Ion Movement Explains Huge V OC Increase despite Almost Unchanged Internal Quasi-Fermi-Level Splitting in Planar Perovskite Solar Cells

Light soaking under “ 1 sun ” is performed on planar p – i – n perovskite solar cells with a Cs 0.05 MA 0.10 FA 0.85 Pb(I 0.95 Br 0.05 ) 3 absorber while measuring current and voltage transients simultaneously to spectral photoluminescence (PL). From theory a tenfold increase in PL intensity is expected for every 60 mV rise in V OC (at 300 K). However, the solar cells investigated show a reversible V OC increase from as low as 0.5 up to 1.05 V during light soaking, whereas the PL intensity hardly changes. A model is developed based on mobile ions in combination with a nonideal contact. It reproduces the decoupling of the V OC and PL as well as the transient behavior in great detail. Using state-of-the-art materials and passivation layers shows that light soaking is still a relevant feature of high-ef ﬁ ciency perovskite solar cells. The ionic liquid additive 1-butyl-3-methylimidazolium tetra ﬂ uoroborate slows down the light-soaking behavior, giving an example of how ionic motion in perovskite solar cells can be in ﬂ uenced.

DOI: 10.1002/ente.202001104 Light soaking under "1 sun" is performed on planar p-i-n perovskite solar cells with a Cs 0.05 MA 0.10 FA 0.85 Pb(I 0.95 Br 0.05 ) 3 absorber while measuring current and voltage transients simultaneously to spectral photoluminescence (PL). From theory a tenfold increase in PL intensity is expected for every 60 mV rise in V OC (at 300 K). However, the solar cells investigated show a reversible V OC increase from as low as 0.5 up to 1.05 V during light soaking, whereas the PL intensity hardly changes. A model is developed based on mobile ions in combination with a nonideal contact. It reproduces the decoupling of the V OC and PL as well as the transient behavior in great detail. Using state-of-the-art materials and passivation layers shows that light soaking is still a relevant feature of high-efficiency perovskite solar cells. The ionic liquid additive 1-butyl-3-methylimidazolium tetrafluoroborate slows down the light-soaking behavior, giving an example of how ionic motion in perovskite solar cells can be influenced. (1) where E G denotes the bandgap, k B the Boltzmann constant, T the temperature, k r the radiative recombination coefficient, N C and N V the effective density of states for the conduction and valence band, respectively, and R rad the radiative recombination rate, which itself is determined by with n e and n h the electron and hole densities, respectively, and e denoting the elementary charge. The last step assumes a solar cell with constant ΔE F throughout the bulk of the absorber. Then, ΔE F =e is externally measurable as the open-circuit voltage V OC . Integrated over the volume of the absorber, R rad is proportional to the PL signal (neglecting reabsorption) of the solar cell and exponentially dependent on V OC . In this case, it can be easily calculated with Equation (1) that at 300 K a tenfold increase of R rad will result in an increase of ΔE F of roughly 60 meV. In return, this implies that even small changes in V OC will have a huge impact on the measured PL intensity if ΔE F is constant throughout the bulk of the absorber. We built PSCs with a mixed-cation, mixed-halide lead-based perovskite Cs 0.05 MA 0.10 FA 0.85 Pb(I 0.95 Br 0.05 ) 3 absorber layer in planar p-i-n architecture (indium tin oxide (ITO)/[2-(3,6-dimethoxy-9H-carbazol-9-yl)ethyl]phosphonic acid (Meo-2PACz)/ perovskite/ [6,6]-phenyl-C61-butyric acid methyl ester (PCBM)/ aluminum-doped zinc oxide (AZO)/aluminum (Al); layer structure shown in Figure S1, Supporting Information, details of the device fabrication can be found in the Experimental Section). With this architecture, we are able to regularly achieve power conversion efficiencies of 20% in our lab, with a corresponding V OC of around 1.1 V under 1 sun illumination (simulated AM 1.5G, corrected for spectral mismatch). In the dark and under inert atmosphere, those cells seemingly degrade within a few days, mainly by a decrease in V OC of up to 500 mV. On these cells with low V OC , light-soaking experiments have been conducted with simultaneous measurement of V OC and spectrally resolved PL intensity. Figure 1a shows the V OC increase with the corresponding PL signal. When switching on the illumination, V OC increases very fast (on this time scale apparently instantaneously) to around 800 mV. At the same time, an initial PL intensity can be measured. For the shown device, V OC increases by 250 mV until it saturates at around 1.05 V within 500 s. During the V OC rise the PL intensity stays-in great contrast to Equation (2)-almost constant and also the shape of the PL spectrum does not change ( Figure S2a, Supporting Information). This indicates that the discussed light soaking is not caused by halide segregation because this has been linked in mixed-halide perovskites to pronounced spectral changes (e.g., an increase in bandgap in Br-rich regions). [29] Figure S2a, Supporting Information, also shows that when switching the solar cell to short circuit condition a significant amount of charge carriers is extracted, resulting in a lower bulk QFL splitting and a quenched PL signal. This implies that the measured PL signal is indeed, at least to a significant fraction, caused by the radiative recombination of charge carriers that are electronically available and not, for example, by electronically disconnected islands in the perovskite absorber, which could not be influenced by charge extraction or transport layer properties.
The whole process of increasing V OC is reversible by letting the solar cell rest in the dark for a longer time span ( Figure S3, Supporting Information). Measuring JV curves before and after the light soaking reveals that the performance has increased drastically ( Figure 1b). Importantly, the performance increase also happens during maximum power point (MPP) tracking and is shown in Figure S4, Supporting Information, for a solar cell delivering an efficiency of 20%. This shows that the discussed effect is of relevance for highly efficient PSCs in real operation conditions. Hysteresis effects occurring during JV scans are comparably small and are discussed in the Supporting Information ( Figure S5, Supporting Information). The large increase of V OC together with an almost unchanged PL contradicts the logarithmic dependence of V OC on PL signal in Equation (2). According to this, an increase of the PL signal by more than four orders of magnitude would be expected from the increase of V OC by 250 mV. To illustrate this discrepancy, Figure 1a also shows the theoretically expected PL signal calculated from the measured V OC increase as well as the theoretically expected V OC calculated from the PL measurement (red and black dotted lines, respectively).  This combination of an increase in V OC of 250 mV together with a PL signal that is changed by less than a factor of 2 (and even decreasing) can only be explained by a gradient of the majority charge carrier QFL toward the respective contact. Figure 2a shows a simplified representation of the QFLs of a solar cell with rather selective contacts under illumination at open-circuit conditions. The hole contact is at the left end and the electron at the right end of the device and for sake of simplicity, the conduction and valence band are drawn as flat lines. As contact we refer here to the combination of the high-conductivity electrode (metal or strongly doped metal oxide layer) and the electron or HTL. Recombination due to a poor selectivity of the contact actually occurs at the interface between the absorber and transport layer. Note that band diagrams from the drift-diffusion simulations are shown in Figure S8, Supporting Information, including the transport layers (wide-bandgap semiconductors with a thickness of 20 nm). The results of the simulations will be discussed further subsequently.
The relation between the splitting of the QFL ΔE F and the radiative recombination is given in Equation (1). The externally measurable V OC can be taken from Figure 2 as the difference between the QFL of the valence band at the hole contact and the QFL of the conduction band at the electron contact. Radiative recombination depends exponentially on the area between the QFLs of the valence and conduction band, respectively. Note that for the solar cell with rather selective contacts (Figure 2a), some charge carriers may get lost due to surface recombination but ΔE F is constant throughout the bulk and therefore identical to eV OC (measurable between the contacts). When at least one contact has a strongly reduced selectivity (as shown in Figure 2b), there will be a large surface recombination current toward this contact under open-circuit conditions. The corresponding loss of charge carriers reduces ΔE F and V OC in the same manner as long as there is no significant gradient in the majority-carrier QFL close to the contact. For this reason, the situation shown in Figure 2b leads to a lower V OC than in the case of Figure 2a and a significantly reduced PL signal of roughly one order of magnitude for every 60 mV decrease in V OC , in accordance with Equation (1). To maintain roughly the same PL intensity despite a (strongly) reduced V OC , the same ΔE F is required throughout almost the entire absorber layer together with a significant gradient of at least one of the majority carrier QFL close to its respective contact.
The QFL gradient ∇E F,e=h is determined by the ratio of the particle current density J e=h and the corresponding electrical conductivity σ e=h .
Therein, the electrical conductivity is the product of the elementary charge and the mobility and concentration of the corresponding charge carriers. Therefore, a stronger gradient of a QFL does not necessarily cause a larger (surface recombination) current if the conductivity is lower. As a consequence, this can lead to the case shown in Figure 2c, where the number of charge carriers getting lost due to surface recombination is comparable to Figure 2a (thus maintaining a similar QFL splitting and therefore PL intensity throughout the bulk) but still a significantly reduced V OC is measured.
For organic solar cells, the low majority charge carrier conductivity in the vicinity of a nonselective contact was found to cause a very large QFL gradient, which leads to a strong decoupling of V OC and PL intensity. [30,31] Also, in silicon heterojunction solar cells (i.e., crystalline silicon absorber sandwiched between thin layers of amorphous silicon) this phenomenon has been observed for weakly doped (and thus low conductive) a-Si transport layers. [32] The transient V OC and PL intensity data in Figure 1 strongly indicate that such a large gradient as shown in Figure 2c must be present initially and is subsequently reduced during light soaking under open-circuit conditions. The reversibility and the timescale of the phenomenon hint toward movement of ionic species as the origin of the temporal evolution. Deng et al. discussed the way the movement of positively charged methylammonium ions and iodide vacancies can cause this behavior and termed it "light-induced self-poling" (LISP). [15] As proposed by John et al., the timescale for halide motion should be in the microsecond range, whereas the much larger activation energies for Cs þ -, MA þ -, and FA þ -vacancy movement indicate a timescale up to minutes. [33] As the experimental data in this study (using a CsMAFAPbIBr photoactive layer) revealed a timescale of the order of minutes for the light-soaking effect, only www.advancedsciencenews.com www.entechnol.de the monovalent cations can be made accountable for the rather slow changes observed. In the following we will present our model with the assumption of negative mobile ion vacancies (corresponding to the negatively charged Cs þ , MA þ , or FA þ vacancies), positive immobile counter charges, a hole contact with reduced selectivity, and a selective electron contact. Note that by hole contact again the combination of electrode and HTL is meant. Similarly, electron contact includes the electrode and the electron transport layer (ETL) in the following. When left at 0 V in the dark, the ions arrange according to their electrochemical equilibrium between drift (due to the built-in field) and diffusion. This accumulates negative ions in front of the electron contact and leaves behind a positive space charge in the vicinity of the hole contact, as shown schematically in Figure 3, left graph (referred to as "unconditioned" in the following). The positive space charge leads to a decreased hole density near the hole contact and thereby lowers their conductivity in this region. Under illumination and open-circuit conditions, a surface recombination current will flow because of the reduced selectivity of the hole contact. For a given (surface recombination) current, the decreased hole conductivity resulting from this specific ion distribution increases the gradient of the QFL of the valence band ∇E F;h according to Equation (3) and as shown in Figure 2c. Simultaneously the ion distribution will increase the electron conductivity near the hole contact, allowing for a higher electron current to the hole contact and creating a situation that the rate of surface recombination is actually limited by the hole current, i.e., by the majority charge carriers. With ongoing light soaking, the ions will redistribute according to changes of the internal electric field due to the buildup of photovoltage and this will finally resemble the case shown in Figure 3, right graph (referred to as "conditioned" in the following). As shown further subsequently, this redistribution can also be caused by application of a forward voltage in the dark. As now the hole density in front of the hole contact is much less reduced by ions, their conductivity increases. This decreases the gradient according to Equation (3), which in turn results directly in a higher V OC . This increase in majority carrier conductivity would lead to a higher surface recombination current, thus lowering the PL signal. However, simultaneously the ions lower the conductivity of the minority carriers (i.e., the electrons) in the vicinity of the hole contact, rendering the surface recombination current electron limited. Depending on the exact parameters (especially the electron and hole mobilities), the changes of the conductivities can counterbalance each other, which keeps the number of carriers lost due to surface recombination and with that the PL signal rather constant. However, the surface recombination current can even increase during light soaking. This happens when the effect of the increased hole conductivity (which is the limiting factor for surface recombination in the unconditioned state) is larger than the decrease of the electron conductivity. This leads to a decreasing PL signal with a simultaneously increasing V OC , opposite of what would be expected from Equation (2).
This model was implemented in the semiconductor simulation tool Sentaurus Device [34] to perform numerical driftdiffusion simulations as in our previous studies on organic solar cells. [30,[35][36][37] The standard parameter set for the simulations is listed in Table S1, Supporting Information. In addition to electrons and holes, negative mobile ions are included. These ions are initially placed homogeneously in the perovskite layer and, to obey charge neutrality, the mobile ion density is outbalanced by the same density of immobile counter charges (positively charged, also placed homogenously). The ion movement is restricted to the perovskite layer (especially no ion flow through the contacts possible) and no ion generation or recombination mechanisms are considered. Only direct recombination is considered in the bulk. The absorber/HTL interface is made nonselective by setting the Shockley-Read-Hall (SRH)-recombination velocity to a large value at said interface, while the absorber/ETL interface is considered selective (without SRH recombination). For simplicity, the generation of electron-hole pairs was implemented to be homogeneous and restricted to the absorber layer.
To simulate the unconditioned and the conditioned state of the solar cell, the mobile ions were allowed to reach their equilibrium position at a certain starting voltage (0 V for unconditioned device, 1.1 V for the conditioned device). For the sake of simplicity, the voltage scan rate was chosen to be large enough to consider the ions frozen during the subsequent JV scan. www.advancedsciencenews.com www.entechnol.de Figure 4a shows the unconditioned and conditioned JV curves for the parameter set from Table S1, Supporting Information, with different ion concentrations. Clearly, the different ion distributions (shown in Figure S6, Supporting Information) of the unconditioned and conditioned state affects V OC as it affects the surface recombination losses as described earlier. The V OC difference between the unconditioned and conditioned states increases with the ion concentration; however, above a certain ion concentration the JV curve shows features not observed in the experiments, e.g., kinking in forward direction. We found an ion concentration of 3 Â 10 16 cm À3 to deliver a large V OC difference while still obtaining a fill factor comparable to the experiments. The PL intensity of the unconditioned device at V OC is a factor of five higher than in the conditioned state, whereas from Equation (2) it would be expected to be more than four orders of magnitude lower. This shows that a strong decoupling of V OC and PL is reproduced in the simulation, corresponding very well to the experimental results. Further, Figure S8, Supporting Information, shows the band diagram at V OC corresponding to Figure 4a before and after light soaking at an ion concentration of 3 Â 10 16 cm À3 . The band diagram of the unconditioned state fully validates the presence of the aforementioned QFL gradient in the valence band toward the HTL. Note that the model is invariant upon a change of the ionic charge (from positive to negative ions) if at the same time the nonselective contact is changed as well (from hole contact to electron contact). This means the results alone cannot tell which ionic species is responsible for the effects seen in the experiments without precise knowledge about which contact comprises insufficient selectivity. However, when assuming that the mobile species are negatively charged a nonselective hole contact was needed to reproduce the experiments in good accordance, which was not possible with a nonselective electron contact ( Figure S9, Supporting Information).
The model also allowed for the simulation of a transient V OC increase. For this, the ions were at first allowed to reach their equilibrium at 0 V. Subsequently the (optical) charge carrier generation was activated and the V OC increase was traced, as shown in Figure 4b for the previously used parameters. The ion diffusion coefficient at 300 K was set to 5 Â 10 À13 cm 2 s À1 to fit the V OC increase duration in the simulations to the experimental data at room temperature (cf. Figure 1a). To obtain a better fit for the first 100 s of the V OC increase, it is useful to assume a pre-light soaking. Without this, the device in the simulation is assumed to be in the equilibrium position for a light intensity of exactly zero, whereas realistically the sample will always be subjected to a certain background light intensity during storage or handling. For this reason, an initial background illumination corresponding to 10 À4 suns was assumed and the curves shown in Figure 4 were simulated using this pre-light soaking. In the Supporting Information the difference in V OC increase with and without initial background illumination is shown ( Figure S10, Supporting Information). It can be seen also that the transient light-induced V OC increase and the PL data from the experiments are consistently reproduced by our model.
As the movement of ionic species is driven by the electric field and diffusion, two postulations can be made, which in the following shall be verified by experiments: 1) When forward biasing the device in the dark, the ions should also rearrange, bringing the device into the conditioned state with a (much) higher V OC in a subsequent IV measurement; 2) in contrast to light soaking at open circuit conditions, light soaking the device at 0 V should not rearrange the ions and therefore also no V OC increase should be observed.
To show that forward biasing the solar cell (without any illumination) also causes the same changes, electroluminescence (EL) measurements were performed. Figure 5 shows the EL measurement and its effect on solar cell performance for the same device for which the light-soaking behavior is displayed in Figure 1.
In the beginning the EL intensity is below the detection limit. This in combination with a high PL (Figure 1a) is a strong indication for the presence of an initial injection barrier at the nonselective contact. [30,32] Note that the fact that a forward current density of 20 mA cm À2 can be injected at these reasonably low voltages (around 1.1 V) indicates that only one contact inhibits nonselectivity. If both contacts showed a poor selectivity, this current injection would require higher voltages. With the QFL gradient present close to the hole contact, as discussed previously, hole injection is limited by the corresponding low hole conductivity. Meanwhile, the injection of electrons at the selective electron contact is unhindered. Therefore, these electrons flow through the entire bulk of the device and recombine nonradiatively at the hole contact, allowing for a rather high (almost www.advancedsciencenews.com www.entechnol.de Energy Technol. 2021, 9,2001104 electron-only) forward current in the device. However, as the applied forward bias rearranges the ions, the gradient is subsequently reduced (in the same manner as described previously for the light-soaking case under open-circuit conditions). Thus, more holes are injected at the hole contact. Now the charge carriers can recombine radiatively in the bulk, giving rise to an EL signal. It should be noted that during the forward biasing/EL experiment also no spectral changes were observed ( Figure S2b, Supporting Information). Measuring the JV curve of the device directly before and after the EL measurement (Figure 5b) shows that forward biasing indeed causes similar effects as light soaking under open-circuit conditions (Figure 1b), in accordance with what was postulated previously. It could be assumed that even at short-circuit conditions, the device will react to the illumination and get eventually into the light-soaked or conditioned state with higher V OC at a subsequent JV scan. However, as the model postulates, the ions react to changes in the electric field. At 0 V the contacts are not recharged and thereby no change in the electric field is present for the ions to react upon. To verify this experimentally, light soaking at 0 V was performed over 2 h ( Figure S7, Supporting Information). During this the short circuit current J SC stayed constant and a subsequent V OC measurement showed no increase of V OC , in perfect agreement with the model. With these results, both postulations have been confirmed, fortifying the correctness of the assumptions made in the model.
To further analyze the behavior of the solar cells, light-soaking experiments under open-circuit conditions with simultaneous transient voltage and PL measurements as well as EL experiments were performed at different temperatures. The series of measurements started at a temperature T ¼ 260 K, prior to which the device was kept in the dark. At each temperature, the solar cell was light-soaked under open-circuit condition for 20 min. After V OC light soaking, the cell was left in the dark and without bias for 10 min, after which the EL experiment was performed for 10 min. In between the subsequent measurements, the cell was left in the dark for 30 min, during which time the temperature was increased and stabilized. Consistent with the picture of ionic movement the V OC increase slows down for lower temperatures as the ion diffusion coefficient decreases [17] (Figure 6a). The transient temperature-dependent PL measurements (Figure 6a) show a similar trend, with a slower change in PL intensity for lower temperatures, however remaining rather constant compared to the huge changes in V OC . To further investigate this, temperature-dependent simulations were performed for the transient V OC increase, which are shown in Figure S11, Supporting Information. For these simulations, it was for simply assumed that only the diffusion coefficient changes upon temperature variation. With an activation energy of 0.3 eV for the ion diffusion, the time scale changes due to temperature in the V OC increase can be very well remodeled. John et al. reported a value of 0.32 eV for the activation energy Cs þ -vacancy movement, [33] well in line with the value used in the simulation. The EL measurements show again a huge increase of EL intensity following the increase in charge carrier selectivity suggested by the voltage necessary to drive the constant forward current. The temperature dependence of the EL measurement is the same as for the V OC light soaking, again being fully consistent with the picture of ionic movement. To demonstrate the universality of the light-soaking phenomenon, measurements were conducted on a completely different PSC architecture as well. Figure S12, Supporting Information, shows temperaturedependent V OC and PL measurements of a mesoporous n-i-p cell using a high-bandgap double-cation perovskite formulation. Even though the device architecture is completely different, a quite similar light-soaking behavior can be observed.
As the discussed light-soaking effect is supposedly governed by ionic movement in the perovskite layer, it is worthwhile to investigate the impact of additives to the photoactive layer. For this case, the ionic liquid BMIMBF 4 was used. With this additive, remarkable increases in device performance and stability have been reported by Bai et al. [38] In their study, PL-quenching experiments of samples with in-plane electrodes led to the conclusion that ion movement is drastically slowed down for samples containing the ionic liquid additive. Employed in the solar cells used for this publication, BMIMBF 4 increases the steady-state opencircuit voltage as well as the PL intensity, suggesting that the ionic liquid has a general passivating effect on the perovskite bulk. For the light-soaking experiments, the concentration of BMIMBF 4 was varied between 0.4 and 0 mol% with respect to lead atoms. Figure 7a shows the time-dependent V OC and PL behavior. The PL intensity increases for increasing amounts  www.advancedsciencenews.com www.entechnol.de the ionic liquid additive slows down ion movement when its concentration in the investigated samples increases. Scanning electron microscope (SEM) images of the samples are shown in Figure S13, Supporting Information. Those images suggest that there is no significant change in perovskite crystallinity (grain boundaries, crystallite size) that could be made accountable for the change of light-soaking behavior, leading to the conclusion that the ionic liquid additive hinders ion movement rather on the molecular scale than due to a change in perovskite crystallinity.

Conclusion
In this work, we have presented data from mixed-cation, mixedhalide Cs 0.05 MA 0.10 FA 0.85 Pb(I 0.95 Br 0.05 ) 3 PSCs showing a V OC increase upon light soaking by more than 250 mV while at the same time maintaining a rather constant PL intensity. It was found that a similar V OC increase can also be achieved by forward biasing the devices in the dark. The combination of transient V OC , PL, and EL data led us to the conclusion that the origin of the effect is an initially rather strong gradient in the QFL of the majority charge carriers in the vicinity of the hole contact. By conditioning the device either by light soaking under open-circuit conditions or by forward biasing in the dark, this gradient is reduced, which leads to the observed increase in V OC . The rather constant PL intensity indicates that the rate of surface recombination hardly changes during this time. Further, temperature-dependent light-soaking experiments were performed. The results showed the same general behavior but on significantly longer time scales at lower temperatures. This is well in accordance with ionic movement and the reduction of their diffusion coefficient with decreasing temperature. A quantitative model was developed which reproduced the experimental findings in great detail. It shows that the modified internal electric field (due to buildup of the photovoltage or due to the applied forward bias) redistributes the mobile ions. This causes a redistribution of electrons and holes, thus reducing the gradient of the majority-carrier QFL. This finally leads to an increased V OC and decouples the V OC from the PL intensity in accordance with the experimental results. This last point is especially important to consider when drawing conclusions about the external V OC from techniques such as PL mapping, where a so-called implied open circuit voltage (iV OC ) is determined from PL data. This study shows that a high PL intensity is a necessary but not sufficient condition for achieving a high open-circuit voltage and highlights the importance of mobile ionic species for the transient behavior of PSCs also on timescales of days.