Charles kittel introduction to solid state physics wiley (2005)

ir "7 lnfroduction to Y - t;' L EIGHTH EDlTlGlv - d' - > Solid State Physics - '- t - - CHARLES KITTEL n - Name Actinium Aluminum Americium Antimony Argon Arsenic Astatine Barium Berkelium Beryllium Bismuth Boron Bromine Cadmium Calcium Californium Carbon Cerium Cesium Chlorine Chromium Cobalt Capper Curium Dysprosium Einsteinium Erbium Europium Fermium Fluorine Francium Gadolinium Gallium Germanium Gold Symbol Name Hafnium Helium Holmium Hydrogen Indium Iodine Iridium Iron Krypton Lanthanum Lawrencium Lead Lithium Lutetium Magnesium Manganese Mendelevium Mercury Molybdenum Neodymium Neon Neptunium Nickel Niobium Nitrogen Nobelium Osmium Oxygen Palladium Phosphorus Platinum Plutonium Poloni~~m Potassium Symbol Name Praseodymium Promethium Protactinium Radium Radon Rhenium Rhodium Rubidium Ruthenium Samarium Scandium Selenium Silicon Silver Sodium Strontium Sulfur Tantalum Technetium Tellurium Terbium Thallium Thorium Thulium Tin Titanium Tungsten Uranium Vanadium Xenon Ytterbium Yttrium Zinc Zirconium Symbol H' Periodic Table, with the Outer Electron Configurations of Neutral Atoms in Their Ground States Is Li:, Be' 2y "' ~ ~ ~ T h e notation used to descrilx the electronic configuratior~of atoms ;nrd ions is discussed in all textl,nokc uf introdoctory atomic physics The letters s, p , d, signifj flectrorrs having nrlrital angular tnomentum 0, , 2, in units fi; the rruml,er to the left of the 3s 3s' K'Y cato sex OX Nel0 FY Zs22p ~ ~ 25122~1 ~ ' 2~~211' 2sZ2pi 2*'2p0 letter $i dcwotrs the principal quantum nurnl~erof o n e c~rl)it, and the ~ superscript to the right denotes the nrlrnher of electn)rrs in the r~rl)it > ~ N' 8"' PI-S'~ sit4 A ~ ~ X cln7 3s23p 3s23pZ3s23p:' 3s*3p4 3s13pi 3S23p6 ~i'z Co" ~ ' $ Ni*" Cu'Y Zn:" Ga3' Ger' As33 Se71 Br3"r3@ XeS4 4d Ss 7s \ 5s' ssz 7S2 6d 7s2 s , 4d2 5sZ 4d4 58 4d5 5s 4d6 5s 4d7 5~ 4dX 5s 4dIU 4dn1' 4dlU 5s 5sZ 5s25p 5S'5p2 5s25p75s25p' 5Y'5p5 5s25p6 - CeSX prSY Nd6O Pm61 SmlZ EUI? Gd61 Tb6i DYC6 HOIl 6168 Tm69 YblD LUIl 4f2 4f4 4f5 4f' 4fX 5d 6sZ 4f1° 4fl3 4f13 4f14 6sZ 6y2 Cs2 4f14 5d 6s1 Bk91 Cf98 E9.9 FmlOO MdlOl N08.2 4f3 4f6 6s' 6s' 6s2 4f 5d 63% NPII pU94 Am95 Cm96 7sZ Sf' 6d 7S1 4fI2 -X 6x2 6s' ThW Pa81 "82 6d2 7sZ Sf2 6d 7s2 - sf" Sf"f6 6d 7sZ 7s2 7s2 sf' 6s2 6s2 Lr'Yi B! t I - - Introduction to EIGHTH EDITION Charles Kittel Pr($essor Enwritus L'nitiersity of Cal$c~nlia,Berkeley Chapter 18, Nanostructures, was written by Professor Paul McEuen of Cornell University John Wiley & Sons, Inc EXECUTIVE EDITOR Stuart Johnson SENIOR PRODUCTION EDITOR Patricia McFadden SENIOR MARKETING MANAGER DESIGN DIRECTOR Robert Smith Madclyn Lesure SENIOR MEDIA EDITOR Martin Batey PRODUCTION MANAGEMENT Suzanne Ingrao/lngrao Associates This book was set in 10112 New Caledonia by GGS Books Services, Atlantic Highlands and printrd and bound by hfalloy Litt~ugraphing.Tlt: cover was printed by Phoenix Color This book is printed on acid free paper a, Copyright 62 2005 John Wiley & Sons, Inc All rights reserved No part of this publication may be reproduced, stored in a retrieval system or transmitted in any fonn or hy any means, electronic, mechanical, photucopying, recording, scanning or otbenvise, execpt as permitted under Sections 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Publisher or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, Inc 222 Rosewood Drive Danvers, MA 01993, (97R)i50-8400.fax (978)646-8600.Requests to the Publisher for permission should be addressed to thc Permissions Department, John Wiley & Sons, Inc., 111 River Street, Hobaken, NJ 07030-5774, (201)748-6011,fax (201)748-6008 To order books or for customer service please, call 1-800~CALL WILEY (225-5945) Library ojCongress Cataloging in Publication Data: Kittcl, Charles Introduction to solid state physics Charles Kitte1.-8th p cm ISBN 0-471-41526-X Solid state physics 1, Title ~ K 2005 5304+>dc22 ISBNV-471-41526-X WIE ISBN 0-471-68057-5 Printed in the United States of America cd About the Author Charles Kittel did his undergraduate work in physics at M.1.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 Preface This book is the eighth edition of an elementary text on solid state/ condensed matter physics fur seniors and beginning grad~ratestudents of the physical sciences, chemistry, and engineering In the years since the first edition was pnhlished the field has devcloped \,igoronsly, and there are notable applications The challenge to the author has been to treat significant new areas while maintaining the introductory level of the text It would be a pity to present such a physical, tactile field as an exercise in formalism At the first editic~nin 1953 superconductivity was not lmderstood; Fermi snrfaces in metals were beginning to he explored and cyclotron resonance in semiconductors had just been observed; ferrites and permanent magnets were beginning to be understood; only a few physicists then believed in the reality of spin waves Nanophysics was forty years off In other fields, the structure of DNA was determined and the drift of continents on the Earth was demonstrated It was a great time to be in Science, as it is now I have tried with the successivt: editions of lSSY to introduce new generations to the same excitement There are several changes from the seventh edition, as well as rnucll clarification: An important chapter has been added on nanophysics, contributed by an active worker in the field, Professor Paul L McEuen of Cornell University Nanophysics is the science of materials with one, two, or three small dimensions, where "small" means (nanometer 10-%m) This field is the most exciting and vigorous addition to solid state science in the last ten years The text makes use of the simplificati(~nsmade possible hy the nniversal availability of computers Bibliographies and references have been nearly eliminated because simple computer searches using keywords on a search engine slreh as Google will quickly generate many useful and rnore recent references As an cxamplc of what can ho dons on the Web, explore the entry http://\mw.physicsweb.org'hestof/cond-mat No lack of honor is intended by the omissions of early or traditiorral references to the workers who first worked on the problems of the solid state The order nf the chapters has been changed: superconducti\ity and magnetism appear earlier, thereby making it easier to arrange an interesting one-semester course The crystallographic notation conforms with current usage in physics Important equations in the body of the text are repeated in SI and CGS-Gaussian units, where these differ, except where a single indicated substitution will translate frnm CGS to SI The dual usage in this book has been found helpful and acceptable Tables arc in conventional units The symbol e denotes the charge on the proton and is positive The notation (18) refers to Equation 18 of the current chapter, but (3.18)refers to Equation 18 of Chapter A caret (^) over a vector denotes a nnit vector Few of the problems are exactly easy: Most were devised to carry forward the subject of the chapter With few exceptions, the problems are those of the original sixth and seventh editions The notation QTS refers to my Quantum Theory of Solirls, with solutions by C Y Fong; TP refers to Thermal Physics, with H Kroemer This edition owes much to detailed reviews of the entire text by Professor Paul L McEuen of Cornell University and Professor Roger Lewis of Wollongong University in Australia They helped make the book much easier to read and understand However, I must assume responsibility for the close relation of the text to the earlier editions, Many credits for suggestions, reviews, and photographs are given in the prefaces to earlier editions I have a great debt to Stuart Johnson, my publisher at Wiley; Suzanne Ingrao, my editor; and Barbara Bell, my personal assistant Corrections and suggestions will be gratefully received and may be addressed to the author by rmail to kittelQberke1ey.edu The Instructor's Manual is available for download at: \m.wiley.coml collegelkittel Charles Kittel Contents E CHAPTER 1: CRYSTAL STRUCTURE Periodic Array of Atoms Lattice Translation Vectors Basis and the Crystal S t ~ c t u r e Primitive Lattice Cell Fundamental Types of Lattices Two-Dimensional Lattice Types Three-Dimensional Lattice Types Index Systems for Crystal Planes Simple Crystal Structures Sodium Chloride Structure Cesium Chloride Structure Hexagonal Close-Packed Structure (hcp) Diamond Structure Cubic Zinc Sulfide Structure Direct Imaging of Atomic Structure Nonideal Crystal Structures Random Stacldng and Polytypism Crystal Structure Data Summary Problems CHAPTER 2: WAVE DIFFRACTION AND THE RECIPROCAL LATTICE Diffraction of Waves by Crystals Bragg Law Scattered Wave Amplitude Fourier Analysis Reciprocal Lattice Vectors Diffraction Conditions Laue Equations Brillonin Zones Reciprocal Lattice to sc Lattice Reciprocal Lattice to hcc Lattice Reciprocal Lattice to fcc Lattice Fourier Analysis of the Basis Structure Factor of the bcc Lattice Structure factor of the fcc Lattice Atomic Form Factor Summary Problems Crystals of Inert Gases Van der Wads-London Interaction Repulsive Interaction Equilibrium Lattice Constants Cohesive Energy Ionic Crystals Electrostatic or Madelung Energy Evaluation of the Madelung Constant Covalent Crystals Metals Hydrogen Bonds Atomic Radii Ionic Crystal Radii Analysis of Elastic Strains Dilation Stress Components Elastic Compliance and Stiffness Constants Elastic Energy Density Elastic Stiffness Constants of Cubic Crystals Bulk Modulus and Compressibility Elastic Waves in Cubic Crstals Waves in the [I001 Direction Waves in the [I101 Direction Summary Problems CIIAPTER 4: PHONONS I CRYSTAL VIBRATIONS Vibrations of Crystals with Monatomic Basis First Brillouin Zone Group Velocity coherence length and of the wavefunction used in the theory of the Josephson effects in Chapter 12 We introduce the order parameter $(r) with the property that $*(r)$(r) = ns(r) , (1) the local concentration of superconducting electrons The mathematical formulation of the definition of the fiinction $(r) will come out of the BCS theory We first set lip a form for the free energy density Fs(r) in a superconductor as a function of the order parameter We assume that in the general vicinity of the transition temperature with the phenomenological positive constants a, P, and m, of which more will be said Here: FNis the free energy density of the normal state -aI$I" $$PI$I~ is a typical Landau form for the expansion of the free energy in terms of an order parameter that vanishes at a second-order phase transition This term may be viewed as -ans + ifin: and by itselc is a minimum with respect t o n s when ns(T) = alb The term i11 lgrad $I2 represents an increase in encrgy caused by a spatial variation of the order parameter I t has the form of the kinetic energy in quantum mechanics.' The kinetic momentum -ifiV is accompanied by the field momentum -qNc to enslire the gauge invariance of the free energy, as in Appendix G Here q = -2e for an electron pair The term -$M dB,, with the fictitious magnetization M = (B - Ba)/4.rr, represents the increase in the superconductir~gfree energy caused by the expulsion of magnetic flux from the superconductor The separate terms in (2) will be illustrated by examples as we progress further First let us derive the GL equation (6).We minimize the total free energy JdV Fs(r) with respect to variations in the function $(r) We have We integrate by parts to obtain if 89" vanishes on the boundaries It follows that SJdVF, = JdVS$*[-a$ + P1$12$ + (1/2m)(-ifiV - q ~ l c ) ~ $+] C.C (5) 'A oo~~tribution of the form IVMI2, where M is the magnetization, was introduced hy Landau and Lifshitz to represent the exchange energy density in a fcrromagnet; see QTS,p 65 Appendix This integral is zero if the term in brackets is zero: This is the Ginzburg-Landau equation; it resembles a Schrvdinger equation for $ By minimizing (2) with respect to SA we obtain a gauge-invariant expression for the supercurrent flux: At a frcr surface of the specimen we must choose the gauge to satisfy the hoi~ndarycondition that no current flows out of the superconductor into the vacuum: ii js = 0, where ii is the surface normal Coherence Length The intrinsic coherence length may be defined from (6) Let A = and suppose that /3l+l2 may be neglected in comparison with a In one dimension the GL equation (6) reduces to This has a wavelike solution of the form exp(ix/(), where &isdefined by = (fi2/2ma)'" (9) A more interesting special solution is obtained if we retain the nonlinear term p1$I2 in (6) Let us look for a solution withI+!I = at x = and with II,+ I$, as x + m This situation represents a boundary between normal and superconducting states Such states can coexist if there is a magnetic field H , in the normal regon For the moment we neglect the penetration of the field into the si~perconductingregion: we take the field penetration depth h < 5, which defines an extreme type I superconductor The solution of subject to our boundary conditions, is $(x) = ( a / / ) l f t a n h ( d ~ ) (11) This may be verified by dlrect substitution Deep inside the superconductor we have Go = as follows from the minimization of the terms -a1+l2 ipl$14 in the free energy We see from (11)that marks the extent of the coherence of the superconducting wavefunction into the normal region We have seen that deep inside the superconductor the free energy is a minimum when 1$," a/P, SO that + 669 by definition of the thermodynamic critical field H , as the stabilization free energy density of the superconducting state It follows that the critical field is related to a and P by H, = (4m2/p)'" (13) Consider the penetration depth of a weak magnetic field ( B < H,) into a superconductor We assume that 1+12 in the superconductor is equal to II)~~', the value in the absence of a field Then the equation for the supercurrent flux reduces to js(r)= - ( q / ~ ) l I ) 2,A (14) which is just the London equation js(r) = -(c/4.rrh2)A, with the penetration depth The dimensionless ratio K = A/[ of the two characteristic lengths is an important para~neterin the theory of superconductivity From (9) and (15) we find We now show that the value K = / f i divides type I superconductors ( K < / f i ) from type I1 superconductors ( K > / f i ) Calculation of the Upper Critical Field Superconducting regions nucleate spontaneously within a normal conductor when the applied magnetic field is decreased below a value denoted by H,, At the onset of superconductivity I+I is small and we linearize thc GL equation ( )to obtain The magnetic field in a snperconducting region at the onset of superconductivity is just the applied field, so that A = B(O,x,O)and (17)becomes This is of the same form as the Schrodinger equation of a free particle in a magnetic field We look for a solution in the form exp[i(kyy + kzz)]p(x)and find Appendix this is the equation for an harmonic oscillator, if we set E ( k t + k:) as thc eigenvalne of = a - (h2/2m) The term linear in x can be transformed away by a shift of the origin from to x, = hkyqB/2mc, so that ( )hecomes, with X = x - x,, The largcst valiie of the magnetic field B for which solutions of ( )exist is given by the lowest eigenvalue, which is fhw = fiqB,,/2n~ =a - fi2k:/2m , (22) where w is the oscillator frequency yB/mc With k , set equal to zero, B,, = H , = 2amclqh (23) This result may be expressed by (13) and ( ) in terms of the thermodyrianiic critical field H , and the GL pararnetcr K = A/(: When A/( > l / f i , a superconductor has H,, > H, and is said to be of type 11 It is helpful to write H,, in terms of the flux quantum @, = 27rfic/q and E2 = h2/2ma: This tells us that at the upper critical field the flux density HC2in the material is equal to one flux quantum per area 2n%, consistent with a fluxoid lattice spacing of the order of ( APPENDIX 1: ELECTRON-PHONON COLLISIONS Phonons distort the local crystal structure and hence distort the local band structure This distortion is sensed by the conduction electrons The important effects of the co~iplingof electrons with phonons are Electrons are scattered from one state k to another state k', leading to electrical resistivity 671 Phonons can be absorbed in the scattering event, leading to the attenuation of ultrasonic waves An electron will carry with it a crystal distortion, and the effective mass of the electron is thereby increased A crystal distortion associated with one electron can be sensed by a second electron, thereby causing the electron-electron interaction that enters the theory of superconductivity The deformation potential approximation is that the electron energy ~ ( k ) is coupled to the crystal dilation A(r) or fractional volume change by ~ ( k , r=) ~,,(k)+ CA(r) , (1) where C is a constant The approximation is useful for spherical band edges c0(k) at long phonon wavelengths and low electron concentrations The dilation may be expressed in terms of the phonon operators uq, a: of Appendix C by - A(r) =i C, ( f i / ~ o , ) 'I q~ l[agexp(ig r) - a;exp(-iq r)] (2) as in QTS, p 23 Here M is the mass of the crystal The result (2) also follows from (C.32) on formingq, - q,?-,in the limit k In the Born approximation for the scattering we are concerned with the matrix elements of CA(r) between the one-electron Bloch states Ik) and Ik'), with Ik) = exp(ik r ) u k ( r ) In the wave field representation the matrix element is * = icC, cGck2 (~5/2Mw~)"~1qI(a,J d3x U ~ - U L ~ " ~ - ~ + ~ ) " k'k q (3) where where c t , ck are the fermion creation and annihilation operators The product ui (r)uk(r)involves the periodic parts of the Rloch filnctinns and is itself periodic in the lattice; thus the integral in (3) vanishes unless k-k'*q= (" vector in the reciprocal lattice In semiconductors at low temperatures only the possibility zero (N proccsses) may be allowed energetically Appendix Let 11s limit orirselves to N processes, and for convenience we approximate J d3x uk.ukby unity Then the deformation potential perturbation is Relaxation Time I n the presence of the electron-phonon interaction the wavevector k is not a constant of the motion for the electron alone, but the sum of the wavevectors of the electron and virtual phonon is conserved Suppose an electron is iliitially in the state Ik); how long will it stay in that state? We calculate first the probability w per unit time that the electron in k will emit a phonon q If n, is the initial population of the phonon state, by time-dependent perturbation theory Here The total collision rate W of an electron in the state tem at absolute zero is, with nq = 0, Ik)with a phonon sys- where p is t l ~ eInass density The argunient of the delta function is where y,, = 2hm' c, with c, the velocity of sound The minimum value of k for which the argument can be zero is k,,, = + q,), which for q = reduces to k, = ',q, = m'c,lh For this value of k thc clcctron group velocityug = k,,/m' i(q is cqual to the velocity of soilnd Thus the threshold for the emission of phonons by electrons in a crystal is that the electron group velocity should exceed the acoustic velocity This requirement resembles the Cerenkov threshold for the emission of photons in crystals by fast electrons The electron energy at the threshold is im'c; 10" 10-Ifi erg K An electron of energ) below this threshold will not be slowed down in a perfect crystal at ahsolutc zero, even by higher order electron-phonon interactions, at least in the harmonic approximation for the phonons F o r k % q, we may neglect the qq, term in (9).The integrals in (8) become - - - - 673 and the phonon emission rate is directly proportional to the electron energy ek The loss of the component of wavevector parallel to the original direction of the electron when a phonon is emitted at an angle to k is given by cj cos The fractional rate of loss of k, is given by the transition rate integral with the extra factor ( q / k ) cos in the integrand Instead of ( l o ) , we have so that the fractional rate of decrease of k, is W(k,)= 4C2m'k2/5~pcSfi2 This quantity enters into the electrical resistivity The above results apply to absolute zero At a temperature k,T % Ac,k the integrated phonon emission rate is For electrons in thermal equilibrium at not too low temperatures the required inequality is easily satisfied for the rms value of k If we take C = lo-'' erg; m* = g; k = 10' cm-I; c, = X 10; cm s-I; p = g ~ m - then ~ ; W 1012s-' At absolute zero (13)gives W = x 10lOs-Iwith these same parameters - Absolute thermoelectric power, 215 Accrptor ionization energies, 212 Acceptor states, 211 Acoustical phonou branch, 95 Activatinn energ): 589 Adiabatic demagnetization, 312 Al~aru~~ov-Bohm cffcct, 543 Alfven waves, 425 Alkali halide crystals, table, 66 Alk~ys.621 strength, 613 transitiou metal, 634 Alnico V, 353 Amorphous solids, 568 rerrornagnets, 575 semicnndllctnrs 577 Anharmonic interactions, 119 Allisotropy cncrgy, 348 Annihilation operators, 651 Antiferroelectric crystals, 478, 479 Antiferrornagnetism 340 rnagnons, 344 N6el temperature, 343 Anti-stokes line, 445 Atomic force microscope, 526 Atomic form factor, 41 Atomic radii, 70 tahlc, 71 Band bending, 507 Rand gap, 165,187 Band structure, germanium, 203 Barium titanate, 470 Basis, 4, BCS tlwury, 270,277 Biomagnetism, 354 Bloch equations, 369 Bloc11frequency, 217 Bloch function, 167 Bloch oscillator, 217 Bloch theorem, 173 Bloch T3,' law, 334 Bloch wall, 349 Bohr magneton, 303 Boltzmann transport equation 656 Boson operators, 651 Boundary conditions, periodic, 110 Bragg law, 25 Bravais lattice, R Brillnuill function, 304 Brillo~~in scattering, 428 Brillouin zone, 33,223,252 first, 44, 93, 224 v o l ~ ~ m44 e, Bulk modulus, 80 Bulk modulus, clcctron gas, 157 Bnrgers vector, 604 Biittiker-Landauer formalism, 540 Cauchy integral, 431 Causality, 450 Cell, primitive, unit, Wigner-Seitz, 34 Centipoise, 573 Ceutral eqwation, 174 Cesium chloride structure, 14 Chalcogenide glasses, 577 Charge density waves, 424 Charging energe 549 Chemical potential, 137, 157 Classical distribution, 658 Clausius-Mossotti relation, 464 Clogston relation, 272 Coercive force, small particle, 358 Cocrcivity, 347,352 Coherence length, 276,669 intrinsic, 277 Cohcsive cnergy, 49, 59, 73 Fermi gas, 159 Sodium metal, 237 Square well potential, 253 Cohesive energy, table, SO Collisionless electron gas, 433 Colur centers, 592 Compressibility 80 Concentration, table, 21 Conductance, quantum, 534 Conduction electron ferromagnetism, 320 Conduction band edge, 190 Conduction electrons, 315 susceptibility, 315 Conductivity, electrical, 147, 209,420 impurity, 209 ionic, 420 thermal, 156 Condu~tivitysuru rule, 450 Configurational heat capacity, 640 Contact hyperfine interaction, 374 Cooper pain,279,556,665 Coulomb blockade, 551 Covalent bond, 67 Covalent crystals, 67 Critical points, 434 Contilluum wave equation, 103 Creation operators, 651 Creep, 615 Critical field, 262,295 thin films 295 Critical shear stress, 599 Critical temperature, ferroelectric, 469 Crystallography, surface, 490 Crystal field, 309 splitting, 309 Crystal momentum, 100,173 Crystal struchlre, elements, 20 Cubic lattices, 10 Cubic zinc sulfide structure, 17 Curie constant, 305 law, 305 Curie-Weiss law, 324 Cyclotron frequency, 153 Cyclotron resonance, 200,219 spheroidal energy surface, 219 Dangling honds, 488 Uavydov splitting, 452 Dehye model, density of states, 112 Dehye temperature, 112 table, 116 Dehye 'P law, 114 Dehye-Waller factor, 642 Defects, paramagnetic, 375 Deficit semiconductors, 209 Degenerancy, 135 Degenerate semiconductor, 409 De Haas-van Alphen effect, 244 period, 253 De~nagnetizationfactors, 380 Demagnetization isentropic, 312 Density of states, 108, 149 Dehye model, 112 Einstein model, 114 finite system, 520 general result, 117 one dimension, 108 singularity, 119 three dimensions, 11 Density, table, 21 Depolarization factors, 458 Depolarization field, 48.5 Diamagnetism, 299 Diamond stnlctnre, 16, 45, 182,187 Dielectric constant, 463 semiconductors, 211 susceptibility, 459 Dielectric function, 429 electron gas, 433 Lindhard, 406 Thomas-Fermi, 405 Diffraction cnnditions, wave, 25 Diffraction, Josephson junction, 282 Diffusion, 371 588 Diffusivity, 588 Dilation, 75 Direct gap semiconductor, table, 201 Direct photon absorption, 189 Dislocation densities, 610 Dislocatio~~ rnultiplicatio~~ 611 Dislocations, 601 Dispersion relation, phonons, 92 electro~nagneticwaves, 92, 397 Displacive transition, 471 Dissipation sum rule, 450 Distribntion, classical, 130 Fermi-Dirac, 107 Planck, 107 dog:^ bone orbit, 250 Domains, origin of, 350 closure, 351 Donor ionizatinn energies, 211 Donor states, 209 Doping, 209 Dulong and Petit value 117 Edge dislocation, 601 Effective mass, 197 negative, 199 semiconductors, table, 201 Einstein model, density of states, 114 thermal, 145 Elastic stiffness, 78, 84 Elastic strain, 73 Elastic \vatrequantization, 80 Electrical resisti~ity,148 table, 149 Electric field, local, 460 macroscopic, 456 Electric conductivity, 147,661 table, 149 Electric quadruple moment, 379 Electronic polarizahilities table, 465 Electronic structure, surface, 494 Electron affinities, 62 Electron beam lithography, 521 Electrun co~npourrd,624, 625 Electron-electron collisions, 417 Electron heat capacity, table, 148 Electron-hole drops, 441,443 Electron-electron interaction, 417 one dimension, 532 Electron-lattice interaction, 420 Electron orbits, 230 Electron-phonon collisions, 671 Electron spin resnnance, 362 Electron work functions, 494 table, 494 Electrostatic screening, 403 Elementary excitations, 90 Empirical pseudopotential method, 239 Empty core model, 240 Empty lattice approximation, 176 Energy band calculation 232 Energy bands, 163,164 Energy gap, 165, 167 superconductors 266,268 table, seniiconductors 189 E n e r a levels, one dimension, 134 Energy loss, fast particles, 448 Entropy, superconductors 265 Entropy of mixing, 631 Equations of motion, electron, 191 Equation of motion, hole, 196 ESCA, 447 Eutectics, 632 Ewald-Kornfeld method, 647 Ewald construction, 32 sphere, 493 sums 644 Exchaigc cnergy, 326 field, 325 frequency resonance, 391 integral, 325 interaction, 325 narrowing, 371,386 Exclusion principle, Pauli, 56 Exotic snpercnnd~lctors.147 Extremd orbits, 248 Excito~is,435 Extended zone scheme, 226 Extinction coefficient, 429 Extre~natorbits 248 Factor, ato~nictirrtn, 41 structure, 45 F centers, 376, 592, 595 Fermi-Dirac distribution, 136,652 Fermi energy, 135 Fermi gas, 134 Permi level, 137 Fcrmi liquid, 417 Fermi snrface, copper, 249 Fermi surface, gold Fermi surface yaramcters, table, 1.39 Fermi surfaces, 225 Fermiu~n,heavy, 147 Ferroelectric crystals, 467 domains, 479 linear array, 485 Ferromagnetism, crystals, 321,328 amorphnns, i conduction electron, 320 domains, 345 order, 338 resonance, 379 Fiber optics, 581 FickS law, 588 Fine structure constant, 499 First Brillouin zune, 36.93, 165 First-order transition, 477 Fluyoid, 281 Flux quantization, 279 Fourier analysis, 27, 39, 169 Fractional quantized Hall effect (FQHE), 503 Frank-Head source, 612 Free-cnerw, snpercnndnctors, 267 Frenkel defect, 586,595 Freukel cxciton, 437 Friedel oscillations, 407 Fullerenes, 262 Fused quartz, 570 Gap, direct, 190 Gap, indirect, 190 Gap plasmons, 426 Gauge transformation, 664 Geomagnetism, 354 Ginzburg-Landau equation, 667 Ginzburg-Landau parameter, 667 GLAG theow 283 Glass, 573 transition tcmpcraturc, 573 Grain honndary, small-angle, 607 Group velocity, 94 Grunciscn constant, 129 Gyromagnetic ratio, ?O2 Gyroscopic equation, 366 Hagen-Rubens relation, 451 Hall coefficient, 154 table, 155 Hall effect, 153 ballistic jnnction, 542 two-carrier types, 218 Hall resistance, 155 Hall resistivity, 498 Hardness, 617 Hcavy fcrmions, 147 Heat capacity, configurational, 640 electron gas, 141 glasses, 378 metals, 145 one-dimension, 561 phonon, 107 superconductors 264 He3 liquid, 158 Heisenberg model, 325 IIelicon waves, 425 Heierojunction, 505 Heterostrnchlrrs 507 Ilexagonal close-packed structure, 15 Hexagonal lattice, 44 High temperature superconductors, 293 Hole, eqnation of motion, 104,194 Holc orbits, 230 Hole trapping 422 Hooke's law, 73 HTS, 293 Hume-Rothery rules, 624 Hund roles, 306 Hydrogen bonds, 70 Hyperfine constant, 375 Hyperfine effects, ESR in metals, 391 Hypcrfinc splitting, 373 Hystrresis, 352 Kronig-Penney model, 174,182 reciprocal space, 174 Ilmenite, 470 Impurity conducti~ty,209 Impurity orbits, 218 Index system, 10 Indirect gap, 190 Indirect photon absorption, 189 Inelastic scattering, phonons, 100 Inert gas crystals, table, 53 Injection laser, 510 Insulators, 181 Interband transitions, 434 Interface plasmons, 425 Interfacial polarization, 484 Intrinsic carrier conce~ltratiun, 188,205 Intrinsic coherence length, 277 Intrinsic mobility, 208 Intrinsic semiconductors, 187 Inverse spinel, 338 Ionic bond, 60 Ionic character, table, 69 Ionic conductivity, 420, Ionic crystals, Ionic radii, 72 table, 71 lnnization energies, acceptor, 209 donor, 209 table, 54 Iron garnets, 339 Iron group, 307 Isentropic demagnetization, 312 Isotope effect, 269 superconductors, 269 Isotope effect, thermal conduction, 127 LA modes, 95 Lagrangian equations, 662 Landaner forrnnla, 535 Landau gauge, 503 Landau-Ginzburg equations, 276, 667 Landau level, 245,254,493 Landau theory, Ferrni liquid, 417 Landau theory, phase transition, 474 Langevin diamagnetism, 299 Langevin result, 301 Lanthanide group, 306 Larmor frequency, 300 Larmor theorem, 300 Laser, 389 injection, 510 ruby, 389 semiconductor, 510 Lattice, Bravais, Lattice constants, equilibrium, 58 Lattice frequencies, table, 416 Lattice momentum, 193 Lattice sums, dipole arrays, 647 Lattice types, R,10 Lattice vacancies, 585 Lattices, cubic, 10 Lane equation, 33,513,641 Law of mass action, 206 LCAO approxi~nation.233 LEED, 511 Lennard-Jones potential, 58 Lcnz's law, 299 Lindhard dielectric function, 406 Line width, 370 Liquid He" 158 Liquidus, 632 Localization, 539 Local electric field, 460 London equation, 273,665 London gauge, 665 London penetration depth 275,294 Longitudinal plas~rla oscillations, 398 Longitudinal relaxation time, 366 Long-range order, 630 LO modes, 95 &rent2 field, 462 Lorenz number, 157 Low-angle grain boundary, 607 LST relation, 414,416 Jahn-Teller effect, 209 trapping, 420 Josephsnn t~~nneling, 289 Jump frequency, 590 Junction, superconducting, 287 Jnnctinns, p-n, 503 k p perturbation theory, 253 Kelvin relation, 215 Knight shift, 377, 378 Kohn anomaly, 103 Kramers-Heisenberg dispersion, 431 Kramers-Kmnig relations, 430,432 Luminescence, 437 Luttinger liquid, 532 Lyddane-Sachs-Tcllcr relation, 414 Madclung constant, 64 Madelnng energy, 60 Magnetic breakdown, 251 Magnetic force niioroscupy, 355,527 Magnetic susceptibility, 298, 315,318 Magnetite, 337 Magnetoconductivity, tensor, 159,254 Magnetocrystalline energy, 347 Magnctoclastic coupling, 357 Magnetogyric ratio, 302,363 Magneton numbers, 308 Magnctoplas~nafrcqucncy, 425 Magnetore~istance,giant, 359 Magnetoresistance, 408 two carrier types, 219 Magnetic resonance, 361 Magnetotaxis, 355 Magnetization 303 saturation, 304 Magnons, 330 antiferromapetic, 344 dispersion relation, 357 Maser action, 386 Matthiassen's rule, 150 Maxwell equations, 455 Mean field appruximatiuo 323 Meissner effect, 259 sphere, 296 Meltingpoints, table, 51 Melt-spin velocity, 576 Mesh, 490 Mesoscopic regime, 543 Metal-insulator transition, 407 Metals, 69 Metal spheres, 484 Metglas, 576 Mioroelectro~nechanical systems, 561 Miller indices (see index system), 11 Mobility edges, 501 Mobility gap, 501 Mobility, intrinsic, 208 Mobilities, table, 208 Molecular crystals, 440 Molecnlar hydrogen, 68, 86 Momentum crystal, 100,173 field, 661 lattice, 193 phonon, 100 MOSFET, 497 Motional narrowing, 371.373 Mott exciton, 441 Mott transition, 407 Mott-Wannier excitons 441 np product, 206 Nanocrystals, 517 fluorescence, 522 e n e r a levels, 54.5 Nanostructures, 517 Nanotuhes, 518 density of states, 529 band structure, 562 N6el temperature, 341,342, 343 NBel wall, 358 Negative effective mass, 199 Neutron diffraction, 45 NMK tomography, 363 Noncrystalline solid, 519 Nonideal structures, 18 Normal mode enumeration, 108 Normal proccsscs, 124,125 Normal spinel, 338 Nuclear demagnetization, 314 Nuclear ~rlagrieticresonance, 363 table, 365 Nuclear magneton, 364 Nnclear paramagnetism, 314 Nuclear quadrupole resonance, 379 Ohm's law, 147, 538 Open urbits, 230 magnetoresistance, 254 Optical absorption, 190,521 Optical microscopy, 521 Optical phonon branch, 95 Optical phonons, soft, 473 Orbit, dog's bboe, 250 Order-disorder transformation, 627 Order, long-range 630 short-range, 631 Order parameter, 668 Oscillations, Friedel, 407 Oscillator strength, 466 p-n junctions, 503 Paramagnetic defects, 375 Paramagnetism, 302 conduction electrons, 315 Van Vleck, 311 Particle diffusion, 657 Fauli exclusion principle, 56 Pauli spin magnetization, 316,319, 377 Peierls instability, 422,532 insulator, 424 Peltier coefficient; 215 Penetration depth, London, 296 Peliodic boundary conditions, 110 Periodic zone scheme, 225 Perovskite, 470 Persistent currents, 282 Phase diagrams, 625,632 Phase transitions, structural, 467 Phonons, 100,101,107 coordinates, 649 dispersion relations, 117 gas, ther~nalresistivity, 123 heat rapacity, 107 inelastic scattering, 100 rriean free path, 122 metals, 409 modes, soft, 103 morner~tu~n, 100 Photolithography, 522 Photovoltaic detectors, 506 Piezoelectricity, 481 Planck distribution, 107 Plasrnon frequency, 90, 397, 398 interface, 425 mode, sphere, 425 uptics, 396 oscillation, 398 surface, 403,424 Poise, 573 Poisson equation 403 Poisson's ratio, 87 Polaritons, 410 Polarizability, 463 conducting sphere, 484 electronic, 464 Polarization, 455 interfacial, 484 saturation, 484 Polaron, coupling constant, 420, 422,426 Polytypism, 19 Power absorption, 370 Primitive cell, , , 180 p-n junctions, 503 Pseudopotential, components, 239 metallic sodium, 240 method, 239 Pyroelectric, 469 PZT system, 479,481 Qi~anti~ation elastic wave, 99,648 orbits in xr~agr~etic field, 242 spin waves, 382 Quantum corral, 525 Quautu~mdots, 517, 545 charge states, 549 Quantum interference, 282,292 Quar~turnsolid, 85 Quantum theory, diamagnctism, 301 paramagnetism, 302 Quasi-lcermi levels, 510 Quasi particles, 417 Quenching, nrhital angular momentum, 308 QHE, 499 Radial breathing mude, 558 Radial distribution function 569 Raman effect, 444 scatteling, 428 surface enhanced, 549 nanntuhcs, 558 Random network, 572 Random stacking, 19 Rarc carth ions, 305 Rayleigh attenuation 582 I'teciprocal lattice points, 29 Rcciprooal lattice vectors, 29 Recombination radiation 442 Reconstruction, 489 Rectification, 504 Reduced zone scheme 223 Reflectance, 430 ReHection, normal incidence 450 Reflectivity coefficient, 429 Refractivc indcx, 429 Relaxation, 366 direct, 368 Orbaclr, 368 Raman, 368 Relaxation time, longitudi~~al, 366 spin-lattice, 366 ltemanence, 347 Resistance per square, 159 Resistance quantum 534 Ilesistance, surface, 159 Resistivity, electrical, 147, 159 Resistivity ratio, 150 Resonant tunneling, 538 Respo~~se, electron gas, 426 Response function, 430 Rf saturation, 391 RHEED, 493 Richardso~l-Dushman equation 49.5 RKKY theory, 638 Rotatlng coordinate system, 391 Ruby laser, 389 Saturation magnetization, 326 Saturation polarization, 485 Saturatinn rf, 391 Scanned probe microscopy, 520 Scanning clcctro~imicroscope, 521 Scanning tnnneling microscope, 523 Schottky barrier, 506 Schottky defect, 58.5 Schottb vacancies, 585,595 Screened Coulomb potential, 406 Screening, electrostatic, 403 Screw dislocation, 603 Second harmonic generation, 549 Second-order transition, 475 Self-diffusion, 591 Self-trapping, 209 Semiconductor crystals, 187 Scmico~lductor.degenerate, 409 Semiconduvtor lasers, 510 Semiconductors, deficit, 209 S e ~ ~ ~ i ~ n e162, t a l s215 ; Shear constant, 87 Shear strength, silrglc crystals, 599 Shear stress, critical, 599 Short-range order, 631 Single-domain particles, 353, 358 Single-electron tranaistor, 551 Singularities, Van Hove, 119 Slatcr-Pauling plot, 636 Slip, 600 Sodium chloride structure, 13 Sodiu~nn~etal,132 Soft modes 474,485 Solar cells, 506 Solidus, 632 Solubility gap, 632 Spheres, metal, 484 Spectruscupic splitting factnr, 31 Spinel, 337 Spin-lattice interaction; 367 Spin-lattice relaxation time, 366 Spin wave (see also magnon), 330 quantization, 333 resonance, 382 Square lattice, 8, 182 Stability criteria, 88 Stabilization free energy, 272 Stacking fault, 601 STM, 523 Stokes line, 445 Strain component, 75 Strength of alloys, 613 Stress component, 75 Structural phase transitions, 467 Structure [actor, 39 bcc lattice, 40 diamond, 45 fcc lattice, 40 Substrate, 489 Surface plasmon resonance, 547 Superconducti\lty, table, 261 type I, 259 type 11,283 Superlattices, 628, 640 Superparamagnetism, 354 Surface crystallography, 490 surcace electronic stnlchlre, 494 surface nets, 490 surfacc plasmons, 279,302 surface resistance, 159 surface states, 495 surface transport, 497 Susceptibility, dielectric, 459 TA modes, 95 Temperaturc, Debye, 112 Temperature dependence reflection lines, 643 Tetrahedral angles, 22 Thermal conductivity, 121,156 glasses, 534 isotope effect, 127 metals, 156 one-dimension, 561 tablc, 116 Thermal dilation, 128 Thermal effective mass, 145 Tl~rrxnalexcitation, magnons, 334 Thermal expansion, 120 Thermal ionization, 213 Thermal resistiviv, phonon gas, 133 Thermionic emission, 495 Thermodynamics, superconducting transition, 270 Ther~noclcctriceffects, 214 Thomas-Fermi approximation, 403 Thomas-Fermi dielechic function, 405 Three-level maser, 388 Tight-binding method, 232 TO modes, 615 To~nography,lnagnetic resonance, 363 Transistor, MOS, 507 Transition, displacive, 471 first-order, 477 metal insulator, 107 order-disorder, 471 second-order, 47.5 Transition metal alloys, 634 Transition temperature, glass, 573 Transistor, MOS, 497 Translation operation, Translation vector, Transmission electron microscopy, 520 Transmission probability, 534 Transparency, alkali metals, 388 Transport, surface, 497 Transverse optical modes, plasma, 398 Transverse relwatio~itime, 368 Triplet excited states, 318 Tunneling, 287 Josephson, 289 Tunneling probability, 524 Twinning, 601 n*n*o-fluidmodel, 295 Two-level system, 320 264 Type I superco~~ductors Type I1 superconductors, 264,283 Ultraviolet transmission limits, 399 Umklapp processes, 125 Unit cell, Upper critical field, 670 UPS, 447 Wanuier functions, 254 Wave eqwatio~i,co~itinuum,103 periodic lattice, 169 Weiss field, 323 Whiskers, 616 Wiedemann-Franz law, 1.56 Wiper-Seitz boundaly condition, 237 Wigner-Seitz cell, 6, 8, 34, 238 Wiper-Seitz method, 236 Work hnction, 494 Work-hardening, 614 XPS, 447 Valence hand edge, 190 Van der \Vaals interaction, 53 Val1 Hove singularities, 119,528 Van Vleck paramagnetism 311 Vector potential, 661 Vickers hardness nulnler, 618 Viscosity ,574 Vitreous Silica, 570 Vortex state, 264, 284, 295 Young$ modulus, 87 Yttriuni iron ganlct, 381 Zener breakdown, 217 Zener tnnneling, 217 Zero-field splitting, 386 Zero-puint motion, 56,85 Table of Values Quantity Symbol \Jclocity of light Proton charge c Planck's constar~t h e R =h l ~ Avogadro's number Atomic mass unit Electron rest mass Proton rest mass Proton rnass/electron mass N Rec~procaltine structure constant hcle2 Electron radius e2/mc2 Electron Compton wavelrrrgth hlmc Bohr radius h2/rne" Bohr rnagneton ehl2mc Rydberg constant me4/2h2 llu electron volt amu rn MP M,/m CCS Value 2.997925 1.60219 4.80:125 6.62620 1.05459 10'' crn s SI I 10-lo esu erg s lo-'' erg s 6.02217 X loz3nrolk' 1.66053 lo-" g 10 g 9.10956 1.67261 10.~' 1836.1 10B rn s-' 10-I=C J s J s lo-z7kg l o kg kg - - - cm lo-" cm rn 10-l3 rn 5.29177 9.27410 2.17991 13.6058 eV cm erg C-I lo-'' erg lo-" m lo-=' j T-I J 1.64219 2.41797 x loL4Hz 8.06546 1.16048 x 10' K lo-'' erg 10-l9 J k~ 1.38062 e0 - 10-16 erg K-I 1 re A? TO p, R , or Ry eV eVIh cVlhc eVlkB 137.036 2.81794 3.86159 - - 103 cm-' 1W m-' - - - Bol tzlnar~rlconstant Permittivity of frep spacc Permeability of free bpare p,, J K~I 107/4~c2 4~ x S,,urcr D N Taylor W H Parker and U N Langcnbrrg Hev Mud Phys.41, 375 (1969) See rlav E R Cohrn and N.Taylor Journal of Phyrical and Chcm~calReference Data 2(4l, 663 (1973) ... books or for customer service please, call 1-800~CALL WILEY (225-5945) Library ojCongress Cataloging in Publication Data: Kittcl, Charles Introduction to solid state physics Charles Kitte1.-8th... received and may be addressed to the author by rmail to kittelQberke1ey.edu The Instructor's Manual is available for download at: m .wiley. coml collegelkittel Charles Kittel Contents E CHAPTER 1:... great importance to the birth of solid state physics Related studies have been extended to noncrystalline solids and to quantum fluids The wider field is h o w n as condensed matter physics and is