SOLID STATE PHYSICS. Second Edition. John Wiley & Sons. J. R. Hook H. E. Hall. Department of Physics, University of Manchester

Size: px

Start display at page:

Download "SOLID STATE PHYSICS. Second Edition. John Wiley & Sons. J. R. Hook H. E. Hall. Department of Physics, University of Manchester"

Marylou Shanon Walsh
6 years ago
Views:

1 SOLID STATE PHYSICS Second Edition J. R. Hook H. E. Hall Department of Physics, University of Manchester John Wiley & Sons CHICHESTER NEW YORK BRISBANE TORONTO SINGAPORE

2 Contents Flow diagram Inside front cover Editor's preface to the Manchester Physics Series.. xv Foreword xvii Author's preface to second edition xix 1 CRYSTAL STRUCTURE Introduction Elementary Crystallography The crystal lattice Thebasis Crystal planes and directions Typical Crystal Structures Cubic and hexagonal close-packed structures The body-centred cubic structure Structures of ionic solids The diamond and zincblende structures X-ray Crystallography TheBragglaw Experimental arrangements for x-ray diffraction. 22 if Starred sections may be omitted as they are not required later in the book.

3 viii Contents jlrl.5 Quasi-crystals Interatomic Forces Van der Waals bonding Ionic bonding Covalent bonding Metallic bonding Hydrogen bonding Mixed bonding 31 PROBLEMS CRYSTAL DYNAMICS Introduction Sound Waves Lattice Vibrations of One-dimensional Crystals Chain of identical atoms Chain of two types of atom Lattice Vibrations of Three-dimensional Crystals Phonons Heat Capacity from Lattice Vibrations Energy and heat capacity of a harmonic oscillator The density of states The high- and low-temperature limits The Debye interpolation scheme Anharmonic Effects Thermal expansion Phonon-phonon collisions Thermal Conduction by Phonons Kinetic theory Conduction at high temperatures Conduction at intermediate temperatures Conduction at low temperatures PROBLEMS FREE ELECTRONS IN METALS Introduction The Free Electron Model Ground State of the free electron gas The free electron gas at finite temperature Heat capacity of the free electron gas Soft x-ray emission spectrum Metallic binding 85

4 Contents ix 3.3 Transport Properties of the Conduction Electrons The equation of motion of the electrons The electrical conductivity The thermal conductivity The Wiedemann-Franz law and the temperature dependence of the electrical and thermal conductivities The Hall effect 97 PROBLEMS THE EFFECT OF THE PERIODIC LATTICE POTENTIAL ENERGY BANDS Nearly Free Electron Theory Classification of Crystalline Solids into Metals, Insulators and Semiconductors The Tight Binding Approach Coupled probability amplitudes The H^" ion covalent bonding Electron states on a one-dimensional chain Electron states in diamond, Silicon and germanium Band Structure Effective Masses 124 PROBLEMS SEMICONDUCTORS Introduetion Holes Methods of Providing Electrons and Holes Donor and acceptor impurities Thermal excitation of carriers Intrinsic behaviour Extrinsic behaviour Absorption of Electromagnetic Radiation Transport Properties Electrical conductivity Hall effect Cyclotron resonance Non-equilibrium Carrier Densities The continuity equations Electrical neutrality Generation and recombination Injection of minority carriers at a steady rate Injection of a pulse of minority carriers PROBLEMS 5 168

5 x Contents 6 SEMICONDUCTOR DEVICES Introduction The p-n Junction with Zero Applied Bias The p-n Junction with an Applied Bias Other Devices Based on the p-n Junction Light emitting diodes and lasers Solar cells The junction transistor The junction-gatefield-effecttransistor Metal-oxide-semiconductor technology and the MOSFET Molecular Beam Epitaxy and Semiconductor Heterojunctions 192 PROBLEMS DIAMAGNETISM AND PARAMAGNETISM Introduction Paramagnetism The origin of permanent dipole moments The interaction of a permanent dipole moment with an applied magnetic field Calculation of the magnetization of paramagnetic ions Conduction electron paramagnetism Diamagnetism Momentum in a magnetic field Screening by induced currents Calculation of the diamagnetic susceptibility PROBLEMS MAGNETIC ORDER Introduction The Exchange Interaction Ferromagnetism The Weiss molecular field Calculation of ferromagnetic properties using the mean field theory The Neel Model of Antiferromagnetism SpinWaves Ferromagnets at low temperatures Spin waves in a one-dimensional crystal Magnetization and heat capacity at low temperatures 236 -jar8.5.4 Ferromagnetic resonance and the experimental Observation of spin waves 239

6 Contents xi ^ 8.6 Other Types of Magnetic Order Ferrimagnetism Spin density wave antiferromagnetism in chromium Magnetic ordering in rare-earth metals Ferromagnetic Domains The energy and thickness of a Bloch wall Why do domains occur? Magnetization curves of ferromagnets. 250 PROBLEMS ELECTRIC PROPERTIES OF INSULATORS Dielectrics Dielectric constant and susceptibility Polarization due to relative motion of electrons and nuclei Orientation of permanent dipole moments. 260 ^9.1.4 Dielectric constant and lattice vibrations of ionic crystals Pyroelectric Materials 271 ^ The Landau model Piezoelectricity 275 PROBLEMS SUPERCONDUCTIVITY Introduction Magnetic Properties of Superconductors Type I superconductors Thermodynamics of the superconducting transition Type II superconductors The London Equation The Theory of Superconductivity The energy gap and electron pairing frlo.4.2 The Cooper problem 292 "fcl0.4.3 Origin of the attractive interaction "fclo.4.4 Nature of the superconducting ground State Explanation of infinite conductivity Macroscopic Quantum Phenomena The superconducting order parameter Flux quantization Quantized flux lines and type II superconductivity Josephson effects 304 -fc Quantum interference High-temperature Superconductors 310 PROBLEMS

7 xii Contents 11 WAVES IN CRYSTALS Introduction Elastic Scattering of Waves by a Crystal Amplitude of the scattered wave Laue conditions for diffraction and the reciprocal lattice Examples of reciprocal lattices The structure factor Wavelike Normal Modes Bloch's Theorem Normal Modes and the Reciprocal Lattice Periodicity of the dispersion relation Brillouin zones and the plotting of dispersion relations 333 PROBLEMS SCATTERING OF NEUTRONS AND ELECTRONS FROM SOLIDS Introduction Comparison of X-rays, Neutrons and Electrons Interaction of x-rays, neutrons and electrons with atoms Inelastic scattering Neutron Scattering Techniques Neutron sources Neutron detectors Time-of-flight methods Crystal monochromators Determination of Phonon Spectra Magnetic Scattering Determination of magnetic structure Determination of magnon spectra Electron Scattering.... PROBLEMS REAL METALS Introduction Fermi Surfaces Fermi surface of a nearly free electron two-dimensional metal Fermi surface of three-dimensional metals Density of states at the Fermi surface. 366

8 Contents xiii 13.3 Electron Dynamics in a Three-dimensional Metal Equation of motion and effective mass ^ Relation of the electrical conductivity to the Fermi surface Experimental Determination of the Fermi Surface Cyclotron orbits Cyclotron resonance in metals Quantization of cyclotron orbits The de Haas-van Alphen effect Why do Electrons Behave Independently? Electrical neutrality in metals Plasma oscillations Screening The exclusion principle and scattering ^ Fermi liquid effects The Mott transition Electromagnetic Waves in Metals PROBLEMS LOW-DIMENSIONAL SYSTEMS Introduction The Two-dimensional Electron Gas The electron states Density of states of the two-dimensional electron gas The Quantum Hall Effect Resonant Tunnelling Devices 412 PROBLEMS APPENDIX A Coupled probability amplitudes 417 APPENDIX B Electric and magnetic fields inside materials APPENDIX C Quantum mechanics of an electron in a magnetic field. 430 APPENDIX D The exchange energy 432

9 xiv Contents Bibliography 435 Solutions to problems Index 464 Table of constants.. Inside back cover

Harald Ibach Hans Lüth SOLID-STATE PHYSICS. An Introduction to Theory and Experiment

Harald Ibach Hans Lüth SOLID-STATE PHYSICS An Introduction to Theory and Experiment With 230 Figures Springer-Verlag Berlin Heidelberg New York London Paris Tokyo Hong Kong Barcelona Budapest Contents