Optimization of lead - free CsSnI 3 - based perovskite solar cell structure

: Perovskites are considered the most promising material for the latest generation of solar cells. However, due to the presence of lead in their composition, the development of non - toxic Perovskite cells has become an essential goal to enable their large - scale production. In this work, we have simulated, modeled and optimized the structure of a single solar cell that consists of a non - toxic cesium – tin – iodine CsSnI 3 Perovskite absorber with a low band gap energy value of 1.3 eV, between TiO 2 and PTAA materials as ETL and HTL layers, respectively. A simulation model describing the charge carrier processes and the e ﬀ ect of interface defect density is presented. Several structures based on alternative ETL and HTL materials are proposed. An optimal device structure is proposed based on the results obtained. An e ﬃ ciency of 19.92% is obtained with V oc = 0.829 V, J sc = 30.68 mA/cm 2 and FF = 73.33% using SnO 2 and Spiro - OMeTAD as ETL and HTL materials. However, 29.22% is achieved using the optimal structure as the bottom cell in a tandem con ﬁ guration.


Introduction
Solar cell technology has evolved since its inception through three generations, the first is based on thick wafers of silicon semiconductor material, which despite their high manufacturing costs continue to dominate [1]. The second generation cells is based on amorphous nanocrystalline or polycrystalline semiconductor thin films deposited on cheap substrates [2].
Perovskite cells, which belong to the third generation of solar cells, are currently the focus of interest and exploitation of scientists and research groups specialized in this field. Power conversion efficiencies of solar cells utilizing these materials expanded from ∼3.8% in 2009 to ∼25.5% in 2020 [3]. The Perovskite material is typically composed of three parts according to the ABX 3 stoichiometry. A represents, in most cases, the organic part like methylammonium CH 3 NH 3+ , MA, or formamidinium HC (NH 2 ) 2+ , FA, but can also be inorganic like cesium Cs. B is a metal ion, bivalent in the conventional composition, usually lead Pb 2+ , or one of its substitutes like germanium Ge 2+ , selenium Se 2+ , etc. B can also be trivalent or tetravalent like bismuth Bi 4+ , antimony Sb 4+ or titanium Ti 4+ . X is a halide anion such as the chlorine anion Cl − , the bromine anion Br − , or the iodine anion I − [4] Photovoltaic devices based on the absorber Perovskite MAPbI 3 are still the most efficient and most widely studied Perovskite solar cells. However, the instability of the Methylammonium MA cation hinders their commercialization [5] The conversion record achieved so far is 25.6% for the FAPbI 3 -based Perovskite cell, in which the more stable Formamidinium FA replaces MA [6]. Several methods have been detailed in the literature to address the instability problem and to increase efficiency, such as the additive engineering-based approach [7].
Lead Pb 2+ is still essential to ensure excellent photoelectric properties of Perovskite films. However, lead can be toxic to the environment, humans, and other species. For this reason, lead-free Perovskites have attracted much attention recently. Several non-or less toxic elements can replace lead in the composition of Perovskite, tin Sn is one of them. It has even been reported that tin-containing Perovskites have equally good optoelectronic properties. However, tin has a tendency to oxidize to Sn 4+ , so it is recommended to use encapsulation in the manufacture of tin-based Perovskite cells [8]. Cesium tin iodide CsSnI 3 , with a band gap of 1.3 eV, is one of the candidates to replace the conventional lead-based Perovskite material. The latter is completely inorganic, has similar optoelectronic properties to its lead-based counterpart, and can be deposited using low-cost processes [9]. In addition, several authors have reported the excellent mechanical and electronic properties of cesium-based perovskite films [10,11].
In this article, we have presented a work that consists in modeling and simulating, then optimizing the structure of a single solar cell whose absorber material is the lead-free and inorganic Perovskite CsSnI 3 . We have particularly focused on the impact of the increase of the defect density at the interfaces between the absorber layer and the neighboring layers. We have then simulated the performance of the structures with alternative ETL and HTL layers.
The goal of the study is the optimization of the structure that leads to the best performance and photovoltaic parameters with minimum interface recombination rate and appropriate bandgap energy shifts at the absorber boundaries, and this with minimal fabrication cost, in addition to adapting to a tandem configuration as a bottom cell in combination with an appropriate top sub-cell.

Simulation model
A drift-diffusion model was considered to express the transport of photo-generated carriers [12]. Photogenerated current density was calculated with expressions derived by using the numerical solutions of the Poisson equation and the continuity equations for holes and electrons [13] Equation (1) represents the expression of photogenerated current density [14] ( ) ( ) where λ min and λ max are minimum and maximum wavelengths, q is the electron charge, F( ) λ is the solar spectrum, and EQE( ) λ is the external quantum efficiency of the cell.
A two model equivalent circuit was considered to evaluate the current-voltage behavior where R s and R sh are parasitic resistances. J 0 is the reverse dark saturation current density due to the radiative recombination assuming the Shockley-read-Hall recombination theory. And J s is the interface recombination contribution in current density losses reported as a function of the interface recombination velocity [15] expressed in equation (3). Minority carrier concentration and bandgap energy offsets at the boundaries of the absorber were evaluated using equations (4) and (5).
n,p n,p th tn,p Here, N tn,p is the front/back interface density, V th is the thermal velocity, and σ n,p is the electron/hole capture cross section at interfaces.
Conduction band offset (CBO) and valence band offset (VBO) are given in the following equations: where χ is the electron affinity and E g is the bandgap energy.
where J Max and V Max are the current and voltage at the maximum power point. J sc and V oc are the short circuit current density and the open circuit voltage, respectively. P inc is the incident power.

Results and discussion
In this study, the basic structure, configured as follows: Glass/FTO/TiO 2 /CsSnI 3 /PTAA/Au, is considered [17]. Cesium-tin-iodine CsSnI 3 is the studied lead-free Perovskite absorber, which has a band gap energy of 1.3 eV, while titanium oxide TiO 2 and PTAA (poly-triyaril amine) are the materials used for the ETL and HTL electron and hole transport layers A schematic representation of the proposed solar cell is shown in Figure 1. The data of the physical parameters of the materials used in this simulation were carefully selected from the literature [18][19][20].

Investigation of the interface density of defects
The density of defects at the interfaces between the Perovskite absorber and the neighboring ETL and HTL layers has a profound influence on the collection of carriers since they are considered as obstacles that prevent their passage. This influence on the photovoltaic parameters, especially on the conversion efficiency, has been studied by varying their value from 10 12 to 10 20 cm −3 . Figure 2 shows the behavior of the photovoltaic parameters as a function of the above-mentioned defect density increase.
The results revealed the degradation of the performance from the increase of the front or back interfaces defect density higher than 10 14 cm −3 due to the increase of the recombination velocity at the considered interface, which favors the capture of the carriers by the trap states. The influence was more significant for the increase in the front interface defect density. It was noticed that the photocurrent density was not affected by the augmentation of the back interface defects, because it mainly comes from the photo-generated electrons. This study shows the importance of keeping the defect density at the interfaces below a value of 10 15 cm −3 to achieve the best performance.

Investigation of appropriate ETL and HTL materials
The dissociation of photogenerated pairs of carriers (electrons and holes) in the absorber occurs at the front and back interfaces between the ETL layer and the absorber, and the HTL layer and the absorber, respectively. For this reason, the amount of defects at these locations must be taken into account because of its relationship with the recombination rate. On the other hand, the shift of energy bands at the interfaces strongly affects the amount of collected carriers. Therefore, the choice of the materials used for ETL and HTL layers is important. In this section, several materials have been proposed for investigation to reach high performance. Zinc sulfide (ZnS), tin dioxide (SnO 2 ), cadmium zinc sulfide (CdZnS), and 1-(3-methoxycarbonyl)propyl-1phenyl [6,6]C61 (PCBM) were investigated as ETM. The alternative materials studied for the hole transport layers were the organic semiconductor 2,2′,7,7′-tetrakis[N,N-di(4-methoxyphenyl)amino]-9,9′-spirobifluorene (Spiro-OMeTAD), cuprous oxide (Cu 2 O), nickel oxide (NiO), and poly(3,4-ethylenedioxythiophene) polystyrene sulfonate (PEDOT:PSS). Data and material input parameters used in the simulation are taken from the literature [13,19,20]. The conversion efficiency of the different structures is plotted in Figure 2.   Figure 3(a) shows that the structure based on the SnO 2 -ETL material gives the best efficiency of 19.92% with a narrower conduction band offset than the base cell. However, the front interface recombination velocity value remains unchanged. While Figure 3(b) reveals that using Spiro-OMeTAD-HTL material leads to the best efficiency with a more appropriate value of valence band offset 0.3 eV and an unchanged back interface recombination velocity. A better performance of the organic-HTL materials was noted compared to the inorganic materials. However, the structure based on inorganic Cu 2 O-HTL still recorded a high yield of 18.31% and appropriate values of VBO and S p . The simulation results allow us to consider the structure SnO 2 /CsSnI 3 /Spiro-OMeTAD as the optimal configuration which reaches the best performance with the most appropriate values of bandgap energy offsets and recombination velocity at the interfaces. However, in order to favor a totally inorganic cell, the SnO 2 /CsSnI 3 /Cu 2 O structure can be considered, although the conversion efficiency is slightly lower. The current-voltage curves of the mentioned structures are represented in Figure 4. Simulation results are detailed in Table 1.    In order to close this study, the suggested structures were simulated as bottom sub-cell in two-terminal tandem configuration in association with the top sub-cell having the following structure: PCBM/CsSnGeI 3 /Spiro-OMeTAD with an absorber bandgap energy of 1.5 eV [21]. The results of the simulation are shown in Table 2. In literature, it is possible to find many simulation works which were done using different code for different purposes [22][23][24][25][26][27][28][29][30][31].

Conclusion
In this work, a Perovskite solar cell structure based on the lead-free Perovskite absorber CsSnI 3 was simulated and optimized. The effect of defect density on the solar cell performance at the front ETL/Perovskite and back Perovskite/HTL interfaces was studied. Different cell structures with various alternative ETL and HTL materials were simulated, and the obtained results were presented. An optimal structure with selected ETL and HTL materials with appropriate values of interface recombination velocity and band gap shift at the absorber boundaries was suggested based on the obtained results. An efficiency of 19.92% was achieved with the optimal structure: SnO 2 /CsSnI 3 /Spiro-OMeTAD, and 18.31% with the fully inorganic and non-toxic structure: SnO 2 / CsSnI 3 /Cu 2 O. An improvement was observed over the baseline device. The structure was simulated as a bottom cell in a two-terminal tandem solar cell, and an efficiency of 29.22% was achieved. The results of this study can provide useful information before proceeding to the manufacturing stage.
Acknowledgments: I thank my husband Djamel for his love and support. I thank Professor Dr. Ülku Bayhan, Burdur Mehmet Akif Ersoy University, Turkey, for her help, and Professor Dr. Iskender Akkurt, Süleyman Demirel University, Isparta, Turkey, for his valuable guidance.
Funding information: There is no funding for this article.

Conflict of interest:
The author declares no conflict of interest.
Ethical approval: The conducted research is not related to either human or animal use. Data availability statement: Derived data supporting the findings of this study are available from the corresponding author on request.