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