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j o ur na l ho me pa g e :w w w . e l s e v i e r . c o m / l o c a t e / a p s u s c
Theoretical
band
alignment
in
an
intermediate
band
chalcopyrite
based
material
J.E.
Castellanos
Águila
a,d,
P.
Palacios
a,b,∗,
J.C.
Conesa
e,
J.
Arriaga
d,
P.
Wahnón
a,caInstitutodeEnergíaSolar,UniversidadPolitécnicadeMadrid,28040Madrid,Spain
bDpt.FísicaAplicadaalasIngenieríasAeronáuticayNaval,UniversidadPolitécnicadeMadrid,ETSIAeronáuticaydelEspacio,28040Madrid,Spain
cDpt.TecnologíaFotónicayBioingeniería,UniversidadPolitécnicadeMadrid,ETSITelecomunicación,28040Madrid,Spain
dInstitutodeFísica,BeneméritaUniversidadAutónomadePuebla,Av.SanClaudioy18Sur,C.U.72570Puebla,Mexico
eInstitutodeCatálisisyPetroleoquímica,CSIC,MarieCurie2,Cantoblanco,28049Madrid,Spain
a
r
t
i
c
l
e
i
n
f
o
Articlehistory:
Received25October2016 Receivedinrevisedform 29December2016 Accepted30December2016 Availableonlinexxx
Keywords:
Photovoltaics Theoreticalcalculations Heterostructures
a
b
s
t
r
a
c
t
Bandalignmentiskeytoenhancetheperformanceofheterojunctionforchalcopyritethinfilmsolar cells.InthispaperwereportabinitiocalculationsoftheelectronicstructuresofCuGaS2:Crwithvarious Crcompositions,CuAlSe2andZnSeandthebandalignmentbetweentheirinterfaces.Weusedensity functionaltheoryandthemoreaccurateself-consistentGWschemetoobtainimprovedbulkband-gaps andbandoffsets.BandalignmentsoftheinterfacialregionforCuGaS2:Cr/CuAlSe2andCuGaS2:Cr/ZnSe systemswerealignedwithrespectofanaverageelectrostaticpotential.Ourresultsareingoodagreement withexperimentalvaluesforthebulkband-gaps.Thesetheoreticalbandalignmentsshowacharacteristic staggeredbandalignmentforthedesignofheterojunctiondevicesinphotovoltaicapplications.
©2016ElsevierB.V.Allrightsreserved.
1. Introduction
Current Cu(In,Ga)Se2 photovoltaics devices, on a laboratory
scale,reachconversionefficienciesabout22.3%[1].This improve-mentontheefficiencyismainlyduetotheimprovementtotheCIGS absorberlayerandthejunctionformationprocess.However,the efficiencyisstilllowerthanthesinglegapShockley–Queisserlimit [2].Oneoftheproposalswhichpromiseshighconversion efficien-ciesistheintermediateband(IB)solarcellsconcept[3].AnIBcould provideadditionalopticaltransitionsduetoelectronicstatesinside thefundamentalband-gapofthehostsemiconductor.Ithasbeen reportedthattheCuGaS2whichhasa2.43eVband-gap,isa
suit-ablehostmaterialfortheIBconcept[4,5].IfweconsiderChromium transitionatomreplacingGalliumatominaCuGaS2semiconductor,
additionalstateswithintheband-gapareobservedduetotheCr,as describedinRef.[6–10].However,uptodateitisnotknownwhich willbethebehaviouroftheintermediatebandmaterialtakinginto accounttherestofmaterialswhichareincontactinthecomplete solarcell.Forthisreason,apreciseknowledgeofthebandstructure oftheseheterojunctionsbecomesnecessary.
∗ Correspondingauthorat:Dpt.FísicaAplicadaalasIngenieríasAeronáuticay Naval,UPM,ETSIAeronáuticaydelEspacio,28040,Madrid.
E-mailaddress:[email protected](P.Palacios).
Inapreviousreport[11],wehavestudiedthebandalignmentof theheterointerfacesbetweenCuGaS2andseveralsemiconductors.
We have found that the CuAlSe2/CuGaS2 and CuGaS2/ZnSe
heterointerfaces show good characteristics for the design and developmentofthinfilmsolarcells.Thejunctionsformedby mate-rialswithdifferentband-gapsand latticeconstantshave strong influenceonthevalenceandconductionbandoffsets,and more-over thepossibilitythat localstates canoccurattheinterfaces oftheseheterostructures whichmight haveaninfluencein the electronicand transport properties.Aproperdescriptionof the structure and electronicproperties ofsurfaces and heterointer-facesmustbetakenintoaccountinordertodesign,tobuildandto analyzesuchheterostructuresdevices.
In this work, we present a systematic procedure for the calculationoftheenergybandalignmentatanabruptIB material-semiconductor heterojunction [12,13]. The procedures requires onlyaknowledgeoftheenergybandstructuresoftheparticipating semiconductors,anddoesnotinvokeanyproperties–empiricalor theoretical–ofthefreesurface,butneedstoassociatetheenergy levelsofthesemiconductorswhichcomprisetheheterostructure withacommonreferenceenergylevel.Thislevelisobtainedusing anaverageelectrostaticpotential.Theaccuracyofthemethodis believedtoreflectdirectlythequalityofthebandstructures.Once accurate bandstructures and an adequate sophisticated model of thecharge distribution near the interface are obtained, the methodshouldbecapableofservingasanaccuratetoolforthe
quantitative prediction of band lineups at heterojunctions for whichnoexperimentaldatayetexist.
2. Modelandcomputationaltechnique
We perform first-principles calculations based on the GGA approximation[14]and manybody perturbationtheory (quasi-particleenergycalculations)[15,16]asimplementedintheVienna abinitiosimulationpackage(VASP)[17].Theinteractionsbetween theioniccoresandthevalenceelectronswereintroducedusing theprojector-augmentedwavemethod(PAW)[18,19].Thevalence configurationsusedinthePAWpseudopotentialswere:3d104s1
for Cu; 4s24p1 for Ga;3s23p4 for S, 3d54s1 for Cr, 4s24p4 for
S,3s23p1 forAland4s23d10forZn. Gapotentialwithout
semi-core d states reproduces quite well the experimental valence band levels in CuGaS2 semiconductor so they have not been
included. The Perdew–Burke–Ernzerhof (PBE) [14] functionals are employed for the GGA exchange-correlation potential. The valenceelectronicwave-functionsareexpandedinaplanewave basis set up to a kinetic energy cut-off of 450eV. The quasi-particleenergycalculationsarebasedonarestrictedself-consistent scGW schemes,where, the wave-functionsand energies of the PBEcalculationswereusedasthestartingpointtocomputethe quasiparticlebandstructure,subsequently,weupdatethe quasi-particlewave-functionfourtimesinbothGreen’sfunctionGand screenedpotentialW[20].Thetotalnumberofvalenceand con-ductionbandstatesinthescGWprocedurewassetto320forall materials.
Tocalculate the bandalignment from first principles calcu-lationsweusenon-polarinterfacesbecausetheirstructuresare relativelywellestablished.TheheterointerfacesbetweentheIB materialandCuAlSe2 orZnSephasesarestudiedusingatypical
supercellapproach.Basicallyasupercellconsistsofaunitcellofn monolayersofonesemiconductorfollowedbymmonolayersofthe other.Eightatomiclayersforeachofthetwomaterialsarestacked inthe[110]direction.Supercellscomposedof16layers,correspond toa∼32 ˚Athickness.Here,-centredk-pointMonkhorst–Pack[21] meshof6×6×1wasused,duetotherelativelylargesupercellsize. Forthebulkcalculationsweusea6×6×2k-pointmesh.Theplane wavecut-offandtheBrillouinzonesamplingbothwereverifiedto provideconvergenceintotallatticeenergywithin1meV.The calcu-lationforCuGaS2:Crwascarriedoutusingamonoclinicunitcellin
whichoneoftheGaatomswasreplacedbyaCratom(attetrahedral sites),whichcorrespondstothe25%dopantconcentration.
Twotypesofcalculationswereperformedtoobtainthreetypes ofenergyleveldifferences.First,heterointerfacecalculationswere carriedoutattheGGAleveltoobtainthedifferencebetween elec-trostaticpotentials near thecentre of slabs of the two phases. Second,bulkcalculationsprovidethedifferencefromthe electro-staticpotentialtothevalencebandmaximumforeach phase.It shouldbenotedthatinthefirstcalculation,weincorporatedthe effectofthestrainduethelattice-mismatchheterojunction, how-ever,thisCuGaS2:Crmismatchandthedifferentsemiconductors
arereducedrespecttothelattice-mismatchwithoutchromium, fortheCuGaS2:Cr/CuAlSe2 thelatticemismatchis4.72%andfor
theCuGaS2:Cr/ZnSe is 5.9%, meanwhile in the CuGaS2/CuAlSe2
interface,thelatticemismatchis5.96%andfortheCuGaS2/ZnSe
interfaceis 5.68%.Thisis dueforthepresenceof threecationic species.Forthatreasonwetookthelatticeconstantandatomic positionwithout distortion. Finally, for these undistorted cells, wehaveusedthemanybody GWapproximationtocarriedout quasiparticleenergycalculations.Usingthismethodwehave pre-dictedtheelectrostatic potentialand thebandstructures more accurately.
Fig.1.Densitiesofstatesinthefirstseventop-layerCuGaS2(110),comparedtothe bulkdensityofstates.ThezeroofenergyisattheFermilevel.
3. Results
Inapreviousstudy,wefoundthatnon-polarsurfacesofCuGaS2
aretechnologicallyveryimportantbecauseinthinfilmsolarcell structuresarethemostsuitabletoformcation–anionbondsacross theinterface,minimizinganychargeaccumulation.Weconsiderfor theinterfacethe(110)plane,whichisformedbyanatomiclayer havingthestoichiometricCu–S–Ga–Scomposition.Inthiscasewe useslabswhichstackeightsuchmonolayers.
Fig.1showstheprojecteddensityofstates(PDOS)forthe unre-laxedsurfaceandthefirstsixsub-surfaceslayersfortheCuGaS2
(110),comparedwiththebulk-DOS.Accordingtothewellknown DFTproblem,thepredictedband-gapsareunderestimatedandthe trendsinthepredictedgapshouldbemeaningful.Isimportantto notethatthepurposeofthispartoftheworkistodeterminethe depthofthesurfacestatesinthechalcopyrite,whichallowsusto determineanintegernumberofCuGaS2formulaunitstoensure
thattheeffectoftheinterfaceonthelevelpositionsattheslab centreisnegligible.
WeseethatthePDOSofthetopmostatomiclayerreflectsthe densityofsurfacestateswhereasthePDOSofdeeperlayersbecome identicaltothedensityofbulkstates.Significantperturbations aris-ingfromthesurfacedonotpenetratedeeperthanthreelayersinto thebulk,whichjustifiesusingslabscontainingeightatomicplanes each.Forthesurfacelayer,twosurfacestates(E1andE2)appearat
0.3eVand1.2eVfromthevalenceband.Theselevelscorrespond to3dofCuand4pofGa,respectively.Amoreextensiveanalysis oftheLDOSshowsthatthisisaconsequenceoftwocovalentCu–S andGa–Sbondsbreakinginthezdirectionofaprimitive transla-tionvectorofthesurfaceunitcell.Particularly,E1aremostlyofdz2 symmetry(wherethenormaltothesurfaceistakenaszdirection), meanwhilethestateE2isprimarilyofpzsymmetry.
Fromthis,thecreatedsupercellcontainssixteenatomiclayers forboththeCuGaS2:Cr/CuAlSe2andCuGaS2:Cr/ZnSeinterfaces,as
itisshowninFig.2afortheinterfacetoCuAlSe2case.Thetotal
Fig.2.(a)Structureofthesupercelland(b)projecteddensityofstatesasafunction ofthedistancefortheCuGaS2:Cr/CuAlSe2(110)interface.FortheCuGaS2:Cr/ZnSe interface,thesupercellisconstructedsimilarly.
equalandthebulkfeaturesconvergesveryquicklyasonemoves awayfromtheinterface.FortheCuGaS2:Crinterfaciallayer,the
hybridizationfromtheCu3dz2stateswiththeSe4py,zorbitalsofthe ZnSeslab,expandsthevalencebandandtheband-gapdecreases. TheminimumoftheconductionbandintheCuGaS2:Crinterfacial
layer,comesfromthe4px,zoftheGalliumandthe4sorbitalofthe Selenium,andpushesdownintotheupperpartofthegap.The oppositeeffectisobservedfortheinterfaciallayerofCuAlSe2.
However,thebandalignmentbetweentwomaterialscannotbe achievedfromadirectcomparisonofthecorrespondingbandedges onbothsidesoftheinterfaces[23].Thereasonforthatisdueto:(i) thelackofancommonreferenceenergybetweentheenergylevels ofthematerialswhichcomprisetheheterostructure,inthiscase, theaverageelectrostaticpotential,and(ii)theunderestimationof theband-gaps,asthisaffectsmainlytheconductionbandoffset.
Therefore,tocalculatethebandalignmentbetweentwo materi-als,wefollowtheprocedureintroducedbyVandeWalleandMartin [13],wherewefirstcomputetheplanaraverageofthepotential electrostaticacrossthesupercell,whichisaveragedintheregion awayfromtheinterfacewheretheelectrostaticpotentialreaches aconstantvalue.Second,thepositionofthevalencebandedge withrespecttotheaverageelectrostaticpotentialisdetermined. Toobtainthealignment,separatecalculationusingahighly accu-ratemethodoftheelectronicstructureandelectrostaticpotential, for thecorrespondingbulk materialsforming theinterface,are required.
Thevalencebandalignmentateachinterfaceiscalculated,as explainedindetailinRef.[11],EV=EPint−EP+EVB,where
EPint isthediscontinuityinthis referencepotentialacrossthe interfaces,EPandEVBarethedifferencesbetweenthevalence bandedgesandtheelectrostaticpotentialobtainedfromthetwo independentbulkcalculationsofthesinglesphases.
However,theconventionalDFTapproacheshavedeficienciesin describingtheband-gapduetotheself-interaction.Besidesthis approachistotallyinadequatetostudytheelectronicstructureof materialswheretheband-gapisinfluencedbythehybridization ofthedorbitalsofatransitionmetalwithporbitalsofotheratom
Fig.3. SpinpolarizedtotalDOScurvesobtainedwithinGGAandscGWforthe CuGaS2:Cr.ThedottedlineindicatestheFermilevel.
[24].Sowehaveusedaself-consistentGWprocedurewhichhas beenextremelysuccessfulindescribingquasi-particlesenergiesfor transitionmetalcompounds,whereperturbativeGWfails[25,26]. AnotherreasontogobeyondDFTremainsintheneedto calcu-lateexcitedstatesforapplicationinthedomainofphotovoltaics, whereitisnecessarytoevaluatequasi-particleenergies,absorption spectraandexcitonbindingenergy[22,26].
Under thescheme of the scGW calculations, the band-gaps ofpureCuGaS2,CuAlSe2 and ZnSewereof2.24eV,2.41eVand
2.69eVrespectively. These results showthat the standard DFT approachunderestimatetheband-gap(0.65eVforCuGaS2,0.87eV
forCuAlSe2 and1.18eVforZnSe),andtheself-consistent
quasi-particleGWcalculationsagreesprettywellwiththeexperimental values (2.43eV [5], 2.49eV [27] and 2.82eV [28] for CuGaS2,
CuAlSe2andZnSerespectively).
Fig. 3 shows thedensities of states of CuGaS2:Cr calculated
withinGGAandthescGWapproach.Inbothcases,theIBislocated intheband-gapformedbyspinupstatesfromCrdopantandis par-tiallyoccupiedwiththeFermilevelcrossingit.Atthe25%dopant concentration,theIBislocatedattheenergyregionfrom−0.35eV to0.73eV,whichisverywide,generatingaslightoverlapwiththe valenceband,becauseoftheweakhybridizationofthet2statesof
theCrwiththe3pstatesoftheneighbouringSatoms.TheIBis com-posedofthreestatesandaccordingtothetetrahedralcrystalfield,is mainlycontributedfromthet2states,sincetheCr3dstatesaresplit
intothelowerenergye(dz2,dx2–y2)states,whichwillcontaintwo ofthethreeelectronsinthe3dbandofthe(formally)Cr(3+)ion,and
higherenergyt2states(dxy,dyz,dzx)whichwillcontainthethird
electron.ThissplittingshowshowintheCuGaS2:Crmaterialthe
mainband-gapisdividedintotwosub-bands,whichisan impor-tantfeaturetoconsiderwhencarryingoutthebandalignmentwith CuAlSe2andZnSe.
Forthespindownstates,itcanbeseenthatchromiumdoesnot changesthehostelectronicstructuresignificantly,however,under thescGWscheme,theeandt2statesbreakthehybridizationwith
theconductionbandandarelocalizedatlowerenergies.
InordertohaveabetterunderstandingofthepositionoftheIB, westudyattheGGAleveltheeffectofthedopantconcentrationat 25%,12.5%,6.25%,4.16%and3.125%asweseeinFig.4.Theuseof largesupercellsshowsonlyaslightlychangeinthepositionofthe IB.Besides,asthesizeofthesupercellisincreased,thewidthofthe intermediatebanddecreasesasexpected.
Fig.4.DOSobtainedattheGGAlevelfordifferentCrdopingsinCuGaS2.TheFermi levelissetto0eV.
concentrations.Itisshownthatthisdifferenceissimilarfor dif-ferentconcentrations.Therefore,theuseofa16atomsupercellis reasonable,sincescGWisaexpensivetechniqueandscalesasn3
withthenumberofatomsintheunitcell,souptodateisunpractical forthestudyoflargesystems.Theseresultssuggestthattheuseof largesupercells(lessdopantconcentration)isolatestheIBfromthe valencebandandtheconductionbandandwillallowusthe absorp-tionoftwophotons(EIB–EVBandECB–EIB)inadditiontothephoton absorbedinthehostsemiconductorband-gap(ECB–EVB)without facilitatingtransferofphotogeneratedcarriersbetweentheIBand theVBorCBviathermalization.
Therefore, for the CuGaS2:Cr/CuAlSe2 supercell, EPint= 0.503eV, and the EP and EVB are 0.786eV and −0.0069eV respectively.FromthesevaluestheEVfortheCuGaS2:Cr/CuAlSe2
interface has a value of −0.29eV, where the valence band of theCuGaS2:Crlying in energybelow the correspondingone of
theCuAlSe2.Resultsfor theCuGaS2:Cr/ZnSeinterfacewerealso
obtainedina similarway,nevertheless,thevalencebandoffset givesEVequalto0.92eV,withCuGaS2:Crvalencebandabovethe
ZnSevalenceband.
Finally, from the correct description of the band-gaps and thepositionof theIB intheCuGaS2:Crinconjunction withthe
relative position of the valence bands for each interface, the
Table1
EF–EVB(eV)calculatedatGGAlevelfordifferentconcentrationsofCr.
Concentration EF–EVB
25% 0.368
12.5% 0.383
6.25% 0.350
4.166% 0.377
3.125% 0.372
Fig.5.BandalignmentfortheCuGaS2:Cr/CuAlSe2andCuGaS2:Cr/ZnSe
heteroint-erfaces.
resultingbandalignmentsareshowninFig.5.Fromthefigure,the CuGaS2:Cr/CuAlSe2interfaceshowsatypeII(staggered)alignment,
withboththevalenceandconductionbandofCuGaS2:Crlyingin
energybelowthecorrespondingonesoftheCuAlSe2,EC=0.66eV. This facilitatesthat electrons and holes tobe locate on differ-entsidesoftheinterface,thusavoidingdirectrecombination.The CuGaS2:Cr/ZnSeinterfacealsoexhibitsastaggeredbandlineup,
wheretheECofCuGaS2:Cris0.27eVhigherthanZnSe.
ThereforeaZnSe/CuGaS2:Cr/CuAlSe2 setupwouldbeidealto
efficientlyseparateelectronsandholesgeneratedwiththehelpof theintermediateband.Isimportanttonotethatthepositionofthe Fermilevelinthesealignmentsarenotoverlappingthevalenceor conductionbandintheheterointerfaces.
4. Conclusions
In summary, we present density functional calculations for band alignment of CuAlSe2/CuGaS2:Cr and CuGaS2:Cr/ZnSe
heterointerfaces. The used scGW calculations reproduce accu-rately experimental band-gaps and hence correct band offsets can be obtained. The alignment, using as reference the aver-ageelectrostaticpotential,predicts thatCuGaS2:Cr/CuAlSe2 and
CuGaS2:Cr/ZnSeinterfaces are fromtype II and possess a
stag-geredalignment.Thesearetheappropriate conditionstomatch twointerfacesintoaheterostructurewiththreesemiconductors (CuAlSe2/CuGaS2:Cr/ZnSe) so that electrons and holes
photo-generated in the CuGaS2:Cr absorber layer, can be extracted
selectivelyasdesired,atbothsidesofthedevice.Itisexpected,that thesetheoreticalvaluesofEVandECwillprovidefurther under-standingofthefundamentalpropertiesofCuGaS2:Cr/CuAlSe2and
CuGaS2:Cr/ZnSeheterojunctions,whichwillbeveryusefulinthe
design,modellingandanalysisoftheoptoelectronicdevices.
Acknowledgements
ThisworkwaspartiallysupportedbyCONACyTunderdoctoral scholarshipNo.271481.Theauthorsthankfullyacknowledgethe computerresources,technicalexpertiseandassistanceprovidedby theRedEspa ˜noladeSupercomputación,theCentrode Supercom-putaciónyVisualizacióndeMadrid(CeSViMa)andtheLaboratorio NacionaldeSupercómputodelSurestedeMéxico(LNS1).
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