半导体.docx
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半导体.docx
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半导体
semiconductor
Asemiconductorisamaterialthathasanelectricalconductivitybetweenthatofaconductorandaninsulator,thatis,generallyintherange103siemenspercentimeterto10−8S/cm.Devicesmadefromsemiconductormaterialsarethefoundationofmodernelectronics,includingradio,computers,telephones,andmanyotherdevices.Semiconductordevicesincludethevarioustypesoftransistor,solarcells,manykindsofdiodesincludingthelight-emittingdiode,thesiliconcontrolledrectifier,anddigitalandanalogintegratedcircuits.Solarphotovoltaicpanelsarelargesemiconductordevicesthatdirectlyconvertlightenergyintoelectricalenergy.Anexternalelectricalfieldmaychangeasemiconductor'sresistivity.Inametallicconductor,currentiscarriedbytheflowofelectrons.Insemiconductors,currentcanbecarriedeitherbytheflowofelectronsorbytheflowofpositively-charged"holes"intheelectronstructureofthematerial.
Commonsemiconductingmaterialsarecrystallinesolidsbutamorphousandliquidsemiconductorsareknown,suchasmixturesofarsenic,seleniumandtelluriuminavarietyofproportions.Theysharewithbetterknownsemiconductorsintermediateconductivityandarapidvariationofconductivitywithtemperaturebutlacktherigidcrystallinestructureofconventionalsemiconductorssuchassiliconandsoarerelativelyinsensitivetoimpuritiesandradiationdamage.
Siliconisusedtocreatemostsemiconductorscommercially.Dozensofothermaterialsareused,includinggermanium,galliumarsenide,andsiliconcarbide.Apuresemiconductorisoftencalledan“intrinsic”semiconductor.Theconductivity,orabilitytoconduct,ofcommonsemiconductormaterialscanbedrasticallychangedbyaddingotherelements,called“impurities”tothemeltedintrinsicmaterialandthenallowingthemelttosolidifyintoanewanddifferentcrystal.Thisprocessiscalled"doping"
Energybandsandelectricalconduction
Theelectronsinsemiconductorscanhaveenergiesonlywithincertainbands(i.e.rangesoflevelsofenergy)betweentheenergyof
thegroundstate,correspondingtoelectronstightlyboundtotheatomicnucleiofthematerial,andthefreeelectronenergy,
whichistheenergyrequiredforanelectrontoescapeentirelyfromthematerial.Theenergybandseachcorrespondtoalarge
numberofdiscretequantumstatesoftheelectrons,andmostofthestateswithlowenergy(closertothenucleus)arefull,up
toaparticularbandcalledthevalenceband.Semiconductorsandinsulatorsaredistinguishedfrommetalsbecausethevalenceband
inthesemiconductormaterialsisnearlyfilledunderusualoperatingconditions,thuscausingmoreelectronstobeavailablein
the"conductionband,"whichisthebandimmediatelyabovethevalenceband.
Theeasewithwhichelectronsinasemiconductorcanbeexcitedfromthevalencebandtotheconductionbanddependsonthebandgapbetweenthebands,anditisthesizeofthisenergybandgapthatservesasanarbitrarydividingline(roughly4eV)betweensemiconductorsandinsulators.
Inthepictureofcovalentbonds,anelectronmovesbyhoppingtoaneighboringbond.BecauseofthePauliexclusionprincipleithastobeliftedintothehigheranti-bondingstateofthatbond.Inthepictureofdelocalizedstates,forexampleinonedimension-thatisinananowire,foreveryenergythereisastatewithelectronsflowinginonedirectionandonestatefortheelectronsflowingintheother.Foranetcurrenttoflowsomemorestatesforonedirectionthanfortheotherdirectionhavetobeoccupiedandforthisenergyisneeded,inthesemiconductorthenexthigherstateslieabovethebandgap.Oftenthisisstatedas:
fullbandsdonotcontributetotheelectricalconductivity.However,asthetemperatureofasemiconductorrisesaboveabsolutezero,thereismoreenergyinthesemiconductortospendonlatticevibrationand—moreimportantlyforus—onliftingsomeelectronsintoanenergystatesoftheconductionband.Thecurrent-carryingelectronsintheconductionbandareknownas"freeelectrons",althoughtheyareoftensimplycalled"electrons"ifcontextallowsthisusagetobeclear.
Electronsexcitedtotheconductionbandalsoleavebehindelectronholes,orunoccupiedstatesinthevalenceband.Boththeconductionbandelectronsandthevalencebandholescontributetoelectricalconductivity.Theholesthemselvesdon'tactuallymove,butaneighboringelectroncanmovetofillthehole,leavingaholeattheplaceithasjustcomefrom,andinthiswaytheholesappeartomove,andtheholesbehaveasiftheywereactualpositivelychargedparticles.
Onecovalentbondbetweenneighboringatomsinthesolidistentimesstrongerthanthebindingofthesingleelectrontotheatom,sofreeingtheelectrondoesnotimplydestructionofthecrystalstructure.
Holes:
electronabsenceasachargecarrier
Themotionofholes,whichwasintroducedforsemiconductors,canalsobeappliedtometals,wheretheFermilevellieswithintheconductionband.WithmostmetalstheHalleffectrevealselectronstobethechargecarriers,butsomemetalshaveamostlyfilledconductionband,andtheHalleffectrevealspositivechargecarriers,whicharenottheion-cores,butholes.Contrastthistosomeconductorslikesolutionsofsalts,orplasma.Inthecaseofametal,onlyasmallamountofenergyisneededfortheelectronstofindotherunoccupiedstatestomoveinto,andhenceforcurrenttoflow.Sometimeseveninthiscaseitmaybesaidthataholewasleftbehind,toexplainwhytheelectrondoesnotfallbacktolowerenergies:
Itcannotfindahole.Intheendinbothmaterialselectron-phononscatteringanddefectsarethedominantcausesforresistance.
Fermi-Diracdistribution.StateswithenergyεbelowtheFermienergy,hereµ,havehigherprobabilityntobeoccupied,andthoseabovearelesslikelytobeoccupied.Smearingofthedistributionincreaseswithtemperature.
Theenergydistributionoftheelectronsdetermineswhichofthestatesarefilledandwhichareempty.ThisdistributionisdescribedbyFermi-Diracstatistics.Thedistributionischaracterizedbythetemperatureoftheelectrons,andtheFermienergyorFermilevel.UnderabsolutezeroconditionstheFermienergycanbethoughtofastheenergyuptowhichavailableelectronstatesareoccupied.Athighertemperatures,theFermienergyistheenergyatwhichtheprobabilityofastatebeingoccupiedhasfallento0.5.
Thedependenceoftheelectronenergydistributionontemperaturealsoexplainswhytheconductivityofasemiconductorhasastrongtemperaturedependency,asasemiconductoroperatingatlowertemperatureswillhavefeweravailablefreeelectronsandholesabletodothework.
Energy–momentumdispersion
Intheprecedingdescriptionanimportantfactisignoredforthesakeofsimplicity:
thedispersionoftheenergy.Thereasonthattheenergiesofthestatesarebroadenedintoabandisthattheenergydependsonthevalueofthewavevector,ork-vector,oftheelectron.Thek-vector,inquantummechanics,istherepresentationofthemomentumofaparticle.
Thedispersionrelationshipdeterminestheeffectivemass,m*,ofelectronsorholesinthesemiconductor,accordingtotheformula:
Theeffectivemassisimportantasitaffectsmanyoftheelectricalpropertiesofthesemiconductor,suchastheelectronorholemobility,whichinturninfluencesthediffusivityofthechargecarriersandtheelectricalconductivityofthesemiconductor.
Typicallytheeffectivemassofelectronsandholesaredifferent.Thisaffectstherelativeperformanceofp-channelandn-channelIGFETs.
Thetopofthevalencebandandthebottomoftheconductionbandmightnotoccuratthatsamevalueofk.Materialswiththissituation,suchassiliconandgermanium,areknownasindirectbandgapmaterials.Materialsinwhichthebandextremaarealignedink,forexamplegalliumarsenide,arecalleddirectbandgapsemiconductors.Directgapsemiconductorsareparticularlyimportantinoptoelectronicsbecausetheyaremuchmoreefficientaslightemittersthanindirectgapmaterials.
Carriergenerationandrecombination
Formoredetailsonthistopic,seeCarriergenerationandrecombination.
Whenionizingradiationstrikesasemiconductor,itmayexciteanelectronoutofitsenergylevelandconsequentlyleaveahole.Thisprocessisknownaselectron–holepairgeneration.Electron-holepairsareconstantlygeneratedfromthermalenergyaswell,intheabsenceofanyexternalenergysource.
Electron-holepairsarealsoapttorecombine.Conservationofenergydemandsthattheserecombinationevents,inwhichanelectronlosesanamountofenergylargerthanthebandgap,beaccompaniedbytheemissionofthermalenergy(intheformofphonons)orradiation(intheformofphotons).
Insomestates,thegenerationandrecombinationofelectron–holepairsareinequipoise.Thenumberofelectron-holepairsinthesteadystateatagiventemperatureisdeterminedbyquantumstatisticalmechanics.Theprecisequantummechanicalmechanismsofgenerationandrecombinationaregovernedbyconservationofenergyandconservationofmomentum.
Astheprobabilitythatelectronsandholesmeettogetherisproportionaltotheproductoftheiramounts,theproductisinsteadystatenearlyconstantatagiventemperature,providingthatthereisnosignificantelectricfield(whichmight"flush"carriersofbothtypes,ormovethemfromneighbourregionscontainingmoreofthemtomeettogether)orexternallydrivenpairgeneration.Theproductisafunctionofthetemperature,astheprobabilityofgettingenoughthermalenergytoproduceapairincreaseswithtemperature,beingapproximatelyexp
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