Gerald Burns Solid State Physics

Solid State Physics

Gerald Burns

Yorktown Heights, New York

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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.

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

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

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

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

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

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