All-inorganic perovskite photovoltaics for power conversion efficiency of 31%

The lead-free perovskite halides emerge as the great alternative for highly efficient and environment friendly photovoltaics due to the inherent optoelectronic properties. In this paper, the numerical study of all-inorganic regular n–i–p structured perovskite photovoltaics using solar cells capacitance simulator (SCAPS-1D) has been performed. The optimised device structure using rGO provided best performance compared to the other hole transport layers (HTLs) like CuI, CuSCN, Cu2O, NiO, WSe2, MoO3 with CsSnI3 as an active material and TiO2 as electron transport layer (ETL). Furthermore, WS2 as an ETL compared to TiO2, Li-TiO2, ZnO, Al-ZnO, etc. provided the best performance with rGO as HTL and CsSnI3 as active material. Therefore, the optimized solar cell structure (FTO/WS2/CsSnI3/rGO/Pt) showed best photovoltaic performance with power conversion efficiency (PCE) of 31%, fill factor (FF) of 88.48%, open circuit voltage (VOC) of 1.15 V, and short circuit current density (JSC) of 30.47 mA/cm2, respectively. Consequently, the effect of variation of temperature, thickness, defect density, doping density of active layer and variation of illumination intensity on the photovoltaic performance of the optimised device are also analysed. Furthermore, this study is also focused on the analysis of photovoltaic parameters for the optimized structure using concept of ideality factor associated with the illumination intensity. Therefore, this analysis suggests a route for further development of all-inorganic, lead-free perovskite photovoltaics experimentally with improved photovoltaic performance.

PSCs 14 .The rGO based on graphene scaffold as interface layer between the ETL and active layer got achieved a PCE up to 17.2% 15 .It is found that rGO-HBS (rGO-4-hydrazino benzenesulfonic acid) as HTL in an inverted planar PSCs exhibits a PCE of 16.4% 16 .As the rGO has low oxygen content, which may lower the oxidation state of Sn 2+ to Sn 4+ in the interface of rGO-CsSnI 3 , whereas it enhances the stability of the device.Also, the increased hole extraction behaviour of rGO and presence of fewer trap states in the interface of HTL-perovskite layer increases PCE value of the device.Due to the excellent optoelectronic behaviour like maximum absorption and high carrier mobility in the rGO molecule, we consider it as a HTL in our model to enhance the efficiency of the device.Furthermore, among different transition metal dichalcogenides (TMDCs), tungsten disulfide (WS 2 ) is implemented as an ETL due to its excellent behaviour towards conductivity (~ 10 -3 Ω −1 cm −1 ) and carrier mobility 17 .Chalcogenide like WS 2 is an earth-abundant, direct band gap semiconducting material with non-toxic and adhesive properties and for better carrier conduction behaviour, it is used as an ETL in lead-free PSC having Sb 2 Se 3 as an active layer 18 .Furthermore, due to its layer translational properties and lattice matching with CsPbI 3 active layer, it is used as a lubricant in between the substrate and active layer in an inorganic CsPbI 3 based solar cell to bring down the tensile strain developed between the interface of ETL and perovskite layer 19 .Its tuneable band gap between 1.3 and 2.2 eV helps for easy conduction of electron in the solar cell 20 .It is also reported that using 2D WS 2 nanosheet as an ETL in PSC achieved a PCE of 18.21% due to its high interfacial carrier extraction properties in PSCs 21 .It can be deposited by solution processed low temperature technique or RF sputtering method 22 .Thus, it may be considered as a good candidate for practical application as ETL in the fabrication of PSCs.
The optimised simulated structure based on ITO (500 nm)/PCBM (50 nm)/CsSnI 3 (1000 nm)/CFTS (200 nm)/Se provided a PCE of 24.73% 30 .Also, by considering inorganic TiO 2 as ETL and organic Spiro-OMeTAD as HTL a PCE of 28.76% was obtained from a device structure of CuS (100 nm)/B-γ-CsSnI 3 (600 nm)/ TiO 2 /(50 nm) ITO (50 nm) after minimization of the recombination of charge carrier at the HTL/perovskite interface 31 .Another attempt to obtain PCE of 26.4% has been optimised through FTO/TiO 2 (40 nm)/CsSnI 3 (800-1000 nm)/P3HT (200 nm)/Au device structure with a direct bandgap of 1.3 eV in CsSnI 3 absorber layer 32 .Very recent study for the optimized structure on FTO/n-TiO 2 (50 nm)/CsSnI 3 (1250 nm, E g ~ 1.35 eV)/p-NiO (50 nm)/Au provided the PCE of 31.09% 33 .It is also reported that perovskite layer thickness is inappropriate using thinner (< 200 nm) or thicker (> 700 nm) film in the device.If the thin layer used, the low photocurrent results due to less absorption, but carrier extraction is high.Meanwhile, for the thick perovskite layer, although more carriers are generated in the device due to an increase in absorption, lower collection efficiency is because of recombination which affects the Voc 34 .Therefore, to achieve the excellent PV performance, it is required to improve the band alignment with absorber layer into ETL and HTL by optimizing the several input parameters like total defect density, band gap of active layer, acceptor level density, donor level density, and suitable film thickness of each layer, etc.
In view of the above, to achieve a remarkable PCE value for lead-free PSC, we have proposed a model of n-i-p structure simulated by SCAPS-1D simulation software.The variation of HTL and ETL is performed taking CsSnI 3 as an absorber layer.Where 2D layered structured materials like rGO and WS 2 are used as HTL and ETL, respectively.Therefore, the novelty of the work is to study the photovoltaic performance of optimised structure in comparison with the lead based one.Furthermore, a theoretical study of different PV parameters is performed by varying the absorber layer thickness, defect density, carrier doping density and probe temperature of the device.In addition to that, the obtained electrical and optical parameters from the above study can provide us an overall knowledge about ideality factor in association with recombination phenomena occurring inside the device, which gives deep understanding for experimental approach in device fabrication.

Device structure and simulation parameters
To evaluate or estimate the photovoltaic performance of different PSCs, device structures are simulated by various simulation software like SCAPS-1D, PC-1D, AMPS-1D, wxAMPS, COMSOL, Silvaco, etc. 43 .Among which SCAPS-1D version-3.3.09 is used in this study for simulating and modelling the PSC having CsSnI 3 as the active layer.This version is developed by the Department of Electronics and Information Systems (ELIS), University of Gent, Belgium 44,45 .The simulation is based on SCAPS-1D for multijunction (tandem) as well as single junction solar cell using three semiconductor equations.Equation (1) corresponding to Poisson equation 46 provides the relation between carrier concentrations and electrostatic potential.Equations ( 2) and (3) refer to the continuity equations for electrons and holes, respectively 43 for the relation between charge carrier generation and recombination mechanism in semiconductor.All the equations are shown below: where ɛ and ψ represent the permittivity and electric potential, q is charge of electron, n(x) and p(x) refer to the concentration of electron and hole, N D + and N A − represent the donor and acceptor doping density, n t (x) and p t (x) show the defect density, R refers to recombination rate of electron and hole, G is the generation rate of excitons, J n and J p are the current density of electron and hole, respectively.The charge transport mechanism can be understood using drift-diffusion model to be determined by the following Eqs.( 4) and (5) 45,47 : where D n and D p are the diffusion coefficient for electron and hole, µ n and µ p are electron and hole mobility, respectively.The SCAPS-1D is performed using the following Eq.( 6) for the calculation of absorption coefficient 4 : where α is the absorption coefficient (function of wavelength), A and B are the constants which is generally taken as 10 +5 and 10 -12 , respectively, h is the Planck's constant, ν is the incident photon frequency and E g denotes the band gap of absorbing layer.The various models having CsSnI 3 as an active layer has been simulated using several HTLs and ETLs in the present study.The HTLs (p-type) extract holes from the active layer to electrode for functioning the PSC.An efficient HTL must have high charge carrier mobility and high work function for the easy transportation of carriers 48 .Here, we have compared photovoltaic performance of the device for different inorganic HTLs like Cu 2 O, NiO, CuSCN, WSe 2 , CuI, MoO 3 , rGO and for organic HTL (Spiro-OMeTAD) whereas TiO 2 used as the ETL.Due to the high electron extraction capacity of TiO 2 (n-type) from the perovskite absorber layer with an appropriate band-alignment for blocking the holes, it can reduce the hysteresis loss to increase the PCE and stability of the PSCs 46,49 .Furthermore, a comparison is drawn between the device for different ETLs like Li-TiO 2 , WS 2 , ZnO, Al-ZnO meanwhile taking rGO as HTL.For ETL, generally we used metal oxides having semiconducting properties like ZnO, TiO 2 , SnO 2 and their doped ones.But evolution of surface defects and oxygen vacancies by these materials can be minimised by replacing these with TMDCs like WS 2 as ETLs 21 .Another comparison is done between lead-free (CsSnI 3 ) and lead based (CsPbI 3 ) active material with structure FTO/WS 2 /Perovskite/rGO.All the physical parameters are listed in Tables 1, 2, and 3 for the structural simulation of PSC using SCAPS-1D.All the basic simulation process is performed under AM 1.5G (1000 W m −2 ) illumination intensity and at room temperature (RT).Furthermore, the intensity of illumination and probe temperature are varied to evaluate its effect on the photovoltaic parameters like V OC , PCE, J SC and FF of the PSC.Also, the impact of thickness variation, doping density, and defect density of absorber layer on the given PSC parameters have been analysed.In the SCAPS-1D action panel, thermal velocity of electron and hole are taken to be 1.0 × 10 7 cm s −1 .The defect type is selected to be neutral, meanwhile, the band-to-band recombination data has been ignored in this simulation.The single energetic distribution is taken with characteristic energy of 0.1 eV for all the layers, whereas series resistance (R S ) and shunt resistance (R Sh ) are ignored in the initial calculations.In this simulation, the optical reflection from each layer and interfaces are not included, and the work function of the front contact (FTO) is taken as 4.4 eV with 100% transmission as a default value.Figure 1 displays the energy level diagrams of different HTLs, ETLs, CsSnI 3 and CsPbI 3 layer.Furthermore, Fig. 2 gives the optimised device structure representation of lead-free all-inorganic PSC. (1)

Results and discussion
Figure 3a,b exhibit the variation of current density with voltage (J-V) and the variation of external quantum efficiency with wavelength of incident light for different device structures.Also, Figure S1a shows the J-V curves and Figure S1b shows the variation of external quantum efficiency with wavelength for CsSnI 3 and CsPbI 3 based devices with rGO as HTL and WS 2 as ETL.The external quantum efficiency (EQE) of any PSC is the spectral Thermal velocity of electron (V th,e ) (cm s −1 ) 10 7 10 7 10 7 10 7 Thermal velocity of hole (V th,h ) (cm s −1 ) 10 7 10 7 10 7 10 7 Electron mobility (µ e ) (cm   response or the current obtained by photon absorption from the incident solar spectrum 66 .The EQE spectra is related to short circuit current (J SC ) of the device obeyed the following Eq.( 7) 67 .
where F(λ) represents the photon flux as a function of wavelength and q is the charge of free carriers.The computed result or PV parameters for different device structures are tabulated in Table 4. Best cell performance obtained from the above is for device structure FTO/WS 2 /CsSnI 3 /rGO with PCE = 30.84%,FF = 87.54%,J SC = 30.31mA cm −2 and V OC = 1.162V, which is taken as ideal structure for further analysis.Most importantly, using rGO as a HTL for both the CsSnI 3 and CsPbI 3 based devices, the EQE increases for wavelength ranging from 300 to 360 nm rapidly then it is almost constant up to 650 nm after which it decreases up to 900 nm.This trend shows the high photon absorption in visible region (400-700 nm) which is essential for better performance of PSCs. Figure 4 manifests the energy band diagram for simulated CsSnI 3 based device using rGO as HTL and WS 2 as ETL.It is observed that the band gap ranging from 1.3 to 2.15 eV for lead free PSCs gives better  www.nature.com/scientificreports/photovoltaic result, which is satisfied by our simulated device where the E g for CsSnI 3 (active layer) is taken as 1.3 eV and achieved a better PV performance.It is observed that increase in bandgap of active layer decreases the I SC value due to decrease in absorption of photons whereas V OC increases because of easy segregation of charge carriers inside the active layer 58 .Furthermore, to minimise the charge recombination and simultaneously to maximize carrier extraction from interfaces of different layers inside the device structure, the bandgap matching between HTL, ETL and absorber layer is very much essential.To achieve the above, conduction band offset (CBO) between ETL and absorber layer as well as valence band offset (VBO) between HTL and absorber come into consideration 68 .The above facts can be explained using the following Eqs.( 8) and ( 9): where χ Abs , χ HTL and χ ETL define the electron affinity of absorber layer, HTL and ETL, respectively.E gHTL and E gAbs denote the bandgap of HTL and absorber layer, respectively.The value of CBO and VBO depend on barrier height at interfaces formed by the photo generated carriers, which simply depends on the electron affinity of ETL, HTL and absorber layer as shown in the above-mentioned Eqs. ( 8) and (9).For better performance of PSC, the VBO and CBO should be a small positive value, as high value of VBO create hinderance for the conduction of hole from absorber to HTL and negative value of VBO enhance the carrier recombination 69 .Figure 4 shows the energy     4, we find a cliff at the WS 2 and CsSnI 3 interface.This provides a negative value of CBO i.e., − 0.05 eV.This negative value of CBO allows the easy conduction of electrons from absorber to front contact through ETL.Moreover, we find a spike at the rGO and CsSnI 3 interface, providing a positive value of VBO i.e., + 0.05 eV.However, this hinders the flow of holes from HTL to back electrode but this small VBO, may not impact the overall performance of the device.Also, in Fig. 5, we have shown the conduction band minima (CBM) and valance band maxima (VBM) of the perovskite, HTL and ETL layer of the device.It is shown that the energy difference in between the CBM of WS 2 and absorber layer is smaller than that of the VBM of WS 2 and absorber layer.As a result, it allows the easy  www.nature.com/scientificreports/conduction of electron from the conduction band of absorber to FTO through WS 2 layer and blocks the conduction of holes from VBM of absorber to VBM of WS 2 layer.Similarly, the difference in energy between the CBM of absorber layer and rGO is larger than that of the VBM of absorber and rGO layer.These differences allow the easy conduction of holes from VBM of absorber to the VBM of rGO and blocks the electron conduction from CBM of absorber to CBM of rGO layer.

Thickness variation of absorber layer
The thickness of absorber layer is the most important factor for variation in photovoltaic parameters (i.e., PCE, FF, J SC and V OC ) and for photo generated carriers (electron and hole) generated in this layer as incident light is absorbed 70 .From Fig. 6, we can observe the impact of variation in thickness on the device performance of FTO/ WS 2 /CsSnI 3 /rGO structured one.It is observed that J SC of the device increases gradually with the increase of thickness from 100 to 500 nm of active layer (optimum value) and then decreases slightly with the increase in thickness.The reason behind the increase in J SC is due to the increase in charge carrier generation by enormous amount of light absorption, but J SC value decreases slightly when the carrier recombination is more dominant with the increase of thickness 62 .PCE also follows the same trend whereas V OC decreases with increase in thickness due to the reduction in diffusion length of charge carriers which results carrier recombination.The V OC reaches its minimum value at 500 nm, so we consider 400 nm as the optimum value instead of 500 nm for our further analysis.Here, FF behaves in a zig-zag manner by variation in thickness of the absorber layer, which may be analysed in future study.

Variation in temperature
Environmental factors considerably affect the cell performance including stability and quality of the PSCs.Here we have varied the temperature from 300 K (27 °C) to 373 K (100 °C) by taking other parameters as constant to observe the effect on photovoltaic performance of FTO/WS 2 /CsSnI 3 /rGO structured device.Generally, increase in temperature affects the electron and hole mobility, energy bandgap and absorption coefficient of the different layer in solar cell.Therefore, when temperature increases the carrier recombination increases as a result there is a decrease in PCE value 66 .However, J SC increases with increase in temperature which is associated with the increase in number generation of electrons and holes by decreasing the bandgap 70 .From the Fig. 7, we found the V OC and FF decrease substantially with increase in temperature.This observation can be analysed using the following Eq.( 10): where the rate of change of V OC is inversely proportional to the temperature.Overall, we found an adverse effect on the PV performance as the temperature increases.Therefore, we consider 300 K as the optimised one for the simulation. (

Defect density variation
It is already explained that the presence of defects in absorber layer is the main cause for electron-hole recombination phenomena, so it behaves as recombination centres or trap sites.This recombination phenomena are associated with the decrement in diffusion length and lifetime of carriers resulting decay in cell performance.This type of recombination is explained by Shockley-Read-Hall effect 71,72 calculated using the following Eq.( 11): where R SRH represents the recombination rate, n and p is the concentration of electron and holes, E t denotes the energy level of trap states, τ n,p is the lifetime of electron and hole.Furthermore, the lifetime of the carriers can be calculated using the following Eq.( 12): where σ n,p represents the capture cross-sectional area for electrons and holes, N t is the density of trap sites and V th shows the thermal velocity of mobile carriers.The relation between the diffusion length L and lifetime is given using the following Eq.( 13) Using the above formulae, the following parameters can be calculated such as carrier recombination lifetime and diffusion length with the variation in defect density as listed in Table 5.For which, we have considered V th = 10 7 cm s −1 , σ = 10 -15 cm 2 , K B = 1.381 × 10 -23 J K −1 , T = 300 K, q = 1.6 × 10 -19 C, respectively.From the Table 5, it is clearly identified that the carrier lifetime and the diffusion length decrease gradually with the increase of defect density.Figure 8 exhibits the variation of PV parameters with defect density of the absorber layer from 10 14 to 10 17 cm −3 in FTO/WS 2 /CsSnI 3 /rGO structured one.It can be noted that the overall cell performance drops with

Doping density variation
It can be observed from the Fig. 9a that, increase in doping density will enhance the photovoltaic performance because of the increase in electric potential at perovskite surface.To find the optimum value for dopant concentration, doping density of absorber layer is varied from 2 × 10 14 to 2 × 10 20 cm −3 for FTO/WS 2 /CsSnI 3 /rGO device structure and it is inferred that, all parameters like FF, PCE, V OC of the device gradually increases except J SC .The J SC remains constant up to doping density of 2 × 10 16 cm −3 , then it decreases gradually.Furthermore, the J SC remains again constant from 2 × 10 19 to 2 × 10 20 cm −3 of doping density.This behaviour of J SC is due to the decrease in diffusion length of minority charge carriers at higher acceptor doping concentration 73 .Because of the opposite trend in variation of J SC , we consider 2 × 10 18 cm −3 as the absorber doping density in our further calculation.However, increase in doping concentration increases V OC of the cell because of decrement in reverse saturation current by Eq. ( 14) 70 .
Here, J 0 denotes reverse saturation current, J SC is the short circuit current, n is the ideality factor, T is the temperature and K is the Boltzmann constant, respectively.Also, FF and PCE increase due to increase in number of charge carriers.From the above analysis it can be concluded that using the optimum doping concertation we can get an improved V OC and FF simultaneously with increased PCE value.At a particular defect density of 10 14 cm −3 , we analysed the recombination phenomenon with the variation of doping concentration from 2 × 10 14 to 2 × 10 20 cm −3 for the absorber layer of PSC.Here, Fig. 9b shows that at constant defect density if we increase the doping concentration, the recombination rate increases, and thus, it shows reduction in the diffusion length of mobile charge carriers.

Variation of electrode
Here, we have simulated the PSC structure (FTO/WS 2 /CsSnI 3 /rGO) using different back contact electrodes i.e., Silver (Ag), Copper (Cu), Gold (Au), Nickel (Ni), Palladium (Pd), Platinum (Pt) and Selenium (Se) having different work function 46,73 .The work function of these materials and the PCE obtained from simulation using these as electrodes in the device are listed in Table 6.From where, we observed that with the increase in work function, the PCE of device increases.The back contact of the solar cell forms a junction with the HTL (rGO).If work function of the electrode is less than the HTL, then it prohibits the flow of holes from HTL due to the Schottky barrier formation at the junction 50,74 .To avoid this effect, the selection of proper back electrode having higher work function value is very important.Also, we obtained similar PCE (31%) value for Pt, Pd and Se electrodes.But, due to the toxic nature of Se and Pd, it is better to select Pt as a suitable back contact electrode for the present study.A comparative study of PV parameters with respect to other works as reported elsewhere are listed in www.nature.com/scientificreports/rGO/Pt structured device.The selected electrode (Pt) forms an ohmic contact instead of Schottky contact at the rGO-Pt interface and this can be represented by the given Eq. ( 15) 46 .
where φ B denotes the surface potential barrier at the anode-rGO interface.E g is the band gap of rGO, χ is the electron affinity of rGO and φ m is the electrode work function.Therefore, decrease in value of work function, the surface potential energy barrier increases, the PCE decreases obtained by the above Eq.( 15).

Variation of R S and R Sh
It is already proven that the variation in series resistance (R S ) and shunt resistance (R Sh ) has a significant impact on the PV parameter especially on FF and J SC .The R S is attributed to ohmic resistance present in between the junction of HTL and electrode whereas R Sh is contributed to defects and trap assisted recombination mechanism   www.nature.com/scientificreports/carried out inside the device.In this work, we have varied the R S from 0 to 6 Ω-cm 2 and the R Sh varied from 10 to 10 7 Ω-cm 2 with constant R S of 0.5 Ω-cm 2 (due to the presence of some amount of sheet resistance in the device).
Figure 10a shows the effect of R S variation on PV performance of FTO/WS 2 /CsSnI 3 /rGO/Pt structured cell.The FF, PCE and J SC of device decrease gradually with increase in R S .The variation in R S does not affect the V OC as it behaves constant during the entire process.The R S is associated with device current density followed by Eq. ( 16): whereas the relation between the R S and FF is given by Eq. ( 17) 73 .
where FF 0 is the FF in absence of R S and R Sh and FF S is the FF in presence of series resistance.Figure 10b exhibits the effect of variation in R Sh on the PV parameters of FTO/WS 2 /CsSnI 3 /rGO/Pt structured device.All the parameters increase up to a certain level for increase in R Sh , and after that it provides a stable cell performance with further increase in R Sh value.The FF and output current variation in presence of R Sh are given by the following Eqs.( 18) and ( 19) 73 .
(16) Ω Ω where FF Sh represents the FF in presence of shunt resistance.Figure S2a-d (contour plots) show the combinational effect of series and shunt resistance on PV parameters.From where we observed that the region having maximum value of R Sh and minimum value of R S shows enhancement in photovoltaic performances.From the Fig. 10a, we obtained a highest PCE of 31% for a R S of 0 Ω-cm 2 .It is experimentally verified that R S never become zero due to the sheet resistance of substrates whereas all the photovoltaic parameters are constant from R Sh of 10 5 Ω-cm 2 as shown in Fig. 10b.Therefore, we consider a R S of 0.5 Ω-cm 2 and R Sh of 10 5 Ω-cm 2 for further analysis.It is found that for an ideal solar cell the FF must be 1.But due to presence of some unavoidable losses arisen from the internal resistances (i.e., R S and R Sh ) and recombination of carriers (Auger, SRH, Band-to-Band), it will be less than unity (real model).The upper limit for the fill factor (FF) could be obtained 89% as reported elsewhere 81 .In the present study, we obtained FF of 88.47% for the rGO as a HTL and WS 2 as a ETL in lead-free device which approaches the upper limit as described above.

Electrical parameter analysis
Electrical impedance spectroscopy (EIS) is a technique used to characterize different phenomena (electronic and ionic process) running inside the PSCs i.e., recombination process, charge accumulation process at the interfaces, carrier transport mechanism, especially the transport rate, variation of capacitance and conductance, etc. 82 .Basically, the complex impedance plots i.e., Nyquist Plot (Z′ vs. Z″) and Bode plot (Frequency vs. Z Phase ) describe the carrier transport mechanism with a wide range of frequency associated with different resonance time.The Nyquist plot provides the effect of RC component associated in circuit whereas Bode plot indicates the achievable peak frequency.The size or width of arc in Nyquist plot provides the nature of charge transfer and the resistance associated with it 83 .For electrical analysis, we consider R S and R Sh to be 0.5 Ω-cm 2 and 10 5 Ω-cm 2 , respectively and a comparison of electrical performance is conducted among the Pb-based and Pb-free structures with rGO as HTL and WS 2 as ETL. Figure 11a shows the semi-circular arc of Nyquist plot formed due to the presence of parallel RC component in the circuit for FTO/WS 2 /CsSnI 3 /rGO/Pt and FTO/WS 2 /CsPbI 3 / rGO/Pt structured devices.Figure 11b represents the frequency variation of Bode plot and gives a peak frequency of 0.015 MHz and 0.01 MHz for device structure of FTO/WS 2 /CsPbI 3 /rGO/Pt and FTO/WS 2 /CsSnI 3 /rGO/Pt, respectively.Accordingly, the associated resonance time are calculated to be 63 µs and 100 µs, respectively using the following Eq.( 20): where T denotes the resonance time and f denotes the associated frequency.Figure 12a shows the highest capacitance of 158.93 nF cm −2 for FTO/WS 2 /CsSnI 3 /rGO/Pt based one, meanwhile the capacitance of 17.76 nF cm −2 is detected for FTO/WS 2 /CsPbI 3 /rGO/Pt based device.It is reported that increased value of capacitance corresponds to the absorption of lower wavelength photons 50 .Figure 12b represents the conductance vs. voltage relationship,  84 .Figure S3a,b represent the capacitance vs. frequency and conductance vs. frequency relationship provided the high value of capacitive response in low frequency range related to ionic movement and it can be used to analyse value of dielectric constant 85 .Figure S3c,d provide the complex capacitance data as it is related with frequency obeys the following Eqs.( 21) and ( 22): where ω represents the angular frequency.

Variation of illumination intensity
We already obtained the optimal value for series (R S ) and shunt resistance (R Sh ) from the above analysis.Now we vary the series and shunt resistance with incident light intensity to examine its effect on PV parameters of FTO/ WS 2 /CsSnI 3 /rGO/Pt structured PSCs or on the overall cell performance.The value of R S from 0 to 2 Ω-cm 2 and R Sh from 10 2 to 10 5 Ω-cm 2 are varied in this study.
From the Fig. 13a, it is obvious that, the increase in R S reduces FF of the device.The effect of R S on FF becomes less prominent with the decrease in light intensity, and it appears more significant at high light intensity region.From the Fig. 13b, it must be demonstrated that the increment in R Sh enhances FF of the device.The optimum FF is measured in high light intensity region with high R Sh value, whereas the low value of R Sh is visible only at low light intensity region.The PCE of device also follows the same trend as FF with the variation of Rs and R Sh , which are shown in Fig. 13c,d, respectively.

Illumination intensity and Ideality factor
The light intensity study of J-V curves not only says about the photovoltaic parameters but also provides the insight into different type of recombination occurs at the bulk or interfaces of the junction layers.Here, the ideality factor comes into consideration, which provides knowledge about the dominant recombination mechanism at a particular region in different layers of the device 86 .The variation of ideality factor and reverse saturation current with different light intensity gives an idea about electrical conduction at the junction.It is reported that, ideality factor can be estimated from the slope of Log(J + J SC ) vs. Voltage plot for illumination condition and Log(J) vs. Voltage plot for dark condition without consideration of series and shunt resistance in the circuit.In standard condition of small R S and large R Sh value, the ideality factor can be determined from the slope q/nKT of straight line obtained from Log(J + J SC ) vs. V′ plot.Where V′ is taken as V + J SC R S 87 .Figure 14a exhibits the J-V variation for different light intensity from 10 -4 to 10 Suns illuminations in absence of R S and R Sh for FTO/WS 2 /CsSnI 3 /rGO/Pt structure.The ideality factor of 2.21 KT/q for 1 Sun illumination can be extracted from the graph as shown in Fig. 14b.From the Table 8, it is observed that ideality factor increases up to 0.01 Suns intensity then, it gradually decreases with the decrease of light intensity.It is generally found that  the low light intensity region is affected by the bulk recombination, which further gives rise to the increment in ideality factor with decrease in light intensity.However, the high light intensity region is affected by interface recombination.From Fig. 15, we obtained the ideality factor of 2.13 KT/q in presence of R S = 0.5 Ω-cm 2 and R Sh = 10 5 Ω-cm 2 for one sun illumination of FTO/WS 2 /CsSnI 3 /rGO/Pt structure.All the ideality factor associated with the light intensities varying from 0.0001 to 10 Suns are listed in Table 9.We observe a zig-zag pattern of ideality factor  variation with the decrement in light intensity.If we see the light intensity variation from 10 Suns to 1 Sun, ideality factor decreases signifying the enhancement of interface recombination.Then ideality factor gradually increases up to 0.01 Suns.When light intensity variation from 0.01 to 0.0001 Suns, it shows a zig-zag pattern of ideality factor.It is reported that the value of ideality factor ranges from 1 to 1.5 KT/q provided the domination of interface recombination 86 and domination of SRH recombination is found for ideality factor of 1-2 KT/q 88 .In this study, the Auger recombination is neglected as it shows its effectiveness at very high light intensity (i.e., for high carrier concentration region).

Conclusion
A thorough study of regular n-i-p structured PSCs is performed by varying the HTLs (both the organic and inorganic) and then ETLs for the device.After the variation of HTLs and ETLs, highest efficiency of 30.84% is achieved from FTO/WS 2 /CsSnI 3 /rGO structured device.Then the optimised structure is simulated to examine the photovoltaic performance by varying the device temperature, thickness, defect density and doping density of absorber layer, back contact electrodes (BCE), series resistance (R S ) and shunt resistance (R Sh ), etc.By taking optimum thickness of 400 nm, doping density of 2 × 10 18 cm −3 , defect density of 10  Table 9. Ideality factor variation with light intensity in presence of R S and R Sh .

Figure 2 .
Figure 2. Optimised device structure of lead-free all-inorganic PSC.

Figure 3 .
Figure 3. (a) J-V curves and (b) variation of external quantum efficiency curves for CsSnI 3 and CsPbI 3 based devices having different HTLs and ETLs.

Figure 5 .
Figure 5. Schematic representation of charge transfer mechanism in lead-free all inorganic PSC structure.

Figure 9 .
Figure 9. (a) Analysis of photovoltaic parameters with the variation in doping density of absorber layer for FTO/WS 2 /CsSnI 3 /rGO, (b) variation of recombination rate with depth from surface for different doping density with a defect density of 10 14 cm −3 in the absorber layer.

Figure 10 .
Figure 10.Analysis of photovoltaic parameters with the variation of (a) series resistance (R S ) and (b) shunt resistance (R Sh ) in the device (FTO/WS 2 /CsSnI 3 /rGO/Pt).

Figure 13 .Figure 14 .
Figure 13.Contour plot of (a) R S , and FF vs. light intensity, (b) R Sh , and FF vs. light intensity, (c) R S and PCE vs. light intensity, (d) R Sh and PCE vs. light intensity for FTO/WS 2 /CsSnI 3 /rGO/Pt structured device.

Figure 15 .
Figure 15.Determination of ideality factor in presence of R S and R Sh for FTO/WS 2 /CsSnI 3 /rGO/Pt structured device.

Table 1 .
Simulation parameters for different layers of PSC.

Table 3 .
Simulation parameters of different ETLs.

Table 4 .
Photovoltaic performance of different device structures.
Energy band diagram for FTO/WS 2 /CsSnI 3 /rGO based device and representation of spike at perovskite/HTL and cliff at perovskite/ETL interface (inset).

Table 5 .
Analysis of photovoltaic parameters with the variation in temperature of FTO/WS 2 /CsSnI 3 /rGO structure.Calculation of diffusion length and carrier lifetime with variation in defect density.

Table 7 .
Furthermore, using Pt electrode we have achieved a PCE of 20.29% for FTO/WS 2 /CsPbI 3 / Analysis of photovoltaic parameters with the variation in defect density of perovskite layer for FTO/ WS 2 /CsSnI 3 /rGO structure.

Table 6 .
Work function and corresponding PCE to several metal electrodes.

Table 7 .
Comparative study of simulation based CsSnI 3 perovskite solar cell.

Table 8 .
14cm −3 and Pt as BCE, we have achieved a maximum efficiency of 31% for FTO/WS 2 /CsSnI 3 /rGO/Pt (lead-free) structured device whereas the PCE obtained for FTO/WS 2 /CsPbI 3 /rGO/Pt (lead-based) is 20.29% only.A comparative study is performed through Nyquist plot, Bode plot, and capacitance, conductance value of FTO/WS 2 /CsSnI 3 /rGO/Pt as Ideality factor variation with light intensity in absence of R S and R Sh .