Numerical Modeling and Optimization of Lead-Free Hybrid Double Perovskite Solar Cell by Using SCAPS-1D

)e highest power conversion efficiency (PCE) for organic-inorganic perovskite solar cells based on lead is reported as 25.2% in 2019. Lead-based hybrid perovskite materials are used in several photovoltaics applications, but these are not highly favored due to the toxicity of lead and volatility of organic cations. On the other hand, hybrid lead-free double perovskite has no such harm. In this research study, SCAPS numerical simulation is utilized to evaluate and compare the results of perovskite solar cell based on double perovskite (FA)2BiCuI6 and standard perovskite CH3NH3PbI3 as an active layer. )e results show that the power conversion efficiency obtained in the case of (FA)2BiCuI6 is 24.98%, while in the case of CH3NH3PbI3, it is reported as 26.42%. )is indicates that the hybrid organic-inorganic double perovskite (FA)2BiCuI6 has the ability to replace hybrid organic-inorganic perovskite CH3NH3PbI3 to expand next-generation lead-free harmless materials for solar cell applications.


Introduction
A perovskite solar cell (PSC) incorporates a perovskite material whose configuration and crystallographic structure is the same as the perovskite mineral. In single intersection designs, power conversion efficiencies of solar cells utilizing these materials expanded from ∼ 3.8% in 2009 to ∼ 25.2% in 2019. Perovskite solar cells along these lines present the quickest progressing solar-powered innovation. Considerably, superior efficiencies and low-generation expenses make hybrid perovskite solar cells industrially appealing. is innovation of hybrid organic-inorganic PSCs has seen a rapid movement, and each time, the new level of power conversion efficiency had been achieved.
Perovskite materials have been noticeable for a long time. But in 2009, A. Kojima et al. presented the first design of a solar cell which was organic metallic perovskites (CH 3 NH 3 PbBr 3 and CH 3 NH 3 PbI 3 ) into dye-sensitized solar cells (DSSCs) and achieved efficiencies up to 3.13% and 3.8% [1]. A perovskite cell of size 2-3 nm nanocrystal has achieved productivity (PCE) of 6.54% after two years in 2011 [2]. Later on, Johnston and Sanith et al. created a planar heterojunction perovskite solar cell with the electron transport layer of minimized TiO 2 film rather than scaffold TiO 2 .
ese thin-film-like solar cells boost the efficiency up to perovskite solar cells (PSCs) performance enhanced quickly from the last decade by numerous researchers, still the efficiencies of perovskite solar cells have not surpassed the maximum theoretical limit of Shockley-Queisser, which was around 31.4% [11,12]. At that point, various scientists were working on lead-based perovskite solar cells and presented different strategies to achieve superior performance and high outcomes. SCAPS-1D is utilized intensively investigating thin-film solar cells throughout the years for modeling of thickness of layered structures and to examine the outcome of device design and materials parameters on their photovoltaic performance. Kai Tan et al. designed solid-state PSCs with SCAPS-1D. ey reported that the function of the preferred hole transport material (HTM) candidate on the outcome of solar cells with a group of copper conductors (CuI) and thiophene polymer (PTAA) reached PCE relatively higher because of their high bandgap, large conductivity, and superior chemical interaction with a perovskite absorber [13]. Lin et al. structured the HTM-free perovskite solar cell by a SCAPS device simulator and achieved PCE over 15% under fair conditions [14]. Narender et al. had simulated electrically organic solar cells at different charge carrier mobilities. ey conducted a maximum efficiency of the organic solar cell at maximum short circuit current at the electron and hole mobility of 0.510×10 − 6 m 2 v − 1 s − 1 [15]. Usha et al. designed the organic-inorganic PSC by using the SCAPS-1D device simulator and investigated the effect of active layer thickness and defect density on the outcome of the solar cell and got the power conversion efficiency (PCE) of 31.77% and maximum current density (Jsc) value of ∼ 25.60 mA cm − 2 [16]. Afterward, Zulqarnain Haider et al. studied the leadbased organic-inorganic PSC with the hole transport material (HTM) as CuI by simulation program SCAPS. ey analyzed that CuI as an alternate HTM can be used with CH 3 NH 3 PbI 3 and can substitute spiro-MeOTAD, which is expensive HTM for lead-based organic-inorganic PSC [17]. Abdel Hadi et al. analyzed the lead-based perovskite solar cells with different parameters by using SCAPS-1D. ey studied that the optimized performance can be achieved by varying thickness and doping levels of the active material and attained the energy conversion of this solar cell up to 30.15% [18]. Enebe et al. showed the effect of annealing of nanostructured CuO/TiO 2 heterojunction solar cells and interpreted that, with an annealed sample within the range of 300 K-423.15 K, the change in the efficiency of the solar cell is quite significant [19]. e significant problems that perovskite solar cells face are stability and toxicity. e instability of PSCs is mainly concerned with the ecological effects. However, PSCs are still away from industrialized purposes as a clean, renewable energy source because it contains lead as the prime material for absorbing sunlight, which is a harmful material for the environment. Pollution of lead can cause long-term ecological damage due to high degradation time and high toxicity. In this research article, the organic cation is replaced by formamidinium (FA) [20,21], which is the strongest candidate to replace methylammonium (MA) in PSCs, and the inorganic cation is replaced with bismuth (Bi) while lead (Pb) is replaced by the copper (Cu) to avoid instability and toxicity issues. We analyzed and compared the performance of the device with a standard lead-based hybrid PSC by the SCAPS device simulator, which is developed at the University of Gent [22].

Methodology and Modeling.
e device modeling and simulation in the accompanying segments were executed by SCAPS (version 3.3.07). e program composed of various panels by which the user can optimize the parameters and determine outcomes. Figure 1 shows the step-by-step simulation procedure for the SCAPS program.
It is based on coupled continuity differential equations and Poisson's differential equation for electrons and holes. e fundamental theory of this program is to solve continuity differential equations and Poisson's differential equation by numerical differentiation and the Gummel type iteration method [22,23].
where ε represents the dielectric permittivity, q represents the electron charge, G represents the rate of generation, D represents the diffusion coefficient, φ represents the electrostatic potential, E represents the electric field, p(x) represents the free holes, n(x) represents the free electrons, p t (x) represents the trapped holes, n t (x) represents the trapped electrons, N d+ represents the donor ionized doping concentration, N a− represents the acceptor ionized doping concentration, and x represents the thickness. e adopted planar heterojunction structure is a characteristic perovskite solar cell structure. e cell consists of an absorber layer (FA) 2 BiCuI 6 , hole transport layer (spiro-MeOTAD (2,2′,7,7′-tetrakis[N,N-di(4-methoxyphenyl) amino]-9,9′-spirobifluorene), electron transport layer (TiO 2 ), fluorine doped tin oxide layer (FTO), and gold (Au) as shown in Figure 2.
Other parameters of materials such as electron and hole thermal velocity are both set as 10 7 cm/s respectively, whereas the effective density of state for valence and conduction band is 1.8 × 10 18 and 2 × 10 18 cm − 3 . e absorption coefficient data have been taken from different works of literature to make things easier for device simulation [35,[49][50][51] (Supplementary Materials). e spectrum used in device simulation is AM1.5 G, and the operating temperature is set at 300 K. Furthermore, the working point, including numerical setting, has been set to default values. e scanning voltage is set as V1 � 0 V to V2 � 1.2 V. All the simulations in this software run under these settings.

Comparison between Perovskite (CH 3 NH 3 PbI 3 ) and
Double Perovskite (FA) 2 BiCuI 6 . Lead-based metallic perovskite solar cells are associated with instability and toxicity issues. On the other side, lead-free double PSC has no such issues. Lead-free organic-inorganic double perovskite has drawn considerable concern for solar cells and other optoelectronic properties. We had taken the copper-based perovskite material (FA) 2 BiCuI 6 which is an indirect bandgap semiconductor having a bandgap value of 1.55 eV, which is comparable to the bandgap value of perovskite CH 3 NH 3 PbI 3 . e dielectric constant of copper-based double perovskite is 5.27, while the dielectric constant of lead-based perovskite is 6.3. More particularly, copper-based double perovskite has finer optoelectronic properties due to its high extinction coefficient, large optical conductivity, and potential dielectric properties. e numerical study and comparison are performed on organic-inorganic perovskite and copper-based double organic-inorganic perovskite. From the simulation, it is found that in the case of (FA) 2 BiCuI 6 , the output parameters short-circuit current density (Jsc), open-circuit voltage (Voc), power conversion efficiency (PCE), and fill factor (% FF) at absorber layer thickness 300 nm is 32.95 mA/cm 2 , 0.94 V, 24.98%, and 80.73%, while in the case of CH 3 NH 3 PbI 3 , these (Jsc, Voc, PCE, and FF) are 34.96 mA/ cm 2 , 0.94 V, 26.43, and 80.39%, respectively. Furthermore, the J-V and PCE curves of their comparison are shown in Figure 3. is clearly shows that there is a very slight difference in values of Jsc, but both curves end at the same  e numerical analysis on lead-based perovskite and leadfree double perovskite solar cells is also compared with experimental data indicated in Table 3. Simulated device performance parameters are found to be quite close to experimental results published in the scientific literature. is study also gives theoretical guidance towards the efficient realization of perovskite solar cells by optimizing their parameters.
Results signify that lead-free double perovskite is a potential alternative to lead-based perovskite, which can be used to manufacture next-generation organic-inorganic PSC and can evade instability and stability issues linked with lead-based perovskites.

Influence of Absorber Layer ickness.
e absorber layer of the perovskite solar cell plays an essential role in device performance and outcome. erefore, the variation can considerably affect the performance and outcome of a solar cell in the thickness of an active layer of a solar cell. In this study, absorber layer thickness varies from 100 nm to 1000 nm, and we observed the effect on output parameters while all other parameters are set constant. Figure 4 and Table 4 show the deviation in device outcomes with the thickness of the active layer. e simulation results signify that with the increase in thickness of the active layer, short-circuit current density (Jsc) increases and approaches to the optimum value of ∼39 mAcm − 2 as shown in Figure 4(a). Excess carrier concentration increases by increasing thickness due to the absorption of light, which eventually increases Jsc values. Perovskite material has very high extinction and high conductivity, and it can attain very high values of current density (Jsc) and efficiency (PCE) as its thickness increases. In FF/thickness graph (Figure 4(b)), the fill factor constantly drops from 83.60% to 67.28% by changing thickness from 100 nm to 1000 nm. Fill factor is measured as the capability of a device to transfer maximum obtainable power to the generated electrical load. e decrease in the fill factor value with the increase in thickness is due to internal power depletion build-up, which leads to a decrease in the fill factor.
In Voc/thickness graph (Figure 4(c)), Voc increases with the increasing thickness due to low electron-hole recombination and high generation rate. If we increase the thickness more, the recombination rate balances the generation rate, and Voc will remain the same. On the other hand, more increase in thickness leads to a decrease in Voc due to a high recombination rate and low generation rate. Voc increases to the maximum value of ∼0.95 V with the increase in thickness.
Voc can be explained by the following equation: where "n" is a factor, (kt/q) is a thermal voltage, "I l " represents the current produced by light, and "I 0 " represents the dark saturation current. In PCE/thickness graph (Figure 4(d)), device efficiency (PCE) reaches the utmost point at 26.50% at 600 nm and then drops rapidly with the further increase in thickness. e optimal absorber thickness range lies between 400 and 700 nm to achieve the high PCE. As the absorber thickness exceeds the optimal value (600 nm), energy conversion efficiency decreases due to the high recombination rate.

Influence of Interface Defect Density (N t ).
e performance and outcome of the organic-inorganic PSC performance are highly affected by the structure and quality of the active perovskite layer. Defect density plays a key role in obtaining efficient outcomes for the device. If the quality of the film is not good, then trap density and rate of recombination of charge carriers increase, which eventually degrade the performance and outcome of the device.

Journal of Renewable Energy
In this simulation, two interface defect layers are introduced, namely, IL1 (TiO 2 /(FA) 2 BiCuI 6 ) and IL2 ((FA) 2 BiCuI 6 /spiro-MeOTAD interface), to study their influence on device performance. e defect densities of the first interface layer (IL1) varied from 10 13 cm − 3 to 10 17 cm − 3 and second interface layer (IL2) varied from 10 13 cm − 3 to 10 21 cm − 3 , respectively, while remaining parameters are kept at the default value. Figures 5 and 6 show the current density-voltage (J-V) curves and power conversion efficiencies (PCEs) of double PSCs at various defect (trap) densities of TiO 2 /(FA) 2 BiCuI 6 and (FA) 2 BiCuI 6 /spiro-MeOTAD. Table 5 and Figure 7 show the deviation in perovskite solar cell (PSC) outcome parameters with different values of defect density (N t ). It can be analyzed that the interfaces with low defect densities are favorable for device performance. Because in that case, low traps are present, and the generation rate is high. Voc and Isc increase which may lead to high PCE and FF. While on the other hand, interfaces with high defect densities cause more recombination centers and traps, which ultimately degrade the device's performance.

Influence of Carrier Mobility.
e charge carrier mobility of the active layer has a significant influence on device performance. In this simulation, there are two types of charge carriers: free charge carriers (electrons and holes) and trapped charge carriers (electrons and holes). e free charge carriers have limited mobility, while the mobility of trapped charge carriers is zero, which means they cannot move. erefore, the average mobility of charge carriers is equal to the ratio of multiplication of free charge carriers and free carrier mobility to the sum of free charge carriers and trapped charge carriers, which is elaborated in the following equation.    300  320  340  360  380  400  420  440  460  480  500  520  540  560  580  600  620  640  660  680  700  720  740  760  780  800  820  840  860  880  900 Wavelength ( 300  320  340  360  380  400  420  440  460  480  500  520  540  560  580  600  620  640  660  680  700  720  740  760  780  800  820  840  860  880  900 Wavelength ( In this study, charge carrier mobility varied from 2 × 10 − 3 cm 2 V − 1 s − 1 to 20 cm 2 V − 1 s − 1 to examine the influence on device performance as shown in Figure 8 and Table 6, and it is analyzed that best power conversion efficiency is achieved in mobility range of 2 × 10 − 1 to 2 cm 2 V − 1 s − 1 . Figures 9 and 10 show the J-V characteristics and PCE curves of double copper-based PSC at different values of charge carrier mobility. In Voc/mobility graph, open-circuit voltage decreases with the increase in charge carrier mobility due to fall of internal power depletion that weakens the effect of a built-in electric field. If the carrier mobility is decreased, then short circuit current density decreases due to dissociation probability and scattering of charge carriers, leading to a decrease in energy conversion efficiency and fill factor. If the carrier mobility is increased, then the short-circuit current density increases because of better carrier transport at respective interfaces, leading to high efficiency and fill factor. Furthermore, an increase in mobility leads to a decrease in short circuit current density due to the extraction of charge carriers, reducing charge carrier density at a steady state. While in Voc/mobility graph, the open-circuit voltage decreases with the increase in charge carrier mobility due to fall of internal power depletion that weakens the effect of an electric field in the depletion region. e optimum efficiency of double PSC is obtained at carrier mobility of 2 cm 2 V −1 s −1 .

Conclusion
e organic-inorganic double perovskite solar cell structured as FTO/TiO 2 /(FA) 2 BiCuI 6 /spiro-MeOTAD/Au was designed by the SCAPS device simulator. From the simulation, it is found that in the case of (FA) 2 BiCuI 6 ,the output parameters Jsc, Voc, PCE, and %FF at absorber layer thickness 300 nm is 32.952 mA/cm 2 , 0.94 V, 24.98%, and 80.73%, compared with standard hybrid organic-inorganic perovskite performance under the same parameters. We analyzed that the hybrid organic-inorganic double perovskite would have the ability to replace CH 3 NH 3 PbI 3 for next-generation lead-free harmless materials for perovskite solar cells and other optoelectronic applications. Furthermore, the influence of absorber layer thickness, defect density, and carrier mobility on device performance was studied. Moderate thickness minimized defects and moderate charge carrier mobility of the perovskite absorber layer show superior outcomes.

Data Availability
e data used to support the findings of this study are included within the article.