ELECTRONIC MATERIALS SCIENCE

ELECTRONIC MATERIALS SCIENCE

ELECTRONIC MATERIALS SCIENCE Eugene A. Irene University of North Carolina Chapel Hill, North Carolina A John Wiley & Sons, Inc., Publication

Copyright 2005 by John Wiley & Sons, Inc. All rights reserved. Published by John Wiley & Sons, Inc., Hoboken, New Jersey. Published simultaneously in Canada. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning, or otherwise, except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, 978-750-8400, fax 978-646-8600, or on the web at www.copyright.com. Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030, (201) 748-6011, fax (201) 748-6008. Limit of Liability/Disclaimer of Warranty: While the publisher and author have used their best efforts in preparing this book, they make no representations or warranties with respect to the accuracy or completeness of the contents of this book and specifically disclaim any implied warranties of merchantability or fitness for a particular purpose. No warranty may be created or extended by sales representatives or written sales materials. The advice and strategies contained herein may not be suitable for your situation. You should consult with a professional where appropriate. Neither the publisher nor author shall be liable for any loss of profit or any other commercial damages, including but not limited to special, incidental, consequential, or other damages. For general information on our other products and services please contact our Customer Care Department within the U.S. at 877-762-2974, outside the U.S. at 317-572-3993 or fax 317-572- 4002. Wiley also publishes its books in a variety of electronic formats. Some content that appears in print, however, may not be available in electronic format. Library of Congress Cataloging-in-Publication Data: Irene, Eugene A. Electronic materials science / Eugene A. Irene. p. cm. Includes bibliographical references and index. ISBN 0-471-69597-1 (cloth) 1. Electronics Materials. 2. Electronic apparatus and appliances Materials. I. Title. TK7871.I74 2005 621.381 dc22 2004016686 Printed in the United States of America. 10 9 8 7 6 5 4 3 2 1

CONTENTS Preface xi 1 Introduction to Electronic Materials Science 1 1.1 Introduction / 1 1.2 Structure and Diffraction / 3 1.3 Defects / 4 1.4 Diffusion / 5 1.5 Phase Equilibria / 5 1.6 Mechanical Properties / 6 1.7 Electronic Structure / 6 1.8 Electronic Properties and Devices / 7 1.9 Electronic Materials Science / 8 2 Structure of Solids 9 2.1 Introduction / 9 2.2 Order / 10 2.3 The Lattice / 12 2.4 Crystal Structure / 16 2.5 Notation / 17 2.5.1 Naming Planes / 17 2.5.2 Lattice Directions / 19 2.6 Lattice Geometry / 21 2.6.1 Planar Spacing Formulas / 21 2.6.2 Close Packing / 22 2.7 The Wigner-Seitz Cell / 24 v

vi CONTENTS 2.8 Crystal Structures / 25 2.8.1 Structures for Elements / 25 2.8.2 Structures for Compounds / 26 2.8.3 Solid Solutions / 28 Related Reading / 29 Exercises / 29 3 Diffraction 31 3.1 Introduction / 31 3.2 Phase Difference and Bragg s Law / 33 3.3 The Scattering Problem / 37 3.3.1 Coherent Scattering from an Electron / 38 3.3.2 Coherent Scattering from an Atom / 40 3.3.3 Coherent Scattering from a Unit Cell / 40 3.3.4 Structure Factor Calculations / 43 3.4 Reciprocal Space, RESP / 45 3.4.1 Why Reciprocal Space? / 45 3.4.2 Definition of RESP / 46 3.4.3 Definition of Reciprocal Lattice Vector / 48 3.4.4 The Ewald Construction / 50 3.5 Diffraction Techniques / 53 3.5.1 Rotating Crystal Method / 53 3.5.2 Powder Method / 53 3.5.3 Laue Method / 55 3.6 Wave Vector Representation / 55 Related Reading / 58 Exercises / 58 4 Defects in Solids 61 4.1 Introduction / 61 4.2 Why Do Defects Form? / 62 4.2.1 Review of Some Thermodynamics Ideas / 62 4.3 Point Defects / 66 4.4 The Statistics of Point Defects / 67 4.5 Line Defects Dislocations / 71 4.5.1 Edge Dislocations / 73 4.5.2 Screw Dislocations / 74 4.5.3 Burger s Vector and the Burger Circuit / 76 4.5.4 Dislocation Motion / 77

CONTENTS vii 4.6 Planar Defects / 77 4.6.1 Grain Boundaries / 77 4.6.2 Twin Boundaries / 78 4.7 Three-Dimensional Defects / 79 Related Reading / 79 Exercises / 80 5 Diffusion in Solids 81 5.1 Introduction to Diffusion Equations / 81 5.2 Atomistic Theory of Diffusion: Fick s Laws and a Theory for the Diffussion Construct D /83 5.3 Random Walk Problem / 87 5.3.1 Random Walk Calculations / 89 5.3.2 Relation of D to Random Walk / 89 5.3.3 Self-Diffusion Vacancy Mechanism in a FCC Crystal / 90 5.3.4 Activation Energy for Diffusion / 91 5.4 Other Mass Transport Mechanisms / 91 5.4.1 Permeability versus Diffusion / 91 5.4.2 Convection versus Diffusion / 94 5.5 Mathematics of Diffusion / 94 5.5.1 Steady State Diffusion Fick s First Law / 95 5.5.2 Non Steady State Diffusion Fick s Second Law / 97 Related Reading / 108 Exercises / 108 6 Phase Equilibria 111 6.1 Introduction / 111 6.2 The Gibbs Phase Rule / 111 6.2.1 Definitions / 111 6.2.2 Equilibrium Among Phases The Phase Rule / 113 6.2.3 Applications of the Phase Rule / 115 6.2.4 Construction of Phase Diagrams: Theory and Experiment / 116 6.2.5 The Tie Line Principle / 120 6.2.6 The Lever Rule / 121 6.2.7 Examples of Phase Equilibria / 125 6.3 Nucleation and Growth of Phases / 130 6.3.1 Thermodynamics of Phase Transformations / 130 6.3.2 Nucleation / 133 Related Reading / 137 Exercises / 138

viii CONTENTS 7 Mechanical Properties of Solids Elasticity 139 7.1 Introduction / 139 7.2 Elasticity Relationships / 141 7.2.1 True versus Engineering Strain / 143 7.2.2 Nature of Elasticity and Young s Modulus / 144 7.3 An Analysis of Stress by the Equation of Motion / 147 7.4 Hooke s Law for Pure Dilatation and Pure Shear / 150 7.5 Poisson s Ratio / 151 7.6 Relationships Among E, e, and v / 151 7.7 Relationships Among E, G, and n / 153 7.8 Resolving the Normal Forces / 156 Related Reading / 157 Exercises / 158 8 Mechanical Properties of Solids Plasticity 161 8.1 Introduction / 161 8.2 Plasticity Observations / 161 8.3 Role of Dislocations / 163 8.4 Deformation of Noncrystalline Materials / 175 8.4.1 Thermal Behavior of Amorphous Solids / 175 8.4.2 Time-Dependent Deformation of Amorphous Materials / 177 8.4.3 Models for Network Solids / 179 8.4.4 Elastomers / 183 Related Reading / 186 Exercises / 186 9 Electronic Structure of Solids 187 9.1 Introduction / 187 9.2 Waves, Electrons, and the Wave Function / 187 9.2.1 Representation of Waves / 187 9.2.2 Matter Waves / 189 9.2.3 Superposition / 190 9.2.4 Electron Waves / 195 9.3 Quantum Mechanics / 196 9.3.1 Normalization / 197 9.3.2 Dispersion of Electron Waves and the SE / 197 9.3.3 Classical and QM Wave Equations / 199 9.3.4 Solutions to the SE / 200

CONTENTS ix 9.4 Electron Energy Band Representations / 215 9.4.1 Parallel Band Picture / 215 9.4.2 k Space Representations / 216 9.4.3 Brillouin Zones / 219 9.5 Real Energy Band Structures / 221 9.6 Other Aspects of Electron Energy Band Structure / 224 Related Reading / 226 Exercises / 227 10 Electronic Properties of Materials 229 10.1 Introduction / 229 10.2 Occupation of Electronic States / 230 10.2.1 Density of States Function, DOS / 230 10.2.2 The Fermi-Dirac Distribution Function / 232 10.2.3 Occupancy of Electronic States / 235 10.3 Position of the Fermi Energy / 236 10.4 Electronic Properties of Metals: Conduction and Superconductivity / 240 10.4.1 Free Electron Theory for Electrical Conduction / 240 10.4.2 Quantum Theory of Electronic Conduction / 244 10.4.3 Superconductivity / 247 10.5 Semiconductors / 253 10.5.1 Intrinsic Semiconductors / 253 10.5.2 Extrinsic Semiconductors / 257 10.5.3 Semiconductor Measurements / 261 10.6 Electrical Behavior of Organic Materials / 264 Related Reading / 266 Exercises / 266 11 Junctions and Devices and the Nanoscale 269 11.1 Introduction / 269 11.2 Junctions / 270 11.2.1 Metal Metal Junctions / 270 11.2.2 Metal Semiconductor Junctions / 271 11.2.3 Semiconductor Semiconductor PN Junctions / 274 11.3 Selected Devices / 275 11.3.1 Passive Devices / 276 11.3.2 Active Devices / 279

x CONTENTS 11.4 Nanostructures and Nanodevices / 290 11.4.1 Heterojunction Nanostructures / 290 11.4.2 2-D and 3-D Nanostructures / 293 Related Reading / 294 Exercises / 295 Index 297

PREFACE Starting in the 1960s the field of materials science has undergone significant changes, from a field derived largely from well-established disciplines of metallurgy and ceramics to a field that includes microelectronics, polymers, biomaterials, and nanotechnology. The stringent materials requirements, such as extreme purity, perfect crystallinity and defectfree materials for the microelectronics revolution in the 1960s, were the prime movers. Major developments in other technologically significant fields, such as polymers, optics, high-strength materials that can withstand hostile environments for space and atmospheric flight, prosthetics and dental materials, and superconductivity, have along with microelectronics changed materials science from a primarily metallurgical field to a broad discipline that includes ever-growing numbers of classes of materials and subdisciplines. This book is a textbook that ambitiously endeavors to present the fundamentals of the modern broad field of materials science, electronics materials science, and to do so as a first course in materials science aimed at graduate students who have not had a previous introductory course in materials science. The book s contents derive from course notes that I have used in teaching this first course for more than 20 years at UNC. The initial challenge in teaching a one semester first course in this broad discipline of electronics materials science is the selection of topics that provide sufficient fundamentals to facilitate further advanced study, either formally with advanced courses or via self study during the course of performing advanced degree research. It is the main intent of this book to provide fundamental intellectual tools for electronic materials science that can be developed through further study and research. The book is specifically directed to materials scientists who will focus on electronics and optical materials science, although with an emphasis on fundamentals, the material selected has benefited polymer and biomaterials scientists as well, enabling a wide variety of materials science, chemistry, and physics students to pursue diverse fields and qualify for a variety of advanced courses. With such a broad intent virtually all of materials science would be relevant, since modern electronics materials include many diverse materials, morphologies, and structures. However, there was a self-limiting mechanism, namely it all had to fit into one semester. Consequently fundamentals are stressed and descriptive material is limited. The next challenge for the instructor is to consider the level of students. In materials science curricula typically found in engineering schools, a first course in materials science is usually required before the end of the second undergraduate year, so as to provide the basis for more specialized and advanced junior and senior level undergraduate courses in the various areas of materials science. Thus most introductory (first course) materials science texts are written for first or second year engineering students, and therefore assume meager mathematical experience, and only elementary chemistry and physics. In xi

xii PREFACE these texts principles are often introduced using formulas that are not derived, followed by descriptive material and examples to reinforce the ideas and provide practice with problem solving. There are numerous high-quality texts available at this level. Over the years I have used a number of them either as primary texts and/or as reference materials for the materials science courses that I teach at UNC. However, the level of the available introductory texts is too low for a first course in materials science offered to graduate students and to chemistry and physics undergraduates in their senior year. For the undergraduates at UNC where there is no materials science department, the first materials science course was part of an Applied Sciences Curriculum with Materials Science (electronic materials and polymers) as a track. For the chemistry and graduate students who will do graduate level research in materials science, there are only few advanced materials courses available at UNC. Thus the first materials science course offered to these students must not only be at a higher level, it must also more completely equip the students for advanced courses and independent study in their respective research interests. This text has been written from the notes that I have generated over the years of teaching this higher level, but introductory materials science course at UNC. The notes were used to supplement and raise the level of the available introductory texts. Chapters 1 through 11 are covered in their entirety in a single semester course at UNC. The result is a fast paced course with a dearth of descriptive material. In this course I assume that the students have had at least two semesters of calculus, general chemistry, elementary but calculus-based physics, and the equivalence of two semesters of physical chemistry, which includes thermodynamics and quantum mechanics. Most of the students taking the course have had significantly more preparation than assumed. With these assumptions I am able to move more quickly through the material. Also there is not the usual initial treatment of chemical bonding, since it is assumed that students have already had at least two chemistry courses that cover atomic and molecular structure and chemical bonding and chemical reactions. Derivations of important formulas usually omitted in a first materials course are included where it is felt that the derivation is instructive, and not simply a mathematical exercise. Nonetheless, this author believes that it is necessary to have the student reach a comfort level with some more physical and mathematical areas so that they can read original papers without trepidation. The early introduction of reciprocal space is considered essential to understand diffraction as a structural tool, and also electron band theory (as k space) and much of solid state physics. Reciprocal space is the natural coordinate space. The mathematical nature of diffusion is introduced to present the flavor of the field. Electron energy bands are treated from the Kronig-Penney model, and not simply assumed to exist from semantic arguments, as is done for typical second-year texts. The area of defects, phase equilibria, and mechanical properties are treated similarly to introductory materials science texts with the addition of some important derivations so that a students can glean an appreciation of the origin of the formulas as well as the methodology used in various fields of materials science. I am grateful to all my students, past and present, for all their help with this textbook. It was their questions and enduring curiosity that have often driven me to seek better, clearer explanations. Over the years my graduate students have made perceptive (and usually tactful) comments about my course pointing out both strong and weak areas. During the writing and editing of this book my Ph.D. graduate students (N. Suvorova, C. Lopez, R. Shrestha, and D. Yang) and post doctoral (Dr. Le Yan) have read and commented on the many drafts. I have tried to make the changes and corrections that they suggested, but I assume responsibility for the remaining unclear discussions and errors.

PREFACE xiii I am grateful to my colleagues at IBM (Thomas J. Watson Research Laboratory) where I spent my first professional 10 years in science, and where I was able to learn electronics materials science from leading scientists, and to the people at Wiley for having confidence in me through the publishing process. Finally, I am grateful to my family (my wife Mary Ann, and Michael and Christina) who endured my long hours of work over many years that led to this book, as well as all my other scientific endeavors.