应变纤锌矿GaN_AlxGa1-xN柱形量子点中的束缚极化子_百度文库
应变纤锌矿GaN_AlxGa1-xN柱形量子点中的束缚极化子
BoundpolaroninastrainedwurtziteGaN/AlxGa1?xNcylindricalquantumdot?
ZhangBin(张彬)1,YanZuwei(闫祖威)1;2;?,andZhangMin(张敏)3
ofPhysicalScienceandTechnology,InnerMongoliaUniversity,Hohhot010021,ChinaofSciences,InnerMongoliaAgriculturalUniversity,Hohhot010018,China
3CollegeofPhysicsandElectronInformation,InnerMongoliaNormalUniversity,Hohhot010022,China
Abstract:Withintheeffective-massapproximation,avariationalmethodisadoptedtoinvestigatethepolaroneffectinastrainedGaN/AlxGa1?xNcylindricalquantumdot.Theelectroncoupleswithbothbranchesoflongi-tudinaloptical-like(LO-like)andtransverseoptical-like(TO-like)phononsandthebuilt-inelectricfieldaretakenintoaccount.Thenumericalresultsshowthatthebindingenergyoftheboundpolaronisreducedobviouslybythepolaroneffectontheimpuritystates.Furthermore,thecontributionofLO-likephononstothebindingenergyisdominant,andtheanisotropicangleandAlcontentinfluenceonthebindingenergyaresmall.Keywords:electron–strainDOI:10.26/32/6/062003PACC:;6320K
1.Introduction
III–Vnitridesemiconductorsandtheiralloyswithhexag-onalwurtzite(WZ)crystalstructuresandcomplicatedvalence
bandstructuresarecharacterizedbydirectandlargebandgaps.Thebandgapenergyofaluminumgalliumindiumnitride(Al-GaInN)variesbetween6.2and1.9eV,dependingonitscom-position,atroomtemperature.Thus,GaNandrelatedmateri-alshavebeenconsideredaspromisingsystemsforopticalde-vicesemittinglightatwavelengthsfromultraviolettoredOE1?4?.Ontheotherhand,thegroup-IIInitridesarecommonlypro-ducedintheWZcrystalstructurewithastrongspontaneousmacroscopicpolarization.Moreover,duetothelargelatticemismatchbetweenGaNandAlGaN,thewurtziteGaN/AlGaNheterostructurescaninducearemarkablepiezoelectricpolar-ization,whichleadstoastrongbuilt-inelectricfieldoftheorderofMV/cminheterostructures.Suchastrongfieldwillgiverisetoaremarkablereductionineffectivebandgapsinquantumwellsorquantumdots(QDs).Furthermore,theelec-tronic,dielectricandopticalpropertiesoftheheterostructuresarestronglyaffectedbythebuilt-inelectricfield.Recently,XiaandWeiOE5?havestudiedhydrogenicimpuritystatesinawurtziteInGaNQD.ItwasfoundthattheAlcontentintheAlxGa1?xNpotentialhilllayerhasaclosecorrelationwiththediscontinuityandpolarizationeffectontheinterfaceconduc-tionbandinaGaN/AlxGa1?xNheterostructure.
Theelectron–phonon(e–p)interactionplaysanimportantroleindeterminingthephysicalpropertiesofQDsconsistingofpolarmaterialsOE6?.Therefore,therehasbeenmuchinterestininvestigatingthee–pinteractioneffectsontheenergiesofelectronstates.Anumberofstudieshavefocusedonthein-fluenceofe–pinteractionsontheimpuritypropertiesinthesingleQD.XieandChenOE7?investigatedthephononcontribu-tiontothebindingenergyoftheon-centerandoff-centerim-puritiesinasphericalQD.Szafranetal.OE8?studiedtheeffect
oftheelectron–phononcouplingonthepropertiesofanega-tivelychargeddonorcenterconfinedinasemiconductorspher-icalQDembeddedinaglassmatrix.ThebindingenergyanddipolemomentofahydrogenicimpurityconfinedinaQDwiththeshapeofasphericalcaparecalculatedbyYuanetal.OE9?.LiandChenOE10?havederivedthelongitudinaloptical(LO),topsurfaceoptical(TSO)andsidesurfaceoptical(SSO)modesinfreestandingcylindricalQDs.ConsideringtheelectronandioncouplewiththeconfinedLO,TSOandSSOphononmodes,Charrouretal.OE11;12?,andWangetal.OE13?calculatedthebind-ingenergyofanon-centerdonorimpurityinacylindricalQD.Vartanianetal.OE14?presentedasystematicstudyofthebindingenergyfortheground-stateofahydrogenicimpurityinacylin-dricalQDinthepresenceofbothanappliedelectricfieldandthecouplingbetweenanelectronandLOphonons.Recently,ZhongandLiuOE15?havederivedthegeneralexpressionsoftheinterfaceoptical(IO)phononmodes,thedispersionrelation,andanelectron–IOphononFr¨ohlichinteractionHamiltonianinthecylindricalQDheterostructurewithintheframeworkofadielectriccontinuumapproximation.Unfortunately,theyne-glectedthecouplingbetweentheimpurityandthephonons.Inthispaper,consideringtheuniaxialanisotropy,thebuilt-inelectricandtheinteractionsbetweentheimpurityandphononmodes(LO-likephononandTO-likephononmodes),wecalculatedthee–pinteractioneffectonanon-centerhydro-genicimpuritystateinthestrainedGaN/AlxGa1?xNcylindri-calQD.Withavariationaltechnique,thebindingenergyandpolaronicshiftwereperformedasfunctionsoftheQDsizes,theanisotropyangleandtheAlcontent.AneffectiveHamil-tonianforthegroundstateofaboundpolaroninthestrainedGaN/AlxGa1?xNcylindricalQDwithaninfinitepotentialisobtainedbyusingaLee–Low–Pines(LLP)-likemethodOE16;17?,andthevariationalcalculationsfortheimpuritystatebindingenergyanditspolaronicshiftareperformed.Thenumericalre-sultsandsomedetaileddiscussionsarepresented.
*ProjectsupportedbytheNationalNaturalScienceFoundationofChina(No.)andtheResearchFundsfortheScienceandTechnologyInnovationTeamofInnerMongoliaAgriculturalUniversity(No.NDPYTD2010-7).?Correspondingauthor.Email:zwyan@,
c2011ChineseInstituteofElectronicsReceived11October2010,revisedmanuscriptreceived7February2011?
贡献者：scuay
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