Barrier Effects on Exciton Binding Energies in Zinc-blende CdZnSeZnSSe

JournaloftheKoreanPhysicalSociety,Vol.57,No.1,July2010,pp.71?74

BarrierE?ectsonExcitonBindingEnergiesinZinc-blendeCdZnSe/ZnSSe

QuantumWellStructures

Seoung-HwanPark,?Jong-JaeKimandHwa-MinKim

DepartmentofElectronicsEngineering,CatholicUniversityofDaegu712-702

(Received20April2010,in?nalform18May2010)

Barriere?ectsontheexcitonbindingenergiesofCdZnSe/ZnSSequantumwell(QW)structureswereinvestigatedwithintheframeworkofe?ectivemasstheory.Theexcitonbindingenergygrad-uallyincreaseswithincreasingScompositioninthebarrierfortheQWstructurewitharelativelythinwellwidth(Lw=10?A).Ontheotherhand,inthecaseoftheQWstructurewitharelativelythickwellwidth(Lw=30?A),theexcitonbindingenergyisfoundtobeaweakfunctionoftheScompositioninthebarrier.Also,theQWstructurewithathinwellwidth(Lw=10?A)hasalargerexcitonbindingenergythanthatwithathickwellwidth(Lw=30?A).Thiscanbeexplainedbythefactthatthethree-dimensionalcharacteroftheexcitonisrestoredduetotheincreaseofthespatialextentoftheelectronandtheholewavefunctionsfortheQWstructurewiththethickwellwidth.

PACSnumbers:42.55.Px,42.60.-v,71.22.+i,72.80.Ey

Keywords:CdZnSe,ZnSSe,Quantumwell,Excitonbindingenergy,CdSe,ZnSeDOI:10.3938/jkps.57.71

I.INTRODUCTION

Wideband-gapsemiconductorshaveattractedmuchattentionduetotheirpotentialapplicationsforshort-wavelengthoptoelectronicdevices.Currently,III-VGaN-basedmaterialsaretheleadingmaterialsforthefabricationofblue-light-emittingdevices[1].ThecommercializationofInGaN-basedwhite-light-emittingdiodes(LEDs)hasledtowidespreadexpectationsfortheirpotentialapplicationsinareassuchasgeneral-purposeindication,backlightingforliquidcrystaldis-plays,andplug-inreplacementforincandescentlamps.Recently,however,II-VIZnSe-basedmaterialshavebeenextensivelystudiedforthefabricationofblue-greenlasersalthoughthedevelopmentoftheselasershasbeenslowbecauseofthedi?cultyingrowinghigh-qualityhet-erostructures[2–5].AdvancesingrowthtechnologyforII-VIsemiconductorsnowpermitthegrowingofhigh-qualityheterostructures.Forexample,optoelectronicdevicessuchasLEDsandavalanchephotodiodes(APDs)intheblue-violetspectralrangehavebeensuccessfullydemonstratedbyseveralgroups[6,7].Inaddition,Naka-muraetal.[8]demonstratedZnSe-basedwhite-light-emittingdiodeswithlongerlifetimesofover10,000hat14.5A/cm2.Thus,withthecurrentprogressinZnSe-basedquantum-well(QW)structures,studiesonthefun-damentalopticalpropertiesofthissystemareneededforthedesignofshort-wavelengthoptoelectronicdevices.In

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theseQWstructures,excitonice?ectsareveryimpor-tantinunderstandingtheiropticalproperties.However,correspondingtheoreticalstudiesofII-VIsemiconduc-torQWstructuresarefew,comparedtothoseofGaN-basedQWstructures[9,10].Inparticular,therehasbeenverylittleworkcarriedoutonbarriere?ectsontheexci-tonbindingenergiesofzinc-blendeCdZnSe/ZnSSeQWstructures.

Inthisresearch,weinvestigatedbarriere?ectsontheexcitonbindingenergiesofCdZnSe/ZnSSeQWstruc-tures.ThebandstructuresandthewavefunctionsfortheQWstructuresareobtainedbysolvingtheSchr¨odingerequationforelectronsandthe3×3Hamiltonianforholes[11].WeassumethataCdZnSewellisgrownonaZnSesubstrateandthattheCdZnSewellandtheZnSSebarrierareundercompressiveandtensilestrains,respec-tively.

II.THEORETICALMODEL

IntheQWsemiconductor,thefreeelectronandholestatesinteractthroughthescreenedCoulombinterac-tiontoformQWexcitons.Theexcitonwavefunctionismadeupofalinearcombinationofdirectproductsofthesubbandstatesforelectronsandholes:

??????

??

Ψex=Fnm(k??,k??(1)??)|k??,n |k??,m ,

n,mk??

k??

??

shpark@cu.ac.kr

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wherenandmarethesubbandindicesforelectronsandholes,respectively,andthesummationrunsoverthein-planewavevectorsk||(k??||).Fnm(k??,k??envelopefunctionofthenmexciton,which??)denotestheisdescribedby

Fnm(k??,k????)=δ(k??+k??

??)Gnm(k??).

(2)

Here,Gnm(k??),theexcitonrelativemotionenvelopefunction,satis?es[12]

[Een(k??)?Ehm(k??)]Gnm(k??)

+????V¯nnm??m??(k??,k????)

Gn??m??(k????)=EGnm(k??)n??,m

??k????(|k???k.(3)??

??|)Inthisexpression,Een(k??)andEhm(k??)aretheenergiesofthen-thconductionandthem-thvalencesubbands,

respectively.V¯nnm??m??(k??,k????)istheCoulombpotentialbe-tweenthenmandthen??m??excitonsandisgivenby[13]

V¯nmn??m??(k??,k??

??)

=

e2

????

2A|kdzedzhψ?

n??(ze)ψn(ze)

???k????|2+λ2s

×??g??√mν??(k????,zh)gνm(k??,zh)e

????s|ze?zh|,(4)ν

whereAistheinterfaceareaofthesample,ψnandgν

aretheenvelopefunctionsforelectronsandholes,respec-mtively,andνdenotesthebasesforablock-diagonalizedHamiltonianforholes.Theinversescreeninglengthλsisgiven,forthecarrierinjectioncasewhereelectronsandholesexistsimultaneously,asfollows[13]:

λ2e2??????s=π????2meEejmefe(Eej)/π??j

+??2mhEhjmhfh(Eh

j)/π??,(5)

wherefeandfharetheFermidistributionfunctionsfortheconduction-andthevalence-bandstates,respec-tively,andthesumoverjmeansallthesubbandswithintheQWareconsideredinthecalculationofλs.

III.RESULTSANDDISCUSSION

Figure1showsthevalencebandstructuresofCd0.2Zn0.8Se/SyZn1?ySe(Lw=30?A)with(a)y=0.0and(b)y=0.3.Theheavy-holee?ectivemassoftheCdZnSe/ZnSSeQWstructurewithasmallerScompo-sitionisshowntoberelativelysmallerthanthatoftheCdZnSe/ZnSSeQWstructurewithalargerScompo-sition.Forexample,theheavy-holee?ectivemassesofCdZnSe/ZnSSeQWstructureswithy=0.0and0.3are0.48and0.65,respectively.Fortheheavy-holee?ec-tivemass,weconsider

theparabolicband?ttedtothe

Fig.1.Valence-band?structuresofCd0.2Zn0.8Se/SyZn1?y

Se(Lw=30A)with(a)y=

0.0and(b)y=0.3.

Fig.2.(a)Excitonbindingenergyand(b)inverse

screeninglengthasfunctionsofthesheetcarrierdensityforCd0.2Zn0.8Se/SyZn1?ySe(Lw=10?A)QWstructureswithy=0.0and0.3.

lowestsubbandoftheexactbandstructure.Thee?ec-tivemassisdeterminedsothat,foragivencarrierden-sityandquasi-Fermilevelforholes,thecarrierdensityandthequasi-Fermilevelagreewiththoseoftheexactbandstructure.Hence,thee?ectivemassofthe?ttedparabolicbandre?ectsanaverageddensityofstatesforagivencarrierdensity.Ontheotherhand,weknowthattheheavy-holee?ectivemassoftheCdZnSe/ZnSSeQWstructureismuchlargerthanthose(?0.2m0)ofcon-ventionalInP-andGaAs-basedQWstructuresandthatthesubbandenergieslieclosertoeachotherthanthoseinthemorewidelystudiedzinc-blendeQWlasers.Thisismainlyduetothelargeheavy-holee?ectivemassofZnSe-basedQWs.

Figure2shows(a)theexcitonbindingenergyand(b)theinversescreeninglengthasfunctionsofthesheetcarrierdensityforCd0.2Zn0.8Se/SyZn1?ySe(L?w=10A)QWstructureswithy=0.0and0.3.Within-

BarrierE?ectsonExcitonBindingEnergiesinZinc-blendeCdZnSe/ZnSSeQuantum···–Seoung-HwanParketal.

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Fig.3.(a)Excitonbindingenergyand(b)inversescreeninglengthasfunctionsoftheScompositionforCd0.2Zn0.8Se/SyZn1?ySeQWstructureswithLw=10and30?A.Theresultshavebeencalculatedatasheetcarrierdensityof1×106cm?2.

creasingsheetcarrierdensity,theexcitonbindingenergy

israpidlyreduced,suggestingthatexcitonsarenearlybleachedattypicaldensities(approximately1013cm?2)forwhichlasingoccurs.Thatis,excitonsinQWstruc-turesarenotstableathighcarrierdensities.SimilarresultswerealsofoundinGaN-basedQWstructures[14].Thiscanbeexplainedbythefactthatthein-versescreeninglengthissigni?cantlyenhancedbecausethemagnitudeoftheFermifunctionrapidlyincreaseswithincreasingsheetcarrierdensity,asshowninEq.(5).Ontheotherhand,e?ectivemassesareaweakfunctionofthesheetcarrierdensity.Also,weknowthattheCdZnSe/ZnSSeQWstructurewithy=0.3showsalargerexcitonbindingenergythanthatwithy=0.0.Thisisattributedtothefactthattheformerhassmallerinversescreeninglengththanthelatter.

Figure3shows(a)theexcitonbindingenergyand(b)theinversescreeninglengthasfunctionsoftheScompo-sitionforCd0.2Zn0.8Se/SyZn1?ySeQWstructureswithLw=10and30?A.Theresultshavebeencalculatedatasheetcarrierdensityof1×106cm?2.Theexci-tonbindingenergygraduallyincreaseswithincreasingScompositioninthebarrierfortheQWstructurewitharelativelythinwellwidth(Lw=10?A).Forexample,theexcitonbindingenergiesforQWstructureswithy=0.0and0.3are38and45meV,respectively.Ontheotherhand,inthecaseoftheQWstructurewitharelativelythickwellwidth(Lw=30?A),theexcitonbindingenergyisfoundtobeaweakfunctionoftheScompositioninthebarrier.Thatis,theexcitonbindingenergyslightlyincreasesfrom36to38meVwhentheScompositionchangesfrom0.0to0.3.Theenhancementoftheexci-tonbindingenergyobservedfortheQWstructurewithalargeScompositionismainlyduetothedecreaseintheinversescreeninglength,asshowninFig.3(b).

Also,theQWstructurewithathinwellwidth(Lw

=

Fig.4.Wavefunctions(C1andHH1)atthezonecen-terin(a)theconductionand(b)thevalencebandsforCd0.2Zn0.8Se/ZnSeQWstructureswithLw=10and30?A.

10?A)hasalargerinversescreening?lengththanthatwithathickwellwidth(Lw=30A).Thus,theQWstructurewithathinwellwidthisexpectedtoshowsmallerexci-tonbindingenergiesthanthatwithathickwellwidth.However,adi?erentresultisobservedinFig.3(a).Thatis,?theQWstructurewithathinwellwidth(Lw=10A)hasalargerexcitonbindingenergythanthatwithathickwellwidth(Lw=30?A).ThiscanbeexplainedbythefactthattheQWstructurewithathinwellwidthhasalargeroverlapintegralofwavefunctions.InFig.4,weplottedthewavefunctions(C1andHH1)atthezonecenterin(a)theconductionand(b)thevalencebandsforCd0.2Zn0.8Se/ZnSeQWstructureswithLw=10and30?A.TheQWstructurewithLw=10?AshowslargerelectronandholewavefunctionsatthewellcenterthanthatwithLw=30?A.Thisin?uencestheoverlapin-tegralbetweentheelectronandtheholewavefunctions.Thatis,increasingwellwidthincreasesthespatialex-tentoftheelectronandtheholewavefunctionsandthethree-dimensionalcharacteroftheexcitonisrestored,resultinginareducedexcitonbindingenergy.

IV.SUMMARY

Insummary,barriere?ectsontheexcitonbindingenergiesofCdZnSe/ZnSSeQWstructureswereinves-tigatedwithintheframeworkofe?ectivemasstheory.Theheavy-holee?ectivemassoftheCdZnSe/ZnSSeQWstructurewithasmallerScompositionisshowntoberelativelysmallerthanthatoftheCdZnSe/ZnSSeQWstructurewithalargerScomposition.Theexcitonbind-ingenergygraduallyincreaseswithincreasingScompo-sitioninthebarrierfortheQWstructurewitharela-tivelythinwellwidth(Lw=10?A).Ontheotherhand,inthecaseoftheQWstructurewitharelativelythickwellwidth(Lw=30?A),theexcitonbindingenergyisfoundtobeaweakfunctionoftheScompositioninthe

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barrier.Also,?theQWstructurewithathinwellwidth(Lw=10A)isshowntohavealargerexcitonbindingenergythanthatwithathickwellwidth(Lw=30?A).

ACKNOWLEDGMENTS

ThisworkwassupportedbyresearchgrantsfromtheCatholicUniversityofDaeguin2010.

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