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第六讲SemiconductorsquantumwellsQuantumconfinedstructuresGrowthandstructureofsemiconductorquantumwellsElectriclevelsOpticalabsorptionandexcitonsOpticalemissionQuantumwiresanddots1第六讲SemiconductorsquantumweQuantumconfinedstructuresTheopticalpropertiesofsolidsdonotusuallydependontheirsize.Ruby!Forverysmallcrystals,thentheopticalpropertiesdoinfactdependonthesize.Semiconductordopedglasses.
Thesizedependenceoftheopticalpropertiesinverysmallcrystalsisaconsequenceofthequantumconfinementeffect.Quantumconfinementeffect(量子限制效应或量子尺寸效应）:TheHeisenberguncertaintyprincipletellsusthatifweconfineaparticletoalength
x,thenweintroduceanuncertaintyinitsmomentumgivenby:Iftheparticleisfreeandhasamassm,theconfinementinthexdirectiongivesitanadditionalkineticenergyofmagnitude：Thisconfinementenergywillbesignificantonlyifitiscomparabletoorgreaterthanthekineticenergyoftheparticle(kBT)2QuantumconfinedstructuresTheQuantumeffectscriterionItmeansquantumsizeeffectswillbeimportantif:
xmustbeofthesameorderofmagnitudeasthedeBrogliewavelength
deB
forthethermalmotioninordertoobtainobviousquantumeffects.Foranelectroninatypicalsemiconductorwithme*=0.1m0atroomtemperature,
xmustbe~5nminordertoobservequantumconfinementeffects.Verythinlayers.3QuantumeffectscriterionItmQuantumWellQuantumWireQuantumDot1Dconfinement2Dconfinement3DconfinementThreebasictypesofquantumconfinedstructuresBulk:3-Dcrystals;Quantumwells:2-Dcrystals;Quantumwires:1-Dcrystals;Quantumdots:0-Dcrystals.Preparationtechniques:QuantumWells:advancedepitaxialcrystalgrowthQuantumWires:lithographictechiniqueorbyepitaxialgrowthQuantumDots:lithographicpatterningorbyspontaneousgrowthtechniques4QuantumWellQuantumWireQuantu第六讲SemiconductorsquantumwellsQuantumconfinedstructuresGrowthandstructureofsemiconductorquantumwellsElectriclevelsOpticalabsorptionandexcitonsOpticalemissionQuantumwiresanddots5第六讲SemiconductorsquantumweGrowthandstructureofsemiconductorquantumwellsEpitaxialcrystalgrowthtechniques:molecularbeamepitaxy(MBE,分子束外延)andmetal-organicchemicalvapourdeposition(MOCVD，金属有机物化学气相沉积)dischosentobecloseto:quantizedmotioninthezdirection,andfreemotioninthex,yplane.Energybandstructure:electronsandholesaretrappedinGaAslayerduetothediscontinuityofenergyband.multiplequantumwells(MQWs):Havelargerbvalues;isolatedSuperlattices:Havemuchthinnerbarbers;coupledandnewextendedstatesareformedinthezdirection;additionalproperties.6Growthandstructureofsemico第六讲SemiconductorsquantumwellsQuantumconfinedstructuresGrowthandstructureofsemiconductorquantumwellsElectriclevelsOpticalabsorptionandexcitonsOpticalemissionQuantumwiresanddots7第六讲SemiconductorsquantumweSeparationofthevariablesTheelectronsandholesinaquantumwelllayerarefreetomoveinthex,yplanebutareconfinedinthezdirection.Thisallowsustowritethewavefunctionsintheform:Freemotioninthex,yplane,thestatescanbydescribedbythewavevectork:Quantizedenergyinthezdirectiondescribedbythequantumnumbern:Thetotalenergyforanelectronorholeinthenthquantumlevelisthereforegivenby:8SeparationofthevariablesThInfinitepotentialwellsTheSchrodingerequation:Theboundarycondition:Thewavefunction:Thisformofwavefunctiondescribesastandingwaveinsidethewell:Theenergythatcorrespondstothenthlevelisgivenby:9InfinitepotentialwellsTheScTheenergyofthelevelsisinverselyproportionaltotheeffectivemassandthesquareofthewellwidth.theelectrons,heavyholesandlightholeswillallhavedifferentquantizationenergies.Inthevalenceband,theheavyholesaredominantinmostsituationsbecausetheyformthegroundstatelevel.Thewavefunctionscanbeidentifiedbytheirnumberofnodes,thenthlevelhas(n-1)nodes.Statesofoddnhaveevenparity,andviceversa.φ(-z)=+φ(z)(evenparity)orφ(-z)=-φ(z)(oddparity).10TheenergyofthelevelsisinFinitepotentialwellsGaAs/Al0.3Ga0.7AsquantumwellInrealquantumwellswithfinitebarriers,theparticlesareabletotunnelintothebarrierstosomeextent,andthisallowsthewavefunctiontospreadoutfurtherandthusreducestheconfinementenergy.Theinfinitewellmodeloverestimatesthequantizationenergy.Thequantizationenergiesofholesaresmallerthanthoseofelectrons(smallermass)(meV)11FinitepotentialwellsGaAs/Al0第六讲SemiconductorsquantumwellsQuantumconfinedstructuresGrowthandstructureofsemiconductorquantumwellsElectriclevelsOpticalabsorptionandexcitonsOpticalemissionQuantumwiresanddots12第六讲SemiconductorsquantumweSelectionrulesTheselectionruleforaninfinitequantumwell:n=0;
(Fermi’sgoldenrule)13SelectionrulesTheselectionInfinitequantumwells,therearesmalldeparturesfromtheaboveselectionrule.n0transitionsareusuallyweak,andtransitionsarestrictlyforbiddenifnisanoddnumber,becausetheoverlapofstateswithoppositeparitiesiszero.14Infinitequantumwells,thereTwo-dimentionalabsorptionThethresholdcorrespondstothetransitionfromthegroundstateofthevalenceband(then=1heavyholelevel)tothelowestconductionbandstate(then=1electronlevel):Ee1Ehh1Eg
isthebandgapofthequantumwellmaterial.Theopticalabsorptionedgeofthequantumwellhasablueshiftby(Ehh1+Ee1)comparedtothebulksemiconductor.Thefrequencyofabsorptionedgecanbetunedbythechoiceofwellwidth.15Two-dimentionalabsorptionTheConsideringthefreemotioninx,yplane,thetotalenergyofelectronandholesrelatedtotheconductionbandbottomorthevalencebandtoshouldbe:TheenergyofthetransitionshownbytheverticalarrowinE-kxydiagram:
istheelectron-holereducedeffectivemass16ConsideringthefreemotioninThejointdensityofstatesfora2-Dmaterialisindependentofenergyandisgivenby:Theabsorptioncoefficientofquantumwellwillhaveastep-likestructure!!!!Thethresholdenergyforthenthtransition:Theblue-shiftoftheabsorptionedgebytheconfinementenergyisevident.Step-likesturctureofQWabsorptionspectra17ThejointdensityofstatesfoThemeasuredabsorptionspectrumHeavyholeLightholen=1n=2Steplikebehavior.Strongpeakattheedgeofeachstep:excitoniceffects.Weakpeaksindentifiedbyarrowsarecausedbyn0transitions.18ThemeasuredabsorptionspectrExcitonsinquantumwellsEnhancementoftheexcitonicbindingenergyinthequantumwellduetoquantumconfinementeffects.(10meVvs.4.2meVforGaAs).ExcitonsinquantumwellsarestillstableatRT.19ExcitonsinquantumwellsEnhan第六讲SemiconductorsquantumwellsQuantumconfinedstructuresGrowthandstructureofsemiconductorquantumwellsElectriclevelsOpticalabsorptionandexcitonsOpticalemissionQuantumwiresanddots20第六讲SemiconductorsquantumweOpticalemissionTheelectronsandholesinjectedelectricallyoropticallyrapidlyrelaxtothebottomoftheirbandsThelowestlevelsavailabletotheelectronsandholecorrespondtothen=1confinedstates.Theluminescencespectrumconsistsofapeakofspectralwidth~kBTatenergy:Theemissionpeakisshiftedtohigherenergycomparedtothebulksemiconductor.21OpticalemissionTheelectrons22Zn0.8Cd0.2Se:Eg=2.55eV22Zn0.8Cd0.2Se:Eg=2.55eVQuantumwellsofferthreemainadvantagesovertheequivalentbulkmaterials:Theblue-shiftoftheluminescencepeakbytheconfinementenergycanbecontrolledbythechoiceofthewellwidth.Theincreasedoverlapbetweentheelectronandholewavefunctionsinthequantumwellmeansthattheemissionprobabilityishigher.Shortradiativelifetimeandhigherenergyefficiency.Thethicknessofthequantumwellsiswellbelowthecriticalthicknessfordislocationformationinnon-latticed-matchedepitaxiallayersandallowstheuseofnon-lattice-matchedcombinationsofmaterials(GaN).2
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