半導(dǎo)體光電子器件

SemiconductorOptoelectronicsProf.Xiaoxia.ZhangRoom225,SchoolofOpto-ElectronicInformationEmail:xxzhang@Webhttp://Tel:(028)83202342-1,Fax:(028)83201412OfficeHours:3-4WednesdayandFridaySummaryofCourseContentIntroductiontosemiconductoroptoelectronicdevicesforcommunicationsandotherapplications,coveringoperatingprinciplesandpracticaldevicefeaturesGoalsUnderstandthemajorsemiconductoroptoelectronicdevices,theiroperatingprinciples,designs,uses,strengthsandweaknesses.Plannedtopics1.Reviewofbasicsemiconductorphysics2.Heterostructures3.Opticalabsorption,emission,andrefractionprocesses4.Semiconductorpnjunctiondiodes5.Light-emittingdiodes(LEDs)6.Semiconductoropticaldetectors7.Modulators8.SemiconductorlasersWhatdeterminesthewavelengthsutilized?1)Humaneyeresponse(IndicatorsandDisplays)2)Transmissionmedia?Fibers?AtmosphericTransmission3)SourceofRadiation(Detectors)?Sun(SolarSpectrum)?Blackbody–T?Lasers4)TechnologicallyavailablematerialsHumanEyeResponseLasersandLEDsfordisplaysorlightingmustemitinthe430-670nmwavelengthregion(bandgapsof3.0-1.9eV).CrystalsCompoundsemiconductorsBlochtheoremBandstructureandtheBrillouinzoneEffectivemassapproximationKanebandtheoryresultsSemiconductorstatisticalmechanics1.ReviewofBasicSemiconductorPhysicsCrystalsAllmaterialsinthiscoursearecrystallinesemiconductorsCrystal-astructurethatcanfillallspacebasedontheregularrepetitionofaparticularunitcellUnitcell-unittoconstructcrystalbyregularrepetition?Primitive-smallestcellwhichwillreplicatethecrystal?LargerCubic-mostsemiconductorsarediamondor

zincblendeforwhichtheprimitiveunitcelliscomplexDiamondandZincblendeLatticesUnitcellsforsilicon(Si)andgalliumarsenide(GaAs)Silicon-diamondlatticeGaAs-zincblende(cubiczincsulfide)lattice(mostotherIII-VandmanyII-VIsemiconductorshavezincblendelattice)Diamondandzincblendelatticebasedontetragonalpatternofbondsfromeachatomtonearestneighbors-twointerlockingfacecentered-cubiclatticeslatticeparameter(orconstant),a-repeatlengthoftheunitcellse.g.,GaAs,a=5.65?(Angstroms)=0.565nm.WurtziteLatticeWurtzitestructureFoundinAlN,GaN,InNThesematerialshaverevolutionizedshort-wavelengthlightemitters(e.g.,blueandgreenLEDs)BasedonthesametetragonalsetofbondsfromeachatomTwointerlockinghexagonalclose-packedlatticesofthetwodifferent("dark"and"light")atoms.Note-WurtzitehasdifferentSymmetryproperties(e.g.,hexagonal,notcubic)andDifferentbandstructuresfromzincblendematerialsCompoundSemiconductorsForoptoelectronics,mostdevicesarefabricatedof“compoundsemiconductors”particularlyIII-Vmaterialsmadefrom?GroupIII(Al,Ga,In)?GroupV(N,P,As,Sb)elements?SometimesSiandGe(GroupIV)areusedasphotodetectors?SometimesII-VI(e.g.ZnSe)andIV-VImaterials(e.g.,PbTe)Alloysofcompoundsemiconductorsusedextensivelytoadjustthebasicmaterialsproperties,e.g.,latticeconstant,bandgap,refractiveindex,opticalemissionordetectionwavelength,etc.EXAMPLE-InxGa1-xAs(wherexisthemolefractionofindium)InxGa1-

xAsisnotstrictlycrystallinebecausenoteveryunitcellisidentical(randomIIIsitelocation),butwetreatsuchalloysascrystallinetoafirstapproximationConduction,valencebandsandbandgapsInthepure,perfect,semiconductor,thereisanenergygap,Eg,betweenhighest,filled,“valence”band(s),andlowestenergy,empty,“conduction”band(s)Inthevalencebands,weusetheconceptof"holes"(positivelychargedpseudo-particlewhichisthe"absenceofanelectron")ValencebandsinthepuresemiconductorareemptyofholesHoleenergyincreasesdownwardsontheE-kdiagramGalliumarsenideisa“directgap”semiconductorlowest“minimum”intheconductionbandisdirectlyabovethehighest“maximum”inthevalencebandinEvsk(momentum)Siliconisan“indirectgap”semiconductor(Geisalsoindirect)lowestCBmin.isatzoneedge,highestVBmax.isatzonecenterConduction,valencebands

andbandgaps(cont)DirectgapsareimportantformostoptoelectronicdevicesTheyhavemuchstrongeropticalabsorptionandemissionnearthebandgapenergyReason-conservationofmomentum(photonhassmallmomentumcomparedtoanelectronorhole)Transitionsare"vertical"onanEvs.kdiagramIndirecttransitionsrequireadditionalmomentum,usuallyfromaphonon(acrystallatticevibration),makingindirecttransitionsathreeparticleprocessandmuchweakerFirstBrillouinzoneEvs.kband

diagramofzincblendesemiconductorsOnerelevantconductionbandisformedfromS-likeatomicorbitals“unitcell”partofwavefunctionisapproximatelysphericallysymmetric.Thethreeuppervalencebandsareformedfrom(three)P-likeorbitalsandthespin-orbitinteractionsplitsofflowest,“split-off”hole(i.e.,valence)band.Theremainingtwoholebandshavethesameenergy(“degenerate”)atzonecenter,buttheircurvatureisdifferent,forminga“heavyhole”(hh)band(broad),anda“l(fā)ighthole”(lh)Band(narrower).Zonecenterbandstructureof

zincblendesemiconductorsMostopticalprocessesofinterestinoptoelectronicdevicesareindirectgapmaterialsandtakeplaceforphotonsnearthebandgapbecausethemomentumofelectronsandholesis>>>momentumofphotonsandtheenergyrelaxationtimesforelectronsandholesareveryshortcomparedtorecombinationtimesHencetheimportantregionofenergybandstructureisnearBrillouinzonecenterThe“goodnews”isthatthezonecenterregoinofthebandstructureforzincblendesemiconductorsisnearly“universal”“k?p”theory

Semiconductorbandstructurescanbecalculatedfromfirstprinciples,butitisquitedifficultandonlyapproximatebecauseitisamanyparticleproblem.Instead,nearmaximaandminima,onecanmakelocallyaccuratecalculationspredictingpropertytrends,presumingsomeparametersareknownIn“k?p”theory,weproceedasifweknewwavefunctionsandenergiesinsemiconductorbandsatspecialpointinBrillouinzone(e.g.,zonecenter,k=0)thentreattheregionnearthisspecialpointanalyticallyWeuseperturbationtheorywheretheperturbingHamiltonianisproportionaltok?pwherepisthemomentumoperator)Result-simplealgebraicrelationsbetweenbandenergiesandeffectivemasses(andopticalabsorption),basedonmeasurableparameters.k?pisaveryusefulsemi-empiricaltheoryOnekeyparameter,momentummatrixelementP(alsoexpressedasanenergy,Ep)isverysimilarinallthesemiconductorsofinterest,hencesimplescalingrelationsbetweenpropertiesofonesemiconductorandanother.KanetheorypredictionsStrongrelationbetweenbandgapenergyandeffectivemassElectronandlightholemassesscalestronglywithEge.g.,forEg<<Δ,theelectronandlightholemasses(inunitsoffreeelectronmass,mo)areboth~3Eg/2EpSinceEg~0.2-5eV,Δ~0.05-1eV,andEp~18-27eVforabroadrangeofsemiconductorsElectronsandlightholeshavesimilarmasses?muchlighterthanthefreeelectronmass(e.g.~0.02-0.15m0)?scalinginproportiontothebandgapenergy.Heavyholemass?notcloselyrelatedtothebandgapenergy?determinedbyinteractionswithbandsmoredistantinenergy?changeslittlebetweenmaterials,andtypicallyrelativelyheavy(e.g.,m*~0.4-0.8mo).Energy-WavelengthConversionBandgap“wavelengths”Conversionbetweenwavelength(inμm)andenergy(ineV)isThenumber1.24isworthremembering,andisquiteprecise(1.23985)MostIII-Vsemiconductorshave(direct)bandgapsatinfraredWavelengths--theexceptionisalloftheNitridebasedmaterials,AlN,GaNandInNandalloysofthesematerials.Theyareresponsiblefortherevolutioninvisiblelightemittingdiodesandsolid-statelighting.Densityofstates

Weneedtoknowhowmanyelectron(orhole)statesarewithinagivenenergyrangei.e.,“densityofstatesinenergy”-numberofstatesperunitenergyperunitcrystalvolumeFirstwewillcalculatethedensityofstatesink-space-thisisauniversalandsimpleresultandthenconvertthistoadensityinenergysincethat’stheparameterspacewenormallyworkin.AllowedStatesinkSpaceIllustrationoftheallowedstatesinkspace,shownhereinatwodimensionalsection,withtheallowedvaluesillustratedbydots.Listhelinearsizeofthe“box”inrealspace(assumedthesameinallthreedirections).Alsoshownisathinannulus(orsphericalshell)ofradiuskandthicknessdk

usedinthecalculationofthedensityofstatesinenergy.Semiconductorstatisticalmechanics-parabolicbandsSemiconductorstatisticalmechanics–

degenerateandnon-degeneratestatisticsTwolimitsLowdensity“non-degenerate”Maxwell-Boltzmannlimitgivessimpleanalyticresultshighdensity“degenerate”limitchemicalpotentialiswellintoband(μ>>kBT)approximateμby(zerotemperature)EFThisisacasewherethestatisticsare“degenerate”Thisshouldnottobeconfusedwithbandorstatedegeneracy,whichismorethanonequantumstatewithagivenenergyDegeneratestatisticsIf,however,theoccupationprobabilityofsomeofthestatesintheconductionbandapproaches1,wecannotusetheclassicalapproximation.WemustusethefullFermi-Diracformfortheoccupationprobabilities.IftheFermienergyrisesmanykBTabovethebottomoftheconductionband,thentheelectronstatisticsaresaidtobedegeneratethepositionoftheFermilevelisgivenapproximatelybyEq.(1.26)EventhoughweareatfinitetemperatureandsomeofthestateswithinkBTbelowtheFermilevelarenotfullyoccupied,thisnumberisapproximatelybalancedoutbythenumberofstatesoccupiedabovetheFermilevel,hencethe“zerotemperature”Eq.(1.26)isvalid.Inthiscase,wesaythatthesemiconductoris“degenerate”orhasdegeneratestatistics.(similarargumentsanddefinitionsholdforholes)TransitionstoDegenerateandNon-

DegenerateDistributionsWecanapproximatelydefinethetransitionsintothedegenerateandnon-degeneratelimitsintermsofwheretheFermilevelisrelativetothebandedge.IftheFermilevelis>2kBTbelowtheconductionbandedge,intothebandgapregion(ormorethan2kBTabovethevalencebandintothebandgapregion),thenthedistributionofelectrons(holes)isapproximatelynon-degenerateIftheFermilevelis>4kBTabovetheconductionbandedgeintotheconductionbanditself(oris>4kBTbelowthevalencebandedgeintothevalencebanditself)thenthedistributionofelectrons(orholes)isapproximatelydegenerate.ThechoicesoftheseparticularnumbersofkBTtodefinetheboundariesofdegenerateandnon-degeneratestatisticsistosomeextentarbitrary,buttheseparticularvaluescorrespondtotheusefulnessoftheselimitsasmathematicalapproximations.Usefulnessofdistinctionbetween

degenerateandnon-degeneratestatisticsIfweareinonelimitortheother,calculationsarerelativelysimple.NotethatnearlyallsiliconandGaAselectronicdevicesareinthenon-degeneratelimit,allowingvarioussimplerelations.ThereisaqualitativelyimportantdistinctionThephysicsisdifferentinthesetwolimitsandsomedevices(mostnotablysemiconductorlasers)onlyrunifatleastoneofthepopulations(electronsorholes)isdegenerate.Thisisrequiredinordertoachievestimulatedemission.Thereisnosuchrequirementforelectronicdevices.FermiintegralandapproximationsItisconvenientforvariouscalculationstoknowexplicitlyhowtodealwiththeFermiintegral(Eq.(1.28))despitethefactthatitcannotbeevaluatedanalytically.TheformoftheFermiintegralisshownfordegenerateandnon-degeneratelimitingcasesTherearetwousefulanalyticallimitstotheFermiintegral.Astemperaturegoestowardszero,theFermifunctiontendstowardsastepfunction,being1uptothechemicalpotential(Fermienergy),andzeroabovethechemicalpotential(Fermienergy),leadingto,Theintermediateregion(lightlyormoderatelydegenerate,thecaseformostsemiconductors)isnotaseasilyhandledSemiconductorstatisticalmechanics-

degeneratecaseRequiresmuchhighercarrierconcentrationstoachievedegeneratedistributionifthecarriermassislarge.Thenumberofcarrierscorrespondingtoaparticularvalueofm/kBT(andhenceofF(μ/kBT))risesas(m*)3/2e.g.heavyholemassinaIII-Vsemiconductorsis~10timeslargerthanelectronmass,henceonewouldneed~30timesasmanyholesaselectronstogettothesamedegreeofdegeneracy(i.e.,thesameμ/kBT).Thisisaproblemforsemiconductorlasersforwhichwedoalotofenergybandengineering(quantumwellsandstrain).Semiconductorstatisticalmechanics-

controllingμ(EF)

Importantcharacteristicsofasemiconductor(asopposedtoametal).Thechemicalpotential(Fermienergy)canbemovedbytheaddingverysmallamountsofdopantsorcreatingfreecarriers(photogeneration).Inanundopedsemiconductor,μliessomewherewithintheenergygap,generallynearmid-gap.Addingn-typedopantaddsextraelectronstothesystemμmovesclosertoorintotheconductionbandlargernumbersofelectrons(andfewerholes)Addingp-typedopant“adds”holestothesystemμmovesclosertoorintothevalencebandslargernumbersofholes(andfewerelectrons).Minoritycarrierdensity,Semiconductorstatisticalmechanics-

controllingμ(EF)(2)Quasi-FermienergiesIfweinjectelectronsand/orholesintothemateriale.g.,forwardbiaseddiodeNumberofelectronsand/orholesisnotgivensolelybydopingbutcontrolledbytheinflowa