Current status of Pb-free PSCs and infer the highest achievable PCE via numerical modeling, and optimization of novel structure FAMASnGeI 3 based PSCs

In this study


Introduction
The main energy sources for supplying the world's energy demand are fossil fuels including coal, gas, and oil.However, most of these energy sources are non-renewable and eventually, they are being depleted.In addition, the by-product, produced after the burning of these fossil fuels, has a detrimental effect on organisms as well as on the environment.To meet the endless and rising demand for energy, renewable energy sources including solar, hydroelectric power, and wind are the alternative and bio-compatible solution.Solar energy is a crucial natural resource that is utilized for power generation using photovoltaic applications such as solar cells.The Sibased solar energy converter is contributing as well as dominating power generation by adopting photovoltaic technology.However, it is very costly.Since 2009, the scientific community has been considering the materials called perovskite as a promising contender of present solar converters in the aspect of efficiency and cost [1].The perovskite compound follows this stoichiometry formula named ABX 3 , where A can refer to a monovalent organic or inorganic cation, B can represent a divalent metal cation and X denotes a halide anion.In addition, carbon, nitrogen, or oxygen can replace halogens.Typically, A and B are considered as divalent and tetravalent ions respectively, while oxygen is used instead of halogen for the neutrality of charge [2,3].There is a metal halide perovskite compound called organic-inorganic hybrid halide perovskite or all inorganic halide perovskite etc The perovskite material was originally used in a dye-sensitized solar cell in 2009 by Kojima et al [4].From that, the researcher communities are employing perovskite materials to make efficient thin-film PSCs because of their outstanding optoelectronic features, low processing temperature, and robust excitonic transitions [5].As an excellent light-absorbing material for solar cell manufacturing, the hybrid perovskite material named methylammonium Pb iodide (MAPbI 3 or CH 3 NH 3 PbI 3 ) has garnered a lot of attention due to its optoelectronic features including high carrier mobility, large carrier diffusion length, appropriate bandgap (1.55 eV), large absorption coefficient and low trap density [6,7].Substantially, it exhibits notable efficiency in energy harvesting [6,7].However, it contains a toxic element named Pb which has adverse effects on lives.Addressing this issue, researchers have currently focused their efforts on the Pb-free PSC [8].
The photovoltaic communities have paid their attention to developing green PSC by avoiding toxic elements like Pb in the PSC structure.In our review section, we have shown some novel theoretical and experimental efforts for developing an eco-friendly PSC.We have found a few works of literature regarding Pb-free FAMASnGeI 3-based PSCs.As an effort of Pb-free PSC, Nozomi Ito, and his research group fabricated a Pb-free FAMASnGeI3-based PSCs with structure ITO/PEDOT: PSS/FAMASnGeI 3 /C 60 /BCP/Ag.The photovoltaic parameters were J SC = 19.50mA cm −2 , V oc = 0.42 V, FF = 0.41 and PCE = 4.48 % [9].In addition, the research group of Hossein Abedini-Ahangarkola has optimized a Pb-free three-active layer PSC by adopting the structure FTO/TiO 2 /MASnI 3 /MAPbI 3 /FAMASnGeI 3 /Spiro-OMeTAD/Au.They obtained J sc of 30.70 mA cm −2 , V oc of 1.2 V, FF of 83.31%, and PCE of 30.77% [10].Moreover, Neelima Singh and his team optimized a tandem solar cell with the structure of Au/Cu 2 O/FAMASnGeI 3 /CH3NH 3 GeI 3 /ZnO/FTO using SCAPS-1D.The observed photovoltaic features were 28.36 mA cm −2 , 1.07 V, 84.39%, and 26.72% for J sc , V oc , FF, and PCE respectively [11].
ETL shows an efficient role in extracting electrons from the absorbing layer and blocking the hole's trespass to the electrode through the ETL.In general, n-type semiconducting materials are considered ETL.In this simulation work, we have utilized CdS as an ETL because of its higher electron mobility than other commonly used ETLs like SnO 2 and TiO 2 .The electron mobility of CdS, SnO 2, and TiO 2 were 350 cm 2 V −1 S −1 , 240 cm 2 V −1 S −1, and 1 cm 2 V −1 S −1 , respectively [12][13][14].The devices based on ETL of CdS displayed a reduced hysteresis and improved stability compared to the devices based on TiO 2 ETL [12,15,16].This might happen due to the decreasing surface defects of the CdS layer.
HTL plays a substantial role in the extraction of holes from the light-absorbing layer and blocking the electron transfer to the back contact metal electrode.Usually, the p-type semiconducting substances attracted the attention more as an HTL in PSC.In this study, we have utilized NiO x as HTL.The NiO x has versatile applications such as HTL with different solar cells such as dye-sensitized, organic solar cells, and new generation solar cells like PSC.The NiO x as HTL has good thermal and moisture stability due to its innate inorganic oxide properties.In addition, the fabrication procedure of NiO x is straightforward and more cost-effective.It has been confirmed that the existence of NiO x as an HTL can suppress non-radiative recombination as well as hinder radiative recombination.Subsequently, the enhanced J sc and V oc of PSCs have been recorded [17].
The statistical status of PSCs and Pb-free PSCs in terms of the number of research publications has been estimated utilizing the data from the Scopus database which is shown in figure 1.For extracting data from the Scopus database, we limited our provided search words to title-abstract-keywords.For the PSC and Pb-free PSC, the used words as well as structure for searching were (perovskite OR perovskite AND material) AND (solar AND cell OR psc) and (Pb AND free OR pb-free) AND (perovskite OR perovskite AND material) AND ( solar AND cell OR psc ) respectively.After searching, we limited our search area to material science, chemistry, energy, physics and astronomy, engineering, chemical engineering, and environmental science.We also limited the document types to articles.All extracted data are presented in figure 1.We have found from the data that the research on Pb-free PSCs is far behind from the research on all types of PSCs.It indicates the demand for research on Pb-free PSCs.That is why we have taken the initiative to design and optimize an efficient Pb-free perovskite solar cell.
In this article, firstly, we have carried out a brief outline of the effort of Pb-free perovskite-based solar cells.Secondly, we optimized and scrutinized the different photovoltaic parameters of a Pb-free hybrid perovskite of the FTO/CdS/FAMASnGeI 3 /NiO/Ag structure by altering the various physical parameters of the absorber layer and ETL (CdS).We have changed the thickness, and defect density of the absorbing layer to observe the impact on photovoltaic parameters.In addition, we have also changed the thickness, donor density, and band gap of ETL to decipher the essence of impact on the performance of the photovoltaic cell.Moreover, we have also analyzed the impact of changing temperature and light intensity.Finally, we have performed the dark current analysis as well as the quantum efficiency of the solar cell.As far as our knowledge, there is no theoretical study on the reviewing, modeling, and optimization of the Pb-free aforesaid structure.

Literature review on Pb-free perovskite solar cell
Due to exceptional optoelectronic features, metal halide perovskites become a new class material that has made revolutionary advances in optoelectronic device applications including light harvesting, LED, photo-detection, and high energy radiation detection [19,20].These materials have been used extensively in solar cell fabrication.The highest PCE 25.8% is obtained by PSC [21].The photodetectors achieved selectivity over 3.15×10 15 Jones [22], and as luminescent materials in LEDs, perovskite attained an external quantum efficiency (EQE) record of over 28% [23].Awkwardly, lead is a common heavy metal that contaminates the environment and accumulates in human tissues through absorption, bio-concentration, bioavailability, and biomagnification.As a result, the neurological, skeletal, hematological, and reproductive systems are all negatively impacted.The peculiar physical and chemical characteristics of lead are harmful to health and have long been linked to human activity [24].That is why research communities have paid their attention to Pb-free perovskite-based solar cells.The simplest method to develop Pb-free perovskites is to substitute non-toxic divalent metal ions for Pb 2+ in ABX 3 .The Sr 2+ , Sn 2+ , Ge 2+ , and transition metal cation (Cu 2+ ) group IIA and IVA cations have gained attention.In Sb-based double perovskites, Sb and Bi are both in group VA; however, because of the difference in ionic radius and the spin-orbit coupling effect, these perovskites' characteristics are considerably different [25].A 3 B(III) 2 X 9 type Pb-free perovskites can be produced by substituting divalent Pb 2+ with trivalent metal cations (Sb 3+ and Bi 3+ ) or monovalent metal cations (Cu + ), respectively [25].
The compositional modification of Pb-free perovskites inevitably leads to lattice stress and structural deformation, hence changing the energy levels and defect states.According to the results, it is important to carefully control the secondary phases MAI, PbI 2 for MAPbI 3 and SnI 4 , SnI 2 , MAI, and Ma 2 SnI 6 for MASnI 3 as they exit the synthesis process [26].The perovskite structure can be changed by environmental factors like temperature and pressure.According to Kanatzidis et al, structural modifications happened throughout the phase transitions at various temperatures [27].The reconstructive phase with the highest symmetry displays the strongest conductivity during such phase changes because it has the most orbital overlap between the metal and the iodine.Large self-doping densities are seen in Sn-based perovskites with rapid Sn 2+ to Sn 4+ oxidation, along with crystal defects and distortion caused by an increase in Sn content.Compared to Pb-based perovskites, Snbased perovskites have more complex and demanding thermodynamic growth conditions [28].Even though the efficiencies via simulation of Pb-free PSCs can get up to 30% [29], the practical performance is still low.The MoS 2 nanoflakes could meaningfully increase the stability of Cs 2 AgBiBr 6 PSCs with a PCE of up to 4.17%, Jsc of 6.12 mA cm −2 , and V oc of 1.10 V when compared to PTAA (Poly(bis(4-phenyl) (2,4,6trimethylphenyl)-amine) m, ) as an HTL [30].It's critical to understand the crystallization technique for these lead-free perovskites because, frequently, it differs considerably from the crystallization method for Pb-based halide perovskites.The Research efforts are actively directed towards enhancing the precision in manipulating the morphology of perovskite materials in solution-based processes for the development of highly efficient Pb-free PSCs.The initial step in industrial application is momentously developing or improving fabrication technology for large-scale production.Years ago, it was simple to spot degeneration in the best PSCs; today, however, the decomposition is more discrete.The Stable contact layers without mobile dopants, perovskite films with ideal average radii at the A, B, and X sites, impervious barrier layers incorporated into the device, non-reactive carbon or TCO electrodes, and efficient packaging are used to fabricate these cells [31].
To understand the efficiencies of PSCs, we must first understand the concept of each process that happens during the light absorption in PV devices.The light absorption can affect the PSCs' performance such as PCE, V oc , and Jsc.The separated electrons travel along the HTL and ETL to the external circuit to create a loop [32].Concerning the ETLs, absorber layer thickness, defect density, and front electrode work function, the performance of Pb-free PSCs may be further investigated.The decrease in shunt resistance brought on by the rise in recombination centers lowers the device's V OC .The study discovered that the total photovoltaic characteristics increased to V OC = 1.07 V, Jsc = 28.33 mAcm −2 , FF = 84.46%,and PCE = 26.72%after optimizing the structure's different physical parameters including absorber layers thickness, defect densities.They also claimed that the work function of the front contact plays a crucial role in this performance [11].K. Kumari et al optimized and fabricated the structure of metal contact/TCO/TiO 2 /CH 3 NH 3 SnI 3 /ZnTe/metal contact.They have attained experimental (theoretical) photovoltaic parameters J sc = 16.83(33.62) mAcm −2 , V oc = 0.79 (0.905) volts, FF = 63.26 (66.31) % and PCE = 8.41 (22.96) %.They also claimed that the relatively lower efficiency is the reason for the higher electron affinity of ZnTe as a hole transport layer [33].The research team of S. Sajid et al has synthesized two Pb-free as well as HTM-free PSCs by using the structure of FTO/TiO 2 /FASnI 3 /Au and FTO/TiO 2 /FASnI 3 /CsSnI 3 /Au.They have found that the efficiency for FASnI 3 and FASnI 3 /CsSnI 3 was 8.94% and 11.77%.They also claimed that the structure for FASnI 3 /CsSnI 3 can preserve 89% more of its initial PCE than FASnI 3 [34].The research group of X. Meng et al fabricated three PSCs by adopting solvent engineering for the structure PEDOT: PSS/perovskite/C 60 /BCP/Ag, where they used FASnI 3 , FASnI 3 -PEAI, and FASnI 3 -FOEI as an absorber layer.They have found the highest certified efficiency 10.16% for the structure of PEDOT: PSS/FASnI 3 -FOEI/C 60 /BCP/Ag.They also claimed that for using pentafluorophen-oxyethylammonium iodide (FOEI), the defect density becomes lower and the lifetime of charge carriers becomes higher [35].X. Zhang and his team fabricated a PSC structure by adopting ITO/poly (3,4 ethylenedioxythiophene): poly (styrene sulfonate)/(PEA) 2 (MA) n-1 Pb n I 3n+1 /6,6-phenyl-C 61 butyric acid methyl ester/bathocuproine/Ag.The obtained PCE of the cell was improved from the original 0.56% (without NH 4 SCN) to 11.01% with the optimized NH 4 SCN addition at n = 5 [36].In table 1, we have provided a brief literature review on the Pb-free PSC to make understandable the scenario of the research on those materials.

Device optimization: a numerical approach by SCAPS-1D
A solar cell capacitance simulator is being utilized to optimize the solar cell structure.Professor Marc Burgelman and his colleagues developed the one-dimensional solar cell simulator known as SCAPS-1D [60].The software can also be used to develop various cell formations.In addition, the structure can have up to 7 different layers.The following differential equations such as Poison's equation, and continuity equation of hole and electron are employed in SCAPS to determine the structure's I-V characteristics, carrier density, band diagram, current density, quantum efficiency, and other output performance parameters.The Poison's equation is given by equation (1).
Here γ is electrostatic potential, x e is the medium's static relative permittivity, q is the electron charge, N D and N A are the density of the ionized donor and acceptor, respectively, and N def is the density of charge in defects.
These Relationships are used to derive the electron and hole continuity equations as shown in equations (2) and (3).
The electron and hole current densities are represented by jn and jp, the recombination rates are represented by Rn andRp, and the rate of photogenerated electron-hole pairs is represented by G.
The electron and hole current densities are computed as follows the equations (4) and (5).The diffusion length can be calculated by using equation (6).
t symbolized as electron lifetime and D n p , as the diffusivity.The diffusivity equation is as follows equation (7).
is the voltage of thermal and n p , m is the electron or hole mobility.
The carrier lifetime is following the equation (8).
Nt Vth The device performance of single-layer PSCs based on the FAMASnGeI 3 active layer has been examined to comprehend the photovoltaic performance of Pb-free perovskite solar cells.For this purpose, the simulation work was conducted on a device configuration of FTO/CdS/FAMASnGeI 3 /NiO/Ag to get a fundamental understanding of the effect of change in different physical parameters such as thickness, defect density, donor density, band gap, light intensity, etc figure 2 illustrates the device structures along with its energy band alignment for a single-layer PSC.

Results and discussion
In this simulation part, we restrained ourselves in explaining the optimization process for our proposed structure of FTO/CdS/FAMASnGeI 3 /NiO/back contact.The initial parameters that have been utilized during the simulation process are tabulated in tables 2 and 3.
Nickel oxide (NiO) has been chosen as the hole transport layer in this simulation work which plays a crucial role in facilitating the movement of positive charges (holes) from the perovskite absorber layer toward the electrode [64].NiO has emerged as a promising material for the hole transport layer in perovskite solar cells.Its high conductivity, good stability, and compatibility with perovskite materials make it an attractive candidate for this application [65].Studies have demonstrated the successful integration of nickel oxide as a hole transport layer, leading to improved performance and stability of perovskite solar cells.The use of nickel oxide has contributed to enhanced charge transport, reduced recombination losses, and improved overall device efficiency [66].Most importantly, it produced positive valence band offset with perovskite layer with value of +0.19, which reflects the spike type band structure at the interface.Previous studies revealed that the spike-like band structure offers better performance in comparison with the cliff-like (for negative VBO) band structure [66].In summary, the utilization of nickel oxide as a hole transport layer in perovskite solar cells presents a compelling opportunity to advance the efficiency and cost-effectiveness of solar energy conversion systems.

Perovskite layer optimization
The absorber thickness is crucial because most of the photovoltaic operations such as charge carrier production, recombination, and transportation occur in the perovskite layer.If the absorber layer thickness is larger than the diffusion length, the produced charge carriers will recombine in the absorber layer [67].As a result, the produced charges will be unable to reach the respective electrode.Because of the longer diffusion length and longer carrier lifetime of this perovskite, the change in V oc and J sc is directly proportional to the absorber layer thickness.Lower trap-assisted recombination is the cause of the rise in V oc that occurs with increasing absorber thickness however at 300 nm thickness of absorber layer, the V oc begins to decline.This phenomenon is mostly because of an increase in series resistance.Short-circuit current and open-circuit voltage, two important solar cell metrics, can generally rise with an increase in absorber thickness.This rise is explained by the solar cell's increased ability to absorb light from the sun, which produces more charge carriers [68].Even though a thicker layer facilitates the absorption of a greater number of photons, generating more electron-hole pairs, it concurrently introduces a rise in the density of defects that function as recombination centers.In consequence, the electron-hole pair's lifespan is lessened, prompting more pairs to recombine prematurely before reaching the electrodes and thus, contributing to a subsequent decline in V OC [69].
According to Nand and his colleagues and Kim et al, the perovskite layer thickness influences the lifetime and diffusion lengths of the photo-generated electrons and holes [70,71].Hence, it is important to optimize the absorber layer's thickness in the production of great efficiencies.The impact of defect density and thickness of the absorber layer on the performance of the solar cell are investigated and optimized for these parameters, where thickness is adjusted from 100 nm to 500 nm for analysis of an effective device.The photovoltaic parameters are increased with the increment of the thickness of the absorber layer except FF.Specifically, the PCE increased from 12.48% to 22.69% due to a change of thickness from 100 nm to 400 nm.After that PCE is decreased due to the increase in series resistance and the recombination rate may also become higher because of the lower diffusion length in comparison with the thickness [63,72].The V oc follows almost constant features over the whole process, however, insignificant change is observed at the third decimal point.The reason for the becoming almost saturated is the recombination in the absorber layer although it increases the probability of generating more charge carriers with increment of thickness [73,74].In addition, the J sc values of the structure are enhanced with the enhancement of absorber thickness.The increment happened from 14.74 mAcm −2 to 28.5 mAcm −2 due to the absorption of more photons and subsequently produced more electron-hole pairs.Consequently, J SC is finally improved.Finally, FF is reduced due to increasing thickness except at 150 nm thickness where we have found a maximum of 80.41% FF.The reason behind the decrement of FF is an increment of series resistance with an increment of thickness.Moreover, all data are graphically represented in figure 3(a).
As mentioned above, increasing absorber thickness will result in more light absorption and more carrier generation.We have seen from figure 3(b) that quantum efficiency is improved with increasing the thickness.However, increasing thickness is the cause of the enhancement of series resistance which can hamper the performance of the cell.That is why thickness should be optimized.
The effectiveness of the PSC is significantly impacted by the defect density (N t ) which can be realized from figure 4. We noticed that all photovoltaic parameters declined with increasing the defect density.Especially, we observed that PCE decreased from 29.99% to 3.35% when we increased the defect density from 1 × 10 15 cm −3 to 1 × 10 18 cm −3 .Thus, high N t indicates that more carriers trap is generated in the cell's film.Moreover, the material's trap states boost up the non-radiative recombination and obstruct the flow of charged particles.Furthermore, the higher defect density shortens the carrier lifetime t ( ) for the charge carriers as shown in equation (8), which leads to a faster recombination rate as well as shorter absorption length (L) (shown in equation ( 6)).Finally, the layer's absorption length decreases as N t rises [46].This implies that the ideal thickness of the absorber layer varies depending on the N t .
One of the strategies to increase the PSCs performance is by introduce the semiconductor heterostructure.For two adjacent semiconductor materials to produce a heterostructure, there must be a lattice match (or very slight mismatch) that permits one to grow epitaxially on top of the other.In addition, when there is a significant lattice mismatch, the strain energy in the bond between two atoms is more than the energy required to break the next neighbor bond.As a result, the atoms rearrange their equilibrium structure and create defects like lattice vacancies or misfit dislocations [75].In particular, compositions containing formamidinium (FA), tin (Sn), and germanium (Ge) favour a stable perovskite structure with improved thermostability, in contrast to the readily volatile methylammonium (MA) cation.

Electron transport layer optimization
Cadmium sulfide (CdS) was chosen as the ETL layer in this work.The CdS has a band gap of 2.45 eV with fascinating optoelectronic characteristics.The simulation research is carried out with variations in ETL thickness from 20 nm to 60 nm to comprehend the change in the device's parameters.All photovoltaic parameters remain almost constant as you can observe in figure 5.The PCE, Jsc, as well as FF of the device, have risen by about 0.12% as the ETL thickness increases from 20 nm to 60 nm.There is no influence on the V oc of the device of changing ETL thickness.The ETL is positioned on the solar cell's front side.As a result, the maximum amount of light must be allowed to flow through it to reach the absorber layer [76].Thus, The CdS required a very thin layer to reduce the resistance and enhance solar cell performance [77].By considering the pragmatic situation including cost, and window of light to reach at active layer, we considered 50 nm as our optimized thickness for ETL.
Energy band alignment at each interfacial layer in PSCs plays a critical role in charge transportation engineering and hence on a device's optoelectronic performance [78,79].The most significant feature of an ETL is that it must have band alignment to the perovskite layer [80], which means it must have a good conduction band offset (CBO) with the perovskite active layer.The bandgap of different layers in PSCs can be tuned for light absorption from ultraviolet to near-infrared wavelengths [81].The bandgap in the ETL layer was modified to improve the band alignment with other layers for more photon absorption and electron extraction in PSCs.The bandgap was altered from 2.10 eV to 2.50 eV.The PCE decreased from 30.05 % to 29.99% when changing the bandgap from 2.10 eV to 2.50 eV as shown in figure 6.That means the best CBO between ETL and the active layer occurs at the band gap of 2.10 eV for the CdS.Hence, the optimized bandgap for the ETL layer is 2.10 eV for the highest PCE of 30.05 % in adjusting the flow of electrons through charge extraction in the PSCs.
The total number of holes and the density of acceptor atoms must be equal to the total number of electrons and the density of donor atoms in a semiconductor for the crystal lattice to be neutral.In the ETL layer, increasing the donor density encourages the production of more charge carriers, which enhances the solar cell's performance and yields high efficiency.We have changed the electron donor density of CdS from the range of 1 × 10 15 cm −3 to 1 × 10 21 cm −3 to observe the essence of the performance of the device.The performance of the device is described by its photovoltaic parameters which are shown in figure 7.In the case of PCE, we have observed that this parameter is increased with the enhancement of donor density.The PCE is improved from 28.16% to 30.48%.In addition, we also observed that it has been almost flattened after 1 × 10 20 cm −3 donor density.The V oc of the device is also increased very slightly from 0.901 Volt to 0.964 with the enhancement of donor density.However, for the value 1 × 10 20 cm −3 of donor density, V oc is reduced drastically.It is needed to investigate why that happened.We have also perceived an unnoticeable change in J sc due to altering donor density.Similarly, the change in donor density has an insignificant impact on the FF of the device.From the figures and data, we have detected that the J sc has been affected more due to altering of the amount of incident light.In addition, J sc is reduced to around 75% of its initial value.After J sc , the PCE is the second that is affected most.According to data, 6.72% PCE is decreased owing to changes in the light intensity.Here, one thing is established more incident energy generates more photoelectrons, thus current as well as power conversion efficiency are also increased.However, the change of incident light energy on the solar cell device has less impact on the other two photovoltaic parameters V oc and FF.
3.1.4.Effects of temperature on the performance of the device Perovskite solar cells have emerged as a promising technology for efficient and low-cost solar energy conversion.Their high power conversion efficiencies and relatively simple fabrication processes make them attractive for large-scale commercialization [82].However, one of the challenges facing perovskite solar cells is their sensitivity to temperature changes [83].As the device will work in sunny and hot environments, it needs to investigate the device's performance in elevated temperatures.For that purpose, we changed the device operating temperature from a range of 300 K to 400 K by considering the practical situation.The effect of temperature on the photovoltaic parameters especially V oc can be explained by the following relations (9).
In a generalized way, the number of electron-hole pairs is enhanced significantly with the elevating of temperature which finally lowers the energy band gap, subsequently, Jsc rises [84].In this context, that can be believed that E q g is always larger than V , oc which denotes that the gradient of V oc for temperature is negative.This also endorses that V oc is reduced with elevation of temperature.Consequently, performance will be hampered.Our study also substantiates the deterioration of the PCE of PSC with the enhancement of the temperature, which is depicted in figure 9.A worsening impact has been observed on the performance, especially the PCE of the device, due to the change in temperature from 300 K to 400 K.
A change in temperature from 300 to 400 Kelvin was found to negatively impact the performance of perovskite solar cells.The worsening impact of the temperature change on the performance of the perovskite solar cell can be attributed to several mechanisms.Firstly, the increase in temperature can lead to an increase in carrier recombination rates within the perovskite material.This can result in a decrease in the overall efficiency of the solar cell.Additionally, the increase in temperature can also cause structural changes in the perovskite material, leading to a degradation of its photovoltaic properties.These structural changes can include the loss of crystallinity, the formation of defects, and the degradation of the perovskite film.The temperature has an impact on the number of vacancies and their migration to the perovskite layer's edges, which can accelerate the deterioration process in perovskite solar cells [85].Furthermore, temperatures can result in an increase in the leakage current within the perovskite solar cell.This increase in leakage current can lead to a decrease in the open circuit voltage and overall performance of the solar cell.

Dark current-voltage analysis
The dark current remarks the electric current that flows over a solar cell device when it is in dark conditions or out of light exposure.This current is usually unwanted in solar cells because it reduces the performance of the device.Researchers and engineers are trying to minimize the dark current by adopting techniques such as material optimization, passivation layers, defect engineering, and careful design of electrical contacts.In the p-n junction, this current density is specified by the summation of the bulk's component current and surface current [86].The diffusion current, generation-recombination current, and tunneling current are considered as part of the bulk's component current.In addition, the shunt current and generation-recombination current are the constituents of the surface current, which in general appear at the interface of the semiconductor and dielectric devices.The electrical properties of a PSC can be decoded by fitting the dark J-V curve into a single p-n junction model.Figure 10 shows the dark J-V curves for the optimized PSC.The ideality factor n , ( ) saturated current I , 0 ( ) shunt resistance R , sh ( ) and series resistance R s ( ) can be estimated by fitting the equation (10) onto the J-V curve of the optimized device.
Where k, T, and q are known as Boltzmann's constant, temperature, and electronic charge respectively.The dark J-V curve is plotted by employing the simulated data which is shown in figure 10.The ideal features curve is fitted on the simulated curve and the, I , 0 R , sh and R s are extrapolated from the fitted curve.The device's ideality factor is the measurement of how closely the device trails the ideal diode equation.The value of n is 1.91.that means trap-assisted SRH recombination happened in the device [87].The saturated current density of 6.73 × 10 −8 mA cm −2 was found for the device.The series resistance and shunt resistance are also the most important parameters that need to analyze the dark I-V curve.As can be seen in figure 10 the R s is the lowest value of 2.8 × 10 −5 Ωcm 2 which is fitted in the ideal solar cell.The highest value of shunt resistance is needed for an ideal solar cell.As can be seen, after all optimization, the R sh value is obtained as 11412.67Ωcm 2 .

Conclusion
In this work, firstly, a comprehensive literature review has been conducted on Pb-free PSCs, uncovering a diverse array of theoretical and practical strategies aimed at enhancing their photovoltaic performance.In addition, it has been observed that researchers displayed significant interest and dedication towards optimizing and synthesizing successful Pb-free PSCs.Secondly, an attention has been paid to optimizing a Pb-free PSC of the structure FTO/CdS/FAMASnGeI 3 /NiO/Ag.Initially, light-absorbing layer's thickness and defect density were changed to perceive the alteration of the photovoltaic properties.As a result, a change of V oc ranging from 0.798 Volt to 0.822 Volt, Jsc from 14.74 mAcm −2 to 28.5 mAcm −2 , FF from 77.9% to 69.82% and PCE from 12.48% to 22.28% were witnessed due to varying of thickness from 100 nm to 500 nm.In addition, it has been witnessed that Jsc, FF, and PCE parameters were influenced more.However, the maximum performance of the device is observed at 400 nm thickness of the absorbing layer.Furthermore, the device's quantum efficiency as a function of thickness was studied and discovered that the quantum efficiency increased as thickness enlarged.Moreover, it has been found that 36.15%,58.55%, 57.65%, and 88.83% decrement have been happened for Voc, Jsc, FF, and PCE owing to changing of the defect density of the absorbing layer from 1 × 10 15 cm −3 to 1 × 10 18 cm −3 respectively.All parameters are affected by the increment of defect density of the absorber layer.Especially PCE was affected more.Hence, the thickness at 400 nm and defect density at 1 × 10 15 cm −3 have been fixed as optimized, respectively.Later, the impact of various parameters including thickness, donor density, and band gap of ETL on the performance of the device were investigated and optimized.The photovoltaic characteristics like V oc , J sc, and FF were insignificantly changed with changing the thickness of CdS from 20 nm to 60 nm.However, PCE was relatively affected more, and a 0.12% declinement was observed due to altering thickness.In addition, the donor density of the ETL was altered from 1 × 10 15 cm −3 to 1 × 10 21 cm −3 and found an impact on the photovoltaic parameter of the device.Specially, The PCE was improved from 28.16% to 30.048%.Moreover, the PCE was decreased from 30.05 % to 29.99% when a change of the bandgap occurred from 2.10 eV to 2.50 eV.That means the best CBO between ETL and the absorbing layer was occurred at the band gap of 2.10 eV.Furthermore, light intensity was varied from 1000 Wm −2 to 251.19 Wm −2 and observed that 75% of J sc and 6.72% of PCE were reduced.Furthermore, a worsening impact on the performance was witnessed due to the change in temperature from 300 to 400 Kelvin.Finally, the dark current analysis of the solar cell have been performed.In addition, the dark J-V analysis explored the reasons behind the outstanding photovoltaic parameters of the optimized PSCs.From the dark J-V analysis, lower current density (6.73 × 10 −8 mA cm −2 ), less series resistance (2.8 × 10 −5 Ωcm 2 ), and higher shunt resistance (11412.67Ωcm 2 ) were perceived, which was expectable for a promising solar cell.The ideality factor of the device was weighed at 1.92, which confirmed that the trap assisted SRH recombination in the PSC.It is believed that the in-depth study and findings of this research will further improve our knowledge of photovoltaic systems and pave the way for the development of very efficient Pb-free perovskite solar cells.

Figure 1 .
Figure 1.Comparison in number of publications between PSCs and Pb-free PSCs (inset shows the recent highest performance conversion efficiency for PSC and Sn-based Pb-free PSCs [18].
p m indicate electron and hole mobility, respectively, and D n and D p represent electron and hole diffusion coefficients, respectively.

Figure 2 .
Figure 2. (a) A schematic structure of a Pb-free PSC, (b) Band alignment of different layers and (c) energy band diagram under illumination of optimized structure.

Figure 3 .
Figure 3. (a, b) Photovoltaic parameters Jsc, Voc, FF, and PCE versus thickness of FAMASnGeI 3 absorber and (c) the quantum efficiency for the thickness of absorber.

Figure 4 .
Figure 4. Variation of J sc , V oc , FF, and PCE of the PSC for defect density of FAMASnGeI 3 absorber layer.

Figure 5 .
Figure 5.The photovoltaic parameter of simulated PSCs versus thicknesses of the CdS ETL.

Figure 6 .
Figure 6.Change of Jsc, V oc , FF, and PCE for the bandgap of CdS.

Figure 7 .
Figure 7. Variation of J sc , V oc , FF, and PCE for donor density of CdS.

3. 1 . 3 .
Effect of light intensityPhotovoltaic properties of solar cell devices, including the J sc , Voc, FF, and PCE are affected by variations in the amount of light shining on the solar cell.To know the effect of intensity, we have conducted a study by changing the light intensity.For that, we have used the AM1.5 solar simulator which produced 1 kWm −2 incident light energy on solar cell devices.The incident light was varied by changing the neutral density from 0 to 0 .6 of the simulators.We have detected the incident light of 1000 Wm −2 ,794.33 Wm −2 , 630.96 Wm −2 , 501.19 Wm −2 , 398.11 Wm −2 , 316.23 Wm −2 , and 251.19 Wm −2 for the neutral density of 0, 0.1, 0.2, 0.3, 0.4, 0.5, and 0.6 respectively.The impact of changing incident light energy on the photovoltaic parameter is shown in figure 8.

Figure 8 .
Figure 8. J-V curve for light intensity.

Figure 9 .
Figure 9. Impact of temperature on the PCE of the device.

Figure 10 .
Figure 10.Dark current analysis with different optoelectronic properties.

Table 2 .
Specification of input parameters of the materials in SCAPS-1D software.