Improving the performance of organic lead–tin laminated perovskite solar cells from the perspective of device simulation

The toxic lead in traditional perovskite solar cells (PSCs) poses a fatal threat to the environment, and it takes time and technology to complete the transition to lead-free perovskite solar cells. In this work, we introduce a lead–tin laminated perovskite solar cell, which can obviously reduce the toxicity of lead. Our ultimate goal is to study the factors that affect the performance of the device. On the basis of reducing the lead-based perovskite layer, use SACPS-1D (solar cell capacitor simulator) to optimize the parameters to maximize the performance of the entire device. Adjusting the physical parameters, we got the power conversion efficiency (PCE) of 17.59% and 6.14% for single-cell lead-based and single-cell tin-based perovskite solar cells respectively, which are close to the experimental results. The simulation results show that under the laminated structure, the thickness of the two perovskite absorber materials based on lead and tin has a certain influence on the performance of the device. After optimization, it is determined that the best thicknesses of lead-based absorption layer (LBA) and tin-based absorption layer (TBA) are 20 nm and 150 nm respectively. Optimize the doping concentration of acceptor and donor of the laminated perovskite absorber layer to obtain higher PCE and open circuit voltage (VOC). The best values are 1015 cm−3 and 1016 cm−3 for LBA and TBA respectively. We also found that when adjusting the positions of LBA and TBA, the recombination rate under different defect densities verified that the laminated absorption layer close to the light source side dominates the device performance. Provide reference for future optimization of laminated perovskite solar cells. Considering these factors comprehensively, we optimized the device performance parameters as follows: VOC = 0.93 V, JSC = 19.56 mA/cm2, FF = 71.12% and PCE = 12.89%.


Introduction
Organic/inorganic hybrid perovskite materials have the advantages of large absorption coefficient, high carrier mobility, long exciton diffusion length and low-temperature preparation process (Marchioro et al. 2014;Stranks et al. 2013;Xing et al. 2013;Zhou et al. 2014;Jeon et al. 2015;Yang et al. 2015;Arora et al. 2017), which are used in light-emitting diodes (Tan et al. 2014;Wang et al. 2016), solar cells (Kojima et al. 2009;Hou et al. 2015), photodetectors (Ahmadi et al. 2017;Dong et al. 2017), lasers (Xing et al. 2014) and other aspects, so that they have gained wide attention. These excellent intrinsic properties make them more suitable as light-absorbing materials for solar cells, and recently achieved a power conversion efficiency (PCE) of 22% (Yang et al. 2017). The rate of perovskite/ monocrystalline silicon laminated solar cells has increased to 28.0%, showing strong application potential. Although perovskite solar cells have the advantages of high efficiency, abundant raw materials, easy preparation, and low cost, they still have issues to be solved, such as instability, difficulty in packaging, and biological toxicity.
In the early stage of research on lead-based halogen perovskite materials, people began to consider replacing lead with tin congener element for the purpose of low toxicity and environmental protection. However, researchers soon discovered that due to the easy oxidation of divalent tin ions, the tin-based perovskite light-absorbing layer has problems such as high defect density and low carrier lifetime, which makes its development slower than that of lead-based perovskite. From the first reported efficiency of 0.9% in 2012 (Chen et al. 2012), to the beginning of 2019, the efficiency of tin-based batteries has not exceeded the efficiency of 10%. However, from the end of 2019 to 2020, several international research groups Meng et al. 2020aMeng et al. , 2020bLiu et al. 2020;Nishimura et al. 2020;) have reported tin-based perovskite solar cells with efficiency over 10% through different stability optimization methods, providing a good reference for Sn-Pb mixed perovskite solar cells. However, tin-based perovskite has the disadvantages of easy oxidation and more vacancy defects, and the faster crystallization rate of tin-based perovskite causes more film defects, which limits the further improvement of tin-based perovskite solar cell efficiency. All these need to be urgently solved.
Although the current highest photoelectric conversion efficiency of perovskite solar cells has reached 25.2%, there is still room for improvement in the efficiency of halogen perovskite solar cells, especially the ideal bandgap perovskite solar cells and perovskite laminated cells. On the one hand, the current wide band gap halogen perovskite has been successfully applied to Perovskite/Si tandem cells and Perovskite/CIGS tandem cells, and has achieved a photoelectric conversion efficiency close to 30%. On the other hand, the development of ideal band gap, narrow band gap halogen perovskite solar cells, that is, tin-lead mixed halogen perovskite is also underway. This makes it possible for more efficient single-cell halogen perovskite solar cells and efficient full perovskite tandem cells.
The organization of halogen perovskite and tin-lead mixing are important directions for the development of halogen perovskite solar cells in recent years. Halogen organic perovskites can solve the problem of instability of the perovskite phase caused by inorganic cations (mainly Cs + ). In addition to obviously reduce the toxicity of lead, tin-lead mixed halogen perovskite can optimize the halogen perovskite band gap, so as to make the halogen perovskite absorbance layer with ideal band gap and narrow band gap possible. Zhou and Padture group (Chen et al. 2019) applied Sn and Ge mixed inorganic halide perovskite to solar cells for the first time. They used CsSn 0.5 Ge 0.5 I 3 perovskite to achieve an efficiency of 7.11%. Hu et al. carried out research on inorganic Sn-Pb mixed halogen perovskite, through the passivation of grain boundaries and surface defects, to achieve a 13.7% conversion efficiency of CsSn 0.4 Pb 0.6 I 3 perovskite solar cells (Hu et al. 2020). Saliba et al. (2016) used Cs/MA/FA mixed cations to obtain perovskite solar cells with good stability and repeatability, with an efficiency of more than 21%.
This work studies a new type of lead-tin laminated halogen perovskite materials, compared with the increasingly mature organic-inorganic hybrid lead-based perovskite materials. On the one hand, halogen-based organic perovskites can solve the problem of instability of the perovskite phase caused by inorganic cations, and the introduction of tin can optimize the band gap of halogen-based perovskites. The general formula of the perovskite structure is AMX 3 : A is a positive monovalent organic cation or inorganic cation, M is an octahedral coordination positive divalent metal ion, and X is a negative monovalent halogen ion (Cl, Br or I). In this article MAPbI 3 and MASnI 3 were selected as the perovskite absorber layers, where M corresponds to the toxic element Pb and the non-toxic element Sn, respectively. The properties of Sn are closest to those of Pb, with both similar ionic radii and electron grouping, and potentially superior semiconductor properties. More importantly, Sn is a non-toxic element, and Sn 2+ degrades to eco-friendly SnO 2 when exposed to air, which is much less harmful to the environment. The article concludes that the optimal thicknesses of MAPbI 3 and MASnI 3 absorber layers in the presently constructed lead-tin laminated perovskite solar cells are 20 nm and 150 nm, respectively, reducing the lead-based perovskite absorber layer involvement. Compared to all-lead-based perovskite solar cells, the toxicity is reduced by 88.2%, driving the commercialization of perovskite solar cells. This is in line with the development trend of assembling more stable and more efficient halogen perovskite solar cell devices. On the other hand, the optimization of lead-tin laminated halogen perovskite solar cells in this work seeks the best ratio of various parameters on the basis of reducing the lead-based perovskite layer, and uses SACPS-1D to optimize the parameters to maximize the overall device Performance.

Device structure and parameters
The simulated lead-tin laminated perovskite structure is shown in Fig. 1a. The device structure is composed of FTO/TiO 2 /MAPbI 3 /MASnI 3 /Spiro-MeOTAD/Au. In the present design of Pb-Tn hybrid perovskite device structure, the organic ammonium ion is CH 3 NH 3 + , the metal ions are Pb 2+ and Sn 2+ , and the halogen anion is Cl − . The photoelectric properties of perovskite ABX 3 are inextricably linked to its elemental composition, and its structure and properties can be regulated by changing different metal cations while following the tolerance factor t = (r A + r X )[2 1/2 (r B + r X )](0.8 < t < 1). Figure 1b shows the energy band diagram of the device structure. The LUMO level of TiO 2 matches the minimum conduction band of the lead-tin multilayer perovskite absorber layer, and effective electron transfer occurs between the absorber layer and the gold electrode. The HOMO level of TiO 2 is also lower than the maximum value of the valence band of the perovskite, and the absorption layer is effectively blocked without hole migration. The energy bands of the laminated absorbers also satisfy the conditions of both electron and hole transitions. Considering the bad recombination process between device interfaces, we added IDL1 and IDL2 interface defect layers (IDL) between TiO 2 /MAPbI 3 and MASnI 3 / spiro-MeOTAD, respectively, to simulate a perovskite area with a large number of defects (Liu et al. 2014a(Liu et al. , 2014b. The selection of device parameters is very important. According to the reported theoretical and experimental research results, we carefully selected relatively reasonable parameters (Liu et al. 2013;Hao et al. 2015;Devi and Mehra 2019;Murata 2014a, 2014b;Löper et al. 2015;Stamate 2003;Poplavskyy and Nelson 2003;Liu and Kelly 2013). Table 1 summarizes the basic physical and device parameter settings of each layer of the simulation. The left and right contact work functions are 4.4 eV (FTO) and 5.1 eV (Au) respectively. All simulations were performed under AM 1.5 lighting.

Numerical simulation
We used SCAPS-1D to numerically simulate the device structure. According to the initial parameter values given in Table 1, we simulated two single-cell perovskite solar cells, FTO/TiO 2 /MAPbI 3 /spiro-MeOTAD/Au and FTO/TiO 2 /MASnI 3 /spiro-MeOTAD/ Au. As shown in Table 2, the performance parameters of the single-cell lead-based and single-cell tin-based PSCs obtained are similar to those of the experiment, which verifies the effectiveness of the modeling. After that, we began to simulate lead-tin laminated perovskite solar cells. Figure 2a defines the panel for SCAPS-1D, showing the light direction and each layer of the device structure. Figure 2b is the energy band diagram, different from single-cell perovskite solar cells, the perovskite absorber layer of the laminated structure generates two built-in electric fields. And HTL and ETL respectively formed a large built-in electric field of 3 V/μm under high doping concentration, which is in line with the perovskite solar cell with n-i-p structure, being consistent with the existing reports (Ke et al. 2015). Figure 2c is the current density-voltage (J-V) obtained by simulation. The mixing of Pb 2+ in the perovskite absorber layer likewise makes the whole device structure more stable, while the higher LUMO energy level of the tin group leads to a larger difference in energy level with the carrier extraction layer, resulting in a larger loss of open-circuit voltage V OC . The mixed metal ions of Pb 2+ and Sn 2+ make the LUMO energy level of the overall perovskite absorber layer decrease and increase the V OC (1.2578 V). According to the initial parameters, we get: V OC = 1.2578 V, J SC = 20.5054 mA/cm 2 , FF = 30.09% and PCE = 8.53%. Laminated cells are a way to break the Shockley-Queisser limit by using two light-absorbing layers,   where the narrow band gap mainly absorbs long-wavelength sunlight, and the wide band gap mainly absorbs short-wavelength sunlight. In Fig. 2d, under the same initial parameters, we obtained the quantum efficiency curves (QE) of lead-based, tin-based and lead-tin laminated perovskite solar cells respectively. The Sn-Pb mixed metal ion has achieved the advantage of continuous wavelength tunability in the near-infrared wavelength band, and also achieved a relatively excellent external quantum efficiency in the 800-900 nm band. The lead-tin laminated solar cells made up for the wavelengths of sunlight that lead-based could not absorb. The range of the external quantum efficiency curve covers the entire visible spectrum, and the absorption value from 350 to 770 nm is the strongest, exceeding 50%.

Results and discussion
The following discussion defaults all to the initial values given in Table 1 when the individual parameters are not changed.

Effect of thickness of laminated perovskite absorption layer on device performance
For perovskite solar cells, the thickness of the perovskite absorber layer is one of the important factors affecting device performance (Liu et al. 2014a(Liu et al. , 2014b. The thickness of the absorption layer is too thin, which is not conducive to effective absorption of photons, resulting in a decrease in solar efficiency. Since the carriers must reach the carrier collection layer from the absorption layer before recombination, too thick absorption layer causes the collection of photogenerated carriers to be hindered. Therefore, reasonable absorption layer thickness can enhance the spectral response of the device, thereby improving the performance of the entire device. It is very meaningful to study the thickness of the absorption layer. Considering the double-layer absorber layer structure of lead-tin laminated perovskite solar cells, we investigated the effects of LBA and TBA perovskite absorber layers on device performance, respectively. The thickness of each absorption layer is between 20 and 500 nm, and we have obtained V OC , J SC , FF and PCE diagrams under different absorption layer thicknesses, as shown in Fig. 3. In Fig. 3a, the effect of TBA thickness on the open-circuit voltage VOC is greater than that of LBA. With the increase of TBA thickness, the V OC tends to decrease, and when the MASnI 3 thickness reaches 350 nm, the V OC value is less than 1. The thickness of TBA is less than 150 nm, and with the increase of LBA thickness, the value of V OC is relatively ideal. When the thickness of TBA is controlled at 50 nm, the thickness of LBA has a small peak in V OC in the range of 20-200 nm. Figure 3b shows the J SC curves of different absorption layer thicknesses. In the interval between low LBA thickness and high TBA thickness, or between high LBA thickness and low TBA thickness, J SC achieves relatively high values. PCE is an important indicator to measure the performance of the device. From the analysis of the PCE diagram in Fig. 3d, when the thickness of the TBA is greater than 150 nm, the PCE of the device decreases rapidly. And when the thickness of TBA is less than 150 nm, PCE tends to increase with the thickness of LBA. Considering the toxicity problem caused by Pb, we choose the thickness of LBA and TBA as 20 nm and 150 nm, respectively. But in order to pursue higher power conversion efficiency PCE, the thickness of LBA can be considered as 300 nm. For tin-based perovskite solar cells (MASnI 3 ), we list the variation of the electron and hole carrier diffusion length Ln (Lp) with the density of defect states, as shown in Table 3 (Du et al. 2016). Varying different TBA thicknesses, Fig. 3e shows the variation of the obtained power conversion efficiency PCE with the diffusion length of the carriers and the thickness of the perovskite layer. With the increase of TBA thickness and diffusion length, the PCE shows first decreasing and then leveling off, as the carriers must reach the carrier collection layer by the absorber layer before compounding, if the absorber layer is too thick, the photogenerated carriers cannot be collected effectively. Carrier diffusion length of 0.5-1 μm is optimal.

Effect of NA/ND of laminated perovskite absorption layer on device performance
Reasonable doping concentration can optimize device performance (Xiao et al. 2015). In semiconductor devices, such as mature silicon solar cells, the acceptor doping concentration (N A ) and donor doping concentration (N D ) are controlled within a reasonable range, and better energy location and carrier transmission characteristics can be obtained. In addition, the unstable Sn 2+ of tin-based perovskite solar cells is easily oxidized to stable Sn 4+ at room temperature, resulting in a self-doping effect. Therefore, it is very important to explore the doping concentration of the absorption layer. Figure 4 shows the performance parameters of different doping concentrations. Figure 4a, when the TBA doping concentration is 10 13 -10 16 cm −3 and the LBA doping concentration is 10 15 -10 17 cm −3 , it is the top region of the doping concentration, and the V OC reaches a high peak and does not cause the electric field to decay. Figure 4b is a J SC diagram of different absorption layer doping concentrations, except that when the LBA doping concentration is between 10 16 and 10 17 cm −3 , the value obtained by J SC is not very ideal. The J SC obtained by the different doping concentrations of the two absorption layers in other intervals is better. Figure 4d is the PCE diagram. What is interesting is that when the TBA doping concentration is 10 16 cm −3 , the LBA doping concentration in the range of 10 10 -10 15 cm −3 has almost no effect on the PCE of the overall device. When the LBA doping concentration was 10 17 cm −3 , PCE began to decrease drastically, resulting in a higher Auger recombination rate. Considering comprehensively, we choose LBA doping concentration of 10 15 cm −3 and TBA doping concentration of 10 16 cm −3 as the optimized values. In order to explain the change of the performance parameters with the doping concentration of the absorber layer. We fixed the N A of MASnI 3 to 10 16 cm −3 and studied the hole quasi-Fermi level (E Fp ) distribution, recombination rate (R) and external quantum efficiency QE at different MAPbI 3 doping concentrations (10 15 cm −3 , 10 16 cm −3 , 10 17 cm −3 ). Figure 5a, with the increase of the doping concentration of MAPbI 3 , the hole quasi-Fermi level (E Fp ) shows a downward trend, which is getting lower and lower than the top of the HTL valence band. This facilitates the transition of holes in the perovskite absorption layer to the hole transport layer, and the open circuit voltage V OC increases. Figure 5b, the doping concentration of MAPbI 3 is 10 17 cm −3 , the recombination rate (R) increases sharply, and the PCE decreases drastically. Figure 5c shows that the external quantum efficiency QE decreases with the increase of MAPbI 3 doping concentration, resulting in the obstruction of absorption of photons by the absorption layer, the decrease of photon absorption rate and the decrease of short-circuit current J SC . We analyzed the effects of dopants on the photovoltaic properties of the material in three directions: hole quasi-Fermi level (E Fp ) distribution, recombination rate (R) and external quantum efficiency QE. Photon absorption is blocked at too low doping concentrations, carrier separation is affected, and PCE and J SC are affected. Too high a doping concentration can cause severe doping effects, where the built-in electric field is no longer enhanced and the carrier separation slows down. It also causes high carrier recombination, which affects device performance.

Effect of defect density of laminated perovskite absorption layer on device performance
The morphology and quality of perovskite films are considered to be important parameters that determine the performance of perovskite solar cells (Ball et al. 2013;Azri et al. 2019;Abdelaziz et al. 2020;Singh et al. 2020). Poor quality perovskite films lead to severe defect density (Nt), and carrier recombination in the perovskite absorber layer can affect device performance. In this simulation we introduce passivation, which is the use of certain chemicals to react with surface components to deactivate their electronic or chemical activity, which is a general way to reduce perovskite defects and improve optoelectronic performance in many semiconductor devices. The use of passivation to reduce defects is critical to improving device efficiency and long-term stability. For example, small molecule passivators such as 2-mercaptopyrimidine (MPM) were introduced to passivate defects on the surface of MAPbI 3 /MASnI 3 perovskite films to reduce perovskite defects.
Research on the influence of perovskite defect density on solar cell performance, based on the Shockley-Read-Hall composite model (SRH). The following formula (1) (2) (Zekry et al. 2018): Here, R SRH is the recombination rate, n and p are the concentrations of electrons and holes, respectively, and τ is the lifetime of carriers. Nt and Et are the defect concentration and defect energy level, respectively, and σ and υ th represent the carrier trapping cross section and thermal velocity respectively.
(1) From the formula (1) (2) (3), we get that the carrier lifetime and diffusion length (L), the recombination of electrons and holes are directly related to the defect density. The greater the defect density, the shorter the carrier lifetime and diffusion length, and the aggravation of electron-hole recombination. In order to explore the main factors affecting the performance of the solar cell, we used the same method to control the defect density of LBA and TBA to simulate the performance parameters of each device to explore the influence on the performance of the device. From the analysis in Fig. 6, we found that as the defect density of LBA and TBA increases, the recombination rate increases, the carrier lifetime decreases, and the overall performance of the device decreases. We found an interesting phenomenon that the high-performance parameter values are close to the LBA side. When the TBA defect density is greater than 10 18 cm −3 , the defect density of the TBA close to the light source has a dominant effect on the overall performance, and the V OC , J SC and PCE are greatly reduced.
In order to explore the above phenomenon more deeply, we set up another structure, that is, swap the positions of LBA and TBA. We call the device on the left side of Fig. 7 structure 1, and the device on the right side as structure 2. The corresponding defect density  Tables 3 and 4, and the performance parameters of each device are simulated for structure 2. From Fig. 8, we find that when the LBA defect density is greater than 10 18 cm −3 , the defect density of the LBA close to the light source has a dominant effect on the overall performance, and the V OC , J SC and PCE are drastically reduced. In order to verify the above phenomenon, we discussed from the perspective of Shockley-Read-Hall Reorganization Model (SRH). Figure 7 shows the recombination rate obtained with different defect densities of different structures. The defect density of fixed LBA is 10 17 cm −3 , and the defect density of TBA is 10 16 cm −3 , 10 18 cm −3 and 10 20 cm −3 , respectively. When the TBA defect density is less than 10 18 cm −3 , the recombination rate of structures 1 and 2 is very small, which is consistent with the above analysis. When the defect density of TBA is greater than 10 18 cm −3 , that is, when 10 20 cm −3 is taken, the recombination rate of structure 1 increases sharply, while that of structure 2 increases a little, which proves that the defect density of the laminated perovskite absorber near the light source side dominates the damage to the overall performance of the device. We need to pay more attention to this phenomenon when manufacturing perovskite solar cells with a laminated structure. Table 5 shows the parameter values of each layer after our final optimization, and Fig. 9 shows the J-V and QE curves obtained after optimization. On the basis of reducing the lead content, the parameters of the lead-tin laminated perovskite solar cell are: V OC = 1.2578 V, J SC = 20.5054 mA/cm 2 , FF = 30.09% and PCE = 8.53%.

Other HTL candidates
In addition to Spiro-MeOTAD as HTL, we enumerate different hole transport layers to optimize this work. Table 6 shows us the parameters after enumerating the different HTL optimizations Murata 2014a, 2014b;Azri et al. 2019;Lin et al. 2019). Table 7 shows the performance parameters of the devices after optimization. From the table, we find that the differences in the performance parameters of each device are not very large for different HTL materials after optimization, where the highest and lowest power conversion efficiencies are obtained for Cu 2 O and CuI as HTL, respectively. Figure 10 shows the J-V curves and the external quantum efficiency QE curves after different HTL optimization.

Conclusion
A lead-tin laminated perovskite solar cell was designed and discussed by us, and the absorber layer was made of lead-tin mixed materials. We used the SCAPS-1D simulator to simulate the lead-tin laminated perovskite solar cell. The simulation results show that when the TBA thickness is greater than 150 nm, the PCE of the device decreases rapidly, and when the TBA thickness is less than 150 nm, the PCE increases with the increase of the LBA thickness. Considering comprehensively, we choose the thickness of LBA and TBA to be divided into 20 nm and 150 nm as the optimized values. The acceptor doping concentration (TBA) and donor doping concentration (LBA) in the laminated structure respectively affect the performance of the device. When the N A of TBA is 10 16 cm −3 and the N D of LBA is 10 15 cm −3 , which is the top region of the doping concentration, the V OC reaches a high peak and the PCE value is better. We use the hole quasi-Fermi level (E Fp ), recombination rate (R) and external quantum efficiency (QE) to reasonably explain the changes of various performance parameters. Defect density is the main culprit for the degradation of device performance. As the defect density of the absorption layer increases, the recombination of carriers in the perovskite light absorption layer will dominate, and each performance parameter has a tendency to decrease. It was finally confirmed that the defect density of LBA and TBA were controlled below 10 17 cm −3 and 10 16 cm −3 , respectively, and relatively good performance could be obtained. We also found an interesting phenomenon that in the laminated perovskite solar cell, through the recombination rate (R) of different laminated perovskite structures, we proved that the defect density of the laminated perovskite absorber near the light source side dominates the damage to the overall performance of the device. We should pay more attention to this phenomenon when optimizing laminated perovskite solar cells. This work can provide reference for the preparation of high-performance laminated perovskite solar energy in the future.