開路電壓起源

Theoriginoftheopen-circuitvoltageinpolyfluorene-based

photovoltaicdevices聚芴材料光伏器件的開路電壓的起源Theinfluenceofdevicestructureontheopen-circuitvoltageofpolyfluorene-basedphotovoltaicdeviceshasbeeninvestigated.Bilayersofhole-andelectron-acceptingpolyfluoreneshavebeenfabricatedusinganaqueous‘‘float-ofT’laminationtechniqueandsubsequentlyincorporatedintoorganicphotovoltaicdeviceswitharangeofcathodesandanodes.Ascalingoftheopen-circuitvoltagewithelectrodeworkfunctiondifferencehasbeenobservedwithanadditionalintensitydependentcontributionfromtheactivelayerwithinthedevice.Thisadditionalcontributionisattributedtophotoinducedgenerationofcarriers,wherebyaccumulationofchargeatthepolymer-polymerheterojunctionresultsinadipoleacrosstheinterfaceandgivesrisetoadiffusioncurrentthatmustbecounterbalancedbyadriftcurrentatopencircuit.本文研究了器件結(jié)構(gòu)對(duì)聚芴光伏器件開路電壓的影響。我們利用含水剝離貼合技術(shù)制備了具有正負(fù)電極的有機(jī)光伏器件。同時(shí)還發(fā)現(xiàn)了開路電壓與電極功函數(shù)差和器件內(nèi)活性層有一定關(guān)系?；钚詫訉?duì)開路電壓有影響是因?yàn)榛钚詫邮盏焦庹蘸螽a(chǎn)生光生載流子，光生載流子在聚合物異質(zhì)結(jié)處積累產(chǎn)生偶極子，在開路狀態(tài)下，產(chǎn)生的擴(kuò)散電流被漂移電流抵消。INTRODUCTION1、引言Thereisincreasinginterestintheuseoforganicphotovoltaicdevicesastheyofferapotentiallycheapalternativetomoretraditionalphotovoltaicmaterialssuchassilicon.However,powerconversionefficienciesarenotyethighenoughfororganicdevicestobecommerciallyviable.Thepowerconversionefficiencyisdetermined,inpart,bytheshortcircuitcurrentandtheopen-circuitvoltageofthedevice.Overthelastfewyears,blendsandbilayersofelectronandholeacceptorshavebeenusedindevicesinsteadofsinglepolymersinordertoincreasetheshort-circuitcurrentbyimprovingchargeseparation.1-3Ithasbeendemonstratedthattheshort-circuitcurrentissensitivetothefilmmorphology,whichcanbecontrolledbyalteringtheevaporationrate,solventtype,ordepositionmethod.4Recentlyithasbeenshownthattheopen-circuitvoltageinorganicphotovoltaicdevicesisalsoaffectedbythemorphologyoftheactivelayer5andbyvariationsintheelectronacceptorstrength.6Consequently,thetraditionalassumptionthattheopen-circuitvoltageisthedifferencebetweentheworkfunctionsofthetwoelectrodesistoosimplistictodescribetheactualbehaviorobservedinmostorganicdevices.Themostefficientdevicesareusuallyfabricatedfromblendsofelectronandhole-acceptingpolymers.However,thesesystemsarecomplicatedtomodelandasimpleplanarheterojunctionstructureismucheasiertodescribe.Therefore,inthiswork,bilayersofelectron-andhole-acceptingpolymerswereusedastheactivelayersinphotovoltaicdevices,inconjunctionwitharangeofcathodes,inordertoexaminetheeffectoftheactivelayeronthevalueoftheopen-circuitvoltage.Theelectron-acceptingpolymerusedwaspoly~9,98-dioctylfluoreneco-benzothiadiazole!~F8BT!andthehole-acceptingpolymerwaspoly~9,98,dioctylfluorene-co-bis-N,N8-~4-butylphenyl!-bis-N,N8-phenyl-1,4-phenylenediamine!~PFB!~Fig.1!.Photoluminescencequenchingmeasurementshaveshownthatefficientphotoinducedchargetransferoccursbetweenthesetwopolymers,makingthemgoodorganicphotovoltaicmaterials.相對(duì)傳統(tǒng)的光伏材料，如：硅，有機(jī)光伏器件的成本更低的有點(diǎn)而受到了更多的關(guān)注。然而，對(duì)于商業(yè)應(yīng)用而言，有機(jī)光伏器件的效率還遠(yuǎn)遠(yuǎn)達(dá)不到要求。器件的短路電流和開路電壓部分決定著能量轉(zhuǎn)換效率。過(guò)去幾年里人們?cè)谟袡C(jī)光伏器件中用混合雙層的電子空穴手提替代單層聚合物以提高電荷分離效率，從而提高短路電流?，F(xiàn)在已經(jīng)證明了短路電流收薄膜形貌的影響很大，所以可以通過(guò)改變蒸發(fā)速率、溶液類型和沉淀方法控制薄膜形貌。最近的研究還發(fā)現(xiàn)有機(jī)光伏器件的開路電壓受到活性層的薄膜形貌和電子受體生長(zhǎng)的變化影響。相應(yīng)的，傳統(tǒng)的認(rèn)為開路電壓時(shí)兩個(gè)電極功函數(shù)之差的理論對(duì)于描述大多數(shù)有機(jī)器件的實(shí)際行為來(lái)說(shuō)太簡(jiǎn)單了。通常利用電子、空穴受體聚合物混合的方法制備器件效率最高。然而，混合異質(zhì)結(jié)需要復(fù)雜的模型描述，而平面異質(zhì)結(jié)卻非常容易描述，所以在本實(shí)驗(yàn)中，所用的器件為雙層結(jié)構(gòu)，并結(jié)合不同功函數(shù)的陰極以證明活性層對(duì)開路電壓是否有影響。實(shí)驗(yàn)中采用的電子受體材料是F8BT，空穴材料為PFB（圖1）。熒光猝滅測(cè)量表明這兩種聚合物之間有很高效的電荷轉(zhuǎn)移，這使得它們成為比較好的光伏材料。EXPERIMENTALMETHOD1、實(shí)驗(yàn)方法Polymersolutionswerepreparedbydissolvingthetwopolymersseparatelyiip-xyleneataconcentrationof15g/l.Polymerfilmswerepreparedbyspincoatingthepolymerfromsolutionontothesubstrateatroomtemperatureunderanitrogenatmosphere.Thehole-acceptingpolymer~PFB!Wasspincoatedontoanindium-tinoxide~ITO!substrateandtheelectron-acceptingpolymer~F8BT!wasspincoatedontoaglasssubstrate.Priortopolymerdeposition,thesubstrateswerecleanedinanultrasonicbath,initiallyinacetoneandsubsequentlyinpropan-2-ol,andwerethentreatedfor10mininanoxygenplasmaetcher.將兩種聚合物溶解在對(duì)二甲苯溶劑中，制成濃度為15g/L的溶液。在室溫、氮?dú)鈼l件下，利用旋涂法制備聚合物薄膜?？昭ㄊ荏w材料（PFB）旋涂在ITO襯底上，電子受體材料（F8BT）旋涂在玻璃襯底上。在淀積之前，襯底先后yoga超聲波清潔池、丙酮、異丙醇中清洗，最后在氧離子刻蝕機(jī)中處理10分鐘。Deviceswerefabricatedbyfloatingtheelectronacceptinglayerofftheglasssubstrateintodeionizedwaterandlaminatingitontothehole-acceptinglayerontheITOsubstrate.Thedeviceswerethenplacedinavacuumoven(1025mbarat115°C!for3htodriveoffexcesswaterandensuregoodcontactbetweenthepolymerlayers.Theyweresubsequentlyplacedovernightinanevaporatorbeforethermalevaporationofthecathode,atapressure,1026mbar.Gold,aluminum,chromium,copper,andcalciumwereusedascathodesintherangeofdevicesunderinvestigationhere.Theactiveareaofeachpixel,definedbytheoverlapofthecathodeandtheITO,was1mm2.ThedevicestructureisdepictedinFig.2.Deviceswerealsofabricatedonquartzsubstratesusingsemitransparentgoldanodesandcathodesinordertodeterminetheopen-circuitvoltageindeviceswiththesamematerialusedforbothelectrodes.在去離子水中，通過(guò)剝離玻璃基板上的電子受體層再層壓到ITO空穴受體層制備器件。之后把器件放入真空箱中(10-5mbar115°C)3小時(shí)，以蒸發(fā)掉多余的水分，確保聚合物層與層之間接觸良好。接下來(lái)蒸渡電極，在蒸渡電極之前需要把器件放入蒸發(fā)器中一個(gè)晚上的時(shí)間，蒸發(fā)器內(nèi)壓強(qiáng)要小于10-6mbar。為研究不同負(fù)極材料對(duì)器件的影響，我們分別蒸渡了金、鋁、銘、銅和鈣五種電極。每個(gè)器件的活性層是負(fù)極與ITO重疊的部分，面積為1mm2.器件結(jié)構(gòu)如圖2。我們也在石英襯底上制作了器件，利用半透明的金正極和負(fù)極以說(shuō)明兩電極用相同的材料是否會(huì)影響開路電壓。Thecurrent-voltage(I-V)characteristicsandquantumefficiencyactionspectraofallthedevicesweredeterminedunderavacuumof1025mbarusingaxenonarclampspectrallyresolvedbyamonochromator,withanintensityofap-proximately0.7mWcm22.Theerrorinthemeasuredopencircuitvoltagesisapproximately±0.05Vbutthedevice-todevicevariationgivesamorerealisticerrorandisaround±0.1V.Thedependenceofthephotocurrentonilluminationintensitywasinvestigatedusingthe458nmlinefromanargon-ionlaser,withaspotsizeof0.87mm-fullwidthathalf-maximum!.Neutraldensityfilterswereusedtovarytheaverageintensityinthepixelbetween1024and100mWcm22.Thetemperaturedependenceoftheopen-circuitvoltagewasinvestigatedusingacontinuous-flowopticalaccessheliumcryostat.所有器件的I—V特性曲線和量子效率都是在10-5mabr真空條件下，用配有單色儀、光強(qiáng)大約為0.7mWcm-2的氙弧燈測(cè)量的。測(cè)量的誤差大約為±0.05V，但是器件與器件之間更真實(shí)的誤差大約是土0.1V。我們使用波長(zhǎng)為458nm的氬離子激光，其光點(diǎn)大小為0.87毫米即半峰全寬，研究光強(qiáng)對(duì)光電流的影響。-??采用連續(xù)的光接入氦低溫恒溫器來(lái)研究溫度對(duì)開路電壓的影響。Polymerbilayersandsinglelayerswerealsodepositedonsiliconandquartzsubstratesforellipsometricmeasurements,whichwereperformedusingaJ.A.WoollamM-2000rotating-compensatorellipsometerwithawhite-lightsourceanddiodedetectorarrayoverawavelengthrange245900nm.Photoluminescence~PL!efficiencymeasurementswerecarriedoutusinganintegratingsphere8coupledtoanOrielInstaSpecIVspectrographusingtheUVlinesfromanargonionlaserastheexcitationsource.雙層聚合物和單層聚合物都淀積在硅襯底和石英襯底上，用橢偏儀測(cè)量其厚度，該橢偏儀使用的是JAWoollamM-2000與一個(gè)白色的光源和在一個(gè)波長(zhǎng)范圍245-900nm的二極管檢測(cè)器陣列的旋轉(zhuǎn)補(bǔ)償橢偏儀進(jìn)行工作的。熒光發(fā)光（PL）效率使用???RESULTS3、結(jié)果Beforemeasuringandanalyzingthephotovoltaicdevices,ellipsometrywasusedtoconfirmthestructureofthebilayers.Theopticalconstantsoftheindividualpolymerswerefirstdeterminedusingacombinationofreflectionandtransmissionellipsometry,asdescribedelsewhere.9Theseopticalconstantswerethenusedtogenerateanopticalmodelofthebilayerstructureassumingflatinterfacesandnointermixingbetweenthepolymers.Thismodelwasthencomparedtotheexperimentalellipsometricdataforabilayer,asshowninFig.3.Thefitofthemodeltotheexperimentaldatawasverygood,withameansquarederrorof2.3.Usingthisbilayermodel,thethicknessofthePFBlayerwasdeterminedas48nmandthatoftheF8BTlayeras99nm.Thegoodagreementofthedatawiththemodelindicatesthatthelayersdonotinterdiffusewhenheatedundervacuumandthattheinterfacebetweenthepolymerlayersremainssharp.Thelayerthicknessesdeterminedintheellipsometricexperimentsarethesameforalldevicestestedduringthisexperiment.在測(cè)試和分析光伏器件之前，需要用橢偏測(cè)量法確認(rèn)雙層器件的結(jié)構(gòu)。首先使用組合反射和投射橢偏儀確定各個(gè)聚合物材料的光學(xué)常數(shù)。之后利用這些光學(xué)常數(shù)生成生成雙層結(jié)構(gòu)的光學(xué)模型，我們認(rèn)為這個(gè)雙層結(jié)構(gòu)只是平面接觸并沒(méi)有聚合物之間的相互混合。再利用這個(gè)模型和橢偏測(cè)量的數(shù)據(jù)對(duì)比，如圖3所示，模型和實(shí)驗(yàn)數(shù)據(jù)吻合很好，均方差只有2.3。利用這個(gè)雙層模型，確定PFB層的厚度為48nm、F8BT的厚度為99nm。模型和實(shí)驗(yàn)數(shù)據(jù)吻合很好說(shuō)明器件在真空加熱是層與層之間沒(méi)有發(fā)生互擴(kuò)散，聚合物層與層的界面依然銳利。在這次實(shí)驗(yàn)中所有器件層的厚度都用橢偏測(cè)量法確認(rèn)了。Figure4showstheactionspectrumofatypicalbilayerdevice,withanaluminumcathode,comparedtothatofa50:50blenddeviceofsimilarthickness,spincoatedfromp-xylene.Theefficiencyofthebilayeriscomparabletothatoftheblenddevice,suggestingthatthelaminationprocedureproducedgoodcontactbetweenthelayers.Also,thebilayerdeviceefficiencieswerereproduciblebetweendifferentdevices,whichfurthersupportsthereliabilityofthelaminationtechnique.Thecomparablepeakefficienciesbetweenthebilayerandblenddevicesalsosuggestthatthetransportofchargestotheelectrodesisimportantindeterminingthedeviceefficiency.DuetothelargerinterfacialareaphotoluminescencequenchingismoresignificantinanF8BT:PFBblend-wherethePLefficiencyis;13%!thaninabilayerdevice-whichhasaPLefficiencyof;55%withexcitationthroughthePFBlayer!.Thephotovoltaicquantumefficiencyintheblenddevicesmust,therefore,belimitedbyinefficienttransportofchargestotheelectrodes,?leadingtorecombination,incontrasttothebilayerdevicewherebothelectronsandholescanmoreeasilybetransportedtoanappropriateelectrodewithoutrecombination.圖4是典型的雙層器件活性光譜，該雙層器件的負(fù)極是鋁。與之對(duì)應(yīng)的同樣厚度的混合異質(zhì)結(jié)（50:50）該混合異質(zhì)結(jié)是對(duì)二甲苯溶液中旋涂制作的。雙層器件的效率比混合器件效率高，說(shuō)明層壓過(guò)程中在層與層之間有良好的接觸，而且在不同的雙層器件效率都是可重復(fù)實(shí)驗(yàn)得來(lái)的，這更加支持了層壓技術(shù)具有良好的穩(wěn)定性。雙層器件和混合異質(zhì)結(jié)器件各自的最高效率同樣說(shuō)明電荷到電極的傳輸對(duì)器件效率有很大的影響。由于混合異質(zhì)結(jié)器件（光致發(fā)光效率為13%）界面面積比雙層器件（光致發(fā)光效率55%）的界面面積大，所以在F8BT:PFB混合異質(zhì)結(jié)中光致發(fā)光猝滅顯得尤為重要。因此，由于電荷到電極的傳輸效率低，光伏器件的量子效率一會(huì)會(huì)受到限制，最終導(dǎo)致空穴電子復(fù)合。而在雙層器件中電子和空穴不會(huì)復(fù)合，更易傳輸?shù)诫姌O。Figure5showstheIVcharacteristicsunderilluminationforITOuPFBuF8BTucathodedeviceswithvariouscathodes.Illuminationwasat459nmwithanintensityof0.7mWcm22andtheabsolutecurrenthasbeenplottedforclarity.TableIshowstheopen-circuitvoltagesmeasuredfromFig.5,comparedwiththedifferenceintheworkfunctions（Df）oftheelectrodes,whereITOistakentohaveworkfunctionof4.8Vandworkfunctionsofthecathodesaretakenfromtheliterature.10TableIshowsthat-withtheexceptionofcalcium!theopen-circuitvoltageincreaseslinearlywiththeworkfunctiondifference（asexpectedintheabsenceofahighdensityofsurfacedefectstates）,butthatthereisanadditionalconstant1Vdifferencecontributiontotheopen-circuitvoltagethatcannotbeaccountedforbythedifferenceinworkfunctions.Calciumgivesaloweropencircuitvoltagethanexpected,consistentwithitsworkfunctionbeingsmallerthantheelectronaffinityofF8BT,leadingtochargetransferattheinterface,whichpinstheelectrodeworkfunctionclosetotheenergyofthelowestunoccupiedmolecularorbitalinthebulkofthepolymer.圖5是在ITOIPFBIF8BT結(jié)構(gòu)上使用不同的負(fù)極材料得到的I—V特性曲線。圖中光波在459nm時(shí)的光強(qiáng)為0.7mWcm-2，為清楚起見(jiàn)也繪制了電流的絕對(duì)值。表1是從圖5中測(cè)量的開路電壓與不同電極功函數(shù)的對(duì)比，其中ITO的功函數(shù)為4.8V，其他電極材料的功函數(shù)是從文獻(xiàn)中查得的。從表1中可以看出（除了鈣）開路電壓隨著功函數(shù)差線性增加（????），但是存在另外的1v常數(shù)電壓差不能用功函數(shù)差解釋。當(dāng)鈣作為負(fù)電極是器件的開路電壓比預(yù)想的還低，這一現(xiàn)象符合它的功函數(shù)小于F8BT的電子結(jié)合能，使得界面處電荷發(fā)生轉(zhuǎn)移，并使電極的功函數(shù)釘扎在聚合物的LUMO能級(jí)附近。Figure6showstheopen-circuitvoltageoftheITOuPFBuF8BTuA1deviceasafunctionofincidentintensity.Thevoltageshowsalogarithmicincreasewithintensity,saturatingatintensitiesabove0.7mWcm22.Theshortcircuitcurrentvarieslinearlywithintensityoverthisrange.Asimilarlogarithmicdependenceofopen-circuitvoltageonintensitywasobservedinlaminatedbilayerorganicphotovoltaicdevicesbyGranstro"m.圖6顯示的是ITOIPFBIF8BTIAl器件的開路電壓隨著入射光光強(qiáng)變化的函數(shù)，電壓隨著光照指數(shù)增加，在光強(qiáng)為0.7mWcm-2時(shí)達(dá)到飽和，在這一范圍內(nèi)短路電流隨著光強(qiáng)線性增加。Figure7showstheIVcharacteristicsunderilluminationfordeviceswithgoldanodesandcathodes.ThedottedlineshowsdataforadevicewherethePFBisspincoatedontothegoldbottomelectrode,followedbylaminationoftheF8BTandthermalevaporationofagoldtopelectrode.,AuuPFBuF8BTuAu.Thedashedlineshowsadevicewherethepolymerlayersarereversed,withevaporationofthegoldtopelectrodeontothePFBlayer?i.e.,AuuF8BTuPFBuAu!.DefiningtheelectrodenexttotheF8BTasthecathode,bothdeviceshaveanopen-circuitvoltageof0.7V,despitehavingthesamematerialasanodeandcathode.圖7顯示的是用金做正極和負(fù)極器件在光照下的 I—V特性曲線。點(diǎn)線表示的是AuIPFBIF8BTIAu器件的I—V特性曲線，虛線是AuIF8BTIPFBIAu器件的I—V特性曲線。我們將緊鄰F8BT的電極作為負(fù)極，盡管用相同的材料作為正極和負(fù)極，但兩種器件的開路電壓都是0.7V。Althoughnotaslargeasthe1VofadditionalopencircuitvoltageseeninFig.5,thisresultprovidesstrongsupportforthepresenceofanadditionalopen-circuitvoltage,whichdoesnotarisefromadifferenceinelectrodeworkfunctions.Whilethedetailsoftheelectronicstructureattheinterfacemaychangedependingonwhetherthepolymerisdepositedongoldorviceversa,thefactthattheopen-circuitvoltageisindependentoftheorderofpolymerlayerdepositionindicatesthatanysuchinterfacialeffectsdonotdominatetheobservedopen-circuitvoltage.Thedifferencesintheshort-circuitcurrentofthedevicesinFig.7arearesultofthestrongerF8BTabsorptionat459nm.Thisreducestheamountoflightreachingtheinterfaceandconsequentlyfewerexcitonsaredissociated.雖然沒(méi)有圖5中1V那樣大的開路電壓，但是這個(gè)結(jié)果強(qiáng)有力的支持了額外開路電壓的存在這一觀點(diǎn)，而且這個(gè)電壓并不是由電極功函數(shù)差引起的。在聚合物上淀積金或者其他材料可能會(huì)界面的電子結(jié)構(gòu)細(xì)節(jié)，實(shí)際上，開路電壓的大小與聚合物薄膜淀積順序無(wú)關(guān)，也就是說(shuō)界面作用不會(huì)影響開路電壓。圖7中器件的短路電流差異是因?yàn)镕8BT在波長(zhǎng)為459nm處吸收更加強(qiáng)烈。這使得到達(dá)界面處的光減少，從而有更少的激子解離。DISCUSSION4、討論Wenowexaminethepossibleoriginoftheadditionalopen-circuitvoltage.Therehasbeenmuchdiscussionintheliteratureregardingtheeffectofthepolymer/electrodeinterfaceontheelectronicpropertiesofdevices.12-14Forsomesystems,ithasbeenshownthatthemodelofcommonvacuumlevels-Schottky-Mottmodel!attheinterfacebetweenthepolymerandthemetalisnotvalid,14duetothepresenceofaninterfacialdipole.Ininorganicsemiconductors,thisdipolecommonlyarisesduetothetrappingofcarriersatsurfacestates.However,conjugatedpolymerstypicallyhavefarfewerinterfacialdefectsites,andoftenexhibitbehaviorclosetotheSchottky-Mottmodel.Inthecaseofacommonlyusedpolyfluorene@poly?9,9-dioctylfluorene!,F8#,forexample,photoelectronspectroscopyhasshownthatthevacuumlevelsofthepolymerandthemetaldoalign.現(xiàn)在我們討論開路電壓可能的起源。在文獻(xiàn)中有諸多討論認(rèn)為聚合物/電極接觸層影響器件的電子學(xué)性質(zhì)。對(duì)于這些系統(tǒng)，由于界面偶極子的存在，在聚合物和金屬界面見(jiàn)形成真空能級(jí)的模型是毫無(wú)根據(jù)的。在無(wú)機(jī)半導(dǎo)體中，偶極子通常是由表面涂層載流子陷阱產(chǎn)生的。然而在共軛聚合物中通常很少有表面缺陷，顯示的特性十分接近肖特基一莫特模型。例如，受到廣泛應(yīng)用聚芴材料的光電子能譜表名該聚合物的真空能級(jí)和金屬電極的真空能級(jí)對(duì)齊。Wecannotruleoutsomecontributiontothemeasuredopen-circuitvoltageinourdevicesduetoground-statedipoleformationatthepolymer-metal?orindeedthepolymer-polymer!interface.However,theadditionalopen-circuitvoltageisstronglydependentonincidentintensity,andisindependentofthecathodeused.Takentogetherwiththeclearevidencefortheabsenceofinterfacialdipolesatthepolymer-metalinterfaceinarelatedpolyfluorene,theseresultsstronglyindicatethatground-statedipoleformationdoesnotdominatetheadditionalopen-circuitvoltage.Wethereforeseekalternativeexplanationsforthephotoinducedcontributiontotheopen-circuitvoltage.由于在聚合物-金屬（或者聚合物-聚合物）界面基態(tài)偶極子的存在，我們不能排除一些其他得對(duì)器件開路電壓有貢獻(xiàn)的因素。然而，額外的開路電壓強(qiáng)烈依賴于入射光強(qiáng)度，與所用的負(fù)電極材料無(wú)關(guān)。綜上所述，有很明顯的證據(jù)表明在聚芴相關(guān)材料聚合物-金屬界面存在界面偶極子，這些結(jié)果表明基態(tài)偶極子的形成不會(huì)產(chǎn)生額外的開路電壓。因此，我們探索其他隊(duì)開路電壓的解釋。Underillumination,chargesareseparatedacrossthepolymer-polymerinterfaceasshowninFig.8.Duetotheconcentrationgradient,carrierswilldiffuseawayfromtheinterface,leadingtoanetdiffusioncurrent.Theeffectofdiffusiononopen-circuitvoltagesinsingle-layerpolymerphotovoltaicdeviceshaspreviouslybeenstudiedbyMalliaraseta16Bydefinition,atopen-circuitvoltage,thenetcurrentiszero,meaningthatthedriftanddiffusioncurrentsmustcanceleverywhereinthedevice.Anelectricfieldmust,therefore,bepresentinthedevicetogenerateadriftcurrenttoopposethediffusioncurrent.Thisfieldcanbegeneratedbytheapplicationofanadditionalvoltageacrosstheentiredevice,asshowninFig.8,leadingtoanintensity-dependentopen-circuitvoltageasseenexperimentally.光照下，電荷在聚合物-聚合物界面處分離如圖8所示。由于濃度梯度存在，載流子在界面處擴(kuò)散，產(chǎn)生凈擴(kuò)散電流。Malliaras等研究了單層結(jié)聚合物光伏器件中擴(kuò)散對(duì)開路電壓的影響。根據(jù)定義，開路電壓時(shí)器件凈電流為零時(shí)的電壓，意味著在器件內(nèi)部各處的漂移電流和擴(kuò)散電流必須互相抵消。因此，一定存在一個(gè)電場(chǎng)使器件產(chǎn)生抵消擴(kuò)散電流的漂移電流?？梢酝ㄟ^(guò)在整個(gè)器件上加額外的電壓產(chǎn)生該電場(chǎng)。Wenowdevelopasimpleanalyticalmodelwhichreproducestheobservedbehavior.WeconsiderjusttheF8BTsideofthedevice,extendingfromc50attheheterojunctiontox5Latthecathode.Neglectingspace-chargeeffects,iftheadditionalopen-circuitvoltagedroppedacrosstheF8BTisV,thenthefieldinthislayerisV/L,andthenetcurrentdensityatopencircuitis現(xiàn)在我們建立一個(gè)簡(jiǎn)單的分析模型，這個(gè)模型可以產(chǎn)生實(shí)驗(yàn)中觀察到的行為效果。我們把F8BT一邊作為異質(zhì)結(jié)的x=0點(diǎn)，負(fù)極處作為x=L點(diǎn)。忽略空間電荷作用，如果在F8BT兩端有二外開路電壓V，那么這層的電場(chǎng)為V/L，開路時(shí)凈電流密度為V d程如氣*心態(tài)=旗 (0wheren,已，andDearetheelectronnumberdensity,mobility,anddiffusioncoefficient,respectively.其中，n、出、De分別表示電子密度、遷移率和擴(kuò)散常數(shù)。AssumingtheEinsteinrelationshipbetweenelectronmobilityanddiffusioncoefficient,thishasthesolution假設(shè)在電子遷移率和擴(kuò)散常數(shù)之間是愛(ài)因斯坦關(guān)系，則有下面的解/召/葛狀町=狀口)己建! ■ (2)I iHl-2jLiI*Thecarrierconcentrationsatthecathoden(L)andattheheterojunctionn(0)arerelatedby負(fù)電極處n(L)和異質(zhì)結(jié)n(0)的載流子濃度的關(guān)系InW(Cl)]—lnW0)]=黑. (3}卜心2Ifweconsiderintensitiessuchthatn(0)ismuchgreaterthanthethermalcarrierconcentrationattheheterojunction,thenwemayassumeapower-lawrelationshipbetweenn(0)andtheincidentintensity如果我們假設(shè)乃(0)比異質(zhì)結(jié)處熱載流子濃度大很多，就可以認(rèn)為*0)和入射光強(qiáng)度之間的關(guān)系為花= (4)(a=0.5forpurelybimolecularrecombinationattheinterface)thenwefindthat(對(duì)于界面處純粹的雙分子復(fù)合a=0.5)之后會(huì)得到=arlnZH-lnA;—(5)iHl-2Toreproducethelogarithmicbehaviorseenintheexperimentrequiresthatn(L)isindependentofintensity.Thisisreasonableifthecontactisnotfarfromthermalequilibrium,butmaybreakdownathighintensities,leadingtosaturationoftheopen-circuitvoltage,asseeninFig.6.Asimilarcontributiontothemeasuredopen-circuitvoltagewillarisefromthePFBlayer.Thesimplemodelis,therefore,sufficienttoexplaintheintensity-dependentadditionalopencircuitvoltage,whichisindependentofdevicethickness.WealsonotethatinthelinearregimeofFig.6,theopen-circuitvoltageincreasesby0.08Vperdecadeofincreaseinintensity,closetothevalueof0.06VperdecadepredictedabovewithT=300Kanda=0.5.為產(chǎn)生對(duì)數(shù)函數(shù)，需要使*乙)與強(qiáng)度無(wú)關(guān)。這樣做是合理的，因?yàn)榻佑|層還遠(yuǎn)沒(méi)有達(dá)到平衡狀態(tài)，但有可能在高強(qiáng)度處不符合，使得開路電壓達(dá)到飽和，如圖6所示。PFB層對(duì)開路電壓也有類似的作用。因此這個(gè)簡(jiǎn)單的模型足以解釋額外開路電壓隨光強(qiáng)度變化的原因，并且和器件厚度無(wú)關(guān)。我們也注意到圖6中的線性變化，光強(qiáng)