Gerald Burns Solid State Physics
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Transcript of Gerald Burns Solid State Physics
Solid State Physics
Gerald Burns IBM Thomas J. Watson Research Center
Yorktown Heights, New York
ЯЙ ACADEMIC PRESS, INC.
Harcourt Brace Jovanovich, Pubiishers Boston San Diego New York
London Sydney Tokyo Toronto
Contents
Symmetry Operations 1-1 A Symmetry Operation 4 1-2 Point Symmetry Operations 5 1-3 The Point Groups of a Molecule 9 1-4 Other Symmetry Operations of Crystals 17
Notes 20 Problems 20
Symmetry Description of Crystals 2-1 Lattice 25 2-2 Primitive Unit Cell 26 2-3 The 7 Crystal Systems 26 2-4 The 14 Bravais Lattices 29 2-5 The 32 Crystallographic Point Groups 35 2-6 Space Groups 38 2-7 Definitions of Directions, Coordinates, and Planes 43
Appendix to Chapter 2 46 Notes 47 Problems 48
Simple Crystal Structures 3-1 Introduction 51 3-2 Several Cubic Symmorphic Structures 51
*1
2
3
The book may be started in Chapter 1, Chapter 6, or Chapter 9.
IX
X
3-3 Diamond and Zinc Blende Structures 56 3-4 Point Group of a Space Group (S) 58 3-5 Examples of Defect Structures 60 3-6 Different Points of View of a Structure 61 3-7 Close Packing (and the Hexagonal Close-Packed
Structure) 62 3-8 Volume Effects for Simple Structures 65 3-9 Wurtzite Structure 66 3-10 Site Symmetry (S) 67
Notes 68 Problems 69
T" X-Ray Diffraction 4-1 Electron, Neutron, and X-ray Diffraction 73 4-2 Bragg's Law 75 4-3 The Laue Formulation 77 4-4 Experimental X-ray Diffraction Methods (S) 81
Notes 83 Problems 83
Э Crystal Symmetry and Physical Properties (S) 5-1 Introduction 87 5-2 Neumann's Principle 88 5-3 Tensors 88 5-4 Crystal Symmetry and Physical Properties 90 5-5 Nonlinear Optics 96
Notes 98 Problems 98
О Classification of Solids 6-1 Summary of Chapters 1-3 103 6-2 Introduction to Classification of Solids 112 6-3 Five Types of Bonds 112 6-4 Repulsive Potential Energy 115 6-5 Molecular Bond 118 6-6 Hydrogen Bond (S) 124
Notes 127 Problems 128
CONTENTS
The Ionic Bond 7-1 Transfer of Electrons 131 7-2 Ionic Radii 133 7-3 Typical Structures 134 7-4 Cohesive Energies of Ionic Crystals 138
Notes 143 Problems 144
The Covalent Bond 8-1 Introduction 149 8-2 Bonding and Antibonding 150 8-3 The Hydrogen Molecule 154 8-4 Maximum Overlap 157 8-5 The Formation of a Crystal 164 8-6 "Classical" Semiconductors 168 8-7 Continuous Range of Bonding (S) 175
Appendix 183 Notes 184 Problems 185
Metals PART A DRUDE'S MODEL 191 9-1 Drude's Free Electron Theory 191 9-2 Drude's Assumptions 195 9-3 DC Conductivity 196 9-4 Wiedemann-Franz Law 197 9-5 Frequency-Dependent Conductivity (S, A) 198 9-6 Problems of Drude's Model 201
PART В QUANTUM MECHANICS APPLIED 203 9-7 Eigenfunctions of Free Electrons in a Metal 203 9-8 Fermi Energy, Density of States, and Fermi
Surface 208 9-9 Soft X-rays, Heat Capacities 213 9-10 Fermi-Dirac Statistics 215 9-11 Low Temperature Expansion Using F-D Statistics 216 9-12 Thermal Properties of the Electron Gas 217 9-13 DC Conductivity (with F-D Statistics) 223 9-14 Electron-Electron Collisions (S) 225 9-15 Hall Effect (and Other Magnetic Field Effects) (S) 228
Xll
9-16 Landau Levels (S, A) 233 Notes 235 Problems 236
Band Theory PART A QUALITATIVE DISCUSSION 243 10-1 Nearly Free Electrons 243 10-2 Classifications of Solids 247 10-3 Effective Mass 248
PART В WAVE FUNCTIONS AND ENERGY LEVELS 10-4 Bloch Functions 252 10-5 Nearly Free Electrons 257 10-6 Brillouin Zones 260 10-7 Examples of Brillouin Zones 263 10-8 Wigner-Seitz Approximation — The Binding
Energy (S) 273 10-9 The Tight Binding Approximation (S) 276 10-10 Crystal Momentum 280
PART С SEMICONDUCTORS, REAL BANDS, AND RELATED CONCEPTS 281
10-11 Holes 281 10-12 Band Preliminaries (A) 289 10-13 / (k) for a Two-Dimensional Square Lattice 293 10-14 Body-Centered Cubic Lattice — Sodium (S, A) 302 10-15 Si,Ge, GaAs, andGaP 304 10-16 Carrier Concentration at Thermal Equilibrium 313 10-17 p-n Junctions 323 10-18 Metal-Semiconductor Junctions 334 10-19 The Gunn Effect (S) 337 10-20 Other Topcis(S) 339 10-21 Summary 345
Notes 348 Problems 349
Some Thermal Effects in Solids PART A HEAT CAPACITY 355 11-1 Specific Heat at Constant Volume and Pressure 355 11-2 Energy and Cv from Statistical Mechanics 357 11-3 Classical Results for Cv 360 11-4 Einstein's Model 362 11-5 Debye's Calculation of Cv 365
CONTENTS
PART В EFFECTS ASSOCIATED WITH DISORDER 371 11-6 Orientational Disorder in Molecular and Ionic
Crystals 371 11-7 Polarization by Orientation (S) 379 11-8 Point Imperfections in Crystals 385 11-9 Diffusion (S) 389 11-10 Color Centers in Ionic Crystals (S) 396 11-11 Localized Vibrational Modes (S) 398
Notes 399 Problems 401
Lattice Vibrations 12-1 Introduction 407 12-2 Vibrations of a One-Dimensional Monatomic
Chain 408 12-3 Vibrations of a One-Dimensional Diatomic Chain 412 12-4 Real Crystal Systems 419 12-5 Phonons (A) 425 12-6 Crystal Momentum (A) 428 12-7 Neutron Diffraction from Phonons 430 12-8 Thermal Conductivity (S) 433
Notes 441 Problems 443
Optical Properties of Crystals PART A MACROSCOPIC THEORY 450 13-1 Dielectric Polarization 450 13-2 Oscillating Fields 452 13-3 Electromagnetic Waves in Solids 454 13-4 Reflectivity at an Interface 457 13-5 Kramers-Kronig Relations (S, A) 458 13-6 Damped Harmonic Oscillator 461 13-7 Dielectric Response of a Quantum System 464
PART В LATTICE VIBRATIONS 465 13-8 Introduction 465 13-9 Long Wavelength Optical Vibrations 466 13-10 Measurements and Results 471 13-11 Polaritons (S) 476 13-12 A Microscopic Model (S) 480 13-13 Clausius-Mossotti (Lorenz-Lorentz) Equations (S) 484
XIV CONTENTS
14
15
PART С FREE CARRIER ABSORPTION 486 13-14 Introduction 486 13-15 Oscillator Model 487 13-16 Experimental Results 490 13-17 Transverse and Longitudinal Free Electron
Modes (S) 495
PARTD INTERBAND TRANSITIONS 498 13-18 Introduction 498 13-19 Fundamental Absorption Near £% 500 13-20 Excitons (Mostly Weakly Bound Excitons) 509 13-21 Fundamental Absorption Above it 520 13-22 UrbachEdge(S) 521
Notes 524 Problems 526
Ferroelectricity and Structural Phase Transitions 14-1 Introduction 531 14-2 The Free Energy 536 14-3 Soft Modes 542 14-4 Microscopic Model of Soft Modes 550 14-5 Renormalization Group 552 14-6 Optical Properties of Ferroelectrics (S) 554 14-7 Other Related Properties
Notes 559 Problems 562
Magnetism PART A DIAMAGNETISM AND PARAMAGNETISM 565
15-1 Introduction 565 15-2 Diamagnetism 567 15-3 Paramagnetism 569
PART В FERROMAGNETISM, ANTIFERRO-MAGNETISM, AND RELATED TOPICS 584
15-4 Introduction 584 15-5 Molecular Field Theory 584 15-6 The Heisenberg Exchange Interaction 588 15-7 Magnetic Structures 590 15-8 Special Techniques Used to Study Magnetic
Structures 596
CONTENTS
PART С OTHER TOPICS 604 15-9 Spin Waves (S, A) 604 15-10 Anisotropy, Hysteresis, Domains, and Bloch Walls 15-11 Metals and Magnetism (S, A) 619 15-12 Spin Glasses (S) 625
Notes 627 Problems 629
Superconductivity 16-1 Introduction (dc Conductivity) 633 16-2 The Occurrence of Superconductivity 634 16-3 Effects that Destroy Superconductivity 635 16-4 Magnetic Properties 637 16-5 The BCS Theory 642 16-6 BCS Predictions 648 16-7 BCS Related Measurements 653 16-8 The Josephson Effect 659
Notes 666 Problems 668
Surface Science 17-1 Introduction — The Need for UH V 674 17-2 Crystal Shape 675 17-3 Preparation of Clean Surfaces and LEED 677 17-4 The Structure of Surfaces 679 17-5 Interaction of Gases with Surfaces 686 17-6 Surface Related Techniques 692 17-7 Electronic Surface Structure 702
Notes 710 Problems 712 Appendix to Chapter 17 712
Artificial Structures PART A SEMICONDUCTORS 716 18-1 Introduction 716 18-2 A Particle in a 1 -D Rectangular Well 717 18-3 3-D Motion with a 1 -D Rectangular Well 719 18-4 Experimental Aspects 724 18-5 Semiconductor Superlattices 726 18-6 Inversion Layers 737
xvi CONTENTS
PART В METALS 747 18-7 Introduction 747 18-8 Sample Preparation 748 18-9 Properties of Layered Metal Structures 749 18-10 Other Artificial Structures (S) 752
Notes 753 Problems 755
Appendix 757
Appendix — Units 792
Bibliography 796 ,
Index 800