Semiconductor Physics and Devices (4th Edition) PDF

 Semiconductor Physics and Devices Basic Principles Fourth Edition Donald A. Neamen University of New Mexico...

 Semiconductor Physics and Devices Basic Principles Fourth Edition Donald A. Neamen University of New Mexico TM nea29583_fm_i-xxiv.indd i 12/11/10 1:01 PM  TM SEMICONDUCTOR PHYSICS & DEVICES: BASIC PRINCIPLES, FOURTH EDITION Published by McGraw-Hill, a business unit of The McGraw-Hill Companies, Inc., 1221 Avenue of the Americas, New York, NY 10020. Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved. Previous editions © 2003, 1997 and 1992. No part of this publication may be reproduced or distributed in any form or by any means, or stored in a database or retrieval system, without the prior written consent of The McGraw-Hill Companies, Inc., including, but not limited to, in any network or other electronic storage or trans- mission, or broadcast for distance learning. Some ancillaries, including electronic and print components, may not be available to customers outside the United States. This book is printed on acid-free paper. 1 2 3 4 5 6 7 8 9 0 DOC/DOC 1 0 9 8 7 6 5 4 3 2 1 ISBN 978-0-07-352958-5 MHID 0-07-352958-3 Vice President & Editor-in-Chief: Marty Lange Vice President EDP/Central Publishing Services: Kimberly Meriwether David Publisher: Raghu Srinivasan Sponsoring Editor: Peter E. Massar Marketing Manager: Curt Reynolds Development Editor: Lora Neyens Project Manager: Melissa M. Leick Design Coordinator: Brenda A. Rolwes Cover Designer: Studio Montage, St. Louis, Missouri Cover Image: © Getty Images RF Buyer: Sherry L. Kane Media Project Manager: Balaji Sundararaman Compositor: MPS Limited, a Macmillan Company Typeface: 10/12 Times Roman Printer: RR Donnelley, Crawfordsville All credits appearing on page or at the end of the book are considered to be an extension of the copyright page. Library of Congress Cataloging-in-Publication Data Neamen, Donald A. Semiconductor physics and devices : basic principles / Donald A. Neamen. — 4th ed. p. cm. Includes index. ISBN 978-0-07-352958-5 (alk. paper) 1. Semiconductors. I. Title. QC611.N39 2011 537.6'22—dc22 2010045765 www.mhhe.com nea29583_fm_i-xxiv.indd ii 12/11/10 1:01 PM  ABOUT THE AUTHOR Donald A. Neamen is a professor emeritus in the Department of Electrical and Computer Engineering at the University of New Mexico where he taught for more than 25 years. He received his Ph.D. from the University of New Mexico and then became an electronics engineer at the Solid State Sciences Laboratory at Hanscom Air Force Base. In 1976, he joined the faculty in the ECE department at the University of New Mexico, where he specialized in teaching semiconductor physics and devices courses and electronic circuits courses. He is still a part-time instructor in the depart- ment. He also recently taught for a semester at the University of Michigan-Shanghai Jiao Tong University (UM-SJTU) Joint Institute in Shanghai, China. In 1980, Professor Neamen received the Outstanding Teacher Award for the University of New Mexico. In 1983 and 1985, he was recognized as Outstanding Teacher in the College of Engineering by Tau Beta Pi. In 1990, and each year from 1994 through 2001, he received the Faculty Recognition Award, presented by gradu- ating ECE students. He was also honored with the Teaching Excellence Award in the College of Engineering in 1994. In addition to his teaching, Professor Neamen served as Associate Chair of the ECE department for several years and has also worked in industry with Martin Marietta, Sandia National Laboratories, and Raytheon Company. He has published many papers and is the author of Microelectronics Circuit Analysis and Design, 4th edition, and An Introduction to Semiconductor Devices. nea29583_fm_i-xxiv.indd iii 12/11/10 1:01 PM  CONTENTS Preface x 2.2 Schrodinger’s Wave Equation 31 Prologue—Semiconductors and the Integrated 2.2.1 The Wave Equation 31 Circuit xvii 2.2.2 Physical Meaning of the Wave Function 32 2.2.3 Boundary Conditions 33 PART I—Semiconductor Material Properties 2.3 Applications of Schrodinger’s Wave CHAPTER 1 Equation 34 The Crystal Structure of Solids 1 2.3.1 Electron in Free Space 35 2.3.2 The Infinite Potential Well 36 1.0 Preview 1 2.3.3 The Step Potential Function 39 1.1 Semiconductor Materials 1 2.3.4 The Potential Barrier and Tunneling 44 1.2 Types of Solids 2 2.4 Extensions of the Wave Theory 1.3 Space Lattices 3 to Atoms 46 1.3.1 Primitive and Unit Cell 3 2.4.1 The One-Electron Atom 46 1.3.2 Basic Crystal Structures 4 2.4.2 The Periodic Table 50 1.3.3 Crystal Planes and Miller Indices 6 2.5 Summary 51 1.3.4 Directions in Crystals 9 Problems 52 1.4 The Diamond Structure 10 1.5 Atomic Bonding 12 CHAPTER 3 *1.6 Imperfections and Impurities in Solids 14 Introduction to the Quantum Theory 1.6.1 Imperfections in Solids 14 of Solids 58 1.6.2 Impurities in Solids 16 *1.7 Growth of Semiconductor Materials 17 3.0 Preview 58 1.7.1 Growth from a Melt 17 3.1 Allowed and Forbidden Energy Bands 59 1.7.2 Epitaxial Growth 19 3.1.1 Formation of Energy Bands 59 1.8 Summary 20 *3.1.2 The Kronig–Penney Model 63 Problems 21 3.1.3 The k-Space Diagram 67 3.2 Electrical Conduction in Solids 72 3.2.1 The Energy Band and the Bond Model 72 CHAPTER 2 3.2.2 Drift Current 74 Introduction to Quantum Mechanics 25 3.2.3 Electron Effective Mass 75 2.0 Preview 25 3.2.4 Concept of the Hole 78 2.1 Principles of Quantum Mechanics 26 3.2.5 Metals, Insulators, and Semiconductors 80 2.1.1 Energy Quanta 26 3.3 Extension to Three Dimensions 83 2.1.2 Wave–Particle Duality 27 3.3.1 The k-Space Diagrams of Si and GaAs 83 2.1.3 The Uncertainty Principle 30 3.3.2 Additional Effective Mass Concepts 85 iv nea29583_fm_i-xxiv.indd iv 12/11/10 1:01 PM  Contents v 3.4 Density of States Function 85 4.7 Summary 147 3.4.1 Mathematical Derivation 85 Problems 149 3.4.2 Extension to Semiconductors 88 3.5 Statistical Mechanics 91 CHAPTER 5 3.5.1 Statistical Laws 91 Carrier Transport Phenomena 156 3.5.2 The Fermi–Dirac Probability Function 91 3.5.3 The Distribution Function and the Fermi 5.0 Preview 156 Energy 93 5.1 Carrier Drift 157 3.6 Summary 98 5.1.1 Drift Current Density 157 Problems 100 5.1.2 Mobility Effects 159 5.1.3 Conductivity 164 CHAPTER 4 5.1.4 Velocity Saturation 169 The Semiconductor in Equilibrium 106 5.2 Carrier Diffusion 172 5.2.1 Diffusion Current Density 172 4.0 Preview 106 5.2.2 Total Current Density 175 4.1 Charge Carriers in Semiconductors 107 5.3 Graded Impurity Distribution 176 4.1.1 Equilibrium Distribution of Electrons and Holes 107 5.3.1 Induced Electric Field 176 4.1.2 The n0 and p0 Equations 109 5.3.2 The Einstein Relation 178 4.1.3 The Intrinsic Carrier Concentration 113 *5.4 The Hall Effect 180 4.1.4 The Intrinsic Fermi-Level Position 116 5.5 Summary 183 4.2 Dopant Atoms and Energy Levels 118 Problems 184 4.2.1 Qualitative Description 118 4.2.2 Ionization Energy 120 CHAPTER 6 4.2.3 Group III–V Semiconductors 122 Nonequilibrium Excess Carriers 4.3 The Extrinsic Semiconductor 123 in Semiconductors 192 4.3.1 Equilibrium Distribution of Electrons and Holes 123 6.0 Preview 192 4.3.2 The n0 p0 Product 127 6.1 Carrier Generation and Recombination 193 *4.3.3 The Fermi–Dirac Integral 128 6.1.1 The Semiconductor in Equilibrium 193 4.3.4 Degenerate and Nondegenerate 6.1.2 Excess Carrier Generation and Semiconductors 130 Recombination 194 4.4 Statistics of Donors and Acceptors 131 6.2 Characteristics of Excess Carriers 198 4.4.1 Probability Function 131 6.2.1 Continuity Equations 198 4.4.2 Complete Ionization and Freeze-Out 132 6.2.2 Time-Dependent Diffusion Equations 199 4.5 Charge Neutrality 135 6.3 Ambipolar Transport 201 4.5.1 Compensated Semiconductors 135 6.3.1 Derivation of the Ambipolar Transport 4.5.2 Equilibrium Electron and Hole Equation 201 Concentrations 136 6.3.2 Limits of Extrinsic Doping and Low 4.6 Position of Fermi Energy Level 141 Injection 203 4.6.1 Mathematical Derivation 142 6.3.3 Applications of the Ambipolar Transport 4.6.2 Variation of EF with Doping Concentration Equation 206 and Temperature 144 6.3.4 Dielectric Relaxation Time Constant 214 4.6.3 Relevance of the Fermi Energy 145 *6.3.5 Haynes–Shockley Experiment 216 nea29583_fm_i-xxiv.indd v 12/11/10 1:01 PM  vi Contents 6.4 Quasi-Fermi Energy Levels 219 8.1.4 Minority Carrier Distribution 283 *6.5 Excess Carrier Lifetime 221 8.1.5 Ideal pn Junction Current 286 6.5.1 Shockley–Read–Hall Theory of 8.1.6 Summary of Physics 290 Recombination 221 8.1.7 Temperature Effects 292 6.5.2 Limits of Extrinsic Doping and Low 8.1.8 The “Short” Diode 293 Injection 225 8.2 Generation–Recombination Currents and *6.6 Surface Effects 227 High-Injection Levels 295 6.6.1 Surface States 227 8.2.1 Generation–Recombination Currents 296 6.6.2 Surface Recombination Velocity 229 8.2.2 High-Level Injection 302 6.7 Summary 231 8.3 Small-Signal Model of the pn Junction 304 Problems 233 8.3.1 Diffusion Resistance 305 8.3.2 Small-Signal Admittance 306 PART II—Fundamental Semiconductor Devices 8.3.3 Equivalent Circuit 313 CHAPTER 7 *8.4 Charge Storage and Diode Transients 314 8.4.1 The Turn-off Transient 315 The pn Junction 241 8.4.2 The Turn-on Transient 317 7.0 Preview 241 *8.5 The Tunnel Diode 318 7.1 Basic Structure of the pn Junction 242 8.6 Summary 321 7.2 Zero Applied Bias 243 Problems 323 7.2.1 Built-in Potential Barrier 243 7.2.2 Electric Field 246 7.2.3 Space Charge Width 249 CHAPTER 9 Metal–Semiconductor and Semiconductor 7.3 Reverse Applied Bias 251 Heterojunctions 331 7.3.1 Space Charge Width and Electric Field 251 7.3.2 Junction Capacitance 254 9.0 Preview 331 7.3.3 One-Sided Junctions 256 9.1 The Schottky Barrier Diode 332 7.4 Junction Breakdown 258 9.1.1 Qualitative Characteristics 332 *7.5 Nonuniformly Doped Junctions 262 9.1.2 Ideal Junction Properties 334 7.5.1 Linearly Graded Junctions 263 9.1.3 Nonideal Effects on the Barrier Height 338 7.5.2 Hyperabrupt Junctions 265 9.1.4 Current–Voltage Relationship 342 7.6 Summary 267 9.1.5 Comparison of the Schottky Barrier Diode and the pn Junction Diode 345 Problems 269 9.2 Metal–Semiconductor Ohmic Contacts 349 9.2.1 Ideal Nonrectifying Barrier 349 CHAPTER 8 9.2.2 Tunneling Barrier 351 The pn Junction Diode 276 9.2.3 Specific Contact Resistance 352 8.0 Preview 276 9.3 Heterojunctions 354 8.1 pn Junction Current 277 9.3.1 Heterojunction Materials 354 8.1.1 Qualitative Description of Charge Flow 9.3.2 Energy-Band Diagrams 354 in a pn Junction 277 9.3.3 Two-Dimensional Electron Gas 356 8.1.2 Ideal Current–Voltage Relationship 278 *9.3.4 Equilibrium Electrostatics 358 8.1.3 Boundary Conditions 279 *9.3.5 Current–Voltage Characteristics 363 nea29583_fm_i-xxiv.indd vi 12/11/10 1:01 PM  Contents vii 9.4 Summary 363 11.1.2 Channel Length Modulation 446 Problems 365 11.1.3 Mobility Variation 450 11.1.4 Velocity Saturation 452 CHAPTER 10 11.1.5 Ballistic Transport 453 Fundamentals of the Metal–Oxide– 11.2 MOSFET Scaling 455 Semiconductor Field-Effect Transistor 371 11.2.1 Constant-Field Scaling 455 11.2.2 Threshold Voltage—First 10.0 Preview 371 Approximation 456 10.1 The Two-Terminal MOS Structure 372 11.2.3 Generalized Scaling 457 10.1.1 Energy-Band Diagrams 372 11.3 Threshold Voltage Modifications 457 10.1.2 Depletion Layer Thickness 376 11.3.1 Short-Channel Effects 457 10.1.3 Surface Charge Density 380 11.3.2 Narrow-Channel Effects 461 10.1.4 Work Function Differences 382 11.4 Additional Electrical Characteristics 464 10.1.5 Flat-Band Voltage 385 11.4.1 Breakdown Voltage 464 10.1.6 Threshold Voltage 388 *11.4.2 The Lightly Doped Drain Transistor 470 10.2 Capacitance–Voltage Characteristics 394 11.4.3 Threshold Adjustment by Ion 10.2.1 Ideal C–V Characteristics 394 Implantation 472 10.2.2 Frequency Effects 399 *11.5 Radiation and Hot-Electron Effects 475 10.2.3 Fixed Oxide and Interface Charge 11.5.1 Radiation-Induced Oxide Charge 475 Effects 400 11.5.2 Radiation-Induced Interface States 478 10.3 The Basic MOSFET Operation 403 11.5.3 Hot-Electron Charging Effects 480 10.3.1 MOSFET Structures 403 11.6 Summary 481 10.3.2 Current–Voltage Problems 483 Relationship—Concepts 404 *10.3.3 Current–Voltage Relationship— Mathematical Derivation 410 CHAPTER 12 10.3.4 Transconductance 418 The Bipolar Transistor 491 10.3.5 Substrate Bias Effects 419 12.0 Preview 491 10.4 Frequency Limitations 422 12.1 The Bipolar Transistor Action 492 10.4.1 Small-Signal Equivalent Circuit 422 12.1.1 The Basic Principle of Operation 493 10.4.2 Frequency Limitation Factors and 12.1.2 Simplified Transistor Current Relation— Cutoff Frequency 425 Qualitative Discussion 495 *10.5 The CMOS Technology 427 12.1.3 The Modes of Operation 498 10.6 Summary 430 12.1.4 Amplification with Bipolar Transistors 500 Problems 433 12.2 Minority Carrier Distribution 501 12.2.1 Forward-Active Mode 502 CHAPTER 11 12.2.2 Other Modes of Operation 508 Metal–Oxide–Semiconductor Field-Effect 12.3 Transistor Currents and Low-Frequency Transistor: Additional Concepts 443 Common-Base Current Gain 509 12.3.1 Current Gain—Contributing Factors 509 11.0 Preview 443 12.3.2 Derivation of Transistor Current 11.1 Nonideal Effects 444 Components and Current Gain 11.1.1 Subthreshold Conduction 444 Factors 512 nea29583_fm_i-xxiv.indd vii 12/11/10 1:01 PM  viii Contents 12.3.3 Summary 517 *13.3 Nonideal Effects 593 12.3.4 Example Calculations of the Gain 13.3.1 Channel Length Modulation 594 Factors 517 13.3.2 Velocity Saturation Effects 596 12.4 Nonideal Effects 522 13.3.3 Subthreshold and Gate Current 12.4.1 Base Width Modulation 522 Effects 596 12.4.2 High Injection 524 *13.4 Equivalent Circuit and Frequency 12.4.3 Emitter Bandgap Narrowing 526 Limitations 598 12.4.4 Current Crowding 528 13.4.1 Small-Signal Equivalent Circuit 598 *12.4.5 Nonuniform Base Doping 530 13.4.2 Frequency Limitation Factors and Cutoff 12.4.6 Breakdown Voltage 531 Frequency 600 12.5 Equivalent Circuit Models 536 *13.5 High Electron Mobility Transistor 602 *12.5.1 Ebers–Moll Model 537 13.5.1 Quantum Well Structures 603 12.5.2 Gummel–Poon Model 540 13.5.2 Transistor Performance 604 12.5.3 Hybrid-Pi Model 541 13.6 Summary 609 12.6 Frequency Limitations 545 Problems 611 12.6.1 Time-Delay Factors 545 12.6.2 Transistor Cutoff Frequency 546 PART III—Specialized Semiconductor Devices 12.7 Large-Signal Switching 549 CHAPTER 14 12.7.1 Switching Characteristics 549 Optical Devices 618 12.7.2 The Schottky-Clamped Transistor 551 *12.8 Other Bipolar Transistor Structures 552 14.0 Preview 618 12.8.1 Polysilicon Emitter BJT 552 14.1 Optical Absorption 619 12.8.2 Silicon–Germanium Base Transistor 554 14.1.1 Photon Absorption Coefficient 619 12.8.3 Heterojunction Bipolar Transistors 556 14.1.2 Electron–Hole Pair Generation Rate 622 12.9 Summary 558 14.2 Solar Cells 624 Problems 560 14.2.1 The pn Junction Solar Cell 624 14.2.2 Conversion Efficiency and Solar Concentration 627 CHAPTER 13 14.2.3 Nonuniform Absorption Effects 628 The Junction Field-Effect Transistor 571 14.2.4 The Heterojunction Solar Cell 629 13.0 Preview 571 14.2.5 Amorphous Silicon Solar Cells 630 13.1 JFET Concepts 572 14.3 Photodetectors 633 13.1.1 Basic pn JFET Operation 572 14.3.1 Photoconductor 633 13.1.2 Basic MESFET Operation 576 14.3.2 Photodiode 635 13.2 The Device Characteristics 578 14.3.3 PIN Photodiode 640 13.2.1 Internal Pinchoff Voltage, Pinchoff 14.3.4 Avalanche Photodiode 641 Voltage, and Drain-to-Source Saturation 14.3.5 Phototransistor 642 Voltage 578 14.4 Photoluminescence and 13.2.2 Ideal DC Current–Voltage Relationship— Electroluminescence 643 Depletion Mode JFET 582 14.4.1 Basic Transitions 644 13.2.3 Transconductance 587 14.4.2 Luminescent Efficiency 645 13.2.4 The MESFET 588 14.4.3 Materials 646 nea29583_fm_i-xxiv.indd viii 12/13/10 6:09 PM  Contents ix 14.5 Light Emitting Diodes 648 15.6.3 SCR Turn-Off 697 14.5.1 Generation of Light 648 15.6.4 Device Structures 697 14.5.2 Internal Quantum Efficiency 649 15.7 Summary 701 14.5.3 External Quantum Efficiency 650 Problems 703 14.5.4 LED Devices 652 14.6 Laser Diodes 654 APPENDIX A 14.6.1 Stimulated Emission and Population Selected List of Symbols 707 Inversion 655 14.6.2 Optical Cavity 657 14.6.3 Threshold Current 658 APPENDIX B 14.6.4 Device Structures and System of Units, Conversion Factors, and Characteristics 660 General Constants 715 14.7 Summary 661 Problems 664 APPENDIX C The Periodic Table 719 CHAPTER 15 Semiconductor Microwave and Power APPENDIX D Devices 670 Unit of Energy—The Electron Volt 720 15.0 Preview 670 15.1 Tunnel Diode 671 APPENDIX E 15.2 Gunn Diode 672 “Derivation” of Schrodinger’s Wave 15.3 Impatt Diode 675 Equation 722 15.4 Power Bipolar Transistors 677 15.4.1 Vertical Power Transistor APPENDIX F Structure 677 Effective Mass Concepts 724 15.4.2 Power Transistor Characteristics 678 15.4.3 Darlington Pair Configuration 682 APPENDIX G 15.5 Power MOSFETs 684 The Error Function 729 15.5.1 Power Transistor Structures 684 15.5.2 Power MOSFET Characteristics 685 15.5.3 Parasitic BJT 689 APPENDIX H 15.6 The Thyristor 691 Answers to Selected Problems 730 15.6.1 The Basic Characteristics 691 15.6.2 Triggering the SCR 694 Index 738 nea29583_fm_i-xxiv.indd ix 12/11/10 1:01 PM  PREFACE PHILOSOPHY AND GOALS The purpose of the fourth edition of this book is to provide a basis for understanding the characteristics, operation, and limitations of semiconductor devices. In order to gain this understanding, it is essential to have a thorough knowledge of the physics of the semiconductor material. The goal of this book is to bring together quantum mechanics, the quantum theory of solids, semiconductor material physics, and semi- conductor device physics. All of these components are vital to the understanding of both the operation of present-day devices and any future development in the field. The amount of physics presented in this text is greater than what is covered in many introductory semiconductor device books. Although this coverage is more extensive, the author has found that once the basic introductory and material physics have been thoroughly covered, the physics of the semiconductor device follows quite naturally and can be covered fairly quickly and efficiently. The emphasis on the underlying physics will also be a benefit in understanding and perhaps in developing new semiconductor devices. Since the objective of this text is to provide an introduction to the theory of semiconductor devices, there is a great deal of advanced theory that is not consid- ered. In addition, fabrication processes are not described in detail. There are a few references and general discussions about processing techniques such as diffusion and ion implantation, but only where the results of this processing have direct im- pact on device characteristics. PREREQUISITES This text is intended for junior and senior undergraduates majoring in electrical en- gineering. The prerequisites for understanding the material are college mathematics, up to and including differential equations, basic college physics, and an introduction to electromagnetics. An introduction to modern physics would be helpful, but is not required. Also, a prior completion of an introductory course in electronic circuits is helpful, but not essential. ORGANIZATION The text is divided into three parts—Part I covers the introductory quantum physics and then moves on to the semiconductor material physics; Part II presents the physics of the fundamental semiconductor devices; and Part III deals with specialized semi- conductor devices including optical, microwave, and power devices. Part I consists of Chapters 1 through 6. Chapter 1 presents an introduction to the crystal structure of solids leading to the ideal single-crystal semiconductor material. x nea29583_fm_i-xxiv.indd x 12/11/10 1:01 PM  Preface xi Chapters 2 and 3 introduce quantum mechanics and the quantum theory of solids, which together provide the necessary basic physics. Chapters 4 through 6 cover the semiconductor material physics. Chapter 4 considers the physics of the semiconduc- tor in thermal equilibrium, Chapter 5 treats the transport phenomena of the charge carriers in a semiconductor, and the nonequilibrium excess carrier characteristics are developed in Chapter 6. Understanding the behavior of excess carriers in a semicon- ductor is vital to the goal of understanding the device physics. Part II consists of Chapters 7 through 13. Chapter 7 treats the electrostatics of the basic pn junction and Chapter 8 covers the current–voltage, including the dc and small-signal, characteristics of the pn junction diode. Metal–semiconductor junctions, both rectifying and ohmic, and semiconductor heterojunctions are con- sidered in Chapter 9. The basic physics of the metal–oxide–semiconductor field- effect transistor (MOSFET) is developed in Chapters 10 with additional concepts presented in Chapter 11. Chapter 12 develops the theory of the bipolar transistor and Chapter 13 covers the junction field-effect transistor (JFET). Once the physics of the pn junction is developed, the chapters dealing with the three basic transistors may be covered in any order—these chapters are written so as not to depend on one another. Part III consists of Chapters 14 and 15. Chapter 14 considers optical devices, such as the solar cell and light emitting diode. Finally, semiconductor microwave devices and semiconductor power devices are presented in Chapter 15. Eight appendices are included at the end of the book. Appendix A contains a selected list of symbols. Notation may sometimes become confusing, so this appendix may aid in keeping track of all the symbols. Appendix B contains the system of units, conversion factors, and general constants used throughout the text. Appendix H lists answers to selected problems. Most students will find this appen- dix helpful. USE OF THE BOOK The text is intended for a one-semester course at the junior or senior level. As with most textbooks, there is more material than can be conveniently covered in one semester; this allows each instructor some flexibility in designing the course to his or her own specific needs. Two possible orders of presentation are discussed later in a separate section in this preface. However, the text is not an encyclopedia. Sections in each chapter that can be skipped without loss of continuity are identified by an as- terisk in both the table of contents and in the chapter itself. These sections, although important to the development of semiconductor device physics, can be postponed to a later time. The material in the text has been used extensively in a course that is required for junior-level electrical engineering students at the University of New Mexico. Slightly less than half of the semester is devoted to the first six chapters; the remain- der of the semester is devoted to the pn junction, the metal–oxide–semiconductor field-effect transistor, and the bipolar transistor. A few other special topics may be briefly considered near the end of the semester. nea29583_fm_i-xxiv.indd xi 12/11/10 1:01 PM  xii Preface As mentioned, although the MOS transistor is discussed prior to the bipolar transistor or junction field-effect transistor, each chapter dealing with the basic types of transistors is written to stand alone. Any one of the transistor types may be cov- ered first. NOTES TO THE READER This book introduces the physics of semiconductor materials and devices. Although many electrical engineering students are more comfortable building electronic cir- cuits or writing computer programs than studying the underlying principles of semi- conductor devices, the material presented here is vital to an understanding of the limitations of electronic devices, such as the microprocessor. Mathematics is used extensively throughout the book. This may at times seem tedious, but the end result is an understanding that will not otherwise occur. Al- though some of the mathematical models used to describe physical processes may seem abstract, they have withstood the test of time in their ability to describe and predict these physical processes. The reader is encouraged to continually refer to the preview sections at the be- ginning of each chapter so that the objective of the chapter and the purpose of each topic can be kept in mind. This constant review is especially important in the first six chapters, dealing with the basic physics. The reader must keep in mind that, although some sections may be skipped without loss of continuity, many instructors will choose to cover these topics. The fact that sec- tions are marked with an asterisk does not minimize the importance of these subjects. It is also important that the reader keep in mind that there may be questions still unanswered at the end of a course. Although the author dislikes the phrase, “it can be shown that... ,” there are some concepts used here that rely on derivations beyond the scope of the text. This book is intended as an introduction to the subject. Those questions remaining unanswered at the end of the course, the reader is encouraged to keep “in a desk drawer.” Then, during the next course in this area of concentration, the reader can take out these questions and search for the answers. ORDER OF PRESENTATION Each instructor has a personal preference for the order in which the course material is presented. Listed below are two possible scenarios. The first case, called the MOSFET approach, covers the MOS transistor before the bipolar transistor. It may be noted that the MOSFET in Chapters 10 and 11 may be covered before the pn junction diode. The second method of presentation listed, called the bipolar approach, is the classical approach. Covering the bipolar transistor immediately after discussing the pn junction diode is the traditional order of presentation. However, because the MOSFET is left until the end of the semester, time constraints may shortchange the amount of class time devoted to this important topic. Unfortunately, because of time constraints, every topic in each chapter cannot be covered in a one-semester course. The remaining topics must be left for a second- semester course or for further study by the reader. nea29583_fm_i-xxiv.indd xii 12/11/10 1:01 PM  Preface xiii MOSFET approach Chapter 1 Crystal structure Chapters 2, 3 Selected topics from quantum mechanics and theory of solids Chapter 4 Semiconductor physics Chapter 5 Transport phenomena Chapter 6 Selected topics from nonequilibrium characteristics Chapter 7 The pn junction Chapters 10, 11 The MOS transistor Chapter 8 The pn junction diode Chapter 9 A brief discussion of the Schottky diode Chapter 12 The bipolar transistor Other selected topics Bipolar approach Chapter 1 Crystal structure Chapters 2, 3 Selected topics from quantum mechanics and theory of solids Chapter 4 Semiconductor physics Chapter 5 Transport phenomena Chapter 6 Selected topics from nonequilibrium characteristics Chapters 7, 8 The pn junction and pn junction diode Chapter 9 A brief discussion of the Schottky diode Chapter 12 The bipolar transistor Chapters 10, 11 The MOS transistor Other selected topics NEW TO THE FOURTH EDITION Order of Presentation: The two chapters dealing with MOSFETs were moved ahead of the chapter on bipolar transistors. This change emphasizes the importance of the MOS transistor. Semiconductor Microwave Devices: A short section was added in Chapter 15 covering three specialized semiconductor microwave devices. New Appendix: A new Appendix F has been added dealing with effective mass concepts. Two effective masses are used in various calculations in the text. This appendix develops the theory behind each effective mass and dis- cusses when to use each effective mass in a particular calculation. Preview Sections: Each chapter begins with a brief introduction, which then leads to a preview section given in bullet form. Each preview item presents a particular objective for the chapter. Exercise Problems: Over 100 new Exercise Problems have been added. An Exercise Problem now follows each example. The exercise is very similar to the worked example so that readers can immediately test their understanding of the material just covered. Answers are given to each exercise problem. nea29583_fm_i-xxiv.indd xiii 12/11/10 1:01 PM  xiv Preface Test Your Understanding: Approximately 40 percent new Test Your Under- standing problems are included at the end of many of the major sections of the chapter. These exercise problems are, in general, more comprehensive than those presented at the end of each example. These problems will also reinforce readers’ grasp of the material before they move on to the next section. End-of-Chapter Problems: There are 330 new end-of-chapter problems, which means that approximately 48 percent of the problems are new to this edition. RETAINED FEATURES OF THE TEXT Mathematical Rigor: The mathematical rigor necessary to more clearly under- stand the basic semiconductor material and device physics has been maintained. Examples: An extensive number of worked examples are used throughout the text to reinforce the theoretical concepts being developed. These examples contain all the details of the analysis or design, so the reader does not have to fill in missing steps. Summary section: A summary section, in bullet form, follows the text of each chapter. This section summarizes the overall results derived in the chapter and reviews the basic concepts developed. Glossary of important terms: A glossary of important terms follows the Sum- mary section of each chapter. This section defines and summarizes the most important terms discussed in the chapter. Checkpoint: A checkpoint section follows the Glossary section. This section states the goals that should have been met and the abilities the reader should have gained. The Checkpoints will help assess progress before moving on to the next chapter. Review questions: A list of review questions is included at the end of each chapter. These questions serve as a self-test to help the reader determine how well the concepts developed in the chapter have been mastered. End-of-chapter problems: A large number of problems are given at the end of each chapter, organized according to the subject of each section in the chapter. Summary and Review Problems: A few problems, in a Summary and Review section, are open-ended design problems and are given at the end of most chapters. Reading list: A reading list finishes up each chapter. The references, which are at an advanced level compared with that of this text, are indicated by an asterisk. Answers to selected problems: Answers to selected problems are given in the last appendix. Knowing the answer to a problem is an aid and a reinforcement in problem solving. nea29583_fm_i-xxiv.indd xiv 12/11/10 1:01 PM  Preface xv ONLINE RESOURCES A website to accompany this text is available at www.mhhe.com/neamen. The site includes the solutions manual as well as an image library for instructors. Instructors can also obtain access to C.O.S.M.O.S. for the fourth edition. C.O.S.M.O.S. is a Complete Online Solutions Manual Organization System instructors can use to create exams and assignments, create custom content, and edit supplied problems and solutions. ACKNOWLEDGMENTS I am indebted to the many students I have had over the years who have helped in the evolution of this fourth edition as well as to the previous editions of this text. I am grateful for their enthusiasm and constructive criticism. I want to thank the many people at McGraw-Hill for their tremendous support. To Peter Massar, sponsoring editor, and Lora Neyens, development editor, I am grate- ful for their encouragement, support, and attention to the many details of this project. I also appreciate the efforts of project managers who guided this work through its final phase toward publication. This effort included gently, but firmly, pushing me through proofreading. Let me express my continued appreciation to those reviewers who read the manuscripts of the first three editions in its various forms and gave constructive criti- cism. I also appreciate the efforts of accuracy checkers who worked through the new problem solutions in order to minimize any errors I may have introduced. Finally, my thanks go out to those individuals who have reviewed the book prior to this new edition being published. Their contributions and suggestions for continued improve- ment are very valuable. REVIEWERS FOR THE FOURTH EDITION The following reviewers deserve thanks for their constructive criticism and sugges- tions for the fourth edition of this book. Sandra Selmic, Louisiana Tech University Terence Brown, Michigan State University Timothy Wilson, Oklahoma State University Lili He, San Jose State University Jiun Liou, University of Central Florida Michael Stroscio, University of Illinois-Chicago Andrei Sazonov, University of Waterloo nea29583_fm_i-xxiv.indd xv 12/11/10 1:01 PM  xvi Preface McGRAW-HILL CREATE™ Craft your teaching resources to match the way you teach! With McGraw-Hill Create™, www.mcgrawhillcreate.com, you can easily rearrange chapters, combine material from other content sources, and quickly upload content you have written like your course syllabus or teaching notes. Find the content you need in Create by searching through thousands of leading McGraw-Hill textbooks. Arrange your book to fit your teaching style. Create even allows you to personalize your book’s appearance by selecting the cover and adding your name, school, and course infor- mation. 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To talk about the e-book options, con- tact your McGraw-Hill sales rep or visit the site www.coursesmart.com to learn more. nea29583_fm_i-xxiv.indd xvi 12/11/10 1:01 PM  P R O L O G U E Semiconductors and the Integrated Circuit PREVIEW W e often hear that we are living in the information age. Large amounts of information can be obtained via the Internet, for example, and can be obtained very quickly over long distances via satellite communications systems. The information technologies are based upon digital and analog electronic systems, with the transistor and integrated circuit (IC) being the foundation of these re- markable capabilities. Wireless communication systems, including printers, faxes, lap- top computers, ipods, and of course the cell phones are big users of today’s IC products. The cell phone is not just a telephone any longer, but includes e-mail services and video cameras, for example. Today, a relatively small laptop computer has more computing capability than the equipment used to send a man to the moon a few decades ago. The semiconductor electronics field continues to be a fast-changing one, with thousands of technical papers published and many new electronic devices developed each year. HISTORY The semiconductor device has a fairly long history, although the greatest explo- sion of IC technology has occured during the last two or three decades.1 The metal– semiconductor contact dates back to the early work of Braun in 1874, who discovered the asymmetric nature of electrical conduction between metal contacts and semicon- ductors, such as copper, iron, and lead sulfide. These devices were used as detectors in early experiments on radio. In 1906, Pickard took out a patent for a point contact 1 This brief introduction is intended to give a flavor of the history of the semiconductor device and integrated circuit. Thousands of engineers and scientists have made significant contributions to the development of semiconductor electronics—the few events and names mentioned here are not meant to imply that these are the only significant events or people involved in the semiconductor history. xvii nea29583_pro_xvii-xxiv.indd xvii 12/11/10 1:18 PM  xviii Prolouge Compliments of Texas Instruments Incorporated nea29583_pro_xvii-xxiv.indd xviii 12/11/10 1:18 PM  Prolouge xix detector using silicon and, in 1907, Pierce published rectification characteristics of diodes made by sputtering metals onto a variety of semiconductors. By 1935, selenium rectifiers and silicon point contact diodes were available for use as radio detectors. A significant advance in our understanding of the metal– semiconductor contact was aided by developments in semiconductor physics. In 1942, Bethe developed the thermionic-emission theory, according to which the cur- rent is determined by the process of emission of electrons into the metal rather than by drift or diffusion. With the development of radar, the need for better and more reliable detector diodes and mixers increased. Methods of achieving high-purity sili- con and germanium were developed during this time and germanium diodes became a key component in radar systems during the Second World War. Another big breakthrough came in December 1947 when the first transistor was constructed and tested at Bell Telephone Laboratories by William Shockley, John Bardeen, and Walter Brattain. This first transistor was a point contact device and used polycrystalline germanium. The transistor effect was soon demonstrated in silicon as well. A significant improvement occurred at the end of 1949 when single-crystal material was used rather than the polycrystalline material. The single crystal yields uniform and improved properties throughout the whole semiconductor material. The next significant step in the development of the transistor was the use of the diffusion process to form the necessary junctions. This process allowed better control of the transistor characteristics and yielded higher-frequency devices. The diffused mesa transistor was commercially available in germanium in 1957 and in silicon in 1958. The diffusion process also allowed many transistors to be fabricated on a single silicon slice, so the cost of these devices decreased. THE INTEGRATED CIRCUIT (IC) The transistor led to a revolution in electronics since it is smaller and more reliable than vacuum tubes used previously. The circuits at that time were discrete in that each element had to be individually connected by wires to form the circuit. The in- tegrated circuit has led to a new revolution in electronics that was not possible with discrete devices. Integration means that complex circuits, consisting of millions of devices, can be fabricated on a single chip of semiconductor material. The first IC was fabricated in February of 1959 by Jack Kilby of Texas Instru- ments. In July 1959, a planar version of the IC was independently developed by Robert Noyce of Fairchild. The first integrated circuits incorporated bipolar transis- tors. Practical MOS transistors were then developed in the mid-1960s and 1970s. The MOS technologies, especially CMOS, have become a major focus for IC design and development. Silicon is the main semiconductor material, while gallium arse- nide and other compound semiconductor materials are used for optical devices and for special applications requiring very high frequency devices. Since the first IC, very sophisticated and complex circuits have been designed and fabricated. A single silicon chip may be on the order of 1 square centimeter and some ICs may have more than a hundred terminals. An IC can contain the arithmetic, logic, and memory functions on a single chip—the primary example of this type of IC nea29583_pro_xvii-xxiv.indd xix 12/11/10 1:18 PM  xx Prolouge is the microprocessor. Integration means that circuits can be miniaturized for use in satellites and laptop computers where size, weight, and power are critical parameters. An important advantage of ICs is the result of devices being fabricated very close to each other. The time delay of signals between devices is short so that high- frequency and high-speed circuits are now possible with ICs that were not practical with discrete circuits. In high-speed computers, for example, the logic and memory circuits can be placed very close to each other to minimize time delays. In addition, parasitic capacitance and inductance between devices are reduced which also pro- vides improvement in the speed of the system. Intense research on silicon processing and increased automation in design and manufacturing have led to lower costs, higher fabrication yields, and greater reliabil- ity of integrated circuits. FABRICATION The integrated circuit is a direct result of the development of various processing tech- niques needed to fabricate the transistor and interconnect lines on the single chip. The total collection of these processes for making an IC is called a technology. The following few paragraphs provide an introduction to a few of these processes. This introduction is intended to provide the reader with some of the basic terminology used in processing. Thermal Oxidation A major reason for the success of silicon ICs is the fact that an excellent native oxide, SiO2, can be formed on the surface of silicon. This oxide is used as a gate insulator in the MOSFET and is also used as an insulator, known as the field oxide, between devices. Metal interconnect lines that connect various devices can be placed on top of the field oxide. Most other semiconductors do not form native oxides that are of sufficient quality to be used in device fabrication. Silicon will oxidize at room temperature in air forming a thin native oxide of ap- proximately 25 Å thick. However, most oxidations are done at elevated temperatures since the basic process requires that oxygen diffuse through the existing oxide to the silicon surface where a reaction can occur. A schematic of the oxidation process is shown in Figure 0.1. Oxygen diffuses across a stagnant gas layer directly adjacent SiO2 Silicon Gas Diffusion of O2 Stagnant gas layer Diffusion of O2 through existing oxide to silicon surface Figure 0.1 | Schematic of the oxidation process. nea29583_pro_xvii-xxiv.indd xx 12/11/10 1:18 PM  Prolouge xxi UV source Photomask Glass UV-absorbing material Photoresist Silicon Figure 0.2 | Schematic showing the use of a photomask. to the oxide surface and then diffuses through the existing oxide layer to the silicon surface where the reaction between O2 and Si forms SiO2. Because of this reaction, silicon is actually consumed from the surface of the silicon. The amount of silicon consumed is approximately 44 percent of the thickness of the final oxide. Photomasks and Photolithography The actual circuitry on each chip is created through the use of photomasks and photolithography. The photomask is a physical representation of a device or a portion of a device. Opaque regions on the mask are made of an ultraviolet-light-absorbing material. A photosensitive layer, called pho- toresist, is first spread over the surface of the semiconductor. The photoresist is an organic polymer that undergoes chemical change when exposed to ultraviolet light. The photoresist is exposed to ultraviolet light through the photomask as indicated in Figure 0.2. The photoresist is then developed in a chemical solution. The developer is used to remove the unwanted portions of the photoresist and generate the appropri- ate patterns on the silicon. The photomasks and photolithography process is critical in that it determines how small the devices can be made. Instead of using ultraviolet light, electrons and x-rays can also be used to expose the photoresist. Etching After the photoresist pattern is formed, the remaining photoresist can be used as a mask, so that the material not covered by the photoresist can be etched. Plasma etching is now the standard process used in IC fabrication. Typically, an etch gas such as chlorofluorocarbons is injected into a low-pressure chamber. A plasma is created by applying a radio-frequency voltage between cathode and anode terminals. The silicon wafer is placed on the cathode. Positively charged ions in the plasma are accelerated to- ward the cathode and bombard the wafer normal to the surface. The actual chemical and physical reaction at the surface is complex, but the net result is that silicon can be etched anisotropically in very selected regions of the wafer. If photoresist is applied on the surface of silicon dioxide, then the silicon dioxide can also be etched in a similar way. Diffusion A thermal process that is used extensively in IC fabrication is diffusion. Diffusion is the process by which specific types of “impurity” atoms can be intro- duced into the silicon material. This doping process changes the conductivity type of the silicon so that pn junctions can be formed. (The pn junction is a basic build- ing block of semiconductor devices.) Silicon wafers are oxidized to form a layer of nea29583_pro_xvii-xxiv.indd xxi 12/11/10 1:18 PM  xxii Prolouge silicon dioxide, and windows are opened in the oxide in selected areas using photo- lithography and etching as just described. The wafers are then placed in a high-temperature furnace (about 1100⬚C) and dopant atoms such as boron or phosphorus are introduced. The dopant atoms gradually diffuse or move into the silicon due to a density gradient. Since the diffusion process requires a gradient in the concentration of atoms, the final concentration of diffused atoms is nonlinear, as shown in Figure 0.3. When the wafer is removed from the furnace and the wafer temperature returns to room temperature, the diffusion coefficient of the dopant atoms is essentially zero so that the dopant atoms are then fixed in the silicon material. Ion Implantation A fabrication process that is an alternative to high-temperature diffusion is ion implantation. A beam of dopant ions is accelerated to a high energy and is directed at the surface of a semiconductor. As the ions enter the silicon, they collide with silicon atoms and lose energy and finally come to rest at some depth within the crystal. Since the collision process is statistical in nature, there is a dis- tribution in the depth of penetration of the dopant ions. Figure 0.4 shows such an example of the implantation of boron into silicon at a particular energy. Two advantages of the ion implantation process compared to diffusion are (1) the ion implantation process is a low-temperature process and (2) very well Doping concentration Diffused impurities Background doping Surface Distance Figure 0.3 | Final concentration of diffused impurities into the surface of a semiconductor. Doping concentration Surface Rp Distance (Projected range) Figure 0.4 | Final concentration of ion-implanted boron into silicon. nea29583_pro_xvii-xxiv.indd xxii 12/11/10 1:18 PM  Prolouge xxiii defined doping layers can be achieved. Photoresist layers or layers of oxide can be used to block the penetration of dopant atoms so that ion implantation can occur in very selected regions of the silicon. One disadvantage of ion implantation is that the silicon crystal is damaged by the penetrating dopant atoms because of collisions between the incident dopant atoms and the host silicon atoms. However, most of the damage can be removed by thermal annealing the silicon at an elevated temperature. The thermal annealing temperature, however, is normally much less that the diffusion process temperature. Metallization, Bonding, and Packaging After the semiconductor devices have been fabricated by the processing steps discussed, they need to be connected to each other to form the circuit. Metal films are generally deposited by a vapor deposition technique, and the actual interconnect lines are formed using photolithography and etching. In general, a protective layer of silicon nitride is finally deposited over the entire chip. The individual integrated circuit chips are separated by scribing and breaking the wafer. The integrated circuit chip is then mounted in a package. Lead bonders are fi- nally used to attach gold or aluminum wires between the chip and package terminals. Summary: Simplified Fabrication of a pn Junction Figure 0.5 shows the basic steps in forming a pn junction. These steps involve some of the processing described in the previous paragraphs. PR SiO2 SiO2 n type n n 1. Start with 2. Oxidize surface 3. Apply photoresist n-type substrate over SiO2 UV light Photomask Exposed PR removed SiO2 etched n n n 3. Expose photoresist 4. Remove exposed 5. Etch exposed SiO2 through photomask photoresist Ion implant or diffuse p regions Apply Al Al contacts p n p n p n p 6. Ion implant or 7. Remove PR and 8. Apply PR, photomask, diffuse boron sputter Al on and etch to form Al into silicon surface contacts over p regions Figure 0.5 | The basic steps in forming a pn junction. nea29583_pro_xvii-xxiv.indd xxiii 12/11/10 1:18 PM  xxiv Prolouge READING LIST 1. Campbell, S. A. The Science and Engineering of Microelectronic Fabrication. 2nd ed. New York: Oxford University Press, 2001. 2. Ghandhi, S. K. VLSI Fabrication Principles: Silicon and Gallium Arsenide. New York: John Wiley and Sons, 1983. 3. Rhoderick, E. H. Metal-Semiconductor Contacts. Oxford: Clarendon Press, 1978. 4. Runyan, W. R., and K. E. Bean. Semiconductor Integrated Circuit Processing Technology. Reading, MA: Addison-Wesley, 1990. 5. Torrey, H. C., and C. A. Whitmer. Crystal Rectifiers. New York: McGraw-Hill, 1948. 6. Wolf, S., and R. N. Tauber. Silicon Processing for the VLSI Era, 2nd ed. Sunset Beach, CA: Lattice Press, 2000. nea29583_pro_xvii-xxiv.indd xxiv 12/11/10 1:18 PM  C H 1 A P T E R The Crystal Structure of Solids T his text deals with the electrical properties and characteristics of semiconduc- tor materials and devices. The electrical properties of solids are therefore of primary interest. The semiconductor is in general a single-crystal material. The electrical properties of a single-crystal material are determined not only by the chemi- cal composition but also by the arrangement of atoms in the solid; this being true, a brief study of the crystal structure of solids is warranted. The formation, or growth, of the single-crystal material is an important part of semiconductor technology. A short discussion of several growth techniques is included in this chapter to provide the reader with some of the terminology that describes semiconductor device structures. 1.0 | PREVIEW In this chapter, we will: Describe three classifications of solids—amorphous, polycrystalline, and single crystal. Discuss the concept of a unit cell. Describe three simple crystal structures and determine the volume and surface density of atoms in each structure. Describe the diamond crystal structure. Briefly discuss several methods of forming single-crystal semiconductor materials. 1.1 | SEMICONDUCTOR MATERIALS Semiconductors are a group of materials having conductivities between those of met- als and insulators. Two general classifications of semiconductors are the elemental semiconductor materials, found in group IV of the periodic table, and the compound semiconductor materials, most of which are formed from special combinations of group III and group V elements. Table 1.1 shows a portion of the periodic table in 1 nea29583_ch01_001-024.indd 1 12/11/10 9:46 AM  2 CHAPTER 1 The Crystal Structure of Solids Table 1.1 | A portion of the periodic table Table 1.2 | A list of some semiconductor materials III IV V Elemental semiconductors 5 6 B C Si Silicon Boron Carbon Ge Germanium 13 14 15 Compound semiconductors Al Si P Aluminum Silicon Phosphorus AlP Aluminum phosphide 31 32 33 AlAs Aluminum arsenide Ga Ge As GaP Gallium phosphide Gallium Germanium Arsenic GaAs Gallium arsenide 49 51 InP Indium phosphide In Sb Indium Antimony which the more common semiconductors are found and Table 1.2 lists a few of the semiconductor materials. (Semiconductors can also be formed from combinations of group II and group VI elements, but in general these will not be considered in this text.) The elemental materials, those that are composed of single species of atoms, are silicon and germanium. Silicon is by far the most common semiconductor used in integrated circuits and will be emphasized to a great extent. The two-element, or binary, compounds such as gallium arsenide or gallium phosphide are formed by combining one group III and one group V element. Gal- lium arsenide is one of the more common of the compound semiconductors. Its good optical properties make it useful in optical devices. GaAs is also used in specialized applications in which, for example, high speed is required. We can also form a three-element, or ternary, compound semiconductor. An example is AlxGa1xAs, in which the subscript x indicates the fraction of the lower atomic number element component. More complex semiconductors can also be formed that provide flexibility when choosing material properties. 1.2 | TYPES OF SOLIDS Amorphous, polycrystalline, and single crystals are the three general types of sol- ids. Each type is characterized by the size of an ordered region within the material. An ordered region is a spatial volume in which atoms or molecules have a regular geometric arrangement or periodicity. Amorphous materials have order only within a few atomic or molecular dimensions, while polycrystalline materials have a high degree of order over many atomic or molecular dimensions. These ordered regions, or single-crystal regions, vary in size and orientation with respect to one another. The single-crystal regions are called grains and are separated from one another by grain boundaries. Single-crystal materials, ideally, have a high degree of order, or regular geometric periodicity, throughout the entire volume of the material. The advantage of a single-crystal material is that, in general, its electrical properties are superior nea29583_ch01_001-024.indd 2 12/11/10 9:46 AM  1.3 Space Lattices 3 (a) (b) (c) Figure 1.1 | Schematics of three general types of crystals: (a) amorphous, (b) polycrystalline, (c) single. to those of a nonsingle-crystal material, since grain boundaries tend to degrade the electrical characteristics. Two-dimensional representations of amorphous, polycrys- talline, and single-crystal materials are shown in Figure 1.1. 1.3 | SPACE LATTICES Our primary emphasis in this text will be on the single-crystal material with its regu- lar geometric periodicity in the atomic arrangement. A representative unit, or a group of atoms, is repeated at regular intervals in each of the three dimensions to form the single crystal. The periodic arrangement of atoms in the crystal is called the lattice. 1.3.1 Primitive and Unit Cell We can represent a particular atomic array by a dot that is called a lattice point. Figure 1.2 shows an infinite two-dimensional array of lattice points. The simplest means of repeating an atomic array is by translation. Each lattice point in Figure 1.2 can be translated a distance a1 in one direction and a distance b1 in a second nonco- linear direction to generate the two-dimensional lattice. A third noncolinear transla- tion will produce the three-dimensional lattice. The translation directions need not be perpendicular. Since the three-dimensional lattice is a periodic repetition of a group of atoms, we do not need to consider the entire lattice, but only a fundamental unit that is being repeated. A unit cell is a small volume of the crystal that can be used to reproduce the entire crystal. A unit cell is not a unique entity. Figure 1.3 shows several possible unit cells in a two-dimensional lattice. The unit cell A can be translated in directions a2 and b2, the unit cell B can be translated in directions a3 and b3, and the entire two-dimensional lattice can be constructed by the translations of either of these unit cells. The unit cells C and D in Figure 1.3 can also be used to construct the entire lattice by using the appropriate translations. This discussion of two-dimensional unit cells can easily be extended to three dimensions to describe a real single-crystal material. nea29583_ch01_001-024.indd 3 12/11/10 9:46 AM  4 CHAPTER 1 The Crystal Structure of Solids b2 A a2 b3 B a3 b1 b4 D b1 a4 a1 C a1 Figure 1.2 | Two-dimensional Figure 1.3 | Two-dimensional representation of a single-crystal representation of a single-crystal lattice. lattice showing various possible unit cells. A primitive cell is the smallest unit cell that can be repeated to form the lattice. In many cases, it is more convenient to use a unit cell that is not a primitive cell. Unit cells may be chosen that have orthogonal sides, for example, whereas the sides of a primitive cell may be nonorthogonal. A generalized three-dimensional unit cell is shown in Figure 1.4. The _relation- _ _ ship between this cell and the lattice is characterized by three vectors a, b, and c, which need not be perpendicular and which may or may not be equal in length. Every equivalent lattice point in the three-dimensional crystal can be found using the vector _ _ _ _ r  pa  qb  sc (1.1) where p, q, and s are integers. Since the location of the origin is arbitrary, we will let _ _ p, q, and s be positive integers for simplicity. The magnitudes of the vectors a, b, and _ c are the lattice constants of the unit cell. 1.3.2 Basic Crystal Structures Before we discuss the semiconductor crystal, let us consider three crystal structures and determine some of the basic characteristics of these crystals. Figure 1.5 shows the simple cubic, body-centered cubic, and face-centered cubic structures. For these _ _ _ simple structures, we may choose unit cells such that the general vectors a, b, and c c b a Figure 1.4 | A generalized primitive unit cell. nea29583_ch01_001-024.indd 4 12/11/10 9:46 AM  1.3 Space Lattices 5 a a a a a a a a a (a) (b) (c) Figure 1.5 | Three lattice types: (a) simple cubic, (b) body-centered cubic, (c) face-centered cubic. are perpendicular to each other and the