Semiconductor Physics and Devices Basic Principles Third Edition Donald A. Neamen Univer.\ip of New Mexico Boston Burr Ridge. lL Dubuque. lA Mad~sonW 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. 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Schnee Media technology senior producer: Phillip Meek Compositor: Interactive Composition Corporation Typeface: 10/12 Times Roman Printer: R. R. Donnelley/Crawfordsville,I N 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 Preface xi Chapter 1 The Crystal Structure of Solids I Chapter 2 lntroduction to Quantum Mechanics 24 Chapter 3 Introduction to the Quantum Theory of Solids 56 Chapter 4 The Semiconductor in Equilibrium 103 Chapter 5 Carrier Transport Phenomena 154 Chapter 6 Nonequilibrium Excess Carriers in Semiconductors 189 Chapter 7 The pn Junction 238 Chapter 8 The pn Junction Diode 268 Chapter 9 Metal-Semiconductor and Semiconductor Heterojunctions 326 Chapter 10 The Bipolar Transistor 367 Chapter 11 Fundamentals of the Metal-Oxide-Semiconductor Field-Effect Transistor 449 Chapter 12 Metal-Oxide-SemiconductorF ield-Effect Transistor: Additional Concepts 523 Chapter 13 The Junction Field-Effect Transistor 570 Chapter 14 Optical Devices 617 Chapter 15 Semiconductor Power Devices 668 Appendix A Selected List of Symbols 703 Appendix B System of Units, Conversion Factors, and General Constants 71 1 Appendix C The Periodic Table 7 15 Appendix D The Error Function 7 17 Appendix E "Derivation" of Schrodinger's Wave Equation 719 Appendix F Unit of Energy-The Electron-Volt 721 Appendix G Answers to Selected Problems 723 Index 731 C O N T E N T S Preface xi 2.3 Applications of Schrodinger's Wave Equation 33 1 2.3.1 Electron in Free Space 33 CHAPTER 2.3.2 The Injnite Potential Well 34 The Crystal Structure of Solids 1 2.3.3 The Step Potential Function 38 Preview 1 2.3.4 The Potential Barrier 42 1.1 Semiconductor Materials 1 *2.4 Extensions of the Wave Theory to Atoms 45 1.2 Types of Solids 2 2.4.1 The One-Electron Atom 45 1.3 Space Lattices 3 2.4.2 The Periodic Table 48 1.3.1 Primitive and Unit Cell 3 2.5 Summary 50 1.3.2 Basic Crystal Structures 4 Problems 51 1.3.3 Crystal Planes and Miller lndices 5 1.3.4 The Diamond Structure 9 3 CHAPTER 1.4 Atomic Bonding 11 Introduction to the Quantum Theory "1.5 Imperfections and Impurities in Solids 13 of Solids 56 1.5.1 Impegections in Solids 13 Preview 56 1.5.2 lmpurities in Solids 15 3.1 Allowed and Forbidden Energy Bands 57 *1.6 Growth of Semiconductor Materials 16 3.1.1 Formation of Energy Bands 57 1.6.1 Growthfrom a Melt 16 *3.1.2 The Kronig-Penney Model 61 1.6.2 Epitaxial Growth 18 3.1.3 The k-Space Diagram 66 1.7 Summary 19 3.2 Electrical Conduction in Solids 70 Problems 21 3.2.1 The Energy Band and the Bond Model 70 3.2.2 Drift Current 72 2 CHAPTER 3.2.3 Electron Effective Mass 73 Introduction to Quantum Mechanics 24 3.2.4 Concept of the Hole 76 Preview 24 3.2.5 Metals, Insulators, and 2.1 Principles of Quantum Mechanics 25 Semiconductors 78 3.3 Extension to Three Dimensions 80 2.1.1 Energy Quanta 25 2.1.2 Wave-Particle Duality 26 3.3.1 The k-Space Diagrams of Si and GaAs 81 2.1.3 The Uncertainty Principle 29 3.3.2 Additional Effective Mass Concepts 82 2.2 Schrodinger's Wave Equation 30 3.4 Density of States Function 83 2.2.1 The Wave Equation 30 3.4.1 Mathematical Derivation 83 2.2.2 Physical Meaning of the Wave 3.4.2 Extension to Semiconductors 86 Function 32 3.5 Statistical Mechanics 88 2.2.3 Boundary Conditions 32 3.5.1 Statistical Laws 88 vi Contents 3.5.2 The Fermi-Dirac Probability Function 89 5 CHAPTER 3.5.3 The Distribution Function and the Carrier Transport Phenomena 154 Fermi Energy 91 3.6 Summary 96 Preview 154 Problems 98 5.1 Carrier Drift 154 5.1.1 Drift Current Density 155 5.1.2 Mobiliv Effects 157 4 CHAPTER 5.1.3 Conductivity 162 The Semiconductor in Equilibrium 103 5.1.4 Velocity Saturation 167 5.2 Carrier Diffusion 169 Preview 103 5.2.1 Dzffusion Current Density I70 4.1 Charge Carriers in Semiconductors 104 4. I. 1 Equilibrium Distribution of Electrons 5.2.2 Total Current Density 173 and Holes 104 5.3 Graded Impurity Distribution 173 4.1.2 The no and p, Equations 106 5.3.1 Induced Electric Field 174 3.1.3 The Intrinsic Carrier Concentration 110 5.3.2 The Einstein Relation 176 4.1.4 The Intrinsic Fermi-Level "5.4 The Hall Effect 177 Position 113 5.5 Summary 180 4.2 Dopant Atoms and Energy Levels 11 5 Problems 182 4.2. I Qualitative Description I15 4.2.2 Ionization Energy 11 7 6 4.2.3 Group 111-V Semiconductors 119 CHAPTER 4.3 The Extrinsic Semiconductor 120 Nonequilibrium Excess Carriers in Semiconductors 189 4.3.1 Equilibrium Distribution of Electrons and Holes 121 Preview 189 4.3.2 The nap, Product 124 6.1 Carrier Generation and Recombination 190 *4.3.3 The Ferrni-Diruc lntegral 125 6.1.1 The Semiconductor in Equilibrium 190 4.3.4 Degenerate and Nondegenerate 6.1.2 Excess Carrier Generation Semiconductors 127 and Recombination 191 4.4 Statistics of Donors and Acceptors 128 6.2 Characteristics of Excess Carriers 194 4.4. I Probability Function 128 6.2.1 Continuity Equations 195 4.4.2 Complete Ionization and Freeze-Out 129 6.2.2 Time-Dependent Diffusion 4.5 Charge Neutrality 132 Equations 196 4.5.1 compensated Semiconductors 133 6.3 Ambipolar Transport 197 4.5.2 Equilibrium Electron and Hole 6.3.1 Derivation ofthe Ambipolar Concentrations 133 Transport Equation 198 4.6 Position of Fermi Energy Level 139 6.3.2 Limits of Extrinsic Doping 4.6.1 Mathematical Derivation 139 and Low Injection 200 4.6.2 Variation of E, with Doping Concentration 6.3.3 Applications of the Ambipolar and Temperature 142 Transport Equation 203 4.6.3 Relevance of the Fermi Energy 144 6.3.4 Dielectric Relaxation Time Constant 211 4.7 Summary 145 "6.3.5 Huynes-Shockley Experiment 213 Problems 148 6.4 Quasi-Fermi Energy Levels 21 6 *6.5 Excess-Carrier Lifetime 21 8 8.1.7 Temperature Effects 284 6.5.1 Shockley-Read-Hall Theory 8.1.8 The "Short" Diode 284 of Recombination 21 9 8.2 Small-Signal Model of the pn Junction 286 of 6.5.2 Limits Extrinsic Doping 8.2.1 Diffusion Resistance 286 and Low Injection 222 8.2.2 Small-Signal Admittance 288 "6.6 Surface Effects 224 8.2.3 Equivalent Circuit 295 6.6.1 Su@ceStates 224 8.3 Generation-Recombination Currents 297 6.6.2 Surjiace Recombination Velocity 226 8.3.1 Reverse-Bias Generation Current 297 6.7 Summary 229 8.3.2 Forward-Bias Recombination Current 300 Problems 231 8.3.3 Total Forwurd-Bias Current 303 8.4 Junction Breakdown 305 7 CHAPTER "8.5 Charge Storage and Diode Transients 309 The pn Junction 238 8.5.1 The Turn-off Transient 309 Preview 238 8.5.2 The Turn-on Transient 312 7.1 Basic Structure of the pn Junction 238 "8.6 The Tunnel Diode 3 13 7.2 Zero Applied Bias 240 8.7 Summary 31 6 7.2.1 Built-in Potential Barrier 240 Problems 3 18 7.2.2 Electric Field 242 9 7.2.3 Space Charge Width 246 CHAPTER Metal-Semiconductor and Semiconductor 7.3 Reverse Applied Bias 247 Heterojunctions 326 7.3.1 Space Charge Width and Electric Field 248 Preview 326 7.3.2 Junction Capacitance 251 9.1 The Schottky Barrier Diode 326 7.3.3 One-Sided Junctions 253 9.1. I Qualitative Characteristics 327 *7.4 Nonuniformly Doped Junctions 255 9.1.2 Ideal Junction Properties 329 7.4.1 Linearly Graded Junction 255 9.1.3 Nonideal Effects on the Barrier Height 333 7.4.2 Hyperabrupt Junctions 258 9.1.4 Current-Voltage Relationship 337 7.5 Summary 260 9.1.5 Comparison rdthe Schottky Barrier Diode Problems 262 and the pn Junction Diode 341 9.2 Metal-Semiconductor Ohmic Contacts 344 8 CHAPTER 9.2.1 Ideal Nonrectifying Barriers 345 The pn Junction Diode 268 9.2.2 Tunneling Barrier 346 9.2.3 Spec$c Contact Resistance 348 Preview 268 9.3 Heterojunctions 349 8.1 pn Junction Current 269 9.3.1 Heterojunction Materials 350 8.1.1 Qualitative Description of Charge Flow in a pn Junction 269 9.3.2 Energy-Band Diagrams 350 8.1.2 Ideal Current-Voltage Relationship 270 9.3.3 Two-Dimensional Electron Gas 351 8.1.3 Boundary Conditions 271 *9.3.4 Equilibrium Electrostatics 354 8.1.4 Minority Carrier Distribution 275 *9.3.5 Current-Voltage Characteristics 359 8.1.5 Ideal pn Junction Current 277 9.4 Summary 359 8.1.6 Summary of Physics 281 Problems 361 viii Contents 10 10.9 Summary 435 CHAPTER The Bipolar Transistor 367 Problems 438 Preview 367 11 CHAPTER 10.1 The Bipolar Transistor Action 368 Fundamentals of the Metal-Oxide- 10.1.1 The Basic Principle of Operation 369 Semiconductor Field-Effect Transistor 449 10.1.2 Simplified Transistor Current Relations 370 Preview 449 10.1.3 The Modes of Operation 374 11.1 The Two-Terminal MOS Structure 450 10.1.4 Amplification with Bipolar 11.1.1 Energy-Band Diagrams 450 Transistors 376 11.1.2 Depletion Layer Thickness 455 10.2 Minority Carrier Distribution 377 11.1.3 Work Function Differences 458 10.2.1 Forward-Active Mode 378 11.1.4 Flat-Band Voltage 462 10.2.2 Other Modes of Operation 384 11.1.5 ThresholdVoltage 465 10.3 Low-Frequency Common-Base 11.1.6 Charge Distribution 471 Current Gain 385 11.2 Capacitance-Voltage Characteristics 474 10.3.1 Contributing Factors 386 11.2.1 Ideal C-V Characteristics 474 10.3.2 Mathematical Derivation of Current 11.2.2 Frequency Effects 479 Gain Factors 388 11.2.3 Fixed Oxide and lnte8ace 10.3.3 Summary 392 Charge Effects 480 10.3.4 Example Calculations of the 11.3 The Basic MOSFET Operation 483 Gain Factors 393 11.3.1 MOSFETStructures 483 10.4 Nonideal Effects 397 11.3.2 Current-Voltage Relationship- 10.4.1 Base Width Modulation 397 Concepts 486 10.4.2 High lnjection 401 "11.3.3 Current-Voltage Relationship- 10.4.3 Emitter Bandgap Narrowing 403 Mathematical Derivation 490 10.4.4 Current Crowding 405 11.3.4 Transconductance 498 *10.4.5 Nonuniform Base Doping 406 11.3.5 Substrate Bias Effects 499 10.4.6 Breakdown Voltage 408 11.4 Frequency Limitations 502 10.5 Equivalent Circuit Models 41 3 11.4.1 Small-Signal Equivalerzt Circuit 502 "10.5.1 Ebers-Moll Model 414 11.4.2 Frequency Limitation Factors 10.5.2 Gummel-Poon Model 416 and Cutoff Frequency 504 10.5.3 Hybrid-Pi Model 418 4' 11.5 The CMOS Technology 507 10.6 Frequency Limitations 422 11.6 Summary 509 10.6.1 Time-DelayFactors 422 Problems 5 13 10.6.2 Transistor Cutoff Frequency 424 10.7 Large-Signal Switching 427 12 CHAPTER 10.7.1 Switching Characteristics 427 Metal-Oxide-Semiconductor Field-Effect 10.7.2 The Schottky-Clamped Transistor 429 Transistor: Additional Concepts 523 *10.8 Other Bipolar Transistor Structures 430 10.8.1 Polysilicon Emitter BJT 430 Preview 523 10.8.2 Silicon-Germanium Base Transistor 431 12.1 Nonideal Effects 524 10.8.3 Heterojunction Bipolar Transistors 434 12.1.1 Subthreshold Conduction 524 12.1.2 Channel Length Modulation 526 13.3.2 Velocitj Saturation Efects 596 12.1.3 Mobility Variation 530 13.3.3 Subthreshold and Gate Current 12.1.4 VelocitySaturation 532 Effects 596 12.1.5 BallisticTransport 534 "13.4 Equivalent Circuit and Frequency 12.2 MOSFET Scaling 534 Limitations 598 13.4.1 Small-Signal Equivalerzt Circuit 598 12.2.1 Constant-Field Scaling 534 12.2.2 Threshold Voltage-First 13.4.2 Frequency Limitation Factors Approximations 535 and Cutc?ff Frequency 600 12.2.3 Generalized Scaling 536 *13.5 High Electron Mobility Transistor 602 12.3 Threshold Voltage Modifications 537 13.5.1 Quantum WellStructures 603 13.5.2 Transistor Performance 604 12.3.1 Short-Channel Effects 537 12.3.2 Narrow-Channel Effects 541 13.6 Summary 609 12.4 Additional Electrical Characteristics 543 Problems 61 1 12.4.1 Breakdown Voltage 544 *12.4.2 The Lightly Doped Drain Transistor 550 CHAPTER 14 12.4.3 Threshold Adjustment by Ion Optical Devices 61 7 Implantation 551 "12.5 Radiation and Hot-Electron Effects 554 Preview 617 12.5.1 Radiation-Induced Oxide Charge 555 14.1 Optical Absorption 61 8 12.5.2 Radiation-Induced Interface States 558 14.1.1 Photon Absorption Coeficient 618 12.5.3 Hot-Electron Charging Effects 560 14.1.2 Electron-Hole Pair Generation Rate 621 12.6 Summary 561 14.2 Solar Cells 623 Problems 563 14.2.1 The pn Junction Solar Cell 623 14.2.2 Conversion Ejjiciency and Solar Concentration 626 13 CHAPTER 14.2.3 Nonuniform Absorption Efects 628 The Junction Field-Effect Transistor 570 14.2.4 The Heterojunction Solar Cell 628 14.2.5 Amorphous Silicon Solar Cells 630 Preview 570 14.3 Photodetectors 63 1 13.1 JFET Concepts 57 1 14.3.1 Photoconductor 632 13.1.1 Basic pn JFET Operation 571 14.3.2 Photodiode 634 13.1.2 Basic MESFET Operation 575 14.3.3 PIN Photodiode 639 13.2 The Device Characteristics 577 14.3.4 Avalanche Photodiode 640 13.2.1 Internal Pinchoff Voltage, Pinchoff 14.3.5 Phototransistor 641 Voltage, and Drain-to-Source Saturation Voltage 577 14.4 Photoluminescence and 13.2.2 Ideal DC Current-Voltage Relutionship- Electroluminescence 642 Depletion Mode JFET 582 14.4.1 Basic Transitions 643 13.2.3 Transconductance 587 14.4.2 Luminescent Ejjiciency 645 13.2.4 The MESFET 588 14.4.3 Materials 645 *13.3 Nonideal Effects 593 14.5 Light Emitting Diodes 647 13.3.1 Channel Length Modulation 594 14.5. I Generation of Light 648 PREFACE PHILOSOPHY AND GOALS The purpose of the third 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 me- chanics, the quantum theory of solids, semiconductor material physics. and semicon- ductor 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 ex- tensive, 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 he covered fairly quickly and efficiently. The emphasis on the un- derlying 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 book is intended for junior and senior undergraduates. The prerequisites for un- derstanding the material are college mathematics. up to and including differential equations, and college physics, including an intn~ductiout o nlodern physics and electrostatics. Prior co~npletiono f an introductory course in electronic circuits is helpful, but not essential. ORGANIZATION The text begins with the introductory physics, moves on to the semiconductor mate- rial physics, and then covers the physics of semiconductor devices. Chapter 1 presents an introduction to the crystal structure of solids, leading to the ideal single-crystal semiconductor material. Chapters 2 and 3 introduce quantum mechanics and the quantum theory of solids, which together provide the necessary basic physics. Chapters4 through6 cover the semiconductorlnaterial physics. Chapter4 presents the physics of the semiconductor in thermal equilibrium; Chapter 5 treats the transport