ELECTRONS IN SOLIDS Third Edition

ELECTRONS IN SOLIDS Third Edition An Introductory Survey RICHARD H. BUBE Department of Materials Science and Engineering Stanford University Stanford...
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ELECTRONS IN SOLIDS Third Edition An Introductory Survey

RICHARD H. BUBE Department of Materials Science and Engineering Stanford University Stanford, California

ACADEMIC PRESS, INC. Harcourt Brace Jovanovich, Publishers Boston San Diego London Sydney

New York Tokyo Toronto

Contents

Preface to the Third Edition

xi

Preface to the Second Edition

xiii

Preface to the First Edition

xv

1

2

3

Particles and Waves

1

Classical Views of Electrons, Light, and Energy Some Challenging Observations The New Approach Topics for Discussion Suggested Background Reading

3 4 8 9 9

General Properties of Waves

n

Basic Wave Properties Wave Equations Traveling Waves and Standing Waves Transverse and Longitudinal Waves Transverse Waves in an Infinite String Transverse Waves in a Finite String Reflection and Transmission of Waves in a String Some Wave Analogies Longitudinal Waves in a Rod Summary of Wave Systems

11 14 15 15 16 18 19 21 22 23

Lattice Waves

25

Transverse Waves in a One-Dimensional Infinite Lattice Transverse Waves in a One-Dimensional Finite Lattice

26 30

Contents

VI«

4

5

6

7

Measurement of Dispersion Curves for Lattice Waves Longitudinal Waves in a One-Dimensional Infinite Lattice Density of States for Lattice Waves Waves in a One-Dimensional Lattice with Two Types of Atom Reststrahlen Absorption

31 32 33 34 38

Light Waves

41

Properties of Electric and Magnetic Fields Dielectric Relaxation Time Electromagnetic Wave Equation The Case of No Absorption Description of Optical Absorption Absorption due to Electrical Conductivity

42 50 51 51 53 54

Matter Waves

57

The Schroedinger Wave Equation Procedure for Solving the Wave Equation Free-Electron Model of a Confined Electron Physical Interpretation of the Wave Function Reflection, Transmission and Tunneling of Electron Waves Linear Harmonic Oscillator The Hydrogen Atom The Periodic Table and the Pauli Exclusion Principle

58 60 60 63 67 70 75 83

The Free-Electron Model

85

What Energies are Allowed? What Is the Density of Allowed States as a Function of Energy? What Is the Probability That a State Is Occupied? Photoemission Thermionic Emission Field Emission Heat Capacity

86 88 92 95 98 101 104

Energy Bands

107

Bonds and Energy Gaps One-Dimensional Periodic Potential The Tight-Binding Approximation Effect of Periodic Potential on Free Electrons Density of States in a Band Summary of Different Band Representations

109 1ю 114 116 119 123

Contents

8

9

ix

Electron Velocity Effective Mass Holes

124 125 128

Optical Properties

131

Reflection Summary of Absorption Processes Transitions across the Band Gap Excitons Imperfections Free Carriers Plasma Resonance Absorption Polarization of Bound Electrons Photoelectronic Effects Optical Spectra Photoelectronic Applications

133 138 140 147 150 151 155 156 159 165 169

Electrical Properties

ni

Ohm's Law and Electrical Conductivity Temperature Dependence of Conductivity Temperature Dependence of Mobility Different Types of Relaxation Time Fermi Level in Semiconductors Intrinsic Semiconductor Donor and Acceptor Imperfections Electrical Conductivity in Extrinsic Semiconductors An Alternative Kinetic Approach Hall Effect Different Kinds of Mobility Other Galvanomagnetothermoelectric Effects Quantum High Magnetic Field Effects Amorphous Semiconductors Other Conductivity Mechanisms and Materials

172 174 174 182 182 185 186 190 195 196 199 201 203 204 208

10 Junctions Surfaces Metal-Metal Junctions Metal-Semiconductor Junctions: Schottky Barriers Metal-Semiconductor Junctions: Ohmic Contacts Semiconductor-Semiconductor Junctions: Homojunctions Applications of the p-n Junction The Tunnel Diode Semiconductor-Semiconductor Junctions: Heterojunctions Quantum Wells and Superlattices

214 215 216 217 223 226 229 234 235 238

11

Magnetic Properties

242

Magnetic Properties of an Atom Diamagnetism Free Electron Paramagnetism Bound Electron Paramagnetism Ferromagnetism Antiferromagnetism Ferrimagnetism Ferromagnetic Domains Ferromagnetic Hysteresis Magnetic Bubble Memories New Magnetic Materials

244 247 248 251 253 255 257 257 261 262 263

Appendix A

Vector Calculus

The Gradient: Чф The Divergence: V • A The Curl: V x A

266 266 267 268

Appendix В

Units and Conversion Factors

270

Appendix С

Electromagnetic Plane Waves and Field Energy

273

Electromagnetic Plane Waves

273

Electromagnetic Field Energy

275

Appendix D

Elements of Formal Wave Mechanics

277

Appendix E

Sample Problems

282

Bibliography

297

List of Problems

300

Answers to Problems

316

Index