Introduction to Solid State Physics

Charles Kittel did his undergraduate work in physics at M.I.T and at the Cavendish Laboratory of Cambridge University. He received his Ph.D. from the University of Wisconsin. He worked in the solid state group at Bell Laboratories, along with Bardeen and Shockley, leaving to start the theoretical solid state physics group at Berkeley in 1951. His research has been largely in magnetism and in semiconductors. In magnetism he developed the theories of ferromagnetic and antiferromagnetic resonance and the theory of single ferromagnetic domains, and extended the Bloch theory of magnons. In semiconductor physics he participated in the first cyclotron and plasma resonance experiments and extended the results to the theory of impurity states and to electron-hole drops.He has been awarded three Guggenheim fellowships, the Oliver Buckley Prize for Solid State Physics, and, for contributions to teaching, the Oersted Medal of the American Association of Physics Teachers, He is a member of the National Academy of Science and of the American Academy of Arts and Sciences.

• Chapter 1: Crystal Structure 1Periodic Array of Atoms 3Lattice Translation Vectors 4Basis and the Crystal Structure 5Primitive Lattice Cell 6Fundamental Types of Lattices 6Two-Dimensional Lattice Types 8Three-Dimensional Lattice Types 9Index Systems for Crystal Planes 11Simple Crystal Structures 13Sodium Chloride Structure 13Cesium Chloride Structure 14Hexagonal Close-Packed Structure (hcp) 15Diamond Structure 16Cubic Zinc Sulfide Structure 17Direct Imaging of Atomic Structure 18Nonideal Crystal Structures 18Random Stacking and Polytypism 19Crystal Structure Data 19Summary 22Problems 22Chapter 2: Wave Diffraction and the Reciprocal Lattice 23Diffraction of Waves by Crystals 25Bragg Law 25Scattered Wave Amplitude 26Fourier Analysis 27Reciprocal Lattice Vectors 29Diffraction Conditions 30Laue Equations 32Brillouin Zones 33Reciprocal Lattice to sc Lattice 34Reciprocal Lattice to bcc Lattice 36Reciprocal Lattice to fcc Lattice 37Fourier Analysis of the Basis 39Structure Factor of the bcc Lattice 40Structure factor of the fcc Lattice 40Atomic Form Factor 41Summary 43Problems 43Chapter 3: Crystal Binding and Elastic Constants 47Crystals of Inert Gases 49Van der Waals—London Interaction 53Repulsive Interaction 56Equilibrium Lattice Constants 58Cohesive Energy 59Ionic Crystals 60Electrostatic or Madelung Energy 60Evaluation of the Madelung Constant 64Covalent Crystals 67Metals 69Hydrogen Bonds 70Atomic Radii 70Ionic Crystal Radii 72Analysis of Elastic Strains 73Dilation 75Stress Components 75Elastic Compliance and Stiffness Constants 77Elastic Energy Density 77Elastic Stiffness Constants of Cubic Crystals 78Bulk Modulus and Compressibility 80Elastic Waves in Cubic Crstals 80Waves in the [100] Direction 81Waves in the [110] Direction 82Summary 85Problems 85Chapter 4: Phonons I. Crystal Vibrations 89Vibrations of Crystals with Monatomic Basis 91First Brillouin Zone 93Group Velocity 94Long Wavelength Limit 94Derivation of Force Constants from Experiment 94Two Atoms per Primitive Basis 95Quantization of Elastic Waves 99Phonon Momentum 100Inelastic Scattering by Phonons 100Summary 102Problems 102Chapter 5: Phonons 11. Thermal Properties 105Phonon Heat Capacity 107Planck Distribution 107Normal Mode Enumeration 108Density of States in One Dimension 108Density of States in Three Dimensions 111Debye Model for Density of States 112Debye T3Law 114Einstein Model of the Density of States 114General Result for D(w) 117Anharmonic Crystal Interactions 119Thermal Expansion 120Thermal Conductivity 121Thermal Resistivity of Phonon Gas 123Umklapp Processes 125Imperfecions 126Problems 128Chapter 6: Free Electron Fermi Gas 131Energy Levels in One Dimension 134Effect of Temperature on the Fermi-Dirac Distribution 136Free Electron Gas in Three Dimensions 137Heat Capacity of the Electron Gas 141Experimental Heat Capacity of Metals 145Heavy Fermions 147Electrical Conductivity and Ohm’s Law 147Experimental Electrical Resistivity of Metals 148Umklapp Scattering 151Motion in Magnetic Fields 152Hall Effect 153Thermal Conductivity of Metals 156Ratio of Thermal to Electrical Conductivity 156Problems 157Chapter 7: Energy Bands 161Nearly Free Electron Model 164Origin of the Energy Gap 165Magnitude of the Energy Gap 167Bloch Functions 167Kronig-Penney Model 168Wave Equation of Electron in a Periodic Potential 169Restatement of the Bloch Theorem 173Crystal Momentum of an Electron 173Solution of the Central Equation 174Kronig-Penney Model in Reciprocal Space 174Empty Lattice Approximation 176Approximate Solution Near a Zone Boundary 177Number of Orbitals in a Band 180Metals and Insulators 181Summary 182Problems 182Chapter 8: Semiconductor Crystals 185Band Gap 187Equations of Motion 191Physical Derivation of ©¤k̇ = F 193Holes 194Effective Mass 197Physical Interpretation of the Effective Mass 198Effective Masses in Semiconductors 200Silicon and Germanium 202Intrinsic Carrier Concentration 205Intrinsic Mobility 208Impurity Conductivity 209Donor States 209Acceptor States 211Thermal Ionization of Donors and Acceptors 213Thermoelectric Effects 214Semimetals 215Superlattices 216Bloch Oscillator 217Zener Tunneling 217Summary 217Problems 218Chapter 9: Fermi Surfaces and Metals 221Reduced Zone Scheme 223Periodic Zone Scheme 225Construction of Fermi Surfaces 226Nearly Free Electrons 228Electron Orbits, Hole Orbits, and Open Orbits 230Calculation of Energy Bands 232Tight Binding Method of Energy Bands 232Wigner-Seitz Method 236Cohesive Energy 237Pseudopotential Methods 239Experimental Methods in Fermi Surface Studies 242Quantization of Orbits in a Magnetic Field 242De Haas-van Alphen Effect 244Extremal Orbits 248Fermi Surface of Copper 249Magnetic Breakdown 251Summary 252Problems 252Chapter 10: Superconductivity 257Experimental Survey 259Occurrence of Superconductivity 260Destruction of Superconductivity of Magnetic Fields 262Meissner Effect 262Heat Capacity 264Energy Gap 266Microwave and Infrared Properties 268Isotope Effect 269Theoretical Survey 270Thermodynamics of the Superconducting Transition 270London Equation 273Coherence Length 276BCS Theory of Superconductivity 277BCS Ground State 278Flux Quantization in a Superconducting Ring 279Duration of Persistent Currents 282Type II Superconductors 283Vortex State 284Estimation of Hc1and Hc2 284Single Particle Tunneling 287Josephson Superconductor Tunneling 289Dc Josephson Effect 289Ac Josephson Effect 290Macroscopic Quantum Interference 292High-Temperature Superconductors 293Summary 294Problems 294Reference 296Chapter 11: Diamagnetism and Paramagnetism 297Langevin Diamagnetism Equation 299Quantum Theory of Diamagnetism ofMononuclear Systems 301Paramagnetism 302Quantum Theory of Paramagnetism 302Rare Earth Ions 305Hund Rules 306Iron Group Ions 307Crystal Field Splitting 307Quenching of the Orbital Angular Momentum 308Spectroscopic Splitting Factor 311Van Vleck Temperature-Independent Paramagnetism 311Cooling by Isentropic Demagnetization 312Nuclear Demagnetization 314Paramagnetic Susceptibility of Conduction Electrons 315Summary 317Problems 318Chapter 12: Ferromagnetism and Antiferromagnetism 321Ferromagnetic Order 323Curie Point and the Exchange Integral 323Temperature Dependence of the Saturation Magnetization 326Saturation Magnetization at Absolute Zero 328Magnons 330Quantization of Spin Waves 333Thermal Excitation of Magnons 334Neutron Magnetic Scattering 335Ferrimagnetic Order 336Curie Temperature and Susceptibility of Ferrimagnets 338Iron Garnets 339Antiferromagnetic Order 340Susceptibility Below the Néel Temperature 343Antiferromagnetic Magnons 344Ferromagnetic Domains 346Anisotropy Energy 348Transition Region between Domains 349Origin of Domains 351Coercivity and Hysteresis 352Single Domain Particles 354Geomagnetism and Biomagnetism 355Magnetic Force Microscopy 355Summary 356Problems 357Chapter 13: Magnetic Resonance 361Nuclear Magnetic Resonance 363Equations of Motion 366Line Width 370Motional Narrowing 371Hyperfine Splitting 373Examples: Paramagnetic Point Defects 375F Centers in Alkali Halides 376Donor Atoms in Silicon 376Knight Shift 377Nuclear Quadrupole Resonance 379Ferromagnetic Resonance 379Shape Effects in FMR 380Spin Wave Resonance 382Antiferromagnetic Resonance 383Electron Paramagnetic Resonance 386Exchange Narrowing 386Zero-field Splitting 386Principle of Maser Action 386Three-Level Maser 388Lasers 389Summary 390Problems 391Chapter 14: Plasmons, Polaritons, and Polarons 393Dielectric Function of the Electron Gas 395Definitions of the Dielectric Function 395Plasma Optics 396Dispersion Relation for Electromagnetic Waves 397Transverse Optical Modes in a Plasma 398Transparency of Metals in the Ultraviolet 398Longitudinal Plasma Oscillations 398Plasmons 401Electrostatic Screening 403Screened Coulomb Potential 406Pseudopotential Component U(0) 407Mott Metal-Insulator Transition 407Screening and Phonons in Metals 409Polaritons 410LST Relation 414Electron-Electron Interaction 417Fermi Liquid 417Electron-Electron Collisions 417Electron-Phonon Interaction: Polarons 420Peierls Instability of Linear Metals 422Summary 424Problems 424Chapter 15: Optical Processes and Excitons 427Optical Reflectance 429Kramers-Kronig Relations 430Mathematical Note 432Example: Conductivity of collisionless Electron Gas 433Electronic Interband Transitions 434Excitons 435Frenkel Excitons 437Alkali Halides 440Molecular Crystals 440Weakly Bound (Mott-Wannier) Excitons 441Exciton Condensation into Electron-Hole Drops (EHD) 441Raman Effects in Crystals 444Electron Spectroscopy with X-Rays 447Energy Loss of Fast Particles in a Solid 448Summary 449Problems 450Chapter 16: Dielectrics And Ferroelectrics 453Maxwell Equations 455Polarization 455Macroscopic Electric Field 456Depolarization Field, E1 458Local Electric Field at an Atom 460Lorentz Field, E2 462Field of Dipoles Inside Cavity, E3 462Dielectric Constant and Polarizability 463Electronic Polarizability 464Classical Theory of Electronic Polarizability 466Structural Phase Transitions 467Ferroelectric Crystals 467Classification of Ferroelectric Crystals 469Displacive Transitions 471Soft Optical Phonons 473Landau Theory of the Phase Transition 474Second-Order Transition 475First-Order Transition 477Antiferroelectricity 479Ferroelectric Domains 479Piezoelectricity 481Summary 482Problems 483Chapter 17: Surface and Interface Physics 487Reconstruction and Relaxation 489Surface Crystallography 490Reflection High-Energy Electron Diffraction 493Surface Electronic Structure 494Work Function 494Thermionic Emission 495Surface States 495Tangential Surface Transport 497Magnetoresistance in a Two-Dimensional Channel 498Integral Quantized Hall Effect (IQHE) 499IQHE in Real Systems 500Fractional Quantized Hall Effect (FQHE) 503p-n Junctions 503Rectification 504Solar Cells and Photovoltaic Detectors 506Schottky Barrier 506Heterostructures 507n-N Heterojunction 508Semiconductor Lasers 510Light-Emitting Diodes 511Problems 513Chapter 18: Nanostructures 515Imaging Techniques for Nanostructures 519Electron Microscopy 520Optical Microscopy 521Scanning Tunneling Microscopy 523Atomic Force Microscopy 526Electronic Structure of 1D Systems 528One-Dimensional Subbands 528Spectroscopy of Van Hove Singularities 5291D Metals — Coluomb Interactions and Lattice Copulings 531Electrical Transport in 1D 533Conductance Quantization and the Landauer Formula 533Two Barriers in Series-resonant Tunneling 536Incoherent Addition and Ohm’s Law 538Localization 539Voltage Probes and the Buttiker-LandauerFormalism 540Electronic Structure of 0D Systems 545Quantized Energy Levels 545Semiconductor Nanocrystals 545Metallic Dots 547Discrete Charge States 549Electrical Transport in 0D 551Coulomb Oscillations 551Spin, Mott Insulators, and the Kondo Effect 554Cooper Pairing in Superconducting Dots 556Vibrational and Thermal Properties of Nanostructures 557Quantized Vibrational Modes 557Transverse Vibrations 559Heat Capacity and Thermal Transport 561Summary 562Problems 562Chapter 19: Noncrystalline Solids 565Diffraction Pattern 567Monatomic Amorphous Materials 568Radial Distribution Function 569Structure of Vitreous Silica, SiO2 570Glasses 573Viscosity and the Hopping Rate 574Amorphous Ferromagnets 575Amorphous Semiconductors 577Low Energy Excitations in Amorphous Solids 578Heat Capacity Calculation 578Thermal Conductivity 579Fiber Optics 581Rayleigh Attenuation 582Problems 582Chapter 20: Point Defects 583Lattice Vacancies 585Diffusion 588Metals 591Color Centers 592F Centers 592Other Centers in Alkali Halides 593Problems 595Chapter 21: Dislocations 597Shear Strength of Single Crystals 599Slip 600Dislocations 601Burgers Vectors 604Stress Fields of Dislocations 605Low-angle Grain Boundaries 607Dislocation Densities 610Dislocation Multiplication and Slip 611Strength of Alloys 613Dislocations and Crystal Growth 615Whiskers 616Hardness of Materials 617Problems 618Chapter 22: Alloys 619General Considerations 621Substitutional Solid Solutions—Hume-Rothery Rules 624Order-Disorder Transformation 627Elementary Theory of Order 629Phase Diagrams 632Eutectics 632Transition Metal Alloys 634Electrical Conductivity 636Kondo Effect 637Problems 640Appendix A: Temperature Dependence of the Reflection Lines 641Appendix B: Ewald Calculation of Lattice Sums 644Ewald-Kornfeld Method for Lattice Sums for Dipole Arrays 647Appendix C: Quantization of Elastic Waves: Phonons 648Phonon Coordinates 649Creation and Annihilation Operators 651Appendix D: Fermi-Dirac Distribution Function 652Appendix E: Derivation of the dk/dt Equation 655Appendix F: Boltzmann Transport Equation 656Particle Diffusion 657Classical Distribution 658Fermi-Dirac Distribution 659Electrical Conductivity 661Appendix G: Vector Potential, Field Momentum, and Gauge Transformations 661Lagrangian Equations of Motion 662Derivation of the Hamiltonian 663Field Momentum 663Gauge Transformation 664Gauge in the London Equation 665Appendix H: Cooper Pairs 665Appendix I: Ginzburg-Landau Equation 667Appendix J: Electron-Phonon Collisions 671Index 675