Simulation and analysis of lead-free perovskite solar cells incorporating cerium oxide as electron transporting layer

The great demand for renewable energy has greatly contributed to the development of the solar cell industry. Recently, silicon solar cells have dominated the world market. The ease of processing gives perovskite solar cells (PSCs) an advantage over conventional silicon solar cells. Regular silicon photovoltaics require expensive, multi-step processes accomplished in a specialized ultraclean-chamber facility at an elevated temperature (>1000 °C) and highly vacuumed workspace. Hence, researchers and the solar cell industry have focused on PSC as a great rival to silicon solar cells. Despite this, the highest efficiency was obtained from lead-based PSC, which has a considerably high toxicity issue and low stability related to lead content, so the research field pays attention to lead-free perovskite solar cells. In this digital simulation, tin-based perovskite in this paper, methylammonium tin iodide (MASnI3) with the use of cerium oxide (CeOx) as an electron transporting layer (ETL) with varying percentages of oxygen, which means different shallow donor densities (ND). The optimum value for the thickness of the absorber layer (perovskite) was made, and the current–voltage characteristics and efficiency calculations were also accomplished for the best cell. Then an improvement was made by changing the ND value of CeOx, and the best-optimized cell parameters were: open circuit voltage (VOC) of 0.92 V, short circuit current density (JSC) of 30.79 mA cm−2, power conversion efficiency (PCE) of 17.77%, and fill factor (FF) of 62.86%.


Introduction
The production of electricity is crucial for world development and is unquestionably the main driver of economic growth in both industrialized and emerging economies. A huge increase in energy demand is being fueled by both a high population growth rate and increased per capita energy consumption. 1-4 Fossil fuel-based energy sources currently meet the majority of the world's energy needs. However, fossil fuel supplies are being depleted more quickly as energy use rises. Renewable energy solutions must be created in order to address these concerns and the growing need for energy. Solar energy, photovoltaic cells that can be used to convert directly into electricity, is the most abundant renewable energy source. [5][6][7][8][9][10][11] Perovskite has gained popularity as a light-harvesting material for photovoltaic applications. Perovskite has a distinct set of optoelectrical properties, including adjustable band gaps, a high absorption coefficient, long carrier diffusion lengths, and high charge carrier mobilities. [12][13][14][15][16] In 2009, Kojima and colleagues reported a power conversion efficiency (PCE) of 3.8% for perovskite solar cells (PSC). 17 Aer a decade, Cui et al. reported a 20.8% PCE for methylammonium lead iodide PSC. 18 CITY U HK/UW established the most recent approved efficiency of close to 25.8% in 2021. 19 Regardless of the rapid evolution of PCE, the present stability of solar cells makes mass production of PSC difficult. [20][21][22] The lead content of lead perovskite solar cells is one of their main disadvantages. 23 Due to lead's toxicity, the Restriction of Hazardous Substances directive of the European Union forbids its use in any electronics or electrical equipment. Alternatives to lead as the metal cation in the perovskite photo-absorber have thus become a signicant area of research. 24 Stepping up or down within group IV of the periodic table of elements provides an easy way to replace lead. The recently found element, scarcely radioactively stable erovium, lies in the row below lead. Due to its radioactivity, it may not be a suitable replacement for lead. 25 Due to its lower toxicity, tin (Sn), which is on the same row as lead, would be an excellent replacement for lead in PSCs. Organic tin halide synthesis has been going on for as long as lead halide synthesis. 26 The MASnI 3 perovskite, with an energy gap (E g ) of 1.3 eV, has been reported to be used in solar cells and produced a PCE of 6.4%. The +2 oxidation state of Sn, which is necessary for the formation of a perovskite, is unstable, and the metal quickly oxidizes to the +4 state when exposed to oxygen or air humidity, 27,28 this affects both the conditions under which the device operates and the technique used to make solar cells. It has only been capable of determining the cell performance of the pure tin halide PSCs with strong sealing of the devices because any interaction with oxygen may instantaneously cause the oxidation of tin. 29 CeO x is regarded as one of the most signicant infrequent oxides because of its wide bandgap, high dielectric constant, strong ionic conductivity, high thermal and chemical stability, matching lattice parameters with silicon, and exceptional capacity to store and release oxygen. 30,31 Wang et al. prepared CeO x (x = 1.87) lms by a facile sol-gel approach at a low temperature (150°C) and used them as an alternative to the high-temperature annealing processed TiO 2 ETL. The optimized PSC achieved a champion PCE of 14.32% by adjusting the CeO x precursor solution. 32 Yang et al. used CeO x as ETL in an inverted structure of PSC, utilizing CsPbIBr 2 perovskite as light harvesting material. The all-inorganic PSC recorded a maximum efficiency of 5.6% with improved stability. 33 Jien et al. reported CeO x lm as a protection layer for perovskite against humidity and metal reactions with the electrode. The device with CeO x as the ETL had a PCE of 17.47%. 34 In this simulation, CeO x is used as an ETL material due to its tunable broad band gap (3.0-3.6 eV) and outstanding optical and dielectric properties. 35,36 Moreover, CeO x may enhance the stability of the PSC against moisture and oxygen. 37 A numerical simulation of the solar cell would be necessary to gure out the best set of parameters and the physical parameters for prediction accuracy. The device is simulated using the SCAPS-1 D soware and the inuence of different properties of the MASnI 3 material and CeO x layer on the efficiency of a tin-PSC is estimated. A unique device structure (uoride tin oxide (FTO)/CeO x / MASnI 3 /2,2 ′ ,7,7 ′ -tetrakis[N,N-di(4-ethoxyphenyl)amino]-9,9 ′ -spi-robiuorene (Spiro-MeTAD)/Au) of a tin-based PSC using the Spiro-OMeTAD as a hole transporting layer (HTL) has been suggested for modeling. The aim of this simulation is to illustrate that the efficiency of lead-free PSCs may be enhanced by varying the ND value of the CeO x and the thickness of the absorber layer (MASnI 3 ).

Architecture and materials properties of suggested PCS
For PV modelling, a one-dimensional SCAPS simulation soware was employed. The SCPAS program employs Poisson's equation, which denes the relationship between the photocarrier and the semiconductor's electrostatic potential, and continuity equations, which represent charge generation and recombination kinetics in materials. 38 Solving both Poisson's equation and the continuity equation gives us the QE and J-V properties. 39 Using Poisson's equation and the continuity equation, it is possible to gure out the density of electrons and holes. 40 Poisson's equation can be used to determine the distribution of the electric eld E(x): Dri and diffusion current densities control the transportation properties of charge carriers in semiconductor. The following equations describe the dri and diffusion current densities for electrons and holes. 38 where m n and m p are to electron hole mobility, respectively, and D n , and D p are electron and hole diffusion coefficients respectively. r(x), 3, and q refer to space charge distribution, dielectric permittivity, and charge of electron, respectively. n(x) and J n represent the concentration and current density of electrons. p(x) and J p represent the concentration and current density of hole. Seven layers, consisting of perovskite absorber, ETL, HTL, and electrodes, can be constructed into a HPSC using the SCAPS soware. All PV computations in this study are performed under AM 1.5G (100 mW cm −2 ) conditions. The structure for the proposed PSC, FTO/CeO x /MASnI 3 / Spiro-OMeTAD/Au, is shown in Fig. 1a. The FTO layer, which is deposited on a glass substrate, acts as a front transparent contact. The CeO x layer represents the crucial layer that determines the performance of the device since the transport of electrons is a major factor affecting the PCE. MASnI 3 perovskite is the absorber material that is responsible for charge carrier generation through light absorption. Spiro-OMeTAD material acts as HTL. The energy band graph of the suggested structure ( Fig. 1b) clearly shows that the conduction bands of the absorbing material MASnI 3 are smaller than those of electron transporting material CeO x , and the mismatch between the conduction band (CB) of MASnI 3 and the CeO x material is very slight. As a direct consequence, electrons can easily pass from MASnI 3 to FTO via CeO x . Electrons can thus move freely through CeO x from MASnI 3 to FTO. A very large valence band (VB) offset (VBO) exists between the absorbing material MASnI 3 and the ETL material CeO x . Therefore, the positive charge (h + ) in the ETL material CeO x will be sealed. As shown in Fig. 1b, the valence bands of the hole transporting material Spiro-OMeTAD are greater than those of the absorbing material MASnI 3 , and the valence band mismatch among those two materials is signicantly small. Furthermore, the offsetting in the conduction bands between the HTL material Spiro-OMeTAD and the absorbing material MASnI 3 is very considerable, forbidding the electrons from MASnI 3 from reaching the back contact.
The physical parameters for the simulations of the FTO/ CeO x /MASnI 3 /Spiro-OMeTAD/Au heterostructure solar cell are listed in Table 1, 41 whereas the physical properties of the defects density in MASnI 3 are listed in Table 2. All simulations are achieved at a temperature of 300 K.

Optimization of MASnI 3 thickness
The thickness of the absorbing material plays a signicant role in solar cell efficiency since it is related to the absorption of the incident light, which leads to enhancing the I-V characteristics. [42][43][44] In this study, all the parameters of the materials in Tables 1 and 2 are kept xed, and different values of the thickness of MASnI 3 are selected in order to estimate the optimum thickness value of the absorber material. Fig. 2 shows the parameters of the suggested PSC as a function of MASnI 3 thickness. As Fig. 2a illustrates the quantum efficiency of the suggested PSC, we can see the inuence of the absorbing material thickness on the QE value. As expected, by increasing the value of the thickness, the QE value increases. Fig. 2b demonstrates the J-V curve of the PSC under the illumination of 100 mW cm −2 (air mass AM 1.5G). Fig. 2c-f shows the V OC , J SC , FF, and, PCE respectively. From Fig. 2b, the V OC is slightly decreased with thickness increases, while Fig. 2c shows a signicant change in the value of J SC . Besides the variant J SC Fig. 1 (a) Schematic layout of the designed PSC and (b) energy bands graph of the PSC.  with the thickness of the absorbing material, the FF is also highly affected by the thickness, as shown in Fig. 2d. As a consequence of the change in the last mentioned parameters, the PCE varies with changing the thickness, as illustrated in Fig. 2e. Table 3 shows the calculated parameters that are used to select the optimum thickness.

Optimization of donor density (ND) of the CeO x
The percentage of oxygen content in CeO x determines the value of ND. 45 In this simulation, different values of ND are chosen in order to understand their effect on the PSC performance. Fig. 3a-e shows the variation of the solar cell parameters as a function of log(ND). All the parameter values increase as the value of ND increases. This is attributed to the enhancement of the conductivity, which makes the movement of the electrons through the ETL much easier. ETL's primary function is to give electrons a low-resistive route so that they can be collected. Additionally, it must prevent electrons from stacking up close to the interface. On the other hand, if this happens because of lower conductivity, unrestricted electrons and holes interact together on the interfacial side, resulting in a decreased generated current. Low conductivity causes a higher series resistance (R s ). The high value of resistance in the cell causes the FF to drop. The inuence of low conductivity in this case caused by low ND will affect both the FF and V OC , as shown in Fig. 3b and d, while the J SC is not signicantly inuenced. Table  4 summarizes the obtained results when varying the ND value. It is obvious that the best PCE obtained of 17.77% at ND is equal to 1 × 10 21 cm −3 . As the ND of CeO x increases to a certain point, the PCE also increases. Aer this point, the ND of the cerium oxide has no effect on the PCE because the CeO x has degenerated (practically). Furthermore, once the ND reaches a certain value where the CeO x serves as a hole-blocking and electrontransporting layer, any further increase in the ND value is unnecessary. 46

Effect of the series and shunt resistance (R s & R sh )
The R s and R sh have signicant control over how well solar cells work. It comes from the metal connections on the solar cell and layer surfaces. The device's efficiency was assessed by changing the value of R s from 0 to 10 (U cm 2 ). Fig. 4a-d show that as R s increases, the FF and PCE decrease, resulting in leakage currents, while the V OC and J SC remain unchanged.    Poor shunt resistance increases power loss in the solar cell by enabling the current produced by light to take an alternative path. A similar deection drops the voltage produced by the photovoltaic cell and minimizes the current owing through the photovoltaic junction. Fig. 5a-d shows that the FF is the most affected parameter, resulting in a decrease in the value of PCE, while the V OC and J SC are almost unchanged.
Notably, the results showed that PSCs designed with a roomtemperature CeO x layer could improve the PCE of MASnI 3 -based photovoltaics, which is a signicant step toward PSC industrialization. Table 5 shows the results of a comparison between the various structures, and it can be stated that adding CeO x into the perovskite-based devices is the most benecial method for using it in PSCs.

Conclusions
The performance of the suggested cell structure FTO/CeO x / MASnI 3 /Spiro-OMeTAD/Au PSC has been examined using the SCAPS 1D simulation soware. Different CeO x and MASnI 3 parameters are tuned in order to investigate the behavior of the device. The open-circuit voltage and efficiency received a signicant contribution from the CeO x layer. Cell performance was shown to be enhanced by the CeO x ETL's higher ND. Cell performance appears to be signicantly inuenced by the MASnI 3 layer's thickness. The density of the MASnI 3 /CeO x / MASnI 3 interfacial defect and the MASnI 3 /Spiro-OMeTAD interfacial defect were determined. The highest PCE ever calculated was 17.77%, with a J SC value of 30.79 mA cm −2 , a V OC value of 0.919 V, and a ll factor of 62.78%. Our ndings indicate that future research may show that the suggested device structure involving both CeO x and MASnI 3 is an effective device for making thin-lm solar cells that are both inexpensive and efficient.

Data availability
Data will be available based on reasonable request.

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