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Semiconductor Physics and Devices Basic Principles Third Edition Donald A. Neamen Univer.\ip of New Mexico Boston Burr Ridge. lL Dubuque. lA Mad~son W New York San Francisco St Louis Bangkok Bogota Caracas KualaLurnpur Lisbon London Madr~d Mex~coClty Milan Montreal NewDeIhl Sant~ago Seoul Singapore Sydney Ta~pel Toronto
McGraw-Hill Higher- Education A llivlsion of The McGraw-Hill Compav~ies SEMICONDUCTOR PHYSICS AND DEVICES: BASIC PRINCIPLES THIRD EDITION Published by McGraw-Hill, a business unit of The McGraw-Hill Companies, Inc., 1221 Avenue of the Americas, New York, NY 10020. Copyright O 2003, 1997, 1992 by The McGrdw-Hill Companies, Inc. All rights reserved. No part of this publication may be reproduced 01 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 transmission, 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. lnternational Domestic 1 2 3 4 5 6 7 8 9 0 DOCIDOC 0 9 8 7 6 5 4 3 2 2 3 4 5 6 7 8 9 0 D O C D O C 0 9 8 7 6 5 4 3 ISBN 0-07-232107-5 ISBN 0-07-1 19862-8 (ISE) Publisher: Elizabeth A. Jones Senior developmental editor: Kelley Butcher Executive marketing manager: John Wannemacher Project manager: Joyce Waiters Production supervisor: Sherry L. Kane Designer: David W Hash Cover designer: Rokusek Design Cover image: OEyewire, Inc. Media project manager: Sandra M. Schnee Media technology senior producer: Phillip Meek Compositor: Interactive Composition Corporation Typeface: 10/12 Times Roman Printer: R. R. Donnelley/Crawfordsville, IN Library of Congress Cataloging-in-Publication Data Neamen, Donald A. Semiconductor physics and devices : basic principles 1 Donald A. Neamen. - 3rd ed. p. cm. Includes bibliographical references and index. ISBN 0-07-232 107-5 (acid-free paper) I. Semiconductors. I. Title. 2002019681 CIP INTERNATIONAL EDITION ISBN 0-07-1 19862-8 Copyright O 2003. Exclusive rights by The McGraw-Hill Companies, Inc., for manufacture and export. This book cannot be re-exported from the country to which it is sold by McGraw-Hill. The International Edition is not available in North America.
A B O U T T H E A U T H O R Donald A. Neamen is a professor emerltus 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 EECE 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 department. 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 EECE 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 EECE 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 Electronic Circuit Analysis and Design, 2nd edition.
C O N T E N T S I N B R I E F Chapter 1 Chapter 2 Chapter 3 Chapter 4 Chapter 5 Chapter 6 Chapter 7 Chapter 8 Chapter 9 Chapter 10 Chapter 11 Chapter 12 Chapter 13 Chapter 14 Chapter 15 Appendix A Appendix B Preface xi The Crystal Structure of Solids I lntroduction to Quantum Mechanics 24 Introduction to the Quantum Theory of Solids 56 The Semiconductor in Equilibrium 103 Carrier Transport Phenomena 154 Nonequilibrium Excess Carriers in Semiconductors 189 The pn Junction 238 The pn Junction Diode 268 Metal-Semiconductor and Semiconductor Heterojunctions 326 The Bipolar Transistor 367 Fundamentals of the Metal-Oxide-Semiconductor Field-Effect Transistor 449 Metal-Oxide-Semiconductor Field-Effect Transistor: Additional Concepts 523 The Junction Field-Effect Transistor 570 Optical Devices 617 Semiconductor Power Devices 668 Selected List of Symbols 703 System of Units, Conversion Factors, and General Constants 7 11 Appendix C The Periodic Table 7 15 Appendix D Appendix E Appendix F Appendix G The Error Function 7 17 "Derivation" of Schrodinger's Wave Equation 719 Unit of Energy-The Electron-Volt 721 Answers to Selected Problems 723 Index 731
C O N T E N T S Preface xi C H A P T E R 1 The Crystal Structure of Solids 1 Preview 1 1.1 Semiconductor Materials 1 1.2 Types of Solids 2 1.3 Space Lattices 3 1.3.1 Primitive and Unit Cell 3 1.3.2 Basic Crystal Structures 4 1.3.3 Crystal Planes and Miller lndices 5 1.3.4 The Diamond Structure 9 1.4 Atomic Bonding 11 "1.5 Imperfections and Impurities in Solids 13 1.5.1 1.5.2 Impegections in Solids 13 lmpurities in Solids 15 *1.6 Growth of Semiconductor Materials 16 1.6.1 Growthfrom a Melt 16 1.6.2 Epitaxial Growth 18 1.7 Summary 19 Problems 21 C H A P T E R 2 Introduction to Quantum Mechanics 24 Preview 24 2.1 Principles of Quantum Mechanics 25 2.1.1 Energy Quanta 25 2.1.2 Wave-Particle Duality 26 2.1.3 The Uncertainty Principle 29 2.2 Schrodinger's Wave Equation 30 2.2.1 The Wave Equation 30 2.2.2 Physical Meaning of the Wave Function 32 2.2.3 Boundary Conditions 32 2.3 Applications of Schrodinger's Wave Equation 33 2.3.1 Electron in Free Space 33 2.3.2 The Injnite Potential Well 34 2.3.3 The Step Potential Function 38 2.3.4 The Potential Barrier 42 *2.4 Extensions of the Wave Theory to Atoms 45 2.4.1 The One-Electron Atom 45 2.4.2 The Periodic Table 48 2.5 Summary 50 Problems 51 C H A P T E R 3 Introduction to the Quantum Theory of Solids 56 Preview 56 3.1 Allowed and Forbidden Energy Bands 57 3.1.1 Formation of Energy Bands 57 *3.1.2 The Kronig-Penney Model 61 3.1.3 The k-Space Diagram 66 3.2 Electrical Conduction in Solids 70 3.2.1 The Energy Band and the Bond Model 70 3.2.2 Drift Current 72 3.2.3 Electron Effective Mass 73 3.2.4 Concept of the Hole 76 3.2.5 Metals, Insulators, and Semiconductors 78 3.3 Extension to Three Dimensions 80 3.3.1 The k-Space Diagrams of Si and GaAs 81 3.3.2 Additional Effective Mass Concepts 82 3.4 Density of States Function 83 3.4.1 Mathematical Derivation 83 3.4.2 Extension to Semiconductors 86 3.5 Statistical Mechanics 88 3.5.1 Statistical Laws 88
vi Contents 3.5.2 The Fermi-Dirac Probability Function 89 3.5.3 The Distribution Function and the Fermi Energy 91 C H A P T E R 5 Carrier Transport Phenomena 154 3.6 Summary 96 Problems 98 C H A P T E R 4 The Semiconductor in Equilibrium 103 Preview 103 4.1 Charge Carriers in Semiconductors 104 4. I. 1 Equilibrium Distribution of Electrons and Holes 104 4.1.2 The no and p, Equations 106 3.1.3 The Intrinsic Carrier Concentration 110 4.1.4 The Intrinsic Fermi-Level Position 113 4.2 Dopant Atoms and Energy Levels 1 15 4.2. I Qualitative Description 4.2.2 Ionization Energy 11 7 4.2.3 Group 111-V Semiconductors 119 I15 4.3 The Extrinsic Semiconductor 120 4.3.1 Equilibrium Distribution of Electrons and Holes 121 4.3.2 The nap, Product 124 *4.3.3 The Ferrni-Diruc lntegral 125 4.3.4 Degenerate and Nondegenerate Semiconductors 127 4.4 Statistics of Donors and Acceptors 128 4.4. I Probability Function 128 4.4.2 Complete Ionization and Freeze-Out 129 4.5 Charge Neutrality 132 4.5.1 compensated Semiconductors 133 4.5.2 Equilibrium Electron and Hole Concentrations 133 4.6 Position of Fermi Energy Level 139 4.6.1 Mathematical Derivation 139 4.6.2 Variation of E, with Doping Concentration and Temperature 142 4.6.3 Relevance of the Fermi Energy 144 4.7 Summary 145 Problems 148 Preview 154 5.1 Carrier Drift 154 5.1.1 Drift Current Density 155 5.1.2 Mobiliv Effects 157 5.1.3 Conductivity 162 5.1.4 Velocity Saturation 167 5.2 Carrier Diffusion 169 5.2.1 Dzffusion Current Density 5.2.2 Total Current Density 173 I70 5.3 Graded Impurity Distribution 173 5.3.1 Induced Electric Field 174 5.3.2 The Einstein Relation 176 "5.4 The Hall Effect 177 5.5 Summary 180 Problems 182 C H A P T E R 6 Nonequilibrium Excess Carriers in Semiconductors 189 Preview 189 6.1 Carrier Generation and Recombination 190 6.1.1 The Semiconductor in Equilibrium 190 6.1.2 Excess Carrier Generation and Recombination 191 6.2 Characteristics of Excess Carriers 194 6.2.1 Continuity Equations 195 6.2.2 Time-Dependent Diffusion Equations 196 6.3 Ambipolar Transport 197 6.3.1 Derivation ofthe Ambipolar Transport Equation 198 6.3.2 Limits of Extrinsic Doping and Low Injection 200 6.3.3 Applications of the Ambipolar Transport Equation 203 6.3.4 Dielectric Relaxation Time Constant 211 "6.3.5 Huynes-Shockley Experiment 213 6.4 Quasi-Fermi Energy Levels 21 6
*6.5 Excess-Carrier Lifetime 21 8 6.5.1 Shockley-Read-Hall Theory of Recombination 21 9 6.5.2 Limits of Extrinsic Doping and Low Injection 222 "6.6 Surface Effects 224 6.6.1 Su@ceStates 6.6.2 Surjiace Recombination Velocity 226 224 6.7 Summary 229 Problems 231 C H A P T E R 7 The pn Junction 238 Preview 238 7.1 Basic Structure of the pn Junction 238 7.2 Zero Applied Bias 240 7.2.1 Built-in Potential Barrier 240 7.2.2 Electric Field 242 7.2.3 Space Charge Width 246 7.3 Reverse Applied Bias 247 7.3.1 Space Charge Width and Electric Field 248 7.3.2 Junction Capacitance 251 7.3.3 One-Sided Junctions 253 *7.4 Nonuniformly Doped Junctions 255 7.4.1 Linearly Graded Junction 255 7.4.2 Hyperabrupt Junctions 258 7.5 Summary 260 Problems 262 C H A P T E R 8 The pn Junction Diode 268 Preview 268 8.1 pn Junction Current 269 8.1.1 Qualitative Description of Charge Flow in a pn Junction 269 Ideal Current-Voltage Relationship 270 8.1.2 8.1.3 Boundary Conditions 271 8.1.4 Minority Carrier Distribution 275 8.1.5 8.1.6 Summary of Physics 281 Ideal pn Junction Current 277 8.1.7 Temperature Effects 284 8.1.8 The "Short" Diode 284 8.2 Small-Signal Model of the pn Junction 286 8.2.1 Diffusion Resistance 286 8.2.2 Small-Signal Admittance 288 8.2.3 Equivalent Circuit 295 8.3 Generation-Recombination Currents 297 8.3.1 Reverse-Bias Generation Current 297 8.3.2 Forward-Bias Recombination Current 300 8.3.3 Total Forwurd-Bias Current 303 8.4 Junction Breakdown 305 "8.5 Charge Storage and Diode Transients 309 8.5.1 The Turn-off Transient 309 8.5.2 The Turn-on Transient 312 "8.6 The Tunnel Diode 3 13 8.7 Summary 3 16 Problems 3 18 C H A P T E R 9 Metal-Semiconductor and Semiconductor Heterojunctions 326 Preview 326 9.1 The Schottky Barrier Diode 326 Ideal Junction Properties 329 9.1. I Qualitative Characteristics 327 9.1.2 9.1.3 Nonideal Effects on the Barrier Height 333 9.1.4 Current-Voltage Relationship 337 9.1.5 Comparison rdthe Schottky Barrier Diode and the pn Junction Diode 341 9.2 Metal-Semiconductor Ohmic Contacts 344 Ideal Nonrectifying Barriers 345 9.2.1 9.2.2 Tunneling Barrier 346 9.2.3 Spec$c Contact Resistance 348 9.3 Heterojunctions 349 9.3.1 Heterojunction Materials 350 9.3.2 Energy-Band Diagrams 350 9.3.3 Two-Dimensional Electron Gas 351 *9.3.4 Equilibrium Electrostatics 354 *9.3.5 Current-Voltage Characteristics 359 9.4 Summary 359 Problems 361
viii Contents C H A P T E R 10 The Bipolar Transistor 367 Preview 367 10.1 The Bipolar Transistor Action 368 10.1.1 The Basic Principle of Operation 369 10.1.2 Simplified Transistor Current Relations 370 10.1.3 The Modes of Operation 374 10.1.4 Amplification with Bipolar Transistors 376 10.2 Minority Carrier Distribution 377 10.2.1 Forward-Active Mode 378 10.2.2 Other Modes of Operation 384 10.3 Low-Frequency Common-Base Current Gain 385 10.3.1 Contributing Factors 386 10.3.2 Mathematical Derivation of Current Gain Factors 388 10.3.3 Summary 392 10.3.4 Example Calculations of the Gain Factors 393 10.4 Nonideal Effects 397 10.4.1 Base Width Modulation 397 10.4.2 High lnjection 401 10.4.3 Emitter Bandgap Narrowing 403 10.4.4 Current Crowding 405 *10.4.5 Nonuniform Base Doping 406 10.4.6 Breakdown Voltage 408 10.5 Equivalent Circuit Models 41 3 "10.5.1 Ebers-Moll Model 414 10.5.2 Gummel-Poon Model 416 10.5.3 Hybrid-Pi Model 418 10.6 Frequency Limitations 422 10.6.1 Time-DelayFactors 422 10.6.2 Transistor Cutoff Frequency 424 10.7 Large-Signal Switching 427 10.7.1 Switching Characteristics 427 10.7.2 The Schottky-Clamped Transistor 429 *10.8 Other Bipolar Transistor Structures 430 10.9 Summary 435 Problems 438 C H A P T E R 11 Fundamentals of the Metal-Oxide- Semiconductor Field-Effect Transistor 449 Preview 449 11.1 The Two-Terminal MOS Structure 450 11.1.1 Energy-Band Diagrams 450 11.1.2 Depletion Layer Thickness 455 11.1.3 Work Function Differences 458 11.1.4 Flat-Band Voltage 462 11.1.5 ThresholdVoltage 465 11.1.6 Charge Distribution 471 11.2 Capacitance-Voltage Characteristics 474 Ideal C-V Characteristics 474 11.2.1 11.2.2 Frequency Effects 479 11.2.3 Fixed Oxide and lnte8ace Charge Effects 480 11.3 The Basic MOSFET Operation 483 11.3.1 MOSFETStructures 483 11.3.2 Current-Voltage Relationship- Concepts 486 "11.3.3 Current-Voltage Relationship- Mathematical Derivation 490 11.3.4 Transconductance 498 11.3.5 Substrate Bias Effects 499 11.4 Frequency Limitations 502 11.4.1 Small-Signal Equivalerzt Circuit 502 11.4.2 Frequency Limitation Factors and Cutoff Frequency 504 '11.5 The CMOS Technology 507 4 11.6 Summary 509 Problems 5 13 C H A P T E R 12 Metal-Oxide-Semiconductor Field-Effect Transistor: Additional Concepts 523 10.8.1 Polysilicon Emitter BJT 430 10.8.2 Silicon-Germanium Base Transistor 431 10.8.3 Heterojunction Bipolar Transistors 434 Preview 523 12.1 Nonideal Effects 524 12.1.1 Subthreshold Conduction 524
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