Interface Optimization via Fullerene Blends Enables Open-Circuit Voltages of 1.35 V in CH3NH3Pb(I0.8Br0.2)3 Solar Cells

Non-radiative recombination processes are the biggest hindrance to approaching the radiative limit of the open-circuit voltage for wide-band gap perovskite solar cells. In addition, to high bulk quality, good interfaces and good energy level alignment for majority carriers at charge transport layer-absorber interfaces are crucial to minimize non-radiative recombination pathways. By tuning the lowest-unoccupied molecular-orbital of electron transport layers via the use of different fullerenes and fullerene blends, we demonstrate open-circuit voltages exceeding 1.35 V in CH3NH3Pb(I0.8Br0.2)3 device. Further optimization of mobility in binary fullerenes electron transport layer can boost the power conversion efficiency as high as 18.6%. We note in particular that the Voc-fill factor product is>1.085 V, which is the highest value reported for halide perovskites with this band gap.


Introduction
One of the main reasons, why halide perovskite solar cells have attracted so much interest over the past years, is their ability to generate high open-circuit voltages relative to their respective band gaps. [1,2] Using simple solution-based processing, open-circuit voltages within ~ 60 mV of the radiative limit have been experimentally realized in solar cells with efficiencies exceeding 20%. [3][4][5][6][7] Approaching the radiative limit that closely requires non-radiative recombination processes to be very slow compared to most other semiconductors. This requirement of slow recombination must be valid in the bulk of the material [8] but also at grain boundaries and at interfaces to charge-transport layers. The fact that recombination can be extremely slow even when charge-transport layers are attached to the absorber layer [4,[9][10][11][12] is most remarkable and allows combining high open-circuit voltages and thereby high luminescence quantum efficiencies with good fill factors and efficient charge extraction. [13] As shown in Figure 1a, high open-circuit voltages relative to the band gap have been shown in halide perovskite solar cells so far mainly for the range of band gaps of 1.5 eV to 1.65 eV. For wider band gaps, approaching the radiative limit has so far been less successful due to increased recombination losses. [14,15] This is unfortunate, because in particular the band gaps around 1.7 eV to 1.8 eV are highly relevant for making efficient tandem cells based on low band gap absorbers such as Si, [16][17][18][19] Cu(In,Ga)Se2 [20,21] or Sn-based low band gap perovskites. [22,23] One reason for the increased recombination losses for widerband gap absorbers is halide segregation that leads to stability problems for perovskites containing higher concentrations of Br than about 20%. [15,[24][25][26][27] Another obvious but less discussed challenge is the choice of electron and hole transport materials that have to be adapted to the energy levels of the absorber material. [12,15,28] Achieving high open-circuit voltages in perovskite solar cells not only requires well passivated surfaces but also the right choice of charge transfer layer (CTL) for a good energy level alignment. [12] In inverted (anode-illuminated) perovskite solar cells, fullerenes are nearly always used as electron transport layers and high efficiency solar cells with fullerene electron transport based on C60 and [6,6]phenyl-C61-butyric acid methyl ester (PCBM) layers have been demonstrated for a range of band gaps. [4,[29][30][31][32][33] However, fullerenes have also restrictions in so far that their energy levels cannot easily be tuned over a wide range. The electron affinity of fullerenes changes with the number and type of adducts attached to the C60 cage with multiadducts leading to lower electron affinities relative to monoadducts such as PCBM or even C60. [34][35][36] For instance, for the classical MAPbI3 composition, PCBM provided a good band alignment, while C60 (higher electron affinity) leads to additional recombination losses. [37] For higher band gap perovskites with lower perovskite electron affinities, the lowest-unoccupied molecular-orbital (LUMO) of PCBM becomes too low (electron affinity too high) to achieve a perfect band alignment. [38] However, alternatives such as the indene-C60 bisadduct (ICBA) with higher-lying LUMO [28,38,39] suffers from increased energetic disorder due to the high number of isomers (i.e. there are many different ways of attaching two indene groups to one C60 cage). This increased disorder leads to a lower mobility [39,40] and has previously led to a generally worse electronic properties in organic polymer:fullerene solar cells. [41][42][43][44] Therefore, it is currently unclear how to design the electron transport material for perovskite absorbers with a wider range of band gaps.   represent the external luminescence quantum efficiency Qe,lum that the solar cells need to have to fulfil the relation [45] ( oc rad − oc ) = Δ oc = − ln( e,lum ) with oc rad the radiative open-circuit voltage, q the elementary charge, k the Boltzmann constant and T the cell temperature. The band gaps were all calculated by the inflection point of the external (photovoltaic) quantum efficiency to enable better comparison between the data points. [46] The most notable achievements among wide-band gap perovskites are cells based on compositions such as Cs0.17FA0.83Pb(I0.6Br0.4)3 [15] , Cs0.05(FAxMAy)0.95Pb(I0.76Br0.24)3 [47] , Cs0.17FA0.83Pb(I0.6Br0.4)3 [48] and CsPb(I0.75Br0.25)3 [49] . The band gaps vary from 1.69 eV [47] to 1.86 eV [49] with efficiencies up to 20.1%, at a band gap of 1.69 eV and a Voc= 1.21 V [47] . The Voc FF product, a proxy for the voltage at the maximum power point, plotted as a function of Eg for the same devices is shown in Figure 1b. The device by Zhang [49] shows a high Voc and high Voc FF product, but a large voltage loss Δ oc . By applying eq. 1 we can estimate the external luminescence quantum efficiency of the solar cell in ref. [49] to be Qe,lum ~ 0.01%. It is important to stress that due to additional recombination at interfaces to charge transfer layers, the calculated Qe,lum of the devices is much smaller than the external luminescence quantum efficiency of well passivated perovskite films, exceeding Qe,lum=35%. [50] In contrast to Zhang [49] , our champion device (blue star) shows low voltage losses leading to high luminescence quantum efficiency Qe,lum~ 5% which is comparable with low band gap devices like Jiang 2019 [3] (violet) and Liu 2019 [4] (red star) (see Figure 1a). Furthermore, the champion device shows a high Voc FF product exceeding 1.08 V (see Figure 1b).  [51,52] and ICBA and all binary combinations of these as electron transport layers (ETLs).
ICBA is known to have a roughly 200 meV [53] lower electron affinity as compared to PCBM and has therefore previously been used in higher band gap perovskites. [28] CMC is also a monoadduct fullerene but with a longer side chain and has been reported to have a slightly higher electron affinity (40 meV) than PCBM. [52] While we find high open-circuit voltages > 1.29 V for all of these ETLs, substantial differences in all device parameters are still observed. We find that the best efficiencies and open-circuit voltages up to 1.35 V are possible using a combination of CMC and ICBA to form a binary layer.

Device Performance
For optimizing wide-band gap CH3NH3Pb(I0.8Br0.2)3 layers grown on PTAA for highest possible open-circuit voltage, lead acetate based perovskite precursors were chosen because they have been shown [4] to yield smooth, low defect-density perovskite layers which enable the highest reported Voc for perovskite layers with a band gap around 1.6 eV. In order to increase the band gap of the perovskite layer, we doped 20% MABr into CH3NH3PbI3 (MAPI) layer to produce perovskite absorber layers with a wide-band gap of 1.72 eV. For bulk passivation, a previous study [54] has shown that addition of MAI into the perovskite precursor solution can lead to passivation of grain boundaries and substantially increased photoluminescence lifetimes . Our study confirms this by achieving continuous improvement in open-circuit voltages when the excess concentration of MAI is increased from 1.67 mol% to 3.33 mol% in CH3NH3Pb(I0.8Br0.2)3 precursor solution ( Figure S4).  (Figures S2 and S3). There could be many reasons for the improvement by light soaking. Possible reasons could be strain reduction in the crystal [55] , electronic doping of the fullerene ETLs [56] or movement of the halide ions, leading to defect passivation in the perovskite. [57,58] In this paper we will not further analyze the cause of the activation effect, but focus on the electrical and optical characterization of the activated cells and layer stacks. During activation, the Jsc slightly decreases causing a 1mA/cm 2 difference between the Jsc computed by integrating the EQE ( Figure S9) and the Jsc measured with the solar simulator. It is important to mention, that all our cells show an increase in Voc if measured again two days after the first measurement ( Figure S5). Our best cell shows a Voc=1.35 V measured on day four after production. Jsc=18.2 mA/cm 2 is by 1 mA/cm 2 higher than the measured Jsc due to current loss during activation ( Figure S9).

Electron Transport Layer Variations
In order to achieve the high Voc, we varied the type of fullerenes used as ETL. In the following we want to show the impact of different fullerenes and their blends on the characteristic values of the cells. drastically reduced FF consistent with the observed charge transport problems of fullerene multiadducts encountered in the past in the context of polymer:fullerene solar cells. [42,43] The apparent solution for this dilemma is found to be the use of the fullerene monoadduct CMC blended with either PCBM orwith even higher efficiencies -ICBA. Thus, the use of binary blends of different fullerenes allows combining their advantages rather than being limited by the shortcomings of the respective molecules.
This is an observation that has also previously been made in the context of organic solar cells, where ternary blends using e.g. two different acceptor molecules combined with one donor have efficiencies that exceed those of the binary blends. [59][60][61]

Loss Analysis
In the following, we will briefly study the key loss mechanisms in our solar cells by comparing the performance indicators Jsc, Voc, FF and efficiency to the values of a cell with the same band gap in the Shockley-Queisser model. We use the methodology that we introduced in refs. [62] and [63] .
In Voc is close to the Shockley-Queisser limit (green curve) for a band gap of 1.72 eV. As described in ref. [63] a better way to compare the quality of the Voc is by comparing the measured and the radiative opencircuit voltage V oc rad . We calculated V oc rad by fitting an Urbach tail to the external quantum efficiency (Figure 4b). The difference Δ oc = oc rad − oc = 70 mV confirms the good Voc comparable to Liu 2019 [4] (Δ oc = 64 mV) and Jiang 2019 [3] (Δ oc = 67 mV). Notably, this loss is compatible with an external luminescence quantum efficiency Qe,lum = 6.56% which is the highest reported value in the band gap region around 1.7 eV.
where sc = sc / sc SQ is the photocurrent loss (yellow Figure 4c). Note that the FF depends on the Voc.
Hence the loss in FF is divided in the loss in maximum fill factor that is due to the loss in Voc , i.e. 0 ( oc real )/ 0 ( oc SQ ) (lilac Figure 4c), and the loss in fill factor that is due to the series resistance and the ideality factor, which we denote as res = real / 0 ( oc real ) (red Figure 4c). Regardless of the fullerene, the loss in Jsc is the highest loss. All cells show a small loss in calculated FF due to a small difference in oc SQ and measured Voc. The resistive loss in FF varies for the different ETL. In case of ICBA res is particularly high suggesting a reduced conductivity of the ICBA layer. The loss in Voc can be divided in the difference between the actual absorption coefficient and the assumed step function in SQ (blue Figure 4c) and non-radiative loss (green Figure 4c). The perovskite and thus the band gap does not change and hence the ratio oc rad / oc SQ is nearly the same for all cells. The ratio oc real / oc rad is highest for cells which contain PCBM in the ETL and lowest for cells with either ICBA, CMC or ICBA:CMC as ETL. Our champion device based on the CMC:ICBA blend ETL shows a moderate normalized efficiency real / SQ = 0.66 , but our non-radiative Voc loss is comparable with high efficiency devices based on much lower band gaps, e.g. Jiang 2019 ref [3] . Figure 4d illustrates the exceptionally low voltage losses of our solar cells compared to the voltage losses in other wide band gap perovskite devices that typically exceed those of lower band gap perovskites. [15,49,64,65]    as described e.g. in ref. [45] . The photovoltaic quantum efficiency is extended by fitting an Urbach tail of EU=16 meV to the measured quantum efficiency as explained in ref. [63] Because the V oc

Interfacial Recombination
The most obvious finding from our previous analysis of device data is the observation of high opencircuit voltages and low non-radiative recombination losses. This implies that our process yields a highquality bulk material which only shows minimal losses due to interface recombination. Interface recombination is affected both by the energy-level alignment [66][67][68] at the interface between absorber and both charge transport layers and by its kinetics that are typically expressed in terms of surface or interface recombination velocities. [69] Here, we will first study the kinetics of recombination using transient photoluminescence measurements and subsequently the energy-level alignment of the different fullerenes by a combination of ultraviolet photoelectron spectroscopy (UPS) and photothermal deflection spectroscopy (PDS).

Recombination kinetics
We measured transient photoluminescence with time-correlated single-photon counting (TCSPC) on half cells without the BCP and silver contact. This was done to reduce the impact of capacitive effects that would be expected from electrode charging and discharging in complete devices. [70] In order to analyze the data, we calculate the differential decay time by first fitting the Tr-PL decays and then differentiating the fits using diff,HLI = −2 ( ( ) ) −1 . ( Where is the luminescence the factor of 2 originates from the assumption of high-level injection (HLI), i.e. ∝ 2 with charge-carrier concentration n. The resulting differential decay times are plotted as a function of the quasi Fermi-level splitting Δ F which is proportional to ln( ) as computed in equation for PCBM:CMC, which could be the reason for the difference to the other mixed fullerenes. The decays are generally comparably slow as those measured on similar MAPI samples as presented e.g. in refs. [4] and [69] .
The first regime (short times) can be affected by charge extraction to the charge transport layers and the ITO electrode as well as by radiative and Auger recombination, leading to relatively low decay times. [71,72] The intermediate and late regime should be dominated by either bulk or interface recombination with an approximately constant lifetime, i.e. some type of defect assisted SRH process.
In contrast to the other fullerenes and blends the differential decay time of CMC increases even further, at lower values of Δ F (long times), representing the flat parts of the Tr-PL decays shown in Figure 5a.
These regimes are representative of the part of the original data with the lowest signal to noise ratio, where the Tr-PL data approaches its background (noise) level. For the other ETLs we cut off the regime with lowest signal to noise as described in Figure S16. In addition, the long time regime can be affected by slow processes such as capacitive discharges of electrodes or contact layers that reinject charge into the perovskite absorber. Therefore, we conclude that the region most representative of the information  (Figure 5e, f). These values of the surface recombination velocity are slightly higher than what was previously estimated for the PTAA/MAPI interface [4] based on Tr-PL measurements but slightly lower than previous estimates [69,71] for recombination at the MAPI/PCBM interface.

Energy Level Alignment and Voc-Losses
In addition to surface quality the energy alignment between perovskite and CTL limits the Voc [12,69] Large offsets e.g. in the conduction band at the absorber-ETL interface would lead to an interfacial band gap at this interface that is substantially lower than the bulk band gap. If recombination is efficient via the interface (i.e. electrons in the ETL can efficiently recombine with holes in the perovskite), the interface may strongly deteriorate the Voc. Therefore, characterization of energy levels is crucial for a complete understanding of interfacial recombination in a solar cell. Typically, UPS is used to measure the work function and the valence-band edge Ev at the surface of the samples. Given that we are interested in the LUMO positions of our ETLs, we have to combine UPS data with data from optical spectroscopy to obtain the band gap and thereby the electron affinity .
We derived the work function and the valence-band edge with UPS measurements as shown in Figure S19 for all fullerenes and blends on glass/ITO/PTAA/perovskite/ETL stacks. We activated the half cells before the UPS measurement by illumination under a white LED lamp as described in SI.

Figure 6c
illustrates the difference between the ionization energy Ei = Evac -EV of PCBM and the other fullerenes. We determined a smaller Ei for ICBA of 160 meV, which is in good agreement with the offset (200 meV) measured by ref. [53] . The relevant quantity for band alignment with the perovskite is however the electron affinity as it determines electron extraction and recombination of electrons in the ETL with holes in the perovskite. However, fullerenes do not show a clear absorption onset that could be used to determine the band gap but feature a weakly absorbing absorption feature at around 1.75eV and then a slow rise until strong absorption is visible in the blue and UV parts of the spectrum. This has led to the situation electron affinities determined from combination of UPS and absorption spectroscopy vary wildly in the literature [40,52,[73][74][75][76] . In order to circumvent this challenge, we again only compare relative changes in band gap that we determine from PDS measurements analyzed at three different constant absorption coefficients = 1 × 10 4 cm −1 , = 5 × 10 3 cm −1 and = 1 × 10 3 cm −1 . The arithmetic mean of the three optical band gap differences is shown in Figure 6b. We observe that the optical band gap of CMC is approximately 40 meV bigger than the bandgap of PCBM while the other fullerenes show slightly lower band gaps than PCBM.

Fill-factor losses
As observed in Figure 4c and d, the fill factor losses are still substantial and even at fill factors ~ 80% generally exceed the losses in Voc in the cells discussed here. The same is true for most high efficiency perovskite solar cells reported in literature and stands out relative to more mature technologies such as Si or GaAs where these losses are substantially lower. [63] These losses partly originate from the high ideality factors observed even in high efficiency perovskite solar cells [13,77] and from the resistive losses induced by the relative low conductivity and low permittivity of the organic charge transport layers. [78] In the following, we will therefore study the general distribution of FF losses in more detail and analyze in particular resistive losses due to low mobilities in the ETLs via space charge limited current measurements.

Analysis of current-voltage curves
In order to distinguish between resistive contributions to the fill factor loss and those based on ideality factor nid higher than one, we use a simple method to determine the series resistance Rs by comparing illuminated and dark JV-curve in the 4 th quadrant. [79,80] When neglecting the parallel resistance and assuming the superposition principle [81,82] holds, the diode equation with k the Boltzmann constant and T the cell temperature and 0 = sc × exp( − oc ⁄ ) describes the JV-curve of a solar cells. In the dark the diode equation is reduced to where the JV-curve is independent of light induced effects. The Jsc/Voc-curve, i.e. Jsc and Voc measured at different illumination intensities is independent of Rs, since the current is zero at Voc.
the mean series resistance for the PCBM cell is s ≈ 4.9 Ωcm 2 (Figure 7c). In Figure 7d and e we plotted the power density vs. voltage for the different JV-curves in a similar manner to Figure 4a. The maximum of the power density curve gives us the efficiency of our solar cell. The difference between illuminated and Jsc/Voc-curve reveals the fill factor loss Δ = l − sc oc = 3.7% due to the series resistance in the cell.. The difference between Jsc/Voc-curve and ideal power density curve gives us the loss due to non-ideal diode behavior, i.e. an ideality factor nid > 1. [83] The ideality factor for PCBM is in the range of roughly nid ~ 1.7 to 1.9 ( Figure S25). The fill factor loss due to non-ideal diode behavior is slightly larger than the loss due to Rs Δ id = id − sc oc = 5.9% (see Table 1). Table 1: Jsc, Voc, FF and for a solar cell based on an PCBM ETL compared to FF and from an ideal JV-curve with the same Jsc and Voc but Rs = 0 and nid = 1 and a curve with zero series resistance (but non-ideal nid), derived from the measurement of the Jsc/Voc curves shown in Figure 8a and b.

Space-charge limited current measurements
The observation of improved FF for the binary ETLs compared to pure fullerene ETLs as shown in Figure 3d, suggests that the choice of fullerene or fullerene blend affects the conductivity of the ETL which in turn could modulate the resistive losses caused by the ETL. Hence, we studied the difference in electron mobility across the different ETLs using space-charge-limited current (SCLC) measurements. Therefore, we constructed electron only devices, similar to the cell stack. As shown in Figure 8a, we used ZnO nanoparticles and the standard BCP/Ag contact also used in the solar cells as electron injecting and extracting contact for the electron-only devices. In SCLC measurements, the current should follow the Mott-Gurney law [84] where 0 is the vacuum permittivity, = 3 the assumed relative permittivity and d the thickness of the fullerenes and fullerene blends if certain conditions are met. These conditions include most notably the absence of diffusionan assumption that is typically violated if there are either charged defects or asymmetric injection barriers present in the device. In order to distinguish between both effects, we measured the dark JV-curve from -4 V to 4 V with the difference between forward and reverse bias being indeed substantial (see Figure S21). [85,86] To minimize the influence of diffusion on the data, we use the curve obtained by injecting electrons at the BCP/Ag electrode and extracting them at the ZnO electrode and limit ourselves to voltages V > 1 V. the Mott-Gurney law can only be applied in the region of the flat slope. [87] All samples except the ICBAbased sample show a transition from a high slope at lower voltages (diffusion limited region) to a smaller slope at higher voltages that approaches the value of 2 expected from the Mott-Gurney law. The curves for the different fullerenes are approximately parallel suggesting that they differ essentially in mobility.
On the contrary the ICBA-based sample shows a substantially higher slope than 2 throughout the whole voltage region suggesting that energetic disorder affects charge transport. [88] Figure 8a leads to the conclusion that PCBM:CMC and CMC have the highest mobility while ICBA shows the lowest mobility of all six fullerenes andgiven the higher slope of current vs. voltage -is affected by energetic disorder. [88] To extract the mobility, we simulated the complete JV-curve with the drift-diffusion simulation solver Advanced Semiconductor Analysis (ASA) to compute the mobility as described in SI. Figure 8b shows the result of numerically fitting the curves and extracting the electron mobility for the different ETLs. This electron mobility is then plotted as a function of fill factor FF. The ZnO nanoparticles form a rough layer which leads to uncertainties in the thickness of the fullerene layers that are reflected in the error bar of the mobility. The fill factor is the median of all measured cells at a AAA sun simulator on day 4 after activation, while the error bars represent 1.5×IQR.With the exception of the CMC sample that shows a fairly good mobility relative to a modest FF, we observe a monotonous increase of FF with electron mobility from ICBA (worst FF) to PCBM:CMC (best FF). 1D-drift-diffusion simulations of JV-curves ( Figure S23) confirm the electron mobility trend shown in Figure 8b for all ETLs but CMC.
Note that the CMC sample is inhomogeneous (Figure S24), thus the thickness measurements may have a larger error bar, or the material properties could be different to those properties present in a cell with much thinner CMC layer.

Conclusion
Reaching high open-circuit voltage is one of the main challenges for wide band gap perovskite solar cells. Using CH3NH3Pb(I0.8Br0.2)3 with a band gap of Eg = 1.72 eV and a blend of CMC:ICBA as electron transport layer we managed to fabricate solar cells with a high Voc = 1.35 eV leading to a non-radiative loss of only Δ oc = 70 mV without compromising in FF. Using transient photoluminescence spectroscopy and a combination of ultraviolet photoelectron spectroscopy and photothermal deflection spectroscopy, we were able to assign the high Voc to low interfacial recombination and partly improved energy alignment. In addition, we studied the losses in fill factor, which are substantial given that corresponding FF in the SQ model is nearly 91% for a Voc of 1.35 V. By using a comparison of measured current-voltage curves and suns-Voc measurements, we find that the FF losses are distributed approximately equally between losses due to the ideality factor nid > 1 and due to resistive losses. The resistive losses most likely originate from the finite conductivity of the charge transport layers. Spacecharge-limited current measurements show that the electron mobility in the ETL materials varies for all fullerenes and fullerene blends, showing a monotonic correlation between FF and electron mobility that holds for all samples but one. This suggests that further pathways towards higher efficiencies can be based on higher conductivities and mobilities in the electron transport layers combined with a better understanding of ideality-factor losses. The latter losses may be reduced by either further approaching the radiative limit for example by better surface quality or by moving the most recombination active parts of the device into low level injection.