Modeling Enhanced Performances by Optical Nanostructures in Water-Splitting Photoelectrodes - Photoelectrodes et al. - 2021 - Unknown

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pubs.acs.org/JPCCArticleModelingEnhancedPerformancesbyOpticalNanostructuresinWater-SplittingPhotoelectrodesLucDriencourt,BenjaminGallinet,*CatherineE.Housecroft,SörenFricke,andEdwinC.Constable*CiteThis:J.Phys.Chem.C2021,125,7010−7021ReadOnlineACCESSMetrics&MoreArticleRecommendations*sıSupportingInformationABSTRACT:Materialnanostructuringandopticalphenomenaonananoscalesuchasplasmoniceffectsandlightscatteringhavebeenwidelystudiedforimprovingthesolar-to-hydrogenefficiencyofphotoelectrochemical(PEC)water-splittingelectrodes.Inthiswork,wereportamethodforanalyzingthecontributionsofopticaleffectsfromnanostructuresforenhancingthePECperformances.Electro-magneticsimulationsareperformedfortheprecisecalculationofgeneratedpowerdensityinasemiconductormaterial.Inaddition,thetransportandtransferofphotogeneratedchargestotheelectrolytearemodeledbyusingtheconservationofminoritycarriers.Thesurfacelossparameter,diffusionlength,anddopingdensityofthesemiconductormaterialaredeterminedbyfittingthemodeltoanincidentphotontocurrentefficiency(IPCE)curveexperimentallymeasuredonthebarereferencephotoelectrode.TheseparametersarethenusedtocomputetheIPCEspectraofthephotoelectrodeforwhichanopticalenhancementstrategyisused,suchasnanostructuringorplasmonics.Themethodisvalidatedusingpublishedexperimentaldata.ThecalculatedIPCEenhancementratiooriginatingfromopticaleffectsisinquantitativeagreementwithexperimentalobservationsforbothperiodicandrandomopticalstructures.ThemodelcanbeusedtostudyindetailthekeyenhancementmechanismsfortheIPCEfromopticalnanostructuresand,inparticular,discriminatebetweenopticalandnonoptical(e.g.,catalytic)enhancement.■INTRODUCTIONOpticaleffectshavealsobeeninvestigatedtoimprovetheSolarwatersplittingwithphotoelectrochemical(PEC)cellsperformanceofphotoelectrodes.Thin-filmphenomenahave10,11hasthepotentialofbeingacompetitivetechnologyforbeenexplored,forinstance,back-reflectinglayers.12−1516−18Downloadedvia103.238.105.33onMay14,2021at08:16:47(UTC).hydrogenproductioncomparedtothereformingoffossilPlasmonicnanoparticlesornanostructurescom-fuels.1Intensiveresearchisstillongoingtodevelophigh-binedwithawater-splittingsemiconductormaterialcanyieldperformance,inexpensivephotoelectrodesthatcanoperateforanincreasedphotocurrentwithrespecttothebarephoto-severalyears.MetaloxidesemiconductorsarepromisingelectrodeasaconsequenceofmodifiedlightabsorptioninsidecandidatesforpracticalPECwatersplitting,thankstotheirthesemiconductor.Moreover,plasmonichotcarriergen-Seehttps://pubs.acs.org/sharingguidelinesforoptionsonhowtolegitimatelysharepublishedarticles.lowcostandinherentstabilityunderaqueousconditions.erationandsubsequenttransfertothesemiconductorhasbeenHowever,theyfaceseveralissuesthatlimittheirsolar-to-demonstratedasawayofusinglightwithlessenergythanthehydrogenefficiency.Ononehand,nometaloxidesemi-19−22bandgapofthesemiconductor.Includinglightscatterersconductorhasbeenfoundtomeetbothrequirementsofaninthephotoelectrode23,24canincreasetheopticalpathoftheenergybandgapclosetothetheoreticaloptimum(1.84eVforlightandbehelpfulforovercomingthehighabsorptiondepth2thetopabsorberinadualstackedtandemcell)andlowbulk/ofmanymetaloxides.Microstructuredandnanostructured3surfacerecombinations.Ontheotherhand,athinlayermorphologies25−29andhost−guestarchitectures30−35whereathicknessshouldbeusedtoachievedecentchargetransportthinsemiconductorlayerisdepositedonahighlymicro-becauseoftheshortminoritycarrierdiffusionlengthofmoststructuredornanostructuredconductiveguestscaffoldhave4,5metaloxides(e.g.,2−20nmforα-Fe2O3)resultinginpoorlightabsorptionasaconsequenceoftheindirectnatureofthebandgap.SeveralenhancementstrategieshavebeenReceived:December21,2020elaborated.Dopingofmetaloxides,eitherduringsynthesis6Revised:March5,2021orwithapost-treatment,7,8hasbeenreportedasanefficientPublished:March26,2021wayofimprovingtheelectricalproperties.Depositionofa9surfacecatalystsuchascobalt-phosphate(Co-Pi)resultsinacathodicshiftofthephotocurrentonsetpotential.©2021TheAuthors.PublishedbyAmericanChemicalSocietyhttps://doi.org/10.1021/acs.jpcc.0c113427010J.Phys.Chem.C2021,125,7010−7021

1TheJournalofPhysicalChemistryCpubs.acs.org/JPCCArticleFigure1.Sketchofann-typesemiconductorphotoelectrodeilluminatedfromtheelectrolytesideanddifferentopticaleffectsthatcanimprovethewater-splittingefficiency.Theinsetontherightillustratesthatseparationbetweenphotogeneratedelectronsandholescanbeachievedonlyinthespacechargeregion(SCR)orclosetoitwithrespecttotheminoritycarrierdiffusionlength.beenwidelystudied.Suchstructuresenableadditionallightnotconsiderthephotogeneratedchargeseparation,transport,absorptiontotakeplaceclosetothesemiconductor/electrolyteandtransfertotheelectrolyte.interfaceduetotheincreasedsurfaceareawithrespecttoaflatInthiswork,wecombinenear-fieldelectromagneticconfiguration.simulationswithachargetransportmodeltostudyopticalModelingapproachesareimportantforunderstandingtheenhancementatthenanoscaleinwater-splittingphoto-limitationsassociatedwiththeobservedwater-splittingelectrodes.Preciseopticalmodelingofthephotoelectrodeisperformancesandinvestigatingthepotentialofdifferentperformed,whereasthetransportandtransferofphoto-35,3637enhancementstrategies.GaudyandHaussenerdemon-generatedchargesaretreatedsemianalyticallybyconsideringstratedafastanalysisandoptimizationmethodpartiallybasedtheminoritycarriers.Thepresentedmethodenablestoanalyze38ontheworkofWilson.Itmodelstheincidentphotontothecontributionofvariousopticaleffectsbyconsideringthecurrentefficiency(IPCE)andcanbeusedtoextracttheentirewater-splittingprocess.Inparticular,opticalandoptical,bulk,andsurfacelossesofaphotoelectrodefromannonopticalcontributionscanbediscriminatedinanobservedIPCEmeasurement.Withthistool,theauthorscouldIPCEenhancement.Insightsintothemainmechanismsofinvestigateforseveralmaterialsifnanostructuringisasuitableopticalenhancementareunveiled,suchasitsresonantorwayofimprovingtheperformances.Themodelassumesaflatnonresonantnature,thelocationofelectromagneticfieldhotstructureoftheelectrodeaswellasauniformlightabsorptionspotscontributingtophotocurrentgeneration,theinfluenceofinthematerialdescribedbytheBeer−Lambertlaw,whichnanometricgeometricalfeaturesontheefficiency.Itismakesitunsuitableforstudyingheterojunctionsandopticalapplicabletoanynear-fieldelectromagneticcalculationeffectswheretheabsorptionprofilecannotbeconsideredasmethod,thusallowingausertochoosethemostappropriate10exponentiallydecaying(e.g.,plasmonics).Dotanetal.andefficientapproachtothesystemathand.investigatedtheoreticallyandexperimentallyopticalbackInthefollowing,thecalculationofIPCEincludingopticalreflectorstoenhancethephotocurrentofultrathinhematitenear-fieldenhancementeffectsandachargetransportmodelis(α-Fe2O3)photoanodes.Asimplifiedmodelwasusedtofirstdescribed.Anexperimentalvalidationofthewholeaccountfortheminoritycarrier’sseparation,transport,andmethodisthenperformedbycomparingtheopticalenhance-transfertotheelectrolyte.Moreover,byconsideringanideallymentcalculatedwiththemodeltopublisheddata.Foreachreflectivesubstrate,theycouldobtainananalyticalexpressioncase,theopticalmodelandtheopticalpropertiesoftheforthephotonfluxinthehematitelayer.Encinaandmaterialsarefirstvalidatedbycomparisonwithmeasurements.39CoronadostudiedplasmoniceffectsinisolatedhybridThestudiedgeometriesinvolveseveralsemiconductorhematite/metal(metal=Al,Ag,Au)nanocylinderswithmaterials(α-Fe2O3andBiVO4),differenttypesofopticalnear-fieldsimulations.Theabsorptionefficiencyintheelements(periodicallydistributedhostscaffoldandrandomlyhematiteregionwassimulatedwithdiscretedipoleapprox-distributednanoparticles),anddifferentelectromagneticimation.Althoughthepresentedmethodprovidedtheoreticalsimulationmethods(rigorouscoupledwaveanalysis,RCWA,insightsintotheimportantparameterscontributingtotheandsurfaceintegralequations,SIE).Finally,wediscusshowplasmonicenhancement,thestudywaspurelyopticalanddidthetypesofopticaleffectsresponsiblefortheobserved7011https://doi.org/10.1021/acs.jpcc.0c11342J.Phys.Chem.C2021,125,7010−7021

2TheJournalofPhysicalChemistryCpubs.acs.org/JPCCArticleenhancementcanbeidentifiedfromnear-fieldstudiesandL−d()/xLU*=()xeIPCEenhancementspectra.LDS+/(3)■withd(x)beingthedistancebetweenxandtheedgeoftheMODELDESCRIPTIONSCRregion,Sisaboundaryparameter(fullderivationintheThemethodforcalculatingtheIPCE(orexternalquantumSupportingInformation),andD=μVthistheEinsteinefficiency,EQE)isdescribedinthenextsection.First,thediffusioncoefficientwithμbeingthemobilityoftheminoritygeneratedpowerdensityinthesemiconductormaterialischargecarrier.calculatedwithnear-fieldopticalsimulationsandcombinedTheparameterζineq2expressestheratioofchargeswithachargetransportmodeltocomputetheEQE.InageneratedintheSCRthatarereachingthesemiconductor/secondstep,amethodtoanalyzeopticalenhancementin37electrolyteinterfacenanostructuredelectrodesispresented.OpticalSimulations.Figure1showsdifferenttypesofL2ϕSCRopticaleffectsthathavebeenreportedtoimprovetheζ=22performancesofwater-splittingphotoelectrodes.11,15,23,31LWϕSCR+SCRVth(4)4041EitherSIEwithperiodicboundaryconditionsorRCWAwhereListheminoritycarrierdiffusionlength,Vth=kBT/qisisusedtocalculatethelightintensitydistributioninthethethermalpotential,andϕsc=Va−Vfbisthepotentialdropsemiconductorregion.SIEisknowntobehighlyrobustforacrosstheSCR,withVabeingtheappliedvoltageandVfbtheplasmonicnear-fieldcalculations,whereasRCWAismore42flatbandpotentialofthematerial.adaptedtolargeperiodicdielectricstructures.Throughout45WSCRisthethicknessoftheSCRdefinedasthiswork,thecalculationsaremadeinaunitcellcontainingasinglefeatureinordertoreducecomputationalcosts.2εε0rHowever,thepresentedmodelcanbereadilyadaptedtoWSCR=−()ϕSCRVthqNd/a(5)fastersimulationtechniquesthatenable“supercells”witha43largenumberoffeatures,suchasthefastmultipolemethod.whereε0isthevacuumpermittivity,εristherelativeTheelectricfieldintensityiscalculatedinasetofrandomlypermittivityofthematerial,andNd/aisthedensityofgeneratedpointsinsidethesemiconductorregion.Thedonors/acceptors.44generatedpowerdensityateverypointisthengivenbyIntheworkofGaudyandHaussener,37theBeer−Lambertc2lawwasusedtocomputeG(x,λ).ThismodelwasthenG(,)xEλ={}πεIm0ε()(,)λ||xλvalidatedonpublisheddataforseveralsemiconductorthinλ(1)filmsincludingp-typesilicon,bycomparingthedeterminedwherecisthespeedoflightinvacuum,λisthevacuumdiffusionlengthwiththereportedvalues.Inthiswork,wewavelength,εisthevacuumpermittivity,ε=(n+ik)2isthe0studythecontributionofopticalnanostructuresbyperformingcomplexpermittivityofthesemiconductormaterial,andanumericalcalculationofU*(x)andG(x,λ)inasetofE(x,λ)istheelectricfieldatpositionxandwavelengthλ.randomlygeneratedintegrationpoints.Theintegralsofeq2Equation1willthenbeusedinthenextsectiontocomputearethencomputednumericallyfromthenear-fielddistributiontheEQEinthesemiconductormaterialwithandwithoutopticalnanostructuring.iNSCRcπε0jjjjVSCR2IPCEDeterminationfromOpticalSimulations.TheEQE()Nλ={Im()ελ}Rsjjζ∑||Ex(,)iλλP0kNSCRi=1semiconductorvolumecanbeseparatedintoaSCRwherebandbendingexistsduetothepresenceofasemiconductor/VNBulkyzzelectrolytejunction(upwardbendingforn-typesemiconduc-+*Bulk∑U()(,)xEx|λ|2zzNiizztorsanddownwardbendingforp-typesemiconductors)andaBulki=1{(6)45bulkregionwherenobandbendingexists(Figure1).Thestudyofchargeseparation,transport,andtransferisbasedonwhereNSCRandNBulkarethenumberofintegrationpointsinthefindingsofWilson38andGaudyandHaussener.37theSCRandbulkregion,respectively.ThevaluesofRs,L,andConsideringthattheperformanceislimitedonlybyminorityNd/ainthisequationarechosenaccordingtodirectorindirect37characterization.Thesizeparametersofthephotoelectrodecarriers,theEQEatawavelengthλcanbeexpressedasandtheopticalconstantsofthematerialsaredeterminedfromRijjyzzapriorcharacterizationoftheelectrodestructureandasEQE()λζλ=+jj∫∫GxUGx(,)dxx*()(,)dxλzzcomparisonofthesimulatedopticalproperties(transmission,P0kVVSCRBulk{absorption,absorbance,etc.)withmeasurements.TheEQEof(2)aphotoelectrodeincludingopticalnanostructurescanthenbektcalculatedandcomparedtothebarephotoelectrode.ThiswillwhereP0istheincidentilluminationpower,R=skktr+bediscussedindetailinthesection“OpticalEnhancementaccountsforthesurfacerecombinationlosses,withktandkrCalculation”.beingtherateconstantsforthechargetransferandthesurfaceOurchargetransportmodelconsidersthatonlytherecombination,respectively.G(x,λ)isthepowerdensityoftheelectron/holepairsgeneratedintheSCRorclosetothegeneratedelectron−holepairsatpositionx.VSCRandVBulkareSCRwithrespecttotheminoritycarrierdiffusionlengththevolumeoftheSCRandthebulk,respectively.contributetothecalculatedEQE(Figure1).ThisaspectisaU*(x)istheprobabilitythataminoritycarriergeneratedinkeyfactortooptimizeopticalcontributionstothephoto-thebulkatpositionxreachestheSCR.Itsexpressionisderivedcatalyticperformancesandisnotconsideredwhenonlytheanalyticallyfromtheminoritycarrierconservationequationinoveralllightabsorptioninthesemiconductorregionisstudied,ref38andisgivenbyasinref39.7012https://doi.org/10.1021/acs.jpcc.0c11342J.Phys.Chem.C2021,125,7010−7021

3TheJournalofPhysicalChemistryCpubs.acs.org/JPCCArticleFigure2.Flowchartoftheprocedureforcomputingtheopticalenhancementbetweenahybridphotoelectrodeincludingopticalelementsandabarephotoelectrode.ThestepsinreddetermineRS,L,andNd/afromanexperimentalEQEcurvemeasuredonthebarephotoelectrode.Thesestepsdonotneedtobeperformediftheseparametersarealreadyknownfortheconsideredelectrode.14,48Scope.Majoritycarriertransportandtransferarenottakenelectrolyte,suchaswhenplasmonicnanoparticlesareused.intoaccount;therefore,thedescriptiongivenbythemodelisInthesecases,theEQEgivenbythemodelcanbecomparednotaccurateiftheseparametersarethelimitingperformancewithexperimentalmeasurementswherethechargetransferfactors.Minoritycarrierrecombinationsatthebackcontactofefficiencycanbeassumedtobe100%andreducedsurfacethephotoelectrode(e.g.,duetodefectstateattheFTO/lossesduetotheopticalelementsdonotplayarole.semiconductorinterface)arealsonotconsidered.Experimen-Depositinganadditionalcatalystonthesurfaceofthetally,theycanbedrasticallyreducedbydepositingablockingphotoelectrode(e.g.,Co-Pi)orusinganelectrolytethatlayerforminoritycarriersbetweenthesubstrateandthecontainsasacrificialsubstance(hole/electronscavengerfor4647semiconductor(suchasWO3orSnO2).Backcontactphotoanodes/photocathodes)canhelpachievingsucharecombinationsarealsonegligiblewhentheelectrodeisconfiguration.Inahole/electronscavenger,theassumptionilluminatedfromtheelectrolyteside(frontillumination),iftheof100%chargetransferefficiencyisonlyvalidathighapplied49,50minoritycarrierdiffusionlengthissmallerthanthesemi-potentialsformetaloxideelectrodes.Fittingthechargeconductorthickness.transferparameterRs(section“OpticalEnhancementCalcu-Itisassumedthattheadditionofopticalelementsmodifieslation”)canindicateiftheassumptionisvalidornot.TheonlythelightabsorptionprofileinthesemiconductorandhastechniqueofcombiningEQEmeasurementsinelectrolytesnoeffectonthechargeseparation,chargetransport,andwithandwithoutholescavengershasalreadybeenreportedfortransferefficiency.OpticalenhancementisdefinedastheexperimentallydiscriminatingthecatalyticandopticalimprovementofPECperformances(EQE,photocurrent)duecontributionscomingfromtheadditionofmetallicnano-13,24,51toopticaleffects.Anyphotocurrentor/andEQEenhancementparticles.However,modifiedchargeseparationanddescribedwithourmodelisanopticalenhancement.transportinthehybridstructurecannotbedifferentiatedTherefore,theoverallpredictedenhancementcanbedifferentfrompurelyopticalenhancement.fromtheexperimentallyobservedone.ReducedsurfacelossesWeassumedineq6that100%oftheabsorbedphotonscanbeexpectedwhentheaddedopticalelementshaveagenerateusefulchargecarriersforwateroxidation/reduction.surfacecatalyticeffect(e.g.,whentheyaremadeofpreciousHowever,ithasbeenrecentlyreportedforsomematerialsthat11,15metal)orareabletolocallyheatthesemiconductororthenotallopticaltransitionscontributingtotheabsorption7013https://doi.org/10.1021/acs.jpcc.0c11342J.Phys.Chem.C2021,125,7010−7021

4TheJournalofPhysicalChemistryCpubs.acs.org/JPCCArticle52−54spectrumgeneratemobilechargecarriers.Toaccountforwhichanopticalenhancementstrategyisused)areperformedthisphenomenon,eq6canbemultipliedwiththephoto-first,fromwhichthepowerdensityofthephotogeneratedgenerationyieldspectrumifitisknownforthematerialelectron/holepairsinthesemiconductorlayeriscalculated(eqconsidered.Theminoritycarriermobilityμ(expressionofthe1).AsinputforcalculationofEQE,theparametersVfb,Eg,andEinsteindiffusioncoefficientineq3)intheconsideredεrshouldbeprovided(TableS1)aswellasthesurfacesemiconductorisnotrequiredtobeknowniftheappliedrecombinationparametershouldbeprovidedaswellasthevoltageVaissuchthattheSCRpotentialislargerthan0.23surfacerecombinationparameterRS,theminoritycarrier37V.ThisisthecaseforallexamplesstudiedinthenextdiffusionlengthL,andthedonors/acceptorsdopingdensitysection;therefore,aconstantvalueofμwasused.TheSCRNd/a.Thesethreelastparameterscanbedeterminedbyfittingpotentialisassumedtobeunperturbedbytheincidentlight,eq6toanexperimentalEQEcurvemeasuredonthebareandauniformdonors/acceptorsconcentrationisassumedinphotoelectrodesuchthattheoptimalvaluesmaximizethethesemiconductor.Finally,themodeldoesnotaccountforthecoefficientR215,19,21plasmonichotelectroninjectionmechanismandcanbe2∑|−EQE()λλEQE(;RLN,,)|thereforecombinedwiththetheoreticalframeworksdeveloped2iexpiiNSd/a55R=−12forhotelectrongenerationforanalyzingplasmonicEQE∑i|−EQE()expλiEQEexp|enhancementanddiscriminatingbetweenhotelectron(9)injectionandnear-fieldeffects.OpticalModelingofMaterialsandGeometry.ThewhereEQEexp(λi)istheexperimentallymeasuredEQEatopticalmodelmustbecomparedtoopticalmeasurementswavelengthλi,EQENisgivenbyeq6andEQEexpistheaveragebeforeconsideringtheoptoelectronicpropertiesofthesystem.valueoftheexperimentalEQEfromthelowestmeasurementThisvalidationcanbeperformedinvariousways,dependingwavelengthλ0tothewavelengthcorrespondingtothebandontheopticalenhancementstrategychosen.Inthiswork,wegapofthesemiconductor.Ifoneorseveraloftheseparameterswillinvestigatetwotypeofstrategies:host−guestnano-arealreadyknown,thisprocedurecanbeperformedwiththestructuringofthesubstrateandadditionofnanoparticles.Theunknownparametersonly.ThevaluesofRS,L,andNd/aareparametersofthesimulatedgeometryandtheopticalassumedtobeidenticalforthebareandhybridphoto-constantsofthematerialsconsideredshouldbechosentoelectrodes.Forallsimulations,thevalueofholemobilityμandrealisticallydescribethefabricatedsample.Thisneedstobechargetransferrateconstantktwereassumedasinref37tobeinvestigatedthroughacarefulcharacterizationofthefabricated1cm2V−1s−1and10−2cms−1,respectively.TheEQEspectrastructureandcomparisonofthesimulatedopticalpropertiesforbareandhybridphotoelectrodesarecalculatedwitheq6(transmission,absorption,absorbance...)withexperimentalfromtheinputparametersandthevaluesof|E(x)|inthemeasurements.Thesimulatedgeometryshouldincludethesemiconductorobtainedwithelectromagneticsimulations.Theinterfacesthatareopticallynotnegligible(e.g.,semi-photocurrentenhancementbetweenthehybridandbareconductor/substrate).TheporosityofthesemiconductorsampleiscalculatedfromtheEQEspectralayercanbeconsideredopticallyusinganeffectivemediumapproximationforthepermittivityofthesemiconductor.56J∫EQE()AM1.5G()d2λλ·λh=Inthesection“Ti/Fe2O3FilmontheNanostructuredJb∫EQE()AM1.5G()d1λλ·λ(10)Substrate”,thedesignedgeometryisvalidatedbycomparingthemodelwiththemeasuredabsorptionspectrawhereAM1.5G(λ)isthesolarspectrum,EQE2(λ)istheEQEA()1λλ=−RT()−()λ(7)spectrumofthehybridsample,andEQE1(λ)istheEQEspectrumofthebaresample.PhotocurrentenhancementbeingwhereR(λ)andT(λ)arethereflectanceandtransmittancearesultofintegrationoftheentirespectrum,apropermodelspectra,respectively.validationcanbefirstsoughtthroughcomparisonwithEQEInthesection“BiVO4ElectrodewithAg@SiO2Nano-measurement.particles”,thenanoparticlesarenotconsideredperfectlyFinally,thegeometry,material,andrelativepositionofthemonodispersedandweusealinearcombinationofseveralopticalelementsandsemiconductorlayerinthehybridsystemnanoparticlesizesintheEQEcalculations.Themeasuredcanbeoptimizedthroughseveraliterations.distributionisusedtoselectthesizes,andweimposethatthemostoccurringvaluehasthehighestweightinthedistribution.■RESULTSANDDISCUSSIONThecoefficientsaredeterminedbyfittingthemeasuredInthefollowing,themodelisappliedtoexperimentallyabsorbancewithalinearcombinationofextinctionefficiencyfabricatedphotoelectrodespreviouslyreportedwhereopticalspectra,definedaseffectsfromnanostructureswereclaimedtobetheoriginofCCabs()λλ+sca()theobservedEQEenhancement.TheinvestigatedsystemsQext()λ=2involvetwodifferentmetaloxidematerials(hematiteandπR(8)bismuthvanadate),differentstrategiesforopticalenhancementwhereCabs(λ)andCsca(λ)aretheabsorptionandscattering(periodicnanostructuringandrandomlydistributedmetalliccrosssections,respectively,andπR2isthephysicalcrossnanoparticles),anddifferentopticalsimulationmethods(SIEsectionofthenanoparticle.andRCWA)inordertodemonstratethebroadapplicabilityofOpticalEnhancementCalculation.Asemi-analyticalthemethod.SimulateddataarecomparedtoreportedmethodforthecalculationofEQEhasbeenestablished.Wemeasurementstoconfirmthevalidityofthemodel.Wereportnowonaproceduretocomputetheopticalenhance-illustratethroughtheseexamplesthatthismodelallowsustomentbynanostructures(Figure2).Opticalsimulationsfortheclearlyandnonambiguouslyidentifytheoriginofopticalbarephotoelectrode(referencesamplewithnospecificopticalenhancement.Inparticular,thecontributionofplasmonenhancementstrategy)andthehybridphotoelectrode(forresonancesiscomparedtononresonantscattering.7014https://doi.org/10.1021/acs.jpcc.0c11342J.Phys.Chem.C2021,125,7010−7021

5TheJournalofPhysicalChemistryCpubs.acs.org/JPCCArticleFigure3.(a)SEMimageofafabricatedsamplewhereTi/Fe2O3wasdepositedonananostructuredFTOscaffold.Reprinted(adapted)withpermissionfromref57.Copyright2014AmericanChemicalSociety.(b)Calculatedabsorbanceofa100nmhematitelayerdepositedonFTO-coatedglass(plaincurve),comparedwithmeasurementsfromref57(dashedcurve).(c)Schemeoftheperiodicdesignusedforsimulationsofthenanostructuredsamplewitha100nmhematitefilm.(d)Absorptionspectracalculatedfortheflatandnanostructuredcases,comparedwithmeasurementsfromref57.Ti/Fe2O3FilmontheNanostructuredSubstrate.WeresonanceintheFTOlayer.Itsspectralpositionvarieswithconsiderfirstahost−gueststructurewhereathinfilmofTi-theangleofincidence(FigureS1a)anditdisappearswhendopedhematite(Ti/Fe2O3)isdepositedonananostructuredFTOisreplacedbyplatinum(FigureS1b).Theroughnessof57FTOscaffold.Qiuetal.demonstratedanincreasedEQEandthedepositedfilms,whichisnotconsideredinthemodeledphotocurrentforsuchananostructurecomparedtotheplanargeometry,couldexplainthatitisnotobservedinthemeasuredcase.Thescaffoldwasmadeofnanopillarsarrangedinaspectrum.periodicsquarepattern,andtheelectrodewasilluminatedInthenextstep,theparametersNd,L,andRsoftheTi/fromtheelectrolyteside(frontillumination).TheEQEandFe2O3filmwerededucedbyfittingthesimulatedEQEforthe57photocurrentweremeasuredbyQiuetal.in1MNaOHplanarconfigurationtotheexperimentallymeasuredcurveinaqueouselectrolytewithoutasacrificialholescavenger.the1MNaOHaqueouselectrolyte.ItwasrecentlyshownthatTherefore,ouranalysiswillhelptodiscriminatebetweennotallopticaltransitionsinhematiteareabletogenerateopticalandnonopticalenhancement.Weperformedtheusefulchargecarriersforwateroxidation.52,53ToaccountforopticalsimulationsofthesestructureswithRCWA.Thesizethat,eq6wasmultipliedbythewavelength-dependentparametersusedtodesignthesimulatedgeometrywerephotogenerationyieldofhematiteexperimentallymeasuredextractedfromtheSEMimagesshowninref57(devicewith53bySegevetal.(FigureS2).Thefittingprocedureforthe1000nmperiodshowninFigure3a).ThethicknessoftheTi/2planar(bare)configurationgaveR=0.97(eq9).ThevalueofFe2O3waschosentobe100nmbycalculatingtheabsorbance19−3L,Nd,andRsare4.1nm,2.16×10cm,and0.75,ofalayerdepositedonFTO-coatedglassandcomparingwithrespectively.Thediffusionlengthfoundiswithinthereportedthemeasurementsfromref57(Figure3b).Theoptical4,5constantsofhematiteweretakenfromref53,andtheopticaldataforα-Fe2O3.However,thedonordensityNdishigher61,62thanthepublishedvaluesforpurehematite,andthiscanconstantsofFTOandglassweretakenfromref58.The57beexplainedbythehighTi-doping(Ti/Feratioof3:35).simulatedgeometryisshowninFigure3c.TheopticalconstantsofAlO,Ti,andPtweretakenfromrefs,59,60,53SampleswithalargeTifractionwerereportedtohaveahigher2362respectively.Structureshavingperiodsof1000and1500nmdonorconcentrationthantheundopedmaterial.wereinvestigated.InagreementwiththeSEMimagesshownThesimulatedEQEforthenanostructured(hybrid)samplebyQiuetal.,57theheightoftheFTOpillarswassetto110%ofwith1000nmperiod(Figure4a)isinoverallgoodspectraltheperiodandtheirdiameterwassetto40%oftheperiod.andquantitativeagreementwiththemeasureddatafromrefThecalculatedabsorptionspectraoftheflatandnano-57.ThemodelpredictstheEQEtobeslightlyhigherthanthestructuredgeometrywith1000nmperiod(Figure3d)agreeexperimentaloneintherange360−430nmandabitlowerinreasonablywellwiththemeasurementsfromref57.Intheinterval450−530nm.Thismismatchcouldoriginatefromparticular,theopticalmodelshowscorrectlythatthethedeviationintheabsorptionspectrumfortheflatnanostructuredsamplehasalmost100%absorptionintheconfiguration(Figure3d)andalsofromthedifferencebetweenwholevisiblerange.Thepeakat580nminthesimulatedthephotogenerationyieldspectraofpurehematiteandTi/spectrumfortheflatconfigurationoriginatesfromathin-filmFe2O3.TheEQEspectrainref57weremeasuredfrom360nm7015https://doi.org/10.1021/acs.jpcc.0c11342J.Phys.Chem.C2021,125,7010−7021

6TheJournalofPhysicalChemistryCpubs.acs.org/JPCCArticleBiVO4ElectrodewithAg@SiO2Nanoparticles.Intheprevioussection,periodicnanostructuringhasbeenstudiedasanexample.Now,inordertoshowthebroadapplicabilityof24themethod,weconsiderplasmonicnanoparticles.Abdietal.havereportedthattheEQEofa∼100nmthickBiVO4photoelectrodecouldbeincreasedbyaddingAg@SiO2nanoparticlesatthesurfaceofthesemiconductor,intheconfigurationwheretheelectrodeisilluminatedfromthesubstrateside(backillumination).TheEQEenhancementratiobetweenthesampleswithandwithoutAg@SiO2Figure4.(a)SimulatedEQEofthestructurewith100nmhematitenanoparticleswasfoundtobemuchhigherinapurebufferdepositedonplanarandnanostructuredsubstrates,comparedwiththaninanelectrolytecontaininganadditionalholescavenger,57theexperimentalresultsobtainedbyQiuetal.ThesimulatedcurvewhichsuggeststhatthecontributionoftheAg@SiO2fortheplanarconfigurationrepresentsthebestfittothemeasurednanoparticlesisnotonlyoptical.Measurementswithandata.ThesimulatedEQEforthestructurewith1500nmperiodisadditionalholescavengerelectrolytewerethereforeusedforshowninFigureS3.(b)Photocurrentenhancementbetweenthecomparisonwithourmodelwhichstudiesopticalenhance-nanostructuredandflatsamples(calculatedusingeq10)comparedtotheexperimentalvaluesextractedfromphotocurrentmeasurementsinment.Theopticalpropertiesofthesestructureswereref57.calculatedwithSIEsimulations.Aunitcellofthesimulatedgeometryandsketchesofthefabricatedsamplesareshowninwhereastheabsorptionandabsorbancespectra(Figure3b,d)Figure5a−c.TheSnO2underlayerservesasaholeblocking47areshownonlyfrom400nm.layerandpreventsholerecombinationsatthebackcontact.Figure4bshowsthephotocurrentenhancementbetweentheElectrontransportisknownasalimitingfactorofperform-nanostructured(hybrid)andplanar(bare)samples.AveryancesinBiVO4,butthiswasspecificallyidentifiedforthickergoodagreementwithenhancementobtainedfromphoto-BiVO4filmsthaninthisexample(evidencedfrom200nmincurrentmeasurementwasobtainedforthesamplewith1000ref46).Inaddition,theelectrodeisilluminatedfromthebacknmperiod(2.3/2.0formeasurement/simulations),whereasaside,whichresultsinmostelectronsbeinggeneratedclosetoperfectagreementwasobtainedforthesamplewith1500nmthebackcontact.Thisjustifiestheapplicabilityofourmodelperiod.Thissuggeststhatthenanostructuredscaffolddoesnotwhichdoesnotconsidermajoritycarriertransportandhaveaneffectinimprovingthechargetransferefficiency,holerecombinationsattheback-contact.Thechosenperiodanddiffusionlength,orSCRsizebutcontributesonlythroughroughness(modeledinaperiodicway)werechosentomatchopticaleffects.Asaconclusion,ourmethodshowedcorrectlyrealisticallytheAFMdatashowninref24.thatthePECperformancesofthestructurewith1000nmTheexactBiVO4filmthicknessandthedimensionsoftheperiodishigherthantheonewith1500nmperiodandnanoparticleswerechosenbycomparingouropticalmodelto24providedaquantitativeagreementwithEQEandphotocurrentthemeasureddatabyAbdietal.Theabsorbanceofthebaremeasurementsfromref57.structure(withoutnanoparticles)wasfirstcalculated(FigureFigure5.(a)Schemeofthesimulatedunitcellforthehybridsample.(b,c)SchemeofthebareBiVO4sample(b)andthehybridsamplecontainingAg@SiO2nanoparticles(c),reproducedwithpermissionfromref24.Copyright2014RoyalSocietyofChemistry.(d)CalculatedabsorbanceofthebaresamplefordifferentBiVO4filmthicknessesandcomparisonwithmeasurementsfromref24(e)ExtinctionefficiencyspectraofAg@SiO2nanoparticlesinwaterwithashellthicknessof10nm.(f)ComparisonofabsorbancecalculatedasalinearcombinationofthethreespectraofFigure5e(plainredcurve)withthemeasuredabsorbancefromref24(dashedcurve).7016https://doi.org/10.1021/acs.jpcc.0c11342J.Phys.Chem.C2021,125,7010−7021

7TheJournalofPhysicalChemistryCpubs.acs.org/JPCCArticle245d).TheopticalconstantsofBiVO4weretakenfromref63,workofAbdietal.ThephotocurrentenhancementwasandtheopticalconstantsofSnO2,FTO,andglassweretakencalculatedwitheq10.Thefittingprocedureforthebarefromref58.Themeasuredabsorbancewaswellreproducedsamplewasperformedonlyintheinterval400−540nm.whena57nmBiVO4filmwassimulated,especiallyintheIndeedqualityofthefitwaspoorerwhenthewholerangerange380−450nmwhereBiVO4hasahighabsorption.This350−540nmwasconsidered(FigureS5).ItshouldbevalueofthethicknessisrealisticwithrespecttotheAFMmentionedthatexperimentalerrorsarehigherintheUVmeasurementsshowninref24.Thesizeofthesilverspectralrange,wheresolarlightandartificiallightsourcesusednanoparticleswasdeterminedbyassumingaconstantshellforEQEmeasurementsirradiatelessthaninthevisibleregion.thicknessof10nmandusingthemethoddescribedintheTherefore,performingthefittingprocedureintheintervalsection“OpticalModelingofMaterialsandGeometry”.The400−540nmhasasmallimpactonthecalculatedphoto-sizedistributionofthenanoparticlesreportedinref24wascurrent.Theentirerange350−540nmwasconsideredforused,withtheconstraintthatthemostoccurringsize(55nm)calculatingthephotocurrentenhancement,buttheEQEhasthehighestweightinthelinearcombination.Theopticalspectrausedisthebestfitintheinterval400−540nm.Aconstantsofsilverweretakenfromref64.Itwasfoundthattheweightedaveragebetweenthecurvesobtainedwith35,55,andcombinationof35,55,and65nmcoresizes(Figure5e)65nmcorenanoparticleswasperformedtocalculatetheEQEreproducesreasonablythemeasuredabsorbancefromref24ofthehybridsamples,usingthecoefficientsfoundinFigure5f(Figure5f).Thenarrowerpeakcouldbeduetothenonperfect(giveninFigureS4).Theaveragefillingfactoris31%,whichsphericalshapeofthenanoparticlesinreality.AcomparisonmatchesrealisticallywiththeSEMimagesofthefabricatedwiththesizedistributionmeasuredbyAbdietal.24isshownin24samplesshownintheworkofAbdietal.TheEQEcurvesforFigureS4.thesinglenanoparticlesizesareshowninFigureS6.TheparametersNd,L,andRsweredeterminedbyfittingtheFirst,itcanbeseenqualitativelythatthepositivecalculatedEQEforthebareBiVO4electrodetothecontributionofAg@SiO2nanoparticlestothePECperform-experimentalcurveintheholescavengerelectrolyte.Theancesiswellreproducedbythemodel.Thestructureincludingfittingprocedurewasperformedforthethreefilmthicknessesa57nmfilmthicknessgivesanoveralllowerEQEthanthatweretestedinFigure5d,andtheoptimizedparametersexperimentally,exceptintherange470−550nmwhichareshowninTable1.Itcanbeseenthatforallthreevaluesacontributeslesstothephotocurrent.However,thecalculatedphotocurrentenhancementissimilartotheexperimentalvalueTable1.DeterminedMaterialParameterforDifferentFilmcalculatedfromphotocurrentmeasurements(1.26/1.15forThicknessesmeasurements/simulations).ThereisanimportantdifferencebetweenthephotocurrentenhancementsderivedfromL[nm]N[cm−3]RR2DSmeasuredEQEspectra(1.39)andphotocurrent(1.26),45nmBiVO33.22.5×10180.980.964whichindicatesthatthedifferencebetweenmodeland57nmBiVO13.52.7×101810.954measurementsisintherangeofmeasurementuncertainties.80nmBiVO13.11.4×10180.980.914WhentheBiVO4filmthicknessisdecreasedto50nm,thesimulatedEQEforthehybridsamplematchesrelativelywellreasonablefittingqualitycanbeachieved(R2valuesfrom0.91theexperimentalobservations.Finally,boththesimulatedEQEto0.96).However,thevalueoftheoptimizedparametersandthephotocurrentenhancementarehigherthanthediffers.Asthe57nmBiVO4filmbestreproducesthemeasuredexperimentaldatawhena45nmfilmisconsidered.Ingeneral,absorbance,theoptimizedvalueofNd,L,andRscanbetrustedtheseresultsshowthatthepredictedenhancementcanbeonlyinthiscasetomatchthepropertiesofthefabricatedhigher,similar,orlowerthantheexperimentalobservationsBiVO4,showingtheimportanceofapriorvalidationofthewhenasmallvariationintheBiVO4thicknessisconsideredphotoelectrodeopticalproperties.(12nmdifferencebetweenthethinnestandthethickestThefittedEQEforthebaresample,simulatedEQEfortheconfiguration).ThiscouldpossiblybeduetoaslightlyhybridsampleandphotocurrentenhancementareshownindifferentBiVO4thicknessbetweenthehybridandbaresamplesFigure6andcomparedwithPECmeasurementsfromtheortosomethicknessvariationacrosssamplescomingfromtheFigure6.(a)BestEQEfitforthebaresample,fordifferentBiVO4filmthicknesses.(b)SimulatedEQEsforthehybridsample,comparedtothe24measureddataintheholescavengerelectrolytefromAbdietal.Theywerecalculatedasaweightedaverageofthecurvescorrespondingtonanoparticleswith35,55,and65nmcore,usingthesamecoefficientsasinFigure5f.(c)Photocurrentenhancementbetweenthehybridandbaresamples(calculatedusingeq10)fordifferentBiVO4filmthicknessesandcomparisonwiththeexperimentalvaluecalculatedfromthemeasuredphotocurrentintheholescavengerelectrolyte(dashedcurve)inref24.7017https://doi.org/10.1021/acs.jpcc.0c11342J.Phys.Chem.C2021,125,7010−7021

8TheJournalofPhysicalChemistryCpubs.acs.org/JPCCArticle65depositionmethod(spraypyrolysis).Asaconclusion,theplasmonresonanceofAg@SiO2nanoparticlesplacedattheresultsgivenbyourmodelagreequantitativelywithbothEQEinterfacebetweenwaterandBiVO4.andphotocurrentmeasurementswithinexperimentaluncer-Wenowanalyzetheoriginoftheopticalenhancement.Thetainties.Thisisaremarkableresultgiventhatweuseperiodicplasmonresonanceof55and65nmcorenanoparticlesisataboundaryconditionstodescribeasystemofrandomlylongerwavelengthcomparedtotheabsorptionmaximumofdistributednanoparticles.BiVO4,whereasthepeakfor35nmnanoparticlesmatches.Figure7ashowstheEQEenhancementspectrumfor50nmInterestingly,55and65nmnanoparticlesyieldahigherBiVO4thicknessresultingfromsimulationsandcomparisonenhancementinthehighabsorptionregionofBiVO4,whichletusthinkthatbothresonant(plasmonic)andnonresonantscatteringcontributetotheenhancement.Indeed,thefieldintensityintheBiVO4layerislowerinFigure7bthanin7c,d,asaresultoftheinteractionbetweenlightandnanoparticlesoff-resonance.Inordertostudythecontributionoftheresonantscatteringoriginatingfromplasmonicpropertieswithrespecttonon-resonantscattering,structuresincludinggoldandsilvernanoparticleswith65nmcoreand10nmSiO2shellwerecompared(Figure8a).TheEQEobtainedwithAu@SiO2nanoparticlesismuchlowercomparedtoAg@SiO2andalmostcoincideswiththeEQEofthebarestructure.Figure8bshowsthattheplasmonresonanceofAu@SiO2nanoparticlesisatalongerwavelengthcomparedtotheabsorptionmaximumofBiVO4butnosignificantEQEenhancementisobservedintheregion380−450nm(Figure8b),incontrastwithAg@SiO2.AsvisibleinFigure8c,thereisnotmuchinteractionbetweenlightandnanoparticles,resultinginafieldintensityinBiVO4comparablewiththebarestructure(Figure7b).Theseresultsenabletoconcludethattheplasmonicpropertiesofsilverhighlycontributetotheenhancementmechanism.Figure7.(a)EQEenhancementspectraofthehybridandbare■BiVO4sampleswith50nmfilmthicknesscorrespondingtosingleCONCLUSIONSnanoparticlesizesandtheirweightedaverage.(b−d)ElectricfieldWepresentedamethodforstudyingopticalenhancementintensitymapat427nmforthe(b)baresample,(c)hybridsamplefromnanostructuresinwater-splittingphotoelectrodesanditswith55nmsilvercorenanoparticles,and(d)hybridsamplewith65contributiontothephotocatalyticperformances.Itinvolvesnmsilvercorenanoparticles.Theelectricfieldintensitymapforthepreciseopticalmodeling,computationofthelightdistribution35nmcorenanoparticlesisshowninFigureS7.Thelightisnormallyinthephotoelectrode,andasimplifiedtreatmentofchargeincidentandpolarizedontheplaneofthecrosssection.carrierseparation,transport,andtransfer.Thisenablesaccuratedescriptionoftheopticaleffectswhilelimitingthewiththeexperimentalobservation.Agoodgeneralspectralcomputationalcost.Incombinationwithexperimentalagreementwiththemeasurementsisobserved,showingthatmeasurementsinanelectrolytecontainingsacrificialhole/thelowerEQEforthehybridsampleatshortwavelengthwithelectronscavengers,themodelwasdemonstratedtobearespecttotheexperimentalcurve(Figure6b)isaconsequencepowerfultoolfordiscriminatingbetweenopticalandnon-ofthesamephenomenonhappeningforthebaresamplebelowopticalenhancements.Themethodwasvalidatedonseveral415nm(Figure6a)whichhasbeendiscussedpreviously.Theexperimentallyfabricatedphotoelectrodes.Averygoodspectracorrespondingtosinglenanoparticlesizesshowqualitativeandquantitativeagreementbetweenthecalculatedresonantfeaturesat427,470,and490nmforthe35,55,andmeasuredopticalenhancementofthePECperformancesand65nmsilvercore,respectively.Thiscoincideswiththewasobtainedforbothaperiodicandarandomstructure.WeFigure8.(a)SimulatedEQEforabareBiVO4samplewith50nmfilmthicknessandhybridsamplesincludingeitherAg@SiO2orAu@SiO2with65nmcoreand10nmshell.(b)EQEenhancementspectrabetweenthehybridandbaresamples.(c)ElectricfieldintensitymapfortheBiVO4+Au@SiO2sampleat427nm.Thelightisnormallyincidentandpolarizedontheplaneofthecrosssection.7018https://doi.org/10.1021/acs.jpcc.0c11342J.Phys.Chem.C2021,125,7010−7021

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