Guidelines for Fabricating Highly Efficient Perovskite Solar Cells with Cu2O as the Hole Transport Material

Organic hole transport materials (HTMs) have been frequently used to achieve high power conversion efficiencies (PCEs) in regular perovskite solar cells (PSCs). However, organic HTMs or their ingredients are costly and time-consuming to manufacture. Therefore, one of the hottest research topics in this area has been the quest for an efficient and economical inorganic HTM in PSCs. To promote efficient charge extraction and, hence, improve overall efficiency, it is crucial to look into the desirable properties of inorganic HTMs. In this context, a simulation investigation using a solar cell capacitance simulator (SCAPS) was carried out on the performance of regular PSCs using inorganic HTMs. Several inorganic HTMs, such as nickel oxide (NiO), cuprous oxide (Cu2O), copper iodide (CuI), and cuprous thiocyanate (CuSCN), were incorporated in PSCs to explore matching HTMs that could add to the improvement in PCE. The simulation results revealed that Cu2O stood out as the best alternative, with electron affinity, hole mobility, and acceptor density around 3.2 eV, 60 cm2V−1s−1, and 1018 cm−3, respectively. Additionally, the results showed that a back electrode with high work-function was required to establish a reduced barrier Ohmic and Schottky contact, which resulted in efficient charge collection. In the simulation findings, Cu2O-based PSCs with an efficiency of more than 25% under optimal conditions were identified as the best alternative for other counterparts. This research offers guidelines for constructing highly efficient PSCs with inorganic HTMs.


Introduction
Perovskite solar cells (PSCs) utilizing organic-inorganic halide perovskites have been realized as emerging solar cells, with rapidly progressing power conversion efficiencies (PCEs), ease of processing, and relatively low-cost production, among other photovoltaics [1,2]. The first use of organic-inorganic halide perovskites was reported in dye-sensitizer solar cells with a PCE of 3.9% in 2009, which was a huge achievement in the field of excitonic solar cells [3]. Following that, perovskite quantum dots were utilized in PSCs, which had a 6.5% PCE with low stability due to liquid electrolytes [4]. Then, 2,2 ,7,7 -Tetrakis[N,N-di(4-methoxyphenyl)amino]-9,9 -spirobifluorene (spiro-OMeTAD) was used as a hole transport material (HTM), which increased the stability of PSCs in 2012, achieving a PCE of 9.1% [5]. The PCE of PSCs was improved further by modifying the halide mixture, deposition techniques, and HTMs in organic-inorganic halide perovskites, resulting in a PCE of 22.1% in 2016. Subsequently, most of the PSCs with significant increases in PCE over 25% have been reported with organic HTMs [6]. High-performance organic HTMs, however, are frequently made of costly organic conjugated molecules, such

Simulation Parameters and Computational Details
Simulation methods can help explain the phenomena existing in solar cells [33][34][35][36][37]. In order to gain a better understanding, a theoretical study using SCAPS software was conducted. A planar PSC configuration (FTO/TiO 2 /MAPbI 2 Br/HTM/Au) was simulated as a baseline to evaluate the impact of our method, as depicted in Figure 1a,b. The basic physical parameters for the simulation are listed in the Table 1. Most of them were chosen from recent publications [38][39][40]. The solar radiation spectrum of AM1.5G was used in this simulation as a light source. The light reflection was set to 0 and 1 for the top and bottom contacts, respectively. With a Gaussian energy distribution, defects in the energy levels were considered in the middle of their characteristic energy bandgap of 0.1 eV in the simulated thin films.
electron-hole has a tremendous effect on the solar cell efficiency, so the total recombination in the as-simulated PSCs was taken into account by SCAPS. SCAPS software does not take into account the recombination of charges at the corresponding interfaces. Therefore, two thin defect layers were stacked at the HTM-perovskite and electron transport material (ETM)-perovskite interfaces to overcome the interfacial defect density, as presented in Table 2. This structure allowed for the evaluation of the role of interface adjustment in the simulated and experimental effects in determining the device efficiency [44,45].   Modeling techniques define fundamental phenomena in photovoltaic devices, which allows for the instinctive classification of optimized operating conditions for each parameter [41]. For further practical applications of heterojunction solar cells, SCAPS is ideal for intraband tunneling and trap-assisted tunneling [42]. The strength of this modeling technique was initially simulated using various inorganic HTMs in the PSCs, and later, the results were compared with experimental results [30,39]. For holes and electrons, capture cross-sections were set to 10-16 cm 2 , which resulted in perovskites having carrier diffusion lengths of approximately 1 µm [43]. Active layer thickness was set to 400 nm in order to provide the efficient collection of charges. The recombination rate of the bimolecular electron-hole has a tremendous effect on the solar cell efficiency, so the total recombination in the as-simulated PSCs was taken into account by SCAPS. SCAPS software does not take into account the recombination of charges at the corresponding interfaces. Therefore, two thin defect layers were stacked at the HTM-perovskite and electron transport material (ETM)-perovskite interfaces to overcome the interfacial defect density, as presented in Table 2. This structure allowed for the evaluation of the role of interface adjustment in the simulated and experimental effects in determining the device efficiency [44,45].

Identifying the Best HTM
In order to identify the best HTM for efficient PSCs, the photovoltaic parameters with different HTMs, such as NiO, Cu 2 O, CuI, and CuSCN, were simulated. The schematic diagram of the simulated devices and the energy band diagrams are given in Figure 1a,b. The basic parameters of the used materials are given in Table 1. While modeling for various HTMs, the parameters of the ETM and perovskite layers were fixed. Additionally, the same values for both bulk and interface defect densities were used to maintain a consistent analysis.
The current-voltage (J-V) characteristic curves and external quantum efficiency (EQE) of the as-simulated PSCs are depicted in Figure 2a,b, respectively. The photovoltaic metrics of the as-simulated devices are presented in Table 3. The simulation results showed that, when the HTM parameters (mentioned in Table 1) were altered, the photovoltaic metrics varied, particularly the Voc and fill factor (FF), as shown in Figure 2a and Table 2. Furthermore, it can be seen from Figure 2b that there was a little variance in the EQEs of the as-simulated PSCs. From the simulation results, it was noticed that the PSC with the Cu 2 O HTM delivered a higher performance compared to the other HTMs. The superior performance of the Cu 2 O-based PSC was attributed to the alignment of frontier energy levels, suitable electron affinity, and hole mobility of the as-simulated materials, as discussed below. Additionally, the simulation results closely match the experimental findings of previous published research [29,30].  For the efficient flow of electrons from perovskite to the ETM, the conduction band of the ETM should align with the perovskite's conduction band [57,58]. It is also essential that the valance band of the HTM match with the absorber layer in order to facilitate the transport of holes between them [59,60]. In other words, this can increase the built-in potential, which is critical for improving the Voc values of the PSCs. To observe the energy band matching between HTMs and the perovskite layer, the energy band levels of the assimulated PSCs were analyzed, as shown in Figure 3. It can be seen from the energy levels of the as-simulated PSCs that there was a formation of an energy barrier in the cases of the NiO, CuI, and CuSCN HTMs. This energy barrier hindered the transportation of holes from the perovskite layer to the HTM, and as a result, the performances of the PSCs dropped. Energy barriers with values of −0.48 eV, −0.40 eV, −0.21 eV, and −0.11 eV were calculated for NiO, CuSCN, CuI, and Cu2O, respectively. Since NiO had the highest energy barrier, therefore the lowest Voc of 0.72 V and lowest PCE of 8.5% were obtained. On the other hand, the Cu2O HTM had the lowest energy barrier of −0.11 eV to the flow of holes, and thus, the PSC delivered the highest PCE of 25.2%. With regard to the low energy barrier resulting from frontier energy level alignment with the perovskite layer, Cu2O had a superior performance. Cu2O was, therefore, regarded as the best HTM for usage in the PSCs. In the following sections, we examine and analyze various factors of Cu2O that affect the performance of PSCs.  For the efficient flow of electrons from perovskite to the ETM, the conduction band of the ETM should align with the perovskite's conduction band [57,58]. It is also essential that the valance band of the HTM match with the absorber layer in order to facilitate the transport of holes between them [59,60]. In other words, this can increase the built-in potential, which is critical for improving the V oc values of the PSCs. To observe the energy band matching between HTMs and the perovskite layer, the energy band levels of the as-simulated PSCs were analyzed, as shown in Figure 3. It can be seen from the energy levels of the as-simulated PSCs that there was a formation of an energy barrier in the cases of the NiO, CuI, and CuSCN HTMs. This energy barrier hindered the transportation of holes from the perovskite layer to the HTM, and as a result, the performances of the PSCs dropped. Energy barriers with values of −0.48 eV, −0.40 eV, −0.21 eV, and −0.11 eV were calculated for NiO, CuSCN, CuI, and Cu 2 O, respectively. Since NiO had the highest energy barrier, therefore the lowest V oc of 0.72 V and lowest PCE of 8.5% were obtained. On the other hand, the Cu 2 O HTM had the lowest energy barrier of −0.11 eV to the flow of holes, and thus, the PSC delivered the highest PCE of 25.2%. With regard to the low energy barrier resulting from frontier energy level alignment with the perovskite layer, Cu 2 O had a superior performance. Cu 2 O was, therefore, regarded as the best HTM for usage in the PSCs. In the following sections, we examine and analyze various factors of Cu 2 O that affect the performance of PSCs.

Electron Affinity of Cu2O and PSC Performance
The PCE of a PSC can be improved by ensuring that the HTM and perovskite layer are aligned in terms of frontier energy levels. In this context, the valence energy band (Ev) must be taken into account in order to understand this difference between the HTM and the perovskite layer. The mismatching between the Ev of perovskite and an HTM is generally denoted by valance band offset (VBO), which can be determined by the electron affinities of the corresponding materials. In addition, if the VBO between the HTM and perovskite layer is small, the performance of the PSC is superior compared to higher values of VBO. In the simulation, it was observed that the electron affinity of Cu2O had a significant impact on the performance of PSCs. There were essentially no differences in the patterns of photovoltaic parameters with varied electron affinities of HTM from those reported in a previous work [61]. In order to obtain the optimal value for the electron affinity of Cu2O, the affinity was varied from 1.5 eV to 3.7 eV, as depicted in Figure 4a,b. The major impacts obtained were on the Voc and FF values of the PSCs. The Voc and FF values were improved substantially when the affinity was changed from 2.0 eV to 3.2 eV. Correspondingly, the PCE was boosted from 19.6% to 25.2%.

Electron Affinity of Cu 2 O and PSC Performance
The PCE of a PSC can be improved by ensuring that the HTM and perovskite layer are aligned in terms of frontier energy levels. In this context, the valence energy band (E v ) must be taken into account in order to understand this difference between the HTM and the perovskite layer. The mismatching between the E v of perovskite and an HTM is generally denoted by valance band offset (VBO), which can be determined by the electron affinities of the corresponding materials. In addition, if the VBO between the HTM and perovskite layer is small, the performance of the PSC is superior compared to higher values of VBO. In the simulation, it was observed that the electron affinity of Cu 2 O had a significant impact on the performance of PSCs. There were essentially no differences in the patterns of photovoltaic parameters with varied electron affinities of HTM from those reported in a previous work [61]. In order to obtain the optimal value for the electron affinity of Cu 2 O, the affinity was varied from 1.5 eV to 3.7 eV, as depicted in Figure 4a,b. The major impacts obtained were on the V oc and FF values of the PSCs. The V oc and FF values were improved substantially when the affinity was changed from 2.0 eV to 3.2 eV. Correspondingly, the PCE was boosted from 19.6% to 25.2%.  The simulation results revealed that high or low values of electron affinity resulted in inferior device performance, which was due to mismatch the in Ev levels of HTM and perovskite. In order to achieve the highest PCE, we assumed that the optimal electron affinity for Cu2O was 3.2 eV, and that for perovskite was 3.93 eV. Furthermore, aligning the frontier energy levels was desirable to reduce the recombination rate at the interface between Cu2O and perovskite, as shown in Figure 4c. Consequently, the PCEs of the PSCs could be improved by manipulating the Ev of the HTM relative to the perovskite layer.

Hole Mobility of Cu2O and PSC Performance
Since the HTM is responsible for collecting and transporting holes from the perovskite layer to the back electrode, the hole mobility (µh) of the used HTM should be high enough to transport holes before they recombine. An optimum value of hole mobility up to 90 cm 2 V −1 s −1 for Cu2O was considered from the previous literature [61]. However, the µh of Cu2O was adjusted from 20 to 100 cm 2 V −1 s −1 to examine the effect on the performance of the PSCs. The J-V curves and PCEs of the as-simulated PSCs as a function of the hole mobility of Cu2O are depicted in Figure 5. It can be seen that the short-current density (Jsc) remained nearly constant, whereas the FF and Voc improved as the µh of Cu2O was increased. Because of the improvement in hole conduction across the Cu2O HTM, the PCE increased from 15.4% to 25.2% when the µh was increased from 20 to 100 cm 2 V −1 s −1 . The improvement in PCE could be attributed to the high µh that reduced the series resistance within the PSCs [62]. It should be noted that the simulation results showed almost no changes in the PCEs for µh from 60 to 100 cm 2 V −1 s −1 , which is consistent with previous results [63,64]. The simulation results suggested that the optimal value of µh that corresponded to the highest PCEs was in the range from 60 to 100 cm 2 V −1 s −1 . These results provide guidelines for the optimization of PSC performance by adjusting the hole mobilities of HTMs. The simulation results revealed that high or low values of electron affinity resulted in inferior device performance, which was due to mismatch the in E v levels of HTM and perovskite. In order to achieve the highest PCE, we assumed that the optimal electron affinity for Cu 2 O was 3.2 eV, and that for perovskite was 3.93 eV. Furthermore, aligning the frontier energy levels was desirable to reduce the recombination rate at the interface between Cu 2 O and perovskite, as shown in Figure 4c. Consequently, the PCEs of the PSCs could be improved by manipulating the E v of the HTM relative to the perovskite layer.

Hole Mobility of Cu 2 O and PSC Performance
Since the HTM is responsible for collecting and transporting holes from the perovskite layer to the back electrode, the hole mobility (µ h ) of the used HTM should be high enough to transport holes before they recombine. An optimum value of hole mobility up to 90 cm 2 V −1 s −1 for Cu 2 O was considered from the previous literature [61]. However, the µ h of Cu 2 O was adjusted from 20 to 100 cm 2 V −1 s −1 to examine the effect on the performance of the PSCs. The J-V curves and PCEs of the as-simulated PSCs as a function of the hole mobility of Cu 2 O are depicted in Figure 5. It can be seen that the short-current density (J sc ) remained nearly constant, whereas the FF and V oc improved as the µ h of Cu 2 O was increased. Because of the improvement in hole conduction across the Cu 2 O HTM, the PCE increased from 15.4% to 25.2% when the µ h was increased from 20 to 100 cm 2 V −1 s −1 . The improvement in PCE could be attributed to the high µ h that reduced the series resistance within the PSCs [62]. It should be noted that the simulation results showed almost no changes in the PCEs for µ h from 60 to 100 cm 2 V −1 s −1 , which is consistent with previous results [63,64]. The simulation results suggested that the optimal value of µ h that corresponded to the highest PCEs was in the range from 60 to 100 cm 2 V −1 s −1 . These results provide guidelines for the optimization of PSC performance by adjusting the hole mobilities of HTMs.

Acceptor Density of Cu2O and PSC Performance
It was reported that p-type doping of an HTM produced more positive charges (majority charge carriers) and, thus, improved the bulk conductivity of the HTM and the performance of the PSCs [35]. Majority charge carriers that can be created at suitable acceptor densities (Na) can greatly boost the photovoltaic parameters of PSCs. When using PSCs, an iterative approach of doping concentration aids in the improvement of their overall performance [65]. In order to understand the influence of Na on the performance of PSCs, the Na values were changed from 10 7 to 10 18 cm −3 in the Cu2O. As a function of the Na values of Cu2O, the J-V curves, Voc, FF, and PCE of the as-simulated devices are presented in Figure 6a, b, and c, respectively. As the Na of Cu2O increased, the Voc increased from 1.13 to 1.29 V. It was the rise in the built-in electric potential at the Cu2O-perovskite interface that was responsible for the greater values of Voc observed at higher Na values. The FF and PCE increased from 76.6 to 83.6% and 20.2 to 25.2%, respectively, with the increase in Na of Cu2O. The larger Na value raised the electric potential, and therefore, the built-in electric field at the interface of the perovskite and HTM increased. The built-in electric field promoted the oriented charge carrier transportation and, thus, minimized the recombination losses [66]. In addition, the reduced recombination rate of charge carriers boosted the PCE of the PSCs by reinforcing the separation of charge carriers. From the simulations, the optimal value for Na, which resulted in the highest PCE, was 10 18 cm −3 . This optimal Na value of Cu2O is consistent with earlier reports [47]. This was attributed to shallow coulomb traps, which increased the hole mobility of Cu2O.

Acceptor Density of Cu 2 O and PSC Performance
It was reported that p-type doping of an HTM produced more positive charges (majority charge carriers) and, thus, improved the bulk conductivity of the HTM and the performance of the PSCs [35]. Majority charge carriers that can be created at suitable acceptor densities (N a ) can greatly boost the photovoltaic parameters of PSCs. When using PSCs, an iterative approach of doping concentration aids in the improvement of their overall performance [65]. In order to understand the influence of N a on the performance of PSCs, the N a values were changed from 10 7 to 10 18 cm −3 in the Cu 2 O. As a function of the N a values of Cu 2 O, the J-V curves, V oc , FF, and PCE of the as-simulated devices are presented in Figure 6a-c, respectively. As the N a of Cu 2 O increased, the V oc increased from 1.13 to 1.29 V. It was the rise in the built-in electric potential at the Cu 2 O-perovskite interface that was responsible for the greater values of V oc observed at higher N a values. The FF and PCE increased from 76.6 to 83.6% and 20.2 to 25.2%, respectively, with the increase in N a of Cu 2 O. The larger N a value raised the electric potential, and therefore, the built-in electric field at the interface of the perovskite and HTM increased. The built-in electric field promoted the oriented charge carrier transportation and, thus, minimized the recombination losses [66]. In addition, the reduced recombination rate of charge carriers boosted the PCE of the PSCs by reinforcing the separation of charge carriers. From the simulations, the optimal value for N a , which resulted in the highest PCE, was 10 18 cm −3 . This optimal N a value of Cu 2 O is consistent with earlier reports [47]. This was attributed to shallow coulomb traps, which increased the hole mobility of Cu 2 O.

Contact of Back Electrode with Cu2O and PSC Performance
Because the Cu2O layer was placed on top of the perovskite and the back electrode made contact with this HTM, it was critical to explore charge carrier transport when Ohmic or Schottky formations occurred, as these could alter charge collection [67]. The proper collection of holes through the back electrode requires the establishment of an Ohmic or Schottky contact with a small barrier. In this context, various metal electrodes, such as Ag, Cu, and Au with work functions of 4.74 eV, 4.90 eV, and 5.10 eV, respectively, were integrated in the as-simulated PSCs. It was revealed that the performance of the PSCs was affected by varying the work function value, as can be seen in Figure 7. In the presence of variable work function, the obtained behaviors of Voc, FF, and PCE matched those reported in previously published research [67]. It was revealed that a metal electrode with high work function resulted in an improved Voc of 1.29 V. Furthermore, the FF climbed to a maximum value of 83.65% with rising work function. Due to the improved built-in voltage, the Voc increased as the work function of the metal electrode increased. For the work function value of 5.1 eV, the PCE improved, reaching a maximum value of 25.21%. The improvement in the performance of PSCs could be attributed to the small series resistance resulting from a decrease in the Schottky barrier at the interfaces of Cu2O-HTM and Au-electrode. In Figure 7b,c, it is shown that Schottky barriers were formed in the energy band diagram for the work functions of electrodes of 4.74 eV and 4.90 eV, respectively. In Figure 7d, a Schottky barrier for holes was significantly reduced when the work function was equal to or smaller than the valence energy band of the HTM [68], resulting in a significant enhancement in the efficiency of PSCs. The findings of the simulation showed that Cu2O could be utilized in the PSCs, but the deposition of inorganic HTMs in the regular designs of PSCs should also be taken into consideration. For instance, inorganic HTMs are challenging to dissolve in the non-polar solvents needed to preserve the perovskite layer. In this regard, surfactant modifications [29] or chemical solvents, such as dipropyl sulfide [30] and isopropanol suspension [69], that are less aggressive to the degradation of the perovskite layer might be used to deposit solution-processed inorganic HTMs in regular PSCs.

Contact of Back Electrode with Cu 2 O and PSC Performance
Because the Cu 2 O layer was placed on top of the perovskite and the back electrode made contact with this HTM, it was critical to explore charge carrier transport when Ohmic or Schottky formations occurred, as these could alter charge collection [67]. The proper collection of holes through the back electrode requires the establishment of an Ohmic or Schottky contact with a small barrier. In this context, various metal electrodes, such as Ag, Cu, and Au with work functions of 4.74 eV, 4.90 eV, and 5.10 eV, respectively, were integrated in the as-simulated PSCs. It was revealed that the performance of the PSCs was affected by varying the work function value, as can be seen in Figure 7. In the presence of variable work function, the obtained behaviors of V oc , FF, and PCE matched those reported in previously published research [67]. It was revealed that a metal electrode with high work function resulted in an improved V oc of 1.29 V. Furthermore, the FF climbed to a maximum value of 83.65% with rising work function. Due to the improved built-in voltage, the V oc increased as the work function of the metal electrode increased. For the work function value of 5.1 eV, the PCE improved, reaching a maximum value of 25.21%. The improvement in the performance of PSCs could be attributed to the small series resistance resulting from a decrease in the Schottky barrier at the interfaces of Cu 2 O-HTM and Au-electrode. In Figure 7b,c, it is shown that Schottky barriers were formed in the energy band diagram for the work functions of electrodes of 4.74 eV and 4.90 eV, respectively. In Figure 7d, a Schottky barrier for holes was significantly reduced when the work function was equal to or smaller than the valence energy band of the HTM [68], resulting in a significant enhancement in the efficiency of PSCs. The findings of the simulation showed that Cu 2 O could be utilized in the PSCs, but the deposition of inorganic HTMs in the regular designs of PSCs should also be taken into consideration. For instance, inorganic HTMs are challenging to dissolve in the non-polar solvents needed to preserve the perovskite layer. In this regard, surfactant modifications [29] or chemical solvents, such as dipropyl sulfide [30] and isopropanol suspension [69], that are less aggressive to the degradation of the perovskite layer might be used to deposit solution-processed inorganic HTMs in regular PSCs.

Conclusions
A numerical analysis was performed to find the optimum conditions for PSCs with inorganic HTMs. Several factors that could affect the performance of PSCs were thoroughly investigated. According to the simulation results, the optimal electron affinity, hole mobility, and acceptor density of Cu2O were found to be 3.2 eV, 60 to 100 cm 2 V −1 s −1 , and 10 18 cm −3 , respectively. The simulation findings showed that a matched valance energy band of Cu2O resulted in improvements in the performance of the PSCs, whereas an unmatched valance energy band of Cu2O led to a high charge recombination rate and poor device performance. Low work function electrodes impeded charge transport by forming large Schottky barriers; hence, high work function of a metal electrode is needed for a low charge transport barrier. A PCE of 25.2% was attained under optimal conditions, demonstrating that Cu2O-based PSCs are promising for future applications.  Data Availability Statement: All the data presented in the manuscript can be obtained from the corresponding author by reasonable request.

Acknowledgments:
The authors acknowledge the UAEU-Strategic Research Program for providing financial support and Professor Marc Burgelman, Gent University, Belgium, for providing SCAPS software.

Conflicts of Interest:
The authors do not have any conflicts of interest to disclose.

Conclusions
A numerical analysis was performed to find the optimum conditions for PSCs with inorganic HTMs. Several factors that could affect the performance of PSCs were thoroughly investigated. According to the simulation results, the optimal electron affinity, hole mobility, and acceptor density of Cu 2 O were found to be 3.2 eV, 60 to 100 cm 2 V −1 s −1 , and 10 18 cm −3 , respectively. The simulation findings showed that a matched valance energy band of Cu 2 O resulted in improvements in the performance of the PSCs, whereas an unmatched valance energy band of Cu 2 O led to a high charge recombination rate and poor device performance. Low work function electrodes impeded charge transport by forming large Schottky barriers; hence, high work function of a metal electrode is needed for a low charge transport barrier. A PCE of 25.2% was attained under optimal conditions, demonstrating that Cu 2 O-based PSCs are promising for future applications.