材料物理课件chapter 12 electrical properties

材料物理课件chapter12electricalproperties*Top:Scanningelectronmicrographofanintegratedcircuit.Center:Asilicondotmapfortheintegratedcircuitabove,showingregionswheresiliconatomsareconcentrated.Dopedsiliconisthesemiconductingmaterialfromwhichintegratedcircuitelementsaremade.Bottom:Analuminumdotmap.Metallicaluminumisanelectricalconductorand,assuch,wiresthecircuitelementstogether.Approximately200.IntroductionConsiderationoftheelectricalpropertiesofmaterialsisoftenimportantwhenmaterialsselectionandprocessingdecisionsarebeingmadeduringthedesignofacomponentorstructure.Theelectricalbehaviorsofthevariousmaterialsarediverse.Someneedtobehighlyelectricallyconductive(e.g.,connectingwires),whereaselectricalinsulativityisrequiredofothers(e.g.,theprotectivepackageencapsulation).**Objectives1.Describethefourpossibleelectronbandstructuresforsolidmaterials.2.Brieflydescribeelectronexcitationeventsthatproducefreeelectrons/holesin(a)metals,(b)semiconductors(intrinsicandextrinsic),and(c)insulators.3.Calculatetheelectricalconductivitiesofmetals,semiconductors(intrinsicandextrinsic),andinsulatorsgiventheirchargecarrierdensity(s)andmobility(s).4.Distinguishbetweenintrinsicandextrinsicsemiconductingmaterials.5.Notethemannerinwhichelectricalconductivitychangeswithincreasingtemperaturefor(a)metals,(b)semiconductors,and(c)insulatingmaterials.**6.Forap–njunction,explaintherectificationprocessintermsofelectronandholemotions.7.Calculatethecapacitanceofaparallel-platecapacitor.8.Definedielectricconstantintermsofpermittivities.9.Brieflyexplainhowthechargestoringcapacityofacapacitormaybeincreasedbytheinsertionandpolarizationofadielectricmaterialbetweenitsplates.10.Nameanddescribethethreetypesofpolarization.**12-1.ELECTRICALCONDUCTION12.2.OHM’SLAWTheeasewithwhichasolidmaterialtransmitsanelectriccurrent(12.1)V,I,andR:voltageinvolts(J/C),currentinamperes(C/s),andresistanceinohms(V/A).Risinfluencedbyspecimenconfiguration,resistivityisindependentofspecimengeometry(12.2)**:ohm-meters(-m)(12.3)12.3ELECTRICALCONDUCTIVITY(12.4)Capabilityofconductionganeletriccurrent,:[(-m)-1,ormho/m],Ohm’slawmaybeexpressedas(12.5)*J:currentdensity,thecurrentperunitcrosssectionalareaofspecimeni.e.,I/A,ε:electricfieldintensity,orthevoltagedifferencebetweentwopointsdividedbythedistance(12.6)※Conductors,semiconductors,andinsulatorsConductors:e.g.,metals,σ=~107(-m)–1Insulators:10-20(-m)-1Semiconductors:10-6to104(-m)12.4ELECTRONICANDIONICCONDUCTIONelectronicconduction:electrons,Ionicconduction:ions*12.5.ENGERYBANDSTRUCTRUESINSOLIDS5-1.AtomicStructure(singleatoms)◎Shells:designatedbyintegers(principlequantumnumber,I.e.,1,2,3,etc),subshells:byletters(s,p,d,andf)◎Eachofs,p,d,andfsubshells:one,three,five,andsevenstates◎Twoelectronsofoppositespinperstate:Pauliexclusionprinciple*5-2.MoleculesandSolidMaterials◎Astheatomscomewithincloseproximityofoneanother,electronsareactedupon,orperturbed,bytheelectronsandnucleiofadjacentatoms.Eachdistinctatomicstatemaysplitintoaseriesofcloselyspacedelectronstates:electronenergyband.◎ThenumberofstateswithineachbandwillequalthetotalofallstatescontributedbytheNatoms.Forexample,ansbandwillconsistofNstates,andapbandof3Nstates.Eachenergystatemayaccommodatetwoelectrons,whichmusthaveoppositelydirectedspins.**EnergystatesofindividualatomsapreciselevelEnergybandofsolid(particle)abandwithawidthInteractionInteractionEnergybandwidthbandgapValenceelectronsatamoreoutershelldopingofimpurityothershigherextentOfinteractionsmallerbandgap*◎Theelectricalpropertiesareaconsequenceofitselectronbandstructure:thearrangementoftheoutermostelectronbandsandthewayinwhichtheyarefilledwithelectrons.(Eletricalconductionoccursonlywhenthereareavailablepositions(emptystatesorholes)forelectronstomove.)◎Fourdifferenttypesofbandstructuresarepossibleat0k:•Thefirst:partiallyfilled(valence)band:conductor(Eg=0,i.e.,nobandgap),e.g.,copper,one4selectron(peratom),onlyhalftheavailableelectornpositionswithinthis4Sbandarefilled.◎ForSolid：*•Thesecond:overlapofanempty(conduction)bandandafilled(valence)band:conductor(Eg=0,i.e.,nobandgap),e.g.,Mg,the3sand3pbandsoverlap.•Thefinaltwo:valenceband(completelyfilled)isseparatedfromconductionband(empty)byaenergybandgap.Formaterialsthatthebandgapisrelativelywide(Eg>2eV,Figure12.4c):insulations;forEg=0.02-3eV:semiconductors(Figure12.4d)◎Theenergycorrespondingtothehighestfilledstateat0kiscalledtheFermienergyEf.***OnlyelectronswithenergiesgreaterthantheFermienergymaybeactedonandacceleratedinthepresenceofanelectricfield.Thesearetheelectronsthatparticipateintheconductionprocess:freeelectrons.Anotherchargedelectronicentity:holefoundinsemiconductorsandinsulators.HoleshaveenergieslessthanEfandalsoparticipateinelectronicconduction.Distinctionbetweenconductorsandnonconductors(insulatorsandsemiconductors):numbersofthesefreeelectronandholechargecarriers.12.6.CONDUCTIONINTERMSOFBANDANDATOMICBONDINGMODELS*6-1.METALS◎Foranelectrontobecomefree,itmustbeexcitedorpromotedintooneoftheemptyandavailableenergystatesaboveEf(Figures12.4aand12.4b).Generally,theenergyprovidedbyanelectricfieldissufficienttoexcitelargenumbersofelectronsintotheseconductingstates.(alsothermalenergyatroomtemperature)◎ForthemetallicbondingmodeldiscussedinSection2.6,althoughthevalenceelectronsarenotlocallyboundtoanyparticularatom,theymustexperiencesomeexcitationtobecomeconductingelectronsthataretrulyfree.**6-2.INSULATORSANDSEMICONDUCTORS◎Tobecomefree,electronsmustbepromotedacrosstheenergybandgapandintoemptystatesoftheconductionband.ThisispossibleonlybysupplyingenergyapproximatelyequaltothebandgapenergyEg.Formanymaterialsthisbandgapisseveralelectronvoltswide.Mostoftentheexcitationenergyisfromanonelectricalsourcesuchasheatorlight,usuallytheformer.◎Thenumberofelectronsexcitedthermally(byheatenergy)intotheconductionbanddependsontheenergybandgapwidthaswellastemperature.*Distinctionbetweensemiconductorsandinsulatorsliesinthewidthofthebandgap;semiconductors:narrow(0.03-2eV);insulatingmaterials:wide(>2eV)Forelectricallyinsulatingmaterials,interatomicbondingisionicorstronglycovalent(Section2.6).Thebondinginsemiconductorsiscovalent(orpredominantlycovalent)andrelativelyweak.*12.7ELECTRONMOBILTTY◎Accordingtoquantummechanics,thereisnointeractionbetweenanacceleratingelectronandatomsinaperfectcrystallattice:aslongastheelectricfieldisapplied,anelectriccurrentiscontinuouslyincreasingwithtime.◎Infact,acurrentreachesaconstantvaluetheinstanttheafieldisapplied:thereexistfrictionalforces,frictionalforces:scatteringofelectronsbyimperfectionsincludingimpurityatoms,vacancies,interstitialatoms,dislocations,andeventhethermalvibrationsoftheatomsthemselves.◎electriccurrent:netelectronmotion*Extentofthisscattering:driftvelocityandthemobilityofanelectronDriftvelocity,vd:averageelectronvelocityinthedirectionoftheforceimposedbytheappliedfield,ε(12.7)e:electronmobilityTheconductivityofmostmaterials:(12.8)n:numberoffreeorconductingelectronsperunitvolumee:absolutemagnitudeoftheelectricalchargeonanelectron(1.6×10-19C)*12.8ELECTRICALRESISTIVITYOFMTALS◎Mostmetalsareextremelygoodconductors:becauseofthelargenumbersoffreeelectronsthathavebeenexcitedintoemptystatesabovetheFermienergy(nhasalargevalue)◎Crystallinedefectsserveasscatteringcentersforconductionelectronsithasbeenobservedexperimentallythatthetotalresistivitytotalofametalisthesumofthecotributionsfromthermalvibrationstimpuritiesi,andplaticdeformation(d,coldwork):(scatteringmechanismsactindependently)(12.9)Matthiessen’srule*INFLUENCEOFTEMPERATURE(12.10)0anda:constantsDependenceofthethermalresistivityontemperature:thermalvibrations(热振动)andotherlatticeirregularities(晶格不规则即缺陷,e.g.,vacancies)increasewithtemperature,whichserveaselectron-scatteringcenters.*INFLUENCEOFIMPURITIESForasolidsolution(12.11)A:composition-independentconstant,ci:impurityconcentrationelectronsarescatteredbyimpurities.Ci<0.5：iistheminorphaseCi>0.5：iisthemajorphase*Foratwo-phasealloyconsistingofandphases(12.12)V’sand’s:volumefractionsandindividualresistivitiesINELUENCEOFPLASTICDEFORMATIONElectron-scatteringbydislocations(whichareincreasedinconcentrationduetodeformation)***12.9.ELECTRICALCHARACTERISTICSOFCOMMERCIALALLOYS◎Solidsolutionalloyingandcoldworking:improvestrengthattheexpenseofconductivity(duetoincreasesinimpurityanddislocationconcentrations),atradeoffmustbemade.◎Forsomeapplications,suchasfurnaceheatingelements,ahighelectricalresistivityisdesirable,analloyinsteadofpuremetalisused:e.g.,anickel-chromiumalloy(Nichrome)isusedasheatingelements.*SEMICONDUCTIVITY◎Theelectricalpropertiesofthesematerialsareextremelysensitivetotemperature(Intrinsic)orthepresenceofevenminuteconcentrationsofimpurities(extrinsic).12.10.INTRINSICSEMICONDUCTION◎Figure12.4d:at0K:acompletelyfilledvalenceband,emptyconductionbandandrelativelynarrowbandgap(<2eV.)twoelementalsemiconductors:silicon(Si)germanium(Ge)1.1and0.7EV*◎Compoundsemiconductingmaterials:betweenelementsofGroupsIIIAandVA,e.g.,galliumarsenide(GaAs)andindiumantimonide(InSb);(III-Vcompounds).GroupsIIBandVIA,e.g.,cadmiumsulfide(Cds)andzinctelluride(ZnTe).◎Asthetwoelementsformingthesecompoundsbecomemorewidelyseparatedwithrespecttotheirrelativepositionsintheperiodictable(i.e.,theelectrongegativitiesbecomemoredissimilar,Figure2.7).Theatomicbondingbecomesmoreionicandthemagnitudeofthebandgapenergyincreases-thematerialstendtobecomemoreinsulative.**◎Treatingamissingelectronasapositivelychargedparticlecalledahole(空穴).Aholeisconsideredtohaveachargethatisofthesamemagnitudeasthatforanelectron,butofoppositesign(+1.6×10-18C).Inthepresenceofanelectricfield,excitedelectronsandholesarescatteredbylatticeimperfections.CONCEPTOFAHOLE**INTRINSICCONDUCTIVITY◎Twotypesofchargecarrier:freeelectrons(自由电子)andholes(空穴).(12.13)P:numberofholespercubicmeter,h:holemobility;hisalwayslessthaneforsemiconductors.Forintrinsicsemiconductors,n=p=ni(12.14)(12.15)ni:intrinsiccarrierconcentration*12.11EXTRINSICSEMICONDUCTIONElectricalbehaviorisdeterminedbyimpurites(inevenminuteconcentrations):introduceexcesselectronsorholesn-TYPEEXTRINSICSEMICONDUCTION◎Considertheelementalsemiconductorsilicon.Animpurityatomwithavalenceof5isaddedasasubstitutionalimpurity(GroupVA,e.g.,P,As,andSb):Theextranonbondingelectronislooselyboundbyaweakelectrostaticattraction,bindingenergy:ontheorderof0.01eV.***◎Foreachofthelooselyboundelectrons,itsenergylevel,orenergystate,islocatedwithintheforbiddenbandgap,justbelowthebottomoftheconductionband.Theelectronbindingenergycorrespondstotheenergyrequiredtoexcitetheelectrontotheconductionband.◎Eachexcitationeventsuppliesordonatesasingleelectrontotheconductionband:animpurityofthistypeistermedadonor.Noholeiscreatedwithinthevalenceband.*Atroomtemperature,thethermalenergyavailableissufficienttoexcitelargenumbersofelectronsfromdonorstates;intrinsicvalence-conductionbandtransitionsisnegligible,numberofelectronsintheconductionbandfarexceedsthenumberofholesinthevalenceband(orn>>p)(12.16)Amaterialofthistypeissaidtobeann-typeextrinsicsemiconductor.Electrons:majoritycarriers;holes:minoritychargecarriers.Forn-typesemiconductors,theFermilevelisshiftedupwardtowithinthevicinityofthedonorstate.*P-TYPEEXTRINSICSEMICONDUCTION◎Inadditiontosiliconorgermaniumoftrivalentsubstitiutionalimpurities,e.g.,aluminum,boron,andgalliumfromGroupIIIA,eachoftheseatomsisdeficient(欠缺)inanelectron:aholethatisweaklyboundtotheimpurityatom.Theelectronandtheholeexchangepositions.◎Eachimpurityatomofthistypeintroducesanenergylevelwithinthebandgap(acceptorstate.),aboveyetveryclosetothetopofthevalenceband(Figure12.14a).**◎Aholeisimaginedtobecreatedinthevalencebandbythethermalexcitationofanelectron:onecarrierisproduced-aholeinthevalenceband.Animpurityofthistypeiscalledanacceptorbecauseitiscapableofacceptinganelectronfromthevalenceband◎Forthistypeofextrinsicconductionp>>n,holes:majoritycarriers,electrons:minorityconcentrations(18.17)*◎TheFermilevelispositionedwithinthebandgapandneartotheacceptorlevel.◎Extrinsicsemiconductors(bothn-andp-type)areproducedfrommaterialsthatareinitiallyofextremelyhighpurity,commonlyhavingtotalimpuritycontentsontheorderof10-7at％.Donorsoracceptorsarethenintentionallyadded:doping.◎Inextrinsicsemiconductiors,largenumbersofchargecarrierseitherelectronsorholes,arecreatedatroomtemperature,electronicdevicesaretobeoperatedatambientconditions*12.12.THETEMPERATUREDEPENDENCEOFCARRIERCONCENTRATIONIntrinsiccarrierconcentration(electronsandholes)increasewithtemperaturebecause,withrisingtemperature,morethermalenergyisavailabletoexciteelectronsfromthevalencetotheconductionband.“－”：remainsunchangedCarrierconcentrationinGeisgreaterthanforSiduetogermanium’ssmallerbandgap(0.67versus1.11eV,Table12.2).PnEgT－－***◎Foranextrinsicsemiconductor.Forexample,electronconcentrationversustemperatureforsiliconthathasbeendopedwith1021m-3phosphorusatoms(Figure18.16)threeregions:Atintermediatetemperatures(betweenapproximately150kand450k)electronconcentrationisconstant:“extrinsic-temperatureregion”theelectronconcentrationisapproximatelyequaltothePcontent(1021m-3);atlowtemperatures,(belowabout100k),thethermalenergyisinsufficienttoexciteelectronsfromthePdonorlevelintotheconductionband:“freeze-outtemperatureregion”;athightemperature“intrinsictemperatureregion”thesemiconductorbecomesintrinsic.**FACTORSTHATAFFECTCARRIERMOBILITY◎Electronandholemobilitiesareaffectedby:crystallinedefects(sameareresponsibleforthescatteringelectronsinmetals):thermalvibrations(i.e.,temperature)andimpurityatoms.INFLUENCEOFDOPANTCONTENT◎Atdopantconcentrationslessthanabout1020m-3,bothcarriermobilitiesareattheirmaximumlevelsandindependentofthedopingconcentration.Bothmobilitiesdecreasewithincreasingimpuritycontent.Themobilityofelectronsisalwayslargerthanthemobilityofholes.*INFLUENCEOFTEMPERATURE◎Fordopantconcentrationsof1024m-3andbelow,bothelectronandholemobilitiesdecreaseinmagnitudewithrisingtemperature.◎Forbothelectronsandholes,anddopantlevelslessthan1020m-3,mobilityisindependentofacceptor/donorconcentration◎Whendopantconc.1024m-3,bothdopantconc.andtempeffectareevident(important).◎Whendopantconc,>1024m-3,dopantconc.effectisevident(important),buttempeffectisnot.****12.13HallEffectThisHalleffectisaresultofthephenomenonwherebyamagneticfieldappliedperpendiculartothedirectionofmotionofachargedparticleexertsaforceontheparticleperpendiculartoboththemagneticfieldandtheparticlemotiondirections.*Thus,avoltage,termedtheHallvoltageVH,willbeestablishedintheydirection.ThemagnitudeofVHwilldependonIx,Bz,andthespecimenthicknessdasfollows:InthisexpressionRHistermedtheHallcoefficient,whichisaconstantforagivenmaterial.Formetals,whereinconductionisbyelectrons,RHisnegativeandequalto*Thus,themagnitudeofμemayalsobedeterminediftheconductivityσhasalsobeenmeasured.Forsemiconductingmaterials,thedeterminationofmajoritycarriertypeandcomputationofcarrierconcentrationandmobilityaremorecomplicatedandwillnotbediscussedhere.*Theelectricalconductivityandelectronmobilityforaluminumare3.8×107(Ω-m)-1and0.0012m2/V-s,respectively.CalculatetheHallvoltageforanaluminumspecimenthatis15mmthickforacurrentof25Aandamagneticfieldof0.6tesla(imposedinadirectionperpendiculartothecurrent)Problems*Solution*12.14SEMICONDUCTORDEVICESTwofamiliarexamples:diodes(二极管)andtransistors(晶体管,replacedold-fashionedvacuumtubes).Advantagesofsemiconductordevices(sometimestermedsolid-statedevices):smallsize,lowpowerconsumption,andnowarmuptime.THEp-nRECTIFYINGJUNCTIONArectifier(整流器),ordiode:allowsthecurrenttoflowinonedirectiononly;e.g.,transformsanalternatingcurrentintodirectcurrent.Before,vacuumtubediode.**◎Forwardbias:Largenumbersofchargecarriersflowacrossthesemiconductorasevidencedbyanappreciablecurrentandalowresistivity.Electron+hole◎Reversebias:Thejunctionregionisrelativelyfreeofmobilechargecarriers,thejunctionishighlyinsulative.Athighreversebiasvoltages,orderofseveralhundredvolts,largenumbersofchargecarriers(electronsandholes)aregenerated.Averyabruptincreaseincurrent:breakdown.energy(12.18)**THETRANSISTOR◎Twoprimarytypesoffunction:First,thetriode(三极管):amplifyanelectricalsignal;Second,serveasswitchingdevicesincomputersfortheprocessingandstorageofinformation.Twomajortypes:junction(orbimodal)transistorandmetal-oxide-semiconductorfield-effecttransistorMOSFET)JUNCTIONTRANSISTORS◎Averythinn-typebaseregionissandwichedinbetweenp-typeemitterandcollectorregions.Thecircuitthatincludestheemitter–basejunction(junction1)isforwardbiased,whereasareversebiasvoltageisappliedacrossthebase–collectorjunction(junction2).*◎Asmallincreaseininputvoltagewithintheemitter-basecircuitproducesalargeincreaseincurrentacrossjunction2.Thus,avoltagesignalthatpassesthroughajunctiontransistorexperiencesamplification.◎Similarreasoning,n-p-ntransistor:electronsinsteadofholesareinjectedacrossthebaseandintothecollector*TheMOSFET◎OnevarietyofMOSFET:twosmallislandsofp-typesemiconductorthatarecreatedwithinasubstrateofn-typesilicon.Appropriatemetalconnections(sourceanddrain)aremadetotheseislands;aninsulatinglayerofsilicondioxideisformedbythesurfaceoxidationofthesilicon.Afinalconnector(gate)isthenfashionedontothesurfaceofthisinsulatinglayer.Apositivefieldonthegatewilldrivechargecarriers(inthiscaseholes)outofthechannel,therebyreducingtheelectricalconductivity.Thus,asmallalterationinthefield(negative)atthegatewillproducearelativelylargevariationincurrentbetweenthesourceandthedrain.*◎TheprimarydifferencebetweenjunctiontransistorandMOSFETsisthatthegatecurrentisexceedinglysmallincomparisontothebasecurrentofajunctiontransistor.MOSFETsare,therefore,usedwherethesignalsourcestobeamplifiedcannotsustainanappreciablecurrent.*SemiconductorsinComputers◎Transistorsanddiodesmayalsoactasswitchingdevices:forarithmeticandlogicaloperationandforinformationstorage.Computernumbersandfunctionsareexpressedintermsofabinarycode(desinated0and1)transistorsanddiodesalsohavetwostates-onandoff,(orconductingandnonconducting)◎Theprocessbeginswiththegrowthofrelativelylargecylindricalsinglecrystalsofhigh-puritysiliconfromwhichthincircularwafers(晶圆)arecut.MICROELECTRONICCIRCUITRY**◎Achip(晶片)isrectangular,typicallyontheorderof6mm(¼in.)onasideandcontainsthousandsofcircuitelements:diodes,transistors,resistors,andcapacitors.◎Atthistime,microprocessorchipscontaining500milliontransistorsarebeingproduced,andthisnumberdoublesaboutevery18months.Microelectroniccircuitsconsistofmanylayers.Usingphotolithographictechniques(光刻技术).Circuitelementsareconstructedbytheselectiveintroductionofspecificmaterials(bydiffusion(扩散)orionimplantation(离子植入))intounmaskedregionstocreatelocalizedn-type,p-type,high-resistivity,orconductiveareas.*ELECTRICALCONDUCTIONINIONICCERAMICSANDINPOLYMERS◎Mostpolymersandionicceramicsareinsulatingmaterialsatroomtemperature:(Figure12.4c)afilledvalencebandisseparatedfromanemptyconductionbandwithabandgapgreaterthan2eV.12.15.CONDUCTIONININOICMATERIALS◎Bothcationsandanionsarecapableofmigrationordiffusionwhenanelectricfieldispresent.Thetotalconductivityofanionicmaterialtotalisthusequaltothesumofbothelectronicandioniccontributions.(12.25)*MobilityI(12.26)nIandDI:valenceanddiffusioncoefficeientofparticularion;theioniccontributiontothetotalconductivityincreaseswithincreasingtemperature.Howevermostionicmaterialsremaininsulative,evenatelevatedtemperatures.Exceptthosedopedwithsmallions.12.16ELECTRICALPROPERTIESOFPOLYMERSMostpolymericmaterialsarepoorconductorsofelectricity(unavailabilityoffreeelectrons)*CONDUCTINGPOLYMERS◎Conductivitiesashighas1.5×107(-m)-1havebeenachievedinthesematerials;(onavolumebasis,one-fourthoftheconductivityofcopper,ortwiceitsconductivityonthebasisofweight)e.g.,polyacetylene,polyparaphenylene,polypyrrole,andpolyanilinethathavebeendopedwithappropriateimpurities.◎Asisthecasewithsemiconductors,thesepolymersmaybemadeeithern-type(i.e.,free-electrondominant)orp-type(i.e.,holedominant)dependingonthedopant.However,unlikesemiconductors,thedopantatomsormoleculesdonotsubsitutefororreplaceanyofthepolymeratoms.*◎Highpuritypolymershaveelectronbandstructurescharacteristicofelectricalinsulators.Themechanismbywhichlargenumbersoffreeelectronsandholesaregeneratedintheseconductingpolymersiscomplexandnotwellunderstood.Itappearsthatthedopantatomsleadtotheformationofnewenergybandsthatoverlapthevalenceandconductionbandsoftheintrinsicpolymer,giv