Survey
* Your assessment is very important for improving the work of artificial intelligence, which forms the content of this project
Download Introduction to Solid State Physics
Document related concepts
no text concepts found
Transcript
© 2008 AGI-Information Management Consultants May be used for personal purporses only or by libraries associated to dandelon.com network. Introduction to Solid State Physics EIGHTH EDITION Charles Kittel Professor Emeritus University of California, Berkeley Chapter 18, Nanostructures, was written by Professor Paul McEuen of Cornell University. John Wiley & Sons, Inc Contents C H A P T E R 1: CRYSTAL STRUCTURE 1 Periodic Array of Atoms Lattice Translation Vectors Basis and the Crystal Structure Primitive Lattice Cell 3 4 5 6 Fundamental Types of Lattices Two-Dimensional Lattice Types Three-Dimensional Lattice Types 6 8 9 Index Systems for Crystal Planes 11 Simple Crystal Structures Sodium Chloride Structure Cesium Chloride Structure Hexagonal Close-Packed Structure (hep) Diamond Structure Cubic Zinc Sulfide Structure 13 13 14 15 16 17 Direct Imaging of Atomic Structure 18 Nonideal Crystal Structures 18 Random Stacking and Polytypism 19 Crystal Structure Data 19 Summary 22 Problems 22 CHAPTER 2: WAVE DIFFRACTION AND THE RECIPROCAL LATTICE 23 Diffraction of Waves by Crystals Bragg Law 25 25 Scattered Wave Amplitude Fourier Analysis Reciprocal Lattice Vectors Diffraction Conditions Laue Equations 26 27 29 30 32 Brillouin Zones Reciprocal Lattice to sc Lattice Reciprocal Lattice to bec Lattice Reciprocal Lattice to fee Lattice 33 34 36 37 viii Fourier Analysis of the Basis Structure Factor of the bcc Lattice Structure factor of the fee Lattice Atomic Form Factor 39 40 40 41 Summary 43 Problems 43 CHAPTER 3: CRYSTAL RINDING AND ELASTIC CONSTANTS Crystals of Inert Gases 47 49 Van der Waals—London Interaction Repulsive Interaction Equilibrium Lattice Constants Cohesive Energy 53 56 58 59 Ionic Crystals Electrostatic or Madelung Energy Evaluation of the Madelung Constant 60 60 64 Covalent Crystals 67 Metals 69 Hydrogen Bonds 70 Atomic Radii Ionic Crystal Radii 70 72 Analysis of Elastic Strains Dilation Stress Components 73 75 75 Elastic Compliance and Stiffness Constants Elastic Energy Density Elastic Stiffness Constants of Cubic Crystals Bulk Modulus and Compressibility 77 77 78 80 Elastic Waves in Cubic Crstals Waves in the [100] Direction Waves in the [110] Direction 80 81 82 Summary 85 Problems 85 CHAPTER 4 : PHONONS I. CRYSTAL VIRRATIONS Vibrations of Crystals with Monatomic Basis First Brillouin Zone Group Velocity 89 91 93 94 Contents Long Wavelength Limit Derivation of Force Constants from Experiment 94 94 Two Atoms per Primitive Basis 95 Quantization of Elastic Waves 99 Phonon Momentum 100 Inelastic Scattering by Phonons 100 Summary 102 Problems 102 CHAPTER 5: PHONONS 11. THERMAL PROPERTIES Phonon Heat Capacity Planck Distribution Normal Mode Enumeration Density of States in One Dimension Density of States in Three Dimensions Debye Model for Density of States Debye T3 Law Einstein Model of the Density of States General Result for D(w) 105 107 107 108 108 111 112 114 114 117 Anharmonic Crystal Interactions Thermal Expansion 119 120 Thermal Conductivity Thermal Resistivity of Phonon Gas Umklapp Processes Imperfecions 121 123 125 126 Problems 128 CHAPTER 6: FREE ELECTRON FERMI GAS Energy Levels in One Dimension 131 134 Effect of Temperature on the FermiDirac Distribution 136 Free Electron Gas in Three Dimensions 137 Heat Capacity of the Electron Gas Experimental Heat Capacity of Metals Heavy Fermions Electrical Conductivity and Ohm's Law Experimental Electrical Resistivity of Metals Umklapp Scattering 141 145 147 147 148 151 Motion in Magnetic Fields Hall Effect 152 Thermal Conductivity of Metals Ratio of Thermal to Electrical Conductivity 156 Problems 157 CHAPTER 7: ENERGY RANDS 153 156 161 Nearly Free Electron Model Origin of the Energy Gap Magnitude of the Energy Gap 164 Bloch Functions 167 Kronig-Penney Model 168 Wave Equation of Electron in a Periodic Potential Restatement of the Bloch Theorem Crystal Momentum of an Electron Solution of the Central Equation Kronig-Penney Model in Reciprocal Space Empty Lattice Approximation Approximate Solution Near a Zone Boundary 165 167 169 173 173 174 174 176 177 Number of Orbitals in a Band Metals and Insulators 180 Summary 182 Problems 182 CHAPTER 8: SEMICONDUCTOR CRYSTALS 181 185 Band Gap 187 Equations of Motion Physical Derivation of hi. = F Holes Effective Mass Physical Interpretation of the Effective Mass Effective Masses in Semiconductors Silicon and Germanium 191 Intrinsic Carrier Concentration Intrinsic Mobility 205 Impurity Conductivity Donor States Acceptor States Thermal Ionization of Donors and Acceptors 209 193 194 197 198 200 202 208 209 211 213 Contents CHAPTER 9: Thermoelectric Effects 214 Semimetajs 215 Superlattices Bloch Oscillator Zener Tunneling 216 Summary 217 Problems 218 FERMI SURFACES AND METALS Reduced Zone Scheme Periodic Zone Scheme 217 217 221 223 225 Construction of Fermi Surfaces Nearly Free Electrons 226 Electron Orbits, Hole Orbits, and Open Orbits 230 Calculation of Energy Bands Tight Binding Method of Energy Bands Wigner-Seitz Method Cohesive Energy Pseudopotential Methods 232 Experimental Methods in Fermi Surface Studies Quantization of Orbits in a Magnetic Field De Haas-van Alphen Effect Extremal Orbits Fermi Surface of Copper Magnetic Breakdown 242 Summary 252 Problems 252 CHAPTER 10: SUPERCONDUCTIVITY 228 232 236 237 239 242 244 248 249 251 257 Experimental Survey Occurrence of Superconductivity Destruction of Superconductivity of Magnetic Fields Meissner Effect Heat Capacity Energy Gap Microwave and Infrared Properties Isotope Effect 259 Theoretical Survey Thermodynamics of the Superconducting Transition London Equation 270 260 262 262 264 266 268 269 270 273 Coherence Length BCS Theory of Superconductivity BCS Ground State Flux Quantization in a Superconducting Ring Duration of Persistent Currents Type II Superconductors Vortex State Estimation of Hcl and Hc2 Single Particle Tunneling Josephson Superconductor Tunneling Dc Josephson Effect Ac Josephson Effect Macroscopic Quantum Interference 276 277 278 279 282 283 284 284 287 289 289 290 292 High-Temperature Superconductors 293 Summary 294 Problems 294 Reference 296 CHAPTER 11: DIAMAGNETISM AND PARAMAGNETISM Langevin Diamagnetism Equation 297 299 Quantum Theory of Diamagnetism of Mononuclear Systems 301 Paramagnetism 302 Quantum Theory of Paramagnetism Rare Earth Ions Hund Rules Iron Group Ions Crystal Field Splitting Quenching of the Orbital Angular Momentum Spectroscopic Splitting Factor Van Vleck Temperature-Independent Paramagnetism Cooling by Isentropic Demagnetization Nuclear Demagnetization 302 305 306 307 307 308 311 311 312 314 Paramagnetic Susceptibility of Conduction Electrons 315 Summary 317 Problems 318 CHAPTER 12: FERROMAGNETISM AND ANTIFERROMAGNETISM Ferromagnetic Order Curie Point and the Exchange Integral 321 323 323 Contents Temperature Dependence of the Saturation Magnetization Saturation Magnetization at Absolute Zero 326 328 Magnons Quantization of Spin Waves Thermal Excitation of Magnons 330 333 334 Neutron Magnetic Scattering 335 Ferrimagnetic Order Curie Temperature and Susceptibility of Ferrimagnets Iron Garnets 336 Antiferromagnetic Order Susceptibility Below the Neel Temperature Antiferromagnetic Magnons 340 343 344 Ferromagnetic Domains Anisotropy Energy Transition Region between Domains Origin of Domains Coercivity and Hysteresis 346 348 349 351 352 Single Domain Particles Geomagnetism and Biomagnetism Magnetic Force Microscopy 354 355 355 Summary 356 Problems 357 CHAPTER 13: MAGNETIC RESONANCE 361 338 339 Nuclear Magnetic Resonance Equations of Motion 363 366 Line Width Motional Narrowing 370 371 Hyperfine Splitting Examples: Paramagnetic Point Defects F Centers in Alkali Halides Donor Atoms in Silicon Knight Shift 373 375 376 376 377 Nuclear Quadrupole Resonance 379 Ferromagnetic Resonance Shape Effects in FMR Spin Wave Resonance 379 380 382 Antiferromagnetic Resonance 383 Electron-Paramagnetic Resonance Exchange Narrowing Zero-field Splitting 386 Principle of Maser Action Three-Level Maser Lasers 386 Summary 390 Problems 391 CHAPTER 14: PLASMONS, POLARITONS, AND POLARONS 386 386 388 389 393 Dielectric Function of the Electron Gas Definitions of the Dielectric Function Plasma Optics Dispersion Relation for Electromagnetic Waves Transverse Optical Modes in a Plasma Transparency of Metals in the Ultraviolet Longitudinal Plasma Oscillations 395 Plasmons 401 Electrostatic Screening Screened Coulomb Potential Pseudopotential Component [7(0) Mott Metal-Insulator Transition Screening and Phonons in Metals 403 Polaritons LST Relation 410 Electron-Electron Interaction Fermi Liquid Electron-Electron Collisions All 417 417 Electron-Phonon Interaction: Polarons 420 395 396 397 398 398 398 406 407 407 409 414 Peierls Instability of Linear Metals Summary 422 Problems 424 OPTICAL PROCESSES AND EXCITONS Optical Reflectance Kramers-Kronig Relations Mathematical Note 424 427 429 430 432 Contents Example: Conductivity of collisionless Electron Gas Electronic Interband Transitions 433 434 Excitons Frenkel Excitons Alkali Halides Molecular Crystals Weakly Bound (Mott-Wannier) Excitons Exciton Condensation into Electron-Hole Drops (EHD) 435 Raman Effects in Crystals Electron Spectroscopy with X-Rays 444 Energy Loss of Fast Particles in a Solid 448 Summary 449 Problems 450 CHAPTER 16: DIELECTRICS AND FERROELECTRICS Maxwell Equations Polarization 437 440 440 441 441 447 453 455 455 Macroscopic Electric Field Depolarization Field, Ej 456 Local Electric Field at an Atom Lorentz Field, E2 Field of Dipoles Inside Cavity, E 3 460 Dielectric Constant and Polarizability Electronic Polarizability Classical Theory of Electronic Polarizability 463 Structural Phase Transitions 467 Ferroelectric Crystals Classification of Ferroelectric Crystals 467 Displacive Transitions Soft Optical Phonons Landau Theory of the Phase Transition Second-Order Transition First-Order Transition Antiferroelectricity Ferroelectric Domains Piezoelectricity 471 Summary 482 Problems 483 458 462 462 464 466 469 473 474 475 477 479 479 481 CHAPTER 17: SURFACE*AND INTERFACE PHYSICS Reconstruction and Relaxation 487 489 Surface Crystallography Reflection High-Energy Electron Diffraction 490 Surface Electronic Structure Work Function Thermionic Emission Surface States Tangential Surface Transport 494 494 495 495 497 Magnetoresistance in a Two-Dimensional Channel Integral Quantized Hall Effect (IQHE) IQHE in Real Systems Fractional Quantized Hall Effect (FQHE) 498 499 500 503 p-n Junctions Rectification Solar Cells and Photovoltaic Detectors Schottky Barrier 503 504 506 506 Heterostructures 507 493 n-N Heterojunction 508 Semiconductor Lasers 510 Light-Emitting Diodes 511 Problems 513 CHAPTER 18: NANOSTRUCTURES 515 Imaging Techniques for Nanostructures Electron Microscopy Optical Microscopy Scanning Tunneling Microscopy Atomic Force Microscopy 519 520 521 523 526 Electronic Structure of ID Systems One-Dimensional Subbands Spectroscopy oi Van Hove Singularities ID Metals — Coluomb Interactions and Lattice Copulings 528 528 529 Electrical Transport in I D Conductance Quantization and the Landauer Fonnula Two Barriers in Series-resonant Tunneling Incoherent Addition and Ohm's Law 533 531 533 536 538 Contents Localization Voltage Probes and the Buttiker-Landauer 539 Formalism 540 Electronic Structure of OD Systems Quantized Energy Levels Semiconductor Nanocrystals Metallic Dots Discrete Charge States Electrical Transport in OD Coulomb Oscillations Spin, Mott Insulators, and the Kondo Effect Cooper Pairing in Superconducting Dots 545 545 545 547 549 551 551 554 556 Vibrational and Thermal Properties of Nanostructures 557 Quantized Vibrational Modes Transverse Vibrations Heat Capacity and Thermal Transport 557 559 561 Summary Problems CHAPTER 19: NONCRYSTALLINE SOLIDS Diffraction Pattern Monatomic Amorphous Materials Radial Distribution Function Structure of Vitreous Silica, SiO2 Glasses Viscosity and the Hopping Rate Amorphous Ferromagnets Amorphous Semiconductors Low Energy Excitations in Amorphous Solids Heat Capacity Calculation Thermal Conductivity Fiber Optics Rayleigh Attenuation Problems 562 562 565 567 568 569 570 573 574 575 577 578 578 579 581 582 582 CHAPTER 20: POINT DEFECTS 583 Lattice Vacancies Diffusion 585 Metals 588 591 xvii xviii Color Centers F Centers Other Centers in Alkali Halides Problems CHAPTER 2 1 : DISLOCATIONS 592 592 593 595 597 Shear Strength of Single Crystals Slip 599 600 Dislocations Burgers Vectors Stress Fields of Dislocations Low-angle Grain Boundaries Dislocation Densities Dislocation Multiplication and Slip 601 604 605 607 610 611 Strength of Alloys 613 Dislocations and Crystal Growth Whiskers 615 616 Hardness of Materials 617 Problems 618 CHAPTER 22: ALLOYS 619 General Considerations 621 Substitutional Solid Solutions— Hume-Rothery Rules 624 Order-Disorder Transformation Elementary Theory of Order 627 629 Phase Diagrams Eutectics 632 632 Transition Metal Alloys 634 Electrical Conductivity 636 Kondo Effect 637 Problems 640 APPENDIX A: TEMPERATURE DEPENDENCE OF THE REFLECTION LINES 641 APPENDIX B: EWALD CALCULATION OF LATTICE SUMS 644 Ewald-Kornfeld Method for Lattice Sums for Dipole Arrays 647 Contents APPENDIX C: QUANTIZATION OF ELASTIC WAVES: PHONONS Phonon Coordinates Creation and Annihilation Operators 648 649 651 APPENDIX D: FERMI-DIRAC DISTRIBUTION FUNCTION 652 APPENDIX E: DERIVATION OF THE dk/dt EQUATION 655 APPENDIX F: BOLTZMANN TRANSPORT EQUATION 656 Particle Diffusion Classical Distribution Fermi-Dirac Distribution Electrical Conductivity APPENDIX G: 657 658 659 661 VECTOR POTENTIAL, FIELD MOMENTUM, AND GAUGE TRANSFORMATIONS Lagrangian Equations of Motion Derivation of the Hamiltonian Field Momentum Gauge Transformation Gauge in the London Equation 661 662 663 663 664 665 APPENDIX H: COOPER PAIRS 665 APPENDIX I: GINZBURG-LANDAU EQUATION 667 APPENDIX J: ELECTRON-PHONON COLLISIONS 671 INDEX 675
Related documents