Comparative Performance Analysis of Lead-Free Perovskites Solar Cells by Numerical Simulation

Research of lead-free perovskite based solar cells has gained speedy and growing attention with urgent intent to eliminate toxic lead in perovskite materials. The main purpose of this work is to supplement the research progress with comparative analysis of different lead-free perovskite based solar cells by numerical simulation method using solar cell capacitance simulator (SCAPS-1D) software. In this work, the device simulation is carried out in the n - i - p configuration of FTO/[6,6]-Phenyl-C61-butyric acidmethyl ester (PCBM) /Perovskite layer/ Poly[bis(4-phenyl)(2,4,6-trimethylphenyl)amine(PTAA)/Au using six different lead-free perovskite materials. The impact of different perovskite materials layers including hole and electron transport layer thickness, doping concentration on solar cell performances has thoroughly been investigated and optimized. CsSnI 3 based perovskite solar cell shows the highest power conversion efficiency of 28.97 % among all the lead-free perovskite based devices. This clearly indicates that it ’ s possible to achieve high-performance lead-free perovskite solar cells experimentally at par with lead based perovskite solar cells in future research.


INTRODUCTION
Perovskite solar cells have experienced a major leap in their power conversion efficiency (PCE) just over a decade due to their very simple manufacturing process, comparatively low processing cost, high absorption coefficient, low surface recombination rates and relatively high efficiency 1,2 . It has increased from 3.8% in 2009 to 25.5% till date in single-junction architectures, which is quite close enough to the crystalline silicon solar cells at 26.7% 3,4 . The hybrid organic-inorganic perovskites have opened new doors towards more efficient light harvesting materials. Owing to the property of tuneable frequency, these solar cells can be quite effective in absorbing different light frequencies by different layers which can lead to a boost in their efficiencies unlike the conventional solar cells. Despite this, lead based perovskites have two major challenges: a) poor stability which is being addressed by improved device engineering and encapsulation as well as incorporating the use of 2D perovskites, b) high toxicity that is raising a concern on an environmental level. Lead free perovskite materials, which are non-toxic and are also being looked upon as another alternative 5 . These lead free materials will be a preference in the solar cell market which will help in commercialization of perovskite solar cells if they do not compromise with the device performance. Ideally, Pb-free perovskites when used as light harvesting layers in solar cells, should have low toxicity, high optical absorption coefficients, low exciton-binding, narrow direct band gaps, high mobilities. Perovskites in the form of double perovskites, some Sn/Gebased halides, and also some Bi/Sb-based halides with perovskite-like structure show fascinating properties and are low-toxicity materials. Up to 2020, the highest efficiency for Sn-based perovskites has been reported to have reached 13.24% 6 .
In these Pb-free perovskite materials, comparatively only Sn-based PSCs have shown very promising performance. In Sn-based PSCs, certain factors like the poor air-stability caused due to quick oxidation of Sn 2+ leading to increased recombination losses, small formation energy of vacancies, high intrinsic carrier density etc. leads to poor device performance as compared to their corresponding lead-based analogues. The anti-bonding coupling between Sn-5s and I-5p is comparatively weaker in FASnI3 (FA = CH (NH2)2) than CsSnI3 and MASnI3 as a result of the larger ionic size of FA which is also the reason behind the increase in formation energies of Sn-vacancies 7,8 15 . It was observed that Sn 2+ present in the lead-free light absorbing perovskite material transformed into Sn 4+ under ambient atmosphere, in order to attain a more stable state. As a result, SnO2 and methyl ammonium iodide (MAI) is formed as a result of the breaking of charge neutrality in the active perovskite. So, stability raises a concern when it comes to lead free Sn-based perovskites. However, the tin-based perovskites can use the same technologies to address the stability issues. When Pb-free perovskite candidates are concerned, which have already reached an efficiency of 13.24% by partial substitution of formamidinium cation with ethylammonium cation which also reduces the trap density by one Oder magnitude 6 . VOC in the range of 0.8 to 1.00 V can be achieved if the Sn 4+ oxidation issue is completely addressed and the photo carrier recombination rates are lowered down to the levels of the APbI3 materials. This in turn could help in drastically improve the PCE beyond 15% and help them emerge as a viable lead-free contender in the near future 16 .
In the field of lead free perovskites, several experiments are being performed to obtain information about their properties, possibilities and applications. The main concerns that are associated with Pb-free perovskites are (i) high-efficiency but poor stability (Sn 2+ -based), or (ii) good stability but poor performance (Sn 4+ /Sb/Bi-based etc.). A lead free perovskite that offers a good balance between the stability and performance needs to be found. An ideal Pbfree perovskite which has both good optical and electrical properties needs to be looked into.
Along with experiments, simulation also plays a vital role in analysing various properties of these materials and the corresponding performance parameters for various such materials.
This work aids in studying the relation of the properties with the parameters, comparing multiple materials with the help of theoretical analysis by designing a device model. Here, a comparative study of various Pb-free perovskites on a similar configuration is done which helps us know about the distinguishing properties, their impacts on device performance and further work for achieving high efficiencies for Pb-free perovskites.

Device Architecture and modelling
In this simulation work, a comprehensive performance analysis has been studied on different lead free perovskite solar cell using the SCAPS-1D software. The undeniable feature of lead free perovskite material has gained importance in the past few years is its non-toxic nature unlike the lead based perovskite materials. The device configuration considered holds one of the most crucial aspects in the simulation being performed. In this work, the device simulation is carried out in n-i-p configuration of FTO/ [6,6]-Phenyl-C61-butyric acidmethyl ester (PCBM) /Perovskite layer/Poly[bis(4-phenyl)(2,4,6-trimethylphenyl)amine(PTAA)/Au, which is illustrated in Fig.1a. Here, PCBM has been used as an electron transport layer (ETL) and PTAA has been incorporated as a hole transport layer (HTL). Different lead free perovskite layer such as FASnI3 (1.41eV), CsSnI3 (1.3eV) Cs2AgBiI6 (1.6eV), CsSnCl3 (1.52eV), Cs2TiBr6 (1.8eV) and MASnI3 (1.35eV) are used as main absorber layer, which is sandwiched between ETL and HTL. Fluorine doped tin oxide FTO performs a dual function of serving as a front contact and as well as transparent conductive oxide through which light passes. Au acts as a back metal contact. In this study, the main focus has been laid on studying the behaviour of various lead free halide perovskites on the same device configuration. This will show the impact of the properties of each of the perovskites on the device performance and will also help in determining the lead free perovskite that performs the best on this particular configuration. Figure 1b   optimum values of each of the layers, which further helps in obtaining the optimized performing solar cell. This is done for all the lead free perovskites taken into consideration in this work which helps in analysing the performance and impact of the properties of each material. The equations that play a significant role in the simulation study are inscribed below. Poisson's Equation for a semiconductor can be represented as follows: .

.… (1)
Where, ε is the permittivity of the semiconductor, NA represents the acceptor concentration, ND is the donor concentration and ψ resembles the electrostatic potential.
Now, the electron and hole continuity equations for a semiconductor are given by: Electron continuity equation: Hole continuity equation: In the above equations (2) and (3), Jn is the current density for electrons, JP is symbolic of the current density for holes and R represents the rate of carrier recombination.
Another very important set of equations is the Drift-Diffusion current relations that are given by the continuity equations shown in (4) and (5). There are two ways in which current is conductor in a semiconductor. First and foremost, diffusion current which is produced due to the concentration gradient developed due to the difference in carrier concentration on either sides of the device. Secondly, and drift current that is build up due to the drift of minority charge carriers under the influence of electric field.
Where, Dp is the diffusion coefficient for holes and Dn is the diffusion coefficient for electrons. E represents the electric field, q is the quantity of charge, n and p represents the number of electrons and holes. and represents the mobility of electron and holes respectively. Other relations that govern the performance parameters are as follows: For open circuit voltage: = ln ( + 1) .…… (6) Where, JSC is the short circuit current density (or, light generated current), JS is the reverse saturation current.
For short circuit current density: = − ……… (7) Fill factor and efficiency is given by the relation: For better device performance, light absorbing layer of solar cell has a major role. In this simulation different lead free perovskite materials will be used to find out best configuration to achieve higher performances. Major attention is given to optimise different parameters in a way through which we can get a clear insight of device performances. The     34 . It was also observed from the generation and recombination depth profile of the charge carrier that the charge carrier generation is high at PCBM and perovskite interface and carrier recombination is less whereas in the PTAA and perovskite interface, generation is less and carrier recombination is high. Therefore, from this simulation work, it is clear that CsSnI3 based lead free perovskite solar cell definite be best alternate to the lead based perovskite solar cells.   Impact of thickness variation on the performance parameters of Pb-free perovskites Impact of doping and thickness variation of ETL, HTL on PSC performance