The Oxford Solid State Basics

Transcription

1 The Oxford Solid State Basics Steven H. Simon University of Oxford OXFORD UNIVERSITY PRESS

2 Contents 1 About Condensed Matter Physics What Is Condensed Matter Physics Why Do We Study Condensed Matter Physics? Why Solid State Physics? 3 1 Physics of Solids without Considering Micro scopic Structure: The Early Days of Solid State 5 2 Specific Heat of Solids: Boltzmann, Einstein, and Debye Einstein's Calculation Debye's Calculation Periodic (Born-von Karman) Boundary Conditions Debye's Calculation Following Planck Debye's "Interpolation" Some Shortcomings of the Debye Theory Appendix to this Chapter: (4) 16 Exercises 17 3 Electrons in Metals: Drude Theory Electrons in Fields Electrons in an Electric Field Electrons in Electric and Magnetic Fields Thermal Transport 22 Exercises 25 4 More Electrons in Metals: Sommerfeld (Free Electron) Theory Basic Fermi-Dirac Statistics Electronic Heat Capacity Magnetic Spin Susceptibility (Pauli Paramagnetism) Why Drude Theory Works So Well Shortcomings of the Free Electron Model 35 Exercises 37 II Structure of Materials 39 5 The Periodic Table 41

3 x Contents 5.1 Chemistry, Atoms, and the Schroedinger Equation Structure of the Periodic Table Periodic Trends Effective Nuclear Charge 45 Exercises 46 6 What Holds Solids Together: Chemical Bonding Ionic Bonds Covalent Bond Particle in a Box Picture Molecular Orbital or Tight Binding Theory Van der Waals, Fluctuating Dipole Forces, or Molecular Bonding Metallic Bonding Hydrogen Bonds 59 Exercises 61 7 Types of Matter 65 III Toy Models of Solids in One Dimension 69 8 One-Dimensional Model of Compressibility, Sound, and Thermal Expansion 71 Exercises 74 9 Vibrations of a One-Dimensional Monatomic Chain First Exposure to the Reciprocal Lattice Properties of the Dispersion of the One-Dimensional Chain Quantum Modes: Phonons Crystal Momentum 84 Exercises Vibrations of a One-Dimensional Diatomic Chain Diatomic Crystal Structure: Some Useful Definitions Normal Modes of the Diatomic Solid 90 Exercises Tight Binding Chain (Interlude and Preview) Tight Binding Model in One Dimension Solution of the Tight Binding Chain Introduction to Electrons Filling Bands Multiple Bands 105 Exercises 107 IV Geometry of Solids Crystal Structure 113

4 Contents xi 12.1 Lattices and Unit Cells Lattices in Three Dimensions The Body-Centered Cubic (bcc) Lattice The Face-Centered Cubic (fee) Lattice Sphere Packing Other Lattices in Three Dimensions Some Real Crystals 123 Exercises Reciprocal Lattice, Brillouin Zone, Waves in Crystals The Reciprocal Lattice in Three Dimensions Review of One Dimension Reciprocal Lattice Definition The Reciprocal Lattice as a Fourier Transform Reciprocal Lattice Points as Families of Lattice Planes Lattice Planes and Miller Indices Brillouin Zones Review of One-Dimensional Dispersions and Brillouin Zones General Brillouin Zone Construction Electronic and Vibrational Waves in Crystals in Three Dimensions 136 Exercises 137 V Neutron and X-Ray Diffraction Wave Scattering by Crystals The Laue and Bragg Conditions Fermi's Golden Rule Approach Diffraction Approach Equivalence of Laue and Bragg conditions Scattering Amplitudes Simple Example Systematic Absences and More Examples Geometric Interpretation of Selection Rules Methods of Scattering Experiments Advanced Methods Powder Diffraction Still More About Scattering Scattering in Liquids and Amorphous Solids Variant: Inelastic Scattering Experimental Apparatus 157 Exercises 159

5 xii Contents VI Electrons in Solids Electrons in a Periodic Potential Nearly Free Electron Model Degenerate Perturbation Theory Bloch's Theorem 169 Exercises Insulator, Semiconductor, or Metal Energy Bands in One Dimension Energy Bands in Two and Three Dimensions Tight Binding Failures of the Band-Structure Picture of Metals and Insulators Band Structure and Optical Properties Optical Properties of Insulators and Semiconductors Direct and Indirect Transitions Optical Properties of Metals Optical Effects of Impurities 181 Exercises Semiconductor Physics Electrons and Holes Drude Transport: Redux Adding Electrons or Holes with Impurities: Doping Impurity States Statistical Mechanics of Semiconductors 191 Exercises Semiconductor Devices Band Structure Engineering Designing Band Gaps Non-Homogeneous Band Gaps p-n Junction The Transistor 203 Exercises 205 VII Magnetism and Mean Field Theories Magnetic Properties of Atoms: Para- and Dia-Magnetism Basic Definitions of Types of Magnetism Atomic Physics: Hund's Rules Why Moments Align Coupling of Electrons in Atoms to an External Field Free Spin (Curie or Langevin) Paramagnetism Larmor Diamagnetism 217

6 Contents xiii 19.6 Atoms in Solids Pauli Paramagnetism in Metals Diamagnetism in Solids Curie Paramagnetism in Solids 220 Exercises Spontaneous Magnetic Order: Ferro-, Antiferro-, and Ferri-Magnetism (Spontaneous) Magnetic Order Ferromagnets Antiferromagnets Ferrimagnets Breaking Symmetry Ising Model 228 Exercises Domains and Hysteresis Macroscopic Effects in Ferromagnets: Domains Domain Wall Structure and the Bloch/Neel Wall Hysteresis in Ferromagnets Disorder Pinning Single-Domain Crystallites Domain Pinning and Hysteresis 238 Exercises Mean Field Theory Mean Field Equations for the Ferromagnetic Ising Model Solution of Self-Consistency Equation Paramagnetic Susceptibility Further Thoughts 247 Exercises Magnetism from Interactions: The Hubbard Model Itinerant Ferromagnetism Hubbard Ferromagnetism Mean Field Theory Stoner Criterion Mott Antiferromagnetism Appendix: Hubbard Model for the Hydrogen Molecule 257 Exercises 259 A Sample Exam and Solutions 261 B List of Other Good Books 275 Indices 279 Index of People 280 Index of Topics 283