SCAPS-1D Simulation for Device Optimization to Improve Efficiency in Lead-Free CsSnI 3 Perovskite Solar Cells

: In this study, a novel systematic analysis was conducted to explore the impact of various parameters, including acceptor density (N A ), individual layer thickness, defect density, interface defect density, and the metal electrode work function, on efficiency within the FTO/ZnO/CsSnI 3 /NiO x /Au perovskite solar cell structure through the SCAPS-1D (Solar Cell Capacitance Simulator in 1 Dimension) simulation. ZnO served as the electron transport layer (ETL), CsSnI 3 as the perovskite absorption layer (PAL), and NiO x as the hole transport layer (HTL), all contributing to the optimization of device performance. To achieve the optimal power conversion efficiency (PCE), we determined the ideal PAL acceptor density (N A ) to be 2 × 10 19 cm − 3 and the optimal thicknesses to be 20 nm for the ETL (ZnO), 700 nm for the PAL (CsSnI 3 ), and 10 nm for the HTL (NiO x ), with the metal electrode remaining as Au. As a result of the optimization process, efficiency increased from 11.89% to 23.84%. These results are expected to contribute to the performance enhancement of eco-friendly, lead-free inorganic hybrid solar cells with Sn-based perovskite as the PAL.


Introduction
Because of environmental concerns and resource scarcity, it is considered difficult for energy production based on fossil fuels to be sustainable [1,2].Solar energy has emerged as a promising alternative over the past few decades, offering a solution to these challenges [3,4].In particular, perovskites, with their superior properties, have gained attention as a leading contender for next-generation solar cells [5,6].The chemical formula of perovskite is ABX 3 , where A comprises large cations (Cs + , NH 2 CH 3 NH 2 + , CH 3 NH 3 + ), B comprises divalent cations (Pb 2+ , Sn 2+ ), and X comprises monatomic halogen anions (I − , Br − , Cl − ) [7,8].Due to their long diffusion lengths and high absorption coefficients (10 4 cm −1 ), along with the benefits of flexibility, lightweight, and transparency, these materials hold economic advantages, spurring extensive research in the field [9][10][11].
PSCs have demonstrated rapid performance improvement, achieving efficiencies comparable to conventional solar cells, with a remarkable efficiency of 26.1% reported in 2023 [12].Moreover, the parameters of the maximum theoretical limit (SQ-limit) employing the CH 3 NH 3 PbI 3-x CL x absorber (E g ~1.55 eV) have been reported as follows: current density (J SC ) is 27.20 mA/cm 2 , open-circuit voltage (V OC ) is 1.28 V, fill factor (FF), and power conversion efficiency (PCE) is 90.2% and 31.4%,respectively [13,14].This demonstrates the potential for the further advancement of perovskite solar cells, indicating a promising future.
However, several challenges remain unresolved for PSCs, including the development of commercially feasible next-generation perovskite materials and advancements in manufacturing technology [15,16].Additionally, hybrid perovskites, such as methylammonium lead triiodide (MAPbI 3 ) and formamidinium lead triiodide (FAPbI 3 ), which have been extensively studied, exhibit poor stability against heat and moisture [17,18].As a result, the fabrication of hybrid PSCs requires careful environmental control, such as glove boxes or drying chambers [19,20].Currently, due to these drawbacks of organic-based perovskites, there is an increasing amount of research being conducted on photovoltaic solar cells that utilize inorganic perovskites [21][22][23].
Therefore, in this study, we selected an inorganic perovskite material to fabricate an all-inorganic PSC.Among them, one of the primary concerns in all-inorganic perovskites is the use of lead (Pb) in the PAL of most high-efficiency photovoltaic cells (PVs) [24][25][26].Lead-based perovskites produce harmful by-products like PbI 2 when decomposed, which can cause oxidative stress when exposed to the human body, potentially harming the nervous, reproductive, blood, and kidney systems [27,28].As an alternative to solving these issues, research into tin-based (Sn-based) perovskites has emerged as a new area of focus [29].This tin-based inorganic perovskite (CsSnX 3 ) provides benefits such as a bandgap close to 1.4 eV, high mobility, and a high absorption coefficient (greater than 10 5 cm −1 ) [30,31].
In particular, CsSnI 3 has a bandgap of 1.3-1.4eV and exhibits a high absorption coefficient of 10 4 cm −1 in the visible range [32].Additionally, its low exciton binding energy (10-20 meV) facilitates easier carrier separation compared to typical organic absorbers [33].In addition, it has the advantage of superior thermal stability with a melting point of 451 • C, which is higher than that of conventional perovskites such as MASnI 3 and FASnI 3 , which have a melting point of 200 • C [34].Because of these characteristics, CsSnI 3 has demonstrated the highest experimental efficiency of 10.1% among reported Pb-free Snbased perovskite materials [35].
As for ZnO, used as the electron transport layer (ETL) material, it is environmentally friendly and exhibits high carrier mobility [36].With a wide bandgap (3.3 eV) and a significant exciton binding energy, ZnO is being studied as one of the most interesting ETL materials [37,38].Especially for ZnO single nanowires, they feature electron mobility of up to ~1000 cm 2 /V•s and can be doped with both n-type and p-type materials [39].
Regarding NiO x , which serves as the hole transport layer (HTL) material, it exhibits a large bandgap (>3.5 eV) with superior transparency in the visible range [40].This characteristic can minimize losses such as charge recombination, enhance charge transport, and provide optimal energy-level alignment with various photoactive absorbers due to its sufficient conductivity and chemical stability [38,41].
Based on these properties, we selected CsSnI 3 as PAL, ZnO as ETL, NiO x as HTL and constructed an environmentally friendly Sn-based Pb-free PSC device (FTO/ZnO/CsSnI 3 / NiO x /Au).However, there are few studies systematically analyzing the influence of each parameter (such as acceptor density, layer thickness, interface defect density, and metal electrode work function) in the FTO/ZnO/CsSnI 3 /NiO x /Au structure [42].
Therefore, in this study, based on the consideration of each parameter, we systematically analyzed the effect of key parameters, such as acceptor density, layer thickness, defect density, interfacial defect density, and metal electrode work function, on the performance of photovoltaic solar cells and proposed an optimized solar cell structure, FTO/ZnO/CsSnI 3 /NiO x /Au, which is a completely inorganic device architecture.
Of course, practically, in the experimental phase, controlling interface defects is crucial due to their significant impact on device performance.Such defects can arise from material inhomogeneity, varying process conditions, and the nature of surface treatments [43,44].Notably, material inhomogeneity, particularly the intrinsic surface defects of zinc oxide, can lead to severe carrier recombination, as highlighted in reference [45].Therefore, for the scope of this simulation research, we are concentrating on the alteration of specific parameters-the density of interface defects and overall defect density-to determine their impact on the power conversion efficiency (PCE) of the device.These parameters need to be closely studied and adjusted as necessary before we proceed with full-scale practical experiments.

Simulation under Initial Conditions
The device performance was analyzed based on key parameters such as open-circuit voltage (V OC ), short-circuit current density (J SC ), fill factor (FF), and power conversion efficiency (PCE).Importantly, the FF was calculated using Equation (1), as reported in references [46,47].
The parameter for power conversion efficiency (PCE) was determined by the following in Equation ( 2): where I SC is the short-circuit photocurrent, and P in is the input power.The quantum efficiency (QE) is the ratio of the number of charge carriers collected by the solar cell to the number of incident photons at a specific energy, which is calculated as follows in Equation ( 3) [48].
The initial simulation results for the current density-voltage (J-V) plot and the quantum efficiency (QE) curve for FTO/ZnO/CsSnI 3 /NiO x /Au PSC are depicted in Figure 1a,b, respectively.The parameters for the current density-voltage (J-V) characteristics, including V OC , J SC , FF, and PCE, were 1.01 V, 15.55 mA/cm 2 , 75.78%, and 11.89%, respectively.The initial efficiency obtained was low at 11.89%, and accordingly, the levels of parameters were adjusted to investigate the effects of V OC , J SC , and FF on PCE for the optimization of this perovskite solar cell device.
need to be closely studied and adjusted as necessary before we proceed with full-scale practical experiments.

Simulation under Initial Conditions
The device performance was analyzed based on key parameters such as open-circuit voltage (VOC), short-circuit current density (JSC), fill factor (FF), and power conversion efficiency (PCE).Importantly, the FF was calculated using Equation (1), as reported in references [46,47].
The parameter for power conversion efficiency (PCE) was determined by the following in Equation ( 2): where ISC is the short-circuit photocurrent, and Pin is the input power.The quantum efficiency (QE) is the ratio of the number of charge carriers collected by the solar cell to the number of incident photons at a specific energy, which is calculated as follows in Equation (3) [48].
The initial simulation results for the current density-voltage (J-V) plot and the quantum efficiency (QE) curve for FTO/ZnO/CsSnI3/NiOX/Au PSC are depicted in Figure 1a,b, respectively.The parameters for the current density-voltage (J-V) characteristics, including VOC, JSC, FF, and PCE, were 1.01 V, 15.55 mA/cm 2 , 75.78%, and 11.89%, respectively.The initial efficiency obtained was low at 11.89%, and accordingly, the levels of parameters were adjusted to investigate the effects of VOC, JSC, and FF on PCE for the optimization of this perovskite solar cell device.

Efficiency Variation Depending on Acceptor Density (NA) of PAL
Figure 2 illustrates the variation in VOC, JSC, FF, and PCE with PAL acceptor density (NA) within the range of 2 × 10 19 to 10 21 cm −3 .The initial setting value was 1 × 10 20 cm −3 , referenced to the optimal value determined in a prior study, while 2 × 10 19 cm −3 represents the minimum NA providing a certain PV response [49,50].The PCE exhibited an overall decreasing trend as NA increased, with a PCE of 22.05% when NA was 2 × 10 19 cm −3 , in contrast to a PCE of 0.53% when NA was 1 × 10 21 cm −3 , indicating the significant impact of

Efficiency Variation Depending on Acceptor Density (N A ) of PAL
Figure 2 illustrates the variation in V OC , J SC , FF, and PCE with PAL acceptor density (N A ) within the range of 2 × 10 19 to 10 21 cm −3 .The initial setting value was 1 × 10 20 cm −3 , referenced to the optimal value determined in a prior study, while 2 × 10 19 cm −3 represents the minimum N A providing a certain PV response [49,50].The PCE exhibited an overall decreasing trend as N A increased, with a PCE of 22.05% when N A was 2 × 10 19 cm −3 , in contrast to a PCE of 0.53% when N A was 1 × 10 21 cm −3 , indicating the significant impact of N A on PCE.J SC and FF exhibited similar trends to PCE, while V OC increased up to 7 × 10 19 cm −3 before decreasing.This increase in V OC is attributed to the fermi level (E f ) approaching the valence band (VB) due to increased acceptor doping [51].Subsequently, the increase in charge carriers led to a decrease in V OC .Two predominant factors contributed to the efficiency decrement with increasing N A ; firstly, this included the increase in sheet resistance [52,53].With the increase in doping density, the sheet resistance of PAL for N A in p-type perovskite materials increases, impeding hole mobility to HTL, accelerating the recombination of photo-generated carriers, decreasing the generation of electron-hole pairs, and resulting in a decrease in efficiency owing to a reduction in the minority carrier concentration, mobility, and diffusion length.Equation (4) describes the decrement in saturation current (I O ) with increasing N A [54].
where I O is the saturation current, n i is the intrinsic concentration, A is the diode quality factor, q is the elementary charge, N A and N D are the acceptor and donor charge concentrations, L e and L h are the electron and hole diffusion length, and D e and D h are diffusion coefficient, respectively.
Inorganics 2024, 12, x FOR PEER REVIEW 4 of 15 NA on PCE.JSC and FF exhibited similar trends to PCE, while VOC increased up to 7 × 10 19 cm −3 before decreasing.This increase in VOC is attributed to the fermi level (Ef) approaching the valence band (VB) due to increased acceptor doping [51].Subsequently, the increase in charge carriers led to a decrease in VOC.Two predominant factors contributed to the efficiency decrement with increasing NA; firstly, this included the increase in sheet resistance [52,53].With the increase in doping density, the sheet resistance of PAL for NA in p-type perovskite materials increases, impeding hole mobility to HTL, accelerating the recombination of photo-generated carriers, decreasing the generation of electron-hole pairs, and resulting in a decrease in efficiency owing to a reduction in the minority carrier concentration, mobility, and diffusion length.Equation ( 4) describes the decrement in saturation current (IO) with increasing NA [54].
where IO is the saturation current, ni is the intrinsic concentration, A is the diode quality factor, q is the elementary charge, NA and ND are the acceptor and donor charge concentrations, Le and Lh are the electron and hole diffusion length, and De and Dh are diffusion coefficient, respectively.The secondary causative factor is the incidence of Auger recombination due to high doping concentrations [55,56].In devices where the concentration exceeds 10 18 cm −3 , dopants trigger Auger recombination, ultimately leading to a reduction in the performance parameters of the photovoltaic device.
Consequently, by setting the optimal NA value of 2 × 10 19 cm −3 for the PAL, JSC, and PCE achieved a notable enhancement from 15.55 mA/cm 2 to 27.58 mA/cm 2 and from 11.89% to 22.05%, respectively.The other parameters were maintained consistent with previous settings.According to a previously published paper, the optimal NA value of 2 × 10 19 cm −3 aligns with CsSnI3, typically exhibiting a maximum p-type doping concentration of 10 19 to 10 20 cm −3 even in the undoped case at room temperature, and the addition of Sn can increase the NA value [57].This occurrence is ascribed to the presence of hydrogen anions in Sn-rich environments, facilitating a shift in the Fermi level (Ef) towards the valence band maximum (VBM) and considerably increasing the doped hole concentration [58].The NA value of 2 × 10 19 cm −3 selected in this study aligns with the optimal values previously reported at 10 19 and 7 × 10 19 cm −3 [59,60].The secondary causative factor is the incidence of Auger recombination due to high doping concentrations [55,56].In devices where the concentration exceeds 10 18 cm −3 , dopants trigger Auger recombination, ultimately leading to a reduction in the performance parameters of the photovoltaic device.
Consequently, by setting the optimal N A value of 2 × 10 19 cm −3 for the PAL, J SC , and PCE achieved a notable enhancement from 15.55 mA/cm 2 to 27.58 mA/cm 2 and from 11.89% to 22.05%, respectively.The other parameters were maintained consistent with previous settings.According to a previously published paper, the optimal N A value of 2 × 10 19 cm −3 aligns with CsSnI 3 , typically exhibiting a maximum p-type doping concentration of 10 19 to 10 20 cm −3 even in the undoped case at room temperature, and the addition of Sn can increase the N A value [57].This occurrence is ascribed to the presence of hydrogen anions in Sn-rich environments, facilitating a shift in the Fermi level (E f ) towards the valence band maximum (VBM) and considerably increasing the doped hole concentration [58].The N A value of 2 × 10 19 cm −3 selected in this study aligns with the optimal values previously reported at 10 19 and 7 × 10 19 cm −3 [59,60].

Optimization of Each Layer's Thickness
Each layer of the PSC serves a distinctive role in the performance of the cell, so it is important to adjust the thickness of each layer for optimal cell performance.The optimization of layer thickness was executed by preserving the uniform thickness for two layers and varying the thickness of the residual layers.

Optimization of ZnO Thickness
ZnO is employed as an electron transport layer (ETL) material in the n-i-p structure as the initial substance to be exposed to incoming light.For the initial device fabrication, optimizing the thickness of ZnO is important.Thus, referencing the 16 nm and 20 nm ZnO coating thicknesses fabricated using spin-coating in papers [61,62], our study conducted optimization within the range of 10 to 500 nm for ZnO coating.The graph in Figure 3 describes the impact of ZnO thickness on V OC , J SC , FF, and PCE.As the thickness of ZnO increased from 10 nm to 20 nm, PCE increased from 22.05% to 22.32%.The low PCE at a ZnO thickness of 10 nm can be attributed to insufficient layer thickness for effective electron extraction and transport, leading to inefficiencies in charge collection, resulting in lower FF and PCE [63,64].In the thickness range of 20 nm to 50 nm, the FF value exhibited an overall decrease followed by an increase thereafter.This phenomenon was ascribed to the relatively small decrease in J SC compared to V OC at this thickness.Similar observations were reported in a previous study [65].Furthermore, the decrease in PCE with increasing thickness is associated with the acceleration of electron-hole pair recombination due to the surface roughness with thicker layers [66].This precipitates an increase in series resistance, causing a reduction in J SC and V OC .Therefore, we derived the conclusion that a thinner ETL thickness leads to an increase in efficiency.Based on this conclusion, we set the optimal thickness to 20 nm.

Optimization of Each Layer's Thickness
Each layer of the PSC serves a distinctive role in the performance of the cell, so it is important to adjust the thickness of each layer for optimal cell performance.The optimization of layer thickness was executed by preserving the uniform thickness for two layers and varying the thickness of the residual layers.

Optimization of ZnO Thickness
ZnO is employed as an electron transport layer (ETL) material in the n-i-p structure as the initial substance to be exposed to incoming light.For the initial device fabrication, optimizing the thickness of ZnO is important.Thus, referencing the 16 nm and 20 nm ZnO coating thicknesses fabricated using spin-coating in papers [61,62], our study conducted optimization within the range of 10 to 500 nm for ZnO coating.The graph in Figure 3 describes the impact of ZnO thickness on VOC, JSC, FF, and PCE.As the thickness of ZnO increased from 10 nm to 20 nm, PCE increased from 22.05% to 22.32%.The low PCE at a ZnO thickness of 10 nm can be attributed to insufficient layer thickness for effective electron extraction and transport, leading to inefficiencies in charge collection, resulting in lower FF and PCE [63,64].In the thickness range of 20 nm to 50 nm, the FF value exhibited an overall decrease followed by an increase thereafter.This phenomenon was ascribed to the relatively small decrease in JSC compared to VOC at this thickness.Similar observations were reported in a previous study [65].Furthermore, the decrease in PCE with increasing thickness is associated with the acceleration of electron-hole pair recombination due to the surface roughness with thicker layers [66].This precipitates an increase in series resistance, causing a reduction in JSC and VOC.Therefore, we derived the conclusion that a thinner ETL thickness leads to an increase in efficiency.Based on this conclusion, we set the optimal thickness to 20 nm.

Optimization of PAL Thickness
Upon light incidence on the absorption stratum of a solar cell, electron-hole pairs are generated.For effective operation of the solar cell, it is important that these pairs reach each electrode without recombination [67].To achieve this, optimizing the thickness of the perovskite absorption layer (PAL) is essential.When the PAL thickness is excessively thick, it increases the time required for the absorption and conversion of light energy, leading to recombination [68].Conversely, an excessively thinner PAL can impede light

Optimization of PAL Thickness
Upon light incidence on the absorption stratum of a solar cell, electron-hole pairs are generated.For effective operation of the solar cell, it is important that these pairs reach each electrode without recombination [67].To achieve this, optimizing the thickness of the perovskite absorption layer (PAL) is essential.When the PAL thickness is excessively thick, it increases the time required for the absorption and conversion of light energy, leading to recombination [68].Conversely, an excessively thinner PAL can impede light absorption, decreasing the current density [69].To find the optimum thickness, optimization was performed in the range of 100 to 1200 nm.The graph in Figure 4 illustrates the influence of PAL thickness on V OC , J SC , FF, and PCE.V OC , J SC , and PCE predominantly exhibited an overall increasing trend, while FF increased in the range of 100 to 200 nm and then decreased from 200 to 1200 nm.The initial increase in FF was attributed to the efficient charge transport with increasing thickness, while the subsequent decrease was due to a reduction in shunt resistance and an increase in series resistance [70].Furthermore, PCE increased in the range of 100 to 700 nm, reaching its highest efficiency of 22.64% at a thickness of 700 nm.This was due to the substantial photon absorption by PAL, resulting in the generation of the most electron-hole pairs [71].However, from 700 to 1200 nm, PCE decreased due to the resistance caused by recombination [72,73].
Inorganics 2024, 12, x FOR PEER REVIEW 6 of 15 absorption, decreasing the current density [69].To find the optimum thickness, optimization was performed in the range of 100 to 1200 nm.The graph in Figure 4 illustrates the influence of PAL thickness on VOC, JSC, FF, and PCE.VOC, JSC, and PCE predominantly exhibited an overall increasing trend, while FF increased in the range of 100 to 200 nm and then decreased from 200 to 1200 nm.The initial increase in FF was attributed to the efficient charge transport with increasing thickness, while the subsequent decrease was due to a reduction in shunt resistance and an increase in series resistance [70].Furthermore, PCE increased in the range of 100 to 700 nm, reaching its highest efficiency of 22.64% at a thickness of 700 nm.This was due to the substantial photon absorption by PAL, resulting in the generation of the most electron-hole pairs [71].However, from 700 to 1200 nm, PCE decreased due to the resistance caused by recombination [72,73].Equation (5) depicts the mathematical relation between the thickness and absolute absorption rate of the absorber [74].By employing this equation, the absolute absorption rate of the absorber can be computed, facilitating the determination of the optimal thickness of PAL.
Here, Rabsorber is the absorber resistance, p is the resistance of the PAL, t is the thickness of PAL, and A is the cross-sectional area.This results in Equation ( 5); as the PAL thickness increases, the absorber resistance rises.This phenomenon generally leads to an increase in VOC, JSC, and FF values.However, the increase in absorber thickness also enhances the photon energy absorption rate [75].Considering these electrical and optical property changes, an optimal PCE at 22.64% was achieved when the absorber thickness was 700 nm.

Optimization of NiOX Thickness
The hole transport layer (HTL) serves a crucial role in enhancing the transport of charge carriers (holes) and prevents direct contact between the PAL and anode through capping [76,77].Figure 5a illustrates the influence of NiOX thickness within the range of 10 to 500 nm on VOC, JSC, FF, and PCE.The peak efficiency of 22.76% was achieved at the smallest thickness of 10 nm, while PCE decreased as the thickness increased, reaching its lowest efficiency of 19.1% at the maximum thickness of 500 nm.This result was primarily Equation (5) depicts the mathematical relation between the thickness and absolute absorption rate of the absorber [74].By employing this equation, the absolute absorption rate of the absorber can be computed, facilitating the determination of the optimal thickness of PAL.
Here, R absorber is the absorber resistance, p is the resistance of the PAL, t is the thickness of PAL, and A is the cross-sectional area.This results in Equation ( 5); as the PAL thickness increases, the absorber resistance rises.This phenomenon generally leads to an increase in V OC , J SC , and FF values.However, the increase in absorber thickness also enhances the photon energy absorption rate [75].Considering these electrical and optical property changes, an optimal PCE at 22.64% was achieved when the absorber thickness was 700 nm.

Optimization of NiO x Thickness
The hole transport layer (HTL) serves a crucial role in enhancing the transport of charge carriers (holes) and prevents direct contact between the PAL and anode through capping [76,77].Figure 5a illustrates the influence of NiO x thickness within the range of 10 to 500 nm on V OC , J SC , FF, and PCE.The peak efficiency of 22.76% was achieved at the smallest thickness of 10 nm, while PCE decreased as the thickness increased, reaching its lowest efficiency of 19.1% at the maximum thickness of 500 nm.This result was primarily attributed to the increase in HTL thickness, causing an increase in the series resistance of the solar cell [78].Consequently, it became challenging for holes to reach the anode, resulting in recombination and causing a decrease in V OC , J SC , FF, and overall PCE.
sulting in recombination and causing a decrease in VOC, JSC, FF, and overall PCE.
Following NiOx thickness optimization, the optimal thickness for ZnO and CsSnI3 were determined to be 20 nm and 700 nm, respectively.As shown in Figure 5b, the corresponding values for VOC, JSC, FF, and PCE were 1.01 V, 28.02 mA/cm 2 , 80.5%, and 22.76%, respectively.The PCE graphs based on the thickness of each layer demonstrated that the thickness of each layer had a substantial impact on the performance of the PSC.

Optimization of PAL Defect density and Interface Defect Density
The defect density typically increases the recombination of photogenerated carriers at both the bulk material and interface defects, leading to an increase in the quasi-saturation current density (J0) and consequently reducing both JSC and VOC [79,80].Therefore, to investigate the effect of defect density on Jsc, Voc, FF, and PCE, simulations were conducted for the defect density of the PAL. Figure 6a demonstrates the influence of the PAL defect density varying from 10 11 to 10 18 cm −3 on VOC, JSC, FF, and PCE.Following NiO x thickness optimization, the optimal thickness for ZnO and CsSnI 3 were determined to be 20 nm and 700 nm, respectively.As shown in Figure 5b, the corresponding values for V OC , J SC , FF, and PCE were 1.01 V, 28.02 mA/cm 2 , 80.5%, and 22.76%, respectively.The PCE graphs based on the thickness of each layer demonstrated that the thickness of each layer had a substantial impact on the performance of the PSC.

Optimization of PAL Defect Density and Interface Defect Density
The defect density typically increases the recombination of photogenerated carriers at both the bulk material and interface defects, leading to an increase in the quasi-saturation current density (J 0 ) and consequently reducing both J SC and V OC [79,80].Therefore, to investigate the effect of defect density on Jsc, Voc, FF, and PCE, simulations were conducted for the defect density of the PAL. Figure 6a demonstrates the influence of the PAL defect density varying from 10 11 to 10 18 cm −3 on V OC , J SC , FF, and PCE.The efficiency remained stable within the initial defect density range of 10 11 ~10 15 cm −3 ; however, a sharp decrease in efficiency was observed from 10 16 cm −3 onwards.This phenomenon can be attributed to the increase in defect density, which leads to an increase in recombination current and accelerated carrier recombination [81].
As described in Figure 6b, the graph of bulk recombination current density caused The efficiency remained stable within the initial defect density range of 10 11 ~10 15 cm −3 ; however, a sharp decrease in efficiency was observed from 10 16 cm −3 onwards.This phenomenon can be attributed to the increase in defect density, which leads to an increase in recombination current and accelerated carrier recombination [81].
As described in Figure 6b, the graph of bulk recombination current density caused by the PAL defect density confirmed the increase in the recombination current at a defect density of 10 16 cm −3 .Ultimately, the lowest efficiency of 19.24% was observed at the maximum value of 10 18 cm −3 .This was attributed to a degradation in film quality due to the surge in defect density, leading to an accelerated recombination rate and shortened carrier lifetime, and consequently leading to decreased efficiency [82,83].Based on these results, the optimal defect density was adjusted to the conventional value of 10 14 cm −3 , thereby maintaining the original efficiency of 22.76%.These results also exhibited a similar tendency as those reported in previously conducted research [84,85].
The performance of the device significantly varies depending on the defect density of the interface layer, as shown in Figure 7a The efficiency remained stable within the initial defect density range of 10 11 ~10 15 cm −3 ; however, a sharp decrease in efficiency was observed from 10 16 cm −3 onwards.This phenomenon can be attributed to the increase in defect density, which leads to an increase in recombination current and accelerated carrier recombination [81].
As described in Figure 6b, the graph of bulk recombination current density caused by the PAL defect density confirmed the increase in the recombination current at a defect density of 10 16 cm −3 .Ultimately, the lowest efficiency of 19.24% was observed at the maximum value of 10 18 cm −3 .This was attributed to a degradation in film quality due to the surge in defect density, leading to an accelerated recombination rate and shortened carrier lifetime, and consequently leading to decreased efficiency [82,83].Based on these results, the optimal defect density was adjusted to the conventional value of 10 14 cm −3 , thereby maintaining the original efficiency of 22.76%.These results also exhibited a similar tendency as those reported in previously conducted research [84,85].
The performance of the device significantly varies depending on the defect density of the interface layer, as shown in Figure 7a As the defect density increases at both interfaces, the PCE initially remains stable without significant changes.However, for the ZnO/PAL interface, the PCE begins to gradually decrease, starting from 10 11 cm −3 in Figure 8a.In contrast, in the case of the PAL/NiOx interface, efficiency remained within the range of 10 8 to 10 15 cm −3 , but it began to decrease sharply, starting from 10 16 cm −3 in Figure 8b.This decrease in efficiency is attributed to defects acting as recombination centers, leading to a reduction in charge carrier density as the defect density increases [86].The sharp decrease at a certain interface defect density is attributed to a rapid decline in photon absorption when exceeding a specific Nt value at each interface [87].As a result, PCE was enhanced from 22.76% to 23.84% by setting the optimal interface defect density for both interfaces at 10 8 cm −3 .As the defect density increases at both interfaces, the PCE initially remains stable without significant changes.However, for the ZnO/PAL interface, the PCE begins to gradually decrease, starting from 10 11 cm −3 in Figure 7a.In contrast, in the case of the PAL/NiO x interface, efficiency remained within the range of 10 8 to 10 15 cm −3 , but it began to decrease sharply, starting from 10 16 cm −3 in Figure 7b.This decrease in efficiency is attributed to defects acting as recombination centers, leading to a reduction in charge carrier density as the defect density increases [86].The sharp decrease at a certain interface defect density is attributed to a rapid decline in photon absorption when exceeding a specific N t value at each interface [87].As a result, PCE was enhanced from 22.76% to 23.84% by setting the optimal interface defect density for both interfaces at 10 8 cm −3 .

Optimization of Metal Electrode Work Function
For the design of high-performing solar cells, the choice of suitable electrodes is critical.For this part, experiments were carried out using metal electrode materials such as Al (4.2 eV), Cu (4.6 eV), Ag (4.7 eV), Fe (4.8 eV), and Au (5.1 eV) [88].Figure 8 illustrates the influence of metal electrode work functions on V OC , J SC , FF, and PCE.As the work function increased, all parameters exhibited a tendency to increase proportionally.As a result, PCE was lowest at 4.17% for Al, which had the lowest work function of 4.2 eV, while Au, with the highest work function of 5.1 eV, achieved an optimal efficiency of 23.84%.A reason for the decrease in efficiency as the work function of the metal electrodes decreased was due to the increased Schottky barrier impeding hole transport, leading to a decrease in FF [89].Furthermore, regarding higher work functions mentioned in Ref. [90], such as W (5.22 eV), Ni (5.5 eV), Pt (5.7 eV), Se (5.9 eV), PCE shows saturated behavior indicating the absence of additional chemical interactions between the PAL and these metals (W, Ni, Pt, Se).Based on these results, this study utilized Au as the optimal metal electrode.These findings concur with various simulation results [91,92].

Optimization of Metal Electrode Work Function
For the design of high-performing solar cells, the choice of suitable electrodes is critical.For this part, experiments were carried out using metal electrode materials such as Al (4.2 eV), Cu (4.6 eV), Ag (4.7 eV), Fe (4.8 eV), and Au (5.1 eV) [88].Figure 8 illustrates the influence of metal electrode work functions on VOC, JSC, FF, and PCE.As the work function increased, all parameters exhibited a tendency to increase proportionally.As a result, PCE was lowest at 4.17% for Al, which had the lowest work function of 4.2 eV, while Au, with the highest work function of 5.1 eV, achieved an optimal efficiency of 23.84%.A reason for the decrease in as the work function of the metal electrodes decreased was due to the increased Schottky barrier impeding hole transport, leading to a decrease in FF [89].Furthermore, regarding higher work functions mentioned in Ref. [90], such as W (5.22 eV), Ni (5.5 eV), Pt (5.7 eV), Se (5.9 eV), PCE shows saturated behavior indicating the absence of additional chemical interactions between the PAL and these metals (W, Ni, Pt, Se).Based on these results, this study utilized Au as the optimal metal electrode.These findings concur with various simulation results [91,92].

Numerical Modeling
The numerical simulations performed in this study were based on the SCAPS-1D (Solar Cell Capacitance Simulation in 1 Dimension) (ver.3.3.11)simulator.This computational tool, developed by Dr. M. Burgelman of the University of Gent in Belgium, enables the design and simulation of up to seven heterojunction layers [93].The simulations were based on Poisson's Equation ( 6) and the continuity Equations ( 7) and (8) for each electron and hole, respectively [94,95]

Numerical Modeling
The numerical simulations performed in this study were based on the SCAPS-1D (Solar Cell Capacitance Simulation in 1 Dimension) (ver.3.3.11)simulator.This computational tool, developed by Dr. M. Burgelman of the University of Gent in Belgium, enables the design and simulation of up to seven heterojunction layers [93].The simulations were based on Poisson's Equation ( 6) and the continuity Equations ( 7) and ( 8) for each electron and hole, respectively [94,95].
In this equation, ε is the dielectric constant, q is the charge of an electron, G is the generation rate, D is the diffusion coefficient, ψ is the electrostatic potential, E is the electric field, and p(x), n(x), p t (x), and n t (x) are free holes, free electrons, trapped holes, and trapped electrons, respectively.N + d refers to doping concentration-like ionized donors, N − a represents doping concentration-like ionized acceptors, and x is the direction along the thickness.In this study, following the standard test conditions (STC), the spectrum used in all simulations was the AM1.5G spectrum, the incident light power was set at 1000 W/m 2 , the operating point voltage set to 0 V, and the temperature was set at 300 K [96].

Device Structure
Figure 9a illustrates a solid-state planar heterojunction p-i-n structure device composed of FTO/ZnO/CsSnI 3 /NiO x /Au.In this device, the perovskite material (CsSnI 3 ) is sandwiched between the n-type hole transport layer (HTL) NiO x and the p-type electron transport layer (ETL) ZnO, with Au serving as the metal electrode.Figure 9b  electrons, respectively.N + d refers to doping concentration-like ionized donors, N − a represents doping concentration-like ionized acceptors, and x is the direction along the thickness.In this study, following the standard test conditions (STC), the spectrum used in all simulations was the AM1.5G spectrum, the incident light power was set at 1000 W/m 2 , the operating point voltage set to 0 V, and the temperature was set at 300 K [96].

Device Structure
Figure 9a illustrates a solid-state planar heterojunction p-i-n structure device composed of FTO/ZnO/CsSnI3/NiOX/Au.In this device, the perovskite material (CsSnI3) is sandwiched between the n-type hole transport layer (HTL) NiOX and the p-type electron transport layer (ETL) ZnO, with Au serving as the metal electrode.Figure 9b  Table 1 presents the initial parameters of each material used in the FTO/ZnO/CsSnI3/NiOX/Au PSC simulations.The initial thicknesses of FTO, ZnO, CsSnI3, and NiOX were 500 nm, 100 nm, 1000 nm, and 30 nm, respectively [103][104][105].The bandgap and electron affinity for each material are given as follows: FTO (3.2 eV, 4.4 eV), ZnO (3.3 eV, 4.0 eV), CsSnI3 (1.4 eV, 3.6 eV), and NiOX (3.6 eV, 1.8 eV) [106][107][108][109].For the perovskite absorption layer (PAL), the band-to-band recombination model was maintained at a radiative recombination coefficient of 3 × 10 −11 cm 3 and an Auger capture rate of 1 × 10 −29 cm 6 /s for both carriers (electrons and holes) [110,111].The dielectric permittivity values for each material were 9, 8.656, 9.93, and 10.7, respectively.The thermal velocity of charge carriers Table 1 presents the initial parameters of each material used in the FTO/ZnO/CsSnI 3 / NiO x /Au PSC simulations.The initial thicknesses of FTO, ZnO, CsSnI 3 , and NiO x were 500 nm, 100 nm, 1000 nm, and 30 nm, respectively [103][104][105].The bandgap and electron affinity for each material are given as follows: FTO (3.2 eV, 4.4 eV), ZnO (3.3 eV, 4.0 eV), CsSnI 3 (1.4eV, 3.6 eV), and NiO x (3.6 eV, 1.8 eV) [106][107][108][109].For the perovskite absorption layer (PAL), the band-to-band recombination model was maintained at a radiative recombination coefficient of 3 × 10 −11 cm 3 and an Auger capture rate of 1 × 10 −29 cm 6 /s for both carriers (electrons and holes) [110,111].The dielectric permittivity values for each material were 9, 8.656, 9.93, and 10.7, respectively.The thermal velocity of charge carriers (electrons and holes) in all layers was maintained at 10 7 cm/s.For interfacial layers, the defect type was set as neutral, with a Gaussian energy distribution, and the reference energy level for defect (E t ) was set above E V .The capture cross-section for both types of charge carriers (electrons and holes) was 10 −19 cm −3 , and the total charge carrier density was set at 1.0 × 10 11 cm −3 .The variations in the parameters are listed in Table 2. Additionally, the band-to-band recombination model was maintained at zero for FTO, ETL, and HTL layers.Furthermore, the tunneling effect was not considered in the simulation.

Conclusions
In this study, in the device structure of FTO/ZnO/CsSnI 3 /NiO x /Au, various parameters, including the acceptor density (N A ) of the perovskite absorber layer (PAL), the thickness of each material layer, the defect density of PAL, the interface defect density, and work function of the metal electrode, were optimized.The parameters were optimized such that the N A of the PAL was 2 × 10 19 cm −3 , the thicknesses of the ETL (ZnO), PAL (CsSnI 3 ), and HTL (NiO ) were 20 nm, 700 nm, and 10 nm, respectively, the PAL defect density was 10 14 cm −3 , and interface defect density for ZnO/PAL and PAL/NiO x was 10 8 cm −3 .As a result, the performance of the device was enhanced, with V OC , J SC , FF, and PCE improving from 1.01 to 1.05 V, 15.55 to 28.02 mA/cm 2 , 75.78 to 81.22%, and 11.89 to 23.84%, respectively.This emphasizes the potential for the high-efficiency design of environmentally friendly, lead-free perovskite solar cells based on CsSnI 3 .

Figure 1 .
Figure 1.(a) Simulated initial J-V curve of PSC cell; (b) simulated initial QE curve of PSC cell.

Figure 1 .
Figure 1.(a) Simulated initial J-V curve of PSC cell; (b) simulated initial QE curve of PSC cell.

Figure 2 .
Figure 2. The variation in VOC, JSC, FF, and PCE with the acceptor density (NA)of PAL.

Figure 2 .
Figure 2. The variation in V OC , J SC , FF, and PCE with the acceptor density (N A )of PAL.

Figure 3 .
Figure 3.The variation in VOC, JSC, FF, and PCE with ZnO thickness.

Figure 3 .
Figure 3.The variation in V OC , J SC , FF, and PCE with ZnO thickness.

Figure 4 .
Figure 4.The variation in VOC, JSC, FF, and PCE with PAL thickness.

Figure 4 .
Figure 4.The variation in V OC , J SC , FF, and PCE with PAL thickness.

Figure 6 .
Figure 6.(a) The variation in VOC, JSC, FF, and PCE with PAL defect density; (b) the variation in bulk recombination current density with PAL defect density.

Figure 6 .
Figure 6.(a) The variation in V OC , J SC , FF, and PCE with PAL defect density; (b) the variation in bulk recombination current density with PAL defect density.

Figure 6 .
Figure 6.(a) The variation in VOC, JSC, FF, and PCE with PAL defect density; (b) the variation in bulk recombination current density with PAL defect density.

Figure 7 .
Figure 7. (a) The variation in PCE with ZnO/PAL interface defect density; (b) the variation in PCE with PAL/NiOX interface defect density.

Figure 7 .
Figure 7. (a) The variation in PCE with ZnO/PAL interface defect density; (b) the variation in PCE with PAL/NiO x interface defect density.

Inorganics 2024 , 15 Figure 8 .
Figure 8.The variation in VOC, JSC, FF, and PCE with back contact material work function.

Figure 8 .
Figure 8.The variation in V OC , J SC , FF, and PCE with back contact material work function.
Figure9aillustrates a solid-state planar heterojunction p-i-n structure device composed of FTO/ZnO/CsSnI 3 /NiO x /Au.In this device, the perovskite material (CsSnI 3 ) is sandwiched between the n-type hole transport layer (HTL) NiO x and the p-type electron transport layer (ETL) ZnO, with Au serving as the metal electrode.Figure9bpresents a simplified flat band energy diagram of the PSC.The work functions of FTO and Au are 4.4 eV and 5.1 eV, respectively[97,98].The highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) levels for ZnO, CsSnI 3 , and NiO x were 4.0 eV and 7.3 eV, 3.6 eV and 5.0 eV, and 1.8 eV and 5.4 eV, respectively[99][100][101].Upon light irradiation, weakly bounded excitons were generated in the PAL of this device.These excitons undergo a dissociation process, rapidly separating into electrons and holes prior to recombination, promoting effective carrier transport within the device[102].The structure depicted in the band diagram in Figure9bfacilitates the efficient movement of electrons and holes in the conduction and valence bands, respectively, significantly influencing the overall performance of the device.

Figure 9 .
Figure9aillustrates a solid-state planar heterojunction p-i-n structure device composed of FTO/ZnO/CsSnI3/NiOX/Au.In this device, the perovskite material (CsSnI3) is sandwiched between the n-type hole transport layer (HTL) NiOX and the p-type electron transport layer (ETL) ZnO, with Au serving as the metal electrode.Figure9bpresents a simplified flat band energy diagram of the PSC.The work functions of FTO and Au are 4.4 eV and 5.1 eV, respectively [97,98].The highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) levels for ZnO, CsSnI3, and NiOX were 4.0 eV and 7.3 eV, 3.6 eV and 5.0 eV, and 1.8 eV and 5.4 eV, respectively [99-101].Upon light irradiation, weakly bounded excitons were generated in the PAL of this device.These excitons undergo a dissociation process, rapidly separating into electrons and holes prior to recombination, promoting effective carrier transport within the device [102].The energy structure depicted in the band diagram in Figure 9b facilitates the efficient movement of electrons and holes in the conduction and valence bands, respectively, significantly influencing the overall performance of the device.

Figure 9 .
Figure 9. (a) The basic schematic diagram of the FTO/ZnO/CsSnI 3 /NiO x /Au perovskite solar cell device structure; (b) the energy band diagram of the PSC layers. .

Table 1 .
The initial parameters of each material used in the FTO/ZnO/CsSnI 3 /NiO x /Au PSC simulations.

Table 2 .
The initial parameters of interfacial layers.