Simulating Proton Radiation Tolerance of Perovskite Solar Cells for Space Applications

Perovskite solar cell technology offers a promising power option for space applications due to its potential properties of high power‐to‐weight ratios and space‐radiation tolerance. Herein, a new simulation‐based method is introduced to predict the degradation of perovskite solar cells under proton radiation. The approach uses ion scattering simulations to generate depth‐dependent defect profiles as a function of proton energy and fluence, which are then incorporated into optoelectronic simulations to predict the degradation. The method to study the impact of perovskite compositions on radiation tolerance is applied and an inorganic perovskite CsPbI2Br and an organic–inorganic perovskite FAMAPbI3 is compared. The simulations predict that CsPbI2Br and FAMAPbI3 cells retain 62% and 65% of their initial efficiencies after a 100 keV fluence of 1e14 cm−2, respectively. For comparison, unshielded III–V solar cells display similar degradation for proton fluences 3–4 orders of magnitude lower. It is also shown that the radiation direction must be considered when interpreting and predicting radiation tolerance, as the spatial overlap between photogenerated carriers and radiation‐induced defects has a significant impact on cell performance. Finally, a method to predict mission end‐of‐life performance of perovskite cells is demonstrated, taking into account the full proton radiation energy spectrum and fluence and the incident direction.

Assessing and predicting the impact of space radiation on solar cell performance in ground-based experiments is challenging for several reasons.First, ground-based testing is typically limited to only a few discrete particle (electron/proton) energies, whereas space radiation spans a wide range of energies and fluences.Second, accelerated degradation tests at very-high-particle fluxes are required to generate the total radiation dose of long space missions (years-decades), but this can induce thermal and other changes in the test samples that would not occur under realistic radiation conditions.Third, space radiation testing facilities are not widely available, and testing is a slow and expensive process, so it is not feasible to test many sample variations or to characterize every sample under a full range of particle types and energies.Thus, testing of solar cells for space applications usually involves some combination of validated damage models or numerical simulations with targeted experimental measurements.There are two main methods used to predict the degradation of solar cells in space, which were developed by the NASA Jet Propulsion Lab (JPL) and the US Naval Research Lab (NRL).The standard JPL approach uses experimental solar cell performance data for four electron energies and eight proton energies at a range of fluences to calculate a "relative damage coefficient" referenced to 1 MeV electrons. [11]With this data, it is possible to convert the radiation energy spectrum and dose for a given space mission into an equivalent 1 MeV electron fluence.Thus, if cell performance versus fluence is known for 1 MeV electrons, one can predict end-of-life (EOL) performance for the mission, and the relative performance of different cell types can be compared.In the NRL approach, the displacement damage dose (DDD) is calculated for a given mission based on particle radiation simulations to determine the nonionizing energy loss (NIEL) of protons and electrons incident on devices. [11]The NIEL is a measure of how much energy is transferred to the semiconductor materials, creating atomic displacement and lattice vacancies.Energydependent NIEL simulations are combined with experimental radiation tests (typically for one proton energy and two electron energies) to obtain the dependence of DDD on NIEL and fluences.With this data, radiation exposure for a specific mission can be converted to an equivalent DDD, which can then be used to predict cell performance based on tabulated performance versus DDD data.
Most studies of PSC radiation tolerance to date include results for only a small number of cells exposed to single-particle (electron or proton) energy: 1 MeV electron, [7,9] 50 keV proton, [8,9] 75 keV, [12] 100 keV, [13] 300 keV, [14] 68 MeV proton. [15,16]This is most likely due to the testing facility, cost, or time limitations (or all three), but it limits the reliability of the data and makes interstudy comparisons difficult.There have also been some limited flight tests such as in a high-altitude balloon (35 km height) [10] or on a rocket (240 km height for only 6 min). [17]owever, these experiments cannot accurately reflect the working conditions of cells in the outer space environment, such as at Geosynchronous equatorial orbit (GEO) (%36 000 km height) or in deep space [8] with multienergy electron/proton radiation.Moreover, in many of the studies, ambient moisture and oxygen during storage, transport, and characterization resulted in significant environmental degradation of cell performance before the radiation tests.These degraded cells with initial efficiencies in the range of 6-12% [9,10,15,16] (far lower than the state-of-the-art efficiency for PSCs-25.7% [18] ) cannot accurately represent the response of fresh cells under the same conditions.Recently, in situ characterization [19] of PCSs under proton radiation was developed to avoid differences in individual cell performance, but the number of cells was still very limited.Furthermore, lab-based tests performed with fluxes much higher than actual working conditions in space can cause heating and subsequent self-annealing of radiation damage, [20] especially for high particle energies.These make an accurate assessment of particle radiation on the cell performance more challenging.
Ultimately, the main goal of radiation tolerance studies is to develop optimized solar cell structures for space missions.For perovskite technology, the wide range of perovskite compositions, charge transport materials, and device architectures makes it impractical to experimentally evaluate the radiation tolerance of all possible combinations.Additionally, theoretically, the devices should be studied under single-energy radiation, and the combination of these results can be used to evaluate/estimate their behaviors under the real condition with multienergy radiations.The established protocols developed by JPL and NRL require a wide range of calibration/calculation for an equivalent dose/ DDD.The method was suitable for "traditional" solar cell technologies like silicon or III-V solar cells, but it is not practical for the perovskite technology.Thus, at this early stage of investigating PSCs for space applications, it is important to identify what parameters are most important when choosing materials and device architectures for radiation tolerance.Understanding what design factors do (and do not) influence radiation tolerance will help guide research activities on space PSC development.This information is not yet available from experimental studies.
On the other hand, simulations offer a promising tool not only for prediction, but also for optimization of space cells.Simulating the effects of radiation exposure on solar cell performance involves two separate steps.The step first is to estimate the type and distribution of damage through the cell after exposure to high-energy particles.For a given type and energy of incident radiation, the damage is mostly determined by the elemental composition and the thickness of each layer of the cell.The second step is to simulate the impact of this damage on the device performance.This will depend on the optoelectronic properties of each layer and the resulting changes to these properties from the radiation damage.
In this study, we propose and demonstrate the combination of established radiation damage models with state-of-the-art PSC optoelectronic device simulations to investigate proton-induced degradation of PSC performance.[23] This radiationinduced defect distribution is then incorporated into a PSC semiconductor device model using the commercial finite-element solver COMSOL Multiphysics. [24]Calculations are validated against experimental data from the literature, demonstrating the potential for predicting solar cell performance as a function of proton energy and fluence.This approach provides a tool to investigate the role of chemical composition on the radiation tolerance of perovskite materials and to compare the radiation blocking properties of different substrates, electrodes, and charge transport layers.We also compare performance differences between cells exposed to radiation from the front (sunward) side, and the rear side, as this has practical implications for interpreting lab-based studies where rear-side radiation is common to avoid absorption in thick glass superstrates.Finally, we demonstrate how the proposed method can incorporate a distribution of incident particle energies to predict the EOL performance of a PSC used for space mission.

Results and Discussion
Figure 1a describes the steps in our approach based on SRIM particle simulations and COMSOL device models.While SRIM models the cell in terms of component materials, densities, and other parameters related to particle radiation, COMSOL models the cell in terms of optoelectronic properties.After obtaining the defect profiles from SRIM for a range of proton energies, the total radiation-induced defect profile can be calculated for a mission based on the expected proton spectrum and fluence.This defect profile is then transferred to the optoelectronic model to evaluate the impact of the generated defects on the cell performance.Figure 1b shows an example of the model with a defect production rate profile obtained from SRIM superimposed on the photogeneration rate within the perovskite layer.
Before discussing radiation and optoelectronic modeling, we first clarify our key assumptions in the model.As all layers in the perovskite cell structure are exposed to the particle radiation, defects could be generated at any point within the cell.However, photogenerated electron-hole pairs are only present in the perovskite (active layer).Therefore, we only consider the electronic impact of defects formed in the perovskite active layer and ignore potential radiation damage to charge transport layers or electrodes.We assume all other layers are not impacted to make sure that radiation-induced defects within perovskite layers are fairly compared.Additionally, radiation-induced darkening of substrates [25] (a particular issue with glass) is not considered to allow a fair comparison between radiation from different sides of the cell.Finally, all vacancies predicted by the SRIM simulation are treated as a single defect type defined by a discrete energy level in the bandgap.While it would be possible to assign different energy levels to each vacancy type (I, Pb, H, etc.), there is insufficient reliable data to do so with confidence.The single-level approximation here can be thought of as representing an "effective" defect energy level [26] approximating the combined contribution from different defect types.These will also be discussed in the following sections.

Vacancy Distributions from Stopping and Range of Ions in Matter (SRIM) Simulations
Radiation damage simulations involve the solution of particle transport equations to determine the interaction between the incoming particles and the materials through which they pass (in this case the different layers of the solar cell).Simulation codes are based on either statistical Monte Carlo methods (MCM) or deterministic methods (DM), with the former being more widely used due to their versatility, although this comes at the cost of computational intensity.Examples of MCM-based tools include CREME96, [27] Integrated Tiger Series (ITS), [28,29] NOVICE, [30] MCNP, [31] MCNPX, [32] Geant4, [33] and SRIM.[23] Hence it is selected for this study.
The purpose of the SRIM simulations is to generate a depthdependent defect profile in the perovskite active layer, accounting for any particle scattering or absorption in the surrounding layers.This requires a material composition model for the whole PSC structure.Structure and parameters for each layer are listed in Table S1, Supporting information.SRIM uses a Monte Carlo approach, based on a binary collision approximation, that provides a rigorous treatment of elastic scattering to determine the energy loss of the incident ion to target primary knock-on atoms (PKA) along the ion path.Ion-induced damage profiles can be calculated via two different approaches, depending on the calculation time and accuracy requirements.Here we use the full damage cascade option, as previous comparisons with experimental data have shown this to provide a more accurate determination of damage energy, number of displacements, and damage depth profiles compared to the quick calculation option. [34]Default SRIM values were used for the threshold displacement energies of the component atoms as used by Messenger et al. [11] Before simulating the defect profile in a complete cell stack in Section 2.3, we first consider proton irradiation of two perovskite films (inorganic cation perovskite: CsPbI 2 Br and organic cation perovskite: FA 0.86 MA 0.14 PbI 3 ) to isolate the effects of proton energy and perovskite composition.It's well known that ion migration will happen when voltage is applied on PSCs (or light exposure).Zai et al. [35] pointed out that perovskites without MA þ could suppress light-induced ion migration.Senocrate et al. [36] observed that MA 0.8 FA 0.2 PbI 3 exhibited reduced ionic migration 30 times comparing to pure MAPbI 3 .Therefore, we could assume that ion migration in two perovskite components is neglectable as the concentration of MA þ in the component is very low (or none).Thus, we only consider that radiation-induced defects from a full damage cascade calculation include the vacancy production rate for each type of atom in the sample, as shown in Figure 2 for a 1 μmthick perovskite film.For a more realistic structure, we include a 100 nm gold electrode layer on top of the perovskite, which acts as a thin shield providing some limited radiation protection.These results reveal two key observations.First, the amount and distribution of the damage depend strongly on the incident proton energy: lower-energy protons cause more damage, and the damage is at a shallower depth compared to higher energies.This result is also confirmed by Miyazawa Y. et al. [9] Along their tracks, protons lose their energy.At a certain point, they will completely stop and become trapped inside the material causing damage at that location (in addition to interacting with target atoms along their track).Thus, the damage produced per unit path length increases as the proton energy decreases.As a result, when a low-energy proton is stopped in a solar cell, a large amount of damage is concentrated at the end of the proton track.This phenomenon is clearly visible in the case of low-energy protons in Figure 2a,e (considering total damage only).This behavior suggests that thinner solar cell technologies are likely to be more tolerant to proton irradiation, as low-energy protons are more likely to pass straight through the cells.
On the other hand, higher-energy protons pass through the sample and create a small number of defects, as shown in Figure 2d,h.Thus, thin perovskite films are relatively insensitive to very high proton energies such as 20 MeV [37] or 68 MeV. [15,16]o, to create significant damage at such energies, experiments require very large fluences, resulting in unrealistic sample heating as mentioned before.
These results also reveal significant differences in vacancy formation for different elements in the perovskite film, which also depends on proton energy.In Figure 2b, close to the irradiated surface, iodide vacancies dominate and continue to increase to a depth of %500 nm before decreasing again.Hydrogen vacancies have a lower density at the surface but become dominant at depths >400 nm.This observation indicates that lower-energy protons interact more efficiently with low mass atoms, while higher-energy protons are more likely to cause heavy atom vacancies.This is confirmed by Figure 2e-g with a different perovskite composition of CsPbI 2 Br, which is heavier than FA 0.86 MA 0.14 PbI 3 .Note that the number of iodide vacancies is far higher than other heavy atoms as its ratio in perovskite is higher.For example, the number of iodine atoms is roughly three times higher than lead (Pb) in organic cation perovskite (a -d); thus, the iodide vacancy density is also %3 times higher.
Overall, lower proton energies (<50 keV) cause more damage on the lightweight material while higher-energy ones are more harmful to the material with higher average atomic mass.Considering a full range of proton energies (from 10 keV to 1 MeV), we clearly see that the material with higher average atomic mass receives more damage than the lighter material.Thus organic-inorganic perovskites may be naturally more radiation tolerant than fully inorganic perovskites (such as CsPbI 2 Br in this case) due to their lighter elemental composition.This contrasts to the generally higher thermal and environmental stability of inorganic perovskites.Furthermore, organic cation perovskites are likely to have higher proton irradiation tolerance than other thin-film solar cells such as GaAs, CdTe, and CIGS which can also offer high-power-to-weight ratios for space applications.

Solar Cell Performance Calculations with COMSOL Multiphysics
In this section, we model planar PSCs with two different perovskite compositions (same as Section 2.1) to fit experiment results.These models are then used in Section 2.3 to predict the impact of proton irradiation on the different cell structures.
To predict the PSC performance degradation caused by radiation-induced defects (atomic vacancies), we used a wellestablished, 1D optoelectronic device model implemented in the semiconductor module of COMSOL Multiphysics.Details of the model implementation have been described in several previous works and will not be repeated here. [24]We note that the contribution of mobile ions is omitted in this study to focus on recombination-active defects caused by radiation damage; however, future studies should include mobile ionic species as these may also be affected by proton radiation.In particular, ionic vacancies are responsible for currentvoltage hysteresis and other slow transient effects observed in PSCs.
Two high-efficiency PSC designs with different perovskite compositions are chosen for this study: a fully inorganic perovskite CsPbI 2 Br [38] and an organic-inorganic perovskite FA 0.86 MA 0.14 PbI 3 [39] and the reported current-voltage curves are used to define the initial (unirradiated) simulation parameters.As we are interested in how perovskite chemical composition affects the radiation tolerance, it is desirable to minimize changes to other simulation parameters that may affect the comparison.In particular, both cells are modeled with the same initial defect density (bulk and surface) and as many as possible other parameters are in common.As the energy arrangement will strongly affect the Voc and fill factor (FF), we chose to fix the energy offset between perovskite and transport layers (both sides) and also assume that the energy offset is unchanged during proton radiation.To do that, the electron transport layer's parameters and the electron affinity of the active layers (perovskite) were fixed.To have the same energy-level offset between perovskite and hold transport layer, electron affinity of hole transport layers was changed based on the perovskite bandgap while their bandgap was kept the same.The photogeneration rate used in the simulations was scaled to match the experimental shortcircuit current (Jsc) values.Although the fit material parameters may not be accurate values for the fabricated cells, they are within a reasonable range for many PSCs, and thus, the simulated trends with proton exposure are considered representative of high-efficiency PSCs.The full list of device parameters can be found in Table S2, Supporting information, and a comparison of experimental and simulated current voltage curves is provided in Figure S1, Supporting information.
The two reference cells chosen for this study were not evaluated for space applications, so experimental device performance was only available for AM1.5 G illumination.Therefore, to estimate the performance under AM0 operation, we apply a generation scaling factor to all two cells following Soucase et al.'s results. [40]The scaled current voltage curves for the two PSC types are plotted in Figure 3 representing the simulated unirradiated (beginning of life-BOL) performance of the cells.

Method Validation and Comparison of Common Perovskite Compositions
We first adjust our model parameters and validate our approach by reproducing (by simulation) the results reported by Malinkiezicz et al. for MAPbI 3 perovskite cells exposed to 100 keV proton irradiation. [13]This work was selected as a reference because the measurements were taken at a low proton energy, and a reasonable low flux, and thus self-annealing effects should be minimized.In the article, MAPbI 3 PSCs were exposed to 100 keV proton radiation with fluences of 3e10, 3e11, and 3e12 particles cm À2 .We note that different cells were used for each proton fluence, so there was some variability in the experimental data.However, the normalized performance trends with fluence are assumed to be representative.The experimental results are labeled as experimental (Exp) data in Figure 4 while the results calculated by our method are noted as calculation (Cal) values.
To simulate degradation of the cell due to proton radiation, we first fit the COMSOL device model to reproduce the J-V curve of the unirradiated cell as described in the previous section (Figure S2, Supporting information).Next, the depth-dependent total vacancy production rate (defects cm À3 .protonÀ1 ) was calculated in SRIM for the cell structure shown in Figure 4a with protons incident from the rear side.From this, the radiation-induced defect profile in the perovskite layer was obtained by multiplying the vacancy production rate by the desired fluence.The defect profile (inset image-Figure 4b) was then added to the optoelectronic model (COMSOL).As discussed in Section 2.2, we treated all radiation-generated vacancies as equivalent and assigned them a single "effective" defect energy level in the device simulations to represent their contribution to carrier recombination and trapping in the perovskite active layer.Due to low formation energy, various charge states , and higher atomic percentage, halide atoms create main trapping states for both electrons   [13] and holes [37,41] while other components contribute far less defects after radiation.We, therefore, assume the same defect energy level for the studying perovskites.The defect energy level was adjusted as a fitting parameter to match the observed experimental trend in the cell performance parameters (V oc , J sc , FF, and PCE) (Figure S2b, Supporting information).The best fit was found for a defect energy level of 0.1 eV below the conduction band, and the modelled cell performance parameters are shown in Figure 4b and compared to the experimental results.It's noted that in our simulation, the defect level of 0.1 eV below the conduction band shows the same result as the defect level is of 0.1 eV above the valance band.Although this approximation is insufficient to validate the individual defects within perovskites, it shows that our proposed method can predict realistic degradation trends with proton fluence, relative to the initial device performance.We therefore choose to set the defect energy level to 0.1 eV for the remainder of this article to allow direct comparison between the different perovskite compositions.This shallow defect assumption is supported by previous studies of intrinsic defects in perovskite materials which found that atomic vacancies typically result in defect states close to the conduction or valance bands. [41,42]n this example, the protons are incident from the rear of the cell, as is common in lab-based experiments of PSCs to avoid the strong radiation absorption in the glass substrate and/or glass darkening during irradiation.As a result, the maximum defect density coincides with the maximum charge carrier generation rate close to the front of the perovskite layer, as shown in Figure 1b and inset in Figure 4b.This suggests that proton irradiation from the rear of a cell may degrade cell performance more severely than radiation from the front side.We explore this, and the implications for interpreting lab results, further below.
After validating our simulation approach, we can use it to compare the predicted radiation tolerance of PSCs incorporating the two selected perovskite compositions CsPbI 2 Br and FA 0.86 MA 0.14 PbI 3 (Figure 3). Figure 5 shows the predicted trends in V oc , FF, J sc , and PCE for each type of cell as a function of proton fluence for a proton energy of 100 keV.As each cell type has a different starting efficiency, performance is plotted as the "remaining factor" which is the ratio between the simulated

post-irradiation performance parameters over the initial values (before radiation).
Both samples experience similar trends in all optoelectronic parameters including V oc , J sc , FF, and PCE.We note that FA 0.86 MA 0.14 PbI 3 is slightly more stable than CsPbI 2 Br in terms of J sc and FF while the V oc trend is similar.As a result, the organic perovskite exhibits a higher PCE tolerance to radiation which is consistent with the previous SRIM simulations showing that the inorganic perovskite suffers higher radiation damage.Note that the V oc of the inorganic perovskite degrades faster than that of the organic perovskite in absolute value.However, because of a higher initial value (1.31 vs 1.15 V), the relative V oc trend is similar for both devices.
The simulation results in Figure 5 predict that for a fluence of 1e14 proton cm À2 100 keV protons, the FA 0.86 MA 0.14 PbI 3 and CsPbI 2 Br PSCs would degrade to 65% and 62% their initial efficiencies, respectively, without any shielding.In contrast, Li, J. et al. [43] reported that GaAs/Ge solar cells degrade to less than 50% of their initial performance at a dose of 1e12 proton cm À2 100 keV protons.Additionally, Wang, R. et al. [44] reported that a triple-junction solar cell (GaInP/GaAs/Ge) reduced to roughly 30% of its initial efficiency and failed completely at a fluence of 1e13 proton cm À2 (100 keV protons).8,44,45] They also suggest that organic cation perovskite devices may be more stable than their inorganic counterparts, all else being equal.Thus, the following sections will focus on organic cation PSCs.

Impact of Proton Energies and Direction of Radiation
In this part, we investigate the effect of different proton energies and the direction of incident radiation on PSC performance.
Figure 6a shows the remaining PCE factor plotted as a function of proton energy and fluence for a FAMAPbI 3 cell exposed to protons from the rear.The proton energy range of 10 keV-1 MeV is chosen as this is the approximate range of energies experienced in GEO (Figure S3, Supporting information).We observe that %50 keV protons cause the highest performance loss, as can also be seen in the upper half of Figure 6b (red curve) which plots the remaining PCE factor as a function of proton energy for a fluence of 1e13 protons.cmÀ2 .The blue curve in the lower half of Figure 6b shows the total vacancy production rate as a function of proton energy, integrated across the perovskite layer.The vacancy peak occurs for proton energies of 40-50 keV, about 10 keV below the energy that causes the highest loss in cell performance.We will discuss the reasons for this offset shortly.
The proton energy that produces the most vacancies is a function of the protons' ability to penetrate the different layers of the cell.For energies <<50 keV, most protons are blocked by the outer layers of the cell (such as the gold electrode) and cannot reach the active layer, as seen in the proton scattering diagram for 10 keV protons (Figure 6d).In contrast, protons with energies >>50 keV pass right through the cell with negligible impact, as seen for 1 MeV particles in Figure 6f.Therefore, the maximum number of vacancies are generated for the lowest energy at which most protons reach the perovskite.This depends on the device structure and specifically the density and thickness of the layers between the incoming protons and the perovskite.Further increasing the proton energy above this threshold results in more protons passing through the active layer, reducing the vacancy generation rate.
As discussed previously, the overlap of the proton-generated defect profile and the photon-generated carrier profile has a significant impact on the performance of radiated cells.To illustrate this, we plot in Figure 6b-red curve and Figure 6c the case of proton irradiation from the front of the cell.The idea of this comparison is illustrated in Figure S4, Supporting Information.To allow a direct comparison between front and rear irradiation, we use the same cell structure and photogeneration profile to have the same "unradiated" performance.For the defect profiles, we inverted the defect profile in case of rear radiation to have the front radiation case to ignore the different layer structure on the front and rear of the cell as the material difference surely makes a different defect profile.We note that including the thick glass superstrate in such a comparison would be pointless since even 1 MeV protons can only penetrate %30-40 μm into glass.
Figure 6b shows that in the case for front irradiance, lowenergy protons at %30 keV produce the most damage, while for rear irradiance, protons at %50 keV are most impactful.This energy offset can be understood by considering the overlap of defect and carrier generation profiles.At lower energies, damage is concentrated where the protons enter the active region, as most of them are stopped in the first few tens of nm (Figure 6d  and 7).Thus, the highest overlap between defects and charge carriers occurs when protons are incident through the front of the cell (Figure 7).At higher energies, protons penetrate deeper, and defect density increases with depth as they slow down (Figure 6e, and 7), in which case the highest overlap with charge carriers occurs for rear-side radiation.As a result, the proton energies that cause the worst cell degradation do not coincide precisely with the energy that produces the most vacancies (defects) in the perovskite (blue curve, Figure 6b).
It is notable that we are considering single-proton energy radiation, which shows a huge difference between different proton energies and radiation directions.Therefore, for lab-based tests which normally consider single-proton energy, the radiation direction is a very important factor, especially at low proton energies.
As described in the introduction, standard methods for predicting EOL performance of solar cells require the total mission radiation dose (energy and fluence) to be converted to an equivalent fluence of single-energy particles (protons or electrons).In the NRL approach, this is derived from the NIEL and vacancy production rate. [14,46,47]However, as shown above, the NIEL or total vacancy production rate is not sufficient to predict final cell performance; the direction and energy of the incident protons is also important.Hence, we demonstrate in the next section how our simulation-based method can be used to subdivide and combine the influence of protons with different energies and incident directions to calculate EOL under space radiation conditions.

GEO-Spectrum Fluence Equivalent
In contrast to the previous sections and published studies on PSCs for space applications, in this section we introduce a method to predict cell performance under a full GEO proton spectrum distributed between both sides of the cell.Such a situation could occur if PSCs are integrated into ultralightweight flexible arrays where the rear of the cell may not be protected from incident radiation.In real space irradiation conditions, the incident proton flux is largely omnidirectional, which results in a different damage distribution compared to normally incident radiation typically generated in the lab.Here, we also restrict our simulations to normally incident radiation and consider two limiting situations: 100% radiation from the front and 100% radiation from the rear.These are considered the worst cases in terms of device degradation as nonnormal incidence will typically result in lower defect densities in the active layer of the cell. [48]o simplify the calculation process, we divide the proton energy range from 10 keV to 1 MeV into 10 equal subranges on a logarithmic energy scale (Figure S3, Supporting information).For each discrete energy range, we calculate the resulting defect profile as a function of fluence, and these are then combined into a total defect distribution according to the relative proton fluence at each energy.The total defect distribution is then used in the device simulation model to calculate device performance as a function of mission time.Further details of the calculations are provided in the Supporting Information.For the GEO proton energy distribution considered in Figure 8b, the cell displays a marginally higher tolerance to proton radiation from the rear side, relative to the front side.This again confirms the importance of the spatial overlap between defect and generation profiles (Figure 8a) to the degradation of the cell efficiency.We note, however, that the difference between front and rear irradiation performance is much smaller than observed in Figure 6b for monoenergetic proton radiation.This is due to the relatively uniform defect profile produced by poly-energetic irradiation: lower energy protons create most defects close to the irradiated side of the cell, whereas defects produced by higher-energy protons increase with depth.The combination results in defects distributed almost uniformly across most of the active layer (Figure 8a).For this reason, single-energy lab-based experiments should be conducted at energies that produce "uniform damage" through the cell [43] with the defect generation rate "flat," as shown in Figure 8b.
In Figure 8b, despite the worst-case scenario of normal incidence without any shielding, the model predicts that after 2 years (24 months) the cell could still retain %45% of its initial performance.This is a much longer lifetime than existing space cells under the same radiation conditions.For example, after only 30 days in GEO, the power output of an unshielded AZUR 3G28 multijunction space cell would fall by more than 70%, and a typical GaAs solar cell would lose more than 90% of its power output in the same period (based on SPENVIS simulations [49] ).

Conclusion
In this work, we introduce a new method to predict the degradation of PSCs under proton radiation based on the combination of ion scattering and optoelectronic device simulations.This approach can supplement time and resource-intensive experimental-based studies which have so far been limited by narrow testing conditions, small sample numbers, and device degradation during transport and storage.Additionally, our method can predict the degradation of cells under more realistic radiation conditions such as the full proton spectrum in GEO.We apply the method to compare the performance of all-inorganic and organic-inorganic hybrid perovskites under a range of proton energies and fluences.By calibrating our model to experimental data, we predict that FAMAPbI 3 -based PSCs have a better radiation tolerance than CsPbI 2 Br-based devices and can retain up to %80% of their initial power output after a fluence of 1e13 p cm À2 of 100 keV proton radiation or %45% of their initial output after 2 years in GEO without protective shielding.We also demonstrate that the spatial overlap of charge carriers and proton-induced defects must be considered when assessing radiation tolerance, and this is strongly dependent on the proton energy and incident direction relative to the light.Thus, radiation direction is a crucial factor to be considered for a single-proton energy radiation experiment.Our results also support previous findings that PSCs may offer proton radiation tolerance several orders of magnitude higher than state-of-the-art space cells based on III-V materials, although more rigorous and carefully designed experimental studies are required to confirm and quantify this.

Figure 1 .
Figure 1.a) Flow chart describing the calculation method for space solar cell EOL prediction.b) Schematic of basic planar perovskite cell with generation rate at AM0 and proton radiation from the rear of a cell.

Figure 2 .
Figure 2. Vacancy production rate within perovskite layer of a-d) FA 0.86 MA 0.14 PbI 3 and e-h) CsPbI 2 Br with 100 nm of gold on top.

Figure 4 .
Figure 4. a) Cell structure and radiation direction and b) result comparison for method validation with experimental data from Malinkiezicz et al.[13]

Figure 6 .
Figure 6.a) Normalized PCE of the FAPbI3 cell at different proton energies and fluences radiated from rear side.b) Comparison of normalized PCE of the FAPbI3 cell at the same fluency of 1e13 particles and difference in radiation sides.c) Normalized PCE of the FAPbI3 cell at different proton energies and fluences radiated from the front side.Vacancy production within solar cell layers under d) 10 keV; e) 100 keV; and f ) 1 MeV proton from the back side.

Figure 7 .
Figure 7.Comparison of photogeneration rate (red curve) and vacancy production rate for rear irradiation a) and front irradiation b) for different proton energies.