. PET: Polyethylene terephthalate (PET) is the most common thermoplastic polyester and is often called just “polyester” [345-348]. PET is a saturated thermoplastic resin made by condensing ethylene glycol and terepthalic acid [349]. It is extremely hard, wear resistant, dimensionally stable, and resistant to chemical and has good dielectric properties. Polyethylene terephthalate (PET) is a hard, stiff, strong, dimensionally stable material that absorbs very little water. It has good gas barrier properties and good chemical resistance except to alkalis (which hydrolyse it). Its crystallinity varies from amorphous to high crystalline. Depending on its processing and thermal history, it may exist both as an amorphous (transparent) and as a semi-crystalline (opaque and white) material [350-353]. The resistivity of PET can be changed by ion implantation. Its monomer can be synthesized by the esterification reaction between terephthalic acid and ethylene glycol with water as a byproduct, or the transesterification reaction between ethylene glycol and dimethyl terephthalate with methanol as a byproduct. Polymerization is through a polycondensation reaction of the monomers (done immediately after esterification/transesterification) with ethylene glycol as the byproduct. Attention has been confined in the first instance to those properties (permittivity, power factor and resistivity) which are more readily correlated with the chemical constitution of a material, and the properties such as electric strength and tracking resistance have not been considered. It is generally used in synthetic fibres; beverage, food and other liquid containers; thermoforming applications; and engineering resins. The majority of the world's PET production is for synthetic fibers [354]. Erbulut et al. [355] have studied microwave heating, dielectric characterization of PET using electromagnetic simulation software and an automatic network analyzer.

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Ref 328.

Figure 8.10. (a) Variation of relative dielectric constant εr of PBFW with temperature at different frequencies. (b) Variation of tanδ of (1−x)Pb(Fe2/3W1/3)O3 + xBiFeO3 with temperature at different frequencies for x=0, 0.10, 0.15, and 0.20. Recent Advances in Dielectric Materials, Nova Science Publishers, Incorporated, 2009. ProQuest Ebook Central,

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Synthetic dielectrics: Generally, polymers have crystalline and amorphous regions. On increasing crystallinity of polymers, their density, hardness, and resistance to chemical attack increase, but there may be a chance of brittleness. Therefore, to improve the efficiency and workability of these materials, some suitable additives are incorporated in polymers. Among the polymers used as dielectrics are; the polyethylenes, polypropylenes, polystyrenes, polyvinyl chlorides, polyamides (nylon), polymethyl methacrylates, and polycarbonates which are popularly known as synthetic dielectrics [356]. Synthetic materials have now become widely useful and acceptable for many industrial applications when filled or combined by natural substances (such as glass and rubber). The advantage of synthetic materials is that they can be designed to produce very specific properties for specialized uses. These properties include not only low dielectric constant but also strength, hardness, resistance to chemical attack, and other desirable qualities. When dilute concentration of metallic particles suspended in a light weight dielectric, then that would be a best material for broadband selected absorption and reflection of electromagnetic wave. Such type of synthetic polymers have a wide application in satellite antennas, communication links, cable television, shielding electronic computers, computer games, microwave ovens etc [357]. Kamal et al. [358] studied the dielectric properties of butyl rubber (a synthetic rubber). Butyl rubber is a copolymer of isobutylene with just a few per cent of isoprene. It has good weathering resistance and good electrical properties due to its paraffinic nonpolar character [359]. They systematically studied the dielectric properties of butyl rubber when it is mixed with carbon black of various particle sizes to get further information about the dielectric absorption associated with various processes. From the dielectric studies, it has been observed that ageing does not affect synthetic rubbers. This is similar to that found previously in the case of butyl rubber loaded with white fillers [360].

9. Complex Impedance Spectroscopy of Dielectric Materials It has been observed that there is a strong correlation between the structure and physical properties of materials which is strongly dependent on frequency and temperature. Complex impedance spectroscopy (CIS) is an experimental technique for the characterization of electrical properties of electronic materials. The technique is based on analyzing the ac response of a system to a sinusoidal perturbation and subsequent calculation of impedance as a function of the frequency of the perturbation. CIS has been carried out in view of its simplicity and importance in describing the electrical processes occurring in a system on applying an ac signal across the sample pellet. The output response of such an experimental measurement, when depicted in a complex plane plot, appears in the form of a succession of semicircles representing the contributions to the electrical properties due to the bulk material, grain boundary effects and interfacial polarization phenomena, if any. In view of this specialty, CIS technique enables us to separate the effects due to each component (bulk, grain boundary, and electrode polarization effects) in a polycrystalline sample very easily. Each representation can be used to highlight a particular aspect of the response of a sample. A parallel resistance-capacitance (RC) circuit with corresponding equivalent to the individual component of the material (i.e., bulk and grain boundary) represents a semicircle. Impedance

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data of materials that have capacitive and resistive components, when represented in the Nyquist plot, leads to a succession of semicircles. The electrical properties are often presented in terms of impedance (Z), admittance (Y), permittivity (ε) and electrical modulus (M) [361]. The frequency dependent dielectric properties of materials can normally be described in terms of complex dielectric constant (ε*), complex impedance (Z*), electric modulus (M*) and dielectric loss (tanδ). The complex impedance of the electrode/ceramic/electrode capacitor can be demonstrated as the sum of the single RC circuit with parallel combination. The effect of temperature on impedance behavior of the material sample becomes clearly visible with rise in temperature. The nature (of pattern) of semicircular arcs changes with rise in temperature. The semicircular arcs in the pattern, the extent of their intercept on the real axis and their number in the spectrum provide very important information relating electrical behavior of the material sample under investigation. As temperature rises, the arcs progressively become semicircular (from straight line at low temperature) with a shift in the center of their arc towards origin of the complex plane plot. With further rise in temperature, appearance of another semicircular arc in the impedance spectrum can be noticed in some samples where the grain boundary contribution is prominent. In addition, appearance of a third semicircular arc can also be noticed if there is a contribution from the electrode – interface. When the point of intercept of the arcs on the real axis is shifted towards the origin of the complex plane plot, then this shift indicates a decrease in the resistive behavior of the sample assisted possibly due to grain boundary conduction with rise in temperature. This type of electrical phenomena in the material can appropriately be modeled in terms of an equivalent electrical circuit, according to brick-layer model [362], comprising of a series combination of two parallel RC circuits attributed to both the grain interior (bulk) and grain boundary effects.

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LiCa2Nb5O15: Some ceramics with the tungsten bronze (TB) structure have attracted much attention due to their unique ferroelectric, pyroelectric, piezoelectric, and electro optic properties for various devices, such as transducers, actuators, capacitors, and ferroelectric random access memory devices [363]. LiCa2Nb5O15 is an important material of TB structural family. Behera et al. [364] have studied the electrical properties of the material using a complex impedance spectroscopy technique in wide temperature (31–500 oC) and frequency (102–106 Hz) ranges. The complex impedance plots reveal the main contribution of bulk effects in it. The bulk resistance, evaluated from complex impedance spectrum, has been observed to decrease with rise in temperature showing a typical negative temperature coefficient of resistance (NTCR) behavior. Figure 9.1 shows the complex impedance spectrum (Z′′ vs. Z′) of LiCa2Nb5O15 at selected temperatures. A single semicircular arc has been observed in a wide temperature range. This indicates that the electrical properties of the material arise mainly due to the bulk effects. The shifting of intercept towards origin with increase in temperature indicates the decrease in the resistive property of the material, and thus gives the bulk resistance (Rb) of the material. This type of electrical behavior can be explained in terms of an equivalent circuit comprising of a parallel combination of RC circuits (inset). Figure 9.2(a) shows the frequency–temperature dependence of Z′′ of LiCa2Nb5O15. The appearance of relaxation process in this system is exhibited by the peak of the plots, which are shifting towards higher frequency side on increasing temperature. Further, the change

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in the peak broadening with temperature, suggests the presence of temperature dependent relaxation processes in the compound. Figure 9.2(b) shows the variation of Z′ as a function of frequency at different temperatures (200–375oC) of LiCa2Nb5O15. It is observed that the magnitude of Z′ decreases on increasing temperature (i.e., negative temperature coefficient of resistance behavior). The plateau region observed in this plot indicates the presence of relaxation process in the material. The use of modulus spectroscopy plot is particularly useful for separating components with similar resistance but different capacitance. The other advantage of electric modulus formalism is that the electrode effect is suppressed. Figure 9.3(a) shows the variation of imaginary part of electric modulus with frequency for LiCa2Nb5O15 at selected temperatures. The maxima M″max shifts towards higher frequencies side with rise in temperature ascribing correlation between motions of mobile ions [365]. The asymmetric peak broadening indicates the spread of relaxation times with different time constant, and hence relaxation is of non-Debye type [366]. The low frequency peaks show that the ions can move over long distances whereas high-frequency peaks merge to spatially confinement of ions in their potential well. The nature of modulus spectrum suggests the existence of hopping mechanism of electrical conduction in the material. Figure 9.3(b) shows the variation of M' as a function of frequency for LiCa2Nb5O15 at selected temperatures. This shows that M' approaches zero in the low frequency region, and a continuous dispersion on increasing frequency may be contributed to the conduction phenomena due to short range mobility of charge carriers. This implies the lack of a restoring force for the flow of charge under the influence of a steady electric field [365]. This confirms elimination of electrode effect in the material. Na1/2Sm1/2TiO3.: With high demand and rapid progress in the miniaturization of electrical components, a considerable attention has been paid to the function and role of interfaces of electroceramics. Grain boundaries in electroceramics such as ferroelectric materials, ionic conductors, voltage-dependent resistors (VDRs) and negative temperature coefficient resistors (NTCRs) play significant role in their electrical/dielectric properties [367–370]. Barik et al. [371] prepared Na1/2Sm1/2TiO3, a compound of perovskite family by a mixed oxide (solid-state reaction) method and studied the electrical property of the material by complex impedance spectroscopic technique in details. For a polycrystalline sample, the complex impedance technique enables to separate the contributions of bulk, grain boundary and electrode in the material very easily [372–373]. The output response of such a measurement in a complex plane plot appears in the form of a succession of semicircles as: (a) the higher frequency semicircular arc generally represents the bulk contribution and (b) the intermediate frequency arc represents the grain boundary contribution.

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Ref 364.

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Figure 9.1. Nyquist plots (Z″ vs. Z′΄) of LiCa2Nb5O15

Ref 364. Figure 9.2. Variation of (a) Z'' and (b) Z' of LiCa2Nb5O15 with frequency.

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Ref 364.

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Figure 9.3. Variation of (a) M'' and (b) M' with frequency of LiCa2Nb5O15 at selected temperatures.

Ref 371.

Figure 9.4. Nyquist plots (Z'' vs. Z') of Na1/2Sm1/2TiO3.

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R.N.P. Choudhary and S.K. Patri Figure 9.4 shows the Nyquist (Z′′ vs. Z′) plot at different temperature (200–400 C) in the complex plane. Below 275 oC, one can vividly observe a good fit of this curve with the general equation of a semicircle. At 275 oC, there is another deviation from the circular nature observed at the low-frequency side of the complex impedance plot, which may possibly the result of the grain boundary equation of a generated semicircle. The high-temperature and low frequency tail is not fully evolved to its true shape because of the limitations of frequency and temperature [371]. Figure 9.5(a) shows the variation of the real part of the contribution, due to its high resistance and high capacitance [374]. The high frequency side originated from the grains. The magnitude of Z′ (i.e., resistance) decreases with rise in temperature and frequency, which indicate the possibility of an increase in the ac conductivity on increasing temperature and frequency [375]. The Z′ values of all the temperatures merge in the higher-frequency region (≥ 100 kHz). This may be due to the release of space charge as a result of a reduction in the barrier properties of the material with the rise in temperature, and may be a responsible factor for the enhancement of the ac conductivity of the material with temperature at higher frequencies [376]. Further, at low frequencies, the Z′ values decrease with rise in temperature, and the compound exhibits a negative temperature coefficient of resistance (NTCR)-type behavior like that of semiconductors [377]. Figure 9.5 (b) shows the variation of the imaginary part of impedance (Z″) as a function of frequency at different temperatures. The loss spectrum (Z″ vs. frequency) is characterized by the appearance peak at different temperatures ≥ 200 oC. The broadening of the peak shifted towards higher frequencies as the temperature increased. A significant broadening of the peak with an increase in temperature suggests the temperature dependence of electrical

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o

Ref 371.

Figure 9.5. Variation of (a) real part of impedance (Z') and (b) imaginary part of impedance (Z'') of Na1/2Sm1/2TiO3 as a function of frequency.

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relaxation phenomenon in the material [378]. The relaxation process may be due to the presence of electrons and/or immobile species at lower temperatures, and defects in the higher-temperature region. Thus, the electrical properties show that (i) the material exhibits grain and grain-boundary conduction at higher temperatures, (ii) a temperature dependent relaxation phenomenon, and (iii) a negative temperature coefficient of resistance (NTCR) behavior. NaCa2V5O15: Some ferroelectric materials are excellent candidates for a wide application in data storage of digital memory systems, piezoelectric, pyroelectric and electro-optics sensors, actuators, transducers, ferroelectric random access memory and microelectromechanical systems (MEMs) [379-382]. NaCa2V5O15 (NCV) belongs to tungsten bronze family. This material has advantages over other dielectrics because of its high dielectric constant and low dielectric loss [383-385]. Behera et al. [386] have prepared NaCa2V5O15 by a solid-state reaction technique, and studied the structure-property relationship by impedance spectroscopy. Figure 9.6 shows the complex impedance plots of Z' vs. Z'' (Nyquists plot) for NCV at different temperatures. All the curves start at the origin, and hence there is no equivalent series resistance of the sample. The semicircles have their centers located slightly away from the real axis, indicating the presence of relaxation species with distribution of relaxation times in the sample. Furthermore, the shape of the curves suggests that the electrical response is completely dominated by the bulk properties of the material. The inherent electrical properties of NCV can be represented by a parallel combination of RC circuits (inset of Figure 9.6). In order to confirm the ambiguity arising in connection with the presence of grain/grain boundary effect [387] at elevated temperatures, the impedance data were replotted in the modulus formalism at high temperatures (i.e., 325–425oC) as shown in Figure 9.6 (inset). It is clear that the modulus plane shows a single semicircle. The intercept on the real axis indicates the total capacitance contributed by the grain. Further, it has been confirmed that the grain boundaries are negligibly small as observed earlier in the M'' vs. frequency plot, and even if present, their contributions to the overall capacitance of the material are less, and have negligible effect on relaxation process. The modulus spectrum shows a marked change in its shape with rise in temperature suggesting a probable change in the capacitance values of the material as a function of temperature. Figure 9.7 shows the variation of Z″ as a function of frequency (usually called as loss spectrum) at higher temperatures (325–425 oC). This plot is suitable for evaluation of the relaxation frequency of the most resistive component. The loss spectrum has some important features: (a) the appearance of the peak, (b) typical peak broadening, and (c) the value of Z″max decreases and shifts to higher frequency side on increasing temperature. It is seen that the peak maxima shifts towards the high frequency side on increasing temperature and the relaxation process occurs over several decades of frequency. The broadening of the peak (due to increase in temperature) suggests the presence of temperature dependence of relaxation processes in the material [81].

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Ref 386.

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Figure 9.6. Variation of Z' vs. Z'' and M' and M'' (inset) at different temperatures of NaCa2V5O15

Ref 386.

Figure 9.7. Variation of Z'' with frequency at different temperatures of NaCa2V5O15.

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Ref 386.

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Figure 9.8. Variation of M' and M'' (inset) with frequency at different temperatures of NaCa2V5O15

•

Figure 9.8 shows the variation of M′ with frequency for NaCa2V5O15 at selected temperatures. A continuous increase in the M′ dispersion on increasing frequency with a tendency to attain a maximum asymptotic value (i.e. M∞) in the high frequency region for all the temperatures is observed. Such observation may possibly be related to a lack of restoring force governing the mobility of the charge carriers under the action of an induced electric field. This behavior supports the long-range mobility of charge carriers. Further, a sigmoidal increase in the value of M′ with the frequency may be attributed to the conduction phenomena due to short-range mobility of charge carriers. Figure 9.8 (inset) shows the variation of M″ of the complex modulus with frequency over a wide temperature range and frequencies. A well-defined relaxation mechanism is observed in the temperature range of 225–425 o C. The relaxation peaks shift towards higher frequency side with rise in temperature. Furthermore, the height of the M″max increases slightly with rise in temperature. This type of effect has been observed in the modulus spectrum of some ionic conductors [388–390]. Pb2Sb3LaTi5O18: Continuous attempts have been made to investigate Pb2A3RTi5O18 (A = Sb or Bi; R = rare-earth ions) compounds with desired characteristics from both theoretical and application points of view for their pyroelectric properties, which make these compounds suitable for pyroelectric infrared (IR) detectors or sensors [391]. Suman et al. [392] have studied extensively the electrical properties of Pb2Sb3LaTi5O18 (PSLT).

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Ref 392.

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Figure 9.9.Variation of imaginary part of impedance of PSLT with frequency at different temperatures. (Inset: Normalized imaginary parts, Z''/ Z''max, of the impedance as a function of frequency for PSLT at different temperatures).

Figure 9.9 shows the variation of the imaginary part of impedance (Z″) with frequency at different temperatures. The curves show that the Z'' values reach a maxima peak (Z''max) for the temperatures ≥ 400°C. This also indicates the occurrence of single relaxation process in the system. The relaxation times (τ) can be calculated from the frequency at which Z''max is observed. The frequency for the maximum fp, called relaxation frequency, shifts to higher values with increasing temperature indicating the increasing loss in the sample. The peak heights are proportional to bulk resistance (Rb) according to equation Z″= Rb[ωτ / (1+ ω2τ2)]. Inset of Figure 9.9 shows the normalized imaginary parts, Z″/Z''max, of the impedance as a function of frequency of PSLT at different temperatures. It seems that high temperature trigger another relaxation process. At the peak, the relaxation is defined by the condition ωmτm = 1, where τm is the relaxation time. Figure 9.10 shows that the relaxation frequency obeys the Arrhenius relation given by ωm = ω0 exp (– Ea/kBT) where ω0 is the pre-exponential factor. The activation energy, Ea, calculated from least-squares fit is 0.786 eV. To study the contributions due to different effects, Cole–Cole analyses have been carried out at different temperatures. It also provides information about the nature of dielectric relaxation. For pure monodispersive Debye process, one expects semicircular plots with the centre located on the Z'-axis whereas, for polydispersive relaxation, these Argand plane plots are close to circular arcs with end points on the real axis and the centre below this axis. The complex impedance in such situations is known to be described by Cole–Cole formalism [182], Z* (w) = Z' + iZ'' = R/[1 + (iω/ω0)1–α],

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where α represents the magnitude of the departure of the electrical response from an ideal condition and this can be determined from the location of the centre of the Cole–Cole circles. When α goes to zero (1 – a → 1), gives rise to classical Debye’s formalism.

Ref 392.

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Figure 9.10. Temperature dependence of relaxation frequency of PSLT. The circles are the experimental points and the solid line is the least squares straight line fit.

Ref 392.

Figure 9.11. Nyquist plots of PSLT at different temperatures.

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Figure 9.11 (a) shows the Nyquist plots at different temperatures. Figure 9.11 (b) depicts two representative plots at T = 425 and 500 °C. It can be seen from these plots that the data is represented by full semicircle i.e., semicircle centered on the abscissa axis (α = 0), suggests that the relaxation to be of Debye type. The resistance of bulk (Rb), grain boundary (Rgb) and interface/polarization (Re), could directly be obtained from the intercept on the Z'-axis. The capacitances (Cb, Cgb and Ce) due to these effects can be calculated using the relation ωR C = 1, where ω is the angular frequency at the maxima of the semicircle for the component. Figure 9.12 shows the temperature variation of Rb, Rgb, Re, Cb, Cgb and Ce obtained from Cole–Cole plots at different temperatures. It can be seen that the values of Rb, Rgb, Re, Cb and Cgb decrease while the value of Ce increases with the increase in temperature.

Ref 392.

Figure 9.12. Variation of resistance and capacitance for grain, grain boundary and electrode contributions with temperature of PSLT.

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LaLiMo2O8: Tungstates and molybdates of different structural forms and stoichiometry based either on rare earth metals (R = La, Nd, Dy, Sm, Gd, etc.) or alkali metals (Li, Na, K, etc.) have drawn considerable attention in recent years. They exist in a wide variety of structural forms and exhibit diversity in their physical properties such as successive phase transition, ferroelectric/ferroelastic behavior [393-394], negative thermal expansion (NTE) / substantial volume contraction over a wide temperature range [395], and ionic conduction. The structural diversity imparts the property of polymorphism in rare earth molybdates arising as a result of flexibility in the coordination number as well as geometry of both rare earth cations (La3+ for example) and molybdate ion (i.e., Mo6+ for example) centers. This property permits possibility of 6–12 as well as 4–7 coordinates with various coordination polyhedra for both trivalent rare earth cation and hexavalent molybdate cation,

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respectively [396]. As a consequence, replacement of rare earth cation with other species in polymolybdates becomes practically feasible although it is accompanied by drastic structural changes. Figures 9.13 (i-iv) show complex impedance spectrum (Nyquist plot) of LaLiMo2O8 [397] obtained at different temperatures. The effect of temperature on impedance behavior of the material sample becomes clearly visible with rise in temperature. As temperature raises progressively, the appearance of a third semicircular arc has also been noticed in the impedance pattern beyond 400 oC (Figure 9.13 (iv)).

Ref 397.

Figure 9.13. (i-iv) Complex impedance spectrum of LaLiMo2O8 as a function of temperature with electrical equivalent circuit (inset).

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R.N.P. Choudhary and S.K. Patri (polarization at the material–electrode interface), typical of an ionically conducting polycrystalline material [398]. It may further be related to the possibility of an electrochemical reaction at metal–electrode interface occurring at elevated temperatures either due to Ag+ ion/or Li+ ion. In fact, the appearance of a third semicircular arc at T≥400 0C (Figure 9.13 (iv)) confirms this hypothesis. The impedance data has been used to evaluate the relaxation time (τ) of the electrical phenomena in the material using the relation ωmaxτ = ωmaxRbCb = 1. It is independent of the sample geometry and depends basically on the intrinsic properties (i.e., microstructures) of the material sample only. The typical variation of relaxation time (τ) as a function of temperature is shown in the (Figure 9.14). The pattern shows a steady increase in the relaxation time with temperature. This result suggests the presence of temperature dependent electrical relaxation phenomena in the material possibly due to the migration of immobile species/defects. The typical variation appears to be of Arrhenius nature governed by the relation: τ = τ0 exp

− Ea . k BT

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Complex modulus formalism is a very important and convenient tool to determine, analyze and interpret the dynamical aspects of electrical transport phenomena (i.e., parameters such as carrier/ion hopping rate, conductivity, relaxation time etc.).

Ref 397.

Figure 9.14.Variation of relaxation time (τ) of LaLiMo2O8 with temperature.

Figure 9.15 shows the complex modulus spectrum of the material sample at different temperatures. The pattern is characterized by the presence of asymmetric semicircular arcs at different temperatures such that they appear to be overlapping for all the temperatures on and above 200 oC. This may possibly be attributed to the presence of electrical relaxation phenomena. The spectrum has been used to evaluate the sample capacitance value at different temperatures. The modulus spectrum has been normalized and represented in Figure 9.16. It is known as modulus master curve, and it shows the scaling behavior of the sample electrical modulus. It is

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characterized by: (i) broad asymmetric pattern with a cross over from short-range mobility to long-range mobility of ions with rise in temperatures, (ii) near perfect overlap of different temperature data superimposed in the single master curve and (iii) FWHM greater than 1.14 decades. These observations indicate the occurrence of dynamical processes within the sample at different frequencies exhibiting the same thermal activation energy and are independent of temperature with nonexponential type of conductivity relaxation.

Ref 397.

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Figure 9.15. Complex modulus spectrum of LaLiMo2O8

Ref 397.

Figure 9.16. Modulus scaling behavior of LaLiMo2O8

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R.N.P. Choudhary and S.K. Patri LaBi8Fe5Ti3O27: Though a large number of ferroelectrics with layered structures are known today, the bismuth layer-structured ferroelectrics (BLSF) play an important role for the existence of ME effect, anisotropic electronic, dielectric, optical and ionic properties [273]. These materials have a wide range of multifunctional applications in spintronics, information storage devices such as multi-state nonvolatile memories, sensors, phase shifters, amplitude modulators and electrooptic devices etc. [399]. In view of the importance of the materials, Patri et al. [400] have studied the electrical properties of an eight layered bismuth based multiferroic, LaBi8Fe5Ti3O27. Figure 9.17 shows the frequency–temperature dependence of Z″ (usually referred as loss spectrum). The appearance of peak in the loss spectrum above 200 oC exhibits the existence of relaxation properties of the material. The broadening of peaks on increasing temperature confirms the existence of temperature dependence of relaxation.

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Ref 400.

Figure 9.17. Variation of Z″ of LaBi8Fe5Ti3O27 with frequency at some selected temperatures.

Table 9.1. Comparison of temperature dependence of electrical parameters corresponding to the equivalent circuit model by using the fitting Temperature °C 300 325 350 400

Rb (in Ω) 1.2795 x 104 5.2360 x 103 2.7310 x 103 9.8940 x 102

Cb (in Farad) 6.5570 x 10-11 9.0570 x 10-11 1.1480 x 10-10 1.5490 x 10-10

Ref 400.

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CPE (Q) 4.0460 x 10-8 1.3030 x 10-7 8.7910 x 10-7 4.5950 x 10-6

n 0.54 0.44 0.32 0.25

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Ref 400.

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Figure 9.18. Nyquist plots (Z″ vs. Z′) at selected temperatures and comparison of complex impedance plots with fitted data of LaBi8Fe5Ti3O27 with equivalent circuit.

Table 9.1. gives the comparison of temperature dependence of electrical parameters corresponding to the equivalent circuit model by using the fitting [Ref. 400] data in the material [401]. Such type of behavior may be due to the presence of immobile species (i.e., electrons) at low temperatures and defect (i.e., vacancies) at high temperatures [402]. Figure 9.18 shows the temperature dependence of complex impedance spectrum (Nyquist plot) with fitted data [403] at different temperatures. The single semicircular arc of Z″–Z′ plots indicate that transport properties of the material arises due to the bulk (intragrain) [404]. The non-coincidence of Z″ and M″ spectra with frequency shows the departure from ideal Debye behavior [405] and justifies the presence of constant phase element (CPE) which is suggested by Jonscher power law [401]. Thus, a constant phase element (CPE) is introduced in the equivalent circuit, which shows the departure from ideal Debye-like response, and confirms the power law dependence of the impedance over several decades of frequency domain [406]. The values of the electrical or transport parameters corresponding to the equivalent circuit (as shown in Figure 9.18) modeled by fitting processes of the measured data at different temperatures are given in Table 9.1. It has been observed that the resistance due to temperature, which may be due to the increase in interaction between the mobile ions with the lattice around them [407]. Figure 9.19(a) shows the temperature–frequency dependence of imaginary part of electric modulus (M″). The shift of asymmetric modulus peaks towards higher frequency side suggests the correlation between motions of mobile ion charges [408]. The asymmetricity in peak broadening shows the spread of relaxation times with different time constant, and hence relaxation is of non-Debye type. The appearance of peaks at low frequency suggests that the ions can move over long distances whereas at high frequency, the confinement of ions in their potential well is

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•

suggested. The nature of modulus spectrum confirms the existence of hopping mechanism of the conduction process in the material. Figure 9.19(b) shows the variation of M′ as a function of frequency at selected temperatures. A continuous dispersion on increasing frequency may be due to the short range mobility of charge carriers. Figure 9.20(a) shows the complex modulus spectrum (M′ vs. M″) of LaBi8Fe5Ti3O27 at selected temperatures. The asymmetric semicircular arc confirms the presence of electrical relaxation phenomena in the material. The scaling behavior of the sample was studied by normalizing the modulus parameters (M″, M′) (M″/ M″max) vs. log (f/fmax)) at different temperatures (Figure 9.20(b) (inset)) where fmax is the frequency corresponding to M″max. The merging of all the curves/peaks of different temperatures into a single master curve indicates the presence of the dynamic processes in the material [409]. Polymer–salt complex: Polymer electrolytes appear to be a promising alternative over their liquid counterpart due to design flexibility, easier processability and possibility of miniaturization for device fabrication. Polymer nanocomposite electrolytes (PNCEs) are a new class of materials in which intercalation of conducting polymer matrix into the nanoscale gallery of clay has been taken place. Thakur et al. [410] have reported the effect of various clay concentration of a sodium ion conducting polymer nanocomposite electrolyte (PEO25–NaClO4 i.e., (PEO)25 NaClO4 + x wt.% Na-MMT (x = 0–50)) on sample structure/microstructure, and electrical properties, where MMT is abbreviated for montmorillonite clay (NaMMT). CIS technique was used to study the electrical properties of PNCE films. The typical Nyquist plots (shown in Figure 9.21 (a)) of the samples comprise of a semicircular arc in the high frequency region followed by a tail in the low frequency region suggesting a trend for another semicircular arc. The existence of more than one arc indicates the presence of multicomponent behavior of the system. The high frequency semicircle may be due to the bulk properties of the PNCE films. The intercept of this semicircle with the real axis (Z′) gives the bulk resistance (Rb) of the materials. Figure 9.22 shows the dc conductivity (σdc) of the PNCE films as a function of clay concentration of the materials at 40 and 100 oC. The behavior of σdc may be attributed to a possible interaction of the negative charges in the silicate layers with the Na+ cation of polymer–salt complex on immediate clay addition. This may cause release of cations and a consequent concentration enhancement of the charge carrier. Hence conductivity may be expected to increase at lower concentration of clay. Figure 9.23 shows σdc versus 103/T plot for different clay concentration. The monotonous increase in σdc with temperature up to crystalline melting (Tm) followed by saturation beyond which conductivity rises with rise in temperature. This behavior may be due to a typical VTF (Vogel–Tamman–Fulcher) pattern governed by the empirical relation:

σT 1 / 2 = σ 0 exp

symbols have their usual meaning [411].

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− Ea , where the k β (T − T0 )

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Ref 400.

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Figure 9.19. (a) Variation of M″ (inset), and (b) M′ of LaBi8Fe5Ti3O27 with frequency at selected temperatures.

Ref 400.

Figure 9.20. (a) Variation of M′ with M″ of LaBi8Fe5Ti3O27 at selected temperatures and (b) modulus scaling behavior into a master curve (inset) of LaBi8Fe5Ti3O27 at selected temperatures.

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Ref 410.

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Figure 9.21. (a) Complex impedance spectrum of PNCE with different concentration (x) of Na+-MMT: (a) x = 0% (inserted), (b) x = 5%, (c) x = 10%, (d) x = 20% and (e) x = 30% concentration.

Ref 410.

Figure 9.22. Variation of dc conductivity (σdc) of PNCE as a function of Na+ montmorillonite concentration.

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Ref 410.

Figure 9.23.Variation of dc conductivity PNCE films (σdc) as a function of temperature with concentration of Na+-MMT: (a) x = 0% (inserted), (b) x = 5%, (c) x = 10%, (d) x = 20%, (e) x = 30% and (f) x = 50%.

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•

Plasticized composite polymer electrolyte (PCPE): Recently, a considerable attention have been received on ionically conductive solid polymers for their technological importance in a wide variety of energy storage/conversion devices such as batteries, fuel cells, super capacitors, and hybrid power sources [412–419]. Generally, composite polymer electrolytes (CPEs) are suitable for the above applications because they satisfy the essential requirements of such applications that are: (i) high ambient ionic conductivity, (ii) thermal, chemical, electrochemical, mechanical and interfacial stability in addition to dimensional flexibility of design [423–427]. The composite polymer electrolytes (CPEs) can be prepared by dispersing ceramic fillers (Al2O3, SiO2, γ-LiAlO2, Na2SiO3, SnO2, etc.) into the matrix of polymer–salt complexes [420–429]. Pradhan et al. [430] have reported the results of systematic investigations of the effect of plasticizer concentration on the electrical properties of a new plasticized composite polymeric system: (PEO)25–NaClO4 + 10 wt.%SnO2 + x wt.%PEG200. [where PEO - polyethylene oxide, PEG - polyethylene glycol]. The impedance spectrum analysis of plasticizer-free (pure CPE) and plasticized CPE has been carried out with an aim to observe the role of plasticizer in governing the electrical properties of solid PCPE films. The room temperature complex impedance spectra of plasticized composite polymer electrolytes with various plasticizer concentrations are shown in Figure 9.24. Each spectrum comprises a semi-circle (x = 0) in the high-frequency region followed by a trend of another semicircle or spike in the low-frequency region. This feature is common for plasticizer-

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free and plasticized composite polymer electrolyte. The high-frequency semi-circle may be attributed to the bulk properties of the material, whereas the low-frequency semi-circle to the grain-boundary effect, which is representative of the presence of an inhomogeneous crystalline phase in the films [424]. The bulk (dc) resistance (Rb) and grain-boundary resistance (Rgb) are found from the intercepts of high-frequency and low-frequency semi-circles on the real axis. The grain-boundary resistance is substantially reduced in the plasticized sample than that of plasticizer-free CPE, which provides a convincing evidence of the role of plasticizer in the reorganization of the physical structure of PCPE films and reduction of the crystallinity of the polymer host that favors long-term stability of the amorphous phase. The variation of the conductivity of (PEO)25–NaClO4 + 10 wt.%SnO2 + x wt.%PEG as a function of plasticizer concentration is shown in Figure 9.25. Substantial enhancement in electrical conductivity of the PCPE films is observed on addition of up to 20 wt % of plasticizer. A maximum enhancement in electrical conductivity by two orders of magnitude at room temperature is found for films containing 20 wt % PEG. This behavior may be attributed to the combined effect of several factors such as reduction in crystallinity, increase in the elastomeric amorphous phase of the host PEO, and lowering of the Tg and grain-boundary resistance as observed in the present investigations.

Ref 430.

Figure 9.24. Variation of real and imaginary part of impedance with different concentration (x) of PEG (a) x = 0%, (b) x = 10%, (c) x = 30%, (d) x = 50%.

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Ref 430.

Figure 9.25. Variation of dc conductivity as a function of plasticizer concentration with different concentration (x) of PEG (a) x = 0%, (b) x = 10%, (c) x = 20%, (d) x = 30%, (e) x = 40%.

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10. Multiferroic Property of Dielectric Materials Multiferroic materials show simultaneous electric and magnetic ordering. Multiferroics have currently gained more attention due to the fact that they are promising for the design of multifunctional devices, and also because of the interesting physics found in this class of materials. Multiferroic materials (with multiple order parameters) offer an exciting way of coupling phenomena such as electronic and magnetic order. The quest for multiferroic materials, where the two phenomena are intimately coupled, is of great technological and fundamental interest. Ferroelectricity and magnetism tend to be mutually exclusive and interact weakly with each other when they coexist. The following discussion explains the multiferroicity in some materials. •

Y Substituted BiFeO3: The orientation of magnetic moments, magnetic moment canting and the spiral spin structure attributed to weak magnetic characteristics of BFO [431]. Bi substitution by rare earth ions improves magnetic properties attributed to structural phase transition, resulting in the release of latent magnetization [432– 434]. It seems logical to attribute, in general, the changes in multiferroic properties on Bi substitution by a rare earth to the cation size effect. Mishra et al. [435] substituted Y (ionic radius = 0.90 Å) at Bi (ionic radius = 1.03 Å) site. Substitution at the Bi site of BFO has caused compositionally driven structural change and facilitates single phase formation of the material by suppressing the pyrochlore phase. This has led to a considerable change in dielectric, ferroelectric (Figures 10.1 and 10.2) and magnetic properties of BFO. Up to 10% Y substitution

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Ref 435.

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Figure 10.1. Variation of relative dielectric permittivity (εr) and loss tangent (tan δ) (inset) of Bi1−xYxFeO3 with temperature at a frequency of 100 kHz.

Ref 435.

Figure 10.2. Room temperature P–E loop of Bi1−xYxFeO3

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Ref 435.

Figure 10.3. Magnetization (M) versus field (H) curve for Bi1−xYxFeO3 at different temperatures.

There is a significant reduction of low frequency dispersion in both permittivity and loss pattern, indicating a considerable control of dc conductivity thereby enhancing ferroelectric behavior. However, with Y substitution at the Bi site we get remarkable increase in macroscopic magnetization and the switching behavior in low fields which is the most interesting observation of the field dependence of magnetization of BYFO samples (Figure10.3). This makes them different from rare earth substituted BFO. This unique magnetic behavior along with the existence of ferroelectricity in these samples makes them probable candidates for obtaining better magnetoelectric coupling. •

Ba substituted Pb(Fe1/2Nb1/2)O3.: Lead iron niobate Pb(Fe1/2Nb1/2)O3 (PFN) belongs to the series of complex perovskite compounds discovered at the end of the 1950s [436]. It was considered to be ferroelectrically and antiferromagnetically ordered below a certain temperature. Its (dielectric) Curie temperature is around 383 K and the antiferromagnetic order begins at about 143 K. Due to their exceptionally high dielectric constant [437], PFN ceramics are one of the most attractive candidates for

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making multilayer capacitors. The presence of magnetic Fe+3 ions in octahedral (BI) sites of (ABIBII)O3 perovskite lattice makes PFN an interesting single-phase multiferroic material. Due to the presence of Fe2+, O2− ion vacancies, PFN and related materials have high-leakage current which limits the materials for any meaningful devices with higher sensitivity [438-444]. In order to obtain suitable materials for devices, several attempts have been made to design and develop materials by substituting isovalent/nonisovalent elements/atoms at the B-site [441] or fabricating composites of 2–3 components or oxides. In view of the above fact, the effect of Ba substitution at the Pb-sites was studied by Varshney et al. [445]. (Pb1−xBax)(Fe1/2Nb1/2)O3 (PBFN) with x = 0, 0.05, 0.07 have been synthesized by high-energy ball milling with particles in nanometer size. A decrease in phase transition temperature was observed in Ba-modified PFN material compared to that of PFN, which may be due to intergranular stress of ferroelectric domain sizes, compositional inhomogeneities, and Ba distribution at the Pb+2 site. The phase transition behavior in PFN provides a signature of normal transition of the paraelectric to ferroelectric phase type. However, on increasing Ba content to x = 70 wt%, a cross-over of phase transition from normal to relaxor ferroelectric was observed (Figure10.4). It is indeed an interesting and new observation on PFN [442].

Ref 445.

Figure 10.4. Temperature dependence of relative dielectric constant εr of Pb1−xBax(Fe0.5Nb0.5)O3 with (a) x = 0, (b) x = 0.05, and (c) x = 0.07 at frequencies 100 kHz (□), 250 kHz (○), 500 kHz (Δ), 1MHz (+). Recent Advances in Dielectric Materials, Nova Science Publishers, Incorporated, 2009. ProQuest Ebook Central,

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Ref 445.

Figure 10.5. Variation of (a) magnetization vs. magnetic field at 300 K, (b) magnetization vs. temperature at 100 Oe, and (c) magnetization vs. magnetic field at 2K of Pb1−xBax(Fe0.5Nb0.5)O3 (x = 0, x = 0.07).

•

•

A weak magnetization in PBFN (Figure 10.5) is observed which may be largely related to structural distortion of the parent structure, since the magnetization is crucially dependent on the symmetry of the system [443-444]. A stable antiferromagnetic G-type phase of PFN is related to ferroelectric tetragonal distortion with large shift of the Pb atom. This is in agreement with the fact that a large polarization of the Pb-based ferroelectric perovskites is provided by the Pbdisplacement [445]. Pb(Mn1/2Nb1/2)O3: The lead-based complex perovskites of a general formula Pb(B΄xB΄΄1−x )O3 are fascinating materials in view of their high dielectric constant, frequency dispersive behavior and diffuse phase transition. When both d0 ion (ferroelectric active) and the partially filled d orbital ion (magnetically active) are accommodated at the B site of these complex lead-based perovskites of a general formula Pb(B+31/2B+51/2)O3, they exhibit multiferroic properties [446–451]. This idea was first conceived by Russian scientists in 1950s leading to the synthesis of many multiferroic materials like Pb(Fe1/2Nb1/2)O3, Pb(Fe1/2Ta1/2)O3, Pb(Mn1/2Nb1/2)O3, etc [449, 452–455]. Astov et al. [456] had reported that the two ferroelectric substances

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Pb(Fe1/2Nb1/2)O3 and Pb(Mn1/2Nb1/2)O3 possessed a spontaneous magnetic moment, which was of magnetoelectric origin in nature. Mishra et al. [457] have reported the detailed dielectric, electrical and magnetic properties of Pb(Mn1/2Nb1/2)O3 Figure 10.6 shows the variations of dielectric constant (εr) and loss tangent (tan δ) with temperature at different frequencies. Strong frequency dispersion is observed in both permittivity and loss pattern above 315 K, which may indicates the presence of appreciable dc conductivity in the system [80] responsible for the hindrance of poling the material to get any hysteresis loop. The appearance of dielectric anomaly may be related to non-ferroelectric phase transition. Figure 10.7 shows the M–H curves for 300 and 2 K. From Figure 10.8 (a) the paramagnetic nature of the sample is observed above 215 K, which is evident from the Curie–Weiss plot (Figure 10.8 (b)) and also the linear M–H behavior at 300 K (upper inset of Figure 10.7). The sharp increase in M may be attributed to ferrimagnetic interactions which are clear from a large positive intercept of 1/χ on the temperature axis in the Curie–Weiss plots [458]. The positive intercept on the M2 axis in Arrott’s plot (M2 versus H/M) indicates a spontaneous magnetization in the sample [459–461] (Figure 10.8 (b)). Therefore, it is assumed that super-exchange resulting from Mn–O–Mn interactions might give rise to the magnetic ordering at low temperature.

Ref 457.

Figure 10.6.Variation of dielectric permittivity and loss tangent of Pb(Mn1/2Nb1/2)O3 with temperature at different frequencies.

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Ref 457.

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Figure 10.7. M–H curve for the sample at 2 K, M–H curve at 2 K with applied field 14 T (inset) and M– H curve at room temperature (inset).

Ref 457.

Figure 10.8. (a) variation of 1/χ with temperature in the range of 150–300 K and (b) Arrott’s plot is also shown in the inset. Recent Advances in Dielectric Materials, Nova Science Publishers, Incorporated, 2009. ProQuest Ebook Central,

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11. Applications 11.1. Dielectric Devices

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(i) Capacitors: Capacitors are basic elements of electrical and electronic circuits. There are wide varieties of capacitors: (a) massive capacitors with high permittivity ferroelectric material, (b) capacitor with barrage layer, (c) capacitors with thin layer magneto-capacitors, (d) ceramic capacitors with a single parallel plate, (e) multilayer ceramic capacitors, (f) semiconductor capacitors, (g) microchip capacitors etc. The capacitors can perform various functions that include blocking, coupling, decoupling, ac-dc separation, filtering, power factor correction, energy storage, etc. These capacitors use dielectric materials with various specifications: low-dielectric constant temperature compensating dielectric materials, intermediate-dielectric constant materials, high dielectric constant materials, nonhomogeneous, barrier layer materials that can have a very high dielectric constant (~105). (ii) Positive temperature coefficient of resistance (PTCR) thermistors: The resistivity of some dielectric materials increases with increase in temperature. This property is used in PTCR thermistors, which can be further utilized as sensor and controller of temperature, in the thermo-setting of electronic equipment, protection of engines, level meters, as sensor for determination of the flow rate of gases and liquids. (iii) Dielectric memory devices: A highly reliable dielectric memory element capable of high density recording in which diffusion of polarized memory area and fatigue abrasion due to aging are retarded to ensure long term use [462].

11.2. Piezoelectric Devices (i) Air transducers: Piezoelectric microphones have been widely used in the past. They are also well used as tuned ultrasonic microphones in remote control of television sets. (ii) Instrument transducers: Piezoelectric materials are generally used to create and to receive the sound waves. The same principle is used in medical diagnosis by reflection of sound waves from interfaces between different body tissues. Miniature ceramic transducers have also been inserted in blood vessels to record periodic pressure changes connected with the heart beat. (iii) Underwater sound and ultrasonic power: Application for underwater detection comprises the passive listening approach (hydrophones) as well as the active method of emitting sound pulses and timing their echo. These devices operate at high power levels for maximum range, and are designed to work near energy levels causing dielectric and mechanical nonlinearities. The hard lead titanate zirconate ceramics may favorably compete the magnetostricitve nickel transducers in these fields [463].

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(iv) Delay line transducers: Delay line transducers are used to convert the high-speed microwave signal to a low-speed acoustic wave and of the dielectric medium to produce the time delay. (v) Wave filters: Here the mechanical resonant frequencies of piezoelectric elastic bodies influence the electric signal. Electric energy is converted into elastic energy and then back to electric. Piezoceramics are suitable for wave filters because of their high piezoelectric coupling coefficient and their design flexibility. (vi) High voltage sources: Some piezoelectric materials are exploited for the generation of sparks for ignition of butane and natural gas in space heaters, cooking stoves, brazing torches, cigarette lighters. (vii) Gas igniters: Generally PZT, PLZT are commonly used for gas igniters. Here two pieces of poled ceramics connected back to back, when a voltage developed due to applied force, then a spark would occur across the gas gap causing the momentary ignition. (viii) Piezoelectric positioners and actuators: These are used widely in areas related to precision position controlling, vibration damping, relays, phonograph pickup, pressure sensing etc. (ix) Piezoelectric transformers: Piezoelectric plates are used to make a piezoelectric transformer, in which there will be a conversion and reconversion of input electrical energy into mechanical energy and mechanical into electrical energy occurs, resulting in the generation of a higher voltage.

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11.3. Pyroelectric Devices (i) Pyroelectric radiation detectors: These are mainly used to detect infrared radiation. The pyroelectric element used in the detector should be very thin, so that it heats up quickly and uniformly. All incident infrared radiation absorbed by the element and rapidly distributed throughout the whole volume of the element ignoring the thermal diffusion. The useful criteria for pyroelectric detectors are the current responsivity and the voltage responsivity. The material should have a high pyroelectric coefficient and low dielectric constant. However, all signal detectors encounter the effect of noise. (ii) Pyroelectric burglar alarm systems: A moving intruder produces variable infrared radiation which, when reaching a pyroelectric detector, will switch on the alarm system. Since pyroelectric materials are also piezoelectric, they would produce electric charges due to external mechanical stresses caused by the expansion or contraction when the ambient temperature of the surrounding rises or falls. The output voltage of the system is to switch on the alarm system. (iii) Pyroelectric thermometry: Pyroelectric thermometers receive energy through conduction or convection. Pyroelectric thermometers can be used to measure the rate of temperature changes or the steps of steady temperature changes. (iv) Pyroelectric energy conversion: Pyroelectric materials are useful for energy conversion, as thermal energy input to a pyroelectric element will cause changes

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11.4. Ferroelectric Devices (i) Capacitors: Dielectric materials with dielectric constants larger than 1000 are mainly ferroelectric materials, and they are very sensitive to temperature, electric field, and frequency. Ferroelectric ceramics used for capacitors are classified into three classes: (i) low dielectric constant materials with low losses can have the operating temperature range (-55 oC to +85 oC), (ii) medium dielectric constant materials with general properties primarily similar to BaTiO3, the dependence of temperature, frequency and electric field is stronger than class-i, (iii) the working voltage of this type of capacitors is low with high permittivity capacitors for the working temperature from -55 oC to +125 oC. (ii) Thermo-Autostabilization Nonlinear Dielectric Elements (TANDEL): When a ferroelectric specimen is switched on to the ferroelectric phase with an alternating field, heat will be produced in the material in each cycle, part of which is due to normal dielectric losses and another part is due to hysteresis losses. As a result the power dissipation in the material increases with temperature. Thus, ferroelectric materials are used to stabilize its own temperature. The elements based on the changes in the dielectric constant, and hence the capacitance with the change of the applied ac field can be used to replace varactors as circuit elements in frequency modulation, thermostat control, etc. (iii) Ferroelctric Memory devices: Ferroelectric materials are suitable for dynamic random access memory (DRAM) and static random access memory (SRAM) because of their high permittivities. However, the disadvantage of these memories is that they are volatile, i.e., the stored information is lost when the power fails. The main advantages offered by ferroelectric random access memories (FRAMs) include non-volatile and radiation hardened compatibility with complementary metal oxide semiconductors (CMOS). The FRAMs made from ferroelectric thin films make use of this phenomena to store data. Data is stored by localized polarization switching in the microscopic regions of ferroelectric thin films. The FRAMs are non-volatile because the polarization remains in the same state after the voltage is removed (as ferroelectrics have a non-linear hysteresis curve). Recently, ferroelectric random access memories (FeRAMs) have achieved fast access speeds (5 ns), high densities (64 Mb) and embodiments in several different materials (lead zirconate titanate, strontium bismuth tantalate and bismuth ferrite) [465]. (iv) Electro-optic devices: PZT and PLZT thin films are better candidates for optical waveguide applications because of their large electro-optic coefficients [466468]. Ferroelectric thin films may replace the use of PLZT bulk ceramics for optical memory and display applications. The advantages offered by thin films for display applications include a simplification of the display device design and lower operating voltages as compared to PLZT ceramic devices. Optical

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memories using PLZT thin films will also need lower operating voltages. The material requirements for thin film optical memory and displays include large electro-optic coefficients and/or strong photo sensitivities for the film. PZT and PLZT thin films are promising materials for these optical applications [469].

11.5. Multiferroic Devices

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Multiferroics are a class of materials with coexisting electric and magnetic order parameters. The application potential for multiferroic magnetoelectrics is enormous. Possible applications include multiple-state memory elements, electric field controlled ferromagnetic resonance devices, and variable transducers with either magnetically-modulated piezoelectricity or electrically-modulated piezomagnetism. Also, the ability to couple either the magnetic or the electric polarization offers an extra degree of freedom in the design of conventional actuators, transducers, and storage devices. Furthermore, these materials are also potential candidates in various novel devices for future generation technology, e.g., oxide based electronics, nonvolatile memory elements, sensor and actuators, electric and magnetic field dependent devices, magnetic tunnel junctions, tunable high frequency devices, and super-conducting junction based devices. (i) Multistate Memory devices: A memory system made up of electrically programmable read only memory (EPROM) or flash electrically erasable and programmable read only memory (EEPROM) cells. An intelligent programming technique allows each memory cell to store more than the usual one bit of information. An intelligent erasable algorithm prolongs the useful life of the memory cells. The input data comprising binary data to be stored are converted into multi-state data. A voltage of a level based on the converted multi-state data is applied to a source region to perform write operation to a memory transistor. As a result, the threshold voltage of the transistor is set to a value corresponding to the potential of the source region. In read operation a drain current generated in the memory transistor is detected and the multi-state data corresponding to the current are obtained. These multi-state data are converted into binary data to be outputted as output data [470]. (ii) Spintronic devices: Spintronics offers opportunities for a new generation of devices combining standard microelectronics with spin-dependent effects that arise from the interaction between spin of the carrier and the magnetic properties of the material. Recent experiments suggest that the storage time of quantum information encoded in electron spins may be extended through their strong interplay with nuclear spins in the solid state. Merging of electronics, photonics, and magnetics will ultimately lead to new spin-based multifunctional devices such as spin-FET (field effect transistor), spin-LED (light emitting diode), spin RTD (resonant tunneling device), optical switches operating at terahertz frequency, modulators, encoders, decoders, and quantum bits for quantum computation and communication [471].

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11.6. Other Applications (i) Polymer films: The direction of future developments in polymer dielectric film technology appears to increase in terms of the thermal stability and long-term electrical reliability. Recent advances in thin films have been proved in producing heat resistant materials better than bulk. Chemical stability may be improved by incorporating inorganic molecular units into the polymer structure. However, there is generally a trade-off between the desirable plastic properties of organic polymers and the chemical stability but brittle mechanical properties of inorganic materials (glasses, crystalline films, and ceramics). Thin dielectric films find their most useful potential employment in the fabrication of thin-film, hybrid, and monolithic integrated electronic circuits. At present, the most important application of thin polymer dielectrics are in capacitors, particularly in applications where a high capacitance per unit area (or unit volume) is desired. Another promising area for application of polymer dielectric films is in the fabrication of cryogenic thin-film circuits. The insulation requirements are particularly stringent in this case, since the dielectric layer must be very thin and uniform, and yet must withstand the stress imposed by differential thermal contraction upon cooling to the temperature of the cryogenic system, about 3 oK. Very thin polymer dielectric films may prove to be useful in fundamental investigations of the behavior of certain systems in very strong electric fields. (ii) Liquid crystals: Liquid crystal technology has a major effect on many areas of science, technology and engineering. a) Liquid Crystal Displays: Liquid crystals (LCs) have become extremely important in several key areas of flat panel displays and fiber-optic communication. With the development of multimedia liquid crystal displays (LCDs), a strong demand has been created for new liquid crystalline materials with clearing temperature, high dielectric anisotropy and low viscosity [472]. LC mixtures with a positive dielectric anisotropy are used for most active matrix displays and the image quality of liquid crystal displays is strongly dependent on the dielectric anisotropy of the liquid crystals. b) Liquid Crystal Thermometers: Special liquid crystal devices can be attached to the skin to show a map of temperatures. Physical problems, such as tumors, have a different temperature than the surrounding tissue. Liquid crystal temperature sensors can also be used to find bad connections on a circuit board by detecting the characteristic higher temperature. Examples of liquid crystal thermometers are aquarium thermometers, forehead thermometers, refrigerator thermometers, and urine specimen thermometers. c) Optical Imaging: LCs can also be explored is optical imaging and recording. In this technology, a liquid crystal cell is placed between two layers of photoconductor. Conductivity of the material increases when light is applied to the photoconductor, and this induces the development of an electric field in the liquid crystal corresponding to the intensity of the light. The electric pattern can be transmitted by an electrode, which enables the image to be recorded. This technology is still being developed and is one of the most promising areas of liquid crystal research.

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d) Other applications: LCs can be explored in many fields. Low molar mass liquid crystals have applications in erasable optical disks, full color electronic slides for computer-aided drawing (CAD), and light modulators for color electronic imaging. They can be useful for nondestructive mechanical testing of materials under stress, which can be used for the visualization of RF (radio frequency) waves in waveguides. (iii) Nanodielectrics: Nanodielectrics is the study of dielectric phenomena of nanoscopic materials having morphology of particles, sheets, wires and tubes etc [473]. In other words, nanodielectrics is a nanocomposite of specific interest in connection with its dielectric characteristics. Nowadays, a vast research on nanodielectrics is going on because of its potential application in energy storage and transducers. It has been realized that one-dimensional metallic nanostructures with localized electronic wave functions show giant dielectric constant. Most of the works on nanodielectrics are comprised of composite materials in which nano sized particles are embedded in insulating matrices [474, 475]. When the nanoparticles are introduced between the interfaces, the specific surface area becomes very large indeed. Because of their length scale and high specific surface area, nanoparticles exhibit novel properties as compared with bulk materials. As a consequence, material properties which depends on mechanisms taking place at the interfaces (involve an interaction zone) is also changed. Since the properties of this interaction zone is different from those of both the base polymer and the nanoparticle material, then, as the particle size is reduced, the material property is dominated by the interaction zone. Thus, the dielectric response of these composite materials is primarily controlled by the interface (which is a nanophase) between the particles and the matrix. Reproducible properties of a composite nanodielectric will require uniform distribution of the nanophase. Electro-deposited metal nanowires have been used to fabricate nanocapacitors. Saha et al. [476] have synthesized gold nanowires (serving as nanoelectrodes) which can be manipulated in between two microelectrodes by dielectrophoresis technique. When nanowires from the two microelectrodes during dielectrophoresis come very close to each other, a very high electric field acts between the wires. Therefore, the surface gold atoms may come out and get trapped at the interface. As a result the interface between the nanoelectrodes form a disordered phase with isolated gold atoms. It has been observed that from the variation of capacitance and the loss factor with frequency that the capacitance and loss factor remain constant over the frequency range 30 Hz to 1 MHz, which is due to wide distribution of relaxation times [477]. They found a very high value of permittivity at the interface between the wires, which may be attributed to the presence of gold atoms which increase the density of states at the interface. Therefore, by the use of novel properties of ultra fine metal particles, it is possible to fabricate nanodielectrics with giant permittivity values between two metal nanoelectrodes to form a nanocapacitor with ultra high capacitance and the loss factor can be controlled by tailoring the structures at the nanoscale level. A common feature of many nanodielectric systems is the behavior of the internal space charge build-up. For many nanodielectrics, the main dominant features are: (a) magnitude of the internal charge is much less for nanocomposites, (b) dynamics of

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R.N.P. Choudhary and S.K. Patri charge decay are much faster for nananocomposites, and (c) there is often a very different distribution of charge with nanocomposites. Principal interest shown for the synthesis of nanodielectrics is on insulating fillers, such as layered silicates (e.g., montmorillonite clay) and ceramic particles (e.g., TiO2 and SiO2), rather than conducting fillers such as graphite platelets and carbon nanotubes. Before making nanocomposites by a nano-filler into a host matrix, it is important to ensure good thermodynamic and chemical compatibility between the filler and the matrix. However, the conducting fillers have received much interest for use in mechanical applications, electromagnetic shielding and for the applications in which a degree of controlled electrical conductivity is required [478]. Nanocomposites with anisotropic electrical properties are desirable for improving partial discharge resistance of the ground wall insulation of rotating machinery. A promising development for high energy density storage materials comes in the form of metal nanoparticle-based composites, in which the confinement of electron wave functions are reported to yield massive permittivities, as high as 1010 [479-481]. Saha et al. [482] have used a completely different approach to create nanodielectric interfaces containing gold atoms between two nanoelectrodes to fabricate a nanocapacitor with an ultra high capacitance. The loss factor of the nanocapacitor can be controlled by tailoring the thickness and number of atoms present in the interface. The resulting nanocapacitors could have applications in energy storage, ultrasensitive transducers, nanoelectronic circuits, and also as high K materials in transistors. The high dielectric strength materials are attracting great interest at present for use in applications such as flexible, organic electronics, where it is necessary to optimize both the breakdown strength of the gate dielectrics and the electric field distribution in the device. Polymer nanocomposites have attracted much interest as a method of enhancing polymer properties and extending their utility. In polymer nanocomposites, chemically dissimilar components are combined at the nanometer scale. The stronger interactions between the polymer and nanoparticles of nanocomposites produce markedly improved materials with better electrical, mechanical, thermal, and rheological performances than conventional microparticulate filled polymer composites. The dielectric properties of polymer composites are affected by (i) the nature of the polymer matrix and filler, (ii) the properties of their interface, (iii) the dispersion of the fillers, filler-filler and fillermatrix interactions [481]. Dielectric spectroscopy of nanodielectrics also explains the significance of reduced particle size and material packing density. At low frequencies, particle surface state effects dominate and the applied electrical energy is stored on the surfaces. This induces surface polarization effects that are normally considered in nanodielectric technology. As the size of the particles is reduced, the surface polarization effects intensify and extend their frequency range towards the higher frequency regions. Dervos et al. [481] have studied the change in effective permittivity of an inorganic solid insulator, when it is ground to form fine powders of equidimensional (i.e., almost spherical) particles ranging from micro-crystalline towards nanocrystalline, i.e., CaCO3 having voids filled with air and the other being the CaCO3 powder produced out of a high quality marble. It was observed that solid calcite mineral exhibits stable dielectric response independent of frequency; its powders

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have properties depending on both the grain size and the packing density. At high frequencies, the relative dielectric constant values determined by the packing density, while at low frequencies the powder dielectrics shows a relaxation, which may be attributed to slow surface polarization mechanisms. Loss currents of powders increase exponentially towards low frequencies. The higher values of loss current for finer powder samples implying that the surfaces may control the overall conductivity. In the long run, with the improving of understanding of dielectric physics at nanoscale, nanostructured dielectric materials or devices could be engineered with many novel dielectric properties and wide applications in energy storage, electrooptic, electrostrictive, and insulating areas. The future of the field of nanodielectrics is thus exciting. Through fundamental understanding of the interface, we can design nanodielectrics with tailored properties and eventually introduce materials that react to the environment in a controlled way. (iv) Low-k dielectrics: A low- k dielectric is an insulating material that exhibits weak polarization when subjected to an electric field. The low-k dielectric materials have a dielectric constant k less than that of SiO2 (3.9). Some oxide dielectrics, organic materials and highly porous oxides with low dielectric constant (i.e., low-k) are useful in VLSI technology, especially high performance logic devices etc. This material is also used to insulate adjacent metal lines (Inter Layer Dielectric, ILD) in advanced CMOS devices using Cu technology. The use of low-k material reduces capacitive coupling – sometimes referred to “cross talk” between metal lines. The common low-k materials used today are classified as following: a) Si Based (with organic constituents) 1. HSQ (JSR’s hydroxl silsequioxane) 2. Black diamond (Applied Materials) 3. Coral (Novellus) b) Non-Si based (Polymers or amorphous carbon) 1. Silk (dow) 2. Flare A new class of low-k (ranging 2.1 to 2.5) dielectric material based on fluorinated polymer technology has been developed [483] by excellent processabilities such as etching, adhesion, stacking and planarization capability of the thermally stable fluorinated material, PSI polymer. The electric properties of this material, useful for advanced microwave and RF devices, have high density interconnect structures to improve device performance and reducing manufacturing costs. Among various candidates for low-k materials with a dielectric constant of 2.0–3.0, refractory Si–C–N nanocomposites are very promising because of their low dielectric constant and high hardness, and other excellent functional properties, such as superplasticity, high strength, enhanced oxidation, and corrosion resistance. Porous low-k dielectric materials have applications in air-gap technology, to by-pass the interim phase of porous dielectrics by introducing air-gaps between interconnect levels. However, efforts are been made from an industry-wide frustration with the failure of low-k dielectric materials to meet the many and various stringent demands. So search of ultra-low-k materials is going on to develop novel approaches to overcome these integration and reliability issues. The diamond-like carbon films can be used for fabrication of optical components. The films are also used as wear and

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corrosion protective coatings of magnetic, mechanical, electrical and optical devices, and for fabrication of optical components. They are the potential candidates for application in passive electrical devices [484]. Patterns with well-defined rectangular profiles can be obtained using anisotropic etching in combination with hard masks of SiO2 or Al [485]. In combination with the IR transparency of the films, this enables the recording of IR diffractive optical components with good control of surface and pattern quality.

12. Conclusion

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In reviewing the growth, development and properties of dielectrics, it is worth discussing the issues of creating new materials and understanding the origin of the properties shown in presence of external stimuli. Beginning with a brief summary of the history of the dielectric materials, this review focuses on the chronological development and recent works with possible future applications. At present, the broad class of dielectrics (i.e., linear, non-linear ferroelectrics, piezoelectric, pyroelectric, low-k dielectrics, nanodielectric, liquid crystals, polymers etc.) become interesting from the point of view of its diverse applications such as capacitors, actuators, sensors, transducers, pyroelectric detectors, light valves, electro-optical modulators, memory and display devices, communication devices, filters, thermistors, multifunctional and spintronics devices. Though a large number of dielectrics and its related materials are known today, a continued research is still going in search of new materials and/or compositions (of known materials) with the fascinating intriguing features in different forms (single crystals, ceramics, thin films and composites). To realize the presence of different properties in a single material at normal conditions, some new materials have been developed, known as functional materials for multifunctional applications. Nowadays attempts are made to understand the coupling mechanism of electric and magnetic orders, which is really the most challenging task of today.

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[430] Pradhan, D.K.; Samantaray, B.K.; Choudhary, R.N.P.; Thakur, A.K. J. Power Sources 2005, vol, 139, 384.. [431] Ederer, C.; Spaldin, N.A. Phys. Rev. B 2005, vol, 71, 224103. [432] Zalesskii, A.V.; Frolov, A.A.; Khimich, T.A.; Bush, A.A. Phys. Solid State 2003, vol, 45, 141. [433] Zhang, S.T.; Pang, L.H.; Zhang, Y.; Lu, M.H.; Chen, Y.F. J. Appl. Phys. 2006, vol, 100, 114108. [434] Kadomtseva, A.M.; Popov, Y.F.; Pyatakov, A.P.; Vorob’ev, G.P.; Zvezdin, A.K.; Viiehland, D. Phase Transit. 2006, vol, 79, 1019. [435] Mishra, R.K.; Pradhan, D.K.; Choudhary, R .N. P.; Banerjee, A J. Phys.: Condens. Matter 2008, vol, 20, 045218. [436] Bokov, V.A.; Myl’nikov, I.E.; Smolensikii, G.A. Sov. Phys., Usp. 1961, vol, 42, 643. [437] Mohan, D.; Prasad, R.; Banerjee, S. J. Am. Ceram. Soc. 2001, vol, 84, 2126. [438] Palkar, V. R ; Johnand, J.; Pinto, R. Appl. Phys. Lett. 2002, vol, 80, 1628. [439] Yoon, S.H.; Kim, H. J. Eur. Ceram. Soc. 2002, vol, 22, 689. [440] Hong, S.H.; Trolier-McKinstry, S.; Messing, G.L. J. Mater. Sci. Lett. 2000, vol, 19, 1661. [441] Singh, M.P.; Prellier, W.; Simon, C., Raveau, B. Appl. Phys. Lett. 2005, vol, 87, 022505. [442] Mizokawa, T.; Khomskii, D.I.; Sawatzky, G.A. Phys. Rev. B 1999, vol, 60, 7309. [443] Pilgrims, S.M.; Suther, A.E.; Winzer, S.R. J. Am. Ceram. Soc. 1990, vol, 73, 3122. [444] Ederer, C.; Spaldin, N.A. Phys. Rev. B 2005, vol, 95, 257601. [445] Varshney, D.; Choudhary, R.N.P.; Rinaldi, C.; Katiyar, R.S. Appl. Phys. A 2007, vol, 89, 793. [446] Hill, N. A.; Filippetti, A.; J. Magn. Magn. Mater. 2002, vol, 976, 242. [447] Hill, N. A. J. Phys. Chem. B 2000, vol, 104, 6694. [448] Fiebig, M. J. Phys. D: Appl. Phys. 2005, vol, 38, R123. [449] Jun, S.G.; Kim, N. K.; Kim, J. J.; Cho, S. H. Mat. lett. 1998, vol, 34, 336. [450] Erenstein, W.; Mathur, N. D.; Scott, J. F. Nature 2006, vol, 442, 759. [451] Moskvin, A S.; Pisarev, R V Phys. Rev. B 2008, vol, 77, 060102. [452] Ananta, S.; Thomas, N.W. J. Euro. Ceram. Soc. 1999, vol, 19, 155. [453] Smolenskii, G. A.; Yudin V. M. Sov. Phys.— Solid State 1965, vol, 6, 2936. [454] Smolenskii, G. A.; Agranovskaia, A. I.; Isupov, V. A. Sov. Phys.—Solid State 1959, vol, 1, 907. [455] Smolenskii, G. A.; Agranovskaya, A. I. Sov. Phys.—Solid State 1960, vol, 1, 1429. [456] Astov, D. N.; Al’shin, B. I., Zorin, R. V.; Drobyshev, L. A . Zh. Eksp. Teor. Fiz. 1968, vol, 55, 2122. [457] Mishra, R.K.; Choudhary, R. N. P; Banerjee, A. J. Phys.: Condens. Matter, 2008, vol, 20, 345212. [458] Cullity, B. D. Introduction to Magnetic Materials; MA: Addison-Wesley, 1972. [459] Shin, H. S.; Lee, J. E.; Nam,Y.S., Ju, H. L.; Park, C.W. Solid State Commun. 2001, vol, 118, 377. [460] Nair, S.; Banerjee, A.; Narlikar, A. V. Phys. Rev. B 2003, vol, 68, 132404. [461] Arrott, A. Phys. Rev. 1957, vol, 108, 1394. [462] Lee, J.H.; Choi, J.S.; Hong, S.; Hwang, I.; Kim, Y.; Ahn, S.J.; Kang, S.O.; Park, B.H. Jpn. J. Appl. Phys. 2007, vol, 46, 6202.

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[463] Taylor, G.W.; Gagnepain, J.J.; Meeker, T.R.; Nakamura, T.; Shuvalov, L.A. Piezoelctrcity; Gordon and Breach Science Publishers: USA, 1992. [464] Kao, K.C. Dielectric phenomena in solids; Elsevier academic press: Amsterdam, 2004. [465] Scott, J. F. Nat. Mat. 2007, vol, 6, 256. [466] Baudrant, A.; Vial, H.; Daval, J. J. Cryst. Growth, 1978, vol, 43, 197. [467] Miyazawa, S.; Uchida, N. Opt. Quant. Elect. 1975, vol, 7, 1. [468] Land, C. E. J. Am. Ceram Soc., 1989, vol, 72, 2059. [469] Swartz, S. L. IEEE Trans.Electrical Insul. 1990, vol, 25, 935. [470] http://www.freepatentsonline.com [471] Wolf, S. A.; Awschalom, D. D.; Buhrman, R. A.; Daughton, J. M.; von Molna, S.; Roukes, M. L.; Chtchelkanova, A. Y.; Treger, D. M. Sci. 2001, vol, 294, 1488. [472] Yakuphanoglu, F.; Okutan, M.; Koysal, O.; Ahn, S.-M.; Keum, S.R.Dyes and Pigments 2008, vol, 76, 721. [473] Lewis, TJ. IEEE Trans. Dielectr. Electr. Insul 1994, vol, 1, 812. [474] Chang, S.; Doremus, R. H.; Ajayan, P. M.; Siegel, R. W. Ceram. Eng. Sci. Proc. 2000, vol, 21, 653. [475] Mukherjee, P. K.; Chakravorty, D. J. Mater. Res. 2002, vol, 17, 3127. [476] Saha, S. K.; Chakravorty, D. Appl. Phys. Lett. 2006, vol, 89, 043117. [477] Saha, S. K.; Bull. Mater. Sci.2008, vol, 31, 473. [478] Jou, W. S.; Cheng, H. Z.; Hsu, C.F. J. Alloys & Comp., 2007, vol, 434, 641. [479] Saha, S. K. Phys. Rev. B. 2004, vol, 69, 125416. [480] Zhang, C.; Stevens, G. C.; IEEE Trans. Diel. Electrical Insulation 2008, vol, 15, 178. [481] Dervos, C.T.; Mergos, J.A.; Iosifides, A.A. Mat. Lett. 2005, vol, 59, 2042. [482] Saha, S.K.; DaSilva, M.; Hang, Q.; Sands, T.; Janes, D.B. Nanotech. 2006, vol, 17, 2284. [483] Ito, M.; Tsuruoka, K.; Yokotsuka, S. IEEE CPMT TC-6 Small Workshop in conjunction with 54th ECTC, 2004. [484] Grill, A. Thin Solid Films 1999, vol, 355, 189. [485] Grill, A.; Patel, V. Diam. Rel. Mater. 1994, vol, 4, 62.

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Chapter 3

UNDERSTANDING THE IMPACT OF HIGH-K GATE AND SPACER DIELECTRICS ON THE DEVICE AND CIRCUIT PERFORMANCE OF NANOSCALE MOSFETS C.R. Manoj, Angada Sachid and V. Ramgopal Rao* Centre for Nanoelectronics, Department of Electrical Engineering, Indian Institute of Technology Bombay, India

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Introduction As the thickness of the SiO2 layer used for the gate dielectric becomes thinner, the gate leakage current due to direct tunneling becomes very high, exceeding 1 A/cm2 at high gate bias conditions as shown in Fig.1. Hence the circuit power dissipation will increase to alarmingly high values [1]. In addition, it becomes increasingly difficult to fabricate thin dielectric films with high uniformity. Also, the reliability of SiO2 films is a serious concern for very thin films. All these reasons prompted the search for a high-k gate dielectric to replace the SiO2 as a gate dielectric. Higher dielectric constant (permittivity) K material generally uses a larger physical thickness compared to the SiO2 layer. Since the K value is large, even with a higher physical dielectric thickness (Tphy) one can achieve the same gate capacitance thus avoiding the direct tunneling current. However there are many challenges for high-K to be used as gate dielectric. Some important challenges among these are (a) the ability to continue scaling to lower effective oxide thickness (EOT) (b) the loss of carrier mobility in Si when using high K oxides (c) degradation in the short channel performance due to fringing field effects and (d) the instabilities caused by the high concentration of electronic defects in the oxides [2].

*

E-mail address: [email protected]

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Figure 1(a). Gate leakage current vs. voltage for different thicknesses of SiO2 layer [1]

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Figure 1(b). Scaling of physical gate length and oxide thickness [2]

The typical qualities required for a good high-K insulator includes the following: a. It must have a high enough K that it will be used for a reasonable number of years of scaling. However very large K values are usually not preferred as they have lower band offset and also cause large fringing fields [2]. b. The dielectric is in direct contact with the Si channel, so it must be thermodynamically stable. If the material is not thermodynamically stable, it can react with Si and form a silicide which will increase the EOT and negate the impact of scaling. c. The high-k material must be kinetically stable, and should be compatible with very high processing temperatures (~ 1000 ◦C) still retaining the amorphous nature. d. It must have a large enough band offset with Si (well over 1 eV) to minimize the carrier injection into its bands, failing which will lead to degradation in the reliability and leakage. e. It must form a good electrical interface with Si and also must have fewer electrically active defects. Further, there are published reports recently which show that use of high-k as a spacer material is also an interesting option from the device scaling point of view. This chapter

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reviews the impact of high-K dielectric integration as a gate- and spacer-material for nano scale MOSFETs and discusses the impact of high-k devices on the circuit performance.

1. Impact of High-K Gate Dielectric on Device Performance

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1.1. Fringe Induced Barrier Lowering (FIBL) Since physical gate dielectric thickness in high-K dielectric is larger than that of the equivalent SiO2 case, it becomes increasingly difficult to confine all the electric field lines just below the gate electrode. Due to the higher physical thickness, some field lines diverge out from the gate electrode and end up in the S/D extension regions. Also with larger Tphy, fringing of the electric fields from source/drain regions into channel can induce lowering of the potential barrier thereby causing lower threshold voltage and increased sub-threshold swing and Ioff. This was reported by Yeap & Krishnan [3] through 2D device simulations. They have termed this phenomenon as Fringe Induced Barrier Lowering (FIBL), which is a problem only for high-K dielectric devices with large Tphy They report that for K > 25, FIBL can be very severe that Ioff can shoot up to unacceptably large values. They also proposed that a buffer SiO2 of 0.75 nm between high-K and Si interface can significantly reduce the FIBL for K < 25 and partially reduce for K > 25. Cheng et al [4] have carried out extensive 2D device simulations and have reported the effect of high-K dielectric in planar devices. They have considered a device with Lg = 70 nm with effective oxide thickness (EOT) of 1 & 1.5 nm, with K value ranging from 3.9 to 200. Here they keep the physical thickness such that the effective Cox remains the same. (i.e. using the rule Tphy = T SiO2 * (K/3.9)). Fig 2(a) shows that as K value increases, Vt roll-off degrades significantly causing sub threshold slope also to increase. Fig 2(b) also shows that degradation is more severe when the physical thickness approaches closer to the gate length value. By examining the 2D simulation field contours, they had shown that, it is the presence of fringing fields from the gate to source/drain regions that cause the SCE degradation. They also showed that a gate stack (double layer structure) comprising a very thin layer of SiO2 and high K material can be a good approach to control the degradation due to high-K dielectric. How ever, a double layer with high-K in the bottom and SiO2 on top will give an adverse effect because the top lower-K dielectric will only help to further diverge the fringe fields in high-K stack. This was shown as a significant problem for high-K and polysilicon gate combination. Polysilicon is known to further react with high-K and form a silicide, which makes the polysilicon technology incompatible with high-k in many cases. How ever, instead of keeping the EOT same, one may keep the Tphy same (i.e 5 nm) for both High-K and SiO2 case. Results in Fig. 3(a) show that the Ion/C (a measure of its delay) is not uniform among all values of K. This is counter intuitive since higher K (i.e higher Cox) will give as high Ion as Cox and hence Ion/C should not be affected. How ever, in reality, the higher vertical field at the interface (for higher K) values would cause (i) more inversion level quantization enhancing the Cox and (ii) higher mobility degradation. This points to the requirement for optimizing the high transverse field at high-K and channel interface which otherwise would negate the advantages of use of high-K for high performance applications.

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Figure 2(a). Vt roll off & subthreshold swing degradation as function of increasing dielectric constant value K (with EOT being the same for all K values). [4]

Figure 2(b). Vt roll off & subthreshold swing degradation as function of ratio of physical oxide thickness to channel length, corresponding to the different dielectric constants considered in [4]

Figure 3(a). Variation of Idsat/Cgate on the dielectric constant with physical oxide thickness kept same (5 nm) for all K values. [4] Recent Advances in Dielectric Materials, Nova Science Publishers, Incorporated, 2009. ProQuest Ebook Central,

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Figure 3(b). Schematic showing the increased coupling of the drain electric field through the high dielectric constant alternate path. [5]

Figure 4(a). Doping profiles such as conventional (CON), Lateral Asymmetric Channel (LAC), Double Halo (DH) considered for high-K study in [5].

Figure 4(b). Impact of various channel engineering methods on the DIBL for increasing value of K (EOT being the same) [5].

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Nihar et al [5] have studied in detail the FIBL effect in nano-scale MOSFETs. They showed that for Kgate > KSi (i.e 3.9), there is a significant electro static coupling between the source and drain through the thicker and high-K gate dielectric region. This fact was further validated with extensive device simulations with different channel lengths and junction overlap lengths. They have also evaluated the impact of various channel engineering methods proposed for sub 100 nm MOSFETs such as Lateral Asymmetric Channel (LAC) and Double Halo (DH) etc [6] and have concluded that irrespective of the kind of channel engineering employed, FIBL effect was observed in high-K devices.

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Figure 5(a). Variation in outer fringing capacitance to K value as a function of various dielectric values for the spacer dielectric for Lg = 70nm device [7].

Figure 5(b). Dependence of inner fringing capacitance and surface potential to K value for Lg = 70nm device [7].

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Nihar et al [7] have further studied the high-k integration issues using a highly accurate Monte Carlo based 3D capacitance extractor. They have showed that (see Fig. 5(a)) high-K integration will cause a decrease in the outer fringe capacitance and gate to channel coupling capacitance. Although they showed that the reduction in outer fringe capacitance is beneficial to the circuit performance, the reduction in gate to channel capacitance coupled with an increase in the inner fringe capacitance, actually degrades the short channel performance. Through calibrated mixed mode device simulations, it has been shown that the DC performance parameters of inverters such as the static noise margin (SNM) will get degraded owing to the degradation in Vt with increasing value of K. The transient performance of highK inverters was also studied for iso-Ioff conditions such as 10, 1, 0.1 nA/μm by increasing the value of the substrate doping to adjust for the Vt degradation caused by high-K dielectrics. The results showed that the performance peaks at a value of K = 25. This is because of the higher substrate doping used for higher K values, which will increase the mobility degradation and cause the delay to increase beyond K=25. Nihar et al [8] have also developed circuit models for the parasitic capacitances in high-K gate dielectric transistors by taking into account the presence of source/drain contact plugs. The accuracy of these models was tested by comparing the modeled results with the results obtained from three-dimensional (3-D) Monte-Carlo simulations and two-dimensional (2-D) device simulations over a wide range of channel length and oxide thickness values.

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1.2. Impact of S/D Junction Overlap (Lov) on the FIBL Most of the investigations performed to understand the effect of FIBL were on channel length above 50 nm, where the overlap length (Lov) also will be significant. The reported results have shown several orders of magnitude increase in Ioff due to FIBL. How ever, it is now clear that the high K dielectrics will not be introduced before the 45-nm technology node. Tsui et al [9] have studied FIBL in detail for a device with Lg = 25 nm and have concluded that S/D overlap length is the most critical factor for controlling the FIBL. Since the main fringing field resulting in barrier lowering originates from the gate/drain (G/D) overlap region, they proposed FIBL should be highly sensitive to the length of the overlap region (Lov). They simulated Lg = 25 nm device with a Lov =1 nm and a longer device with Lg = 50 nm with Lov = 13.5 nm. Comparison of Ioff of these two devices showed that the latter case showed one order higher degradation in Ioff despite being a longer channel device. So they concluded that scaling down of Lov in shorter channel devices will be quite helpful to bring FIBL well under control in high-K devices. The significance of Lov on the Ioff degradation is shown in Fig. 6(a). They have concluded that the decrease in the overlap length (Lov) for future generations is one way to bring the FIBL phenomenon under control. Source-side barrier effects with very high-K dielectrics in 50 nm Si MOSFETs have been studied by Kencke et al [10]. In this study, they examined both ON and OFF-state drain current with very high-K gate insulators and sidewall spacers. They showed that for short channel length such as 50 nm, even with zero drain bias there is sufficient increase in the leakage current and is due to the effect termed as ZIBL (zero induced barrier lowering), which is present due to built in potential itself getting coupled to the channel through high-K material. They showed that out of the total leakage current increase due to the typical FIBL phenomenon (i.e at large drain biases), ZIBL also has a significant contribution. They also

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showed that in high-K spacer devices, a phenomenon called FIBS (Fringe Induced Barrier Shielding) can cause a lowering in the ON current Ion, although the net effect in Ion will be due to all effects such as FIBL, ZIBL and FIBS, among which FIBL is the dominant factor. In a comparative study among different types of devices (such as Kgate-Ksp combinations of SiO2- SiO2, High-K - SiO2, High-K-High-K etc), they showed that Ion/Ioff ratio is always poor for high-K gate and high-K spacer combination devices, when compared to the virgin device with gate-spacer combination of SiO2- SiO2.

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Figure 6(a). Plot showing the significance of overlap length Lov on the FIBL effect. [9]. Minimizing the Lov can minimize FIBL effect. [9]

Figure 6(b). Plot showing the optimum K value for double gate FETs/ FinFETs, from the performance perspective [11].

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1.3. Impact of high-K on Novel Device Structures The impact of high-K on double gate (DG) FETs/ FinFETs was studied by Manoj & Rao [11]. They have performed the study for shorter channel length (Lg = 32 nm) non-planar structures. From the SCEs and device parasitics trends, they had concluded that the fringing effects may be severe even if channel is controlled by two gates. For the purpose of performance comparison of high-K FinFETs with a range of K values (with EOT being the same and for iso-Ioff condition) they have used different options (such as increasing fin doping, adjusting the gate work function and trimming the fin width) to maintain iso-Ioff condition for the different high-K devices. Their simulations showed that use of fin doping/gate work function adjustment gives rise to an optimum K which is much smaller that what was reported for the planar MOSFETs. Fin width adjustment approach gives rise to an optimum K value better than the other two approaches although fin width scaling is a processing challenge. They have showed that an optimum value of K can be extended to what is achievable in planar devices by means of fin width scaling, as shown in Fig. 6(b). Most of the work on high-K FETs was done on the conventional type of overlapped S/D junction devices. How ever, with channel length getting aggressively scaled, there are reports of non-overlapped devices (under lap) using multi gate technology. Kranti et al [12] have studied in detail, the impact of high-K gate dielectrics on double gate devices at Lg = 25 nm and proposed possible device engineering issues for high-K integration in double gate FETs. They have used a device structure as shown in Fig. 7(a) where the S/D junctions are assumed to be away from the gate edge. They have proposed a 2D analytical model for the short channel effects in DGFETs with high-K gate dielectrics and the impact of various short channel device matrices such as DIBL, sub threshold swing (SS) etc have been investigated using the S/D extension geometry parameters such as (i) lateral source/drain doping gradient (d) (ii) spacer width (s) and (iii) spacer to gradient ratio (s/d). For a gate length of Lg = 25 nm, they have considered the geometry parameters ‘s’ varying from 25% to 100% of Lg and ‘d’ varying from 1 nm/decade to 6 nm/decade. Fig. 7(b) shows the Vt degradation of high-K DGFET as a function of lateral doping gradient (d), for a given fin width Tsi=0.4Lg, for different K values ranging from 3.9 to 35. Plots (a) (b) (c) and (d) are in the increasing order of K value such as 3.9, 10, 25 and 35 respectively. In each of the plots, the spacer width of has been varied from 25% to 100% of Lg at equidistant steps. From the Fig. 7(b) it is clear that Vt roll off is higher for a higher value of ‘d’, for a given K and ‘s’ value, which is true because with a higher the value of ‘d’, the junctions will be closer to the gate edge. Also, one can notice that the Vt roll off aggravates for a higher value of K as has been reported earlier. How ever, the important point here is that, excessive Vt roll off due to high-K integration can be significantly improved by using large value of spacer length ‘s’ for a given lateral doping gradient (LDG) ‘d’ value. They conclude that even for aggressively scaled down (sub 20 nm ) high-K devices the ratio of spacer length to LDG (s/d) can be increased to get the same short channel immunity as obtained by a longer channel device.

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Figure 7(a). Double gate FET structure considered for simulation study in [12] showing the underlap spacer.

Figure 7(b). Variation in threshold voltage as function of LDG (d) and spacer length (s). Here symbols ◊ Ο ∆ corresponds to s = 0.25, 0.50 , 0.75 and 1.0 times Lg respectively [12].

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2. Impact of High-K Gate Dielectric on Circuit Performance 2.1. Effect of Charge Trapping in High-K on Circuit Performance Effect of charge trapping in high-k gate dielectric devices on ring oscillator circuit and its comparison with SiO2 devices was reported by Knag et al [13]. They showed that at high Vdd regime, the propagation delay for high-k devices was slightly better than the equivalent SiO2 devices. On the other hand, at low Vdd regime, high-k devices showed a higher propagation delay compared to the SiO2 devices. Thus they showed that the performance of high-k device is improved significantly in case of the high-speed circuits [13]. Fig 8(a) shows the variation of propagation delay as a function of Vdd, both for high-K and SiO2 devices. It can be seen that for lower Vdd value high-K delay is increasing from SiO2 case, due to the presence of charge trapping in high-K. How ever, at a higher Vdd, the delay of high-K is dramatically improved because of the lower charge trapping at higher Vdd. Since these results were obtained for RO circuits, effect of signal shape and frequency on the delay could not be studied. So the study was extended to inverter structures. They showed that for the same input signal (say Vin=Vdd for inverter), the output fall time (tfall) for high-K devices was longer than that of SiO2 devices. This also validated the charge trapping effect in high-K devices. To confirm the dependence of this trapping over frequency, the measurements were taken for SiO2 and high-K device inverter for a range of frequencies. The delay for SiO2 devices was found independent of frequencies where as high-K devices showed an increase with lowering the frequency which in turn confirmed the Vt increase due to charge trapping in high-K devices at lower frequencies.

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2.2. Effect of Leakage in High-K Devices on the Circuit Performance Vinay et al [14] had studied the circuit performance issues of high-K gate dielectric MOSFETs using the Look-up Table (LUT) approach. In the LUT approach, they approximate the behavior of a given device using finite number of table points with a suitable interpolation algorithm. The table points were obtained from device simulations. They showed that the frequency of oscillations (in a ring oscillator, the case they considered) increases with increase in K value, due to lesser outer fringe capacitance and increased Ion due to increased SCEs (as EOT was kept same for a meaningful comparison). To study the effect of subthreshold leakage currents on the circuit performance, they considered a dynamic logic circuit. Here the output was charged to Vdd and in the evaluation phase (when φ=1) the output voltage is determined by the combination of inputs. Initially, the output voltage of the 2- input dynamic NAND gate was pre-charged to Vdd and then kept the gate in evaluation phase for a long time with both inputs grounded. Ideally the output voltage should remain at logic 1. But due to leakage currents, this charge gradually leaks away resulting eventually in malfunctioning of the gate. They showed that with increase in the value of K, this problem becomes more severe. They also showed that in dynamic NOR gates this problem is even more enhanced due to parallel combination of the evaluation transistors.

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Figure 8(a). Plot showing the variation of delay as a function of Vdd for high-K & SiO2 dielectric. Note that in lower Vdd, regime, high-k device shows longer propagation delay. However, with the increase of Vdd, the high-k circuit shows a smaller delay. This suggests that the charge trapping effect in high-k dielectrics is decreased for higher switching speeds [13].

Figure 8(b). Pull-down characteristics of SiO2 and high-k. For the same gate input signal, high-k devices shows higher delay due to the charge trapping and higher threshold voltage [13].

Figure 9(a). Schematic of a high-K dielectric based Domino logic gate simulated in [14].

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Figure 9(b). Output voltage of the high-K domino logic gate simulated in [14] vs time for different high-K ate dielectrics values. Note the higher discharge rate for higher K values.

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3. Effect of High-K Spacers on Nanoscale CMOS Devices Scaling into the sub-100 nm regime has necessitated the use of source-drain extensions (SDE). For better gate control over the channel and for lower short-channel effects (SCE), ultra shallow junctions are required. The depth of the shallow junction is decided by a tradeoff between SCE and SDE resistance (RSD) due to the shallow junctions. SDEs are formed using an offset spacer. The thickness of the offset spacer is a trade-off between the shortchannel effects caused by lateral diffusion of impurity atoms and series resistance due to ultra-shallow junctions. Lateral diffusion is a greater problem in p-MOSFETs due to the higher diffusivities of boron. Hence, in p-MOSFETs, a thicker spacer is used to minimize lateral diffusion. For better short-channel control and higher drain field reliability, the doping in the SDE region is lower than the highly-doped source/drain (HDD) regions. A longer shallow junction with low doping increases the series RSD thereby decreasing the ON-current (ION). To simultaneously achieve better short-channel control and higher ION, the use of a high-K offset spacer was proposed. Use of high-K offset spacer increases the outer fringe capacitance. The stronger fringe fields from the gate cause a stronger inversion in SDE decreasing the RSD. Higher fringe capacitance increases Cgs and Cgd. This affects the AC performance of the device. An optimization strategy in which the increase in ION due to decrease in RSD happens at a higher rate than the increase in Cgs and Cgd is useful in decreasing the delay of circuits [16].

3.1. Demonstration of High-K Offset Spacers in MOSFETs For channel lengths (LG) greater than 30 nm, overlapped, shallow-junction SDE structures with relatively lower doping than the HDD regions are used. Here, the higher RSD is due to the shallow junctions and the lower doping. Using TCAD simulations, it was shown that the incorporation of high-K offset spacer with K = 25 in these devices lowers the RSD by about

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18% and increases ION by about 40% when compared to using SiO2 offset spacers [17]. For SiN offset spacers, ION increased by about 16% when compared to SiO2 offset spacers. Experimentally, in the same work it was shown that fabricated p-MOSFETs with SiN offset spacer showed a 15% increase in ION at equal IOFF when compared to SiO2 offset spacers. There is a good match between the simulated results and the experimental data. Hence, the prediction for the increase in ION by 40% when compared to SiO2 offset spacers using K=25 offset spacers seems fair. However, this work did not look into the dynamic performance of circuits. Recently, 32 nm MOSFETs with high-K offset spacers were demonstrated by Miyashita et al [16]. They reported a 10% increase in linear current for n-MOSFETs and a 7% increase for p-MOSFETs using high-K offset spacer when compared to SiO2 offset spacers. The fringe-capacitance using high-K offset spacer was about 10% higher than that using SiO2 offset spacers. It was reported that the circuit delay decreased by about 6% by using high-K offset spacers.

Figure 10 (b). Simulated data of normalized gate delay and parasitic capacitance versus dielectric constant of the spacer [17].

Figure 10 (a). Simulated data of normalized ION and Rext data versus dielectric constant of the spacer [17].

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Figure 11 (a). High-Epsilon Offset Spacer (HEOS) impact on linear characteristics both for NFET and PFET under matched-VTH condition [16].

Figure 11 (b). Comparison of Cov (overlap and fringe capacitance) between conventional SiO2 offset spacer and HEOS, and its impact on AC delay [16].

3.2. Effect of High-K Spacers on ON- and OFF-Current in Overlapped MOSFETs A detailed study on the effect of high-K spacers on overlapped LDD MOSFETs was conducted by Ma et al [15]. The device parameters of interest were ION, OFF-current (IOFF) and subthreshold swing (S). When the device is in the OFF-state, i.e. VGS = 0 V and VDS = VDD, there is an electric field coupling from the drain to the gate and from the gate to the source region. Due to this, the electric field in the SDE region on the drain side is lowered. This raises the source potential and lowers the drain potential resulting in a decrease in IOFF. When the transistor is in the ON-state, the fringe-field from the gate to the source and drain lowers the resistance of the SDE increasing the ION. The decrease in IOFF and increase in ION increases the ION/IOFF ratio of the transistor.

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Figure 12. (a) SOI device structure and (b) vertical channel electric field with different offset spacer dielectrics at OFF (VGS = 0 V and VDS = 1.0 V) and ON-state (VGS = 1.0 V and VDS = 1.0 V) respectively [15].

Figure 13 (a). Surface potential with different SiO2 and TiO2 spacer dielectrics at OFF-state (VGS = 0 V and VDS = 1.0 V) [15].

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Figure 13 (b). Current ratio of OFF-state leakage ION/IOFF (K = 3.9), and ON-OFF state ION/IOFF of SOI devices with different offset spacer dielectrics and supply voltages [15].

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3.3. Effect of High-K Spacer on VTH Roll-Off in Overlapped MOSFETs Introduction of high-K gate dielectric introduces the fringing-field effect due to the large physical thickness of the gate dielectric to maintain the same effective oxide thickness (EOT). The fringing field effect decreases the threshold voltage (VTH) of a MOSFET. The introduction of high-K spacers enhances the fringing-field effect. Hence, the VTH roll-off in MOSFETs with high-K spacers increases with the increase in the dielectric constant of the spacer [19].

Figure 14. Schematic diagram of a high-K gate dielectric MOSFET with fringing-field lines, where O is the origin of (x, y) system [19].

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Figure 15 (a). Comparison between the model and 2-D device simulation on threshold voltage versus gate dielectric constant [19]

Figure 15 (b). Dependence of threshold voltage roll-off on permittivity (K1) of spacer [19]

3.4. Effect of High-K Spacer on GIDL Current in Overlapped MOSFETs Introduction of high-K gate oxide with lower-K spacers increases the gate-induced drain leakage (GIDL) current in planar MOSFETs with the increase in the dielectric constant of the oxide [18]. This is due to the electric field crowding at the high-K gate oxide and low-K

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spacer interface which is in contact with the LDD region. With the increase in the dielectric constant of the gate oxide, the electric field crowding increases and GIDL current increases. If the gate oxide is spread over the LDD regions, then the electric field spreads over a larger distance, thereby decreasing the peak electric field. This reduces the GIDL current. One technique to achieve a high-K oxide over the LDD regions is to incorporate high-K spacers in the device. Thus, introduction of high-K spacers helps in reducing the GIDL current in deep sub-micron (DSM) MOSFETs.

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Figure 16. Different device schemes with high-K dielectrics.

Figure 17. GIDL current at VGS = -1 V and VDS = 1.5 V as a function of dielectric constant of the spacer (εr) [18].

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Figure 18. Vertical electric field contours under the gate and the drain-side spacer at VGS = -1 V and VDS = 1.5 V: (a) types A and B (dashed line) with εr = 39 (b) type B with εr = 3.9 and 39 [18].

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3.5. Effect of High-K Spacer in Non-Overlapped MOSFETs For sub-30 nm MOSFETs, a non-overlapped source/drain doping profile is an interesting technology option to continue scaling. The source and drain regions are separated by a larger distance than their overlapped counterparts. The short-channel performance parameters like S, VTH roll-off and drain-induced barrier lowering (DIBL) of the non-overlapped structures is better than the overlapped structures. In the non-overlapped structures, due to the undoped region in the SDE, RSD is high. The electron density in the underlap regions is low.

Figure 19 (a). ON-current, gate capacitance, and intrinsic gate delay time of non-overlapped MOS device versus dielectric constant with a condition VGS = VDS = 0.9 V. Lmet = 40 nm, LG = 30 nm and LNO = 5 nm [20].

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Figure 19 (b). Intrinsic gate delay and cut-off frequency as functions of the dielectric constant of the high-K spacer with the condition of VGS = VDS = 0.9 V, Lmet = 40 nm, LG = 30 nm and LNO = 5 nm [20].

Figure 19 (c). ON-current, gate capacitance, and intrinsic gate delay time of modified non-overlap MOS device versus dielectric constant [21].

Hence, ON-current decreases. In this case, the electron density in the underlap regions can be substantially increased by using high-K spacers. As the dielectric constant of the spacer is increased, both ION and Cgg increases. For K < 10, ION increases at a faster rate than the Cgg. This decreases the intrinsic delay (τ = CV/I) of the gate. For K > 10, ION increases at a slower rate than Cgg, increasing τ. For an underlap length of 5 nm and channel length of 30 nm, the optimum value of K was reported to be about 8. As the underlap length increases, the optimum value of K increases. The cut-off frequency (fT) is highest at K = 5. For K > 5, fT decreases due to the higher Cgs and Cgd values.

3.6. Effect of High-K Spacer in Non-overlapped DGFET/FinFETs As we scale down into the sub-20 nm LG regime, the gate appreciably loses control over the channel. Non-planar device structures with multiple gates controlling the channel are proposed as a future technology option. Among the emerging non-planar multiple-gate devices, FinFETs are believed to be technologically the most viable [22]. Generally speaking, FinFETs show excellent short-channel performance. However, as the channel length is scaled

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down, overlapped FinFET structures appreciably lose gate control over the channel, thereby, degrading the short-channel performance [23]. Hence, for sub-20 nm devices, non-overlapped FinFETs are reported to show better short-channel performance [24]. For pragmatic nonoverlapped FinFET structures, ION is low due to the series RSD. It was shown that by using high-K spacers in pragmatic non-overlapped FinFETs, ON-current can be increased by about 80% when compared to a non-overlapped FinFET with Si3N4 spacers. In non-overlapped structures, the channel length of the device in the OFF-state is higher than the channel length in the ON-state. It can be shown that Leff,OFF = LG + 2 LDebye and Leff,ON = LG [24], where LDebye is debye length. At VGS = 0 V and VDS = 1 V, since Leff,OFF > LG the short-channel performance is enhanced with the increased in the non-overlap (underlap) length (LUN). At VGS = 1 V and VDS = 1 V, the ON-current of the non-overlapped device decreases with the increase in LUN due to the increase in the series resistance. The incorporation of high-K spacers increases the ON-current with increase in the dielectric constant of the spacer. A look into the conduction band (CB) energy for a non-overlapped FinFET reveals that at VGS = 1 V and VDS = 1 V, there exists a hump in CB energy in the source underlap region. With increase in electric field coupling due to fringe fields in the source underlap region, the CB energy peak in the source underlap region is lowered. This allows more charge carriers to enter into the channel region. In other words, RSD is lowered. This effect is called gate-fringe induced barrier lowering (GFIBL) [25]. GFIBL is predominant when large underlaps are used. It was shown that as the dielectric constant of the spacer (K) is increased, it not only increases the ON-current, it also increases the OFF-current due to band-to-band tunneling. For LG = 20 nm, fin thickness = 10 nm, EOT = 0.75 nm and LUN = 20 nm, it was shown that the optimum value of K is 18 for maximum ION/IOFF ratio. With increase in K, the fringe capacitance increases along with ION. The delay of the circuit initially decreases with increase in K and then saturates for K > 20 – 25.

Figure 20. (Left) Conduction band energy along the fin in the source extension region with different fringe-field coupling from the gate electrode to the channel. (Right) Conduction band energy along the fin for OFF (VGS = 0 V and VDS = 1 V) and ON-state (VGS = 1 V and VDS = 1 V) [25].

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Figure 21 (a). ON-current and OFF-current versus dielectric constant of the spacer, K. (Inset) ION/IOFF versus K [25].

Figure 21 (b). Gate capacitance and delay of an inverter with fan out 4 versus K [25].

3.7. Effect on High-K Spacer on Reliability At high drain and gate voltages, it was seen that GFIBL modules the potential in the underlap regions reducing RSD. As higher values of dielectric constant of the spacer are used, the transverse electric field component of the total electric field increases. The potential in the drain extension/underlap region (as in the case of overlapped and non-overlapped devices) is raised with the increase in the dielectric constant of the spacer. Hence, the maximum lateral electric field component decreases with the increase in the dielectric constant of the spacer. Going by the Lucky Electron model, the impact ionization rate, α = A exp (-φi / q λ Em), where A is a constant, φi is gate energy, λ is the mean free path of electron, and Em is the drain field. Clearly, as the dielectric constant of the spacer is increased, Em decreases and α is reduced [26].

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Figure 22 (a). Impact ionization rate versus gate bias at VD = 6 V and LG = 0.5 μm for n-MOSFET. Solid and dashed lines show experimental data of Si3N4 HLDD (ε = 7.5) and OLDD (ε = 3.9) respectively [26]

Figure 22 (b). Impact ionization rate versus gate bias at VD = -6 V and LG = 0.6 μm for p-MOSFET. Solid and dashed lines show experimental data of Si3N4 HLDD (ε = 7.5) and OLDD (ε = 3.9) respectively [26]

While the impact ionization is an issue during the ON-state (inversion mode) of the transistor, during the OFF-state (accumulation mode), breakdown between the high-K oxide and the lower-K spacer is a problem [27]. In the commonly used gate-oxide/spacer combinations like HfO2/SiO2 or HfO2/Si3N4, where a high dielectric constant gate oxide forms an interface with a significantly lower dielectric constant spacer, there is significant crowding of electric field lines under accumulation mode stress conditions (large negative values of VGS). Due to the high electric field stress, the breakdown occurs at the gate oxide/spacer interface. This failure mechanism is observed only in the accumulation mode [27]. Integration of high-K dielectric spacer may be beneficial in avoiding this failure and increasing the reliability.

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Figure 23 (a). Simulated lateral quasi-Fermi potential distribution at Si surface near the drain region for n-MOSFET. Bias conditions are VG = 3 V and VD = 6 V, and LG = 0.5 μm. Solid, dashed and dotted, dashed, and dotted lines are simulated results for LDD spacer of ε = 30 (Ta2O3), ε = 7.5 (Si3N4), ε = 3.9 (SiO2) and ε = 1 (Vacuum) respectively [26]

Figure 23 (b). Simulated lateral drain field at Si surface near the drain region for n-MOSFET. Bias conditions are VG = 3 V and VD = 6 V, and LG = 0.5 μm. Solid, dashed and dotted, dashed, and dotted lines are simulated results for LDD spacer of ε = 30 (Ta2O3), ε = 7.5 (Si3N4), ε = 3.9 (SiO2) and ε = 1 (Vacuum) respectively [26]

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Figure 24. TEM and HRTEM micrographs of a narrow nMOSFET (0.25×0.5 μm2) having HfO2 gate dielectric failed at Igl of 2mA during CVS under accumulation mode stress with Vgstress = -3.8V. (a) TEM micrograph showing the BD location at the drain extension region. Dotted circle indicates the breakdown spot. (b) HRTEM micrograph of breakdown spot showing the breakdown through the HfO2/spacer-interface, instead of HfO2 film [27].

Figure 25. TEM micrographs of several narrow nMOSFETs suffered corner BDs through HfO2/spacerinterface at Igl of 2mA during CVS accumulation mode stressing with Vgstress = -4.0 to -4.5 V. (a), (b) & (c) nMOSFETs (0.25×0.5 μm2). (d), (e) & (f) nMOSFETs (0.25×0.05 μm2). Arrows show the S/D extensions BDs through the HfO2/spacer-interface. [27].

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Summary In this chapter we have reviewed the impact of high-K gate & spacer dielectric integration on the device and circuit performance of nano-scale MOSFETs. It is clear that introduction of high-K as the gate dielectric material will worsen the short channel effects due to FIBL phenomenon unless proper device optimizations are carried out. The key factors one can control to keep FIBL under check are; S/D junction overlap length (Lov), spacer length and the lateral doping gradient. From a performance point of view, use of hafnium based dielectrics (K ~20-25) would be ideal for high-K MOSFETs to achieve the best performance for iso- IOFF conditions. Higher values of K may degrade the short channel performance significantly. Studies using the high-K spacers show that use of high-K spacers can give higher Ion and lower Ioff when compared to the case of conventional spacer materials. HighK spacers with under lap S/D junctions, are shown to provide improved short-channel performance and better device scalability. So it can be concluded that use of high-K dielectrics in the gate and spacer regions, associated with proper device engineering, is a powerful option for scaling of CMOS devices to its ultimate limits.

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References [1] Lo, S.-H. Buchanan, D.A Taur, Y. Wnag, W., “Quantum-mechanical modeling of electron tunneling current from the inversion layer of ultra-thin-oxide nMOSFET's”, IEEE Electron Device Letters, VOL 18; NUMBER 5, pages 209-211, 1997. [2] J. Robertson, “High dielectric constant oxides”, Eur. Phys. J. Appl. Phys. 28, 265–291 2004. [3] Yeap G C-F, Krishnan S and Lin M R 1998 Fringing-induced barrier lowering (FIBL) in sub-100 nm MOSFETs with high-κ gate dielectrics Electronics Letters. 34(11), 1150–2, 1998. [4] Baohong Cheng, Min Cao, V.Ramgopal Rao, Anand Inani, Paul Vande Voorde, Wayne M. Greene, Johannes M. C. Stork, Zhiping Yu, Senior Peter M. Zeitzoff, and Jason C. S. Woo, “Impact of High- Gate Dielectrics and Metal Gate Electrodes on Sub-100 nm MOSFETs”, IEEE Trans. Electron Devices, Vol. 46, pp. 1537-1543, July 1999. [5] Nihar R. Mohapatra, Madhav P. Desai and V. Ramgopal Rao, “Detailed Analysis of FIBL in MOS Transistors with High-K Gate Dielectrics”, Proceedings of the 16th International Conference on VLSI Design 2003. [6] B. Cheng, A. Inani, V. Ramgopal Rao and J. C. S. Woo, “Channel engineering for high speed sub-1V power supply deep submicron CMOS”, 1999 Symposium on VLSI Technology, Digest of Technical Papers, pp. 69-70., 1999. [7] Nihar R. Mohapatra, Madhav P. Desai, Siva G. Narendra, and V. Ramgopal Rao, “The Effect of High-K Gate Dielectrics on Deep Submicrometer CMOS Device and Circuit Performance”, IEEE Trans. Electron Devices, Vol. 49, pp. 826-831, May. 2002. [8] N. R. Mohapatra, M. P. Desai, S. G. Narendra, and V. Ramgopal Rao, “Modeling of parasitic capacitances in deep submicrometer conventional and high-K dielectric MOS transistors,” IEEE Trans. Electron Devices, vol. 50, no. 4, pp. 959–966, Apr. 2003. [9] Bing-Yue Tsui and Li-Feng Chin, “A Comprehensive Study on the FIBL of Nanoscale MOSFETs”, IEEE Trans. Electron Devices, Vol. 51, pp. 1733-1735, Oct. 2004.

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[10]D. L. Kencke, W. Chen, H. Wang, S. Mudanai, Q. Ouyang, A. Tasch, and S. K. Banerjee, “Source-side barrier effects with very high-K dielectrics in 50 nm Si MOSFETs”, Device Research Conference Digest, pp-22-23,1999. [11]C.R Manoj and V.Ramgopal Rao, “Impact of High-K Gate Dielectrics on the Device and Circuit Performance of NanoScale FinFETs”, IEEE Electron Device Letters, Vol. 28, No 4, pp.295-298, April 2007. [12]Abhinav Kranti and G Alastair Armstrong, “Optimization of the source/drain extension region profile for suppression of hort channel effects in sub-50 nm DG MOSFETs with high-ê gate dielectrics”, Semicond. Sci. Technol. 21 (2006) 1563–1572. [13]C. Y. Kang, R. Choi, J. H. Si, C. Young, B. H. Lee, G. Bersuker, and Jack C. Lee, “ Charge Trapping Effects in HfSiON Dielectrics on the Ring Oscillator Circuit and the Single Stage Inverter Operation”,. IEDM Technical Digest, pp. 485-488, 2004. [14]D. Vinay Kumar, Nihar R. Mohapatra, Mahesh B. Patil, and V. Ramgopal Rao, “Application of Look-up Table Approach to High-K Gate Dielectric MOS Transistor circuits”, Proceedings of the 16th International Conference on VLSI Design 2003. [15]M.-W. Ma, C.-H. Wu, T.-Y. Yang, K.-H. Kao, W.-C. Wu, S.-J. Wang, T.-S. Chao, T.-F. Lei, Impact of high-κ offset spacer in 65-nm node SOI devices, IEEE Electron Device Letters, Vol. 28, No. 3, pp. 238-240, March 2007 [16]T. Miyashita et al, High-performance and low-power bulk logic platform utilizing FET specific multiple-stressors with highly enhanced strain and full-porous low-k interconnects for 45-nm CMOS technology, International Electron Device Meeting, pp. 251-254, December 2007 [17]Ryuta Tsuchiya, Kazuhiro Ohnishi, Masatada Horiuchi, Shimpei Tsujikawa, Yasuhiro Shimamoto, Naomi Inada, Jiro Yugami, Fumio Ootsuka, and Takahiro Onai, FemtoSecond CMOS Technology with High-k Offset Spacer and SiN Gate Dielectric with Oxygttn-enriched Interface, VLSI Technology Symposium, pp. 150-151, 2002 [18]Sungil Chang, Hyungcheol Shin, Jongho Lee, OFF-state Leakage Currents of MOSFETs with high-K Dielectrics, Journal of the Korean Physical Society, Vol. 41, No. 6, pp. 932936, December 2002 [19]J.P. Xu, F. Ji, P.T. Lai, J.G. Guan, Influence of sidewall spacer on threshold voltage of MOSFET with high-k gate dielectric, Microelectronics Reliability Vol. 48, pp. 181–186, 2008 [20]Hyunjin Lee, Jongho Lee, Hyungcheol Shin, DC and AC characteristics of sub-50-nm MOSFETs with source/drain-to-gate nonoverlapped structure, IEEE Transactions on Nanotechnology, Vol. 1, No. 4, pp. 219-225, December 2002 [21]Hyunjin Lee, Sung-il Chang, Jongho Lee, Hyungcheol Shin, Characteristics of MOSFET with non-overlapped source-drain to gate, IEICE Transactions on Electron, Vol. E85-C, No. 5, pp. 1079-1085, May 2002 [22]P.M. Solomon et al, Two gates are better than one, IEEE Circuits and Devices Magazine, Vol. 19, pp. 48-62, January 2003 [23]M. J. H. van Dal, N. Collaerta, G. Doornbos, G. Vellianitis, G. Curatola, B. J. Pawlak, R. Duffy, C. Jonville, B. Degrootea, E. Altamiranoa, E. Kunnena, M. Demanda, S. Beckxa, T. Vandeweyera, C. Delvauxa, F. Leysa, A. Hikavyya, R. Rooyackersa, M. Kaiserb, R. G. R. Weemaesb, S. Biesemansa, M. Jurczaka, K. Anila, L. Wittersa and R. J. P. Lander, Highly manufacturable FinFETs with sub-10nm fin width and high aspect ratio fabricated

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with immersion lithography, IEEE Symposium on VLSI Technology, pp. 110-111, 12-14 June 2007 [24]V. Trivedi, J. G. Fossum, M. M. Chowdhury, Nanoscale FinFETs with gatesource/drain underlaps, IEEE Transactions on Electronic Device, Vol. 52, No. 1, pp.56-62, January 2005. [25]Angada B. Sachid, Dinesh K. Sharma, V. Ramgopal Rao, Gate fringe induced barrier lowering in underlap FinFET structures and its optimization, IEEE Electron Device Letters, Vol. 29, No. 1, pp. 128-130, January 2008 [26]T. Mizuno, T. Kobori, Y. Saitoh, S. Sawada, and T. Tanaka, Gate-fringing field effects on high performance in high dielectric LDD spacer MOSFETs, IEEE Transactions on Electron Devices, Vol. 39, No. 4, pp. 982-989, April 1992 [27]R. Ranjan, K. L. Pey, C. H. Tung, L. J. Tang, B. Ellatari, T. Kauerauf, G. Groeseneken, R. Degraeve, D. S. Ang, and L. K. Bera, HfO2/spacer-interface breakdown in HfO2 highK/poly-silicon gate stacks, Microelectronic Engineering, Vol. 80, pp. 370-373, June 2005

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In: Recent Advances in Dielectric Materials Editor: Ai Huang, pp. 197-230

ISBN 978-1-60692-266-8 c 2009 Nova Science Publishers, Inc.

Chapter 4

O RIENTATION S ELECTIVITY C ONTROL BY S URFACE P OTENTIAL M ODIFICATION IN OXIDE T HIN F ILM E PITAXIAL G ROWTH Tomoyasu Inoue Iwaki Meisei University, 5-5-1 Chuodai Iino, Iwaki 970-8551, Japan

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Abstract In hetero-epitaxy of oxide layers on silicon substrates, it is well known that epitaxial relations vary in accordance with the overlaying layer materials. The factors determining the growth orientation have been discussed mainly in terms of thermodynamics, but surface polarity of the nuclei is also a very important factor. We describe a new technology of orientation selective epitaxy (OSE), which enables epitaxial growth artificially choosing growth orientation, on the specific material of cerium dioxide (CeO2 ). CeO2 has strong tendency of (111) nucleation due to minimum surface energy, which leads to epitaxial growth of CeO2 (111)/Si(111) at very low temperature as low as room temperature. On the other hand, for most important substrates of Si(100), CeO2 layers usually grow with (110) orientation on Si(100) substrates, which is thought to be due to themodynamical properties and non-existence of Coulombic interaction between neutral CeO2 (110) and substrate surfaces. The key parameter determining the nucleus orientation is thought to be competition of surface energy minimization and electrostatic interaction between nuclei and substrate surfaces. Since CeO2 (100) surfaces have polarity, CeO2 (100) nuclei are hard to adsorb on neutral surface and coalesce together due to electrostatic repulsion. There are two ways to grow CeO2 (100) layers on Si(100) substrates overcoming the surface polarity effect. One is application of substrate bias and the other is charged particle beam irradiation during the epitaxial growth process, both of which are based on the surface potential modification for screening the nuclei surface polarity effect. By the control of substrate bias or charged particle beam irradiation, we can realize OSE growth of CeO2 (100) or CeO2 (110). Details of the two are described; the substrate bias method and an electron beam irradiation method. These are fundamentally applicable widely to most of materials having both polar and non-polar surfaces.

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1.

Tomoyasu Inoue

Introduction

Epitaxial orientation relations between substrates and overlying thin films are not yet fully understood due to its complexity, which is not simply explained by such as the lattice parameter matching and crystallographic symmetry. It is commonly recognized that epitaxial relations vary with material combination of substrates and thin films, where they are empirically known in a wide variety of materials. Although the well known relations are usually believed to be uniquely determined from the specific combination of materials, we found the epitaxially growing orientation can be changed and controlled by the control of surface potential in the oxide thin films. Here we describe details on the method of artificially controlled orientation selective epitaxy (OSE). The principle of the OSE is based on the surface potential distribution of the substrates. In general, oxide materials consist of positive metal atoms and negative oxygen atoms, resulting in polar molecules. Polarity of the oxide crystal lattice varies with crystallographic planes. When oxide molecules are depositing onto non-polar silicon surfaces, non-polar oxide surfaces are preferred. On the contrary, if the surface potential distribution is modified so as to screen the effect of polarity of depositing oxide molecules, epitaxial growth of polar plane oxide becomes possible. Epitaxial oxide layer growth on semiconductor substrates has been attracting widespread attention and studied extensively for various fields of applications; such as optoelectronics, silicon on insulator technology, high-k oxide gate technology, buffer layers between Si substrates and overlying oxide superconducting layers, and optical coatings. [1–3] As a special candidate of the oxide materials on silicon substrates, cerium dioxide (CeO2 ) has many advantageous properties for various applications; such as high dielectric constant, chemical stability, transmission in the visible and infrared regions, and high efficient ultra-violet absorption. For applications to silicon technology, [4–6] epitaxial growth of CeO2 thin films on Si substrates has been studied, where a great deal of effort has been devoted to make use of a close epitaxial relation of CeO2 with silicon: both materials have cubic symmetry and a lattice mismatch parameter between them is very small value of 0.35%. Although CeO2 (111) layers grow on Si(111) substrates at very low temperatures, such as room temperature with excellent crystallinity, [7–12] many experimental results showed that epitaxial growth on Si(100) substrates requires higher growth temperature and has strong tendency to grow with (110) orientation. [7, 13, 14] Epitaxial relations of oxide materials with cubic symmetry on the Si(100) surface are divided into two ways; a cube-on-cube structure and (110)-oriented growth. For example, MgO, MgAl2 O4 , BaO, γ-Al2 O3 and ytteria stabilized zirconia grow in the former way, whereas CeO2 and Y2 O3 grow in the latter. [15] Many works have indicated that it is not easy to grow CeO2 (100) layers directly on Si(100) substrates in spite of very close lattice matching between CeO2 and Si, except for the result using intermediate buffer layer of SrTiO3 . [16] A lot of efforts have been devoted in obtaining single crystalline (110)-layers by preventing double domain structure formation using miscut substrates and lowering of epitaxial growth temperature by electron beam assistance during evaporation. [17–20] The first experiment on a CeO2 (100)/Si(100) structure was reported to grow on atomically cleaned Si(100) surfaces with a 2×1, 1×2 reconstructed structure by molecular beam epitaxy in an ultra-high vacuum. [21] Considering the application to device fabrication,

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reconstructed surface preparation is not preferable because it can be made and kept only in an ultra-high vacuum. In the course of the study of the epitaxial growth of very thin CeO2 layers on Si(100) substrates using reactive dc magnetron sputtering, OSE has been found as the epitaxial CeO2 layer with (100) or (110) orientation is selectively grown by controlling substrate bias. [22–24] For the epitaxial growth of CeO2 (100) layers, this method has superiority in the requirement of only practical H-terminated surfaces obtained by the usual wet cleaning process. As a result, the OSE growth mechanism can be explained in terms of surface potential of Si substrates and the polarity of the growing CeO2 surface; non-polar CeO2 (110) and polar CeO2 (100) surfaces. CeO2 (100) layers can be grown on surface potential modified substrates due to the screening effect of polar surfaces by reconstructed surfaces, substrate bias application and charged particle irradiation. As the latter, we have found the effectiveness of low energy electron beam irradiation for OSE of CeO2 (100)/Si(100) structures, which will give a way to make two dimensionally patterned OSE regions. We describe details on the two growth methods for OSE of CeO2 layers on Si(100) substrates utilizing substrate bias application and electron beam irradiation, including improvements of the growth method utilizing oxygen radical beam irradiation, [25] characterization of the epitaxial layers by X-ray diffraction (XRD), transmission electron microscopy (TEM) and atomic force microscopy (AFM) and consideration on the growth model of OSE.

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2.

Principle of OSE

The fundamental parameter ruling the crystallographic orientation in nucleus generation at the early stage of the epitaxial growth should be the relation between surface energy and interface energy. [26] Goettler et al. explained the hetero-epitaxial relation of CeO2 layers and Si(100) substrates in terms of an intermediate cerium silicide layer; a CeO2 /CeSi2 (100)/Si(100) structure as shown by the schematic diagram of the lattice arrangements in Figure 1, which appeared through the courtesy of them. [27] The lattice arrangement of CeSi2 (100) on Si(100) is illustrated in A region in the figure. The lattice arrangements of CeO2 (110) and CeO2 (100) on CeSi2 (100) are shown in regions B and C, respectively They explained the preferability of CeO2 (110) on CeSi2 (100) from smaller lattice mis-matching [] and thermodynamical considerations. [] If CeO2 (100)/CeSi2 (100)/Si(100) structures are realized, CeO2 (100) layers grow on Si(100) in a cube-on-cube manner. And after CeSi2 (100) vanishes during the CeO2 (100) layer growth due to interfacial oxidation, the CeO2 (100) layer lies directly on Si(100) and should have superior crystallinity due to minimum lattice mis-matching. We, however, think that the parameters determining growth orientation are not only lattice matiching and themodynamical energy but Coulombic interaction between substrate surfaces and polarity of depositing molecules. The crucial parameter is thought to vary in accordance with the kinds of depositing materials. In the case of CeO2 /Si(100), experimental results indicate that the Coulombic interaction is crucial, as described later. Since the CeO2 (110) surface has the stoichiometric amount of both Ce and O atoms leaving every plane elecrostatically neutral, CeO2 (110) surfaces may

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Figure 1. Schematic diagram showing the in-plane orientation of CeSi2 kSi(100) in region A and the lattice matches of CeO2 (110)kCeSi2 and CeO2 (100)kCeSi2 in regions B and C, respectively. This figure is presented by the courtesy of D. G. Schlom. [27]

be preferred in epitaxial growth on non-biased neutral substrates, as illustrated conceptually in the right hand side of Figure 2. On the other hand, CeO2 (100) planes are polar surfaces consisted of positively charged Ce planes and negatively charged O planes by turns, resulting in a plane-to-plane alternating surface potential. Substrate bias may reduce this electrostatic influence, which is due that the biased surface potential screens the alternating electrostatic potential variation with a periodical polarity change, resulting in (100)-nucleus generation and the realization of closer epitaxial relation of CeO2 (100) and Si(100) due to small lattice mismatching. These features are illustrated in the left hand side of Figure 2.

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Figure 2. Sketches indicating relations between substrate surface potential and electric polarity of CeO2 (110) and CeO2 (100) lattice planes.

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3. 3.1.

Experimental Experimantal Procedure for OSE

Mirror polished Si(100) wafers were chemically cleaned to make an H-terminated surface by repeating the following procedure three times: dipping in a hot aqueous solution of HCl and H2 O2 (1:1) for 10 minutes at ∼ 90 ◦ C and in diluted hydrofluoric acid solution (2.5%), followed by rinsing in de-ionized water for 5 minutes. CeO2 layers were grown by dc magnetron sputtering enhanced with an inductively coupled rf plasma (ULVAC MPS2000-HC3), whose base pressure of the growth chamber was below 2.0 × 10−7 Pa. Figure 3 shows a schematic diagram of the sputtering system. In order to prevent oxidation of Si surfaces until the initial stage of epitaxial growth of CeO2 layer is completed, we adopted a two step growth method; ultrathin metallic Ce layer deposition at room temperature followed by silicidation process at an elevated temperature, and subsequent reactive sputtering in an Ar/O2 mixture environment using Ce metal target of 99.9%. The diameter of the metallic Ce target and the distance between the target and the substrate were 50.8 and 200 mm, respectively. The applied dc power to the target was varied in the range of 60 ∼ 160 W, whereas rf power for the induction coil was kept at 50 W. The metallic Ce layer was deposited at the dc power of 120 W. The total pressure was 0.13 Pa, which was resulted from the balance between Ar gas flow of 7 sccm and vacuum evacuation by a 210 ℓ/s turbo molecular pump. After heating the substrates, CeO2

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layers were subsequently deposited by reactive sputtering using a metallic Ce target in an Ar and O2 mixture environment. The Ar gas flow rate was varied in the range between 4 and 15 sccm, whereas the O2 flow rate was kept constant at 1 sccm. The thickness of grown CeO2 layers was 10 ∼ 20 nm, as determined by ellipsometric measurements.

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Figure 3. Schematic diagram of a dc magnetron sputtering apparatus with a radical beam source.

The substrate mounted on an inconel holder was heated by a 2 kW halogen lamp heating system with a water-cooled paraboloidal mirror, where the temperature elevation rate was set at 1 ◦ C/s. The samples in this study were grown at 800 ◦ C, except for the experiments using oxygen radicals. In order to improve uniformity of the temperature distribution within the substrate, a 1.5-mm-thick AlN disk was set on the substrate. The sample manipulation system was electrically isolated from the chamber and connected to a dc power supply for the substrate bias application. The bias voltage was varied from –30 to +30 V by 5 V step. For OSE growth experiments using low energy electron beam irradiation, differentically pumped electron gun (Biemtron, LEP-5) was equipped toward the sample surface in the angle of 33 ◦ , as shown in Figures 3 and 4. The distance between the radical beam source and the sample surface was 50 mm. The electron beam diameter was less than 3 mm. The electron source section and electron optics section of the electron gun were separated by serially located two orifices of 3.0 mm in diameter. In order to protect W-Re filament from an oxidizing ambient during reactive sputtering maintaining an ultra-high vacuum, the electron source section was differentially pumped by a 50 ℓ/s turbomolecular pump. The electron source section was kept at 1.07 × 10−3 Pa, when the pressure of the sputtering chamber was 0.13 Pa. During reactive sputtering, as the second step of the epitaxial growth

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Figure 4. An photograph of the differentially pumped electron gun installed to the sputtering apparatus.

mentioned above, low energy electron beams of 15 ∼ 150 eV were irradiated, while the sample holder was grounded. In the experiments by reactive sputtering assisted by oxygen radicals, an oxygen radical source (ULVAC DOS-1000HE) was used to enhance oxidation reaction at the substrate surfaces, which was operated with 50 W rf power and oxygen gas inlet of 1 sccm. The radical beam source was equipped toward the sample surface in the angle of 33 ◦ , as illustrated in the right hand side of Figure 3. The distance between the radical beam source and the sample surface was 150 mm. The growth rate and the thickness of CeO2 layers were approximately 0.28 nm/s and 15 ∼ 25 nm, respectively. Crystallographic properties of the samples were characterized by reflection high energy electron diffraction (RHEED), θ-2θ XRD (Shimazu XRD-6100), 4-circle goniometer XRD (MAC Science MXC18), and TEM (FEI TECNAI S-twin, 300 keV). Cross-sectional TEM samples were fabricated using focused ion beam (FIB) technology (Hitachi FB-2100). Surface morphology was analyzed by AFM (DI NanoScope III).

3.2.

Two Step Growth Method

In general, it is very important for epitaxial growth of oxide layers on Si substrates to prevent the Si surface from oxidation until oxide layer coverage is fulfilled. Different from thin film deposition technology in an ultra-high vacuum such as molecular beam epitaxy, in sputter deposition, it is somewhat difficult to keep oxidant concentration in the growth environment sufficiently low due to higher operating pressure. In order to pave the way to prevent oxidation of the Si surface until complete CeO2 layer coverage, we proposed the

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two step growth method as mentioned above. The first step is ultrathin metallic Ce layer deposition at room temperature. In the second step, after an elevation of substrate temperature, CeO2 layer deposition was carried out using reactive sputtering by adding oxygen flow. During the substrate heating process, the metallic Ce layer reacts with the underlying Si substrate, resulting in a Ce-silicide layer formed by solid phase epitaxy. Epitaxial growth of CeO2 layers by reactive sputtering was accompanied by simultaneous oxidation of the underlying Ce-silicide layer. The two step growth method similar to this study has already been reported in growing epitaxial CeO2 (111)/Si(111) structures, [11] but our method is different from theirs in the points of the use of a very thin metallic Ce layer and not having an intentional oxidation process before CeO2 deposition but having a silicidation process before CeO2 layer deposition.

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Figure 5. Two step growth procedure.

As the first step, the metallic Ce layer was deposited for 4 seconds at dc plasma power of 120 W with Ar gas flow of 7 sccm, whose thickness was ∼ 1.2 nm. The sample showed a halo RHEED pattern, indicating that it was amorphous. This thickness was experimentally determined so as to attain high quality epitaxial CeO2 layers, below which crystalline quality of the epitaxial layer became poor due to incomplete coverage of the Si substrate surface by Ce-silicide. On the contrary, the thicker Ce layer leads to a polycrystalline Ce-silicide surface because solid phase epitaxy of the CeSi2 layer has a limitation on its thickness. It has been reported that the Ce layer exceeding 5 mono-layers (∼ 1.5 nm) deposited at room temperature is Si and Ce-silicide mixture. [28, 29] At elevated temperature more than 100 ◦ C, it has been also reported to form Ce-silicide, with epitaxial relation of CeSi2 (100)/Si(100). [27] After heating to 800 ◦ C, the surface layer crystallized and metallic Ce layers reacted completely with substrate silicon resulting in the formation of a single crystalline Ce-silicide layer. As the second step, reactive sputter experiments were carried out at the elevated temperature. Details on the experimental parameters are described in the former section. Ce-silicide layers formed in the substrate heating process are oxidized during the CeO2 layer growth period in the second step by in-diffusion of oxidant species through the growing CeO2 layer, which is due to considerably high diffusion coefficient of oxidant in CeO2 . [30, 31]

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OSE by Substrate Bias Application How to Select Growth Orientations

In this section, we show the experimantal results of OSE by substrate bias control. Features of the three typical samples are summarized in Table 1, indicating substrate bias voltages, growth rates, full width at half maximum (FWHM) values of main XRD peaks and their epitaxial orientation. Sample B is a representative of CeO2 (110) layers grown without substrate bias, whereas samples A and C are representatives of CeO2 (100) layers grown with positive and negative bias, respectively. Applied dc plasma power was 120 W. Table 1. Typical samples grown at different substrate bias, growth rate, their orientation and FWHM’s of main XRD peaks.

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sample A B C

bias (V) +15 0 –15

growth rate (nm/s) 0.231 0.294 0.205

FWHM of XRD (◦ ) 0.432 0.568 0.467

orientation (100) (110) (100)

RHEED patterns of samples A, B and C are shown in Figure 6. Figure 6 (b) is the RHEED pattern taken from the CeO2 layer of sample B along with h100i azimuth. This pattern indicates that the CeO2 layer is (110)-oriented single crystalline, as is the same as the results by the conventional growth methods. [7, 13, 14] This result showed that the two step growth method was effective in realizing high quality epitaxial growth without Si surface oxidation. From subsidiary experiments, it was also understood that CeO2 layers grown on the poly-crystalline Ce-silicide layer inevitably became poly-crystalline, which suggested that the epitaxial growth process was explained by the model of CeO2 (110) or CeO2 (100) on CeSi2 (100)/Si(100) proposed by Goettler et al. [27] Figure 7 (b) shows a θ-2ω XRD scan of sample B, indicating that the main component is a (220) peak and no (200) peak exists. A very small (111) peak of less than 100 cps can also be seen, which is thought to result from some irregular generation of (111) nuclei at the early stage of the growth. RHEED patterns taken from CeO2 layers of samples A and C are shown in Figures 6 (a) and (c), respectively. Since these RHEED patterns show the CeO2 (100) pattern of h110i azimuth, CeO2 layers grown under adequate bias of both positive and negative voltages are proved to be (100)-oriented epitaxial layers. Comparing with the result in Figure 6 (a), it is clearly shown that the crystallographic orientation of CeO2 epitaxial layers on Si(100) is able to be selected by controlling substrate bias. Figures 7 (a) and (c) show θ-2ω XRD scans of samples A and C, respectively. It is apparent that spectra of samples A and C consist of a CeO2 (200) peak without (220) nor (111) peak, which are in good agreement with the RHEED results. In Figures 7 (a) and (c), we can also see small peaks of CeSi2 (400), which indicate the residue due from incomplete oxidation of the Ce-silicide layer, but their intensities are very small; less than 100 cps. The XRD results are summarized in Table 1. FWHM values of the (220) peak of sample B, the (200) peak of samples A and C were 0.568, 0.432 and 0.467 ◦ , respectively, which indicated that crystalline quality of CeO2 (100)

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Figure 6. RHEED patterns OSE grown CeO2 layers. (a) and (c) are h100i azimuth of sample A and C, respectively. (b) is h110i azimuth of sample B. layers were somewhat superior to that of CeO2 (110) layers. A summary of epitaxial orientations in relation with substrate bias and the growth rate is shown in Figure 8, which is obtained from systematic growth experiments at cathode dc power of 120 W. This can be used as a map for epitaxial orientation selection, indicating the CeO2 (100) growth region by cross-hatching. Solid and open marks represent (100) and (110) orientations, respectively. CeO2 (100) growth regions are both in the negative bias region (around −15 V) and in the positive bias region (15 ± ∼ 7 V). CeO2 (110) layers grew outside these cross-hatched regions. It is not clearly understood why the CeO2 (100) growth regions are such narrow bands and the absolute value of substrate bias is around 15 V. It may have some correlation with surface potential bending, which leads to the change of the preferential orientation from (110) to (100). The growth rate also influences the orientation selection. It is experimentally clarified that CeO2 (100) layer grows below

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Figure 7. XRD patterns of OSE grown CeO2 layers. (a) and (c) are taken from samples A and C, respectively. (b) is taken from sample B. ∼ 0.24 nm/s, otherwise CeO2 (110) grows irrespective of substrate bias. Since the growth rate varies largely with dc plasma power, it is necessary to adjust the growth rate by the control of Ar gas flow.

4.2.

Orientation Component Variation with Substrate Bias

As described in the previous section, CeO2 (100) layers grow at ±15 V substrate bias and CeO2 (110) layers grow under other bias conditions. [22–24] In this section, we show how orientation components of the CeO2 layers vary with substrate bias. Figures 9 (a), (b) and (c) show θ-2θ XRD scans of the samples grown at 0, +15 and +20 V bias, respectively. CeO2 (110) layers grow without substrate bias, as is confirmed from Figure 9 (b), wherein only (220) peak is seen, whose full width at half maximum (FWHM) is 0.568 ◦ . This feature agreed well with previous results on the samples grown without substrate bias irrespective of growth methods; sputtering, e-gun evaporation and laser ablation. [11, 14, 32] On the

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Figure 8. Selective growth orientation map of CeO2 (100) and CeO2 (110) grown at cathode dc power of 120 W in relation with substrate bias and the growth rate. Open and solid circular marks correspond to (100) and (110) orientations, respectively. CeO2 (100) growth regions are cross-hatched.

contrary, the sample grown at 15 V bias has only (200) peak (FWHM of 0.433 ◦ ) as shown in Figure 9 (b), indicating a pure CeO2 (100) layer. Apart from ±15 V, CeO2 layers become mixture of (100) and (110) orientations having both (200) and (220) peaks and the intensity ratio of them varies with the bias, As an example, Figure 9 (c) shows a θ-2θ XRD scan taken from the CeO2 layer grown at 20 V bias, which shows a small (220) peak (FWHM of 0.519 ◦ ) in addition to the main (200) peak (FWHM of 0.325◦ ). Moreover, the appearance of small (111) peak (FWHM of 0.466 ◦ ) is due to the residual of (111) nucleation discussed later and indicates inferior crystalline quality to samples of Figure 9 (a) and (b). In order to disclose how the orientation preference changes with substrate bias, we carried out systematic XRD analyses on samples grown at various substrate bias varied in the range from –20 to 30 V by 5 V. As a result, (200) and (220) peak component variations were obtained as a function of substrate bias as shown in Figure 10. It was confirmed that pure (100) single crystalline layers grow at ± 15 V bias. (220) component increases as bias apart from ± 15 V, wherein pure (110) layers grow at zero bias. From Figure 10, it is recognized that the (200) peak intensity reaches maximum values at ±15 V bias, both of which form respective CeO2 (100) growth regions with the width of about 10 V. This feature agrees well with the reported result of orientation selection regional map drawn in the graph showing the relation between bias voltage and the growth rate. [23, 24] The FWHM value of the CeO2 (100) growth re-

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Figure 9. θ-2θ scans of CeO2 layers grown at substrate bias of (a) 0 V, (b) +15 V and (c) +20 V.

gion around −15 V bias in Figure 10 seems to be somewhat smaller than that of the region around +15 V bias. Although the reason is not yet clearly understood, we suppose that this is not a natural feature and is due that substrate surface potential is influenced by a small deviation in the potential balance among the substrate, the sputter cathode and the side wall. This feature indicates directly how the nucleation orientation varies depending on the bias voltage, which suggests the nucleation probability of nucleation orientation is strongly influenced by substrate bias, namely surface electrostatic potential at the initial stage of epitaxial growth. First of all, high epitaxial temperature such as 800 ◦ C employed in this study is required to promote (100) and/or (110) nuclei generation suppressing the strong tendency of (111) nucleation due to its lowest surface free energy. In the high temperature epitaxial growth, competitive generation of (100) and (110) nuclei takes place. The fundamental parameter ruling the crystallographic orientation in nucleus generation at the early stage of the growth

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should be the relation between surface energy and interface energy. [26] Goettler et al. explained the hetero-epitaxial relation of CeO2 /CeSi2 (100)/Si(100) by the schematic diagram of the lattice arrangements, where the arrangements of both CeO2 (110) and CeO2 (100) are possible. [27] From thermodynamical consideration, they concluded that CeO2 (110) is preferred in usual growth conditions. Taking into account their conclusion, we think that the key parameter for the explanation of our experimental results is the influence of the surface potential on the orientation of nuclei during deposition. Since the CeO2 (110) surface has the stoichiometric amount of both Ce and O atoms leaving every plane elecrostatically neutral, CeO2 (110) surfaces may be preferred in epitaxial growth on non-biased neutral substrates.This is the case as reported by many workers. [13, 14, 19]

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normalized intensity (arb.)

1000 800

: CeO2 (200) : CeO2 (220)

600 400 200 0 -30 -25 -20 -15 -10 -5

0

5 10 15 20 25 30

substrate bias (V) Figure 10. XRD peak intensities of CeO2 layers as a function of substrate bias.

On the other hand, CeO2 (100) has polar surfaces consisted of positively charged Ce atom planes and negatively charged O atom planes by turns, resulting in a plane-to-plane alternating surface potential. Substrate bias may reduce this electrostatic influence, which is due that the biased surface potential screens the alternating electrostatic potential variation with a periodical polarity change, [24] resulting in (100)-nucleus generation and the realization of closer epitaxial relation of CeO2 (100) and Si(100) due to a small lattice parameter mismatch. The results of Figure 10 showed that the screening effect reached maxima at ±15 V bias and weakened as the bias voltage departed from them. Thus our experimental results determined optimum bias for the CeO2 (100) growth, whereas at present, the quantitative explanation for the optima of ±15 V cannot be given yet. Here, surface potential modulation due to Schottky barrier formation at CeSi2 /Si interface also have to be considered. At present, we think that it gives not so much effect on OSE growth, since its barrier height is too low compared with the applied bias of ±15 V and always grows only CeO2 (110) under non-biased conditions.

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211

Growth Rate Dependence of OSE

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Another epitaxial orientation selection map in terms of dc plasma power and the growth rate is shown in Figure 11, wherein open and solid marks represent the results of CeO2 (100) and CeO2 (110), respectively, and plotted mark variations correspond to substrate bias voltages. It is found that the CeO2 (100) growth region (hatched region) has upper limits in the growth rate and its value linearly increases with cathode dc power. As a matter of course, even below the upper limit, samples grown under zero-bias (solid circles) have (110) orientation. It is thought that generation and coalescence probabilities of (100)-nuclei are small compared with those of (110)-nuclei; in other words, (100)-nucleation needs longer relaxation time than (110)-nucleation. This may cause the existence of the upper limits. On the other hand, the possibility of (100)-nucleus generation is thought to increase with plasma power, which is due to increase in the kinetic energy of adsorbed atoms and/or molecules for their migration needed for occupancy of epitaxial sites and their coalescence. This can explain the linear increase of the upper limit of the growth rate for CeO2 (100) growth. As shown by circular solid marks in Figure 11, it is clarified that the epitaxial layers grown without substrate bias, even at the growth rate below the upper limit, have always (110)-orientation, showing that bias application is essential for CeO2 (100) growth. Since the reported CeO2 (100) layer growth needs the reconstructed surface with no native oxide, [21] our results is considered to be due largely to prevention of Si oxidation by the thin metallic Ce layer. It is important difference that the method of this study enables higher temperature growth and higher crystalline quality irrespective of the epitaxial layer thickness, whereas growth on the reconstructed surface needs low temperature below 200 ◦ C and has crystallinity deterioration as the layer thickness increases. [21] Therefore, we believe that our method leads to wider and easier applicability to microelectronics and nano-technology.

4.4.

Effect of Oxygen Radical Beam Irradiation

As described above, the OSE growth process requires considerably high temperature of 800 ◦ C, which is not preferable for application to device processes. In order to improve the OSE process, we attempted to apply oxygen radical beam irradiation to the substrate surface during reactive sputtering. [25] Samples used in this study are summarized in Table 2. Samples R-800, R-700 and R-600 were grown using reactive sputtering assisted by oxygen radicals at 800, 700 and 600 ◦ C, respectively. For comparison, samples grown by conventional reactive sputtering simply by oxygen gas introduction were prepared; samples C-800 and C-700 grown at 800 and 700 ◦ C, respectively. The RHEED patterns taken from samples R-800, R-700 and R-600 are shown in Figures 12 (a), (b) and (c), respectively. Samples R-800 and R-700 reveal spotty patterns taken along with h100i azimuth, which indicate that these samples are single crystalline CeO2 (100) layers. As we had expected, subsidiary experiments revealed that CeO2 layers grown by the same conditions except for zero substrate bias had (110) orientation, which is the same results performed without oxygen radical irradiation as reported before. [22–24] On the other hand, Figure 12 (c) indicates that the sample is (111)-oriented poly-crystalline, since the CeO2 (111) pattern remains unchanged irrespective of electron beam incidence direction. These results indicate that the growth temperature above 700 ◦ C is sufficient to

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Figure 11. Selective growth orientation map of CeO2 (100) and CeO2 (110) in relation with cathode dc power and the growth rate. Open and solid marks correspond to (100) and (110) orientations, respectively, wherein plotted mark variations correspond to substrate bias voltages, as denoted in the figure. . Table 2. Layer thickness, t and crystallinity of samples made with and without oxygen radical beam irradiation. Sample R-800 R-700 R-600 C-800 C-700

t (nm) 23 22 16 20 20

Crystallinity by RHEED (100) single crystal (100) single crystal (111)-oriented poly-crystal (100) single crystal Poly-crystal (ring pattern)

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Figure 12. RHEED patterns of CeO2 layers grown by reactive sputtering enhanced by oxygen radicals at: (a) 800 ◦ C, (b) 700 ◦ C and (c) 600 ◦ C. RHEED patterns of CeO2 layers grown by conventional reactive sputtering at: (d) 800 ◦ C and (e) 700 ◦ C. RHEED results of (a), (b) and (d) are CeO2 (100) patterns of h110i azimuth. RHEED patterns (c) and (e) indicate (111)-oriented poly-crystalline and poly-crystalline without preferential orientation, respectively.

grow epitaxial CeO2 (100) layers using reactive sputtering assisted by oxygen radicals. Figures 12 (d) and (e) are the RHEED patterns taken from samples C-800 and C-700, respectively. The former is similar to Figures 12 (a) and (b) indicating that sample C-800 is epitaxial CeO2 (100) layer, whereas the latter shows the ring pattern showing that sample C700 is poly-crystalline. These two results show that epitaxial growth of CeO2 (100) layers by conventional reactive sputtering requires growth temperature of ∼ 800 ◦ C. As a result, it is confirmed that assistance by oxygen radicals enables epitaxial temperature lowering by at least 100 ◦ C. Currently how oxygen radicals enhance the CeO2 epitaxial growth is not yet clearly understood, where the fundamental parameter may be chemical effect of oxygen radicals assisting the oxidation process of metallic Ce and Ce-silicide layers. Figure 13 shows an epitaxial growth model of a CeO2 (100) layer on the Si(100) substrate with a thin CeSi2 (100) layer by reactive sputtering using oxygen radical beam irradiation. Under substrate bias around ±15 V, CeO2 (100) layers grow, whereas CeO2 (110) layers grow under other bias conditions. [22–24] It is thought that in the former, (100)-oriented nuclei are preferentially adsorbed on the surfaces and subsequently CeO2 (100) layers grow through their coalescence process, since electrostatic potential distribution above substrate surfaces should be bent by applied bias and as a result, an induced screening effect en-

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epitaxial growth CeSi 2(100)

Ce O radical Ce

Si (100) substrate

CeO 2(100)

O radical Ce O radical Ce O radical Ce

bias

oxidation

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Figure 13. Epitaxial growth model of a CeO2 (100) layer on the Si(100) substrate with a thin CeSi2 (100) layer by reactive sputtering enhanced by oxygen radical beam irradiation. Directions of epitaxial growth and oxidation are indicated by arrows, both of which simultaneously proceed.

ables adsorption of (100)-oriented nuclei having polar surfaces. On the other hand, under other bias conditions, i. e. without adequate screening effect, (110)-oriented nuclei with non-polar surfaces are preferred. Directions of epitaxial growth and oxidation are opposite as indicated by arrows in Figure 13, both of which proceed simultaneously. Here we believe that oxygen radicals considerably enhance oxidation of metallic Ce adatoms and Cesilicide molecules compared with conventional reactive sputtering, and are more effective in enhancement of orientation selectivity through rapid oxidation and nucleus adherence processes. Comparing the intensities of (400) peaks from residuary CeSi2 in Figures 3 (a) and (d), it is clearly recognized how oxygen radicals enhance oxidation. θ-2θ XRD scans of samples R-800, R-700 and R-600 are shown in Figures 3 (a), (b) and (c), respectively. These results closely correlate with the corresponding RHEED results shown in Figures 12 (a), (b) and (c). The scans of samples R-800 and R-700 consist mainly of (200) peaks, and full width at half maximum (FWHM) values of them are 0.96 and 1.30 ◦ , respectively, which indicate fairly good crystalline quality taking into account their ultra-thin layer thickness. We can see no other peaks in Figure 3 (a), whereas there exist considerably large CeO2 (111) and CeSi2 (400) peaks in Figure 3 (b). Because of the absence of these peaks, it is apparent that crystalline quality of sample R-800 is superior to that of sample R-700. The appearance of CeSi2 (400) peak is thought to be due to insufficient oxidation during the reactive sputtering process under lower temperature of 700 ◦ C. The residue of CeSi2 (also seen in Figure 3 (a) below) supports the growth model of epitaxial growth of CeO2 layer on a Ce-silicide intermediate layer on Si substrates. [27] The scan of sample C consists of (111) and (222) peaks, indicating that this sample is purely (111)-oriented polycrystalline without (200) nor (220) oriented grains, which corresponds

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3

4

(a)

(200)

intensity (arb.)

intensity (arb.)

4

2 1

3 2 1

(d)

(200) CeSi2 (400) (111)

0

(b)

(200) 3 CeSi2 (400) 2 (111)

intensity (arb.)

intensity (arb.)

0

1

(111)

(e)

3 2 1 (222)

(200) 0

0 25 30 35 40 45

(111)

intensity (arb.)

215

(c)

3

50 55

60 65

2 theta (degree)

2 1 (222)

0 25 30

35 40

45 50

55 60 65

2 theta (degree)

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Figure 14. XRD θ-2θ scans of: (a) sample R-800, (b) sample R-700, (c) sample R-600, (d) sample C-800 and (e) sample C-700.

with the RHEED pattern in Figure 12 (c). The strong (111)-oriented growth features seen in samples R-700 and R-600 are explained by strong tendency of (111) oriented nucleus generation of CeO2 below epitaxial temperature. [8–10] FWHM values of XRD peaks of samples in Table 2 are summarized in Table 3. Table 3. FWHM values of XRD peaks. Sample CeSi2 (400) R-800 — R-700 0.49 ◦ R-600 — C-800 0.60 ◦ C-700 —

CeO2 (111) — 1.11 ◦ 0.79 ◦ 1.01 ◦ 0.85 ◦

CeO2 (200) 0.96 ◦ 1.30 ◦ — 1.12 ◦ 1.84 ◦

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tively. The scan of sample C-800 is similar to that of sample R-700, except for smaller CeO2 (111) and CeSi2 (400) peaks, which also corresponds well with the single crystalline CeO2 (100) RHEED pattern in Figure 12 (d). The FWHM value of the CeO2 (200) peak is 1.12 ◦ ; somewhat larger than that of sample R-800, indicating inferior crystallinity to sample R-800 grown with assistance by oxygen radicals at the same temperature. Since the peak intensities of both CeO2 (111) and CeSi2 (400), and FWHM of CeO2 (200) peak are smaller than those of sample R-700, the crystalline quality of sample C-800, however, is superior to that of sample R-700, which should result from higher growth temperature even without oxygen radical assistance. Comparing the CeSi2 (400) peak intensities of samples R-800, R-700 and C-800, it is clearly understood that oxygen radical irradiation is very effective in assistance to oxidation kinetics in reactive sputtering. These results show that assistance by oxygen radicals is very effective not only to epitaxial growth temperature lowering but to crystalline quality improvements. On the other hand, the scan of sample C-700 consists of (111), (222) and (200), which correlates with the poly-crystalline ring pattern in Figure 12 (e). It is noteworthy that there are no (220) peaks in the whole samples studied in this study, which is commonly seen in usual epitaxial CeO2 layers [13–16] and poly-crystalline CeO2 layers on Si(100) substrates grown without substrate bias. Therefore, it is also confirmed that the (200) peak appearance is due to substrate bias application at adequate voltage of 15 V. [22–24]

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5.

Electron Beam Induced OSE

The OSE technology has a lot of possibilities for applications to device fabrication processes and for OSE of many other polar materials. For future sophisticated applications, it is desired to develop a new technology for two dimensionally spatially varied OSE. Studies on OSE by substrate bias as mentioned in previous section indicated that OSE is irrespective of surface potential bending directions, which gives us an idea of surface potential modification by irradiation of charged particles; electrons and/or ions. In this section, we introduce OSE by electron beam irradiation, which is a novel technology to realize spatially varied OSE utilizing low energy electron beam irradiation, instead of substrate bias application. [33, 34] We show the experimental results on the CeO2 (100) layer growth in a low energy electron beam irradiated area on Si(100) substrates, wherein the reason why two electron beam energy regions are effective in OSE is explained in terms of electron energy influenced by ionization cross-section of Ar gas introduced in the reactive sputtering process. Also we described details of optimization of growth parameters; such as incident electron energy, oxygen flow during reactive sputtering and resistivity of Si substrates. The effect of oxygen radical beams in reactive sputtering is also shown, comparing with conventional reactive sputtering.

5.1.

Optimum Electron Beam Energy for CeO2 (100) Growth

Orientation selectivity for CeO2 (100) layer growth is thought to correlate with surface potential modification for facilitating adsorption of nuclei with a polar CeO2 (100) surface. In the substrate bias application method, both plus and minus 15 V bias proved to be adequate for CeO2 (100) layer growth. [22, 23] It is found that electron beams with acceleration en-

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sample current (µA)

-40 40 -30 30 -20 20

UHV

-10 10 0 10 20

Ar : 0.13 Pa

30 40 50 60 0 20 40 60 80 100 120 140 160 180 200 220 240

electron energy (eV)

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Figure 15. Sample current as a function of electron beam energy. Broken line rectangles indicate optimum energy regions for CeO2 (100) growth.

ergy around 35 and 90 eV lead to CeO2 (100) layer growth, which is thought to give surface potential modification effect similar to ±15 V bias application. [33–35] Here, we describe experimental results for the determination of exact optimum electron energy. Figure 15 shows the sample current characteristics as a function of electron energy. The upward direction of the vertical axis is negative. Open and closed circles indicate the results measured in an ultra high vacuum (UHV) and in 0.13 Pa Ar, respectively. The sample current in UHV rapidly increases from 10 eV and reaches nearly constant above 30 eV, which is the fundamental characteristics of the electron gun. On the other hand, the sample current in the Ar ambient shows a quite different feature, which has a maximum at 35 eV and then decreases, reaching a zero-crossing point at 60 eV. Above 60 eV, it changes its sign and monotonically increases as a positive current. The zero-crossing at 60 eV is well explained by the ionization cross-section maximum of Ar atoms at 60 eV, [36] where most electrons are consumed to ionize Ar atoms resulting in scare incident electrons into the substrate surface. As the electron energy increases further, ionized Ar atoms also increase, resulting in a positive sample current due to increase in Ar+ ions. A typical RHEED pattern and a θ-2θ XRD scan of CeO2 (100) layers grown with 90 eV electron beam irradiation and oxygen radical beam application are shown in Figures 17 and 18, where oxygen gas flow was the optimum value of 0.8 sccm, as will be explained in the next section. This RHEED image is a (100) pattern of h110i azimuth, which consists of considerably large spots indicating not so good crystallinity. We can see a large (200) and small (111) XRD peaks in Figure 18. The appearance of the (111) peak indicated that the layer was not perfect CeO2 (100) single crystalline, wherein the (111) component was estimated to be 1.9 % from integrated intensities of the peaks and structure factor data. Full width at half maximum (FWHM) values of the (111) and (200) peaks are 0.668 and

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Figure 16. RHEED pattern of CeO2 (100)/Si(100) sample grown with 35 eV electron beam irradiation.

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Figure 17. RHEED pattern of CeO2 (100)/Si(100) sample grown with 90 eV electron beam irradiation. 0.491 ◦ , respectively. Figure 19 shows a XRD scan of CeO2 (100) layers grown under the same conditions as those of the sample in Figures 17 and 18, except for irradiated electron beam energy of 35 eV. FWHM values of the (111) and (200) peaks are 0.779 and 0.598 ◦ , respectively. Comparing with the result in Figure 18, crystalline quality is inferior to that grown with 90 eV electron beam irradiation. Moreover, (111) component is very large, 18.9 %.

Figure 18. θ-2θ XRD scan of CeO2 (100)/Si(100) sample grown with 90 eV electron beam irradiation. Since it is commonly recognized that CeO2 (100) layers do not grow on non-biased Si(100) substrates except for the growth by molecular beam epitaxy on reconstructed surfaces, [21] it is apparent that electron irradiation does have the effect on the CeO2 (100)

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Figure 19. θ-2θ XRD scan of CeO2 (100)/Si(100) sample grown with 35 eV electron beam irradiation. growth. The similar quality CeO2 (100) layers were obtained for electron energies in the two ranges of 30 ∼ 40 and 80 ∼ 100 eV, which were confirmed by RHEED and XRD measurements. These two optimum electron energy regions for the CeO2 (100) growth are indicated by broken line rectangles in Figure 152. The energy window width of the latter region is wider than that of the former. The orientation preferential growth is thought to be due not to joule heating but to surface potential modification, since electron beam power is estimated to be approximately 1.6 mW/cm2 , which corresponds to a substrate temperature rise of 1 ◦ C at most. On the contrary, it is clarified that electron beams with energies in the vicinity of 60 eV and above 100 eV have no effects on the CeO2 (100) growth. These are explained as follows: Since the beam current of 60 eV electrons are nearly zero, electron irradiation effects scarcely occur. Electrons above 100 eV may have too much energy to give surface effects. We think that electrons of 30 ∼ 40 eV are primarily effective in modifying surface potential. The reason why 90 eV electrons are effective is due that 90 eV electrons should reduce their kinetic energy down to ∼ 30 eV, since they lose energy by ∼ 60 eV to ionize Ar atoms. [36] As the absolute values of the sample currents in 35 and 90 eV electron beam irrdiation are similar, the estimated ion current component in the case of 90 eV electron irradiation is twice as that of electrons, which is thought to correlate with higher crystalline quality of the CeO2 (100) layers grown with 90 eV electron irrdaition. We think that the cause of superiority of 90 eV electrons is due to effects of ions such as Ar+ , Ce+ , CeO+ and so on, since kinetic energy of irradiated electrons at substrate surfaces are almost the same in both cases as mentioned above. Considering above described experimental results, for electron beam induced OSE, 90 eV electrons proved to be superior to 35 eV, since it leads to hihger crystallinity and higher orientation selectivity (smaller (111) component). Moreover, 90 eV electron beams have the wider width of optimum energy mentioned above, and will be favorable for beam focusing ability and precise scanning control. In order to exactly determine optimum electron energy, we got the relation between FWHM values of XRD (200) peaks of CeO2 layers and irradiated electron beam energy around 90 eV, as shown in Figure 20. Open circular and square marks indicate results of samples grown without and with oxygen radical beam irradiation. Oxygen gas flow rates in the epitaxial growth experiments were 0.9 and 0.8 sccm without and with oxygen radical

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FWHM of (200) peak (degree)

beam application, respectively, which were employed from the optimized conditions described in the next section. It is found that optimum electron energy is exactly at 90 eV and does not change by oxygen radical beam irradiation. [35] The FWHM minima at 90 eV were 0.617 and 0.490 ◦ for without and with oxygen radical beam irradiation, respectively. From this 20 % decrease, it is worth noting that oxygen radical beam irradiation considerably improves crystalline quality. This crystalline quality improvement by oxygen radicals is quite similar to the results reported in the previous work on OSE growth by substrate bias. [25] 0.8

0.7

0.6

0.5

0.4 80

85

90

95

100

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EB energy (eV) Figure 20. FWHM of XRD (200) peak as a function of electron beam energy around 90 eV. Open circular and square marks indicate results of samples grown without and with oxygen radical beam irradiation, respectively.

5.2.

Optimization of Oxygen Gas Flow Rate

It is indicated that electron beam irradiation during the epitaxial growth leads to not only surface potential modification but an oxidation enhancement effect, [37] from crosssectional transmission electron microscopy (XTEM) observations of interfacial structures as mentioned later. At present, interfacial amorphous layers due to excess oxidation are found in the electron beam induced OSE grown CeO2 (100) layers with oxygen gas flow of 1.0 sccm, whereas no amorphous layers are found in the sample grown by the substrate bias application method under the same growth conditions. [38] We expect that the optimum growth condition of oxygen gas flow should be smaller for electron beam induced OSE than that for OSE by substrate bias. In order to improve crystalline quality and interface properties, we made systemtic experiments to optimize the growth parameter of the oxygen flow rate. Figure 21 shows FWHM values of the XRD (200) peak as a function of the oxygen flow rate, where open circular and square marks indicate results of samples grown without and with oxygen radical beam irradiation, respectively. There are suitable regions for getting low FWHM values;

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FWHM of (200) peak (deg.)

Orientation Selectivity Control by Surface Potential Modification...

221

0.7

0.6

: without O radical

0.5

: with O radical

0.7

0.8

0.9

1.0

oxygen flow (sccm) Figure 21. FWHM of XRD (200) peak as a function of oxygen flow. Open circular and square marks indicate results of samples grown without and with oxygen radical beam irradiation, respectively.

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0.85 ∼ 1.0 and 0.7 ∼ 1.0 sccm for the growth methods without and with oxygen radical beam irradiation, respectively. In the latter, the suitable region widely spreads toward the lower oxygen flow rate side. It is obvious that the outside of these two regions; deficient or excess oxygen gives poorer crystallinity. As a result, the optimum oxygen gas flow rates, where FWHM’s are minimum, were determined to be 0.9 and 0.8 sccm for without and with oxygen radical beam application. This decrease by 0.1 sccm is due to the oxidation enhancement effect of oxygen radials.

5.3.

Lower Limit of Substrate Resistivity

In order to understand the OSE growth mechanism, it is important to clarify how is the potential modulation at the substrate surface. We think that band bending due to irradiated electrons leads to orientation selection of CeO2 (100). [23] Different from OSE by substrate bias application, electron beam induced OSE has potential ability of realizing two dimensinoally patterned OSE, where spatial distribution should be an important parameter to be studied. The spread of the potential modulated region outside the electron beam irradiated area must be influenced by migration of electrons, which should correlate with the conductivity of the silicon substrate. We carried out additional experiments of growing CeO2 layers on Si(100) substrates with different resistivities under the same growth condition. The CeO2 layers grown on low resistivity substrates of 1.0 ∼ 2.0 Ω·cm had (100) orientation and showed similar results to those shown in Figures 17 and 18, whereas CeO2 layer grown on lower resistivity substrates of 0.1 ∼ 0.2 Ω·cm had no longer (100) orientation. It is supposed that surface mobility determines the spreading of OSE region and roughly speaking, substrate resistivity above 2 Ω·cm is needed for OSE. [34]

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6.1.1.

Tomoyasu Inoue

Characterization of OSE Layers Cross-Sectional Lattice Image Observation (XTEM) XTEM Sample Fabrication and Observation of CeO2 (110)/Si(100)

In order to get insight into the origin of orientation selective epitaxy , it is helpful to investigate lattice images of the epitaxially grown samples by XTEM observations. It is, however, somewhat difficult to make samples for XTEM observation by the conventional method using slicing, lapping, polishing and Ar ion milling of bonded wafers. The difficulties are a low yield in getting good samples and exact positioning of a desired observation point. Recently, FIB technique has been widely used in very thin layer fabrication for XTEM observation, where a surface protective metal layer is usually formed by ion-beam-assisted chemical vapor deposition (CVD) to avoid any damage caused by the subsequent highly accelerated ion beam etching. It has been reported that the metal layer deposition itself induces damage at the specimen surface. We adopted metal layer deposition by electron-beam evaporation of 400 nm thick Ti or 700 nm thick Au layers before the W layer deposition in an area for the micro-fabrication. FIB fabrication procedure was as follows: firstly Ga ion beam assisted CVD of W layer of 300 nm in thickness and 3 × 15 µm in area was carried out on the desired position in the wafer, for reinforcement of protection against subsequent Ga ion sputtering. Then rectangular blocks of the same area as the W deposited area and 3 µm in depth were engraved using 40 keV Ga FIB, followed by thinning the central part into the thickness of below 60 nm using fine focused FIB of ∼ 6 nm in diameter. Since the thinned layer have tendency to bend due to stress concentration at the boundary between the thinned and un-thinned parts. In order to relax the stress concentration, we utilized a multi-step structure as shown in Figure 22, which shows plan view photographs of the micro-fabricated sample taken by a scanning ion microscopy (SIM). The central parts were thinned for TEM observation: adequately thinned sample of ∼ 60 nm in thickness (Figure 22 (a)) and bended sample due to over-thinning whose crystallinity was destroyed by the ion beam induced damage (Figure 22 (b)). It is reported that after high energy Ga FIB etching, the side-wall damage layers of more than 20 nm in thickness remains on both sides, which is serious problem not to destroy crystallinity of the specimen. In order to reduce the damage, 10 keV Ga ion beam irradiation was employed as a final step of the etching. The final etching was carried out on the both side of the thinned layer in raster scanning mode at the shallow incidence angle of 2 ◦ , since fine focusing sufficient for required fine etching is unable at that energy. As a protective layer, Au layer seems to be preferable to Ti layer, since empirically speaking, Au coating leads to higher yield in getting good specimens, which may be due to lower chemical activity to reducing CeO2 layers. CeO2 can be reduced by Ti but not by Ga, since standard enthalpy of formation (∆f H ◦ ) of Ce2 O3 , Ti4 O7 and Ga2 O3 are –1796.2, –3404.52 and –1089.1 kJmol−1 , respectively. It is reported that CeO2 decomposes above 690 ◦ C in a vacuum due to Ce-O bond dissociation. [39] During FIB fabrication process, a local temperature rise originated from ion irradiation may induce the reduction by Ti atoms. Therefore, it is preferable to use low current density Ga ion beams. In addition to the multi-step structure in fabricating thinned layers, adopting 10 keV Ga FIB irradiation as a final etching, successful results are obtained in getting cross-sectional

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Figure 22. Plan views of micro-fabricated samples. (a): adequately thinned sample, (b) bended sample due to over-thinning.

Figure 23. XTEM lattice image of an OSE grown CeO2 (110)/Si(100) structure.

TEM samples. Figure 23 shows an example of the XTEM image of a CeO2 (110)/Si(100) structure, where lattice images are seen both in the CeO2 (110) layer and the Si(100) substrate. There are a lot of small angle grain boundaries in the CeO2 (110) layer, which may enhance oxygen diffusion during the 2nd step epitaxial growth. Interfacial amorphous layers are seen in Figure 23, which consist of oxygen deficient CeOx and SiOx double layers, which agree well with reported XTEM observations and are commonly reported in epitaxial CeO2 /Si structures irrespective of growth methods for a long time. [32, 40, 41] Though these amorphous layers have been thought to be inevitable through thermodynamical consideration, [42] recently, we have got some XTEM results of CeO2 (100)/Si(100)

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structures indicating no interfacial layers as shown in Figure 24. This indicates that interfacial oxidation can be effectively controlled by the two step growth method mentioned in section 3.2., resulting in an ideal interface structure. Comparing with the result in Figure 23, there are not so many defects such as small angle grain boundaries, which may lead to normal oxygen diffusion and contribute toward the epitaxial growth without interfacial amorphous layers.

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6.1.2.

Observation of CeO2 (100)/Si(100)

For crystallinity analysis especially on interfacial structures, we made XTEM observations of CeO2 (100)/Si(100) samples. Figure 25 shows an XTEM image taken from the CeO2 (100)/Si(100) sample grown with 90 eV electron irradiation and 0.9 sccm oxygen gas flow without radical source operation, indicating double amorphous layers consisted of dark CeOx and bright SiOx layers. Respective thicknesses of the two layers are evaluated to be 1.4 and 2.1 nm. The double amorphous layer sturucutre is ususally observed in CeO2 (110)/Si(100) and CeO2 (111)/Si(111) structures grown by various methods; vacuum evaporation, sputtering, laser ablation and so on. [11, 32, 38] For reference, an XTEM image taken from the CeO2 (100)/Si(100) sample grown under +15 V substrate bias with 1.0 sccm oxygen gas flow without radical source operation is shown in Figure 24, where no interfacial amorphous layers are seen, resulting from perfect interface control by optimization of the growth parameters in the OSE growth by substrate bias application. [38] Although the sample in Figure 25 was grown with optimized oxygen flow rate of 0.9 sccm, there remained interfacial amorphous layers. These results indicate that interfacial oxidation enhancement due to electron beam irradiation [37] is beyond our expectations. We are proceeding further with XTEM studies. Although samples without interfacial amorphous layers are not yet observed in electron beam induced OSE grown samples, the thickness of the amorphous layer proved to correlate with growth conditions of the oxygen flow rate and oxygen radical beam irradaition. That is, the growth parameters giving thinner amorphous layers agree well with those for smaller FWHM values. The balance between two rates; epitaxial growth and in-diffusion of oxidants, is thought to be essential in an ideal growth model for perfect interface control. The detailed balancing should result in no interfacial amorphous layers. It is needed to gather more XTEM data for the accurate investigation of interfacial properties and for optimization of the other growth parameters, such as the metallic Ce layer thickness at the first step and the growth rate at the second step, including a search for new methods to suppress the oxidation enhancement effect due to electron beam irradiation.

6.2.

Surface Morphology

In most microelectronic applications of oxide thin films, smoother surfaces are preferable, except for dielectric layers in miniaturized capacitors to increase capacitance. It is understood that surface morphology of CeO2 layers closely correlates with crystallinity, including crystallographic orientation and crystalline quality of the layers. [43–45] It has been reported that CeO2 (111) and CeO2 (110) surfaces are made of tetrahedral and gable roof shaped rectangular hillocks, respectively, both of which consist of (111) facets. [17, 46–48]

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Figure 24. An XTEM image of the CeO2 (100)/Si(100) structure grown under substrate bias of +15 V. The oxygen gas flow rate was 1.0 sccm.

Figure 25. An XTEM image of the CeO2 (100)/Si(100) structure grown with 90 eV electron irradiation without radical beam irradiation. The oxygen gas flow rate was 0.9 sccm. Figures 26 (a) and (b) show AFM images of 15 nm-thick-CeO2 (110) and 11 nm-thickCeO2 (100) layer surfaces, respectively. As seen in Figure 26 (a), the CeO2 (110) surface reveals the features mentioned above, which is the same as reported results [46] except that their size is smaller due that the layer is thinner. There are two arrangements, vertical and longitudinal, which corresponds to equivalent two directions of CeO2 (110) on Si(100). The shape of the (110)-oriented CeO2 surface consists of gable roof shaped rectangular hillocks laid in parallel manner along the two h100i directions of the underling Ce-Si lattice epitaxially grown on the Si(100) surface. [43] The Ra value was 0.49 nm, which is larger than that of the CeO2 (100) surface shown in Figure 26 (a). On the other hand, we think that hillocks on the CeO2 (100) surface seen in Figure 26 (b) should have a pyramidal shape made of four (111) facets, though they look like a round shape due to insufficient spatial resolution of our AFM observations. The averaged roughness (Ra) was evaluated to be

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Figure 26. AFM images of (a) CeO2 (100) and (b) CeO2 (110) layers.

0.36 nm, which indicated that the CeO2 (100) surface was smoother than that of CeO2 (110).

7.

Conclusion

Orientation selectivity in epitaxial growth of thin CeO2 layers on Si(100) substrates was extensively studied and revealed to be ruled by Coulombic interraction between depositing molecules and Si substrates. As a new tehcnology, it is clarified that growth orientation is artificially selected by the control of substrate surface potential. Two methods for the OSE growth are described in details; orientation control by substrate bias and electron beam ir-

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radiation, where the latter has potential ability for development into two demensional OSE patterned growth. OSE growth experiments were carried out using reactive dc magnetron sputtering enhanced with an inductively coupled rf plasma and oxygen radical beam irradiation, combining with substrate bias application and low energy electron beam irradiation. The two step growth method was revealed to be effective in attaining stable and reproducible high quality epitaxial growth of CeO2 layers due to prevention of oxidation of Si surfaces at the initial stage of CeO2 layer growth. Combining substrate bias application with the two step growth method, it was found that OSE growth of (100) and (110) orientations was realized by the control of substrate bias and the growth rate. Precise growth conditions for CeO2 (100) epitaxy were clarified as an orientation selection map in terms of substrate bias, the growth rate and plazma power. In order to study the origin of the orientation selectivity, XRD measurements for analyses of orientation component variation as a function of substrate bias and XTEM observations were performed. Lattice images obtained by XTEM observtions utilizing FIB technique for sample fabrication revealed that crystallographic aspects of CeO2 layers and inerfacial structures. The interface without amorphous sub-oxide layers was confirmed to be realized in CeO2 (110)/Si(100) structures, which was owing to precise control of the influence of oxygen in-diffusion by the two step growth method. Surface morphology of both CeO2 (110) and CeO2 (100) layers were analyzed by AFM observations. The CeO2 (100) layer has smoother surface consisted of small pyramidal hillocks, whereas the CeO2 (110) surface consisted of gable roof shaped hillocks. It is still unclear why adequate substrate bias regions for CeO2 (100) growth are around 15 V in both positive and negative bias, why the growth rate for CeO2 (100) growth has an upper limit, and why the upper limit increases with plasma power. More integration of experimental data and precise investigations on the growth mechanism will be needed. On the other hand, electron beam induced OSE was demonstrated and optimization of growth parameters on electron beam energy and oxygen gas flow were reported. The electron beam induced OSE technology has great possibility of development for sophisticated applications, such as getting selectively orientation controlled overlayers, e.g. selected growth of Si(100) and Si(110) layers on a monolithic chip for future advanced extreamly high speed complemetary metal-oxide-silicon (CMOS) devices and orientation controlled high temperature superconductors. Effectiveness of assistance by oxygen radical beams in reactive sputtering was confirmed in the OSE growth of CeO2 (100) layers by both OSE methods. It was confirmed that epitaxial growth temperature was reduced at least by 100 ◦ C compared with conventional reactive sputtering simply adding oxygen gas flow. It was also clarified that oxygen radicals brought nucleus generation into better unification of crystallographic orientation, resulting in improvement of crystalline quality of CeO2 (100) layers, as analyzed by XRD measurements. We hope that the OSE technology widely spread to other polar materials.

Acknowledgements The author is grateful to Dr. K. Kato and Y. Sampei of Fukushima Technology Centre, and Dr. N. Sakamoto, S. Shida, M. Ohashi, H. Ohtake, T. Saito, T. Hikichi and T. Akutsu of Iwaki Meisei University for their help in epitaxial growth experiments, XRD measurements,

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XTEM and AFM observations. A part of this work was conducted in AIST Nano-Processing Facility, supported by ”Nanotechnology Support Project” of the Ministry of Education, Culture, Sports, Sciece and Technology (MEXT), Japan.

References [1] Fork, D. K.; Phillips, J. M.; Ramesh, R.: Wolf, R. M. (Ed.) Epitaxial Oxide Thin Films and Heterostructures, Proc. Mat. Res. Soc. (1994), 341. [2] Speck, J. S.; Fork, D. K.: Wolf, R. M.; Shiosaki, T. (Ed.) Epitaxial Oxide Thin Films II, Proc. Mat. Res. Soc. (1996), 401. [3] Schlom, D. G.; Eom, C. B.; Hawley, M. E.; Foster, C. M.; Speck, J. S. (Ed.) Epitaxial Oxide Thin Films III, Proc. Mat. Res. Soc. (1997), 474. [4] Nakazawa, T.; Inoue, T.; Satoh, M.; Yamamoto, Y. Jpn. Appl. Phys. (1995), 34, 548– 553. [5] Luo, L.; Wu, X. D.; Dye, R. C.; Muenchausen, R. E.; Foltyn, S. R.; Coulter, Y.; Maggiore, C. J.; Inoue, T. Appl. Phys. Lett. (1991), 59, 2043–2045. [6] Nishikawa, Y.; Yamaguchi, T.; Yoshiki, M.; Satake, H.; Fukushima, N. Appl. Phys. Lett. (2002), 81, 4386–4388.

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[7] Inoue, T.; Yamamoto, Y.; Koyama, S.; Suzuki, S.; Ueda, Y. Appl. Phys. Lett. (1990), 56, 1332–1333. [8] Inoue, T.; Osonoe, M.; Tohda, H.; Hiramatsu, M.; Yamamoto, Y.; Yamanaka, A.; Nakayama, T. J. Appl. Phys. (1991), 69, 8313–8315. [9] Yoshimoto, M.; Shimozono, K.; Maeda, T.; Ohnishi, T.; Kumagai, M.; Chikyow, T.; Ishiyama, O.; Shinohara, M.; Koinuma, H. Jpn. J. Appl. Phys. (1995), 34, L688– L690. [10] Furusawa, M.; Tashiro, J.; Sasaki, A.; Nakajima, K.; Takakura, M.; Chikyow, T.; Ahmet, P.; Yoshimoto, M. Appl. Phys. Lett. (2001), 78, 1838–1840. [11] Yaegashi, S.; Kurihara, T.; Hoshi, H.; Hasegawa, H. Jpn. J. Appl. Phys. (1994), 33, 270–274 [12] Huang, D.; Qin, F.; Yao, Z.; Ren, Z.; Lin, L.; Gao, W.; Ren, Q. Appl. Phys. Lett. (1995), 67, 3724–3726. [13] Yoshimoto, M.; Nagata, H.; Tsukahara, T.; Koinuma, H. Jpn. J. Appl. Phys. (1990), 29, L1199–L1202. [14] Inoue, T.; Ohsuna, T.; Luo, L.; Wu. X. D; Maggiore, C. J.; Yamamoto, Y.; Sakurai, Y.; Chang, J. H. Appl. Phys. Lett. (1991), 59, 3604–3606. Recent Advances in Dielectric Materials, Nova Science Publishers, Incorporated, 2009. ProQuest Ebook Central,

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[15] Tarsa, E. J.; McCormick, K. L.; Speck, J. S. Proc. Mat. Res. Sci. (1994), 341, 73–85. [16] Nagata, H.; Tsukahara, T.; Gonda, S.; Yoshimoto, M.; Koinuma, H. Jpn. J. Appl. Phys. (1991), 30, L1136–L1138. [17] Inoue, T.; Ohsuna, T.; Obara, Y.; Yamamoto, Y.; Satoh, M.; Sakurai, Y. J. Cryst. Growth (1993), 131, 347–351. [18] Inoue, T.; Yamamoto, Y.; Satoh, M.; Ohsuna, T.; Myoren, H.; Yamashita, T. Proc. Mat. Res. Soc. (1994), 341, 101–106. [19] Inoue, T.; Yamamoto, Y.; Satoh, M. Proc. Mat. Res. Soc. Symp. (1997), 474, 321–326. [20] Inoue, T. Research Trends (2001), 4, 61–75. [21] Ami, T.; Ishida, Y.; Nagasawa, N.; Machida, A.; Suzuki, M. Appl. Phys. Lett. (2001), 78, 1361–1363. [22] Inoue, T.; Sakamoto, N.; Ohashi, M.; Shida, S.; Horikawa, A.; Sampei, Y. J. Vac. Sci. Technol. (2004), A22, 46–48. [23] Inoue, T.; Ohashi, M.; Sakamoto, N.; Shida, S. J. Cryst. Growth (2004), 271, 176– 183. [24] Inoue, T. Recent Res. Devel. Cryst. Growth (2005), 4, 251–268.

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[25] Inoue, T.; Shida S.; Kato, K. J. Cryst. Growth (2006), 289, 534–539. [26] Chen, X. Y.; Wong, K. H.; Mak, C. L.; Yin, X. B.; Wang, M.; Liu, J. M.; Liu, Z. G. J. Appl. Phys. (2002), 91, 5728–5734. [27] Goettler, R. L.; Maria, J. P.; Schlom, D. G. Mat. Res. Soc. Symp. Proc. (1997), 474, 333–338. [28] Hillebrecht, F. U. Appl. Phys. Lett. (1989), 277, 277–279. [29] Grioni, M.; Joyce, J.; Chambers, A. A.; O’Neill,D. G.; Giudice, M. del; Weaver, J. H. Phys. Rev. Lett. (1984), 53, 2331–2334. [30] Matzke, H. In “Nonstoichiometric Oxides”; Sørensen, O. T.; Ed.; Academic Press: New York, NY, (1981), 155–232. [31] Inoue, T.; Ohsuna, T.; Obara, Y.; Yamamoto, Y.; Satoh, M.; Sakurai, Y. Jpn. J. Appl. Phys. (1993), 32, 1765–1767. [32] Tye, L.; Chikyow, T., El-Masry, N. A.; Bedair, S. M. Mat. Res. Soc. Symp. Proc. (1994), 341, 107–112. [33] Inoue, T.; Saito, T.; Shida, S. J. Cryst. Growth (2007), 304, 1–3. [34] Inoue, T.; Nakata, Y.; Shida, S. J. Phys. Conf. Ser. (2008), 100, 082014. Recent Advances in Dielectric Materials, Nova Science Publishers, Incorporated, 2009. ProQuest Ebook Central,

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[35] Inoue, T.; Ohtake, H.; Otani, J.; Shida, S. Electrochem. Soc. Trans. (2008), 13, 341– 351. [36] http://dpsalvia.nifs.ac.jp/cgi-bin/ala dispdata.cgi?20224+BELI [37] Reuter, W. ; Wittmaack, K. Appl. Sur. Sci. (1980), 5, 221–242. [38] Inoue, T.; Nakata, Y.; Shida, S.; Kato, K. J. Vac. Sci. Technol. (2007), A25, 1128– 1132. [39] Yamamoto, Y.; Arai, S.; Matsuda, T.; Satoh, M.; Inoue, T. Jpn. J. Appl. Phys. (1997), 36, L133–L135. [40] Inoue, T.; Ohsuna, T.; Obara, Y.; Yamanoto, Y.; Satoh, M.; Sakurai, Y. Jpn. J. Appl. Phys. (1993), 32, 1765–1767. [41] Inoue, T.; Yamanoto, Y.; Satoh, M.; Ohsuna, T.; Myoren, H.; Yamashita, T. Mat. Res. Soc. Symp. Proc. (1994), 341, 101–106. [42] Schlom, D. G.; Haeni, J. H. MRS Bulletin (2002), 27, 198–204. [43] Inoue, T.; Nakamura, T.; Nihei, S.; Kamata, S.; Sakamoto, N.; Yamamoto, Y. J. Vac. Sci. Techonol. (2000), A18, 1613–1618. [44] Inoue, T.; Shida, S.; Sakamoto, N.; Horikawa, A.; Takakura, H.; Takahashi, K.; Ohashi, M. J. Vac. Sci. Technol. (2003), A21, 1371–1375.

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[45] Inoue, T.; Shida, S.; Sakamoto, N.; Horikawa, A.; Ohashi, M. J. Cryst. Growth (2003), 253, 366–373. [46] Inoue, T.; Yamamoto, Y.; Satoh, M.; Ide, A.; Katsumata, S. Thin Solid Films (1996), 281-282, 24–27. [47] Inoue, T.; Ohsuna, T.; Yamada, Y.; Wakamatsu, K.; Itoh, Y.; Nozawa, T.; Sasaki, E.; Yamamoto, Y.; Sakurai, Y. Jpn. J. Appl. Phys. (1992), 31, L1736–L1739. [48] Inoue, T.; Yamamoto, Y.; Satoh, M.; Ohsuna, T. Mat. Res. Soc. Symp. Proc. (1995), 367, 323–328.

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Chapter 5

U NUSUAL D IELECTRIC P ROPERTIES OF C AC U 3 T I 4 O 12 1

W. Kobayashi1∗and I. Terasaki2† Waseda Institute for Advanced Study, Waseda University, Tokyo 169-8050 2 Department of Applied Physics, Waseda University, Tokyo

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Abstract The A-site ordered perovskite CaCu3 Ti4 O12 has been extensively studied since the discovery of the huge dielectric constant by Subramanian and the coworkers. This material is clearly different from conventional ferroelectrics, because the dielectric constant comes from neither structure phase transitions nor soft phonons. The huge value is thus most likely to be extrinsic, and can be explained by a barrier layer capacitor model. An important feature is that the dielectric constant is well controlled in the forms of solid solutions and composites. In this article, we will review various aspects of CaCu3 Ti4 O12 such as the basic physical properties, the impurity effects, and the composites with other dielectrics to show how unusual they are. We further introduce some related oxides that have unconventional physical properties originated from the peculiar crystal structure of AA03 B4 O12 .

1.

Introduction

Recent development in electronic technologies requires new materials having dielectric constants much larger than the state-of-the-art dielectrics. Such materials can be applied to smaller and lighter capacitors, and may even be used as a substitute for rechargeable batteries. The A-site ordered perovskite CaCu3 Ti4 O12 (CCTO) has attracted much attention in this respect; Subramanian et al. [1,2] discovered that ceramic samples of CCTO have a very large dielectric constant ε0 of 104 , which is nearly constant from 100 to 400 K below 1 MHz. Homes et al. reported a huge ε0 ∼ 105 at 250 K below 20 kHz in a single crystal sample [3]. ∗ †

E-mail address: [email protected] E-mail address: [email protected]

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A

A’

BO6

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Figure 1. Crystal structure of AA03 B4 O12 -type ordered perovskite.

These works have stimulated many researchers’ interests from both technological and scientific points of view, having caused hot discussion whether the huge dielectric constant is intrinsic or extrinsic. At the moment, a majority of the papers seems to support extrinsic mechanisms. Lixin He et al. [4] performed a first-principles study of CCTO, and found that the dielectric constant is 40, which is much smaller than the observed value of 104 . Kolev et al. [5] did not find any anomalous change with temperature in the Raman spectra of CCTO, which suggests that the huge dielectric constant has no relation with atomic displacements. Sinclair et al. [6] pointed out that the dielectric response is explained in terms of semiconducting-insulating grain boundaries. Lunkenheimer et al. [7] claimed that a huge dielectric constant exceeding 103 is often interpreted by Maxwell-Wagner-type extrinsic effects. On the other hand, pyroelectric effect [8], polarization-electric field hysteresis [8, 9], and relaxor-like behavior [10, 11] were reported, which favor intrinsic mechanisms. As shown in Fig. 1, the AA03 B4 O12 -type oxides (cubic with the space group Im¯ 3) have an ordered perovskite-type structure in which only the Jahn-Teller ions of Cu2+ and Mn3+ occupy the A0 site [12]. The most striking feature of these compounds is that the magnetic ions in the A0 site can interact with conductive and/or magnetic ions in the B site. The A site in this structure accomodates various large cations such as Na+ , Cd2+ , Ca2+ , Sr2+ , Y3+ , R3+ , Th4+ and U4+ (R; lanthanide), while the B site accepts small cations such as Mn3+ , Fe3+ , Al3+ , Cr4+ , Ti4+ , Mn4+ , Ge4+ , Sn4+ , Ru4+ , Ir4+ , Nb5+ , Ta5+ and Sb5+ . The lattice parameter is twice as large as that of the ideal ABO3 perovskite, where the A ions lie at the bcc position in the unit cell. They have wide variety of cation compositions, and various substitutions are possible for the A, A0 and B sites. Owing to this peculiar structure, some of them show interesting physical properties such as large magnetoresistance [13] and electronic phase separation [14] in CaMn3−x Cux Mn4 O12 , valence degeneracy in CaCu3 Cr4 O12 and CaCu3 Ru4 O12 [15], unconventional metal-insulator transition in CaCu3 Ru4−x Tix O12 [16], and insulating ferromagnetic order in CaCu3 Sn4 O12 and CaCu3 Ge4 O12 [17]. A variety of materials is currently being developed; for example, CaCu3 V4 O12 [18] and CaCu3 Cr2 Ru2 O12 [19] have been newly synthesized. Even if the high dielectric constant is extrinsic, many properties are unconventional and probably controllable. In this article, we will review the current status of the CCTO studies,

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Figure 2. Partial density of states of CaCu3 Ti4 O12 (after [4]). The solid and dotted curves are for the up and down spins, where the antiferromagnetic unit cell is assumed.

mainly focusing on our works. After the basic physical properties are briefly summarized in section 2, the impurity effects on dielectric properties are discussed in section 3. Section 4 describes how the dielectric properties are improved in the form of ceramics composites. We show some peculiar features of the related materials in section 5, and finally give concluding remarks in section 6.

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2.

Physical Properties

Figure 2 shows the partial density of states of CCTO calculated by Lixin He et al [4]. While the Cu 3dx2 −y2 -O 2p antibonding bands are located just below the Fermi energy, the Ti 3d bands are 1.5 eV above the Fermi energy. This means that the Ti ions are most likely to be 4+ like other dielectric titanates, and the holes on the Cu ions are in the verge of itinerant states. The calculated magnetic moments on Cu are 0.85 µB , being roughly identical to S = 1/2. They calculated the lattice dynamics as well, and evaluated the oscillation strength and frequencies of all the phonon modes. The dielectric function is given as the summation of the Lorentz oscillators of such phonons, so that the low-frequency dielectric constant is P evaluated as ε0 = i fi /(ωi )2 , where fi and ωi are the oscillator strength and frequency for the i-th phonon modes, respectively. The calculated values are similar to those for other titanates, and the dielectric constant is evaluated to be 40-50, which is far smaller than the value observed by Subramanian et al. Figure 3 shows the dielectric constant ε0 and the loss tangent (dissipation factor) tan δ = 00 ε /ε0 of a single-crystalline sample of CCTO [3]. The values of ε0 at 20 Hz reach near 105 at room temperature, stay almost constant down to 50 K, and rapidly decrease to a small value of 102 towards 0 K. The dielectric constant changes with frequency for all the temperature range above 50 K, where the huge value at high temperature suddenly crossovers to the low value at low temperature. The characteristic temperature above which ε0 begins to increase systematically changes with frequency, and is roughly the same temperature at which tan δ shows a peak. We should note that the peak values of 5-7 in tan δ is too large for practical applications. In other words, CCTO has too large ε00 compared with other dielectrics. This

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Figure 3. Dielectric constant (upper panel) and dissipation factor (lower panel) of a CaCu3 Ti4 O12 single crystal (after [3]).

means that the conductivity (∝ ωε00 ) is significantly large; unwanted free carriers are selfdoped, or fluctuation of the electric dipoles is large. These features are well described by Debye’s dielectric relaxation, in which the relaxation time increases exponentially at low temperatures. Although the infrared [3] and Raman spectra [5] show detectable temperature dependence, neither soft phonons nor additional modes are observed in CCTO. The huge dielectric constant cannot be explained in terms of ferroelectric fluctuation, and no structural phase transition occurs below room temperature. The observed phonon frequencies are quantitatively consistent with the first principles calculation [4]. No anomalies in Raman spectra shows further consistency with the calculated small dielectric constant. These results suggest that the huge dielectric constant is extrinsic, coming from grain boundaries, electrodes, twin domains etc. A typical extrinsic explanation is modeled by an internal barrier layer capacitor. Suppose that a dielectric domain is slightly conductive owing to unwanted self-doped carriers, and separated from other domains by a thin, highlyinsulating barrier layer. Such materials will be highly insulating with respect to dc voltage, because the barrier layer blocks the dc conduction. The capacitance may be measured to be large at sufficiently low frequencies, where the intrinsic capacitance is determined by the thin barrier layer and the doped dielectric domain acts as a conducting lead. The dielectric constant is then seemingly enhanced by d0 /dbl , where dbl and d0 are the barrier thickness and the domain size. On the contrary, the capacitance is measured to be an intrinsic value of the dielectric domain when the measured frequencies are too quick for the doped carriers to move. This model is expressed by two R − C parallel circuits connected in series, and can be examined using impedance spectroscopy. Sinclair et al. [6] found the frequency dependence of the complex dielectric constant of CCTO is well understood by the internal

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Figure 4. Magnetic susceptibility and specific heat of a CaCu3 Ti4 O12 (after [20]). The inset shows the inverse susceptibility.

barrier layer model, and evaluated the resistivity for the bulk and grain boundaries. Aside from the dielectric properties, CCTO has been studied as a magnetic insulator. The Cu2+ ions show localized nature to behave as localized moments of S = 1/2, and exhibit an antiferromagnetic transition near 24 K. Figure 4 shows the magnetic susceptibility and the specific heat of CCTO at low temperatures, in which the two quantities show anomalies characteristic to a second order transition near 24 K [20]. A neutron diffraction experiment reveals that the spins are ordered antiferromagnetically along the (111) direction with a ferromagnetic alignment in the (111) planes [21]. The magnetic interaction is evaluated to be of the order of 30 K between the nearest neighbor sites. This value is close to the Neel temperature, suggesting the three dimensional and classical nature of the S = 1/2 spins. The classical picture is also seen in the temperature dependence of the inverse susceptibility, as shown in the inset of Fig. 4.

3.

Impurity Effects

We tried Na, Sr, and La substitutions for Ca, Mn substitution for Cu, and Sn, Zn, and Fe substitutions for Ti, and found that the Mn doping strongly suppressed the large dielectric constant of 104 to 102 [22, 23]. Figure 5 shows the dielectric constant (ε0 ) of CaCu3−x Mnx Ti4 O12 (x=0 and 0.06). The dielectric constant is 10000 for x=0 at 1 MHz at 300 K, which is similar to that reported in Ref. [2]. Unexpectedly, only 2% Mn substitution dramatically suppresses ε0 over the measured temperature range from 4.2 to 300 K. In usual substitution effects, we expect that 2% impurity induces a 2% change in the response, which is definitely different what is observed here. After our findings, several substitution effects are investigated [24–27], and the strong suppression of ε0 by Mn substitution was verified [24, 26, 27]. Cai et al. propose that the holes induced by Mn ions affect the oxygen vacancies or the compositional nonstoichiometry to compensate the unwanted conribution of doped electrons [27]. Grubbs et al. [25] find that Fe substitution in the 2-5 atomic % range makes CCTO insulating with a low ε0 of the order of 102 . They also propose the carrier compensation for the origin of the suppression. On the contrary, we partially substi-

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ε'

104 103 x=0 (0%)

102 160

Figure

06) [22] 10000

ε'

8000 6000 4000 2000 0

Ca1+xCu3-xTi4O12 -0.1

0 x

0.1

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Figure 6. The dielectric constant of Ca1+x Cu3−x Ti4 O12 (x=−0.1, −0.05, 0, 0.05, 0.1) at 1MHz at 300K [22]

tuted Na+ and La3+ for Ca2+ , but found almost no change in the dielectric response. These results are incompatible with the carrier compensation scenarios, and the doped Mn and Fe ions are unlikely to be simple dopants. Figure 6 shows the dielectric constant of Ca1+x Cu3−x Ti4 O12 (x=−0.1, −0.05, 0, 0.05, and 0.1) at 1 MHz at 300 K. ε0 is severely suppressed with x for x < 0, whereas it is insensitive to x for x > 0. Considering that the bcc structure formed by Ca ions is disordered for x < 0, we claim that the Ca site is important for the large dielectric constant. Fang et al. [28] examined Cu-nonstoichiometry effect on the dielectric properties of Cu poor CaCu2.9 Ti4 O12 and Cu rich CaCu3.1 Ti4 O12 . The Cu-rich sample exhibits ε0 =3500 and the Cu-poor sample shows ε0 =10000 at 300 K and 1 kHz, in which the tendency is opposite to our data. Now we discuss a possible origin of the suppression of the dielectric constant. As an extrinsic scenario, the suppression by Mn substitution can be explained by the compensation of the carriers in grains. Nonstoichiometric effects of Ca and Cu ions on the dielectric properties can be explained by a size effect of the grains. As Fang et al. [28] reported, a sample composed of smaller grains tends to exhibit a smaller dielectric constant, which is naturally understood in the case of the barrier layer capacitor. The other scenario is an

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intrinsic effect due to dipole moments interacted (probably frustrated) in CaCu3 Ti4 O12 , as is seen in the charge-ordered ferroelectrics LuFe2 O4 [29]. Then, the rapid decrease in ε is attributed to pinning or breaking the domain wall of the frustrated ferroelectric domains. Indeed, domain wall and dipole moment are observed in CaCu3 Ti4 O12 . Chung [30] found the polarization switching in CCTO, and explained it in terms of the deviation from the cubic symmetry. Liu et al. [9] propose structurally frustrated relaxor ferroelectric behavior in CCTO showing dielectric hysteresis loop. We should note that certain substitutions improve the dielectric properties of CCTO. Kwon et al. [31] reported that 1-% Cr2 O3 -doped CCTO exhibits a high dielectric constant of 19000 with a low loss tangent of 0.05 at 1 kHz. Patterson et al. [32] found that 0.1 − 0.5 wt. % ZrO2 -doped CCTO exhibits a large dielectric constant of 5000 with a low loss tangent of 0.02 between 50 Hz and 30 kHz.

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4.

CCTO-Based Composites

It is well known that the dielectric properties can be improved in the form of composite materials. We prepared a set of ceramic samples with nominal compositions of Ca1+x Cu3−x Ti4 O12 to try to make solid solutions between CCTO and CaTiO3 (CTO) [23], which is an extension work from Fig. 6. A single phase did not appear in the nominal composition range of 0.1 ≤ x ≤ 2.9. This is rather surprising, because the crystal structure of CCTO is nearly the same as that of CTO. We found that the 1:1 composite of CCTO and CTO (the nominal composition of Ca2 Cu2 Ti4 O12 ) shows the best dielectric properties, which we named CCT-CT-1. Figure 7 shows ε0 and tan δ of CCT-CT-1. A large ε0 of 1800 is almost independent of temperature from 220 to 300 K for 102 to 105 Hz. It should be emphasized that tanδ remains at a low value of 0.02 in the same frequency and temperature ranges. This value is one order of magnitude smaller than that of CCTO, and is small enough for practical applications. Below about 220 K, ε0 rapidly decreases with a peak in tanδ, as is seen in CCTO. Figure 8 shows ε0 and tanδ of state-of-the-art dielectric materials [33], together with the data of partially substituted CCTO ceramics. EIA (Electronic Industries Association in USA) standards classifies high dielectric capacitors into X5R, X7R, Z5U and Y5V, which are roughly represented by dotted rectangles in Fig. 8. The dielectric performance of CCT-CT-1 is in the X5R/X7R standards, which is comparable with those of BaTiO3 and Pb(Sc1/2 Ta1/2 )O3 . Here we will briefly mention how the dielectric properties are improved. Figure 9 shows the room-temperature dielectric properties of (1-y)CaTiO3 + yCa1/4 Cu3/4 TiO3 at 100 kHz, where y represents a volume fraction of CCTO (y = 0.66 corresponds to CCT-CT-1). ε0cal shown by the dotted curve is a calculation from Lichtenecker’s logarithmic law [34] written by ln ε0cal = y ln ε0CCTO + (1 − y) ln ε0CTO , (1) where ε0CCTO and ε0CTO represent dielectric constants of CCTO and CTO, respectively. Equation (2) well explains ε0 and tan δ, and accordingly a low loss tan δ < 0.05 is realized in a wide range of y < 0.8. Preliminarily, we took scanning-electron-microscope images to evaluate the size and distribution of the grains in CCT-CT-1. The grain size of CCTO was 2-3 µm, which was significantly smaller than a typical grain size (several dozen µm) of

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238 2000

ε’

100 Hz 1 kHz 10 kHz 100 kHz 1 MHz

1000

CCT-CT-1 (Ca2Cu2Ti4O12)

0 2

0.05 0.04 0.03 0.02 0.01 0 100

tan

δ

tan

δ

1

0 0

200

300

Temperature (K)

100 200 Temperature (K)

300

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Figure 7. Dielectric constant and dielectric loss tangent of CCT-CT-1 [23].

normally prepared CCTO. Such a small grain size of CCTO shows a high dielectric constant (2000-2500) with remarkably flat temperature dependence [35]. Other composites also exhibit good dielectric properties. Yu et al. [36] found that CaCu3 Ti4 O12 /SrTiO3 composite exhibits a high ε0 (∼ 2000) and a low tanδ (< 0.03) with a good temperature stability from −55 C◦ to 150 C◦ at 1 kHz. They propose that the reduction of the dielectric loss is caused by increase of grain-boundary resistance. Shao et al. [37] found that CaCu3−x La2x/3 Ti4 O12 with segregated CaTiO3 as a secondary phase exhibits a high ε0 (∼ 7500) and a low tanδ (< 0.05) with a small temperature coefficient of ±15 ppm between −80 and 150 C◦ . In addition to the improvement in the dielectric properties, the CCTO-based composite ceramics show remarkable nonlinear conduction, acting as a varistor. Chung et al. [38] reported a giant nonlinear current-voltage (I − V ) characteristics in CCTO ceramics empirically expressed by I = KV α , where K represents a constant related to the resistivity, and α represents the nonlinear coefficient. Note that α is an important parameter for evaluating the performance of a varistor [39]. The observed α in CCTO is 900, being larger than that of the ZnO varistor. Kim et al. [40] investigated the bias voltage dependence of resistance of the grain boundary, and found that the resistance decreases with increasing bias voltage, which indicates that the barrier layer forms Schottky-like barrier. Ramirez et al. [41] found an enhanced nonlinear characteristics (α ∼ 1500) in Ca2 Cu2 Ti4 O12 , in which segregated CaTiO3 has an important role. Cai et al. [42] reported a strong suppression of the nonlinear conduction in Mn-doped CCTO, which is explained by compensation of carrier by Mn doping. Assuming that the barrier is of Shottky type, they found that the barrier height

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ε’

104

H

ceramic capacitors at 1 kHz

L E D

220 K 240 K 260 K 280 K 300 K

K B

CCT-CT-1 (Ca2Cu2Ti4O12)

103

J

Z5U, Y5V F I high dielectric capacitor

X5R, X7R C

A

102

temperature compensating capacitor

10-4

10-3

G

10-2

10-1

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tanδ

Figure 8. Dielectric properties of some famous capacitor materials. Dotted rectangles represent roughly classified categories of dielectric materials. Temperature compensating capacitor is located in the area where 10 < ε0 < 500, |∆ε0 | ≤ 5 % and 10−4 < tanδ < 10−3 . Here ∆ε0 is defined as (ε0 T −ε0 20 ) / ε0 20 ×100 [%], where ε0 20 and ε0 T represent ε0 at 20 ◦ C and ε0 at T ◦ C, respectively. X5R [X7R] is defined as a capacitor that exhibits |∆ε0 | ≤ 15 % in the temperature range from -55 ◦ C (218 K) to +85 ◦ C (358 K) [from -55 ◦ C (218 K) to +125 ◦ C (398 K)]. Z5U is defined as a capacitor that exhibits -55 % ≤ ∆ε0 ≤ +22 % in the temperature range from +10 ◦ C (283 K) to +85 ◦ C (358 K). Y5V is defined as a capacitor that exhibits -82 % ≤ ∆ε0 ≤ +22 % in the temperature range from -30 ◦ C (243 K) to +85 ◦ C (358 K). Alphabetical letters correspond to dielectric materials; A: CaTiO , B: BaTiO , 3 3 C: Pb(Sc1/2 Ta1/2 )O3 , D: Pb(Mg1/3 Nb2/3 )O3 , E: CaCu3 Ti4 O12 , F: CaCu2.97 Mn0.03 Ti4 O12 , G: CaCu2.94 Mn0.06 Ti4 O12 , H: Ca0.95 Na0.05 Cu3 Ti4 O12 , I: Ca0.95 La0.05 Cu3 Ti4 O12 , J: Ca0.95 Sr0.05 Cu3 Ti4 O12 , K: CaCu3 Ti3.8 Sn0.2 O12 and L: CaCu2.85 Zn0.15 Ti4 O12 . The data from A to D are taken from ref. [33].

at the grain boundary decreases with increasing Mn content. These studies show that the nature-made internal barrier layer is essential to the huge nonlinear conduction. The composite structure is further examined in the form of multilayered films. CCTO thin films are synthesized by the pulsed laser deposition (PLD) method [35, 43–45]. Si ˚ CCTO thin film grown on a LaNiO3 electrode layer on a et al. [44] fabricated 6000 A LaAlO3 substrate, and measured ε ∼1500 and tanδ ∼0.1. Zhao et al. [35] investigated the thickness and grain-size dependence of ε. A thick film exhibits large ε (2000 for 1 µm and 14700 for 2 µm) [35], the tendency of which is consistent with the measurements by Si et al. [44] These observations indicate that the mean grain size correlates with the magnitude of ε0 . Fang et al. [46] fabricated a CCTO thin film with double-sided CaTiO3 buffer layers (CTO/CCTO/CTO) grown Pt/Ti/SiO2 /Si substrates using the PLD method, in ˚ , respectively. The which the thickness of CCTO and CTO was chosen to be 5000 and 160 A 0 CTO/CCTO/CTO film exhibits a large ε of 1500 and a small tanδ of 0.1. Their data are consistent with enhanced dielectric properties in multilayered dielectric/ferroelectric thin

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240 0.2 (1-y)CaTiO 3+yCa1/4Cu3/4TiO3 ε’ tanδ ε’cal

ε’

6000 4000

0.1

at 300 K, 100 kHz

tanδ

8000

CCT-CT-1

2000 0 0

0.2

0.4

0.6

0.8

0 1

y

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Figure 9. Room-temperature dielectric properties of (1-y)CaTiO3 + yCa1/4 Cu3/4 TiO3 at 100 kHz.

film [47]. In addition, they find that leakage current density of CTO/CCTO/CTO under high bias voltage significantly suppresses, which is advantageous for applications. Multilayered thin film has advantages to analyze the intrinsic dielectric properties in CCTO. Lunkenheimer et al. [48] demonstrated that the dielectric properties of CCTO is derived from the effect of depletion layers between CCTO sample and electrodes. To elucidate the effect of depletion layers, a multilayer structure where CCTO was interposed in insulating films to eliminate the effect was suggested by Cohen et al. [49]. Mitsugi et al. [50, 51] fabricate multilayered CCTO film to address this issue. They made 16-layer films with different combinations of CTO (16-120 nm) and CCTO (40, 140, and 230 nm) on SrRuO3 (SRO)/SrTiO3 (STO) (001) substrates by the PLD method. A capacitance of zero CTO-thickness is extrapolated from the measured capacitances of the multilayer films with different thicknesses of CTO. The same procedure is repeated for different CCTO thicknesses to eliminate the extra-capacitance due to CCTO/CTO interfaces. Finally, they obtain the intrinsic dielectric constant of CCTO to be 329-435 in between 100 kHz and 464 kHz, and conclude that the huge ε0 of bulk samples comes from internal barrier layers composed of CCTO grains and/or their surrounding boundaries.

5.

Related Oxides

Since the discovery of the huge dielectric constant in CCTO, the related A-site ordered perovskites are newly synthesized and/or revisited. In this section we briefly show our work on CaMn3−x Cux Mn4 O12 [52, 53] and CaCu3 Ru4 O12 [54]. CaMn3 Mn4 O12 is an old material synthesized in 70’s [55] which showed a phase transition from Im3 to R¯ 3 at 440 K in 1980 [56]. This transition is now understood as a chargeordered state [57, 58], in which Mn ions are ligned along the (111) direction with a ratio of Mn4+ :Mn3+ =3:1. As mentioned in section 1, only Cu2+ and Mn3+ ions can occupy the A0 site. Using this property, we made a solid solution between the two ions in the A0 site in CaMn3 Mn4 O12 to dope holes. This type of doping is quite specific to this class of materials, because Mn and Cu ions can often take intermediate valence depending on the conditions. In AA03 B4 O12 , the large space of the A0 site forces them to be Jahn-Teller ions,

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Thermopower (µV/K)

Resistivity (Ωcm)

104 x=0 x=0.05 x=0.1 x=0.15 x=0.25 x=0.5 x=0.75 x=1

103 102 101 100 10-1 10-2 450 400 350 300 250 200 150 100 50 0 -50 0

Ca(Mn3-xCux)Mn4O12

100

200 300 400 500 Temperature (K)

600

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Figure 10. (upper panel) Resistivity and (lower panel) thermopower of Ca(Mn3−x Cux ) Mn4 O12 (x= 0, 0.05, 0.1, 0.15, 0.25, 0.5, 0.75, and 1).

and the doped Cu ion can be an acceptor. Figure 10 shows the resistivity and the thermopower of ceramic samples of CaMn3−x Cux Mn4 O12 . CaMn3 Mn4 O12 (x = 0) exhibits a jump in the two quantities at 440 K, which is consistent with a preliminary study by Troyanchuk et al. [59] As expected, the doped Cu ion acts as an acceptor: the resistivity and the thermopower systematically decrease with increasing Cu content x in Fig. 10. The transition temperature seen as a cusp in the resistivity also exhibits a systemic evolution with x. Note that the positive thermopower at x = 0 suggests that that majority carriers are holes in CaMn3 Mn4 O12 . The x = 1 sample shows weakly temperature-dependent thermopower with the magnitude less than 20 µV/K, suggesting that the carrier density is as large as that of conventional metals. Thus the insulating resistivity indicates that the carriers are localized at the Mn site as a small polaron, whose mobility is of activation type. This is reasonable, because the Mn-O octahedra in the B site are highly tilted to cause a small band width. This situation allows us to use the Heikes formula [60], an asymptotic expression for the high-temperature thermopower of small-polaron conductors. Note that the thermopower above 500 K is negative in spite of the hole-doped system. We propose that this negative thermopower by hole doping is caused by a backflow of entropy current [52, 53]. In the limit of small polaron, the conduction may be understood by exchanging the neighboring ions. Then the hole of +|e| is carried by the Mn4+ ion, while the entropy is carried by both the Mn3+ and Mn4+ ions. Since the Mn4+ ion carries less entropy than the Mn3+ ion, the entropy flow is opposite to the current flow. As a result, the thermopower, which is

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W. Kobayashi and I. Terasaki 106

4

(a)

x=0 x=0.5 x=1 x=1.5 x=4

3

2

1

0 0

100

200

300

Temperature (K)

Thermopower (µV/K) Resistivity (Ωcm)

-5

Magnetic susceptibility (10 emu/g)

CaCu3Ti4-xRuxO12

104 102

x=0.5 (b)

x=1.0

100 10-2 10

x=1.5

-4

x=4.0

10-6 100 (c)

x=0.5 50 x=1.0, 1.5 x=4.0 0 0

100

200

300

Temperature (K)

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Figure 11. (a) Magnetic susceptibility, (b) resistivity and (c) thermopower of CaCu3 Ti4−x Rux O12 [54].

equivalent to the ratio of the entropy flow to the current flow, can be negative. The second example is that the A0 ions form electrical conduction paths owing to the strong hybridization in the d levels of the A0 and B ions through O 2p. CaCu3 Ru4 O12 synthesized by Subramanian et al. [15] exhibits a good metallic conduction down to 4 K. Actually the conductivity of this material is higher than that of CaRuO3 . This is difficult to understand because the tilted angle of the RuO6 octahedra are smaller in the former to give a smaller band width. They proposed a concept of valence degeneracy as a mechanism of the metallic conduction, in which Ru 4d and Cu 3d bands are degenerate in energy, and both contribute to metallic conduction. Since the valence degeneracy is not well defined as a theoretical model, we suggest an alternative explanation similar to the heavy-fermion/valencefluctuation system, in which the Ru 4d and Cu 3d electrons interact through the Kondo effects [54]. We found that an insulator-metal transition occurs in CaCu3 Ti4−x Rux O12 , which can be regarded as a transition from a magnetic insulator to a heavy-fermion metal. Figure 11(a) shows the susceptibility of CaCu3 Ti4−x Rux O12 . We have found that the high-temperature data are well fitted with the expression χ(T ) = χp +χloc (T ), where χp is the Pauli paramagnetic susceptibility, and χloc is the Curie-Weiss-type susceptibility χloc (T ) = C/(T + θW ) (C is the Curie constant, and θW is the Weiss temperature). The doped Ru causes a rapid decrease of C and a linear increase χp , suggesting that the holes on Cu2+ changes from the localized moments to the itinerant carriers. Figure 11(b) shows the resistivity of CaCu3 Ti4−x Rux O12 , which changes from 103 (x = 0) to 10−4 Ωcm (x = 4) at 300 K. The temperature dependence also changes

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from insulating to metallic, and an insulator-metal transition occurs between x = 1.5 and x = 4. Figure 11(c) shows the thermopower of CaCu3 Ti4−x Rux O12 . Unexpectedly, the thermopower suddenly decreases from 100 µV/K for x = 0.5 to a few µV/K for x = 1.0, whereas ρ for x=1.0 is still high. Since the small thermopower is a hallmark of a metal, this indicates that the delocalization of the 3d holes on Cu2+ already occurs at x = 1. Recent experiments and band calculation partly support our scenario. Xiang et al. [61] revealed from first-principle calculation that the conduction mechanism in CaCu3 Ru4 O12 is governed by two factors; one is the Ru-O dpπ coupling around the Fermi level, and the other is the hybridization between Ru 4d electrons and Cu 3d electrons through O 2p orbitals. This hybridization lets the localized Cu 3d ions be itinerant, which realizes the heavy-fermion-like behavior. Tran et al. [62] have found that the valence of Cu is close to 3d9 (Cu2+ ) with localized character, and also suggested the hybridization between Cu 3d and Ru 4d orbitals, which is consistent with the first-principle calculation mentioned above. NMR measurement of CaCu3 Ru4 O12 is also performed. Kato et al. [63] observed the Fermi liquid state at low temperatures which shows that Cu 3d electrons are conductive at low temperatures.

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6.

Concluding Remarks

In this article, we have reviewed the unconventional properties of CaCu3 Ti4 O12 , especially focusing on the huge dielectric constant at room temperature. This particular oxide shows no structure phase transition, soft phonons, ferroelectric transition, and accordingly the huge dielectric constant has no relation to ferroelectricity. A number of papers suggest that models of internal barrier-layer capacitor explain the experimental data fairly well. We have shown that the dielectric properties of CaCu3 Ti4 O12 are reproducible and controllable, even if they are dominated by extrinsic origins. This makes a remarkable contrast to the conventional dielectrics in which barrier layers have to be artificially introduced. Partial substitution for Cu drastically decreases the dielectric constant, possibly by changing the grain sizes or the grain-boundary resistance. The dielectric constant and loss can be tuned in the form of the composite ceramics based on CaCu3 Ti4 O12 . These are consistent with the fact that single crystalline samples always larger dielectric constants than ceramic samples or thin films. We further note that this material is free from the piezoelectric damages thanks to the absence of ferroelectricity; ferroelectric materials usually have a significant volume change with respect to electric field, which deteriorates and limits the lifetime of the ceramic capacitors. Thus we expect that CaCu3 Ti4 O12 -based materials can be used in a complementary way to the state-of-the-art dielectrics.

Acknowledgments The authors would like to thank M. Mitsugi, M. Fukunaga, S. Asanuma, Y. Uesu, and K. Kohn for fruitful discussion and suggestions on CaCu3 Ti4 O12 , M. Mikami, R. Funahashi, T. Nomura and T. Katsufuji for technical supports on the study of Ca(Mn3−x Cux )Mn4 O12 system, J. Takeya, I. Tsukada, Yoichi Ando, T. T. Tran, K. Takubo, and T. Mizokawa for fruitful discussion on CaCu3 Ru4 O12 and technical supports. We also thank S. Ishiwata for fruitful discussion on BiNiO3 , T. Fujii, S. Okada, T. Nakano, and S. Shibasaki for

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technical supports. This study was partially supported by the program entitled ”Promotion of Environmental Improvement for Independence of Young Researchers” under the Special Coordination Funds for Promoting Science and Technology provided by MEXT, Japan.

References [1] M. A. Subramanian, D. Li, N. Duan, B. A. Reisner, and A. W. Sleight, J. Solid State Chem 151 (2000) 323. [2] A. P. Ramirez, M. A. Subramanian, M. Gardel, G. Blumberg, D. Li, T. Vogt, and S. M. Shapiro, Solid State Commun. 115 (2000) 217. [3] C. C. Homes, T. Vogt, S. M. Shapiro, S. Wakimoto, and A. P. Ramirez, Science 293 (2001) 673. [4] L. He, J. B. Neaton, M. H. Cohen, D. Vanderbilt, and C. C. Homes, Phys. Rev B 65, 214112 (2002). [5] N. Kolev, R. P. Bontchev, A. J. Jacobson, V. N. Popov, V. G. Hadjiev, A. P. Litvinchuk, and M. N. Iliev, Phys. Rev B 66, 132102 (2002). [6] D. C. Sinclair, T. B. Adams, F. D. Morrison, and A. R. West, Appl. Phys. Lett. 80, 2153 (2002). [7] P. Lunkenheimer, V. Bohnar, A. V. Pronin, A. I. Ritus, A. A. Volkov, and A. Loidl, Phys. Rev B 66, 052105 (2002). Copyright © 2009. Nova Science Publishers, Incorporated. All rights reserved.

[8] B. S. Prakash and K. B. R. Varma, Appl. Phys. Lett. 90, 082903 (2007). [9] Y. Liu, R. L. Withers, and X. Y. Wei, Phys. Rev. B 72, 134104 (2005); 72, 179901(E) (2005). [10] S. Ke, H. Huang, and H. Fan, Appl. Phys. Lett. 89, 182904 (2006). [11] H. Yu, H. Liu, H. Hao, L. Guo, C. Jin, Z. Yu, and M. Cao, Appl. Phys. Lett. 91, 222911 (2007). [12] Landolt-B¨ornstein, Magnetic Properties of Non-magnetic Inorganic Compounds Based on Transition Elements, Group III, Condensed Matter, Volume 27/F1β (Springer, Berlin), p. 280. [13] Z. Zeng, M. Greenblatt, M. A. Subramanian, and M. Croft, Phys. Rev. Lett. 82 (1999) 3164. [14] R. Przenioslo, I. Sosnowska, E. Suard, A. Hewat, and A. N. Fitch, J. Phys.: Cndens. Matter 14 (2002) 5747. [15] M. A. Subramanian, W. J. Marshall, T. G. Calvarese, and A. W. Sleight, J. Phys. Chem. Solids 64 (2003) 1569. Recent Advances in Dielectric Materials, Nova Science Publishers, Incorporated, 2009. ProQuest Ebook Central,

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[16] W. Kobayashi, I. Terasaki, J. Takeya, I. Tsukada, Yoichi Ando, J. Phys. Soc. Jpn. 73 (2004) 2373. [17] H. Shiraki, T. Saito, T. Yamada, M. Tsujimoto, M. Azuma, H. Kurata, S. Isoda, M. Takano, and Y. Shimakawa, Phys. Rev. B 76, 140403 (2007). [18] V. L. Volkov, N. I. Kadyrova, G. S. Zakharova, M. V. Kuznetsov, N. V. Podvalnaya, K. N. Mikhalev and Yu. G. Zainulin, Russ. J. Inorg. Chem. 52, 329 (2007). [19] Song-Ho Byeon, Seoung-Soo Lee, John B. Parise, and Patrick M. Woodward, Chem. Mater. 18, 3873 (2006). [20] A. Koitzsch, G. Blumberg, A. Gozar, B. Dennis, A. P. Ramirez, S. Trebst, and S. Wakimoto, Phys. Rev. B 65, 052406 (2002). [21] Y. J. Kim, S. Wakimoto, S. M. Shapiro, P. M. Gehring, and A. P. Ramirez, Solid State Commun. 121 (2002) 625. [22] W. Kobayashi, and I. Terasaki, Physica B 329-333, 771 (2003). [23] W. Kobayashi, and I. Terasaki, Appl. Phys. Lett. 87, 032902 (2005). [24] D. Capsoni, M. Bini, V. Massarotti, G. Chiodelli, M. C. Mozzatic, C. B. Azzoni, J. Solid State Chem. 177, 4494 (2004). [25] R. K. Grubbs, E. L. Venturini, P. G. Clem, J. J. Richardson, B. A. Tuttle, and G. A. Samara, Phys. Rev. B 72, 104111 (2005). Copyright © 2009. Nova Science Publishers, Incorporated. All rights reserved.

[26] M. Li, A. Feteira, D. C. Sinclair, and A. R. West, Appl. Phys. Lett. 88, 232903 (2006). [27] J. Cai, Y-H. Lin, B. Cheng, C-W. Nan, J. He, Y. Wu, and X. Chen, Appl. Phys. Lett. 91, 252905 (2007). [28] T-T. Fang, L-T. Mei, and H. F. Ho, Acta Materialia 54, 2867 (2006). [29] N. Ikeda, K. Kohn, N. Myouga, E. Takahashi, H. Kitoh, and S. Takekawa, J. Phys. Soc. Jpn. 69 (2000) 1526. [30] S-Y. Chung, Appl. Phys. Lett. 87, 052901 (2005). [31] S. Kwon, C-C. Huang, E. A. Patterson, D. P. Cann, E. F. Alberta, S. Kwon, W. S. Hackenberger, and D. P. Cann, Mater. Lett. 62, 633 (2008). [32] E. A. Patterson, S. Kwon, C-C. Huang, and D. P. Cann, Appl. Phys. Lett. 87, 182911 (2005). [33] Landolt-B¨ornstein, Ferroelectric oxides, Group III, Crystal and Solid State Physics, Volume 16a (Springer, Berlin, 1981). [34] K. Lichtenecker, Phys. Z. 27, 115 (1926). Recent Advances in Dielectric Materials, Nova Science Publishers, Incorporated, 2009. ProQuest Ebook Central,

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[35] Y. L. Zhao, G. W. Pan, Q. B. Ren, Y. G. Cao, L. X. Feng, and Z. K. Jiao, Thin Solid Films 445, 7 (2003). [36] H. Yu, H. Liu, H. Hao, D. Luo, and M. Cao, Mater. Lett. 62, 1353 (2008). [37] S. F. Shao, J. L. Zhang, P. Zheng, C. L. Wang, J. C. Li, and M. L. Zhao, Appl. Phys. Lett. 91, 042905 (2007). [38] S-Y. Chung, I-D. Kim, and S-J. L. Kang, Nature Mater. 3, 774 (2004). [39] Y-H. Lin, J. Cai, M. Li, C-W. Nan, and J. He, Appl. Phys. Lett. 88, 172902 (2006). [40] I-D. Kim, A. Rothschild, and H. L. Tuller, Appl. Phys. Lett. 88, 072902 (2006). [41] M. A. Ramirez, P. R. Bueno, J. A. Varela, and E. Longo, Appl. Phys. Lett. 89, 212102 (2006). [42] J. Cai, Y-H. Lin, B. Cheng, C-W. Nan, J. He, Y. Wu, and X. Chen, Appl. Phys. Lett. 91, 252905 (2007). [43] Y. Lin, Y. B. Chen, T. Garret, S. W. Liu, C. L. Chen, L. Chen, R. P. Bontchev, A. Jacobson, J. C. Jiang, E. I. Meletis, J. Horwitz, and H.-D. Wu, Appl. Phys. Lett. 81, 631 (2002). [44] W. Si, E. M. Cruz, P. D. Johnson, P. W. Barnes, P. Woodward, A. P. Ramirez, Appl. Phys. Lett. 81, 2056 (2002).

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[45] L. Chen, C. L. Chen, Y. Lin, Y. B. Chen, X. H. Chen, R. P. Bontchev, C. Y. Park, and A. J. Jacobson, Appl. Phys. Lett. 82, 2317 (2002). [46] L. Fang, M. Shen, and Z. Li, J. Appl. Phys. 100, 104101 (2006). [47] C. Wang, Q. F. Fang, Z. G. Zhu, A. Q. Jiang, S. Y. Wang, B. L. Cheng, and Z. H. Chen, Appl. Phys. Lett. 82, 2880 (2003). [48] P. Lunkenheimer, R. Fichtl, S. G. Ebbinghaus, and A. Loidl, Phys. Rev. B 70, 172102 (2004). [49] M. H. Cohen, J. B. Neaton, L. He, and D. Vanderbilt, J. Appl. Phys. 94, 3299 (2003). [50] M. Mitsugi, M. Fukunaga, S. Asanuma, Y. Uesu, W. Kobayashi, and I. Terasaki, Ferroelectrics 357, 191 (2007). [51] M. Mitsugi, S. Asanuma, Y. Uesu, M. Fukunaga, W. Kobayashi, and I. Terasaki, Appl. Phys. Lett. 90, 242904 (2007). [52] W. Kobayashi, I. Terasaki, M. Mikami, and R. Funahashi, J. Phys. Soc. Jpn. 73, 523 (2004). [53] W. Kobayashi, I. Terasaki, M. Mikami, R. Funahashi, T. Nomura and T. Katsufuji, J. Appl. Phys. 95, 6825 (2004). Recent Advances in Dielectric Materials, Nova Science Publishers, Incorporated, 2009. ProQuest Ebook Central,

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[54] W. Kobayashi, I. Terasaki, J. Takeya, I. Tsukada, and Yoichi Ando, J. Phys. Soc. Jpn. 73, 2373 (2004). [55] B. Bochu, J. Chenavas, J. C. Joubert and M. Marezio, J. Solid State Chem. 11, 88 (1974) [56] B. Bochu, J. L. Buevoz, J. Chenavas, A. Collomb, J. C. Joubert, and M. Marezio, Solid State Commun. 36, 133 (1980). [57] I. O. Troyanchuk, L. S. Lobanovsky, N. V. Kasper, M. Hervieu, A. Maignan, C. Michel, H. Szymczak, and A. Szewczyk, Phys. Rev. B 58, 14903 (1998). [58] R. Przenioslo, I. Sosnowska, E. Suard, A. Hewat, A. N. Fitch Physica B 344, 358 (2004). [59] I. O. Troyanchuk, A. S. Chernyi, and Y. G. Zonov, Fiz. Tverd. Tela 31, 193 (1989). [60] W. Koshibae, K. Tsutsui, and S. Maekawa, Phys. Rev. B. 62, 6869 (2000). [61] H. Xiang, X. Liu, E. Zhao, J. Meng, and Z. Wu, Phys. Rev. B 76, 155103 (2007). [62] T. T. Tran, K. Takubo, T. Mizokawa, W. Kobayashi, and I. Terasaki, Phys. Rev. B 73, 193105 (2006).

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[63] H. Kato, T. Tsuruta, T. Nishioka, M. Matsumura, H. Sakai, and S. Kambe, J. Phys. Chem. Solids, 68, 2187 (2007).

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In: Recent Advances in Dielectric Materials Editor: Ai Huang, pp. 249-299

ISBN: 978-1-60692-266-8 © 2009 Nova Science Publishers, Inc.

Chapter 6

DIELECTRIC RESPONSE METHODS FOR DIAGNOSTICS OF POWER TRANSFORMERS Issouf Fofana1, Zié Yéo2 and Masoud Farzaneh3 1

Canada Research Chair on Insulating Liquids and Mixed Dielectrics for Electrotechnology (ISOLIME), Université du Québec à Chicoutimi, QC, Canada 2 Institut National Polytechnique Houphouet Boigny, Département d’Électronique et d’Électrotechnique, Yamoussoukro, Côte d’Ivoire 3 International Research Centre on Atmospheric Icing and Power Network Engineering (CenGivre), Université du Québec à Chicoutimi, Qc, Canada.

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Abstract In these last decades, increasing requirements for appropriate techniques to diagnose power transformer insulation non-destructively and reliably in the field drive the development of diagnostic tools based on changes of the dielectric properties of the insulation. Among these non-destructive monitoring techniques Polarisation/Depolarisation Current (PDC) measurement, Return Voltage Measurement (RVM) and Frequency Domain dielectric Spectroscopy (FDS) are gaining exceptional importance to the utility professionals. These methods, which became recently available as a user-friendly method, offer promising alternatives for an off-line, insulation condition assessment of power equipments and its predictive maintenance non-destructively and reliably in the field. After a short review of commonly used chemical and electrical diagnostic techniques, a description of the state of art of the theories, analyses and interpretation of dielectric spectroscopic techniques for transformer insulation condition assessment along with the future research trends are presented. Because, results from these techniques are highly operating conditions dependant, practical measurements issues that need to be considered are addressed.

1. Introduction Power transformers are important and one of the costliest equipments in electrical power transmission system. They are devices that transfer energy from one AC system to another. At a generating substation, they permit electrical energy generated at relatively low voltages (by

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generators) to be stepped up and transmitted at high voltages and low currents carried over long distances, thus reducing line losses. Close to the centres of consumption the voltages are stepped down for distribution to the loads. Composite oil/paper insulation has been used in transformer for more than 100 years. Despite great strides in electrical equipment design in recent years, the Achilles heel in the chain is still the insulation system. During service, the electrical insulation of transformer is subjected to several types of stresses (electrical, chemical, mechanical and thermal), occurring in different parts of the structure; some of them being inter-related, which degrade the insulation. As power equipment age, their internal insulation degrades, which increases the risk of failure. Insulation degradation/aging is recognized to be one of the major causes of transformer breakdown [1-5]. When electrical equipment fails, more often than not the fault can be traced to defective insulation. Preventing failures and maintaining equipments in good operating condition are very important issues for utilities. Normal temperature operating range for transformers is 60 to 100°C that will allow a relatively slow degradation of insulation paper. However, when the operating temperature is increased above 110°C, premature destruction of the solid insulation may starts. In general, when the solid insulation is severely degraded, the transformer has reached the end of its useful life. Practically speaking, the life span of the transformer is directly related to the life span of the solid insulation. A rewinding then becomes necessary. Insulating paper in serviceaged transformer cannot be replaced with new one without a complete repair of the transformer windings, unlike the oil which can be replaced as needed. Since many transformers in electrical industries around the world, built and installed in post second World War are approaching the end of their design life, their life management has became an essential part of a modern power operation system. Condition monitoring can be utilized to attempt the prediction of the insulation condition and the remaining lifetime of a transformer. In this context, the adequacy of existing and the application of new diagnostic tools and monitoring techniques gain increasing importance. In today’s economic climate, it is important to know the condition, by means of suitable diagnostic tests, of the transformer insulation. Increasing requirements for appropriate tools allowing diagnosing power transformers non-destructively and reliably in the field drive the development of diagnostic techniques based on changes of the dielectric properties of the internal insulation. These modern diagnostic methods include the Recovery Voltage Measurement (RVM), Frequency Domain Spectroscopy (FDS) and Polarization and Depolarization Current Measurements (PDC) [6]. These techniques, available as user-friendly methods, can be used to assess power equipment insulation system condition, nondestructively [7, 8].

2. Insulating Materials Defined The importance of insulating materials has been acknowledged from the early days of electricity. The designs and applications of power equipments are almost infinite in their variety, but all units have one common characteristic. For power equipment to operate normally it is important to isolate live parts from each other and the ground, not leaking from one path to another through materials not intended to be a conducting path.

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Insulating materials are materials with such a low ability to conduct electricity that the flow of current through it is small enough to be neglected; these materials could therefore be classified as nonconductors. In addition to separating electrical circuits, insulating materials must often mechanically support the conductors. The role of insulation is paramount importance, in the sense that it is one of the fundamental conditions for the reliable operation of power equipments. Insulating materials design/selection is one of the most important problem engineers have to face. This is because, a wide variety of insulation are available (oil, air, vacuum, ceramic, etc…) and insulating materials span all three forms of matter (solid, liquid and gas), with sometimes a single form involved but often a combination of forms, such as the solid/liquid or the solid/gas forms. The function of insulation must be studied at the design by taking account of the anticipated/expected operating environment (Figure 1).

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Figure 1. Factors to be taken into account during insulation systems design.

Clearly the design of an insulating system is a complex procedure that should be methodological conducted. Deterioration/degradation of insulation systems is an important aspect that must be addressed at the design. The design of the components must enhance the life expectancy of the assembly as a whole. Another important aspect is environmental concern and security of the materials throughout their lifetime.

3. Power Transformer Insulation Insulating fluid in transformer is mainly of mineral origin, but may be of synthetic and vegetable origin. The most widely used insulation systems for nearly a century [2, 9] are liquid insulation (petroleum-based oil, the so-called transformer oil) combined with solid insulation (kraft paper, pressboard, wood i.e. cellulose products). The solid insulation itself shows modest dielectric performance due to its porous structure. Its dielectric strength is predominantly conditioned by gaseous ionization within the air inclusions. When the solid paper is adequately impregnated with oil, it offers the user a material with insulating and mechanical properties of remarkable suppleness. The ready supply and cost benefit of cellulose and mineral oil has, therefore, made these the materials of choice for nearly a century [2].

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The insulating oil in the transformer changes volumetrically according to the variation in its temperature arising from changes in atmospheric temperature and/or transformer loadings. From the expansion coefficient of the oil and the range of temperature changes (typically -20 to 90°C), its volumetric change is about 9% maximum. The oil reservoir space necessary for this volumetric change is called a conservator, which is installed on the transformer main body. When contacting the atmosphere directly, insulation oil absorbs humidity, which deteriorates its dielectric strength. Therefore, for preventing inhalation of moisture from the atmosphere into the conservator, a dehydrating (silicagel contain in a glass vessel) breather is fitted on the end of the air inlet pipe of the conservator. About half of power transformers worldwide are free-breathing. Two mechanical solutions are available for hindering the contact of oil with the outside atmosphere. One alternative is an elastic rubber or plastic bag (diaphragm) that separates in the conservator the surface of oil from the gas space (most distribution transformers in Western Europe are of that type). Another choice adopted mainly in the United States is to seal transformers under a nitrogen cushion.

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3.1. Mineral Oil Mineral oil is made by refining a fraction of hydrocarbons collected during the distillation of a crude petroleum stock. Depending on the refining process, the proportions of paraffin, naphthene and aromatics can vary between 40 – 60%, 30 – 50% and 5 – 20% respectively [10, 11]. The fluid is used alone as electrical insulation only in regions where, by design, electrical stresses are relatively low. The function of oil is to strengthen the dielectric properties of solid insulation used in the transformer, to electrically insulate active parts from grounded ones to dissipate heat from the core materials to the radiators and to quench eventual arcs. The heat dissipation is enhanced by the low viscosity of oil that allows it to penetrate the solid insulation setting up convection currents for conveying the heat from the core materials to the radiators. Oil is a vital part of the transformer and (similarly to blood in a human being body) keeps responsibility for the condition of the entire equipment. The condition of oil can be a decisive factor, which determines the serviceability of the transformer. Although mineral oils are very carefully refined they undergo a slow decay process, even under normal operating conditions. The resulting decay products gradually affect the physical, chemical and dielectric properties. Additionally, fraction of the decay products, are adsorbed by the large surface of paper insulation leading to premature aging of transformers.

3.2. Paper and Pressboard The solid insulating material is used in regions where electrical stresses are high, or where a particular physical configuration is needed. The solid insulation materials commonly used as wrapping and spacers are cellulose papers and boards made with special care from wood

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pulps. Specially chosen wood and dense synthetic polymers are usually used as insulating support structures [2]. The solid insulation, a low cost base material obtained from wood pulp with outstanding mechanical and electrical properties is a linear polysaccharide consisting of many anhydro ®-D-glucopyranose units linked to each other via a (1→ 4) glycosidic bond (Figure 2) to form a polymeric chain. The main constituent of Kraft paper is cellulose (about 90%), and the remaining components of the paper consist of about 6-7% lignin, 34% hemicelluloses (typically pentosans) and traces of metallic cations [12]. Many long oriented chains, arranged parallel to one another, make up the fibers that form the structure of paper.

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Figure 2. Anhydro β-D-glucopyranose monomer units.

The solid insulation degradation is directly related to its mechanical integrity. Indeed, the chains session is the principal cause of the paper (or pressboard) strength loose. The average number of glucose monomer units (Figure 2) in the cellulose of the paper is referred to as the degree of polymerization (DP), which for new Kraft paper is about 10001300. The molecule length of degraded cellulose may reduce to a DP value of about 200 (about 50% or less of the original tensile strength of the paper remains) with a very little remaining life as solid insulation material. In this condition cellulose is brittle and its resistance against mechanical stresses is strongly reduced [4]. Such a transformer will become susceptible to winding failure during mechanical stresses such as vibration, through-faults and short circuits.

3.3. Moisture in Transformer Moisture is the enemy number one of liquid impregnated transformers [2]. It is particularly detrimental to the dielectric properties of oil-paper insulation systems and its resistance to ageing. When combined with oxygen and excessive heat, the process of ageing accelerates. Moisture in the oil may, under fast decreasing temperature transients, result in free water and lead to electrical breakdown. Water in power transformers originates from residual moisture in bulky construction elements, from the atmosphere (breathing of open conservator systems, through leaky seals, during repair) and from the thermal decomposition of the solid insulating materials. The increase in moisture content can also be the result of mishandling during transport or storage, with/without oil. It can also occur upon installation, during minor repairs involving temporal and partial drainage of the

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insulating fluid, or as the result of defects in the breathing system, etc [13]. Moisture affects the conductivity of the insulation, which in turn increases the dissipation factor [14]. Previous studies [15-17] indicated that the rate of degradation of paper increased in direct proportion to the water content.

3.3.1. Moisture in Oil Moisture in transformer oil is one of the key factors conditioning the health of the unit. The deleterious effects of moisture occur as its relative saturation in oil increases, which also increases the conductivity and reduces the dielectric strength of the oil. In the insulating liquid, water can be present under a number of physical and physico-chemical states that can be simplified as [18]:

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• • •

dissolved water (molecular distributed and associated), dispersed water (colloids and emulsions), bounded water (in clusters, adsorbed by polar aging products, in clathrates and chemisorbed).

"Water content" of insulating liquids is referred to the total amount of water in these liquids, regardless its state. Moisture content W is usually related to oil weight (ppm as μg water / g liquid) or to the saturation value (%). Because the saturation level is a function of pressure and especially of temperature, the relative humidity which is a combined index of the environment, reflects more than only the water content [19]. The relative humidity of liquids is the dissolved water content of the liquid in relation to the maximum amount of water that the liquid can hold at the same temperature. For a given temperature T, The relative humidity Wrel is defined in terms of the absolute water content in liquid Wabs versus the saturation limit WL(T) so that :

W W = abs rel W (T ) L

(1)

The maximum water solubility at a temperature T can be expressed in the form [19]:

WL = K . e

−

H T

(2)

where the constants H and K depend on the liquid itself and have to be determined experimentally. Figure 3 shows some value of WL in mineral oil reported by different authors [19-21].

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Figure 3. Water saturation limit WL in mineral oil as affected by temperature [19-21].

Figure 4 provides the ac breakdown voltage as a function of the relative humidity. Clearly the dielectric strength decreases with an increase in the relative humidity.

kV

60

Breakdown voltage

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80

50

40

30

20

10

0 0

20

40

60 80 Relative Humidity [%]

100

120

Figure 4. AC breakdown voltage versus relative humidity for mineral oil. Recent Advances in Dielectric Materials, Nova Science Publishers, Incorporated, 2009. ProQuest Ebook Central,

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Issouf Fofana, Zié Yéo and Masoud Farzaneh

3.3.2. Moisture in Paper The unit for moisture concentration in paper is typically expressed in %, which is the weight of the moisture divided by the weight of the dry, oil-free paper. During transformer manufacturing, paper insulation is dried out to a value between 0.5 to 1%. Power transformers with voltages ratings below 120 kV, the limit of moisture content of paper for reliable operation is estimated to about 3-4 %, and for larger power transformers, this limit is around 2 % [13]. Water in paper can be found in four states: vapor, free water in capillaries, imbibed free water, and it may be adsorbed to surfaces. The moisture concentration in the paper can be much greater than that of the oil. For example, a 150 MVA, 400 kV transformer with about seven tons of paper with 3% moisture content, contain as much as 210 kg of water [22], and the oil volume in a typical power transformer is about 80,000 liters. Assuming a 40 ppm moisture concentration in oil, the total mass of moisture is about 4 kg, which is much less than that found in the paper.

4. Insulation Ageing In power transformers, it is not only the electric behavior, which is most difficult to control, but the interaction of all the other stresses, leading sooner or later, with possible repetition, to the increase in the stresses on the insulations. Insulation/degradation which is highly dependent on operational conditions is a four dimensional problem due to:

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• • • •

service environment, electrical (partial discharge, short-circuits, over-voltages, voltage transients in the conductors nearby the insulation, etc.), thermal (magnetic and dielectric losses, joules heating, eddy currents, etc) mechanical (short-circuit forces, transient regimes, overload, vibrations, etc)

The insulation system is generally oversized to guarantee its dielectric behaviour under normal operating conditions. However, the application of the operating voltage combined with stresses of various sources and their mutual interactions, reveals a certain number of side effects, which cause a gradual deterioration, and the premature ageing of insulation. By looking at transformer risk factors and breaking each one down into the simplest terms, one common denominator reveals itself in that the insulation system is the key to healthy transformers. Despite great progresses in power equipment design in recent years, the weak link in the chain still remains the insulation system. When power transformers fail, the fault can be traced usually to defective insulation [1-5]. Even though power transformer are properly designed and tested prior to installation there can be no guarantee that a fault within the insulation system will not occur in the future. Oil and other materials in a transformer degrade with time in service. The solid insulation cannot be restored unless the transformer is completely overhauled, unlike oil, which can be replaced when needed. The life of the transformer is actually the life of the internal insulation system. The mechanism of ageing is a complex inter-disciplinary phenomenon. Insulating material ageing /degradation can be defined as an irreversible deleterious change to the

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serviceability of an insulation system. The primal process is that the chemical and physical bonds between the atoms of the insulation substance are repeatedly broken, reorganized and reformed into new configurations. Over time, the individual atomic processes collectively will give rise to microscopic and ultimately to macroscopic and recognizable change in the insulation substance and its ability to function. The ageing or deterioration of insulating oil is normally associated with oxidation under the very harsh environment. Electrical stress together with heat and moisture in the presence of a catalyst (e.g. oxygen from air) oxidises the oil producing free radicals, acids and sludge [1, 5, 10, 23]. These by-products are deleterious to the transformer and catalyze further oxidation of the oil. Aggressive decay products being adsorbed by the solid insulation attack on the cellulose fibres and also kill new oil after refilling. Sludge produced may stick onto the large surface of transformer boards stopping heat being dissipated. The sludge acts as barrier to the flow of heat from the oil to the cooling unit and from the core to the coils to the cool oil. Sometimes the sludge may even block the cooling ducts in which the oil flows. As a result, the transformer insulation and windings becomes too hot and would eventually be damaged. Absorption of oil aging products by cellulose also masks real condition of the oil when traditional characteristics as acidity, dielectric dissipation factor are tested. The cracking process of cellulose (depolymerisation by a succession of chemical reactions) causes chain scissions and the release of gases and water into the surrounding oil, and some large molecules such as furfurals [24]. A simple schematic representation of the main processes and components released is shown in Figure 5. Moisture, which is considered as the enemy number one of the solid insulation, acts as catalyst and by-product at the same time [24, 25].

Figure 5. Interaction between different aging products and power transformer insulation system.

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If the insulation systems were operated in perfect conditions, the need for testing would be needless. However, this insulation system deteriorates in service due to service conditions. In properly designed transformers, according to IEC 76-2 (thermal layout), the paper can last up to 55 years or more, provided there are no other thermal or dielectric defect present [24]. An appropriate maintenance strategy can allow a power transformer to function for 50 to 75 years. However, the maintenance of the insulation system largely determines the extent of a transformer’s life. The Achilles’ heels of paper are temperature and moisture. Cellulose can degrade rapidly at temperatures higher than 90°C [15]. The aging rate doubles roughly for each 8°C rise [15] while showing an approximately proportional aging rate to water content. For example, the life of cellulose pressboards at 110°C is calculated as ten years [26].

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5. Condition Assessment of Power Transformer Insulation The majority of power transformers, currently in service, have been installed after the Second World War. They might be close to their nominal end of life. With increasing age and high level demand of energy, there are potential risks of extremely high monetary losses due to unexpected failures and outages. Extreme reliability is demanded of electric power distribution as when failures occur they inevitably lead to high repair costs, long downtime and possible personnel safety risks. In addition environmental aspects such as consequential damages, fire and pollution are of high risk. Replacing these “old units” with new ones - only because of their age - is clearly uneconomic. Transformers are too expensive to replace regularly and must be properly maintained to maximize their life expectancy. In this connection, the fundamental objective is to promote the longest possible service life, to reduce costs for maintenance and to predict the time ripped to remove the transformer, on a planned basis, for revision or replacement. Due to operations under extreme/severe conditions, rapid ageing and wear and tear will occur, thereby reducing the life of the transformer. Many of the hardware like tap changer contacts, bushings, pumps and fans can be replaced in a timely manner to extend the life of the transformer. But oil-paper insulation system is one component of the transformer which, once subjected to normal and/or abnormal loading conditions cannot be easily replaced. Understanding the design of the transformer as well as the operational history is essential for making reliable diagnosis. Properly conducted insulation system testing, analysis of the data collected and appropriate corrective action can minimize the possibility of failures. Therefore, the significance of understanding insulation systems testing has never been more important. The insulating oil in a transformer becomes increasingly contaminated as the transformer ages in service. Contaminants include particulate debris from thermal, oxidative, or electrical degradation byproducts (sludge, acids, x-wax…) of oil or solid insulation, fibers, gases, moisture, etc. Electrical and chemical techniques can therefore be used to assess the insulation electrical and the chemical properties respectively. The “health” of transformer insulation is checked by examining the oil and paper insulation. While the oil testing does not require shutting down the transformer, the solid insulation testing is performed off-line. However, the solid insulation condition may be accessed indirectly by measuring compounds (furan concentration, carbon dioxide, moisture, etc) in the oil.

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Transformer oil contains about 70% of diagnostic information. The variations in different oil characteristics may therefore be used to identify/detect the type of incipient failure in the transformer. Diagnostic effectiveness by oil tests may be subdivided into four groups (Figure 6): • • • •

Identification/characterization - parameters that can be used to identify/characterize the oil Ageing rate – parameters/properties relevant to the ageing process. Dielectric properties - parameters characterizing the fluid as a good insulant. These parameters are also relevant to the dielectric safety margin. Degradation status - utilization of the oil as an indirect/non destructive diagnostic medium.

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Clearly, transformer failure can be avoided if the condition of the oil in an operational unit is monitored and, based on the results, corrective action is taken.

Figure 6. Functional based classification of oil properties. Specifications in brackets are ASTM standards.

Practically speaking, the lifetime of the transformer is directly related to the lifetime of the solid insulation. The evaluation of its deterioration is reliably performed by shaving at critical locations (leads, outer winding) and determining their tensile strength/degree of polymerization (DP). A non destructive alternative of this method is the measurement of furanic compounds released from the cellulose decomposition and dissolved in oil. Furfuraldehyde (2-FAL) has a strong correlation with the DP and criteria have been established to relate both properties [27]. Another alternative recently proposed to access

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indirectly the DP is the Fast Fourier Transform Infrared (FTIR) which offers promising avenues for an eventual implementation in the transformer body [28]. The flow chart of relevant action allowing following the excessive deterioration of paper is shown in the Figure 7. It should be emphasized that some of the key diagnostic procedures can be performed through oil analysis.

Figure 7. Functional based classification of paper deterioration follow up.

Due to growing economic impact, utilities are changing world wide their philosophy from periodic maintenance to condition based maintenance (CBM) and to effective transformer life management. In this context, the adequacy of existing and the application of new diagnostic tools and monitoring techniques gain increasing importance. The major disadvantages of the classical methods including, but not limited to, Dissolved Gas Analysis (DGA), Degree of Polymerization (DP), High Performance Liquid Chromatography (HPLC) and Dielectric Dissipation Factor (DDF) are: • •

their destructive nature (insulation paper has to be broken down for assessment) empirical nature (subjected to variability and uncertainty)

To meet pressing needs of Power Industry new maintenance technologies, especially new diagnostic tools are necessary. Some of these modern diagnostic methods include the Recovery Voltage Measurement (RVM), Frequency Domain Spectroscopy (FDS) and Polarization and Depolarization Current Measurements (PDC) [6]. These three methods are now available as user-friendly methods, and can be used to monitor, diagnose and check new insulating materials, qualification of insulating systems during/after production of power equipments non-destructively [29-31].

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Contrary to classical techniques (Insulation Resistance, Polarization Index, DDF, etc.), dielectric response measurements provide sufficient information about the condition of insulation, which is necessary for a reliable condition assessment.

6. Polarization Phenomena 6.1. Molecular Polarization

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Charge carriers inside dielectric material can move under electric stress. Polar molecules inside insulating materials will generally depict random orientations in the absence of electric field. The application of dc voltage stress will polarize the material by orienting the dipole moments of the polar molecules (Figure 8).

Figure 8. Molecular polarization.

In the absence of electric stress, the molecules of a dielectric cannot be considered as permanent dipoles (Figure 8a). Under electrical stress, the centres of both positive and negative charges do not coincide, and a dipole appears (Figure 8b). The polarisation P of such a dielectric is the sum of all dipolar momentum pi of each molecule. P = Σ pi

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In absence of the electric field, the dipolar momentum of a given dielectric is null. Under electrical stress E, a dipolar momentum appears due to the orientation of the dipoles. The polarisation is defined by:

P=

dp dv

⎛ dipolar momentum ⎞ ⎜ ⎟ volume ⎝ ⎠

(4)

In a linear, homogeneous and isotropic medium, it yields: P = εo χ E

(5)

D = εo E + P

(6)

where D is the electric induction, χ the electric susceptibility and εo = 8.852 10-12 As/Vm is the vacuum permittivity. By setting: 1 + χ = εr

(7)

D = εo ε r E

(8)

it yields:

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where εr represents the relative dielectric permittivity paper/pressboard and 2.2 for transformer oil).

(typically 4.5 for cellulose

6.2. Different Polarizations Polarization in materials can be due to several mechanisms known as electronic, ionic or atomic, dipolar, interfacial polarization and hopping.

a. Electronic Polarisation This kind of polarization results in electrons displacement with respect to the atom’s nucleus. The time necessary for the occurrence of this polarisation is very short (~ 10-15 seconds). Pe = N αe E1

(9)

E1 being the local electric field, N the number of molecules per unit volume and αe= 4 π εo r3 (r is the radius of the atom).

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b. Ionic polarization (orAatomic) This process is due to the mutual displacement of ions inside the molecule. The corresponding duration is of about 10-13 to 10-12 seconds: Pi = N αi E1

(10)

c. Dipolar Polarization (or Ionisation) This kind of polarization is related to the ionisation of dipolar molecules under electrical stress. It depends on temperature and its corresponding duration is of about 10-10 to 10-7 seconds: Pd = N αd E1 (11) αd =

with

p2 3kT

p being the dipolar momentum of the molecule, k = 1.380658 ·10-23 J/K the Boltzmann’s constant while T represents the temperature.

d. Space Charge Polarisation

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Under electric stress, charge carriers may be injected from the electrodes of any capacitor constituted by the apparently homogeneous insulation; the charges trapped in the insulation will move consequently. The time frame necessary for the occurrence of such a polarisation is of 10-2 to 10-1 seconds.

Figure 9. Mechanisms of polarization.

e. Polarizability Assuming that the four polarization mechanisms (Figure 9) act independently each other, the total polarizability α of a given dielectric material may be written as the sum of the four terms:

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(12)

where each term again may represent a sum of contributions [32].

6.3. Dielectric Dissipation Factor (DDF) or Dielectric Losses Consider a dielectric submitted to a sinusoidal electric field E. The current density flowing through this dielectric is:

J(t) = σ o Ε( t ) +

dD(t ) dt

(13)

where σo is the dc conductivity of the dielectric material and D(t) the electric displacement in the dielectric given by (6): The Transformed-Fourier of equation (13) yields: J(ω) = σ ο E(ω) + j ω D(ω)

(14)

J(ω) = [σο + j ω εo (1 + χ'(ω) - j χ"(ω))] E(ω)

(15)

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The dielectric being under a sinusoidal electric field, the polarization will be complex. Letting: εo(1 + χ'(ω) - j χ"(ω)) = ε'(ω) - j ε"(ω) = ε(ω)

(16)

J(ω) = [σo + ω ε"(ω) + j ω ε'(ω)] E(ω)

(17)

It yields:

J has a component in phase with E. The dielectric losses result from this component because it represents the power dissipated in the dielectric. These losses are due to the irreversible work necessary for the polarisation (ω.ε"(ω) term) and to the residual ohmic conduction of the dielectric (σo term). To describe the dielectric losses, one often uses the real component of the relative dielectric permittivity completed by a losses angle δ:

⎛ σ ⎞ ε"r + ⎜⎜ o ⎟⎟ ⎝ ωε o ⎠ tan δ = ε'r The losses due to the conduction are often neglected and then tanδ will be: tan δ =

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ε "r ε 'r

Dielectric Response Methods for Diagnostics of Power Transformers

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and the dielectric losses per unit volume : PD = εo εr' ω tanδ E2

(19)

6.3.1. Equivalent Circuits of a Dielectric Basically, an insulation material can be modeled as a parallel/series connection of a capacitor and a resistor. a.

Parallel equivalent circuit

The equivalent impedance Zp of the parallel RC circuit (Figure 10) is:

Zp =

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tan δ =

Rp 1 + jR p C p ω

=

Rp 1 + jR 2p C p2 ω2

(1 − jR

p

C p ω)

Cp " S 1 1 ' ; εr = ; εr = and C o = ε o R pCpω Co Co R p ω d

(20)

(21)

Figure 10. Parallel RC cell.

When an alternating voltage is applied across an insulator, the leakage current consists of a resistive component, and a capacitive component. In good dielectric the resistive leakage current is small and constant. In poor insulation, the resistive leakage current may be quite large and may increase with time. For good insulation, IC is 100 times larger than IR, therefore the resultant current is usually strongly capacitive and leads the applied voltage by almost 90° angle. For marginal insulation, IC is about 50 times IR, and the resultant current leads the applied voltage by approximately 88°. The dielectric dissipation factor or in a much simpler word the loss factor of insulation is defined as the ratio between resistive and capacitive currents caused by an alternative voltage applied across the insulation (Figure 11).

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Figure 11. Phasor representation of insulation current; definitions of Power Factor, Dielectric Dissipation Factor, and Loss Factor.

The dielectric losses are represented by Joule losses in Rp: PDt = U2 / Rp = ω Cp U2 tanδ = ω εoεr’ tanδ E2 (S d)

(22)

with U = E/d or when expressed per unit volume, it yields: PD = ω εo εo’ tanδ E2 = (εo E2) / (Rp Co) = ω εo εr”E2

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b.

(23)

Series equivalent circuit

The equivalent impedance Zs of the series RC circuit (Figure 12) is:

ZS = R S − j

1 CS ω

tan δ = R S CS ω ε 'r =

ε "r =

with

Cp

(24)

(25)

1 C o 1 + (R S C S ω)2

(26)

CS R SCSω C o 1 + (R S C S ω)2

(27)

Co = εo

S d

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Figure 12. Series RC cell.

The dielectric losses are represented by Joule losses in Rp:

⎤ ⎡ ⎥ ⎢ RS U 2R ⎡ tan δ ⎤ ⎥ 2⎢ =U ⎢ PDt = = U 2 C S ω⎢ ⎥ RS ⎡ ⎤ ⎣1 + tan δ ⎥⎦ ⎢ ⎢R S2 + ⎛⎜ 1 ⎞⎟⎥ ⎥ ⎜ C 2 ω2 ⎟ ⎥ ⎢⎣ ⎣ ⎝ S ⎠⎦ ⎦

(29)

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6.3.2. Measurement of Dielectric Loss and Dielectric Constant The DDF (tan δ) measurement is mainly performed on capacitors, cables and other power equipments. A four-arm bridge is often used for these measurements. This measuring bridge, the so-called Schering Bridge represented in Figure 13 consisting of the test equipment (C1), a reference capacitance C2 as well as the balancing elements Z3 and Z4. The balance of the bridge is achieved when I = 0. Additional legs may be added to balance out stray impedances. The Wagner ground is an example of this technique [33]. The Shering Bridge coupled with ac source is used to determine the variation of capacitance and loss angle with voltage for power equipment.

Figure 13. Schering Bridge.

Values of voltage used in typical field test vary between 10 V to 12 kV. Voltages lower than the rated voltage of the instrument/equipment, are used. Recent Advances in Dielectric Materials, Nova Science Publishers, Incorporated, 2009. ProQuest Ebook Central,

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The loss factor is sensitive to temperature and frequency. This parameter also depends on the geometrical composition of the oil-paper insulation; reason why loss factor of different insulation system cannot be compared. The value and/or shape of the loss angle vs. voltage curve gives indication of the quality of the insulation. Departure from the normal value/shape of the curve for that particular type of insulation indicates presence of moisture or some other defects.

6.4. Insulation Resistance

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Insulation resistance (IR) is one of the traditional methods used to determine the dryness of the transformer insulation. When a fixed dc voltage (0.25 – 5 kV) is applied across the insulation, there is a surge of current into the dielectric that fast decays. The surge is due to the capacitive current IC and should decay after a few a certain times. There will remain a small current due to the resistive leakage current IR (Figure 14). On new transformer insulation, the true dc level is reached only after a few hours, the dc resistance is therefore very difficult to assess. Usually, IR is measured after 1 minute from the dc voltage application. A guard ring electrode is recommended in IR measurements to avoid influence of unwanted leakages.

Figure 14. Current in a dielectric under dc stress.

In a dry/less contaminated transformer the resistive leakage current is small and constant. In poor insulation, the resistive leakage current may be quite large and may increase with time. IR value have to be compared with values from previous measurements on the unit or a sister unit in order to evaluate the actual condition of the insulation. Otherwise, bushing surfaces must be well cleaned before commencing the measurements. IR is temperature dependant and not reliable enough in identifying partially wet insulation [34].

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6.5. Polarization Index The Polarization Index (PI) is extension of IR measurement. PI which is the ratio of insulation resistance at 600 s (10 min.) to that at 60 s (1 min.) is less temperature-dependant than IR, since it is a ratio of two resistance values a at given temperature. PI is greater than unity for a good insulation system. However the reliability is limited, since PI measured on power transformer is strongly influenced by interfacial polarization and the geometrical composition of oil-paper insulation [34].

7. Dielectric Spectroscopy Techniques

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Power transformers main insulation consists of multiple layers of oil impregnated paper or pressboard (cellulose) immersed in oil separated by oil ducts. The dielectric properties of oil and cellulose and its polarisation phenomena depend on ageing state and water content [7, 8, 35]. The time depending polarisation P(t), caused by electronic, ionic, dipole, space charge and interfacial polarisation is called dielectric response. Dielectric spectroscopy response in time or frequency domain offers new opportunities for an off-line, insulation condition assessment of high voltage electric power equipment and its predictive maintenance non-destructively and reliably in the field. These techniques are global methods, i.e. each test object is regarded as a “black box” accessible only by its electric terminals. Therefore, only global changes of the insulation can be identified but not defects localization [8]. The fundamental theories behind dielectric measurements are already well known [8] while fundamental dielectric phenomena are discussed in Jonscher’s publications [36]. In this chapter, review that includes theory behind time and frequency domain measurement techniques is given.

7.1. Polarization and Depolarization Current (PDC) Measurements 7.1.1. Theoretical Background When stressed with electric field, dielectric materials undergo two types of reactions: conduction and electrical polarization. Basically, conduction may be defined as a continuous movement of charge carriers: i.e. electrons and ions; while polarization is the alignments of dipoles in a material in the direction of electrical field (see section 6). The multilayer insulation of common power transformers consists of oil and paper and therefore shows polarisation and conductivity effects. Polarization and depolarization currents (PDC) measured between low voltage and high voltage windings of a power transformer, is one way for assessing the condition of the insulation [6-8, 34-44]. The procedure consists in applying a dc charging voltage of magnitude Uc to the test object for a long time (e.g., 10,000 s). During this period of time, the polarization current Ipol(t) through the test object/equipment is measured, arising from the activation of the polarization process with different time constants corresponding to different

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insulation materials and to the conductivity of the object, which has been previously carefully discharged. The dielectric properties of oil and cellulose and its polarisation phenomena depend on ageing state and water content. Residues/particles from refinery, pollution and particularly ageing by-products enable the oil to conduct ionic current and also to increase water solubility. Oxidation by-products including carboxylic acids are the contributing factor. Carboxylic acid and water may dissociate into ions to increase considerably conductivity [41]. When a dielectric material is stressed with an electric field the material become polarized. The total current density is the summation of the displacement current density and the conduction current density, which is given by equation (13). The macroscopic polarisation P(t) given by equation (5) depends on the polarizability or susceptibility χ of the material, that covers all kinds of polarization processes in a dielectric. This parameter is null for ideal vacuum. Using equation (7), the dielectric response function f(t) can therefore be defined as :

f (t ) =

dχ (t ) dε r (t ) = dt dt

(30)

A unit step response function 1(t) for the electric field strength E0 can be applied on the dielectric; the polarisation processes in time domain develop as: P(t)= εo E0χ (t) 1(t)

(31)

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Any time dependent polarisation P(t) may therefore be derivate for any time dependent excitation E(t) [1].

P(t) = ε o χ (0)E(t) + ε o ∫ E (τ ) f (t − τ )dτ

(32)

Recall that the high frequency component of the permittivity ε∞, can be rewritten as a function of the susceptibility: ε∞, = 1 + χ (∞)

(33)

the combination of equations (6), (13), (30) and (33) provides the total current density:

J (t ) = σ o E (t ) + ε o E (t )[ε (∞ )δ (t ) + f (t )]

(34)

The polarization (or absorption, or charging) current Ipol(t) through the test object can therefore be expressed by [7, 8, 34, 35, 42]:

⎡σ ⎤ I pol (t ) = Co U c ⎢ o + ε ∞ δ(t ) + f (t )⎥ ⎣ εo ⎦ Recent Advances in Dielectric Materials, Nova Science Publishers, Incorporated, 2009. ProQuest Ebook Central,

(35)

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where: Co: geometrical capacitance of the test object, Uc : the step voltage (charging voltage), δ(t): the delta function arising from the suddenly applied step voltage at t = t0. f(t) : the response function of the dielectric material. The geometric capacitance of a core type-transformer can be estimated by the cylindrical capacitance (equation (2)), where h is the average winding height and ra and rb are, respectively, the inner and outer radius of the insulation between windings [42].

C0 =

ε 0 2πh r log ⎛⎜ b ⎞⎟ ⎝ ra ⎠

(36)

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If the proper geometry of the transformer insulation is available, the geometric capacitance can be calculated. Otherwise, geometric capacitance can be estimated by measuring the capacitance Cm between the two terminals of the insulation system under test (it can be measured with any capacitance measuring ac bridge at/around the power frequency) and dividing by the effective relative permittivity εr of the combination of the composite oilpaper insulation system (Co = Cm/εr) [42]. If the voltage is now disconnected and the object short-circuited at t = tC, the depolarization current (or discharging, or de-sorption) Idpol(t) in the opposite direction can be measured, without contribution of the conductivity. Neglecting the second term in (35) we get for t = (t0 + TC) [7, 8, 34, 35, 42]:

I depol (t ) = −C o U c [f (t ) − f (t + Tc )]

(37)

where Tc is the charging time of the test object. Figure 15 shows schematically the principle of the PDC measuring technique while Figure 16 shows the typical nature of these currents due to a step charging voltage UC [7].

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Figure 16. Relaxation currents during and after charging with a dc voltage UC for a time TC.

The insulation between windings is charged by the dc voltage step Uc. The charging time normally should be at least ten times larger than the time for which the response function is calculated. A charging time of about 10,000 s is generally required to assess the interfacial polarization and paper condition. The initial time dependence of the polarization and depolarisation currents (10 kHZ) at room temperature and for a full range of experimental frequencies *

E-mail address: [email protected]. Phone 787-751-4210, Fax 787-764-2571. (Corresponding author)

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Ashok Kumar, Margarita Correa, N. Ortega et al. near the freezing temperature (~ 240K). Magnetization vs. applied magnetic field of PFWT20 showed weak ferromagnetic properties. The microstructure of PSNT films revealed compressive strain which is capable for producing the relaxor behavior. The well-behaved hysteresis loops were observed in a broad temperature range for PSNT thin films indicating relaxor ferroelectric. PFN films showed high dielectric constant near the Curie temperature (Tc~380K) with spin-phonon coupling at Neel temperature. Multiferroic properties of PFN and PSN-PFN thin films will be discussed. The Second part consists of the fabrication of polycrystalline and epitaxially Pb(Zr,Ti)O3–CoFe2O4 (PZT-CFO) layered nanostructures with 3, 5, and 9 layers by pulsed laser deposition technique. The films were deposited on the polycrystalline Pt/TiO2/SiO2/Si(100) substrates, (001) oriented lattice matched LaSr0 5Co0 5O3/SrTiO3 (LSCO/STO) substrates and oriented LSCO/MgO substrates. X-ray diffraction and Raman analysis revealed that PZT and CFO were in the perovskite and spinel phases respectively in the layered nanostructure, having high quality crystallinity. The TEM and STEM line scan of the multilayer thin films showed that the layered structure was maintained. All the layered nanostructures showed well saturated both ferroelectric and ferromagnetic hysteresis loops at room temperature. The temperature dependence of magnetization, polarization, and magnetoelectric coupling will be discussed.

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Introduction Multiferroic materials that provide coupled ferroelectric and ferromagnetic responses are of potential interest due to their technological application, and scientific development. There are two approaches to achieve goal, first, discover new single phase multiferroic materials with high ME coupling, may be better for memory applications, at present, very few exist in nature, most of them illustrate their multiferroic properties at cryogenic temperature, second, design artificial nanostructure that couple ferroelectric and ferromagnetic layers through magnetostrictive and piezoelectric strain transmitted across the interface [1-10]. The most significant feature of multiferroic materials are their additional degree of freedom, i.e. more than two order parameter, also these materials posses magneto-electric properties, one can easily tuned one of the properties i.e. ferroelectric, ferromagnetic, and ferroelastic by the others. In traditional single phase multiferroic i.e. BiFeO3, and Cr2O3, an intrinsic ME coupling occurs. An electric field change the position of cations from anions, changing shift the dipoles and exchange contribution to the magnetic interaction-also modify the electronic wave function, which further change the magnetic coupling [12,13]. Whereas in inverse condition, the applied magnetic field forced strong spin-orbit coupling which in turns change the polarization. In case of multilayer nanostructure magnetostriction materials combined with electrostriction materials an extrinsic ME coupling is mediated by strain at the interface. For artificially MLs nanostructure, applied electric field causes strain in the FE components which mechanically transfer to the magnetic components and change the magnetization (also vice versa). This class of materials showed large ME components seems promising candidate for device application. However, strain is not the only source to gives ME effects in MLs nanostructure. The other possible cause is the coupling between ferromagnetism and ferroelectricity through interface bonding. FE instabilities change the atomic position at the interface, overlapped atomic orbital at the interface affects the interface magnetization. This produces a ME effects caused by the sudden change in interface magnetization induced by the polarization reversal in the FE under the influence of applied electric field [12].

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ME effects is defined in two ways based on the analogy with direct and converse piezoelectricity. The direct ME effects is defined as change in electrical polarization ( P) or field (E) due to applied magnetic field (H), and the converse ME effects is to change in magnetization due to applied electric field. However, both direct and converse effects are of equal strength if the material is stress free non ferroic with linear coupling.

⎛ ∂M ⎞ ⎛ ∂p ⎞ ⎟ ,where μ 0 permeability of free space [12]. ⎟ = μ0 ⎜ ⎝ ∂E ⎠ H ⎝ ∂H ⎠ E

α =⎜

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The study of magnetoelectric, multiferroic materials has largely been confined to oxides/perovskite. Figure 1 shows the Venn diagram of various subclasses of dielectric crystals having magnetic and electrical ordering, originally [8] depicted by Eerenstein et al. (2005), but later filled nicely by Bibes [8] and review by Scott et al. [9], there are However, practically all the well-studied examples are oxides, and many are perovskites. This is probably because oxides are relatively easy to grow as single crystals and safe to grow as thin films. In Figure 1 the Venn diagram illustrates a wide range of overlapping materials and shows the relationship between multiferroic and magnetoelectric materials. Ferromagnets (ferroelectrics) form a subset of magnetically (electrically) polarizable materials such as paramagnets and anti-ferromagnets (paraelectrics and antiferroelectrics). The intersection (red hatching) represents materials that are multiferroic. Magnetoelectric coupling (blue hatching) is an independent phenomenon that can, but need not; arise in any of the materials that are both magnetically and electrically polarizable. In practice, it is likely to arise in most of these materials, either directly or via strain.

Figure 1. Venn diagram of various subclasses of dielectric crystals having magnetic and electrical ordering.

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A. PFW-PT Related Compounds Natural relaxors were invented as the first magneto-electric materials with a perovskite A(B`B``)O3 ordered/disordered structure in which B site of BO6 position are randomly distributed by B` and B`` cations [13-15]. PFW was considered as a potential candidate for these groups having disordered structure. Modification of PFW at B-site, make it potential candidate for various device applications such as: micro electro mechanical system (MEMS), piezo electric actuators, multi layer capacitors, pyro electric detectors, etc. [1618]. The morphotropic phase boundary (MPB) of the solid solution of PbFe2/3W1/3O3PbTiO3 (PFW-PT) indicates that this material has ferroelectric and antiferromagnetic properties for the lead titanate concentration p satisfying (0.33 > p > 0.20) [19-20]. Extensive studies were carried out by Schmid et al. on PFW single crystals which showed dielectric maxima at 180K and Neel temperature at 343K [15]. On the other hand, we have thorough studied PFW-PT thin films which indicate pure relaxor behavior, strong competition between relaxor and ferroelectric, and second-order ferroelectric phase transitions with increase in lead titanate concentrations respectively [21-23]. Generally, relaxor-type materials may undergo through different dynamical states during the cooling i.e. a ergodic state characterized by the occurrence of randomly oriented polar nano-regions (below Burn temperature (TB) and above freezing temperature (Tf)) , an intermediate nonergodic state characterized by the presence of coupled polar nano-regions but the absence of long-range ferroelectric (FE) order (below Tf) and a proper ferroelectric state (after application of suitable electric field) [9]. The precise balance between local polarization fields supporting ferrolectric distortion and short-range forces favoring the paraelectric state results in nano polar clusters. Due to the compositional fluctuation their nano regions will never reach sufficient interaction between the neighbors to results in a long-range order like normal ferroelectric. Ferroelectric materials possessing polar microscopic domains show a sharp phase transition at the Curie temperature, whereas relaxors pass through different dynamical states [24]. The polar nano regions (PNRs) with short range ordering of the relaxor can be turned into micro polar regions by application of an external electric field or by forming a solid solution with ferroelectric materials above the morphotropic phase transition (MPB) [25]. However, the magnetoelctric properties of the system with mesoscopic order such as in relaxors were not studied until the pioneering work of Levstik et al. last year [26].

B. PSN-PFN Related Compounds As we know, the lead based relaxors, e.g. PMN, PSN, PMN-PT, PSN-PT, PST, PFW, are of special interest because the degree of structural order of the B-site cations (and the relaxor properties) closely depend on the degree of order/disorder in the sample [27-31]. Effect of B-site substitution on ferroelectric phase transition and order-disorder transition temperature on PSN, PST and PSN-PST single crystals and polycrystalline ceramics showed particular interest due to dielectric anomaly at ambient temperature [33-34]. PFN ceramics and single crystals exhibit paraelectric to ferroelectric phase transition near Tc ≈ 385K. The nature of magnetic ordering in PFN, however, remains poorly understood and the reported data in the literature have not provided a consistent picture. A paramagnetic to

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anti-ferromagnetic Neel temperature (TN) is reported to be around 143 K. When cooled down through the anti-ferromagnetic transition with the simultaneous application of electric and magnetic field, Astrov et. al [35] reported the occurrence of weak ferromagnetism in PFN ceramics. On the other hand, Howes et al [36] did not find any anomaly in the magnetic susceptibility up to 4.2 K. Yang et al and Watanabe et. al [37,38] reported a weak ferromagnetic ordering of PFN at 80 K and 9 K respectively. Majumder et al. showed the room temperature ferroelectric and ferromagnetic properties for sol-gel derived PFN fine powder [39], whereas, Yan et al. [40] reported the multiferroics relaxor nature of PFN thin films. Particularly, these compounds in thin films form showed interesting physics due the larger effects of surface, interfaces, nano islands, film thickness, and interfacial strain compare to the bulk counterpart. We will discuss the ferroelectric relaxor nature of PSN-PST thin films. The multiferroic relaxor nature of PFN films will be explained on the basis of spin-phonon-dipole coupling. The dielectric properties were analyzed in context of the induced strain state in the films.

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C. PZT-CFO Layered Nano Structure Several efforts have been done to synthesize and characterize the multiferroic layered nanostructure, supperlattices, and ME composite thick films (several micron) with coexisting ferroelectric (FE) and ferromagnetic (FM) properties, for the next generation miniaturized integrated devices. Different configurations were reported for fabrication of ME composite thin films, such as composite spreads with terminal layers being FE and FM [41], double Pb(Zr,Ti)O3 (PZT)/CoFe2O4 (CFO) multilayers [42], superlattices consisting of alternating FM (Pr0 88Ca0 15MnO3)and FE (Ba0 6Sr0 4TiO3) layers deposited on SrTiO3 [43], epitaxial CoFe2O4-BaTiO3 ferroelectromagnetic nanocomposites by self assembly technique [44], etc. These studies clearly demonstrated that the ME effect in all different configurations. We have also reported the multiferroic, ME effect and electrical properties of PZT/CFO layered nanostructure thin films [45-47]. Complex impedance spectroscopy are used to analyze the microstructure-property relationship, it also allows distinguishing between intrinsic (bulk) and extrinsic contribution (grain boundary, surface layer, and electrode contact problem). The electrical and dielectric properties of layered nanostructure showed similar characteristic as that of barrier layer capacitor i.e. CaCu3Ti4O12 [48], Bi2/3Cu3Ti4O12 [49], ACu3Ti4O12 (A = Ca, Bi2/3, Y2/3, La2/3) [50]. They all exhibit a Debye-like relaxation (Maxwell-Wagner type) and step-type dielectric behaviors as a function of temperature. Due to lack of basic physics on artificially designed nanostructure, we will use several approaches to analyze the polarization and dielectric behavior, among them recently observed improper ferroelectricity in super lattices, diminishing the polarization with lowering the temperature, MaxwellWagner space charge [48-53].

Experimental Procedure PbFe2/3W1/3 (PFW)1-x-PbTiO3 (PT)x (x = 0-0.50) thin films were prepared on Pt/Ti/SiO2/Si(100) substrate using CSD and lead acetate trihydrate, iron 2-4 pentanedieonate, titanium isopropoxide and tungsten isopropoxide are used as precursor materials. To make

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complex precursor sol, iron 2-4 pentanedieonate was dissolves in acetic acid first and then tungsten isopropoxide added dropwise in inert atmosphere to get B site precursor sol. Titanium isopropoxide was dissolve in acetic acid and add to the B-site precursor sol to get proper concentration of PFW-PT. The lead acetate was dissolve in the acetic acid with magnetic stirrer for 30 minute and the resulting solution was added drop wise in the B site precursor solution. The PFW-PT compositions were varied with the variation of titanium isopropoxide concentration. Final solution for all the concentration were stirred for 1 hour and filtered with 0.25μm filter and form the stock solution. For good quality films, the PFWPT(x=0-0.50) solution of 0.2-0.3 molar concentrations was spin coated at 3000 rpm for 30 seconds and pyrolysed at 4000C for 2 minutes. This process was repeated several times to get desired thickness of the films. Rapid thermal annealing (RTA) was performed at 7750C for 120 seconds to get the desired phase and density. DC sputtering was carried out for depositing the Pt top electrode of 3.14X10-4cm2 in area through a shadow mask. PSNT and PFN thin films were grown on MgO substrates using conductive La0 5Sr0 5CoO3 (LSCO) layers as bottom electrode by pulse laser deposition technique. Excimer laser (KrF, 248 nm) with a laser energy density of 1 J/cm2 was used to fabricate the thin films. During deposition the substrate temperature was maintained at 600 ºC and oxygen pressure of 300 mTorr. The LSCO was deposited to 600 ºC and oxygen pressure of 200 mTorr. The thickness of the reported PSNT and PFN films and the LSCO layer were estimated from the TEM cross-sectional view of the thin film slab and were found to be 240 and 80 nm respectively. Layered nanostructure of thin films with 3 (L3), 5 (L5), and 9 (L9) alternating layers of PZT/CFO were deposited from individual PZT and CFO targets on Pt/TiO2/SiO2/Si, and oriented MgO subtracts using pulsed laser deposition technique. The PZT and CFO ceramic targets of 2 cm diameter were prepared by conventional solid-state route. An excimer laser (KrF, 248 nm) with a laser energy density of 2.5 J/cm2 and pulse repetition rate of 10 Hz was used to deposit the ML films. During the deposition the substrate temperature was maintained at 400 °C and oxygen pressure of 100 mTorr. The deposited films were annealed to 650 °C for 150 s using a rapid thermal annealing (RTA) furnace. The total thickness of all the films was ~350 nm in these deposition parameters. The crystal structure was investigated using a scan speed of 0.3 deg/min with X-ray diffractrometer (Siemens). The surface morphology and crossectional area of the films were investigated using Atomic force microscopy (AFM) and scanning electron microscope (SEM) respectively. The electrical properties of the films were studied in metal-insulatormetal configuration and the films were characterized using an impedance analyzer HP4294A (from Agilent Technology Inc.) attached with temperature controlled probe station (MMR technology) The polarization hysteresis loop were traced using a ferroelectric tester system RT-6000 HVS from radiant technology Inc. The Raman measurements were performed in the backscattering geometry using a Jobin-Yvon T6400 Triplemate instrument. Radiation of 51405nm from a coherent Innova 99 Argon laser was focused over less than a 2μm diameter circle area by using a Raman microprobe with an 80Xobjective. A charge-coupled device (CCD) system collected and processed the scattering light. The integration time of the spectrum, the slit width and laser beam power were adjusted in order to have a high signal to noise ratio. Typical spectral resolution for the Raman system with an 1800 groovs mm-1 grating and 1in CCD was less than 1 cm-1. The system was calibrated by Si spectra at room temperature before and after recording the

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film spectra. The sample was held in a closed cycle LN2 cryostat (or furnace) and the temperature was controlled from 80-650K.

I. Relaxor, Multiferroic Relaxor, and Normal Ferroelectric A. Multiferroic Properties of PFW-PT

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Figure 2 ((a), (b), (c)) shows the dielectric properties of Pb(Fe2/3W1/3)1-xTixO3 (x= 0, 0.20 , 0.50 ) thin films over wide range of temperature. Figure 2 (a) represent the pure Pb(Fe2/3W1/3)1-xTixO3 (x =0) PFW compounds which illustrate, high dielectric constant maxima (~1900-2100), broad diffused phase transition in a wide range of frequency, maxima of permittivity (Tm) lies between 120K-150K, Dielectric dispersion in the wide range of temperature i.e. 100 K-200 K and low dielectric loss through out the temperature region.

Figure 2 ((a), (b), (c)) Dielectric constant of Pb(Fe2/3W1/3)1-xTixO3 (x= 0, 0.20 , 0.50 ) thin films over wide range of temperature from 100 Hz to 1 MHz.

Figure 2 (b) demonstrate the dielectric properties of Pb(Fe2/3W1/3)1-xTixO3 (x =0.20) (PFWT20) at ambient temperature. It indicates higher dielectric constant around (1200-1500) over a wide range of temperature, wide range (~40K) of frequency dispersion from 500 Hz to 10 kHz, flat dielectric response for higher frequency over a wide range of temperature (~100K) with very low dielectric loss [21-23]. Further enhancement in doping composition in Pb(Fe2/3W1/3)1-xTixO3 (x =0.50) (PFWT50) i.e. above the morphotropic phase boundary, it shows second order strain free ferroelectric phase transition as shown in Figure 2(c). With increase in lead titanate/titanate concentrations, the matrix material (PFW) passed through

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several physical stage i.e. relaxor to relaxor ferroelectric to normal ferroelectric. We can summarize the changes occurs in PFW with increase in PT concentrations as follows: (i) decrease in the value of dielectric constant (ii) decrease in dielectric dispersion (iii) relaxor to normal ferroelectric (iv) near the morphotropic phase boundary it shows strong competition between short range order and long range order. These experimental facts can be explained on the basis of statistical compositional fluctuation (i.e. the disorder in the arrangement of different ions on the crystallographically equivalent sites) in Fe:W concentration, and the up-down displacement of Ti ions sitting at the center of crystal, which are respectively the main features of relaxor and normal ferroelctrics. The presence of small polar-regions in nano scale leads to the origin of dielectric relaxation phenomena in the order-disorder perovskite PMN [54, 55]. It can be inferred that the same mechanism is responsible for dielectric relaxation in the PFWT films for concentration below the morphotropic phase boundary (MPB). At higher concentration and frequencies these PNRs do not get enough thermal energy to be relaxed; whereas the broader dielectric maxima may be due to the presence of micro polar regions (long range order). The slight shift in dielectric maxima temperature, compared to the values reported for single crystal and bulk polycrystalline ceramics of the same compounds, may be due to built-in space-charge fields [56,57]. The dielectric diffuseness and the shift of Tm with respect to bulk PFW-PT (as reported in literature) were attributed to the thermal mismatch and strain between the substrate and the film [58]. Thin films are usually highly constrained because the growth process is accompanied by several strain factors such as oxygen vacancies, misfit strain due to lattice mismatch between the film and the substrate, and thermoelastic strain generated by the difference between the thermal expansion coefficients of the film and the substrate [59]. In order to check the relaxor nature of PFW-PT thin films, we have employed non-linear Vogel-Fulcher relation:

⎡ − Ea ⎤ f = f 0 exp ⎢ ⎥ ⎣ k B (Tm − T f )⎦ where f is the measured frequency, f0 = pre exponential function, Ea = activation energy for polarization fluctuations of an isolated cluster, kB = Bolltzmann constant, Tm is the temperature corresponding to the dielectric maxima, and Tf is the static freezing temperature. The frequency dependence of temperature maxima of dielectric relaxation peak provides qualitative value for relaxor ferroelectric. The observed non linear dependence of 103/Tm on ln(f) revealed the validity of Vogel-Fulcher relationship (Figure 3 (a)). The parameters; f0 = 0.45x1010 Hz, Ea=0.020 eV, and Tf =78 (±3) were extracted from the non-linear curve fitting which confirmed a typical relaxor behavior in the PFW (x=0) thin films. The same VF nonlinear dependence of 103/Tm on ln(f) were carried out for the PFWT20, which showed the validity of the Vogel-Fulcher relationship (inset Figure 3(b)). The parameters f0 = 0.27x108 Hz, Ea=0.06 eV, and Tf =238 (±5) were extracted from the nonlinear curve fitting, which again confirms a typical relaxor behavior in the PFWT20 thin films.

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Figure 3 (a) & (b) Non linear Vogel-Fulcher relationship of PFW and PFWT20 as a function of 103/Tm vs. ln(f) respectively.

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Figure 4 shows inverse of dielectric constant as a function of temperature of PFWT50 (far above morphotropic phase boundary) for wide range of frequencies. The temperature dependant dielectric constant indicates a continuous second order ferroelectric phase transition. The slope of the reciprocal of the dielectric constant near the ferroelectric phase transition is in the ratio of 2:1, which indicates a second order ferroelectric phase transition with negligible polarization strain coupling.

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Figure 4. Inverse of dielectric constant as a function of temperature of PFWT50 thin films.

The physical interpretation of the second order ferroelectric phase transition can be explained on the basis of Landau theory in the context of Gibbs free energy. The Gibbs free energy can be defined as:

G (P, T ) = A(T − Tc )P 2 + BP 4 + CP 6

(1)

where A, B, C are the constants and P (polarization) ordered parameter for ferroelectric transition. Since the energy is measured from the non-polar phase, and the transition is continuous, β>0 and we can terminate the higher order of P i.e. P6 for mathematical simplicity. The new Gibbs free energy function is given below:

G (P, T ) = A(T − Tc )P 2 + BP 4 The derivative of Gibbs free energy as a function of polarization are given below

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(2)

Design and Development of Multiferroic Relaxors…

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⎛ ∂G ⎞ 3 ⎟ = 2 A(T − Tc )P + 4 BP = 0 ⎜ ⎝ ∂P ⎠

(3)

A(T − Tc ) 1 2 ( ) P ~ T − T c 6B and

(4)

P2 =

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Using equation 3 and 4 we calculate the critical exponents (β=1/2) for ferroelectric materials.

⎛ ∂ 2G ⎞ ⎜ 2 ⎟ = 2 A(T − Tc ) + 12 BP 2 ⎝ ∂P ⎠

(5)

⎛ ∂ 2G ⎞ 1 ⎜⎜ 2 ⎟⎟ = = +4 A(Tc − T ) forT < Tc ⎝ ∂P ⎠ ε

(6)

⎛ ∂ 2G ⎞ 1 ⎜⎜ 2 ⎟⎟ = = 2 A(Tc − T ) forT > Tc ⎝ ∂P ⎠ ε

(7)

Equation 7 represent the paraelectric phase where polarization P = 0. The ratio of equation 6 and 7 gives the slope (2:1) of reciprocal of dielectric constant. Our experimental data matched well with this Landau free energy model. It indicates that the PFWT50 thin films show a continuous, second order displacive ferroelectric phase transition. In order to clarify the origin of strong competition between short range order (SRO) and long range order (LRO) in the PFWT20 thin films, the dc bias dependence of the dielectric/capacitance response at various temperature and frequency with small ac signal amplitude of 50 mV are shown in Figure 5(a,b). At temperatures near the freezing temperature (~240K) it was found that the capacitance versus applied electric field exhibited apparent hysteresis referred as “butterfly loops”. The occurrence of butterfly loops in capacitance versus electric field (C-E) is indicative of polarization reversal, showing the ferroelectric nature of the films. PFWT20 thin films showed the “butterfly loop” at 240K for the whole range of experimental frequencies (Figure 4(b)). However, at room temperature the C-E graphs (Figure 4(a)) show disappearance of the butterfly loop for lower frequency (> 1 . n1

Cylindrical polar coordinate system (r, θ, z) has been used here, z being the direction of propagation (i.e along the axis of waveguide) which is perpendicular to the plane of paper. We use point matching method within the boundary conditions corresponding to the weak guidance condition. Sixty points have been selected on the boundary of the cross section which we find sufficient for obtaining a reasonable stability of the results. The position of these points are registered by the coordinates ( ri θi ) with i = 1,2,3……..60, where ‘r` represents the radial distance and ‘θ` gives angular position of the chosen point. Suppose that the electromagnetic wave propagates along the waveguide axis. Assuming weak guidance approximation, scalar wave equation is solved for the axial components of the electric and magnetic fields Ez & Hz respectively for the region inside and outside of the cross sectional boundary of the waveguide. If ψ represents the field (Ez or Hz as the case may be), the wave equation will be of the form:

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∂ 2ψ 1 ∂ψ 1 ∂ 2ψ + + 2 + (ω 2 με − β 2 )ψ = 0 2 2 r ∂r r ∂θ ∂r

(1)

Here ω is the angular frequency of the unbounded wave in a medium with permittivity ε and permeability μ. The quantity β is the z component of the propagation vector. In the core region we take the solution as a linear combination of the products of Bessel function of first kind i.e Jν(x) of various orders and trigonometric functions, whereas in the outer non guiding region we take the solution as linear combination of the product of modified Bessel functions of the second kind i.e. Kν(x) and the trigonometric functions since in this region the solutions must have decaying character as one goes away from central waveguide axis. We now take ψ1 and ψ2 as the solutions in the guiding and non-guiding regions respectively. Therefore ψ1 and ψ2 can be written as

ψ 1 = A0 J 0 (ur ) + A1 J 1 (ur )Cos θ + B1 J 1 (ur ) Sin θ + A2 J 2 (ur )Cos ( 2θ ) + B 2 J 2 (ur ) Sin ( 2θ ) + A3 J 3 (ur )Cos (3θ ) + B3 J 3 (ur ) Sin (3θ ) + ..........

(2)

ψ 2 = C 0 K 0 ( wr ) + C1 K 1 ( wr )Cosθ + D1 K 1 ( wr ) Sinθ + C 2 K 2 ( wr )Cos (2θ ) + D2 K 2 ( wr ) Sin (2θ )

+ C 3 K 3 ( wr )Cos (3θ ) + D3 K 3 ( wr ) Sin(3θ ) + .......

(3)

Where r and θ represent the polar coordinates of the various points on the boundary surface of the waveguide. We define u and w as Recent Advances in Dielectric Materials, Nova Science Publishers, Incorporated, 2009. ProQuest Ebook Central,

568

H.P. Singh, Vivek Singh and V.P.Arora u=

ω 2 με 1 − β 2 , w =

β 2 − ω 2 με 2

Now to analyze the propagation characteristics, we use the point matching technique in which the field solutions and their first derivatives in inner region of the waveguide close to the boundary at various suitable chosen points on the boundary surface should match. We get the following equations for the waveguide selected after the matching of the field solutions at various chosen points: 29 ⎡ 29 ⎤ ⎢∑ Am Jm (uri )Cos(mθi ) + ∑ Bm Jm (uri )Sin(mθi )⎥ m=0 ⎣m=0 ⎦ 29 29 ⎡ ⎤ − ⎢∑Cm Km (wri )Cos(mθi ) + ∑ DmKm (wri )Sin(mθi )⎥ = 0 m=0 ⎣m=0 ⎦

19 ⎡ 19 ⎤ u ⎢ ∑ Am J m′ (uri )Cos ( mθ i ) + ∑ Bm J m′ (uri ) Sin ( mθ i ) ⎥ m=0 ⎣ m =0 ⎦ 19 19 ⎡ ⎤ − w ⎢ ∑ C m K m′ ( wri )Cos ( mθ i ) + ∑ Dm K m′ ( wri ) Sin ( mθ i ) ⎥ = 0 m=0 ⎣ m=0 ⎦

(4)

(5)

In the above equations the prime ( ' ) indicates differentiation with respect to the argument. The determinant formed by the coefficient of constants Am, Bm, Cm & Dm in above equation is a 100 × 100 as represented by Δ1. A nontrivial solution will exist for this set of equation only if

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Δ1 = 0

(6)

This equation is known as characteristic equation and contains all the information of the proposed waveguide. From solution of the above equation, the normalized propagation constant

β2 2

− n22

b = k2 for the first few guided modes can be found for the proposed waveguide. We n1 − n 22 also define the dimensionless waveguide parameter V =

2πa

λ

n12 − n 22

Where a is maximum value of radius, λ is the wavelength used, n1 and n2 are refractive indices of core and clad respectively. A similar analysis has been done for the case when two sides Fig. (1.c) have been shorted by metal clad in place of dielectric. In this case we will have 80 simultaneous equations involving 80 unknown constants. The determinant formed by the coefficients of the constants Am, Bm, Cm and Dm is a 80×80 determinant Δ2, and the characteristic equation for the case is Δ2 = 0

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(7)

Modal Dispersion Curves of an Optical Waveguide…

569

This equation has been solved and propagation constant has been obtained for few guided modes. Normalized propagation constant b has been plotted against normalized parameter V.

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Figure 2. Cross sectional view of a DDM waveguide.

Figure 3. Cross sectional view of a MMD waveguide.

Figure 4. Normalized dispersion curves( b verses V) for DDM waveguide. Recent Advances in Dielectric Materials, Nova Science Publishers, Incorporated, 2009. ProQuest Ebook Central,

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Figure 5. Normalized dispersion curves( b verses V) for MMD waveguide.

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Numerical Computation Results and Discussion We now proceed to some numerical computation in order to have the modal dispersion curves for the proposed waveguide. This will give us an insight into the modal properties of our waveguides. The usual algorithm for computation is as follows: we choose λ = 1.55 μm, n1 = 1.5, n2 = 1.48 and choose a particular value of a. Feeding these values in the left hand side of equation (6) and equation (7), involving 100×100 and 80×80 determinants respectively, one can obtain their values for a large number of equispaced value of β in the range n1 k 0 > β > n2 k 0 . These values are then normalized i.e. we obtain b. Plotting these normalized values against V yields curves intersecting with the V-axis. The zero crossing gives us the possible cut off values. This exercise is repeated for different value of a. The dispersion curves thus obtained are shown in Fig. 4 for DDM waveguide and Fig.5 for MMD waveguide. A comparative study of these dispersion curves can now be made. We find that numerous modes can be sustained in each case of which we have shown the dispersion curves for some low order mode. The two sets of dispersion curves are similar in nature but on closer inspection we find some significant difference. Both the DDM and MMD guides show the first cutoff values at V=0.50.However, the dispersion curves for the modes of DDM geode are more separated than those of MMD guide near V=10.0. Another important feature is that the curves corresponding to Fig. 5 (MMD waveguide) tend to reach saturation at smaller values of V than the curve corresponding to Fig. 4 for DDM waveguide.

References [1] Akiba. S., “ The future Vol.17,No.1,2003,pp. 20-23.

of

optical

communications.”

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IEEE

Newsletter,

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[2] Bayvel. P., “ Future high capacity optical communication networks, “ Phil. Trans. Royal Society Lodon, Vol.358,2000, pp.303-329. [3] F.G stremler, Introduction to communication systems, 3rd edn, Addision – Wesley(1990) [4] T. Miya, Y. terunuma, T. Hosoka and T. Miyashita,’ Ultimate low loss single mode fiber at 1.55 μm’. Electron Lett., 15(4) , 106-108,1979. [5] W.S.Huxford and J.R.Platt, Survey of near infra-red communication systems, J.Opt. Soc.Am., 38 pp. 253 – 268, 1948 [6] H.F.Wolf ( Ed.), Handbook Of Fiber Optics Theory and Applications, Granada, 1981 [7] P.Russer, Introduction to optical communication’, M.J.Howes and D.V.Morgan (Eds.), Optical fiber communications, pp. 1-26, John Wiley, 1980 [8] D.Handros and P. Debye, ‘Electromagnetic waves along long cylinders of dielectric’, Annal. Physik,32(3), pp. 465 – 476, 1910 [9] S.R.Rangaranjan and J.E.Lewis, Propagation characteristics of elliptical dielectric tube waveguides, Proc Inst Elect Eng 127(1980), 121-126 [10] C.Yeh, Elliptical dielectric waveguide, J. Appl Phys 33 (1962), 3235-3242 [11] C.Yeh, Modes in weakly guiding elliptical optical fibers, Opt Quantum Electron 8 (1976), 43-47 [12] R.B.Dyott, Cutoff of the first order modes in elliptical dielectric waveguide: An experimental approach, Electron lett 26 ( 1990 ) , 1721-1723 [13] L.Levin, Radiation from curved dielectric slab and fibers, IEEE Trans Microwave Theory Tech MTT-22 (1974) , 718 – 727. [14] A.Kumar, V.Thyagarangan. and A.K.Ghatak, Analysis of rectangular core dielectric waveguides: An accurate perturbation approach,Opt Lett 8 (1983),63-65 [15] J.E.Goell, A circular harmonic computer analysis of rectangular dielectric waveguides, Bell Sys Tech J 4S (1969), 2133-2160. [16] S.P.Ojha,P.K.Chaudhary and P.Khastgir, Glass fibers of triangular cross-section with metal loading on one or more sides: A comparative modal study, Proc SPIE 1580 (1991), 278-287. [17] V.Mishra, P.K.Chaudhary, P.Khastgir and S.P.Ojha, Modal propagation of a waveguide with a regular pentagonal cross-section with coducting and non-conducting boundaries, Microwave Opt Technol Lett 8 (1995), 280-282. [18] M.P.Srinivasa Rao, B.Prasad, P.Khastgir and S.P.Ojha, Modal cutoff condition for an optical waveguide with a hypocycloidal cross-section, Microwave Opt Technol Lett 14 (1997), 177-180. [19] M.P.S. Rao, V.Singh, B.Prasad, and S.P.Ojha, Modal cutoff conditions of an hypocycloidal waveguide with various types of metal loading on the core boundaries, Microwave Opt Technol Lett 19 (1998), 152-158. [20] 20. H.P. Singh, Vivek Singh and V.P. Arora, Modal analysis and dispersion curves of a curvilinear triangular cored light guide using Goell's point matching method Optik International Journal for Light and Electron Optics, Volume 119, Issue 1, 7 January 2008, Pages29-33

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In: Recent Advances in Dielectric Materials Editor: Ai Huang, pp. 573-627

ISBN: 978-1-60692-266-8 © 2009 Nova Science Publishers, Inc.

Chapter 17

RECENT ADVANCES IN THE CHARACTERIZATION OF COMPOSITE DIELECTRIC STRUCTURES Stefano Giordanoa and Pier Luca Pallab Department of Physics, University of Cagliari and Sardinian Laboratory for Computational Materials Science (SLACS-INFM/CNR) Cittadella Universitaria, I-09042 Monserrato (Ca), Italy

Abstract

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The central problem in predicting the dielectric behavior of heterogeneous materials (like, e.g., composite or nanostructured systems, powders or mixtures) consists in the evaluation of their effective macroscopic properties, still taking into account the actual microscale material features. This leads to the concept of homogenization, a coarse graining approach addressed to determine the relationship between the microstructure and the effective behavior: the prediction of the effective electromagnetic properties of a composite material from those of its constituent material phases is the major objective of various homogenization models. The resulting effective properties can be observed at the macroscale, where the refined effects of the morphology cannot be directly measured. Dispersions of particles (inclusions with a given shape and a given volume) in a host homogeneous matrix are the most studied heterogeneous structures. From the historical point of view, early mixture theories generally work well when the volumetric proportion of the inclusion phase is small and when the contrast between the electromagnetic properties of the two material phases is not large. More recently, refined and improved models have been developed in order to yield better predictions, also in these critical situations. Recent increases in activity in the field are, at least, partially caused by the interest in selective absorbers of solar and infrared radiation, by an increasing number of applications in astronomy and atmospheric physics, by several applications in the design of novel materials in optics and in material science, and by the indications that the electromagnetic behavior of the composite system may be very different from the behavior of individual components.

a

E-mail address: [email protected], [email protected]. Web: http://www.giordanostefano.it. b E-mail address: [email protected] Recent Advances in Dielectric Materials, Nova Science Publishers, Incorporated, 2009. ProQuest Ebook Central,

574

Stefano Giordano and Pier Luca Palla These approaches can be applied not only to the static (d.c.) electric and magnetic properties, but also to the case of wave propagation in low frequency (l.f.) or high frequency (h f.) regime. It is in fact well known that when any form of energy propagates through a medium containing scatterers (particles), the entrained energy will be either redistributed in various directions by scattering or absorbed by intrinsic absorption mechanisms. The standard homogenization theories can be applied also in such cases provided that the wavelength of the propagating field is much larger than the average size of the particles. Recently, these methodologies have been applied to light scattering from coatings, to heat transfer in powder insulators, to chemical and nuclear reactors, to cryogenic insulation and, finally, to microwave or laser coatings. In all heterogeneous or composite materials, the nonlinear regime and the anisotropic character have not yet been investigated thoroughly. Nevertheless, both the nonlinear and the anisotropic features are relevant in many materials science problems (crystal optics, optical bistability and optical devices). Therefore, we devote this work to the development of some analytical models able to take into account the refined effects of the nonlinearity and the anisotropy of the constituents.

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1. Introduction A widely dealt topic concerning the physical behavior of heterogeneous materials (mixtures) is that of calculating their permittivity starting from the knowledge of the permittivity of each medium composing the mixture as well as of the structural properties of the mixture itself (percentage of each medium, shapes and relative positions of the single parts of the various media). Clearly, it concerns with isotropic linear media, which combine to form linear mixtures. In literature we find a large number of approximate analytical expressions for the effective permittivity of composed media as a function of the permittivity of its homogeneous constituents and some stoichiometric parameter [1-3]. Each of these relationships should yield correct results for a particular kind of microstructure or, in other words, for a well defined morphology of the composite material. From the historical point of view, we remember some theories describing a mixture composed by two linear isotropic components: one of the most famous is the Maxwell formula developed for a strongly diluted suspension of spheres [4]; a similar methodology has been applied to the case of a mixture of parallel circular cylinders [1,3]. An alternative model is provided by the differential scheme, which derives from the mixture characterization approach used by Bruggeman [5]. In this case the relations should maintain the validity also for less diluted suspensions. This procedure is based on the following considerations: let’s suppose that the effective permittivity of a composite medium is known to be ε. Now, if a small additional volume of inclusions is embedded in the matrix, the change in the permittivity is approximated to be that which arise if an infinitesimal volume of inclusions were added to a uniform, homogeneous matrix with permittivity ε. This leads, in the simpler and most studied case, to some differential equations described in the following sections. The first papers concerning mixtures of ellipsoids were written by Fricke [6,7] dealing with the electrical characterization of inhomogeneous biological tissues containing spheroidal particles: he found out some explicit relationships that simply were an extension of the Maxwell formula to the case with ellipsoidal inclusions. In current literature Maxwell’s relation for spheres and Fricke’s expressions for ellipsoids are the so-called Maxwell-Garnett Effective Medium Theory results [8,9]: both theories hold

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on under the hypothesis of the very low concentration of the dispersed component. Once more, we observe that the classical approximation for spheres has been derived in different contexts by Maxwell [4], Maxwell-Garnett [10], Wagner [11] and Bottcher [12] as a generalized Clausius-Mossotti-Lorentz-Lorenz relation [2]. In recent literature some applications of the Bruggeman procedure to mixtures of ellipsoids have been shown in connection with the problem of characterizing the dielectric response of water-saturated rocks [13-15]. In these works the authors have shown that the Bruggeman method, applied to this specific problem, leads to results in good agreement with the empirical Archie’s law [16], which describes the dependence of the dc conductivity of brine-saturated sedimentary rocks on porosity. A complete discussion about the implementation of the differential schemes to dispersions of aligned or random oriented ellipsoids can be found in Ref. [17]. In general, the electrical (thermal, elastic and so on) properties of composite materials are strongly microstructure dependent. The relationships between microstructure and properties may be used for designing and improving materials, or conversely, for interpreting experimental data in terms of micro-structural features. Ideally, the aim is to construct a theory that employs general micro-structural information to make some accurate property predictions. A simpler goal is the provision of property for different class of microstructures. A great number of works has been devoted to describe the relationship between microstructure and properties: in [18] a functional unifying approach has been applied to better understand the intrinsic mathematical properties of a general mixing formula. A fundamental result is given by the Hashin-Shtrikman’s variational analysis [19,20], which provides an upper and lower bound for composite materials, irrespective of the microstructure. In particular, for a two-phase material, these bounds are given by two expressions of the Maxwell-Fricke type. Finally, a method to find the relation between the spatial correlation function of the dispersed component and the final properties of the material is derived from the Brown [21] and Torquato [22-24] expansions. Some other types of microstructures have been taken into consideration. For example, the problem of the mixture characterization has been exactly solved in the case of linear and nonlinear random mixtures, that is, materials for which the various components are isotropic, linear and mixed together as an ensemble of particles having random shapes and positions [25,26]. This approach permits to apply the mixture theories to dielectric poly-crystals and random networks [27-29]. One of the most important problems in homogenization theories is that of describing the interactions among the particles in order to consider arbitrary concentrated mixtures. To this aim, a multipole theory describing the interactions of dielectric cylinders in a uniform field has been developed for considering arbitrarily dense dispersions [30]. Such a multipole expansion has been applied to the dielectric characterization of composite materials formed by a regular array of parallel cylinders, obtaining the effective permittivity with a numerically efficient technique. A similar treatment, concerning multipole interactions of spheres, can be found in earlier literature [31,32]. Several works have been devoted to the quantitative evaluation of the local fluctuations of electric fields (or other observables) in the neighborhood of an inhomogeneity. Such fluctuations can easily extend over a spatial domain so large to result out-of-reach for numerical simulations. On the other hand, homogenization theories simply do not take these features into account. This situation is approached by means of the density of state (DOS)

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Stefano Giordano and Pier Luca Palla

concept [33-35]. The use of the DOS as a tool to characterize some relevant quantities has been made both in the electrical and in the mechanical systems, as well as for multi-cracked materials [36,37]. If we subdivide a region containing an inclusion in a large number of very small domains and we count the number of domains in which a given component E of the electric field has values in the interval (E, E+ΔE), then we can effectively define the stress density. This theoretical concept is a valuable tool to quantify the space distribution of any vector or tensor field. Two important aspects, which have not been taken into account thoroughly in the development of such theories, are the nonlinearity and the anisotropy of the phases of a heterogeneous structure. Therefore, in this work we outline some mathematical procedures able to take into account these specific physical effects. In particular, we describe some generalizations of the Maxwell-Garnett theory obtained by means of the differential scheme and by considering the nonlinear behavior of the materials forming the whole system. Moreover, we describe a complete and detailed approach useful to deal with anisotropic or graded particles embedded in anisotropic matrix. We have solved this problem by adopting a series of mathematical techniques widely used in elasticity theory and in micro- or nanomechanics. The structure of the paper is the following: in Section 2 we briefly review the MaxwellGarnett theory and we present some generalization based on the differential scheme (both for aligned and random oriented ellipsoids). In Section 3 we cope with the problem of homogenizing a dispersion of nonlinear particle embedded in a linear matrix. We obtain the mixing rule for the hypersusceptibility of the material. In Section 4 we describe a new methodology for analyzing anisotropic systems. The study of a single anisotropic particle in anisotropic environment allows us to define the so-called Eshelby tensors, very useful to summarize all the geometrical and physical properties of an arbitrary inhomogeneity. Then, we draw some comparisons between the results obtained with the anisotropic models and those obtained with the standard Maxwell-Garnett approach. Finally, in Section 5 we prove two theorems concerning the case of functionally graded ellipsoidal particles. It must be underlined that from a merely mathematical standpoint, the problem of calculating the mixture permittivity is identical to a number of others, for instance to that regarding permeability (in a magnetostatic situation), conductivity (in d.c. condition), thermal conductivity (in a steady-state thermal regime) and so on. Therefore, each theoretical formula predicts the effective value of any thermal, magnetic or electrical specific quantities.

2. Maxwell-Garnett Theory and Generalizations The Italian astronomer Ottaviano Fabrizio Mossotti (1791-1863) developed a model for interstellar dust by considering it as a gas of little dielectric particles; at the same time, the German physicist Rudolf Clausius (1822-1888) obtained similar results in terms of the refraction index [2]. These contributions led to the remarkable Clausius-Mossotti equation, which is the first result in the theory of heterogeneous material. Successively, the Danish mathematician Ludvig Lorenz (1829- 1891) published some works on the effective refractive index in mixtures and the Dutch physicist Hendrik Lorentz (1853-1928) deduced the same results from the electromagnetism Maxwell equations [2]. These four seminal investigations have given the name to the so-called Clausius-Mossotti-Lorentz-Lorenz relation. Finally, we

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observe that the classical approximation for spheres has been derived in different contexts by Maxwell [4], Maxwell-Garnett [10], Wagner [11] and Bottcher [12], as a generalized Clausius-Mossotti-Lorentz-Lorenz relation, which is the classical starting point of all these theories [2]. The first improving taking into account arbitrarily dense dispersions is given by the differential scheme or differential effective medium theory [5]. The corresponding result is called Bruggeman asymmetric formula or, equivalently, Bruggeman-Hanai formula [2]. It corresponds to our Eq. (2.8) or Eq. (2.20) with the depolarization factors equal to 1/3 (see below for details). In this section we review the application of the Maxwell-Garnett idea to a dispersion of aligned or random oriented ellipsoids. Moreover, we describe recent results obtained with the differential scheme applied to dispersions with arbitrary microstructure.

2.1. Characterization of Dispersions of Aligned Ellipsoids The theory for dispersion of aligned ellipsoids is based on the following result, which describes the behavior of a single ellipsoidal particle (ε2) embedded in a homogeneous medium (ε1). Let the axes of the ellipsoid be ax=a1, ay=a2 and az=a3 (aligned with axes x, y, z

G

(

)

of the reference frame) and let a uniform electrical field E0 = E0 x , E0 y , E0 z applied to the structure. Then, according to Stratton [38] or Landau [39] a uniform electrical field appears inside the ellipsoid and it can be computed as follows. We define the function

R (s ) =

(s + a ) (s + a ) (s +a ) 2

2

x

2

z

y

(2.1)

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and the depolarization factors along each axis

Lj =

ax a y az 2

+∞

ds

∫ (s + a ) R(s ) 2

0

(2.2)

j

We remark that Lx+Ly+Lz=1. Therefore, the electrical field inside the ellipsoid is given, in components, by [38,39]

Esj =

E0 j

ε −ε 1+ Lj 2 1 ε1

(2.3)

This is the main result that plays an essential role in the further development of the theory. Now, we are ready to consider a dispersion of aligned ellipsoids (ε2) embedded in a homogeneous medium (ε1), see Fig. 1. Moreover, let c be the volume fraction of the embedded ellipsoids. To begin, we consider a diluted dispersion (c 1 ⎪ 3 ⎢e ln +∞ e− p ⎪ e dξ ⎦ ⎪2 p ⎣ =⎨ ⎪ Lz = ∫ 3 / 2 2 2 0 (ξ + 1) ξ + e ⎪ 1 ⎡2q − eπ + 2earctg e ⎤ if e < 1 ⎪ ⎪ 2q 3 ⎢⎣ ⎪ q ⎥⎦ ⎩ ⎪ ⎪ 2 2 ⎩where p = e − 1 and q = 1 − e

(

(

581

)

(2.10)

)

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We may verify that 2Lx+Lz=1 for any value of e. For sake of completeness, we show the complete expressions for the depolarization factors in the case of generally shaped ellipsoids. The results have been expressed in terms of the elliptic integrals and have been derived under the assumptions 0