Theory of optical spectra of polar quantum wells T

arXiv:cond-mat/0106078v1[cond-mat.mes-hall]5Jun2001THEORYOFOPTICALSPECTRAOFPOLARQUANTUMWELLS:TEMPERATUREEFFECTSF.J.Rodr´ıguez*DepartamentodeF´ısica,UniversidaddelosAndes,AA4976,Bogot´aD.C.,ColombiaTheoreticalandnumericalcalculationsoftheopticalabsorptionspectraofexcitonsinteract-ingwithlongitudinal-opticalphononsinquasi-2Dpolarsemiconductorsarepresented.InII-VIsemiconductorquantumwells,excitonbindingenergycanbetunedon-andoff-resonancewiththelongitudinal-opticalphononenergybyvaryingthequantumwellwidth.Acomprehensivepictureofthistuningeffectonthetemperature-dependentexcitonabsorptionspectrumisderived,usingtheexcitonGreen’sfunctionformalismatfinitetemperature.Theeffectiveexciton-phononinter-actionisincludedintheBethe-Salpeterequation.NumericalresultsareillustratedforZnSe-basedquantumwells.Atlowtemperatures,bothasingleexcitonpeakaswellasacontinuumresonancestatearefoundintheopticalabsorptionspectra.Byconstrast,athighenoughtemperatures,asplittingoftheexcitonlineduetorealphononabsorptionprocessesispredicted.Possiblepreviousexperimentalobservationsofthissplittingarediscussed.PACSnumbers:71.35.c,71.38,72.10.d,78.66I.INTRODUCTIONLow-dimensionalsemiconductorstructuresprovidewithmanysurprisingpropertiesthathaveneverbeenobservedinbulkmaterials.OneofthemostinterestingpropertiesofII-VIsemiconductorbasednanostructuresistheobservationofwell-resolvedheavy-andlight-holeexcitonpeaksintheabsorptionspectra,evenatroomtemperature.1IthasbeenproposedthatthelasingmechanisminhighlyexcitedII-VIquantumwells(QWs)correspondstoacoherentrecombinationofexcitons.1–4.Itisthereforeexpectedthatexcitonsremainstableinthepresenceofhighcarrierdensities,thusplayinganimportantroleintheoperationofblue-greendiodelasers.However,thepotentialitiesofII-VIcompoundheterostructurestoobtainreliableexcitonicdevicesdependstronglyuponthestrength,thewidthoftheresonancesandthenatureoftheexcitonscatteringprocessesatroomtemperature.Indeedoneofthemainscatteringmechanismstobeconsideredistheinteractionofexcitonswithlongitudinal-optical(LO)phonons,5aproblemofanenormousinterestfromboththeexperimentalandtheoreticalpointofviews.AmajordifferencebetweenIII-VandII-VIsemiconductorsisthehighlypolarcharacterofthelatterones.Asaconsequence,thecouplingofchargecarriers(electronsandholes)withLO-phononsisstrongerinII-VIthaninIII-Vcompounds.AconvenientmeasureofthecouplingstrengthisthedimensionlessFr¨ohlichconstantα.Theelectron-phononcomplexrepresentsaquasiparticle,calledapolaron,whichintheweakcouplinglimit,α≪1asappropriateforGaAs(α=0.06),slightlyrenormalizestheelectronproperties.II-VIcompoundslikeZnSeshouldbedescribedbyanintermediatecouplingtheorysinceforthislastcompoundα=0.43,aboutanorderofmagnitudelargerthaninGaAs.Besidesthat,theexcitonbindingenergy,EX,inII-VIQWscanbemadecomparabletoorevengreaterthantheLO-phononenergy,ωLO(hereandinthefollowing¯h=1),byvaryingthewellwidth.Inparticular,forZnSe,thebindingenergyofthebulkexcitonE3DX≈20meVwhileintwodimensionsE2DX=4E3DX;theLO-phononenergyisωLO≈30meVinbulk.Therefore,threeregimescanbeexpectedinII-VIlowdimensionalstructures:(1)EXωLO;(2)EXωLOand(3)EX≈ωLO,towhichwewillreferfromnowonastheresonantregime.Cases(1)and(2)havebeenextensivellyconsidered:forthefirstcase,asingleLOphononabsorptioncannotdissociatetheexcitonintotheelectron-holecontinuum.Furthermore,theexcitonBohrradiusissmallerthanthepolaronradius,consequentlytheelectron-holepairisweaklyinfluencedbyphonons,i.e.theyinteractthroughaCoulombinteractionscreenedbythestaticdielectricconstant.6Hence,thecouplingofexcitonswithLO-phononsviatheFr¨ohlichinteraction,canbesubstantiallyreducedyieldingtostrongexcitonabsorption,evenatroomtemperature1–4,7–9.Forthesecondcase,theelectron-holeCoulombinteractionwillbescreenedbythelatticevibrationsandotherexcitations6,10.Therefore,theexcitonshouldbeeasilyionizedaffectingtheoptoelectronicpropertiesofthesemiconductorsystem.Thethirdcaseatfinitetemperature,tothebestofourknowledge,hasbeenignoredintheoreticalstudies.Inthelimitofvanishingtemperature,previousworksonII-VIheterostructuresshowthattheexciton-LOphononinteractionweakenswithdecreasingwellwidthandpredictasmallfeatureintheexcitoncontinuumspectrumtheso-calledexciton-LOphononquasi-boundstate.7,11ItisexplainedbasedonthelargeFr¨ohlichcouplingbetweenexcitonsandLO-phononsinthosecompounds.SimilarbutweakereffectshavealsobeenreportedforII-VIbulksystems12–14.Clearly,thereisalackoftheoreticalworksonexciton-LO-phononcomplexesintheresonantregimeathighenoughtemperatures(77K≤T≤330K)forsuchmaterials.1Themaingoalofthisworkistostudytheexcitonabsorptionlineshapeintheresonantregimeasafunctionoftemperature.Athightemperaturesapeaksplittingispredicted,correspondingtoexciton-LO-phononabsorptionprocesses.Intheresonantregimebothofthesesplittedpeakshaveroughlythesameoscillatorstrength.Therefore,thisnewfeatureshouldbeconsideredforunderstandingthestructureanddynamicsoftheopticalresponseofII-VIQWs.15BroadeningandsplittingoftheexcitonpeakatthelowerbandedgeinIII-Vbulksystemshavebeenreported,16andtheyhavebeenexplainedasaconsequenceoftheincreasingofthephonond