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

*1

Symmetry Operations 1-1 1-2 1-3 1-4

A Symmetry Operation 4 Point Symmetry Operations 5 The Point Groups of a Molecule 9 Other Symmetry Operations of Crystals Notes 20 Problems 20

17

2

Symmetry Description of Crystals 2-1 2-2 2-3 2-4 2-5 2-6 2-7

Lattice 25 Primitive Unit Cell 26 The 7 Crystal Systems 26 The 14 Bravais Lattices 29 The 32 Crystallographic Point Groups 35 Space Groups 38 Definitions of Directions, Coordinates, and Planes Appendix to Chapter 2 46 Notes 47 Problems 48

43

3

Simple Crystal Structures 3-1 3-2

Introduction 51 Several Cubic Symmorphic Structures

51

The book may be started in Chapter 1, Chapter 6, or Chapter 9. IX

X

3-3 3-4 3-5 3-6 3-7

Diamond and Zinc Blende Structures 56 Point Group of a Space Group (S) 58 Examples of Defect Structures 60 Different Points of View of a Structure 61 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 4-2 4-3 4-4

Э

Crystal Symmetry and Physical Properties (S) 5-1 5-2 5-3 5-4 5-5

О

Electron, Neutron, and X-ray Diffraction 73 Bragg's Law 75 The Laue Formulation 77 Experimental X-ray Diffraction Methods (S) 81 Notes 83 Problems 83

Introduction 87 Neumann's Principle 88 Tensors 88 Crystal Symmetry and Physical Properties Nonlinear Optics 96 Notes 98 Problems 98

90

Classification of Solids 6-1 6-2 6-3 6-4 6-5 6-6

Summary of Chapters 1-3 103 Introduction to Classification of Solids Five Types of Bonds 112 Repulsive Potential Energy 115 Molecular Bond 118 Hydrogen Bond (S) 124 Notes 127 Problems 128

112

CONTENTS

The Ionic Bond 7-1 7-2 7-3 7-4

Transfer of Electrons 131 Ionic Radii 133 Typical Structures 134 Cohesive Energies of Ionic Crystals Notes 143 Problems 144

138

The Covalent Bond 8-1 8-2 8-3 8-4 8-5 8-6 8-7

Introduction 149 Bonding and Antibonding 150 The Hydrogen Molecule 154 Maximum Overlap 157 The Formation of a Crystal 164 "Classical" Semiconductors 168 Continuous Range of Bonding (S) 175 Appendix 183 Notes 184 Problems 185

Metals PART A 9-1 9-2 9-3 9-4 9-5 9-6

9-9 9-10 9-11 9-12 9-13 9-14 9-15

191

Drude's Free Electron Theory 191 Drude's Assumptions 195 DC Conductivity 196 Wiedemann-Franz Law 197 Frequency-Dependent Conductivity (S, A) Problems of Drude's Model 201

PART В 9-7 9-8

DRUDE'S MODEL

198

QUANTUM MECHANICS APPLIED

203

Eigenfunctions of Free Electrons in a Metal 203 Fermi Energy, Density of States, and Fermi Surface 208 Soft X-rays, Heat Capacities 213 Fermi-Dirac Statistics 215 Low Temperature Expansion Using F-D Statistics 216 Thermal Properties of the Electron Gas 217 DC Conductivity (with F-D Statistics) 223 Electron-Electron Collisions (S) 225 Hall Effect (and Other Magnetic Field Effects) (S) 228

Xll

9-16 Landau Levels (S, A) Notes 235 Problems 236

233

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 10-5 10-6 10-7 10-8

Bloch Functions 252 Nearly Free Electrons 257 Brillouin Zones 260 Examples of Brillouin Zones 263 Wigner-Seitz Approximation — The Binding Energy (S) 273 10-9 The Tight Binding Approximation (S) 276 10-10 Crystal Momentum 280

PART С 10-11 10-12 10-13 10-14 10-15 10-16 10-17 10-18 10-19 10-20 10-21

SEMICONDUCTORS, REAL BANDS, AND RELATED CONCEPTS 281

Holes 281 Band Preliminaries (A) 289 / ( k ) for a Two-Dimensional Square Lattice 293 Body-Centered Cubic Lattice — Sodium (S, A) 302 Si,Ge, GaAs, andGaP 304 Carrier Concentration at Thermal Equilibrium 313 p-n Junctions 323 Metal-Semiconductor Junctions 334 The Gunn Effect (S) 337 Other Topcis(S) 339 Summary 345 Notes 348 Problems 349

Some Thermal Effects in Solids PART A 11-1 11-2 11-3 11-4 11-5

HEAT CAPACITY

355

Specific Heat at Constant Volume and Pressure 355 Energy and C v from Statistical Mechanics 357 Classical Results for C v 360 Einstein's Model 362 Debye's Calculation of C v 365

CONTENTS

PART В 11-6 11-7 11-8 11-9 11-10 11-11

EFFECTS ASSOCIATED WITH DISORDER

371

Orientational Disorder in Molecular and Ionic Crystals 371 Polarization by Orientation (S) 379 Point Imperfections in Crystals 385 Diffusion (S) 389 Color Centers in Ionic Crystals (S) 396 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 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

412

Optical Properties of Crystals PART A 13-1 13-2 13-3 13-4 13-5 13-6 13-7

450

Dielectric Polarization 450 Oscillating Fields 452 Electromagnetic Waves in Solids 454 Reflectivity at an Interface 457 Kramers-Kronig Relations (S, A) 458 Damped Harmonic Oscillator 461 Dielectric Response of a Quantum System

PART В 13-8 13-9 13-10 13-11 13-12 13-13

MACROSCOPIC THEORY

LATTICE VIBRATIONS

464

465

Introduction 465 Long Wavelength Optical Vibrations 466 Measurements and Results 471 Polaritons (S) 476 A Microscopic Model (S) 480 Clausius-Mossotti (Lorenz-Lorentz) Equations (S)

484

CONTENTS

XIV

PART С 13-14 13-15 13-16 13-17

486

Introduction 486 Oscillator Model 487 Experimental Results 490 Transverse and Longitudinal Free Electron Modes (S) 495

PARTD 13-18 13-19 13-20 13-21 13-22

FREE CARRIER ABSORPTION

INTERBAND TRANSITIONS

498

Introduction 498 Fundamental Absorption Near £% 500 Excitons (Mostly Weakly Bound Excitons) Fundamental Absorption Above it 520 UrbachEdge(S) 521 Notes 524 Problems 526

509

and Structural Phase 14 Ferroelectricity Transitions 14-1 14-2 14-3 14-4 14-5 14-6 14-7

Introduction 531 The Free Energy 536 Soft Modes 542 Microscopic Model of Soft Modes 550 Renormalization Group 552 Optical Properties of Ferroelectrics (S) 554 Other Related Properties Notes 559 Problems 562

15 Magnetism PART A

DIAMAGNETISM AND PARAMAGNETISM

15-1 Introduction 565 15-2 Diamagnetism 567 15-3 Paramagnetism 569 PART В 15-4 15-5 15-6 15-7 15-8

FERROMAGNETISM, ANTIFERROMAGNETISM, AND RELATED TOPICS

Introduction 584 Molecular Field Theory 584 The Heisenberg Exchange Interaction 588 Magnetic Structures 590 Special Techniques Used to Study Magnetic Structures 596

584

565

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 16-2 16-3 16-4 16-5 16-6 16-7 16-8

Introduction (dc Conductivity) 633 The Occurrence of Superconductivity 634 Effects that Destroy Superconductivity 635 Magnetic Properties 637 The BCS Theory 642 BCS Predictions 648 BCS Related Measurements 653 The Josephson Effect 659 Notes 666 Problems 668

Surface Science 17-1 17-2 17-3 17-4 17-5 17-6 17-7

Introduction — The Need for UH V 674 Crystal Shape 675 Preparation of Clean Surfaces and LEED 677 The Structure of Surfaces 679 Interaction of Gases with Surfaces 686 Surface Related Techniques 692 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 18-8 18-9 18-10

Introduction 747 Sample Preparation 748 Properties of Layered Metal Structures 749 Other Artificial Structures (S) 752 Notes 753 Problems 755

Appendix

757

Appendix — Units Bibliography Index

800

796

792 ,