Introduction

Light harvesting devices fabricated using non-single-crystal films such as polymers,organic molecules, dye-sensitized structures, nanoparticles as well as perovskites offerthe potential for low cost and large area fabrication. All these systems lack long-rangeelectronic order and have a common feature, i.e., their electrical conduction isinferior to highly-crystalline inorganic semiconductors such as silicon. The relativelypoor electrical conduction arises because of their orders of magnitude lower electronand hole mobilities and the low density of intrinsic charge carriers. The lowphotocarrier mobility causes charge transport losses and limits the performance ofoptoelectronic devices and in particular those designed to harvest or detectphotons.

Charge transport losses are typically described by the average distance that aphotocarrier travels prior to its recombination event. The critical requirement forlossless charge transport is that the drift or diffusion distance (LD)must be longer than the active layer thickness (d). For inorganic crystallinesemiconductors this distance is classically defined by the product of the charge carriermobility and lifetime (μτ) regardless of whether the photocarrierdriving force is the electric field (drift) or concentration gradient (diffusion)1. In strongly non-Langevin materials such as silicon and other inorganiccrystalline semiconductors (where the recombination coefficient is typically >105 times lower compared to Langevin systems2), charges can pass each other at distances closer than Coulomb radius withoutrecombination during transport. The reason for this is that the carrier mean freecarrier path (the average distance between carrier collisions during random thermalmotion) of ∼ 100 nm is much larger than the Coulomb radius(the distance at which the thermal energy equals the Coulomb energy) of ~5 nm.3 This implies that the mutual Coulombic attractionbetween positive and negative charges does not significantly affect the traveltrajectory and the photocarrier lifetime represents the true nature of recombination.Therefore, the mobility-lifetime product can adequately describe the distance chargestravel prior to recombination in these crystalline non-Langevin systems.

In contrast, in disordered organic semiconductors (an archetypal Langevin-system) themean free path is defined by the carrier hopping distance (~ 1 nm), which issubstantially shorter than the Coulomb radius(∼ 20 nm)4. Hence, when the chargecarrier density is such that the average separation distance between charges iscomparable to the Coulomb radius, charge carriers have a high probability ofrecombination because positive and negative charges are not able to escape their mutualCoulomb attraction. The recombination dynamics is then defined by the Langevin rate. Thephotocarrier lifetime under these conditions is strongly dependent upon the physicalseparation of negative and positive charges, which is determined by the carrier density,distribution, and, for example, on the formation of space charge regions5,6. Therefore, a single carrier lifetime cannot adequately characterizethe entire device. In contrast the recombination coefficient is a material property,which is unaffected by the distribution of charge carriers. Futhermore, the photocarrierlifetime depends on its mobility7, which dictates the average velocitywith which charges of opposite signs move with respect to each other. Given this dualdependency and the arguments above, the mobility-lifetime product (and henceLD) is clearly unsuitable as a universal “figure ofmerit” for the transport physics of organic semiconductors which areLangevin-type, as most are4.

Despite these considerations, the mobility-lifetime product is widely used as anappropriate predictive metric by which to assess and explain the performance of organicsolar cell materials and architectures and indeed more broadly photon-harvesting ordetecting devices8,9,10,11,12,13. In this work, we address thefundamental processes determining the photoconductivity and charge transport losses inlow mobility disordered films of organic semiconductors. We demonstrate that theclassical mobility-lifetime approach is not a convenient parameter to describe thecharge transport in these light harvesting systems. We independently measure therelevant charge transport parameters in operational devices and directly relate thesebasic properties to the bimolecular recombination losses. The results show that thecritical carrier density that triggers the onset of the recombination losses isdetermined by the charge density on the device electrodes. Based upon this physics wepropose an alternative figure of merit allowing the minimization of charge transportlosses in undoped disordered systems, where charge trapping does not dictate thephotovoltaic performance. To this end, we employ intensity dependent PhotoCurrent (iPC)and Resistance dependent PhotoVoltage (RPV) measurements in two high efficiency organicsolar cell (OSC) systems – each with quite different transport physics.

Results

Photovoltaic performance of solar cells

The most efficient single junction organic solar cell architecture currentlyemployed is the so-called bulk heterojunction (BHJ). This architecture has anactive layer containing a blend of organic semiconductors with electron acceptorand electron donor characteristics. In our study we employed two high efficiencyblends namely:poly[(4,8-bis{2-ethylhexyloxy}benzo[1,2-b:4,5-b′]dithiophene-2,6-diyl)(3-fluoro-2-{[2-ethylhexyl]carbonyl}thieno[3,4-b]thiophenediyl)]:[6,6]-phenyl-C70-butyricacid methyl ester (PTB7:PC70BM)14 andpoly[N-9″-heptadecanyl-2,7-carbazole-alt-5,5-(4′,7′-di-2-thienyl-2′,1′,3′-benzothiadiazole)](PCDTBT):PC70BM15. The structures of the two differentpolymers are provided Figure 1. These systems havebeen extensively studied16,17,18,19,20 and are known to havequite different charge transport properties (PTB7:PC70BM being superior). Inthis work we varied the junction thickness as an experimental parameter so as toaccess a range of key charge transport properties (recombination and mobility)in a systematic manner and study their impact upon device performance.

Figure 1
figure 1

Average current density-voltage (JV) characteristics under standard AM1.5G illumination of organic solar cells fabricated from (a) PTB7:PC70BM blendswith 100 nm, 230 nm and 700 nm thick activelayers and (b) PCDTBT:PC70BM blends with 75 nm, 230 nm and850 nm thick junctions.

The photovoltaic performance of the PCDTBT:PC70BM blends is much moresusceptible to the film thickness of the active layer compared toPTB7:PC70BM.

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Figure 1 shows white light current density versus voltage(JV) plots obtained under standard AM 1.5G illumination for eachpolymer blend as a function of junction thickness. The plots are representativeof fabrication batches containing multiple devices (see Methods). ForPTB7:PC70BM solar cells shown in Figure 1 (a), theoptimal junction thickness is 100 nm and hence 230 nm and700 nm are essentially sub-optimal and this is borne out by theJV curves. Similarly, Figure 1 (b) showsrepresentative white light JV characteristics for the PCDTBT:PC70BMblend. In this case the optimal junction thickness is 75 nm– 230 nm and 850 nm being sub-optimal. Theperformance metrics including relevant statistics are summarized in Table 1. It has previously been demonstrated that the FillFactor (FF) and PCE fall off rapidly for junctions > 80 nmfor PCDTBT:PC70BM18 and we also observe the sametrend. This has been attributed to poor charge transport in thisblend, in particular low hole mobilities which leads to significantbimolecular recombination in thicker junctions under 1 sun operating conditions.The PTB7:PC70BM cells have considerably better chargetransport and the PCE is maintained past 100 nm – althoughit does fall off for thicker junctions. Loss of FF still limits the optimaljunction thickness to 100 nm–150 nm: increasingthe thickness to 230 nm delivers higher short circuit current but FFlosses lead to a reduced PCE of 5.1%. These observations are in-line withexpectations.

Table 1 Device performance parameters including standard errors of the studiedPTB7:PC70BM and PCDTBT:PC70BM devices
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Photocarrier recombination losses

To quantify these transport losses and relate the observed losses in thephotovoltaic performance in the non-optimal, thick active layer junctions to thelosses in charge transport, we employed two techniques: iPC and RPVmeasurements. The iPC method has been extensively used to assess bimolecularlosses in organic solar cells17,21,22,23,24,25 and reliesupon the accurate measurement of photocurrent as a function of the input lightintensity (typically from 1 to 100 mW cm−2).A linear fit to the photocurrent-intensity in a log-log plot is used (where theslope is often marked as α) to determine whether the deviceperformance is limited by bimolecular recombination or not. Deviation from slope1 shows the presence of significant bimolecular recombination. However, fittinga line to the photocurrent data over a narrow range of light intensities nearthis transition between the linear and the sub-linear regimes22,26,27 can result in an arbitrary slope and is prone to error.iPC measurements over a large range of light intensities are also crucial forcharacterizing organic photodiodes (OPDs) since the point of deviationdetermines the Linear Dynamic Range (LDR)–an important figure of meritin all photodetectors. Once again LDR measurements are often not sufficientlyaccurate to determine the deviation point28,29.

With these considerations in mind, we have extended the measurement range by manyorders of magnitude. Figure 2 shows extended range iPCresults for both polymer blends with photocurrent measured between ~ 3× 10−9 W and ~ 3 ×10−1 W of laser power (note, theilluminated device area is 0.2 cm2). The junctions inboth cases were ~ 230 nm thick and the iPC measurements on otherjunction thicknesses are provided in the SupplementaryInformation for completeness (see SupplementaryFig. 1). We observe that the photocurrent increaseslinearly at low light intensities until a critical current that we call thedeviation current is reached. Beyond the deviation current, the bimolecularrecombination rate becomes comparable with the extraction rate and causes thephotocurrent to deviate from linearity. In the linear regime the photocurrent isonly affected by first order losses (i.e., those with a rate proportional to thefirst power of the illumination power). The origin of the first order losses hasbeen attributed to a number of photophysical processes including incompleteabsorption and geminate recombination21,23. Note, that a linearscaling of the photocurrent with the laser power does not guarantee the absenceof photocarrier recombination in cases where there are a large amount oflong-lived trap states or strong doping17,30,31,32. It hasbeen, however, previously argued that first order photocarrier recombination (ortrap-assisted recombination) is not relevant in optimized and efficientOSCs32,33. In particular, dominant second orderrecombination dynamics have been observed in optimized polymer:PC70BMblends34,35. In this work we have also experimentallyconfirmed the absence of long-lived trap-induced recombination losses byrepetitive RPV shots in the optimized and the 230 nm thick junctions(Supplementary Note 1 and SupplementaryFig. 2), while dark-CELIV transients prove the absence ofdoping induced charges (Supplementary Fig. 3).Since first order recombination is not significant in the polymer-fullerenecombinations of this work we focus on the impact of the charge transportparameters on the transition from the linear to the nonlinear iPC regime, whichcorresponds to the onset of substantial bimolecular recombination losses with anon-linear recombination order.

Figure 2
figure 2

iPC results: the photocurrent measured as a function of the incident laserpower varied by orders of magnitude in PTB7:PC70BM blends and PCDTBT:PC70BMblends with junction thickness of∼ 230 nm.

The 1 sun equivalent laser power is marked by the dashed lines. Thebimolecular recombination losses appear at the highest laser powers when thephotocurrent becomes non-linear.

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In order to better visualize the onset of photocarrier (bimolecular)recombination, in Figure 3 (a) and (b) we have re-plotted the iPCdata as External Quantum Efficiency (EQE – the ratio of thephotocurrent with light power) versus input light power. This processcreates a non-logarithmic y-axis to visualize and compare more accurately thedeviation points for all the junction thicknesses in both systems. We have alsonormalized the x-and-y-axes respectively to 1 sun equivalent power (i.e., thelaser power at the short-circuit current) and the EQE in the constant regime to100%. Note, this normalization sets the absorption and generation efficiency ofthe EQE to 100%. Therefore losses in the normalized EQE directly show losses inthe transport (collection) efficiency. Figure 3 (a) showsthe PTB7:PC70BM data and one observes that there are minimal recombinationlosses for the 100 nm and 230 nm thick junction solarcells up to 1 sun equivalent power (<1% and ~ 6% loss, respectively).However, in the 700 nm junction device, significant recombinationlosses are observed (~ 38%). For the PCDTBT:PC70BM devices, shown in Figure 3 (b), again only minor losses were observed in thehighest efficiency, 75 nm thick junction cell. In contrast to thePTB7:PC70BM system, the 230 nm device displays considerable 1 sunrecombination losses (transport efficiency reduced by ~ 37%). As the activelayer is further increased to 850 nm, recombination decreases thetransport efficiency substantially by ~ 78%. The recombination losses for alldevices are summarized in Figure 3 (c). In both blendsystems, the recombination losses are observed to follow the same trend as thesolar cell performance metrics. It is worth noting that the trends in the twosystems are similar, but with the effect of the recombination losses in thePTB7:PC70BM blends being shifted to thicker junctions.

Figure 3
figure 3

External Quantum Efficiencies (EQEs) (re-plotted from representations such asin Figure 2) shown as a function of the incident laserpower for the different active layer thicknesses of (a) PTB7:PC70BM and (b)PCDTBT:PC70BM blends.

The EQEs were normalized to 100% and the laser power to the 1 sun equivalentpower to visualize the bimolecular recombination losses at the short-circuitconditions. This methodology allows one to quantify the photocarrierbimolecular recombination losses in actual solar cells underclose-to-operational conditions. Figure (c) shows the recombination lossesestimated from the Figures (a) and (b) and plotted as a function of theactive layer thickness.

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Origin of photocarrier bimolecular recombination losses

To further understand the losses in charge transport, we have measured the chargecarrier mobilities and recombination coefficients in the devices. It should benoted that it was essential for this work to compare the mobility values (ortransit times) with the recombination onset on the same devices. The well-knownspace charge limited current measurement technique was not applicable becausethe J ∼ U2 dependence of the Mott-Gurneylaw cannot be observed for the operational devices20 andmobilities obtained on pristine films are usually not the same as in blends oftwo organic semiconductors16. Therefore, we have used theRPV19,20 and High Intensity Resistance dependentPhotoVoltage (HI-RPV)20,36 techniques to determine the mobilityof both electrons and holes as well as the bimolecular recombination coefficientratio βL/β (where β isthe actual and βL the Langevin recombinationcoefficient) (Supplementary Fig. 4 to Supplementary Fig. 7). We found thicknessindependent dispersive carrier mobilities and bimolecular reduction factors:μelectron ~ 3 ×10−3 cm2V−1s−1,μhole ~ 3 ×10−4 cm2V−1s−1 andβL/β ~ 50 in PTB7:PC70BM devices.The mobility of holes is ~ 10 times lower and the bimolecularrecombination coefficient ratio is ~ 2 times lower in thePCDTBT:PC70BM devices, while a similar electron mobility was observed in bothblends. An interesting observation is that the measured charge carrier mobilityand βL/β are almost the same for allthe studied film thicknesses for each polymer:PC70BM blend (Supplementary Fig. 5 and SupplementaryFig. 7). This suggests that the well controlled devicepreparation conditions did not result in any significant change in filmstructure that may have affected the charge transport.

Figure 3 also illustrates that the substantial bimolecularrecombination losses appear at different photocarrier densities, which aredependent upon the junction thickness and blend system. Similarly, the spacecharge limited current (ISCLC) is determined by the density ofspace charge5. The ISCLC has been shown tofollow a square root dependence on the bimolecular recombination coefficientratio37(βL/β)1/2. It hasalso been previously demonstrated that the space charge limited photocurrent isproportional to the extraction rate of the slower charge carriers because theycreate a “bottleneck” for charge transport forming the spacecharge and causing the bimolecular recombination losses23,38.Therefore, the following expression can then be generalized:

(Eq. 1)where C is the device capacitance, U is the effective voltage(superposition of built-in and external) andttrslower is the transit time of slowercharge carrier species.

Using the measured slower carrier mobilities/transit times and recombinationcoefficients we can calculate the ISCLC for each device (seeMethods) and replot the previous EQEs (Figure 3) as afunction of the photocurrent normalized to the ISCLC for thePTB7:PC70BM and PCDTBT:PC70BM blends in Figure 4 (a)and (b), respectively. Note, that the calculatedISCLC values vary over many orders of magnitude mainlybecause of differences in the slower carrier transit times due to the differentjunction thicknesses.

Figure 4
figure 4

Normalized External Quantum Efficiencies (EQEs) shown as a function of themeasured photocurrent for the different active layer thicknesses of (a)PTB7:PC70BM blends and (b) PCDTBT:PC70BM blends.

The photocurrent is normalized to the space charge limited current(ISCLC), which is calculated from the measured chargetransport parameters using Equation 1. Whenthe actual measured photocurrent approaches the space charge limitedcurrent, substantial recombination losses manifest implying that theelectrode defined space charge density controls the critical drift distance(LD ∼ d, where d is the devicethickness). (c) Numerically simulated EQEs as a function of the photocurrentconfirm that the deviation is caused by the ISCLC, wherethe appearance of the first recombination losses can occur at a slightlylower photocurrent compared to ISCLC.

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The key observation from Figure 4 is that the bimolecularrecombination losses start when the photocurrent reaches approximately theISCLC value, regardless of the active layer thickness.This implies that the critical charge carrier density that causes significantbimolecular recombination (compared to the extraction rate) is approximatelyequal to the surface charge density stored on the electrodes (CU), whilethe recombination coefficient ratio allows this critical density to be larger.The results are also confirmed in photodetectors with the same devicearchitectures using applied external voltages to facilitate the charge transportand extraction. The bimolecular recombination losses are typically smaller athigher applied reverse biases, because the applied voltage increases the chargecarrier drift velocity and the value of CU (SupplementaryFigure 8 (a)). Nevertheless, even as the applied biasvoltage is varied, the onset of substantial losses continues to coincide withthe ISCLC (Supplementary Figure 8(b)). When a forward bias is applied (relevant to solar cells atoperational conditions) the recombination losses increase (Supplementary Fig. 9).

Numerical EQE simulations, shown in Figure 4 (c) for asystem with a mobility ratio of 100 and a recombination coefficient ratio of 20further confirm the validity of Equation 1, therole of the μs(βL/β)1/2product and the space charge current limit. Moreover, these simulations can beused to predict the onset of bimolecular recombination losses as a function ofexperimental conditions such as the impact of the mobility ratio, recombinationcoefficient, the series resistance and the light absorption profile (see Supplementary Note 2 and 3;Supplementary Fig. 10 to Supplementary Fig. 12).

Discussion

Space charge determined photocarrier drift distance

Drawing these experimental results together demonstrates that significantbimolecular recombination losses appear at very specific light intensities,junction thicknesses and applied voltages, depending upon the materials systemin question. The experimental results suggest, that when the photocurrentmatches the space charge limited current (i.e., when the photocarrier density isclose to the CU space charge defined by the electrodes in Langevin-typesystems), then the photocarrier drift distance becomes comparable to thejunction thickness (LD ∼ d) and substantialrecombination losses emerge. Referring back to the Introduction, in which wecompared the charge carrier drift distances in two classes of materials,non-Langevin and Langevin, we reiterate that in the latter the criticalphotocarrier lifetime and drift distance are dependent upon carrier density. Thedensity is defined by a number of material and device related parameters such asthe light intensity, optical cavity effects, quantum efficiency of chargegeneration, film thickness, the photocarrier mobility and others. This, inaddition to the observed space charge dependent drift distance, clarifies thatthe µτ product (and therefore the drift distanceitself) is not an independent intrinsic parameter that can be conveniently usedas a comparative figure of merit to understand the charge transport physics.Importantly, the µτ product can also not be used todetermine the critical active layer thickness to minimize the bimolecularrecombination losses. These concepts and results are visualized in Figure 5.

Figure 5
figure 5

Schematic drawing showing the nature of charge carrier transport innon-Langevin (a) and Langevin-type systems (b).

The photocarrier drift distance (LD) in non-Langevinsystems is adequately described by the mobility-lifetime product because inthese typically highly ordered systems the photocarrier mean free path ismuch larger that the Coulomb radius (rc). The photocarrierdrift distance in Langevin-type systems is determined by the physicalseparation between the charges and their mobility. The critical chargedensity that triggers significant recombination (compared to the extractionrate) is determined by the electrode charge density CU. Thissituation is relevant to disordered structures where the photocarrierhopping distance is much smaller that the Coulomb radius (localized chargetransport).

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Based upon these considerations we propose the product of the materialsparameters μs(βL/β)1/2 fromEquation 1 as a comparative transport figureof merit because it determines the decisive ISCLC. It isimportant to note, however, that this figure of merit alone is not sufficientfor describing the performance of the actual devices, because the recombinationlosses are governed by additional device related parameters, such as the filmthickness, dielectric constant (both of which define the device capacitance) andeffective voltage. Figure 4 shows that significantbimolecular recombination losses can be avoided only when theISCLC is greater than the actual photocurrent produced bythe solar cell (see SI Supplementary Fig. 13 forthe minimum μs(βL/β)1/2required to minimize the bimolecular recombination for a given active layerthickness and achievable photocurrent).

Finally, we note the influence of the transport and recombination dynamics in ourtwo studied systems: the observed differences in the junction thicknessdependent recombination losses are explained by the 10 times highervalue of the slower carrier mobility and the∼ 2 times higher bimolecular recombinationreduction factor in the PTB7 blends as compared to the PCDTBT blends. Thisallows the PTB7 devices to work efficiently with slightly thicker junctions(∼ 230 nm). Our results also demonstrate theperformance benefit due to the suppressed non-Langevin bimolecular recombinationrate in all our devices (~ 50 times in PTB7 blends and ~25 times in PCDTBT blends) (see SupplementaryFig. 14). Therefore, improving the carrier mobility is notthe only transport strategy to deliver higher overall PCEs. In summary,increasing the μs(βL/β)1/2product allows: (a) the device to operate efficiently at a higher maximum powerpoint Vmp (increasing the FF), because a lower effectivevoltage is sufficient to extract the carriers without significant recombinationlosses; (b) the short-circuit current density (JSC) to beincreased if the system is limited by bimolecular recombination at theshort-circuit condition; and (c) an increase of Vocvia an enhanced carrier concentration39,40. This meansthat thicker junctions can be used to improve the efficiency of light harvestingsystems.

Conclusions

We have clarified that the conventional figure of merit (theµτ product or the drift distance LD)is not appropriate for a comparative analysis of charge transport losses in organicsolar cells due to the photocarrier mobility and density dependent lifetime. It isargued that this is generally the case for a broad range of high performance lightharvesting systems made of disordered low mobility and undoped materials. We foundthat the electrode charge density marks the onset of significant bimolecularrecombination losses and therefore controls the critical photocarrier drift distance(LD ∼ d). Based upon this physics we propose anew figure of merit for material and device characterization – themobility-recombination-coefficient product μs(βL/β)1/2. Thisparameter allows to minimize photocarrier recombination losses and to maximize thephotovoltaic performance of organic solar cells and photodetectors. We verifythis analysis in our model systems and find that the PTB7:PC70BM blendsare superior compared to PCDTBT:PC70BM blends from a charge transport perspectivebecause of the higher hole mobility and stronger suppressed recombination. Our workestablishes a set of design rules to allow thicker junctions in organic solar cellswhilst maintaining a high fill factor and power conversion efficiency. This isadvantageous from a manufacturing perspective and offers an approach to improve thelight harvesting efficiency of photovoltaic and photodetecting devices fabricatedfrom low mobility materials.

Methods

Device preparation

The substrates (PEDOT:PSS/ITO/glass) were prepared as described in ref. 41 andthe active layer (junction) solution of PTB7 (purchased from 1-Material, = 97.5 kDa, PDI = 2.1) andPC70BM (American Dye Source, Inc., Canada) was fabricated by using a 1:1.5 blendratio by weight in chlorobenzene (CB) with 3% 1,8-diiodoctane (DIO) by volume.Solar cells with three different junction thicknesses were prepared by using atotal concentration of 31 mg/cm3 for the100 nm and 230 nm thick blends respectively, while aconcentration of 45 mg/cm3 was used to fabricate the700 nm thick blend. The solutions were spun cast at2200 rpm, 400 rpm and 600 rpm for120 s, respectively. The films were subsequently dried at70°C. The active layer solution of PCDTBT (SJPC, Canada, = 122 200 g/mol, PDI = 5.4) andPC70BM was prepared by using a 1:4 blend ratio by weight in 1,2-dichlorobenzene(DCB) following the procedure described ref. 42. Solar cells with three activelayer thicknesses, 75 nm, 230 nm and 850 nmwere fabricated by using a total concentration25 mg/cm3 for the 100 nm and230 nm thick blends respectively, while a concentration of40 mg/cm3 was used to fabricate the850 nm thick film. The solutions were spun cast at2000 rpm, 500 rpm and 500 rpm for90 s, respectively. The active layer thicknesses were measured with aDekTak 150 profilometer. All devices were completed by vacuum evaporation of1.2 nm of samarium followed by 75 nm of aluminum under a10−6 mbar vacuum. The device area was0.2 cm2 for JV, iPC and EQE measurements,and a 3.5mm2 for the RPV measurements, respectively. Note, wefound the RPV measurement results were independent of the area of the pixel. Alldevice fabrication took place within a glove box with <1 ppmO2 and H2O and JV and EQE measurements werealso performed inside a glove box. Subsequently the devices were encapsulatedfor the iPC measurements.

Current density-voltage characteristics

JV curves were obtained in a 2-wire source sense configuration and anillumination mask was used to prevent photocurrent collection from outside ofthe active area. The presented PCEs correspond to average values of6 pixels after several JV-measurements and represent theefficiencies of the devices directly before the iPC measurements were conducted.An Abet Class AAA solar simulator was used as the illumination source providing~ 100 mW cm−2 of AM1.5G light. The exactillumination intensity was used for efficiency calculations and the simulatorwas calibrated with a standards traceable NREL photodiode.

Light intensity dependent measurements

iPC measurements were performed with a 532 nm continuous wave laser(Ningbo Lasever Inc.) providing a power of 1 W. Optical filters(ThorLabs) were used to attenuate the laser power and the photocurrenttransients were recorded with an Agilent semiconductor device analyser (B1500A).Each measured data point corresponded to a steady state photocurrent measurementof the OSC at the respective incident laser power, which was simultaneouslymeasured with a Silicon photodetector to improve the accuracy of themeasurement. The error bars in Figure 3 (c) were estimatedfrom the spread of the EQE values at the 1 sun equivalent power and theuncertainty in the short-circuit current. The error analysis for the calculatedISCLC was conducted as follows: The circles in Figure 4 represent the calculated ISCLCfrom the actual measured charge transport parameters on duplicate devices. Inparticular, the mean slower carrier transit time (SupplementaryFigure 4) was used and the built-in voltage(UBI) approximated by Voc. Thevalues of the ISCLC are 78.3 mA, 4.4 mA,0.17 mA for the 100 nm, 230 nm and the700 nm thick PTB7:PC70BM junctions and 15.1 mA,0.34 mA, 0.01 mA for the 75 nm,230 nm and the 850 nm thick PCDTBT:PC70BM junctions. Forthe upper error bar a 10% thicker active layer was assumed, aUBI that is 0.05V higher than Voc,βL/β =βL/β + 5 and forttrslower the lower limit of the dispersiveslower carrier transit time range (SupplementaryFigure 4) was taken. For the lower error bar a 10% thinneractive layer was assumed, Voc as the built-in voltage,βL/β =βL/β −5 and the transittime of the slowest carriers in the device. Note, that the range of the errorbar is mainly determined by the measured dispersive slower carrier mobilityrange, while the upper error bar represents a rather unrealistic case for theISCLC, because that would imply that the fastest of theslower carriers determine the onset of the bimolecular recombination losses.

Mobility, recombination coefficient, trapping and dark-CELIVmeasurements

RPV transients for mobility, βL/β andcharge trapping measurements were recorded with an oscilloscope (LeCroyWaveRunner 6200A) with different external load resistances(RLoad), while a delay generator (Stanford ResearchSystems DG535) was used to trigger a function generator (Agilent 33250A) and apulsed Nd:Yag laser (Brio Quantel) with a pulse length of 10 ns. Anexcitation wavelength of 532 nm was used to generate the chargecarriers, while neutral optical density (OD) filters were used to attenuate the~ 50 mJ energy output. The RPV transients were measured under variousapplied biases. Low laser pulse intensities (∼ OD 7) were used for theRPV mobility measurements to avoid space charge effects19. Incontrast a high laser intensity (OD 3.5) was used to measure the bimolecularrecombination coefficient on the same films. CELIV transients were recorded inthe dark with the same experimental setup.

Numerical simulations

The numerical simulations implement the key processes that occur in organic solarcells, such as carrier drift, diffusion, trapping, non-geminate recombinationand space charge effects by taking into account the circuit resistance and theinfluence of the light absorption profile. Details of this model can be found inthe Supplementary Information Methods.