Chapter Present Status in the Development of IIIV MultiJunction Solar Cells Simon P - PDF document

Chapter1PresentStatusintheDevelopmentofIII–VMulti-JunctionSolarCellsSimonP.Philipps,WolfgangGuter,ElkeWelser,JanSchone,MarcSteiner,FrankDimroth,andAndreasW.BettAbstract S.P.Philipps(A.W.Bett( ©Springer-VerlagBerlinHeidelberg2012 1PresentStatusintheDevelopmentofIIIÐVMulti-JunctionSolarCells3 Fig.1.2IdealefÞcienciesoftriple-junctionsolarcellstructurescalculatedwithetaOpt[]undertheAM1.5dASTMG173-03spectrumwithaconcentrationratioof500sunsandacelltemperatureof65Thisiswhydifferentapproachesforachievingcurrent-matchingconditionshavebeensuggested[].Presently,theuseofmetamorphicstructuresasdiscussedbelowprovestobethemostsuccessfulstrategy.FigureshowshowtheidealefÞciencyofatriple-junctionsolarcelldesignvarieswiththebandgapenergiesofthethreeindividualjunctions.ThisdiagramhasbeencalculatedwiththemodeletaOpt[](fordownloadsee[]),whichisbasedonthedetailedbalancemethodÞrstintroducedbyShockleyandQueisser[Itisassumedthatradiativerecombinationistheonlyrecombinationmechanism.Furthermore,anexternalquantumefÞciency(EQE)ofunityisassumedforeachsubcell.Inordertoimprovecurrentmatchingunderacertainspectrum,photocurrentfromuppersubcellscanbetransferredtolowerones.Inrealitythisisachievedbythinningtheabsorbinglayers.Inordertomodelthiseffect,eachsubcellhasanindividualdegreeoftransparency,whichcanbeadjustedtoimprovecurrent-matching.TheefÞciencytheniscalculatedaccordingtotheone-diodemodel.ThecalculationsarecarriedoutundertheAM1.5dspectrumwithaconcentrationof500sunsandacelltemperatureof65C.TheseoperatingconditionsrepresentareasonableaveragefortodayÕsconcentratorsystems.AsFig.illustrates,theglobalmaximumforAM1.5dliesatabandgapcombinationof1.75,1.18,and0.70eV.Aseparatedlocalmaximumwitha2.4%(rel.)lowerefÞciencyisfoundfortherelativelyhighbandgapcombination1.86,1.34,and0.93eV.Thistwofoldmaximumresultsfromtheabsorptionbandofatmosphericwaterandcarbondioxidearound1,400nm,whichsigniÞcantlydeterioratestheefÞciencyofbandgapcombinationsinbetweenthetwomaxima.Accordingly,undertheextraterrestrialAM0spectrumonlyasinglemaximumexists.AssumingthatÐasaruleofthumbÐabout70Ð80%ofthetheoreticalefÞciencycanbeachievedinpractice,thetheoreticalmodelprovidesareasonableguidelinetoassessthepotentialofasolarcelldesign.ThebandgapcombinationsofÞvespeciÞctriple-junctionsolarcellstructures,forwhichefÞcienciesofover40%undertheconcentratedAM1.5dspectrumhavealreadybeenexperimentally 4S.P.Philippsetal.realized,areindicated:lattice-matchedGa0:500:500:990:01As/Ge(LM)LM)11Ð13];metamorphicGa0:440:560:920:08As/Ge(MM1)[];meta-morphicGa0:350:650:830:17As/Ge(MM2)[];invertedmetamorphic0:500:500:730:27As(Inv1);inverted(double)metamorphicdevice0:630:370:960:04As/GaAs(Inv2)[Today,theindustrystandardisstillthelattice-matchedtriple-junctionsolarcell,assimilarstructureshavebeendeveloped,produced,andsuccessfullytestedforspaceapplications[].Metamorphicorinvertedconceptshavenotbeenproducedinlargequantitiesyet.Standardsforthelong-termstabilitytestofsuchhighlystrainedsolarcellstructureshavetobedevelopedandthedeviceshavetobequaliÞedbeforemassproduction.Asthespace-marketiscomparativelysmall,uptonowthelattice-matchedtriple-junctionsolarcellcanbepurchasedfromonlyafewglobalsuppliers,amongtheseareAZURSPACESolarPowerGmbH(Germany),EmcoreInc.(USA),andSpectrolabInc.(USA).ThefollowingsectionpresentsanoverviewabouttheactualresearchstatusonIIIÐV-basedmulti-junctionsolarcellsatFraunhoferISEregardingnumericaldevicesimulationaswellasdevicefabrication.Subsequently,thepossiblenextstepsincelldesignareoutlined.1.2ResearchStatusInordertooptimizesuchcomplexsolarcellstructuresasmulti-junctioncells,numericalmodelingofthesedevicesisindispensibletoreducethenumberofexpen-siveandtime-consumingexperiments.AtFraunhoferISEsophisticatednumericalmodelingtoolsareusedintheoptimizationprocess.Thesimulationiscloselylinkedtotheexperimentaloptimization,concerningfeasibilityofthesemiconductorstructures,materialquality,andevaluationofthemodels.1.2.1NumericalSimulationThehighnumberoflayersinIIIÐVmulti-junctionsolarcellstructuresmakesapureexperimentaloptimizationveryexpensiveandprotracted.Anaccurateandreliablemodelingisdesirabletoacceleratetheoptimizationprocedureconsiderably.However,apredictivemodelingofthesesophisticatedstructuresischallengingduetothecomplexelectricalandopticalinteractionsbetweenthedifferentlayersandthehighnumberofmaterialparametersandphysicalphenomenathatneedtobeconsidered.Inrecentyears,thecapabilitiesofvariousapproachesandtoolsforthesimulationofIIIÐVmulti-junctionsolarcellshavegreatlyimprovedd18Ð23].IntheIIIÐVgroupatFraunhoferISE,threedifferentapproachesareused.TheoptimalnumberofbandgapsandtheidealbandgapcombinationisevaluatedwithetaOpt(seeSect.).Weanalyzethesemiconductorlayerstructurewiththe 1PresentStatusintheDevelopmentofIIIÐVMulti-JunctionSolarCells5commerciallyavailablesemiconductorsimulationenvironmentSentaurusTCADfromSynopsys.ThegriddesignisoptimizedwiththecircuitsimulatorLTSpicefromLinearTechnologyCorporation[].Inthefollowing,ashortoverviewofthestatusofourmodelingcapabilitiesispresented.TwoprerequisiteshavetobefulÞlledtoenablerealisticsimulationswithSentaurusTCAD:Þrst,thenecessarymodelsdescribingtheoccurringphysicalphenomenaneedtobeimplementedandvalidated.OfparticularimportanceforIIIÐVmulti-junctionsolarcellsareopticalinterferenceeffects,opticalgenerationgeneration25]andrecombinationofminoritycarriers,tunnelingeffects[]andcarriertransportathetero-interfaces[].Second,materialparameterssuchasopticalconstants,carriermobilities,bandgapenergies,electronafÞnityandparametersforradiative,Auger,Shockley-Read-Hallaswellasinterfacerecombinationarerequiredforeachsemiconductorlayerinthestructure.BothprerequisitesaresatisfactoryfulÞlledforthematerialsusedinourGaAssingle-junctionsolarcells,aswellasinourlattice-matchedGa0:510:49P/GaAsdual-junctionsolarcells.However,forothermaterials,especiallythoseinmetamorphicIIIÐVmulti-junctionsolarcells,thelackofmaterialdatalimitsthemodelingcapabilities[].Tokeepthecomputationaleffortwithintolerablelimits,thesmallesttwo-dimensionalsymmetryelementofthesolarcellismodeled,whichisconstructedbyacutthroughthelayersfromcaptosubstrateperpendiculartothegridÞngers.TheelementcoversawidthcorrespondingtohalfoftheÞngerspacingtoensurethatseriesresistanceeffectscausedbylateralcurrentßowinthedevicearetakenintoaccount.FigureshowsacomparisonbetweenmeasuredandsimulatedEQE,reßectionandIÐVcurveoftwoGaAssolarcellswithdifferentmaterialforthefrontsurfaceÞeld(FSF)layer.Themodelandmaterialparametersarebasedon[Thegoodagreementbetweenmeasurementandsimulationprovesthevalidityofthenumericalmodel.NotethatallmaterialparametersofthesolarcellexceptfortheFSFlayerhavebeenidentical.TheGaInPFSFlayerleadstosigniÞcantabsorptionintheshortwavelengthrangebetween300nmandthereforereducestheEQE.ThisunderlinestheimportanceofahighbandgapmaterialfortheFSFlayer.Anadditionalchallengeforthemodelingofmulti-junctionsolaristherequire-mentofaproperandnumericallystablemodelforthetunneldiode,whichconnectsthesubcellsinseries.ItwasfoundthatnonlocalinterbandtunneldiodemodelsreproducemeasuredtunneldiodeIÐVcurvesverywellinalargevoltagerangerange20,28].Thesemodelscoverthefullnonlinearityofthetunnelingmechanismandenablethesimulationofmulti-junctionsolarcellswithinsemiconductorsimulationenvironments.However,detailedquantummechanicalcalculationsproposethatinterbandtunnelingcannotexplainthehighcurrentsoftypicaltunneldiodesformulti-junctionsolarcells[].Ratherresonanttunnelingthroughdefectshomoge-neouslydistributedinthejunctionisidentiÞedaspossibletunnelingmechanism.Thus,thephenomenaoftunnelinginIIIÐVmulti-junctionsolarcellsneedtobeinvestigatedfurtherinthefuture.Yet,withthenonlocalinterbandtunneldiodemodel,wewereabletomodelalattice-matcheddual-junctionsolarcellwithatopcellofGa0:510:49PandabottomcellofGaAs[].Thesophisticateddevicecontainsananti-reßection 6S.P.Philippsetal. b Fig.1.3ComparisonbetweenmeasuredandsimulatedEQEandreßection)andIÐVcurveunderAM1.5g()fortwoGaAssolarcellswithdifferentfrontsurfaceÞeld(FSF)layermaterial.Thedeviceswithanareaof1cmweredesignedforoperationunderAM1.5g((a)reprintedwithpermissionfrom[].Copyright2010MIDEMSociety)coatingofMgF/TiO-GaAs/-GaAsEsakiinterbandtunneldiode,aswellasadistributedBraggreßectorcomposedof20alternatinglayersofAl0:800:20Asand0:100:90As.AsshowninFig.,agoodagreementisachievedbetweenexperi-mentalandsimulatedEQEoftopandbottomcell,reßectionandIÐVcurveundertheAM1.5gspectrum.Theslightdeviationsinthemodeledreßectionforwavelengthshigherthanthebandgapofthebottomcellarecausedbyaminorinaccuracyofthetransfermatrixmethod[]usedforthedescriptionoftheopticalprocesses.AdeviationisalsoobservableintheIÐVcurveintherangeof0.7Vandabout1.7V.Incontrasttotheslightlyincreasingmeasuredcurrent,thesimulatedvalueremainsconstant.Intherealdevice,suchacurrentdecreasecaneitherbecausedbyadistributedseriesresistanceeffectalongthegridÞngersorbyacurrentleakageatthecelledge.Botheffectsarenotcoveredinourtwo-dimensionalmodelingapproach.Thesophisticatednumericalmodelconstitutesaquickandcost-efÞcienttooltostudytheeffectofstructuralchangesonthecellperformance.Asillustratedin 1PresentStatusintheDevelopmentofIIIÐVMulti-JunctionSolarCells7 b Fig.1.4AgoodagreementisachievedbetweensimulatedandmeasuredEQEandreßection()andIÐVcurve()fortheinvestigated0:510:49P/GaAsdual-junctionsolarcell(reprintedwithpermissionfrom[].Copyright2008.Wiley)Fig.,doublingofthetunneldiodethicknessstronglyreducesthebottomcellÕsEQE.WeexplainthisbyabsorptionintheGaAsmaterialofthetunneldiode.Duetothestrongerabsorptionofhighenergyphotons,thedecreaseoftheEQEismorepronouncedforlowerwavelengths.Thesimulationsunderlinethatitisveryimportanttomakethetunneldiodeasthinaspossibleifitconsistsofthesamematerialastheabsorberofthelowercell.Inmostcases,abetteroptionistousehigherbandgapmaterialsforthetunneldiode[].Afurtherapplicationoftherecentlydevelopednumericalsolarcellmodelsisdesignoptimizationoptimization21,22,27,31].Asshownabove,thesemiconductorlayerstructurecanbeverywellmodeledwithatwo-dimensionalsymmetryelement.Yet,fortheoptimizationofthefrontcontactgridsuchamodelisnotsufÞcient.InprincipleitwouldbepossibletomodelandsimulateacompletesolarcellinallthreedimensionswithintheSentaurusTCADsimulationenvironment.However,duetothehighnumberofmeshpoints 8S.P.Philippsetal. Fig.1.5ofthetunneldiodethicknessontheEQEofa0:510:49P/GaAsdual-junctionsolarcell Fig.1.6ComparisonbetweenmeasuredandsimulatedÞllfactorandefÞciencyforaGaAsconcentratorsolarcellwithanactiveareaof5mm.ForthesimulationtheSPICEnetworkmodelpresentedbySteineretal.[]wasusednecessaryforarealisticmodel,thecomputationaleffortwouldbeenormous,leadingtointolerablecomputingtimeofweeksorevenmonths.Therefore,weoptimizethefrontcontactseparatelywithanelectricalnetworkmodel.Thesolarcellismodeledasanetworkofelementarycellsconsistingofdiodes,resistances,andcurrentsourcestomodelthesaturationcurrentsandthephoto-generatedcurrent.Theele-mentarycellsareconnectedinparallelthroughohmicresistancesrepresenting,forinstance,thelateralconductingemitterlayerorthemetalÞngers.Thereby,anetworkofelectricalcomponentsiscreated,whichdescribesthewholesolarcell.TheIV-characteristiciscalculatedwiththecircuitsimulatorLTSpice,whichusesaSimula-tionProgramwithIntegratedCircuitEngineering(SPICE)approach.Moredetailsaboutournetworkmodelcanbefoundin[].Figureshowsacomparison 10S.P.Philippsetal. Fig.1.7Relationbetweenbandgapandlatticeconstantfordifferentbinary(blackdots)andternary(lines)semiconductormaterialsaswellasforgermanium(left).Thetriple-junctionsolarcelllattice-matchedtoGefeaturesaGa0:990:01AsmiddlecellandasGa0:500:50Ptopcell(toprightstructure).TheGa0:830:17AsandtheGa0:350:65Psubcellofametamorphictriple-junctionsolarcell(bottomrightstructure)arelattice-matchedtoeachother,buthavea1.1%mismatchtothesubstrate.Thismismatchismanagedbyabufferstructure Fig.1.8Schematicillustrationofapseudo-morphicallystrainedlayer(left)grownonasubstratewithsmallerlatticeconstant.Asacriticalthicknessisexceeded,thestrainedepitaxiallayerstartstorelaxbythegenerationofmisÞtdislocation(rightconstantoftherelaxedlatticenormalizedbythelatticeconstantofthesubstrate.Figureschematicallyillustratestheprocessofstrainrelaxationofastrainedepitaxiallayer.Uptoacriticalthickness,ÞrstdeÞnedbyMatthewsetal.[],thelayerispseudo-morphicallystrained.Asthelayerthicknessincreasesbeyondthecriticalthickness,ÞrstmisÞtdislocationsaregeneratedwithintheinterfaceduetobendingofpre-existingsubstratedislocations.Withafurtherincreaseofthelayerthickness,severalgenerationmechanismsformisÞtdislocationsetin,whichÞnallyleadtoasigniÞcantstrainrelaxation[ 1PresentStatusintheDevelopmentofIIIÐVMulti-JunctionSolarCells11 Fig.1.9TEMcross-sectionimagesfromaconstantbufferwithabruptchangeinlatticeconstant),alinearlygradedbufferwithlinearchangeinlatticeconstant(),astepgradedbufferwithaboutsevengradingsteps(),andastepgradedmetamorphicGaAsbufferwithincreasingIncontentfrom1%to17%(3Ð1to3Ð7)andanovershootinglayer(3Ð8)with23%In().(TEMimagesmeasuredattheChristian-Albrechts-UniversityinKiel,Germany)FigureshowsTEMcross-sectionimagesofdifferentbufferconceptswhichwehaveinvestigated:aconstantbuffer(a),alinearlygradedbuffer(b),andtwostepgradedbuffers(candd).Incontrasttothegradedstructures,theconstantbuffergrowthleadstothegenerationofalargenumberofthreadingdislocationswhichmayactasrecombinationcentersinthephotoactiveregionofthemulti-junctionsolarcells.Forhighperformancedevicesthreadingdislocationdensitiesbelowarenecessary.Accordingtoourexperience,thiscanonlybeachievedwiththegradedbuffers.Especiallythestepgradedbufferlocalizesthedislocationsgeneratedwithintheinterfaceregionsbetweenthestepsandpreventsthegeneration 1PresentStatusintheDevelopmentofIIIÐVMulti-JunctionSolarCells13Inlattice-matchedaswellasinmetamorphicmulti-junctionsolarcells,theindividualsubcellsareinterconnectedviainterbandtunneldiodes,whichprovidealowelectricresistanceandcanbedesignedtransparentforlightconvertedinthefollowingsubcell.Tunneldiodesessentiallyconsistoftwodegeneratelydopedlayerswithdifferentpolarity.High-dopinglevelsintherangeof10havebeenachievedwithtelluriumorsiliconinGaInAsorGaInP.Veryhigh-dopingintherangeof10isachievedwithcarboninAlGaAs[].Tunnelcurrentdensitiesabove100Acmhavebeenmeasured.However,tunneldiodesinmetamorphicsolarcellsneedlargerlatticeconstants,whichcanberealizedbyaddingIntothementionedcompounds,asalreadydoneforthesubcells.ButthecarbondopingofsuchAlGaInAslayersturnsouttobemoredifÞcult.ThecommonlyusedcarbonprecursorCBrcannotbeusedanymoreasitetchesindiumum38].Intrinsic-dopingfromthealkylgroupsofTMAlhadbeenapplied,butthedopinglevelsachievedareoneorderofmagnitudelowerthanwithIn-freeAlGaAs.Theuseoflattice-mismatchedlayersinthetunneldiode,suchasAlGaAs,generatesdislocations,whichdegradethesolarcellstructure.Thisiswhywedesignedstraincompensatedtunneldiodes.ThesestructuresmakeuseofahighlydopedAlGaAslayer,whichhasatoosmalllatticeconstantandcausestensilestraininthetunneldiodestructure.Inordertoreducethisstrain,aneighboringlayersuchasGaInAsorGaInPisgrownwithatoolargelatticeconstant.Thiscompensatesthestraininthestructureandavoidsthegenerationofdislocations.Figureillustratesthisconceptwitha-AlGaAs/-GaInAstunneldiode.Duetostraincompensation,therestofthestructureisnotaffectedbythehighlystrainedtunneldiodes.Asexplainedabove,thesubcellsofametamorphictriple-junctionsolarcellarealmostideallyadaptedtotheAM1.5dspectrum.FigurecomparestheEQEsofsuchastructurewithalattice-matchedtriple-junctioncell.ThelowerbandgapsinthemetamorphiccellshifttheEQEstohigherwavelengths.ThefavorablebandgapcombinationtogetherwiththeimprovementsregardingthemetamorphicbufferandthetunneldiodesarethekeypointsthatleadtoanefÞciencyof41.1%withourmetamorphictriple-junctionsolarcell(Fig.Theperformanceofaconcentratorsolarcellalsostronglydependsonthecelldesignincludingsize,gridstructure,andintendedoperationilluminationintensity.FigureillustrateshowdifferentfrontsidegridlayoutswithdecreasingamountofmetallizationshiftthemaximumefÞciencytolowerconcentrationsasshadingisreduced.Furthermore,theabsoluteefÞciencymaximumriseswithdecreased Fig.1.11Schematicillustrationofastraincompensatedtunneldiode.Thewidthoftheboxesrepresentsthelatticeconstant.AcompressivelystrainedGaInAslayeriscompensatedwithatensileAlGaAslayer 1PresentStatusintheDevelopmentofIIIÐVMulti-JunctionSolarCells15 Fig.1.13FillfactorandefÞciencyoftwometamorphictriple-junctionsolarcellsasafunctionoftheconcentration.Differentfrontsidemetallization,whichisshowninthephotographs,leadstodifferentmaximumpositions.Thecellin()issuitableforhighconcentrationratioswellabove1,000suns,thecellin)isadaptedfor500sunsForthispurpose,wehavedevelopedatheoreticalenergyharvestingmodel[inwhichthesolarcellismodeledaccordingtothedetailedbalancemodeletaOpt(seeSect.).Here,weinvestigatetheenergyharvestingattwolocationsonEarthwithdistinctspectralconditions:SolarVillageinSaudiArabiawithratherred-richincidentlightandLaParguerainPuertoRicowithahighershareofbluelight.Fortheseplaces,measuredatmosphereparametersfromtheAERONETdatabasee46]areusedtocalculatedirectsolarspectrawiththecomputercodeSMARTS2.9.5[].Adiscretizationofonespectrumperhourwaschosenresultinginmorethan4,400spectraforeachgeographicallocation.Concerningtheoperatingconditions,weassumeaconcentrationfactorof1,000suns,whichisexpectedtobecomestandardforfutureconcentratorsystems.Inaddition,aconstantcelltemperatureof338Kisassumed.Fromourexperiences,thisvaluerepresentsareasonableaverage,whichisalsousedbyothergroups[].Basedonthesimulated 16S.P.Philippsetal.spectratheannualsumoftheproducedenergy,whichiscomputedfromtheproducedenergyforeachdayintheyear,iscalculatedandisthenreferredtotheirradiatedenergy.Theoverallannualincidentenergiesare2,599kWhmatSolarVillageand2,849kWhmatLaParguera.TheratiooftheenergyproducedtotheirradiatedenergydeÞnestheenergyharvestingefÞciency.IIIÐVmulti-junctionconcentratorsolarcellsareusuallyoptimizedandratedunderthereferencespectrumAM1.5d.Followingthisapproach,weÞrstcalculatedtheidealbandgapcombinationunderthereferencespectrum(1,000suns,338K)forsolarcellswith1Ð6subcells.ThentheenergyharvestingefÞcienciesoftheresultingbandgapdesignsatSolarVillage(Fig.a)andLaParguera(Fig.werecalculated.TheresultscorrespondtotheleftbarsineachÞgure.TherightbarsindicatetheenergyharvestingefÞcienciesthatcouldberealizedwiththeoptimalbandgapcombinationfortheintendedplaceofoperation.Theseweredetermined b Fig.1.14ComparisonofthemaximumenergyharvestingefÞciencyversusthenumberofsubcellsatSolarVillage,SaudiArabia()andLaParguera,PuertoRico(TheindicatedbandgapcombinationsresultfromtheoptimizationofthecellefÞciencyunderthereferencespectrumAM1.5dASTMG173-03(leftbars),andoftheenergyharvestingefÞciencyfortheintendedplaceofoperation(rightbars 1PresentStatusintheDevelopmentofIIIÐVMulti-JunctionSolarCells17bymaximizingtheyearlyproducedenergybasedonthemorethan4,400spectraforSolarVillageorLaParguera,respectively.ItisnoteworthythattheenergyharvestingefÞciencyincreaseswiththenumberofsubcellsinallcasesdespitetheconsideredspectralvariationsthroughoutdayandyear.However,therelativegainofaddingadditionaljunctionsissmallformorethanfourjunctions.ComparedtothebandgapcombinationsresultingfromtheoptimizationofthecellefÞciencyunderthereferencespectrumAM1.5d,aratherstrongincreaseinenergyharvestingefÞciencycanberealizedwiththeoptimalbandgapcombinationsforeachlocation.However,thesebandgapcombinationsgointodifferentdirections.AtSolarVillage,slightlylowerbandgapsarefavorableduetothelowshareofbluelightatthislocation.Incontrast,higherbandgapsarefavorableundertheblue-richspectralconditionsofLaParguera.Itshouldbenotedthatthedetailedbalancemodelassumesidealsolarcells.Asaruleofthumb70Ð80%ofthetheoreticalcellefÞcienciescanbeachievedinpractice.However,therealizationofgoodmaterialqualityusuallybecomesmorechallengingforsolarcellswithahighernumberofsubcellsduetothegreatercomplexityofthestructureandthenovelmaterialsinvolved(seediscussionbelow).Thus,itisstillanopenquestionifsolarcellswithmorethanfour-junctionscanberealizedwithsufÞcientmaterialqualitytoharvestthesmallrelativegainspredictedbyourenergyharvestingmodel.FiguresummarizesthedevelopmentroadmapforIIIÐVmultijunctionsolarcellconceptsinvestigatedatFraunhoferISE.Apartfromthealreadydis-cussedlattice-matched(a)andmetamorphic(d)triple-junctionsolarcells,different Fig.1.15RoadmapforthedevelopmentofIIIÐVmulti-junctionsolarcellsatFraunhoferISEandcorrespondingmaximumefÞcienciescalculatedwithetaOpt(AM1.5d,1,000suns,338K).ThenumberofjunctionsandtheefÞciencyofthelattice-matchedGaInP/GaInAs/Geapproach()canbeincreasedbyaddingaGaInNAssubcell().AstheperformanceofthisdeviceislimitedbythediffusionlengthinGaInNAs,asix-junctioncellhasbeendesigned().Analmostidealbandgapcombinationisachievedwithametamorphictriple-junctionsolarcell().Addingasecondbufferleadstoametamorphicquadruple-junctionsolarcell().Inordertogrowasmanyjunctionsaspossiblelattice-matchedtothesubstrate,thestructureisgrowninverted 1PresentStatusintheDevelopmentofIIIÐVMulti-JunctionSolarCells19quadruplecellandhencethesubcellsarethinner.Thus,shorterdiffusionlengthsareacceptable.Asix-junctioncellmayberealizedbyaddingAlGaInPandAlGaInAssubcellstothestack(Fig.c).Thegraph(b)inFig.showstheIQEofsuchasix-junctionsolarcell.TheGebottomcellhasaquitehighcurrentduetothenotidealbandgapcombinationofthisdevice.Smallerbandgapsforthelowercellswouldbefavorable.Awaytorealizesuchcombinationsistousemorethanonelattice-transitionbufferandtogrowthestackinversely(Fig.ThischaptershowedthatIIIÐVtriple-junctionsolarcellshavereachedefÞcien-ciesof41.6%underconcentratedsunlight[].WeexpectthattherecordefÞciencyofthesedeviceswillsoonreachabove43%.ForevenhigherefÞcienciestoward50%IIIÐVmulti-junctionsolarcellswithmorethanthreesubcellsarepromising.References1.W.Guter,J.Schone,S.P.Philipps,M.Steiner,G.Siefer,A.Wekkeli,E.Welser,E.Oliva,A.W.Bett,F.Dimroth,Appl.Phys.Lett.(22),223504(2009)2.R.R.King,A.Boca,W.Hong,D.Larrabee,K.M.Edmondson,D.C.Law,C.M.Fetzer,S.Mesropian,N.H.Karam,inConferenceRecordofthe24thEuropeanPhotovoltaicSolarEnergyConferenceandExhibition,Hamburg,Germany,21Ð25Sep2009,pp.55Ð613.H.Lerchenm¬uller,A.W.Bett,J.Jaus,G.Willeke,inConferenceRecordofthe3rdInternationalConferenceonSolarConcentratorsfortheGenerationofElectricityorHydrogen,Scottsdale,AZ,USA,1Ð5May2005,p.6.4.I.Garcõa,I.Rey-Stolle,B.Galiana,C.Algora,Appl.Phys.Lett.(5),053509(2009)5.W.Shockley,H.J.Queisser,J.Appl.Phys.(3),510(1961)6.D.J.Friedman,J.F.Geisz,S.R.Kurtz,J.M.Olson,J.Cryst.Growth(1Ð4),409(1998)7.K.W.J.Barnham,I.Ballard,J.P.Connolly,N.J.Ekins-Daukes,B.G.Kluftinger,J.Nelson,C.Rohr,Phys.E-Low-DimensionalSyst.Nanostructures(1Ð2),27(2002)8.A.W.Bett,C.Baur,F.Dimroth,J.Schone,Mater.Photovoltaics,223(2005)9.G.Letay,A.W.Bett,inConferenceRecordofthe17thEuropeanPhotovoltaicSolarEnergyConferenceandExhibition.WIP-RenewableEnergies,Munich,Germany,22Ð26Oct2001,pp.178Ð18010.G.Letay,A.W.Bett,etaOpt,www.ise.fraunhofer.de/downloads/software/etaOpt.zip/view11.R.R.King,D.C.Law,K.M.Edmondson,C.M.Fetzer,G.S.Kinsey,H.Yoon,R.A.Sherif,N.H.Karam,Appl.Phys.Lett.(18),183516(2007)12.F.Dimroth,Phys.StatusSolidiCÐCurr.Top.SolidStatePhys.(3),373(2006)13.M.Yamaguchi,T.Takamoto,K.Araki,Sol.Energ.Mater.Sol.Cell.(18Ð19),3068(2006)14.J.F.Geisz,D.J.Friedman,J.S.Ward,A.Duda,W.J.Olavarria,T.E.Moriarty,J.T.Kiehl,M.J.Romero,A.G.Norman,K.M.Jones,Appl.Phys.Lett.(12),123505(2008)15.R.R.King,C.M.Fetzer,D.C.Law,K.M.Edmondson,H.Yoon,G.S.Kinsey,D.D.Krut,J.H.Ermer,P.Hebert,B.T.Cavicchi,N.H.Karam,inConferenceRecordofthe2006IEEE4thWorldConferenceonPhotovoltaicEnergyConversion,Waikoloa,HI,17Ð12May2006,pp.1757Ð176216.P.R.Sharps,A.Comfeld,M.Stan,A.Korostyshevsky,V.Ley,B.Cho,T.Varghese,J.Diaz,D.Aiken,inConferenceRecordofthePVSC:200833rdIEEEPhotovoltaicSpecialistConference,SanDiego,USA,11Ð16May2008,pp.2046Ð205117.A.W.Bett,F.Dimroth,W.Guter,R.Hoheisel,E.Oliva,S.P.Philipps,J.Schone,G.Siefer,M.Steiner,A.Wekkeli,E.Welser,M.Meusel,W.Kostler,G.Strobl,inConferenceRecordofthe24thEuropeanPhotovoltaicSolarEnergyConferenceandExhibition,Hamburg,Germany,21Ð25Sep2009,pp.1Ð6 20S.P.Philippsetal.18.S.Michael,Sol.Energ.Mater.Sol.Cell.(1Ð4),771(2005)19.Z.Li,G.Xiao,Z.Li,HighLowConcentrationSol.ElectricAppl.,633909(2006)20.M.Hermle,G.Letay,S.P.Philipps,A.W.Bett,Progr.Photovoltaics(5),409(2008)21.S.P.Philipps,M.Hermle,G.Letay,F.Dimroth,B.M.George,A.W.Bett,Phys.StatusSolidi-RapidRes.Lett.(4),166(2008)22.M.Baudrit,C.Algora,Phys.StatusSolidia-Appl.Mater.Sci.(2),474(2010)23.M.Steiner,S.P.Philipps,M.Hermle,A.W.Bett,F.Dimroth,Prog.Photovoltaics(1),7324.LTSpice,SwitcherCADIII/LTSpice.Tech.rep.,LinearTechnologyCoorporation(2007)25.G.Letay,M.Breselge,A.W.Bett,inConferenceRecordofthe3rdWorldConferenceonPhotovoltaicEnergyConversion,Osaka,Japan,11Ð18May2003,pp.741Ð74426.G.Letay,M.Hermle,A.W.Bett,Prog.Photovoltaics(8),683(2006)27.S.P.Philipps,W.Guter,M.Steiner,E.Oliva,G.Siefer,E.Welser,B.George,M.Hermle,F.Dimroth,A.W.Bett,InformacijeMIDEM-J.Microelectron.Electron.Compon.Mater.(4),201(2010)28.M.Baudrit,C.Algora,inConferenceRecordofthePVSC:200833rdIEEEPhotovoltaicSpecialistConference,SanDiego,USA,11Ð16May2008,pp.576Ð58029.K.Jandieri,S.D.Baranovskii,O.Rubel,W.Stolz,F.Gebhard,W.Guter,M.Hermle,A.W.Bett,J.Appl.Phys.(9),094506(2008)30.T.Takamoto,M.Kaneiwa,M.Imaizumi,M.Yamaguchi,Progr.Photovoltaics(6),49531.S.P.Philipps,M.Hermle,G.Letay,W.Guter,B.M.George,F.Dimroth,A.W.Bett,inConferenceRecordofthe23rdEuropeanPhotovoltaicSolarEnergyConferenceandExhi-bition,Valencia,Spain,1Ð5Sep2008,pp.90Ð9432.M.A.Green,K.Emery,Y.Hishikawa,W.Warta,Progr.Photovoltaics(5),320(2009)33.F.Dimroth,R.Beckert,M.Meusel,U.Schubert,A.W.Bett,Prog.Photovoltaics(3),16534.J.W.Mattews,A.E.Blakeslee,J.Cryst.Growth,118(1974)35.D.D.Perovic,D.C.Houghton,inMicroscopyofSemiconductingMaterialsed.byA.G.Cullis,A.E.StatonBevan.ConferenceonMicroscopyofSemiconductingMaterials,20Ð23Mar1995,pp.117Ð134(Oxford,England,1995)36.F.K.Legoues,B.S.Meyerson,J.F.Morar,P.Kirchner,J.Appl.Phys.(9),4230(1992)37.J.Schone,E.Spiecker,F.Dimroth,A.W.Bett,W.Jager,Appl.Phys.Lett.(8),081905(2008)38.W.Guter,F.Dimroth,J.Schone,S.P.Philipps,A.W.Bett,inConferenceRecordofthe22thEuropeanPhotovoltaicSolarEnergyConferenceandExhibition,Milan,Italy,3Ð7Sep2007,pp.122Ð12539.D.J.Friedman,J.F.Geisz,A.G.Norman,M.W.Wanlass,S.R.Kurtz,inConferenceRecordofthe2006IEEE4thWorldConferenceonPhotovoltaicEnergyConversion,Waikoloa,Hi,07Ð02May2006,pp.598Ð60240.F.Dimroth,S.Kurtz,MRSBull.(3),230(2007)41.M.Yamaguchi,K.I.Nishimura,T.Sasaki,H.Suzuki,K.Arafune,N.Kojima,Y.Ohsita,Y.Okada,A.Yamamoto,T.Takamoto,K.Araki,Sol.Energ.(2),173(2008)42.S.Kurtz,D.Myers,W.E.McMahon,J.Geisz,M.Steiner,Prog.Photovoltaics(6),537(2008)43.M.Meusel,R.Adelhelm,F.Dimroth,A.W.Bett,W.Warta,Progr.Photovoltaics(4),24344.S.Kurtz,J.M.Olson,P.Faine,Sol.Cell.(1Ð4),501(1991)45.S.P.Philipps,G.Perharz,R.Hoheisel,T.Hornung,N.M.Al-Abbadi,F.Dimroth,A.W.Bett,Sol.Energ.Mater.Sol.Cell.(5),869(2010)46.InternationalAERONETFederation,AERONET(AErosolROboticNETwork)program,aeronet.gsfc.nasa.gov47.C.Gueymard,Sol.Energ.(5),325(2001)48.C.Gueymard.SimpleModeloftheAtmosphericRadiativeTransferofSunshine(SMARTS),Version2.9.5,www.nrel.gov/rredc/smarts