开路电压起源

Theoriginoftheopen-circuitvoltageinpolyfluorene-based

photovoltaicdevices聚芴材料光伏器件的开路电压的起源Theinfluenceofdevicestructureontheopen-circuitvoltageofpolyfluorene-basedphotovoltaicdeviceshasbeeninvestigated.Bilayersofhole-andelectron-acceptingpolyfluoreneshavebeenfabricatedusinganaqueous‘‘float-ofT’laminationtechniqueandsubsequentlyincorporatedintoorganicphotovoltaicdeviceswitharangeofcathodesandanodes.Ascalingoftheopen-circuitvoltagewithelectrodeworkfunctiondifferencehasbeenobservedwithanadditionalintensitydependentcontributionfromtheactivelayerwithinthedevice.Thisadditionalcontributionisattributedtophotoinducedgenerationofcarriers,wherebyaccumulationofchargeatthepolymer-polymerheterojunctionresultsinadipoleacrosstheinterfaceandgivesrisetoadiffusioncurrentthatmustbecounterbalancedbyadriftcurrentatopencircuit.本文研究了器件结构对聚芴光伏器件开路电压的影响。我们利用含水剥离贴合技术制备了具有正负电极的有机光伏器件。同时还发现了开路电压与电极功函数差和器件内活性层有一定关系。活性层对开路电压有影响是因为活性层收到光照后产生光生载流子，光生载流子在聚合物异质结处积累产生偶极子，在开路状态下，产生的扩散电流被漂移电流抵消。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.相对传统的光伏材料，如：硅，有机光伏器件的成本更低的有点而受到了更多的关注。然而，对于商业应用而言，有机光伏器件的效率还远远达不到要求。器件的短路电流和开路电压部分决定着能量转换效率。过去几年里人们在有机光伏器件中用混合双层的电子空穴手提替代单层聚合物以提高电荷分离效率，从而提高短路电流。现在已经证明了短路电流收薄膜形貌的影响很大，所以可以通过改变蒸发速率、溶液类型和沉淀方法控制薄膜形貌。最近的研究还发现有机光伏器件的开路电压受到活性层的薄膜形貌和电子受体生长的变化影响。相应的，传统的认为开路电压时两个电极功函数之差的理论对于描述大多数有机器件的实际行为来说太简单了。通常利用电子、空穴受体聚合物混合的方法制备器件效率最高。然而，混合异质结需要复杂的模型描述，而平面异质结却非常容易描述，所以在本实验中，所用的器件为双层结构，并结合不同功函数的阴极以证明活性层对开路电压是否有影响。实验中采用的电子受体材料是F8BT，空穴材料为PFB（图1）。荧光猝灭测量表明这两种聚合物之间有很高效的电荷转移，这使得它们成为比较好的光伏材料。EXPERIMENTALMETHOD1、实验方法Polymersolutionswerepreparedbydissolvingthetwopolymersseparatelyiip-xyleneataconcentrationof15g/l.Polymerfilmswerepreparedbyspincoatingthepolymerfromsolutionontothesubstrateatroomtemperatureunderanitrogenatmosphere.Thehole-acceptingpolymer~PFB!Wasspincoatedontoanindium-tinoxide~ITO!substrateandtheelectron-acceptingpolymer~F8BT!wasspincoatedontoaglasssubstrate.Priortopolymerdeposition,thesubstrateswerecleanedinanultrasonicbath,initiallyinacetoneandsubsequentlyinpropan-2-ol,andwerethentreatedfor10mininanoxygenplasmaetcher.将两种聚合物溶解在对二甲苯溶剂中，制成浓度为15g/L的溶液。在室温、氮气条件下，利用旋涂法制备聚合物薄膜。空穴受体材料（PFB）旋涂在ITO衬底上，电子受体材料（F8BT）旋涂在玻璃衬底上。在淀积之前，衬底先后yoga超声波清洁池、丙酮、异丙醇中清洗，最后在氧离子刻蚀机中处理10分钟。Deviceswerefabricatedbyfloatingtheelectronacceptinglayerofftheglasssubstrateintodeionizedwaterandlaminatingitontothehole-acceptinglayerontheITOsubstrate.Thedeviceswerethenplacedinavacuumoven(1025mbarat115°C!for3htodriveoffexcesswaterandensuregoodcontactbetweenthepolymerlayers.Theyweresubsequentlyplacedovernightinanevaporatorbeforethermalevaporationofthecathode,atapressure,1026mbar.Gold,aluminum,chromium,copper,andcalciumwereusedascathodesintherangeofdevicesunderinvestigationhere.Theactiveareaofeachpixel,definedbytheoverlapofthecathodeandtheITO,was1mm2.ThedevicestructureisdepictedinFig.2.Deviceswerealsofabricatedonquartzsubstratesusingsemitransparentgoldanodesandcathodesinordertodeterminetheopen-circuitvoltageindeviceswiththesamematerialusedforbothelectrodes.在去离子水中，通过剥离玻璃基板上的电子受体层再层压到ITO空穴受体层制备器件。之后把器件放入真空箱中(10-5mbar115°C)3小时，以蒸发掉多余的水分，确保聚合物层与层之间接触良好。接下来蒸渡电极，在蒸渡电极之前需要把器件放入蒸发器中一个晚上的时间，蒸发器内压强要小于10-6mbar。为研究不同负极材料对器件的影响，我们分别蒸渡了金、铝、铭、铜和钙五种电极。每个器件的活性层是负极与ITO重叠的部分，面积为1mm2.器件结构如图2。我们也在石英衬底上制作了器件，利用半透明的金正极和负极以说明两电极用相同的材料是否会影响开路电压。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特性曲线和量子效率都是在10-5mabr真空条件下，用配有单色仪、光强大约为0.7mWcm-2的氙弧灯测量的。测量的误差大约为±0.05V，但是器件与器件之间更真实的误差大约是土0.1V。我们使用波长为458nm的氩离子激光，其光点大小为0.87毫米即半峰全宽，研究光强对光电流的影响。-••采用连续的光接入氦低温恒温器来研究温度对开路电压的影响。Polymerbilayersandsinglelayerswerealsodepositedonsiliconandquartzsubstratesforellipsometricmeasurements,whichwereperformedusingaJ.A.WoollamM-2000rotating-compensatorellipsometerwithawhite-lightsourceanddiodedetectorarrayoverawavelengthrange245900nm.Photoluminescence~PL!efficiencymeasurementswerecarriedoutusinganintegratingsphere8coupledtoanOrielInstaSpecIVspectrographusingtheUVlinesfromanargonionlaserastheexcitationsource.双层聚合物和单层聚合物都淀积在硅衬底和石英衬底上，用椭偏仪测量其厚度，该椭偏仪使用的是JAWoollamM-2000与一个白色的光源和在一个波长范围245-900nm的二极管检测器阵列的旋转补偿椭偏仪进行工作的。荧光发光（PL）效率使用・・・RESULTS3、结果Beforemeasuringandanalyzingthephotovoltaicdevices,ellipsometrywasusedtoconfirmthestructureofthebilayers.Theopticalconstantsoftheindividualpolymerswerefirstdeterminedusingacombinationofreflectionandtransmissionellipsometry,asdescribedelsewhere.9Theseopticalconstantswerethenusedtogenerateanopticalmodelofthebilayerstructureassumingflatinterfacesandnointermixingbetweenthepolymers.Thismodelwasthencomparedtotheexperimentalellipsometricdataforabilayer,asshowninFig.3.Thefitofthemodeltotheexperimentaldatawasverygood,withameansquarederrorof2.3.Usingthisbilayermodel,thethicknessofthePFBlayerwasdeterminedas48nmandthatoftheF8BTlayeras99nm.Thegoodagreementofthedatawiththemodelindicatesthatthelayersdonotinterdiffusewhenheatedundervacuumandthattheinterfacebetweenthepolymerlayersremainssharp.Thelayerthicknessesdeterminedintheellipsometricexperimentsarethesameforalldevicestestedduringthisexperiment.在测试和分析光伏器件之前，需要用椭偏测量法确认双层器件的结构。首先使用组合反射和投射椭偏仪确定各个聚合物材料的光学常数。之后利用这些光学常数生成生成双层结构的光学模型，我们认为这个双层结构只是平面接触并没有聚合物之间的相互混合。再利用这个模型和椭偏测量的数据对比，如图3所示，模型和实验数据吻合很好，均方差只有2.3。利用这个双层模型，确定PFB层的厚度为48nm、F8BT的厚度为99nm。模型和实验数据吻合很好说明器件在真空加热是层与层之间没有发生互扩散，聚合物层与层的界面依然锐利。在这次实验中所有器件层的厚度都用椭偏测量法确认了。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.图4是典型的双层器件活性光谱，该双层器件的负极是铝。与之对应的同样厚度的混合异质结（50:50）该混合异质结是对二甲苯溶液中旋涂制作的。双层器件的效率比混合器件效率高，说明层压过程中在层与层之间有良好的接触，而且在不同的双层器件效率都是可重复实验得来的，这更加支持了层压技术具有良好的稳定性。双层器件和混合异质结器件各自的最高效率同样说明电荷到电极的传输对器件效率有很大的影响。由于混合异质结器件（光致发光效率为13%）界面面积比双层器件（光致发光效率55%）的界面面积大，所以在F8BT:PFB混合异质结中光致发光猝灭显得尤为重要。因此，由于电荷到电极的传输效率低，光伏器件的量子效率一会会受到限制，最终导致空穴电子复合。而在双层器件中电子和空穴不会复合，更易传输到电极。Figure5showstheIVcharacteristicsunderilluminationforITOuPFBuF8BTucathodedeviceswithvariouscathodes.Illuminationwasat459nmwithanintensityof0.7mWcm22andtheabsolutecurrenthasbeenplottedforclarity.TableIshowstheopen-circuitvoltagesmeasuredfromFig.5,comparedwiththedifferenceintheworkfunctions（Df）oftheelectrodes,whereITOistakentohaveworkfunctionof4.8Vandworkfunctionsofthecathodesaretakenfromtheliterature.10TableIshowsthat-withtheexceptionofcalcium!theopen-circuitvoltageincreaseslinearlywiththeworkfunctiondifference（asexpectedintheabsenceofahighdensityofsurfacedefectstates）,butthatthereisanadditionalconstant1Vdifferencecontributiontotheopen-circuitvoltagethatcannotbeaccountedforbythedifferenceinworkfunctions.Calciumgivesaloweropencircuitvoltagethanexpected,consistentwithitsworkfunctionbeingsmallerthantheelectronaffinityofF8BT,leadingtochargetransferattheinterface,whichpinstheelectrodeworkfunctionclosetotheenergyofthelowestunoccupiedmolecularorbitalinthebulkofthepolymer.图5是在ITOIPFBIF8BT结构上使用不同的负极材料得到的I—V特性曲线。图中光波在459nm时的光强为0.7mWcm-2，为清楚起见也绘制了电流的绝对值。表1是从图5中测量的开路电压与不同电极功函数的对比，其中ITO的功函数为4.8V，其他电极材料的功函数是从文献中查得的。从表1中可以看出（除了钙）开路电压随着功函数差线性增加（・・・・），但是存在另外的1v常数电压差不能用功函数差解释。当钙作为负电极是器件的开路电压比预想的还低，这一现象符合它的功函数小于F8BT的电子结合能，使得界面处电荷发生转移，并使电极的功函数钉扎在聚合物的LUMO能级附近。Figure6showstheopen-circuitvoltageoftheITOuPFBuF8BTuA1deviceasafunctionofincidentintensity.Thevoltageshowsalogarithmicincreasewithintensity,saturatingatintensitiesabove0.7mWcm22.Theshortcircuitcurrentvarieslinearlywithintensityoverthisrange.Asimilarlogarithmicdependenceofopen-circuitvoltageonintensitywasobservedinlaminatedbilayerorganicphotovoltaicdevicesbyGranstro"m.图6显示的是ITOIPFBIF8BTIAl器件的开路电压随着入射光光强变化的函数，电压随着光照指数增加，在光强为0.7mWcm-2时达到饱和，在这一范围内短路电流随着光强线性增加。Figure7showstheIVcharacteristicsunderilluminationfordeviceswithgoldanodesandcathodes.ThedottedlineshowsdataforadevicewherethePFBisspincoatedontothegoldbottomelectrode,followedbylaminationoftheF8BTandthermalevaporationofagoldtopelectrode.,AuuPFBuF8BTuAu.Thedashedlineshowsadevicewherethepolymerlayersarereversed,withevaporationofthegoldtopelectrodeontothePFBlayer〜i.e.,AuuF8BTuPFBuAu!.DefiningtheelectrodenexttotheF8BTasthecathode,bothdeviceshaveanopen-circuitvoltageof0.7V,despitehavingthesamematerialasanodeandcathode.图7显示的是用金做正极和负极器件在光照下的 I—V特性曲线。点线表示的是AuIPFBIF8BTIAu器件的I—V特性曲线，虚线是AuIF8BTIPFBIAu器件的I—V特性曲线。我们将紧邻F8BT的电极作为负极，尽管用相同的材料作为正极和负极，但两种器件的开路电压都是0.7V。Althoughnotaslargeasthe1VofadditionalopencircuitvoltageseeninFig.5,thisresultprovidesstrongsupportforthepresenceofanadditionalopen-circuitvoltage,whichdoesnotarisefromadifferenceinelectrodeworkfunctions.Whilethedetailsoftheelectronicstructureattheinterfacemaychangedependingonwhetherthepolymerisdepositedongoldorviceversa,thefactthattheopen-circuitvoltageisindependentoftheorderofpolymerlayerdepositionindicatesthatanysuchinterfacialeffectsdonotdominatetheobservedopen-circuitvoltage.Thedifferencesintheshort-circuitcurrentofthedevicesinFig.7arearesultofthestrongerF8BTabsorptionat459nm.Thisreducestheamountoflightreachingtheinterfaceandconsequentlyfewerexcitonsaredissociated.虽然没有图5中1V那样大的开路电压，但是这个结果强有力的支持了额外开路电压的存在这一观点，而且这个电压并不是由电极功函数差引起的。在聚合物上淀积金或者其他材料可能会界面的电子结构细节，实际上，开路电压的大小与聚合物薄膜淀积顺序无关，也就是说界面作用不会影响开路电压。图7中器件的短路电流差异是因为F8BT在波长为459nm处吸收更加强烈。这使得到达界面处的光减少，从而有更少的激子解离。DISCUSSION4、讨论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.现在我们讨论开路电压可能的起源。在文献中有诸多讨论认为聚合物/电极接触层影响器件的电子学性质。对于这些系统，由于界面偶极子的存在，在聚合物和金属界面见形成真空能级的模型是毫无根据的。在无机半导体中，偶极子通常是由表面涂层载流子陷阱产生的。然而在共轭聚合物中通常很少有表面缺陷，显示的特性十分接近肖特基一莫特模型。例如，受到广泛应用聚芴材料的光电子能谱表名该聚合物的真空能级和金属电极的真空能级对齐。Wecannotruleoutsomecontributiontothemeasuredopen-circuitvoltageinourdevicesduetoground-statedipoleformationatthepolymer-metal〜orindeedthepolymer-polymer!interface.However,theadditionalopen-circuitvoltageisstronglydependentonincidentintensity,andisindependentofthecathodeused.Takentogetherwiththeclearevidencefortheabsenceofinterfacialdipolesatthepolymer-metalinterfaceinarelatedpolyfluorene,theseresultsstronglyindicatethatground-statedipoleformationdoesnotdominatetheadditionalopen-circuitvoltage.Wethereforeseekalternativeexplanationsforthephotoinducedcontributiontotheopen-circuitvoltage.由于在聚合物-金属（或者聚合物-聚合物）界面基态偶极子的存在，我们不能排除一些其他得对器件开路电压有贡献的因素。然而，额外的开路电压强烈依赖于入射光强度，与所用的负电极材料无关。综上所述，有很明显的证据表明在聚芴相关材料聚合物-金属界面存在界面偶极子，这些结果表明基态偶极子的形成不会产生额外的开路电压。因此，我们探索其他队开路电压的解释。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，电荷在聚合物-聚合物界面处分离如图8所示。由于浓度梯度存在，载流子在界面处扩散，产生净扩散电流。Malliaras等研究了单层结聚合物光伏器件中扩散对开路电压的影响。根据定义，开路电压时器件净电流为零时的电压，意味着在器件内部各处的漂移电流和扩散电流必须互相抵消。因此，一定存在一个电场使器件产生抵消扩散电流的漂移电流。可以通过在整个器件上加额外的电压产生该电场。Wenowdevelopasimpleanalyticalmodelwhichreproducestheobservedbehavior.WeconsiderjusttheF8BTsideofthedevice,extendingfromc50attheheterojunctiontox5Latthecathode.Neglectingspace-chargeeffects,iftheadditionalopen-circuitvoltagedroppedacrosstheF8BTisV,thenthefieldinthislayerisV/L,andthenetcurrentdensityatopencircuitis现在我们建立一个简单的分析模型，这个模型可以产生实验中观察到的行为效果。我们把F8BT一边作为异质结的x=0点，负极处作为x=L点。忽略空间电荷作用，如果在F8BT两端有二外开路电压V，那么这层的电场为V/L，开路时净电流密度为V d程如气*心态=旗 (0wheren,已，andDearetheelectronnumberdensity,mobility,anddiffusioncoefficient,respectively.其中，n、出、De分别表示电子密度、迁移率和扩散常数。AssumingtheEinsteinrelationshipbetweenelectronmobilityanddiffusioncoefficient,thishasthesolution假设在电子迁移率和扩散常数之间是爱因斯坦关系，则有下面的解/召/葛状町=状口)己建! ■ (2)I iHl-2jLiI*Thecarrierconcentrationsatthecathoden(L)andattheheterojunctionn(0)arerelatedby负电极处n(L)和异质结n(0)的载流子浓度的关系InW(Cl)]—lnW0)]=黑. (3}卜心2Ifweconsiderintensitiessuchthatn(0)ismuchgreaterthanthethermalcarrierconcentrationattheheterojunction,thenwemayassumeapower-lawrelationshipbetweenn(0)andtheincidentintensity如果我们假设乃(0)比异质结处热载流子浓度大很多，就可以认为*0)和入射光强度之间的关系为花= (4)(a=0.5forpurelybimolecularrecombinationattheinterface)thenwefindthat(对于界面处纯粹的双分子复合a=0.5)之后会得到=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.为产生对数函数，需要使*乙)与强度无关。这样做是合理的，因为接触层还远没有达到平衡状态，但有可能在高强度处不符合，使得开路电压达到饱和，如图6所示。PFB层对开路电压也有类似的作用。因此这个简单的模型足以解释额外开路电压随光强度变化的原因，并且和器件厚度无关。我们也注意到图6中的线性变化，光强