Abstract

All-inorganic perovskites based on CsPbI_3-xBr_x are promising halides for use in efficient photovoltaic devices due to their high stability. This generated a tremendous research interest from the scientific community to move towards this class of materials. However, perovskite solar cells based on CsPbI_3-xBr_x have not yet achieved the expected conversion efficiencies compared to their hybrid counterpart. In this work we used SCAPS 1D to model the all-inorganic CsPbI_3-xBr_x based solar cell, investigate and discuss the limitations of the device in order to improve its conversion efficiency. For this purpose, we used the normal (n-i-p) configuration with Al/ETL/CsPbI_3-xBr_x/HTL/ITO structuring. By varying the inorganic transport layers HTL and ETL, our study revealed that the best HTL/ETL combination is Cu₂O as HTL and SnO₂ as ETL. We otherwise have shown that acceptor and donor doping of Cu₂O and SnO₂ respectively offers a mean to reduce recombination in the device. The study showed that the acceptor (N_A=10¹⁸cm^-3) and donor (N_D=10¹⁷cm^-3) doping rates are the best dopant values for the cell. By optimizing the various study parameters, we obtained a high-performance normal structure PSC with a conversion efficiency (PCE) of 17.87%.

1. Introduction

In a decade, perovskite-based solar cells have grown dramatically with a rapid improvement in efficiency from 3.8% ^{1, 2, 4, 5, 6, 7, 8, 10, 12} in 2009 to 25.5% ^{9, 10, 14, 19} in 2021, making perovskites a new family of materials with great promise for photovoltaic. This exceptional progress has sparked a great deal of interest from the scientific community to focus more on perovskites. However, several challenges need to be addressed in order to consider a future commercialization of perovskite-based photovoltaic (PV) devices. These include lead toxicity, a rather limited understanding of physical processes such as hysteresis of I-V characteristics, and especially the stability problems of hybrid perovskite-based devices. It is therefore essential to succeed in stabilizing these devices in order to achieve perovskite materials based solar cells, which perform well, have a very long service life and comply with environmental standards. The stability problems noted in the hybrid perovskites have thus redirected researchers towards all-inorganic materials. Compared to hybrid perovskites, all-inorganic perovskites have demonstrated better thermal stability ¹¹ and much more suitable carrier transport properties to theoretically give higher efficiencies. However, experimental efficiencies provided by all-inorganic perovskite-based solar cells are still far below those obtained by their hybrid counterpart. The poor performance of all-inorganic perovskites compared to the theoretical limit ¹³ may be due to intrinsic problems such as high defect densities, energy level mismatch, choice of transport layers used in the device processing, acceptor and donor doping levels, etc... These shortcomings could be overcome by a modelling investigation of the perovskite based photovoltaic device together with an appropriate choice of the perovskite material and electrons and holes transport layers.

In this simulation study we used CsPbI_3-xBr_x as the perovskite material with several materials as electron and hole transport layers (HTL and ETL). Our main objective being to obtain highly stable all-inorganic PSCs (PSCs) composed not only of the inorganic halide perovskite absorber, but also of inorganic hole and electron transport window layers. For this purpose we first performed the validation of our solar cell model on the normal configuration Al/ETL/CsPbI_3-xBr_x/HTL/ITO by comparing our experimental results with those obtained by other research groups. Then, several inorganic materials are tested as electron and hole transport layers. These materials included TiO₂ and SnO₂ as electron transport layer (ETL) with ZnO taken as reference material, and CuI and Cu₂O as hole transport layer with NiO_x as reference material. Finally, investigation on the acceptor and donor doping rate of the HTL and ETL layers was carried out for the best transport layers in order to maximize the conversion efficiency of the device.

2. The Solar Cell Device Structure

SCAPS-1D program developed by GANT University ^{12, 14} for the numerical modelling of thin film solar cells have been used. For this purpose, it is imperative to solve the Poisson equation (1) and the continuity equations of electrons (2) and holes (3), respectively:

(1)

(2)

(3)

In these equations n and p are the free electrons and holes concentrations, respectively, and being the trapped electrons and holes concentrations and and representing the ionized donor and acceptor doping concentrations, respectively.

By solving these three equations, the modelling parameters are obtained. The normal (n-i-p) planar PSCs used in the simulation consists in Al/ZnO/CsPbI_3-xBr_x/NiO_x/ITO as shown in Figure 1, where the CsPbI_3-xBr_x absorber is sandwiched between a layer as the HTL and a layer the ETL. An Indium Tin Oxide (ITO) layer is applied as a back contact and an aluminum metal (Al) layer as a front contact. The material parameters used are taken from the literature and are summarized in Table 1.

In the table, and are the effective conduction-band and valence-band densities, and are the acceptor and donor densities, and are the hole and electron mobilities, is the defect density, χ is the electron affinity and is the relative permittivity of the perovskite material.

In this study, we set for the CsPbI_3-xBr_x absorber, the energy band gap at 1.72 eV ¹⁷, the thickness at 490 nm ²⁰ and the initial defect density at 4.6110¹⁵ cm^-3. Work functions of back and front contact are 4.8 eV (ITO) and 3.3 eV (Al), respectively. The simulation study was done in the standard AM 1.5G (100W/m², T= 300K).

3. Results and Discussions

In our reference solar cell model, ZnO and NiO_x are used as ETL and HTL, respectively together with CsPbI_3-xBr_x perovskite as the absorbing material. The input parameters for the simulation are those shown in Table 1. The current density-voltage (J-V) curve obtained is shown in the Figure 2.

The extracted results from the above curve of our solar cell modeling are compared in Table 2 with experimental data from the literature ²⁰. Our device model shows a conversion efficiency (PCE) of 14.87% corresponding to a short-circuit density of 18.72 mA⁄cm², an open-circuit voltage () of 1.18 V and a fill factor (FF) of 67.44%, which are close to the experimental values reported in 2021 by Jin Hyuck Heo (see Table A1) ²⁰. This preliminary step in this work allowed us to validate both our device model and the values of the parameters used in the simulation. It therefore makes it possible to use the model to investigate and analyze the various other parameters of the solar cell.

The hole transporting layer (HTL) plays an important role in perovskite based solar cells (PSCs). Compared to organic HTL, inorganic HTLs have advantages of simple preparation, good chemical stability, high hole mobility and low cost, making them potential candidates for use in stable PSCs. In this section, various HTL are used with a ZnO film as ETL. The input parameters used in the simulation are given in Table 3.

Figure 3 shows the external quantum efficiency (EQE) plots obtained with the various HTLs. A broad spectral response is observed up to a 750 nm whatever the HTLs used. We also notice from Figure 3 that the external quantum efficiency is not really influenced by the HTL nature. This is due to the fact that the hole transport layer is located at the back of the absorbing layer which causes little influence on the optical absorption. The energy level diagram (Figure 4) shows a good alignment of the HTL energy levels with that of the CsPbI_3-xBr_x absorbing layer. However better aligment is pointed out with the Cu₂O HTL which shows that the Cu₂O performs better as HTL than the other materials (). Figure 5 shows the current density vs. voltage (J-V) characteristics of the perovskite based solar cell as a function of the HTL nature. The solar cell performances are listed in Table 4. These results and those from figure 5confirm that Cu₂O is the best HTL material used in the device with a conversion power of 17.70%, a fill factor (FF) of 79.98%, an open circuit-voltage of 1.18V and a short-circuit current density of 18.77. The high efficiency obtained with Cu₂O is partly due to the fact that it has the best alignment of its valence band with the absorbing layer and therefore has the most occupied molecular orbital (HOMO) than the other HTLs.

We have set Cu₂O as the HTL and we will study the effect of several ETL films (, and ) in this section. The parameters used for the ETLs are listed in Table 5.

Figure 6 highlights the external quantum efficiency (EQE) of solar cells with different ETL. The external quantum efficiency plot is essentially composed of two parts. Between 300 nm and 400 nm, a very slight increase in external quantum efficiency is observed up to a maximum value of 400 nm. In this wavelength range, the solar cell with as ETL has a slightly better response than its homologues. But from 400 nm, the responses of the three ETLs remain almost identical throughout this wavelength range.

Figure 8 shows the J-V characteristics of the solar cells using ZnO and as ETL and Table 5 summarizes the performances of these solar cells. The photovoltaic conversion efficiencies (PCE) are 17.17%, 17.70% and 17.75%, respectively. These results which are very little different are due to a perfect alignment of the material conduction band with that of the molecular orbit (LUMO) of the absorber CsPbI_3-xBr_x layer (Figure 7), which facilitates electrons transport between the absorber and the ETL. However, simulation results (Table 6) show that the solar cell with as ETL has a better conversion efficiency.

We can see that there is not much difference in the J-V curves (Figure 5a) for the ETLs used and they have almost the same spectral response width which is around 720 nm (see Figure 5b).

To study the effect of doping the HTL layer, the acceptor concentration was varied from to and the results are shown in Figure 9, Figure 10 and Figure 11. It can be seen in Figure 10b that the maximum yield of 17.70 % is achieved for the acceptor concentration of . It is important to note that the efficiency (Figure 10a), the fill factor (Figure 10b) and the short-circuit current density (Figure 10d) of the cell increase with the increase of the acceptor doping concentration. On the other hand, figure (Figure 10c) shows that from to the open circuit voltage of the CsPbI_3-xBr_x solar cell decreases with the increase of the acceptor concentration doping rate. This can be explained by the fact, the acceptor doping in the HTL layer avoids the recombination phenomenon in the HTL layer (Cu₂O). Moreover, the electrons that were in the valence band at the HTL will migrate and find holes resulting in the increase of the electrical parameters ( FF and PCE). From to the open circuit voltage increases very little and this will have no effect on the PCE efficiency (Figure 10a) and the fill factor (Figure 10b) of the solar cell. As can be seen in Figure 9, the J-V curves are almost identical under low acceptor density. However, when is greater or equal to the current density decreases while slightly increases. For low values () a high electric field is formed across the absorber, which is beneficial for the separation and collection of light-generated carriers leading to a higher current density ¹². In Figure 11 which shows the external quantum efficiency (EQE) of the Cu₂O/CsPbI_3-xBr_x cell as a function of acceptor doping concentration, it can be seen that doping the HTL layer with acceptor has no effect on the responses of the solar cells. This is simply because the HTL layer (Cu₂O) is at the back contact of the absorber layer.

In this section, SnO₂ which has shown better performance as ETL is used in the simulation. As already highlighted in Figure 6, the upper energy level of SnO₂ being very close to that of the CsPbI_3-xBr_x absorber, allows good electron transport to the back contact and prevents holes from escaping. The results of the effect of N_D donor doping of ETL/PSK are shown in Figure 12, Figure 13 and Figure 14. As can be observed in Figure 12a, the open circuit voltage remains almost unchanged for N_D values below 10¹⁵cm^-3. Between 10¹³cm^-3 and 10¹⁵cm^-3, donor doping level has no effect on the open circuit voltage. The recombination rate neither increases nor decreases in this doping level range. Above 10¹⁵cm^-3, increase in the donor doping level causes a rapid drop in the open circuit voltage resulting in a reduction of carriers recombination between the ETL/PSK layers. An increase in the fill factor is noted from 10¹⁵cm^-3 onwards (Figure 12 c), which then tends toward saturation for even higher donor doping rates.

This can be attributed to an increase in the ETL conductivity and also to a decrease in the series resistance of the solar cell. The PCE of the solar cell follows the same tendency as the fill factor (Figure 12 b) and reaches its maximum value at an N_D value of 10¹⁷cm^-3 which corresponds to a conversion efficiency of 17.87%. The short circuit current density curve follows the same behaviour as the PCE and FF curves up to 10¹⁷cm^-3 (Figure 12 d). From this point onwards, the donor doping rate of the ETL layer causes a drastic decrease in Jsc and the solar cell efficiency. The simulated J-V curves as a function of ETL doping concentration are shown in Figure 13. This plots indicates that the J-V characteristics as well the corresponding photovoltaic parameters ( FF et PCE) are almost similar for doping levels below From onwards, the increase in the donor doping rate of the ETL layer les a progressive improvement of the J-V characteristic shape. On the other hand, it can be noted that a better spectral response is observed between 300 nm and 400 nm when the donor doping rate takes a value of Above 400 nm, the donor doping of the ETL layer has no effect on the external quantum efficiency of the cell (Figure 12). It is also noted for open circuit voltage values between 0.8 and 1.1 V (see Figure 10), the donor doping of the ETL layer leads to an increase in the series resistance of the cell. The highest resistivity of the cell is reached when the doping is thus it can be deduced that this value is not adequate to reduce the recombinations in the /CsPbI_3-xBr_x junction. Therefore, the simulation results of the ETL layer show that the donor doping rate equal to is more favorable for the layer presented better performance for a photovoltaic device.

4. Conclusion

In this work, the inorganic CsPbI_3-xBr_x absorber is studied and numerically optimized by SCAPS-1D software using the (n-i-p) setup device with Al/ETL/CsPbI_3-xBr_x/HTL/ITO structuring. First, we fixed the ETL (ZnO) layer and varied the HTL layer. For the different inorganic hole transport layers used ( and ), the study revealed that Cu₂O is the best candidate due to its good alignment of its valence band with that of the absorber. Subsequently, by setting the best HTL (Cu₂O) and varying the ETLs (, and ), the modelling results showed that with the layer, the device gives better photovoltaic conversion efficiency. So the best HTL/ETL combination is given by Cu₂O and layers respectively. With their better acceptor and donor doping rates of the carrier transport layers, we optimized the conversion efficiency of the CsPbI_3-xBr_x absorber, which increases to 17.87%. Considering the results obtained with the simulation, we can refer to it for the experimental development of promising devices based only on all-inorganic perovskites.

References

Appendix