Table Of ContentElectrical
properties of
materials
EIGHTH EDITION
L. Solymar
DepartmentofElectricalandElectronicEngineering
ImperialCollege,London
D. Walsh
DepartmentofEngineeringScience
UniversityofOxford
1
3
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10 9 8 7 6 5 4 3 2 1
Data on specific materials
in text
Errorsusinginadequatedataaremuch
lessthanusingnodataatall
CharlesBabbage
Table 1.1 Thresholdwavelengthsforalkalimetals 11
Table 1.2 Electricalandthermalconductivitiesmeasuredat 20
293K
Figure 4.5 Theperiodictableoftheelements 60
Table 4.1 Theelectronicconfigurationsoftheelements 62
Table 5.1 Mohshardnessscale(modified) 70
Table 6.1 Fermilevelsofmetals 84
Table 6.2 Workfunctionsofmetals 88
Figure 6.10 Field-ionmicrographofatungstentip 94
Table 8.1 Energylevelsofdonor(groupV)andacceptor 125
(groupIII)impuritiesinGeandSi
Figure 8.7 ElectronandholemobilitiesinGeandSiasa 132
functionofimpurityconcentration
Figure 8.8 ElectronandholemobilitiesinGaAsasa 134
functionofimpurityconcentration
Table 8.2 Sizeofatomsintetrahedralbonds 135
Table 8.3 SemiconductorpropertiesI.Energygapand 136
structure
Table 8.4 SemiconductorpropertiesII.Currentcarriers 142
Figure 8.18 (a)Generalarrangementofanoptical 146
transmissionmeasurementandtheresultfor
(b)GaAsand(c)Si
Exercise 9.6 SpecificdopingdatainGeandSi 219
Table 10.1 Dielectricconstantandrefractiveindexofsome 227
non-polar,weaklypolor,polar,and
semiconductingmaterials
Table 10.2 Frequenciesofmaximumreflection(f )and 233
r
minimumtransmission(f)foranumberof
t
alkalihalides
Table 10.3 Piezoelectricceramics 237
xivDataonspecificmaterialsintext
Exercise 10.5 Dielectriclossinthoria 247
Figure 11.9 Hysteresisloopsof(a)Supermalloyand 259
(b)Alnico5and9
Table 11.1 Majorfamiliesofsoftmagneticmaterialswith 261
typicalproperties
Figure 11.12 Hysteresiscurvesofsomerare-earthmagnetsin 263
thesecondquadrant
Table 11.2 Hardmagneticmaterials 263
Exercise 11.6 MagneticsusceptibilityofNiatvarying 284
temperature
Figure 12.15 Relationshipbetweenenergygapandlattice 307
spacingforsomemixedIII–Vsemiconductors
Table 12.1 Compoundsforlaserdiodes 307
Table 13.1 Electronegativitiesofelements 332
Table 13.2 Propertiesofelectro-opticmaterials 335
Table 13.3 Propertiesofsomematerialsusedfor 342
acousto-opticinteraction
Table 14.1 Thecriticaltemperatureandcriticalmagnetic 364
fieldofanumberofsuperconductingelements
Figure 14.9 Temperaturedependenceofthespecificheatof 370
tinnearthecriticaltemperature(afterKeesom
andKok,1932)
Figure 14.13 Thetemperaturevariationoftheenergygap 378
(relatedtotheenergygapatT =0)asafunction
ofT/T
c
Table 14.2 Thecriticaltemperatureandcriticalmagnetic 383
field(atT =4.2K)ofthemoreimportanthard
superconductors
Figure 14.21 Themaximumcriticaltemperatureagainsttime 385
fortraditionalandoxidesuperconductors
Table 14.3 Approximatecriticaltemperatures(K)ofa 386
selectionofhigh-T superconductors
c
Figure 14.24 Criticalcurrentdensitiesasafunctionof 389
magneticfieldat77K(---)andat4.2K(---)for
BSCCO,Nb–TiandNb Sn
3
Figure A1.4 Thebenzeneseries,showingopticalabsorption 419
progressingfromtheuvtothevisible
Appendix III Physicalconstants 426
Introduction
TillnowmanhasbeenupagainstNature;
fromnowonhewillbeupagainsthisownnature.
DennisGaborInventingthefuture
Itisagoodthingforanuneducatedmantoreadbooksofquotations.
W.S.ChurchillRovingcommissioninmyearlylife(1930)
Engineeringusedtobeadown-to-earthprofession.TheRomanengineers,who
providedcivilizedEuropewithbridgesandroads,didajobcomprehensibleto
all.Andthisisstilltrueinmostbranchesofengineeringtoday.Bridge-building
has become a sophisticated science, the mathematics of optimum structures
is formidable; nevertheless, the basic relationships are not far removed from
commonsense.Aheavierloadismorelikelytocauseabridgetocollapse,and
theuseofsteelinsteadofwoodwillimprovetheload-carryingcapacity.
Solid-state electronic devices are in a different category. In order to
understand their behaviour, you need to delve into quantum mechanics. Is
quantummechanicsfarremovedfromcommonsense?Yes,forthetimebeing,
itis.Weliveinaclassicalworld.Thephenomenawemeeteverydayareclassical
phenomena.Thefinedetailsrepresentedbyquantummechanicsareaveraged
out; wehavenofirst-handexperienceofthelawsofquantummechanics; we
canonlyinfertheexistenceofcertainrelationshipsfromthefinaloutcome.Will
itbealwaysthisway?Notnecessarily.Therearequantumphenomenaknownto
existonamacroscopicscaleas,forexample,superconductivity,anditisquite
likelythatcertainbiologicalprocesseswillbefoundtorepresentmacroscopic
quantum phenomena. So, a ten-year-old might be able to give a summary of
thelawsofquantummechanics—halfacenturyhence.Forthetimebeingthere
isnoeasywaytoquantummechanics; noshortcutsandnobroadhighways.
We just have to struggle through. I believe it will be worth the effort. It will
beyourfirstopportunitytoglancebehindthescenes,topiercethesurfaceand
findthegrandioselogicofahiddenworld.
Shouldengineersbeinterestedatallinhiddenmysteries?Isn’tthattheduty
and privilege of the physicists? I do not think so. If you want to invent new
electronicdevices,youmustbeabletounderstandtheoperationoftheexisting
ones. And perhaps you need to more than merely understand the physical
mechanism.Youneedtogrowfamiliarwiththeworldofatomsandelectrons,
tofeelathomeamongthem,toappreciatetheirhabitsandcharacters.
Weshallnotbeabletogoverydeeplyintothesubject.Timeisshort,andfew
ofyouwillhavethemathematicalapparatusforthefrontalassault.Soweshall
approach the subject in carefully planned steps. First, we shall try to deduce
asmuchinformationaspossibleonthebasisoftheclassicalpicture.Then,we
shalltalkaboutanumberofphenomenathatareclearlyincontrastwithclassical
ideasandintroducequantummechanics,startingwithSchrödinger’sequation.
Youwillbecomeacquaintedwiththepropertiesofindividualatomsandwhat
happens when they conglomerate and take the form of a solid.You will hear
xvi Introduction
aboutconductors,insulators,semiconductors,p–njunctions,transistors,lasers,
superconductors, and a number of related solid-state devices. Sometimes the
statementwillbepurelyqualitativebutinmostcasesweshalltrytogivethe
essentialquantitativerelationships.
Theselectureswillnotmakeyouanexpertinquantummechanicsnorwill
theyenableyoutodesignacomputerthesizeofamatchbox. Theywillgive
younomorethanageneralidea.
Ifyouelecttospecializeinsolid-statedevicesyouwill,nodoubt,delvemore
deeplyintotheintricaciesofthetheoryandintothedetailsofthetechnology.If
youshouldworkinarelatedsubjectthen,presumably,youwillkeepaliveyour
interest,andyoumayoccasionallyfinditusefultobeabletothinkinquantum-
mechanicalterms.Ifyourbranchofengineeringhasnothingtodowithquantum
mechanics,wouldyoubeabletoclaimintenyears’timethatyouprofitedfrom
thiscourse? Ihopetheanswertothisquestionisyes. Ibelievethatonceyou
havebeenexposed(howeversuperficially)toquantum-mechanicalreasoning,
itwillleavepermanentmarksonyou.Itwillinfluenceyourideasonthenature
of physical laws, on the ultimate accuracy of measurements, and, in general,
willsharpenyourcriticalfaculties.
Preface to the eighth edition
Once more we have taken the opportunity to bring our book up to date. The
major change is due to the recent upsurge of interest in artificial materials
(metamaterials in the modern jargon), which persuaded us to turn a small
appendixintoafull-blownchapter.Inordertosupplythetheoreticalfoundations
forthisnewchapterwehaveexpandedourcoverageofplasmaphenomenain
Chapter1,andincludedasectioninChapter10onanomalousdispersionwith
theaimtointroducebackwardwaves.AnotherexpansionofChapter10isdueto
theincreasinginterestinTHzdevices.Wehaveincludedatreatmentofoptical
phononswhichhaveresonancesinthatfrequencyrange.
Given the five years since the last edition, it is not surprising that we had
tomakesomechangesineverychapter,occasionallybecausewethoughtthat
theexistingexplanationcouldbeimprovedupon, butmostlybecauseofnew
developments.Thechapterthatreceivedthegreatestamountofnewadditions
isthatonsemiconductordevices.Wehaveincludedplasmaetching,expanded
the treatment of microelectromechanical systems, and pointed out the means
by which those further miraculous reductions in minimum feature size have
takenplace.Theprogressinspintronicshasbeennotedbytreblingthesizeof
therelevantsection.Themainadditiontothelaserchapterisonquantumdot
devices;wehavealsoaddedabriefsectiononlasercooling.Themainchange
inthechapteronoptoelectronicsisourreassessmentoftoooptimisticprevious
predictionsonLEDs.Somemodestadvancesinsuperconductorshavealsobeen
noted.Wehaveaddednewentriestoexistingtablesandintroducedthreenew
tables:oninfraredresonancesofalkalihalides,onpiezoelectricconstants,and
onthecriticaltemperaturesofhigh-T superconductors.
c
Additionsofwhichwecouldhavethoughtearlierareexplicitreferencesto
NobelPrizeswheneverwewriteabouttherelevanttopics.Weourselveswere
surprisedthatthenumberofNobellaureatesincludedcametoafigureashigh
as50.Perhapsitisnotacoincidencethattheresearchthathashadthegreatest
influenceuponthewaywelivehasalsoattractedthebestscientificminds.A
listoftheseNobellaureatesisgiveninAppendixII.
We wish to thank, first, all those students and lecturers whose comments
helpedustopreparethisedition.WearegratefultoRichardSyms, whogave
us all the information needed to include mass spectrometers in Section 9.26
andwhokindlyreadthefinaldraft.Wealsowishtoacknowledgethehelpwe
receivedfromJohnAllen,KristelFobelets,andPaulStavrinou,allofthemfrom
ImperialCollege,London,inthefieldofsemiconductordevicesandlasers.
Contents
Dataonspecificmaterialsintext xiii
Introduction xv
1 The electron as a particle
1.1 Introduction 1
1.2 Theeffectofanelectricfield—conductivityandOhm’slaw 2
1.3 Thehydrodynamicmodelofelectronflow 4
1.4 TheHalleffect 5
1.5 Electromagneticwavesinsolids 6
1.6 Wavesinthepresenceofanappliedmagneticfield:cyclotronresonance 13
1.7 Plasmawaves 16
1.8 Heat 19
Exercises 21
2 The electron as a wave
2.1 Introduction 23
2.2 Theelectronmicroscope 26
2.3 Somepropertiesofwaves 27
2.4 Applicationstoelectrons 29
2.5 Twoanalogies 31
Exercises 33
3 The electron
3.1 Introduction 34
3.2 Schrödinger’sequation 36
3.3 SolutionsofSchrödinger’sequation 37
3.4 Theelectronasawave 38
3.5 Theelectronasaparticle 39
3.6 Theelectronmeetingapotentialbarrier 39
3.7 Twoanalogies 42
3.8 Theelectroninapotentialwell 43
3.9 Thepotentialwellwitharigidwall 45
3.10 Theuncertaintyrelationship 45
3.11 Philosophicalimplications 46
Exercises 48
vi Contents
4 The hydrogen atom and the periodic table
4.1 Thehydrogenatom 51
4.2 Quantumnumbers 56
4.3 ElectronspinandPauli’sexclusionprinciple 57
4.4 Theperiodictable 57
Exercises 61
5 Bonds
5.1 Introduction 64
5.2 Generalmechanicalpropertiesofbonds 65
5.3 Bondtypes 67
5.3.1 Ionicbonds 67
5.3.2 Metallicbonds 68
5.3.3 Thecovalentbond 68
5.3.4 ThevanderWaalsbond 71
5.3.5 Mixedbonds 72
5.3.6 Carbonagain 72
5.4 Feynman’scoupledmodeapproach 73
5.5 Nuclearforces 78
5.6 Thehydrogenmolecule 78
5.7 Ananalogy 79
Exercises 80
6 The free electron theory of metals
6.1 Freeelectrons 81
6.2 ThedensityofstatesandtheFermi–Diracdistribution 82
6.3 Thespecificheatofelectrons 85
6.4 Theworkfunction 86
6.5 Thermionicemission 86
6.6 TheSchottkyeffect 89
6.7 Fieldemission 92
6.8 Thefield-emissionmicroscope 92
6.9 Thephotoelectriceffect 93
6.10 Quartz–halogenlamps 95
6.11 Thejunctionbetweentwometals 95
Exercises 96
7 The band theory of solids
7.1 Introduction 98
7.2 TheKronig–Penneymodel 99
7.3 TheZimanmodel 102
7.4 TheFeynmanmodel 106
7.5 Theeffectivemass 109
7.6 Theeffectivenumberoffreeelectrons 111
Contents vii
7.7 Thenumberofpossiblestatesperband 112
7.8 Metalsandinsulators 114
7.9 Holes 114
7.10 Divalentmetals 116
7.11 Finitetemperatures 117
7.12 Concludingremarks 118
Exercises 119
8 Semiconductors
8.1 Introduction 120
8.2 Intrinsicsemiconductors 120
8.3 Extrinsicsemiconductors 125
8.4 Scattering 129
8.5 Arelationshipbetweenelectronandholedensities 131
8.6 III–VandII–VIcompounds 133
8.7 Non-equilibriumprocesses 137
8.8 Realsemiconductors 138
8.9 Amorphoussemiconductors 140
8.10 Measurementofsemiconductorproperties 140
8.10.1 Mobility 140
8.10.2 Hallcoefficient 143
8.10.3 Effectivemass 143
8.10.4 Energygap 144
8.10.5 Carrierlifetime 148
8.11 Preparationofpureandcontrolled-impuritysingle-crystalsemiconductors 148
8.11.1 Crystalgrowthfromthemelt 148
8.11.2 Zonerefining 149
8.11.3 Floatingzonepurification 150
8.11.4 Epitaxialgrowth 151
8.11.5 Molecularbeamepitaxy 152
8.11.6 Metal–organicchemicalvapourdeposition 153
8.11.7 Hydridevapourphaseepitaxy(HVPE)fornitridedevices 154
Exercises 155
9 Principles of semiconductor devices
9.1 Introduction 157
9.2 Thep–njunctioninequilibrium 157
9.3 Rectification 162
9.4 Injection 164
9.5 Junctioncapacity 166
9.6 Thetransistor 166
9.7 Metal–semiconductorjunctions 172
9.8 Theroleofsurfacestates;realmetal–semiconductorjunctions 174
9.9 Metal–insulator–semiconductorjunctions 176
9.10 Thetunneldiode 179
9.11 Thebackwarddiode 182
9.12 TheZenerdiodeandtheavalanchediode 182
9.12.1 Zenerbreakdown 183
9.12.2 Avalanchebreakdown 183
9.13 Varactordiodes 184
