Optimization of Inverted All-Inorganic CsPbI 3 and CsPbI 2 Br Perovskite Solar Cells by SCAPS-1D Simulation

: Perovskite solar cells (PSCs) have substantially increased their power conversion efﬁciency (PCE) to more than 25% in recent years. However, the instability of these devices is still a strong obstacle for their commercial applications. Recently, all-inorganic PSCs based on CsPbI 3 and CsPbI 2 Br as the perovskite layer have shown enhanced long-term stability, which makes them potential candidates for commercialization. Currently, all-inorganic PSCs with inverted p-i-n conﬁguration have not yet reached the high efﬁciency achieved in the normal n-i-p structure. However, the inverted p-i-n architecture has recently drawn attention of researchers because it is more suitable to prepare tandem solar cells. In this work, a theoretical study of inverted p-i-n all-inorganic PSCs based on CsPbI 3 and CsPbI 2 Br as the perovskite layer was carried out using SCAPS-1D software (ver. 3.3.09). The performance of different architectures of PSC was examined and compared by means of numerical simulations using various inorganic materials as the hole transport layer (HTL) and the electron transport layer (ETL). The results reveal that CuI and ZnO are the most suitable as HTL and ETL, respectively. In addition, the performance of the devices was signiﬁcantly improved by optimizing the hole mobility in CuI as well as the thickness, doping density, and defect density in the absorber layer. Maximum efﬁciencies of 26.5% and 20.6% were obtained under optimized conditions for the inverted all-inorganic CsPbI 3 - and CsPbI 2 Br-based PSCs, respectively. These results indicate that further improvements in the performance of such devices are still possible


Introduction
The increase in energy consumption in recent years has promoted the use of new technologies based on renewable energy sources to generate electricity, with solar energy being one of the most promising alternatives. In this way, the study of solar cells, devices capable of converting light from the sun directly into electricity, is extremely important today. The study of microscopic properties of materials, in addition to advances in the manufacturing processes of the photovoltaic devices, has provided a path to develop new technologies in solar cells with higher performance and shorter processing time.
One of the developments that have gained special relevance in the last decade are perovskite solar cells (PSCs), which have emerged as a technology with the potential to Solar 2022, 2 561 acceptor densities, and defect densities in the perovskite layer to optimize the design of the structure and to enhance the efficiency of these inverted all-inorganic PSCs.

Electronic Structure Calculations
The electronic band structure of the cubic perovskite CsPbI 3 with space group Pm-3m and CsPbI 2 Br with space group P4/mmm was studied from the first principles theory. These calculations are based on the Density Functional Theory (DFT) [34], and the selfconsistent Kohn-Sham equation was solved using the Full-Potential Linearized Plane-Wave method (FP-LAPW) implemented in the Wien2k code [35,36]. The exchange-correlation (XC) functional was described using the Perdew-Burke-Ernzerhof (PBE) parametrization of the Generalized Gradient Approximation (GGA) [37]. In order to improve the electronic band structure of the compounds, the hybrid XC functional proposed by Heyd-Scuseria-Ernzerhof (HSE06) [38] was used. The muffin-tin radii employed was 2.0 bohr for the Cs, Pb, Br, and I atoms, whereas the parameter related with basic-set size was set to R MT × K max = 9 (RMT is the smallest muffin-tin radii and K max is related with the planewave cutoff). Regarding the reciprocal space, this was sampled using a dense mesh grid of 12 × 12 × 12 k points in the irreducible Brillouin zone.
The theoretical lattice parameters obtained were 6.398 Å and 6.0023 Å for the CsPbI 3 and CsPbI 2 Br, respectively, which are in agreement with experimental values reported [39][40][41]. In order to obtain an accurate description of the electronic structures of the CsPbI 3 and CsPbI 2 Br perovskites, we calculated the total and projected density of state (DOS) and the electronic band gap using the HSE06 hybrid functional, as seen in Figures 1 and 2, respectively. Direct band gaps of 1.78 eV and 1.88 eV were found for the CsPbI 3 and CsPbI 2 Br, respectively, in excellent agreement with the experimental values reported: 1.76 eV [42], 1.77 eV [43], and 1.79 eV [44] for the CsPbI 3 , and 1.82 eV [13], 1.86 eV [45], and 1.92 eV [46] for the CsPbI 2 Br. The band gap of the CsPbI 3 perovskite is formed between the VBM, p-I orbital, and the CBM, p-Pb orbital. In the case of CsPbI 2 Br, the band gap is formed between the VBM, p-I, and p-Br orbitals, and the CBM, p-Pb orbital. For both compounds, the orbitals of the Cs atom are located far of the Fermi energy, as is shown in Figures 1 and 2.

Device Simulations
Device simulations were performed with SCAPS-1D software [47], which is widely used and recognized by the scientific community related to PSCs [3,[48][49][50][51][52][53]. This software numerically solves the system of the Poisson and the continuity equations for electrons and holes. The output parameters such as short-circuit current density (J SC ), open circuit voltage (V OC ), power conversion efficiency (PCE), maximum power point (P MAX ), fill factor (FF), and external quantum efficiency (EQE) can be calculated using the SCAPS-1D software, in order to obtain the response of the device under different design and operating conditions. Figure 3 shows the configuration of the all-inorganic PSC used in this work, which consists of an inverted structure ITO/i-HTL/CsPbI x Br 3−x /i-ETL/Ag, for x equal to 2 and 3, where light enters through the i-HTL. The standard AM1.5G spectrum has been used. Tables 1-3 summarize the main parameters used in the simulations for the perovskite layers, and for the materials chosen as i-HTL and i-ETL, respectively. Here N A and N D are the acceptor and donor density, respectively; ε r is the relative permittivity;  Tables 1-3 summarize the main parameters used in the simulations for the perovskite layers, and for the materials chosen as i-HTL and i-ETL, respectively. Here NA and ND are the acceptor and donor density, respectively; εr is the relative permittivity; Ӽ is the electron affinity; EG is the band gap energy; μn and μp are the electron and hole mobilities, respectively; NT is the defect density; and NC and NV are the effective conduction and valence band density of states, respectively. The band gap energy and NC and NV values of Table  1 were obtained by means of DFT-based calculations. The rest of the values in Tables 1-3 are based on experimental and theoretical studies recently reported in the literature [51,[54][55][56]. The absorption coefficient (α) was calculated from the Beer-Lambert law α = 2.303A/t [57], where A and t are the absorbance and thickness of film (350 nm), respectively. These were obtained from Wang 2020 [14] for the CsPbI3 layer and from Sutton 2016 [13] for the CsPbI2Br layer. The work functions of the front and back contacts are 4.7 eV (ITO) and 4.26 eV (Ag), respectively [58]. Table 1. Physical parameters of the perovskite material used in the simulation. is the electron affinity; E G is the band gap energy; µ n and µ p are the electron and hole mobilities, respectively; N T is the defect density; and N C and N V are the effective conduction and valence band density of states, respectively. The band gap energy and N C and N V values of Table 1 were obtained by means of DFT-based calculations. The rest of the values in Tables 1-3 are based on experimental and theoretical studies recently reported in the literature [51,[54][55][56]. The absorption coefficient (α) was calculated from the Beer-Lambert law α = 2.303A/t [57], where A and t are the absorbance and thickness of film (350 nm), respectively. These were obtained from Wang 2020 [14] for the CsPbI 3 layer and from Sutton 2016 [13] for the CsPbI 2 Br layer. The work functions of the front and back contacts are 4.7 eV (ITO) and 4.26 eV (Ag), respectively [58].  The energy level diagram of the i-ETL and i-HTL materials used in the simulation is shown in Figure 4. These levels play an important role in the performance of the device because they have a significant control on photocarrier transport. In order to facilitate proper electron transport, the conduction band minimum of the perovskite layer should be higher than that of the ETL. Similarly, the valence band maximum of the perovskite layer should be lower than that of the HTL for proper hole transport [59].

Device Simulations
Device simulations were performed with SCAPS-1D software [47], which is widely used and recognized by the scientific community related to PSCs [3,[48][49][50][51][52][53]. This software numerically solves the system of the Poisson and the continuity equations for electrons and holes. The output parameters such as short-circuit current density (JSC), open circuit voltage (VOC), power conversion efficiency (PCE), maximum power point (PMAX), fill factor (FF), and external quantum efficiency (EQE) can be calculated using the SCAPS-1D software, in order to obtain the response of the device under different design and operating conditions. Figure 3 shows the configuration of the all-inorganic PSC used in this work, which consists of an inverted structure ITO/i-HTL/CsPbIxBr3−x/i-ETL/Ag, for x equal to 2 and 3, where light enters through the i-HTL. The standard AM1.5G spectrum has been used. Tables 1-3 summarize the main parameters used in the simulations for the perovskite layers, and for the materials chosen as i-HTL and i-ETL, respectively. Here NA and ND are the acceptor and donor density, respectively; εr is the relative permittivity; Ӽ is the electron affinity; EG is the band gap energy; μn and μp are the electron and hole mobilities, respectively; NT is the defect density; and NC and NV are the effective conduction and valence band density of states, respectively. The band gap energy and NC and NV values of Table  1 were obtained by means of DFT-based calculations. The rest of the values in Tables 1-3 are based on experimental and theoretical studies recently reported in the literature 1 were obtained by means of DFT-based calculations. The rest of the values in Tables 1-3 are based on experimental and theoretical studies recently reported in the literature [51,[54][55][56]. The absorption coefficient (α) was calculated from the Beer-Lambert law α = 2.303A/t [57], where A and t are the absorbance and thickness of film (350 nm), respectively. These were obtained from Wang 2020 [14] for the CsPbI3 layer and from Sutton 2016 [13] for the CsPbI2Br layer. The work functions of the front and back contacts are 4.7 eV (ITO) and 4.26 eV (Ag), respectively [58]. Table 1. Physical parameters of the perovskite material used in the simulation.

Parameters NiO Cu 2 O CuSCN CuI
Thickness (nm) 25 25 25 25 11.7 7.11 10 6.5  Tables 1-3 summarize the main parameters used in the simulations for the perovskite layers, and for the materials chosen as i-HTL and i-ETL, respectively. Here NA and ND are the acceptor and donor density, respectively; εr is the relative permittivity; Ӽ is the electron affinity; EG is the band gap energy; μn and μp are the electron and hole mobilities, respectively; NT is the defect density; and NC and NV are the effective conduction and valence band density of states, respectively. The band gap energy and NC and NV values of Table  1 were obtained by means of DFT-based calculations. The rest of the values in Tables 1-3 are based on experimental and theoretical studies recently reported in the literature [51,[54][55][56]. The absorption coefficient (α) was calculated from the Beer-Lambert law α = 2.303A/t [57], where A and t are the absorbance and thickness of film (350 nm), respectively. These were obtained from Wang 2020 [14] for the CsPbI3 layer and from Sutton 2016 [13] for the CsPbI2Br layer. The work functions of the front and back contacts are 4.7 eV (ITO) and 4.26 eV (Ag), respectively [58]. Table 1. Physical parameters of the perovskite material used in the simulation.

Parameters ZnO TiO 2 SnO 2
Thickness (nm) 25 25 25 3 × 10 18 3 × 10 18 3 × 10 18 ε r 9 9 9 Solar 2022, 2, FOR PEER REVIEW Tables 1-3 summarize the main parameters used in the simulations for the perovskite layers, and for the materials chosen as i-HTL and i-ETL, respectively. Here NA and ND are the acceptor and donor density, respectively; εr is the relative permittivity; Ӽ is the electron affinity; EG is the band gap energy; μn and μp are the electron and hole mobilities, respectively; NT is the defect density; and NC and NV are the effective conduction and valence band density of states, respectively. The band gap energy and NC and NV values of Table  1 were obtained by means of DFT-based calculations. The rest of the values in Tables 1-3 are based on experimental and theoretical studies recently reported in the literature [51,[54][55][56]. The absorption coefficient (α) was calculated from the Beer-Lambert law α = 2.303A/t [57], where A and t are the absorbance and thickness of film (350 nm), respectively. These were obtained from Wang 2020 [14] for the CsPbI3 layer and from Sutton 2016 [13] for the CsPbI2Br layer. The work functions of the front and back contacts are 4.7 eV (ITO) and 4.26 eV (Ag), respectively [58].   The energy level diagram of the i-ETL and i-HTL materials used in the simulation is shown in Figure 4. These levels play an important role in the performance of the device because they have a significant control on photocarrier transport. In order to facilitate proper electron transport, the conduction band minimum of the perovskite layer should be higher than that of the ETL. Similarly, the valence band maximum of the perovskite layer should be lower than that of the HTL for proper hole transport [59].

Results and Discussion
Using the values of Tables 1-3, an analysis of the twelve different possible combinations (i-ETL/i-HTL) of the inverted all-inorganic PSCs was carried out by means of SCAPS-1D software for each perovskite layer under study. The results of the output parameters

Results and Discussion
Using the values of Tables 1-3, an analysis of the twelve different possible combinations (i-ETL/i-HTL) of the inverted all-inorganic PSCs was carried out by means of SCAPS-1D software for each perovskite layer under study. The results of the output parameters (PCE, V OC , J SC , and FF) are summarized in Table 4. The first row in Table 4 corresponds to the materials used in [14]. The value of PCE of 14.03% obtained from simulations for the ZnO/NiO combination can be considered as a good approximation of the experimental result of 13.90% presented in Table 4 for the control device with the non-passivated perovskite film. It can also be observed in Table 4 that for the CsPbI 3and CsPbI 2 Br-based PSCs, the V OC values remain almost unchanged for all considered cases. On the other hand, PCE is the parameter with the greatest variations between their minimum and maximum values, approximately 24% and 14%, for the CsPbI 3 -and CsPbI 2 Br-based PSCs, respectively. For ETL materials, the highest PCE values were obtained for ZnO, while the lowest PCE values were obtained for TiO 2 . TiO 2 and ZnO have very similar properties (band structure, electronic affinity, relative permittivity, band gap energy, among others). However, TiO 2 has higher N C and N V , and therefore higher intrinsic carrier concentration than ZnO. The larger the intrinsic carrier concentration, the higher the recombination rate and the smaller the carrier collection when the electric field is high (at voltages close to V OC ). As a consequence of the aforementioned effects, lower FF and PCE were obtained for TiO 2 compared with ZnO. Therefore, TiO 2 is not the optimal material as ETL for CsPbI 3 and CsPbI 2 Br perovskite solar cells as considered in this work.
On the other hand, the choice of HTL also influences the performance of the device. The band alignment of the HTL with the perovskite layer and the intrinsic carrier concentration of the HTL material are key factors as well as the band gap and the hole mobility. The energy level diagram shown in Figure 4 indicate that there are good band alignments between the valance band of perovskite and the four HTL materials considered in this work. However, Table 4 shows that for a given ETL, the lowest PCE values were obtained for Cu 2 O, while the highest PCE values were obtained for CuI. Although Cu 2 O and CuI have similar band alignment and hole mobility, Cu 2 O has higher N C and N V , and therefore a higher intrinsic carrier concentration and recombination rate than CuI. Cu 2 O also has the lowest band gap. Since light enters through the HTL in a direct (p-i-n) structure, some ultraviolet light does not reach the perovskite layer in Cu 2 O, resulting in the lowest J CC and PCE.
The highest PCE values of 14.13% (for CsPbI 3 ) and 12.35% (for CsPbI 2 Br) were obtained for the ZnO/CuI combination. These materials have a suitable band alignment with the active layer. For this reason, ZnO and CuI can be considered as good options for i-ETL and i-HTL, respectively.
In the rest of this work, PSCs with the inverted structure of ITO/CuI/CsPbI 3 (CsPbI 2 Br) /ZnO/Ag are studied in detail, using different hole mobilities in CuI and different thicknesses, acceptor densities, and defect densities for the perovskite layers. Figure 5 shows the PCE as a function of hole mobility of CuI HTL for CsPbI 3 and CsPbI 2 Br PSC. In both cases, PCE is gradually reduced as the hole mobility decreases below a critical value (around 40 cm 2 V −1 s −1 ), which is directly related to a shorter carrier diffusion length. In a previous work, we have shown a similar result for the MAPbI 3 PSCs [52]. When the carrier diffusion length is less than the thickness of the HTL material, most carriers recombine before reaching the contacts. PCE values of 10.5% (for CsPbI 3 ) and 7.8% (for CsPbI 2 Br) were obtained for the lowest value of hole mobility considered (4 × 10 −5 cm 2 V −1 s −1 ). On the other hand, as hole mobility increases, the carrier diffusion length becomes much greater than the HTL thickness, thereby facilitating carrier transport without significant recombination. Figure 5 shows that the PCE saturates for hole mobility values greater than 40 cm 2 V −1 s −1 . Therefore, the hole mobility value of 44 cm 2 V −1 s −1 used in the simulations is appropriate to obtain a better performance of the devices.  Figure 5 shows the PCE as a function of hole mobility of CuI HTL for CsPbI3 and CsPbI2Br PSC. In both cases, PCE is gradually reduced as the hole mobility decreases below a critical value (around 40 cm 2 V −1 s −1 ), which is directly related to a shorter carrier diffusion length. In a previous work, we have shown a similar result for the MAPbI3 PSCs [52]. When the carrier diffusion length is less than the thickness of the HTL material, most carriers recombine before reaching the contacts. PCE values of 10.5% (for CsPbI3) and 7.8% (for CsPbI2Br) were obtained for the lowest value of hole mobility considered (4 × 10 −5 cm 2 V −1 s −1 ). On the other hand, as hole mobility increases, the carrier diffusion length becomes much greater than the HTL thickness, thereby facilitating carrier transport without significant recombination. Figure 5 shows that the PCE saturates for hole mobility values greater than 40 cm 2 V −1 s −1 . Therefore, the hole mobility value of 44 cm 2 V −1 s −1 used in the simulations is appropriate to obtain a better performance of the devices. From here, the study was focused on the perovskite layer, in which light is absorbed to produce photo-generated carriers, thus playing a decisive role in the device performance. Figure 6 shows the J-V characteristics (a) and EQE spectrum (b) for CsPbI3 and CsPbI2Br devices for two different thicknesses of the absorber film: 350 and 750 nm. We can see that a slight reduction in VOC but a significant increase in JSC were obtained when the absorber thickness increased from 350 to 750 nm. This behavior is consistent with the EQE results. Since it is possible to improve the device efficiency by increasing the absorber thickness, Figure 7 shows the variation in the electrical parameters (PCE, VOC, JSC, and FF) when the CsPbI3 and CsPbI2Br thickness is increased from 250 nm. The values displayed From here, the study was focused on the perovskite layer, in which light is absorbed to produce photo-generated carriers, thus playing a decisive role in the device performance. Figure 6 shows the J-V characteristics (a) and EQE spectrum (b) for CsPbI 3 and CsPbI 2 Br devices for two different thicknesses of the absorber film: 350 and 750 nm. We can see that a slight reduction in V OC but a significant increase in J SC were obtained when the absorber thickness increased from 350 to 750 nm. This behavior is consistent with the EQE results. Since it is possible to improve the device efficiency by increasing the absorber thickness, Figure 7 shows the variation in the electrical parameters (PCE, V OC , J SC , and FF) when the CsPbI 3 and CsPbI 2 Br thickness is increased from 250 nm. The values displayed in this figure are normalized to those corresponding to the thickness of 350 nm, previously shown in Table 4 for ZnO as i-ETL and CuI as i-HTL.
We can see in Figure 7a that when the CsPbI 3 thickness increases from 250 to 1750 nm, the V OC and FF decrease by 4% and 35%, respectively. The drop in V OC can be explained by the dependence of this parameter on the photogenerated current and the dark saturation current. An increase in the dark saturation current promotes carrier recombination, which leads to a drop in V OC with increasing thickness. Furthermore, the strong decrease in FF with increasing thickness of the active layer can be explained by the increase in series resistance. In contrast, the J SC is strongly increased above 80% with increasing CsPbI 3 thickness. This remarkable increase is due to the enhanced light absorption and, consequently, a higher concentration of free carriers that can be generated by photons and collected by the electrode. In the case of the PCE parameter, a significant increase by 30% is seen when the thickness is increased from 250 to 750 nm and then it starts to decrease for thicker films.
crease for thicker films.
Similarly, we can see in Figure 7b that when the CsPbI2Br thickness increases from 250 to 1050 nm, the VOC and FF parameters decrease by 4% and 36%, respectively, whereas JSC increases by 40%, as the increase in the CsPbI2Br thickness. Furthermore, the PCE value is improved by 15% for a CsPbI2Br thickness of 650 nm relative to the thickness of 350 nm. Extending the thickness beyond 650 nm increases the recombination current and series resistance and thus reduces the PCE. In the CsPbI2Br PSC, the maximum value of PCE is reached for a lower thickness compared with the CsPbI3 cell. This is due to the fact that the defect density in the CsPbI2Br layer is two orders of magnitude higher than in CsPbI3 (see Table 1), which reduces the carrier diffusion length. Therefore, values of 750 nm and 650 nm were considered as the optimized values of the CsPbI3 and CsPbI2Br absorber thickness, respectively.  On the other hand, Figure 8 shows the variation of the PCE as a function of the acceptor density in the CsPbI3 and CsPbI2Br perovskite layer, respectively. We can see in both cases that when the acceptor density increases from 10 13 to 10 15 cm −3 , the PCE remains constant, while this parameter decreases for higher values of 10 15 cm −3 . Therefore, an optimal value of 10 15 cm −3 was chosen for NA. Similarly, we can see in Figure 7b that when the CsPbI 2 Br thickness increases from 250 to 1050 nm, the V OC and FF parameters decrease by 4% and 36%, respectively, whereas J SC increases by 40%, as the increase in the CsPbI 2 Br thickness. Furthermore, the PCE value is improved by 15% for a CsPbI 2 Br thickness of 650 nm relative to the thickness of 350 nm. Extending the thickness beyond 650 nm increases the recombination current and series resistance and thus reduces the PCE. In the CsPbI 2 Br PSC, the maximum value of PCE is reached for a lower thickness compared with the CsPbI 3 cell. This is due to the fact that the defect density in the CsPbI 2 Br layer is two orders of magnitude higher than in CsPbI 3 (see Table 1), which reduces the carrier diffusion length. Therefore, values of 750 nm and 650 nm were considered as the optimized values of the CsPbI 3 and CsPbI 2 Br absorber thickness, respectively. On the other hand, Figure 8 shows the variation of the PCE as a function of the acceptor density in the CsPbI 3 and CsPbI 2 Br perovskite layer, respectively. We can see in both cases that when the acceptor density increases from 10 13 to 10 15 cm −3 , the PCE remains constant, while this parameter decreases for higher values of 10 15 cm −3 . Therefore, an optimal value of 10 15 cm −3 was chosen for N A . On the other hand, Figure 8 shows the variation of the PCE as a function of the acceptor density in the CsPbI3 and CsPbI2Br perovskite layer, respectively. We can see in both cases that when the acceptor density increases from 10 13 to 10 15 cm −3 , the PCE remains constant, while this parameter decreases for higher values of 10 15 cm −3 . Therefore, an optimal value of 10 15 cm −3 was chosen for NA. Finally, the simulation results show that when optimized parameters are used with the CsPbI3-and CsPbI2B-based PSCs with the fixed values of NT presented in Table 1, the PCE values increase from 14.13% to 18.9% and from 12.35% to 14.37%, respectively, such as is shown in Figure 9. Additionally, this figure shows that the defect density NT of the perovskite layer has a significant impact on device performance. This is because more defects in the active layer shorten the minority-carrier diffusion length, and hence the photogenerated carriers recombine before reaching their respective electrode and thus do not contribute to improving device performance. Figure 9 shows the performance improvement that could be achieved by reducing the defect density. Optimum efficiencies of 26.5% and 20.6% could be obtained at defect density of the order of 10 12 cm −3 for the inverted device with a structure of ITO/CuI/CsPbI3/ZnO/Ag and ITO/CuI/CsPbI2Br/ZnO/Ag, respectively. Finally, the simulation results show that when optimized parameters are used with the CsPbI 3 -and CsPbI 2 B-based PSCs with the fixed values of N T presented in Table 1, the PCE values increase from 14.13% to 18.9% and from 12.35% to 14.37%, respectively, such as is shown in Figure 9. Additionally, this figure shows that the defect density N T of the perovskite layer has a significant impact on device performance. This is because more defects in the active layer shorten the minority-carrier diffusion length, and hence the photogenerated carriers recombine before reaching their respective electrode and thus do not contribute to improving device performance. Figure 9 shows the performance improvement that could be achieved by reducing the defect density. Optimum efficiencies of 26.5% and 20.6% could be obtained at defect density of the order of 10 12 cm −3 for the inverted device with a structure of ITO/CuI/CsPbI 3 /ZnO/Ag and ITO/CuI/CsPbI 2 Br/ZnO/Ag, respectively.

Conclusions
Inverted p-i-n all-inorganic PSCs based on CsPbI3 and CsPbI2Br perovskite were studied through SCAPS-1D simulations. For each perovskite layer considered, the performance of twelve architectures of PSC was examined and compared, using several potential inorganic materials for HTL and ETL. The simulation results show that CuI as HTL and ZnO as ETL have better performance than the other combinations considered in this

Conclusions
Inverted p-i-n all-inorganic PSCs based on CsPbI 3 and CsPbI 2 Br perovskite were studied through SCAPS-1D simulations. For each perovskite layer considered, the performance of twelve architectures of PSC was examined and compared, using several potential inorganic materials for HTL and ETL. The simulation results show that CuI as HTL and ZnO as ETL have better performance than the other combinations considered in this study, with efficiencies of 14.13% and 12.35% for CsPbI 3 and CsPbI 2 Br, respectively, which is due to proper band alignment with the absorber. In order to improve the performance of ITO/CuI/CsPbI 3 /ZnO/Ag and ITO/CuI/CsPbI 2 Br/ZnO/Ag, the optimal values of hole mobility in CuI and the thickness, doping density, and defect density in the absorber layer were obtained. Values of 44 cm 2 V −1 s −1 and 10 15 cm −3 were chosen for hole mobility in CuI and doping density, respectively. Additionally, values of 750 nm and 650 nm were considered as the optimized values of the CsPbI 3 and CsPbI 2 Br absorber thickness, respectively. From these optimal values, improved efficiencies of 18.9% and 14.37% were achieved for the CsPbI 3 -and CsPbI 2 Br-based PSCs respectively. Finally, maximum efficiencies of 26.5% and 20.6% could be obtained by reducing the defect density up to the order of 10 12 cm −3 for the CsPbI 3 and CsPbI 2 B devices, respectively. The results obtained in this work are helpful for improving the performance of inverted all-inorganic PSCs based on CsPbI 3 and CsPbI 2 B as the perovskite layer, which is also essential to optimize the performance of tandem solar cells.