Research on the lead halide-based perovskite solar cells have obtained considerable interest in photovoltaic industry owing to their higher efficiency, easy manufacturing, light-weight and low cost. However, these lead halide-based solar cells are not suitable to manufacture commercially because of the toxicity of lead-based materials. In this context, a lead-free perovskite, cesium-bismuth iodide (Cs₃Bi₂I₉) is considered as a potential alternative to the lead halide-based cell due to their non-toxicity and stability, but this perovskite cannot be matched with random hole transport layer (HTL) and electron transport layer (ETL) materials compared to lead halide-based perovskite because of their crystal structure and band gap. Therefore, in this study, performance comparison of different ideal HTL and ETL materials for Cs₃Bi₂I₉ perovskite layerwere studied using SCAPS-1D device simulation on the basis of open circuit voltage, short circuit current, power conversion efficiency (PCE) and fill factor (FF) as well as several novel PSC configuration model were designed that can direct for further experimental research for PSC device commercialization. Results from this investigation reveals that the maximum efficiency of 20.96% is obtained for the configuration ITO/WS₂/Cs₃Bi₂I₉/NiO/Au with optimized parameters such as thickness 400 nm, band gap 2.1eV, absorber layer defect density 10¹² cm^-3, donor density of ETL 10¹⁸ cm^-3 and the acceptor density of HTL 10²⁰ cm^-3.

Keywords:

Subject: Engineering - Mechanical Engineering

1. Introduction

The consumption of power and energy is increasing with accelerated commercialization and industrialization[1]. The continuous utilization of conventional fuels such as natural gas, oils, hydrocarbon gas liquids, fossil fuels and the severe environmental effect for using these materials raises serious concerns about the research of alternate energy resources [2,3,4]. To replace the non-renewable energy resources and to fulfill the increasing energy demand in an environment friendly way, proper utilization of renewable energy sources is badly needed [5,6]. Solar energy stands out as a viable renewable energy resource among different potential renewable sources such as wind energy, geothermal energy, hydro power, ocean energy, bioenergy and tidal energy. In recent years, solar cell production is expanding significantly today as the cost of solar cells lowers. However, in order to compete with fossil fuels and transform into a substantial energy source, the expenses of solar cells must be minimized. Considerable initiatives have been taken to create novel cell materials, and recently, a new generation of perovskite solar cells (PSCs) has been established that shows satisfactory performances to go for commercialization. The PSC will most likely have a huge impact on the future solar cell industry due to the low cost of raw materials and the simple manufacturing method, and this kind of cell may also be competitive with natural gas [7].

The solar research field have been recently captured by organic-inorganic PSCs due to having exceptional and excellent properties such as high absorptivity, low atomic energy, improved dielectric constant, favorable deposition by solution processing technique, high electron mobility, high hole mobility, suitable with low manufacturing cost and low-temperature deposition than conventional silicon-based solar cells [8,9]. The efficiency and stability of perovskites solar cells show tremendous improvement such as in just 10 years perovskite solar cells developed from unstable 3% efficiency to stable 32% efficiency [10] and this improvement shows the potentiality of perovskite solar cells for which these solar cells have raised as strong competitor in the photovoltaic industry [11,12,13].

Thin-film PSC technology has improved due to the ease fabrication, energy gap adjustability, and the photon conversion efficiency (PCE) above 30% of lead (Pb)-compounded organic inorganic halide PSCs [14]. Although these achievements, the existence of emerging contaminants (Pb) that causes toxicity is the fundamental issues in the applications of lead-based PSCs and this problem is still a significant barrier to commercialization of PSCs [15]. Additionally, the perovskite layer's organic components contribute to the solar cell's instability. Similarly, the presence of organic elements in the perovskite layer causes instability of the solar cell. Therefore, lead based organic halide perovskite solar cells are not suitable and preferable for industrial application and commercialization. To eliminate the toxicity researchers have carried out experiments to develop lead-free perovskite material and to minimize instability utilizing inorganic materials have gathered attractive attention which can replace organic materials [16,17,18]. Ahmad et al. simulated a Cs₃Bi₂I₉ based 2D PSC device where they employed TiO₂ as ETL material and Spiro-MeOTAD as HTL material with gold as back contact[19]. Their simulation results revealed that their PSC device could gain an efficiency of 11.54% and their experimental results showed 1.66% efficiency for the similar configuration. Researchers are also working for stabilizing experimented PSC devices against several influencing natural factors such as moisture, temperature and dust. Hamukwaya et al.[20] experimented to investigate the performance after adding KI as additive with Cs₃Bi₂I₉ perovskite layer. This mixing of KI caused the highest efficiency as 2.81% the Cs₃Bi₂I₉ perovskite layer highly stabilizes the resultant PSC device against humidity to the extent that it maintains 98% of the initial PCE after 90 days, which is suitable for solar cell applications.

Homo-valent component such as Ge²⁺ and Sn²⁺ can be a potential choice which can eliminate toxicity; however, these components decrease the stability of PSCs when it performs at ambient temperature [21,22,23]. For alternation of such materials different hetero-valent materials are tested in lab-based experiments to investigate their suitability and stability for using in perovskite layers and among those materials Bi³⁺ and Sb³⁺ which have stable +3 oxidation phase have gathered much attention[24]. Bi³⁺ have good optoelectronic properties as Pb²⁺ due to ionic radius and electronic structure similarities of these materials. Among different Bi halide-based materials Cs₂Bi₂I₉ achieved the greatest interest due to its higher PCE and more stability than other Bi based perovskite materials [25,26]. Summary of different works on the PSC performance analysis are listed in Table 1.

Cs₃Bi₂I₉ is a hybrid organic-inorganic perovskite material that has gained attention in the field of photovoltaics as a potential absorber layer in solar cells. This material has a range of advantages that make it an attractive candidate for this application. One of the significant advantages of Cs₃Bi₂I₉ is its high absorption coefficient. This characteristic enables it to absorb light effectively across a broad range of the solar spectrum, which is essential for the efficient operation of solar cells. The high absorption coefficient of Cs₃Bi₂I₉ is comparable to other well-known perovskite absorbers like MAPbI₃ (methylammonium lead iodide). Another advantage of Cs₃Bi₂I₉ is its high stability. Many perovskite materials are known to be unstable under ambient conditions, which can limit their practical applications. However, Cs3Bi2I9 has been shown to be highly stable under various environmental conditions, including humidity, light, and heat. This stability makes it an attractive option for use in real-world applications where stability is crucial. Cs₃Bi₂I₉ also has high carrier mobility, which is a desirable property for efficient charge transport and collection in photovoltaic devices. Furthermore, this material has a direct bandgap, which is crucial for efficient light absorption and conversion into electrical energy in photovoltaic devices[24].

In this study, the simulation has been carried out in two steps, where the first step consists of comparison of suitable ETL and HTL materials with Cs₃Bi₂I₉ absorber layer to find out the best configuration for which higher performance has been observed. In second step, the selected model has been optimized for improving its performance parameters such as J_sc, V_oc, PCE and FF. To achieve the optimized system, around 45 models with different ETL and HTL materials have been performed. In this process, a best performance for ITO/WS₂/Cs₃Bi₂I₉/NiO/Au has been attained. For further improvement of this configuration, optimization of various adjustable attributes such as thickness and bandgap of absorber layer, defect density of absorber layer and charge carrier density of HTL and ETL materials has been done. After tuning input attributes, 20.96% of PCE has been obtained for this model.

2. Model development and perovskite solar cell structure

2.1. Numerical modeling

In order to construct any form of a practical solar cell, numerical models have become a crucial tool. Perovskite solar cells’ numerical modeling is a crucial technique for evaluating the validity of the proposed physical reasons and predicting the impact of physical modifications on cell performance [38]. Numerical modeling is required because perovskite solar cells are so complicated in their behavior [39].

Numerical simulation software offers useful information to select materials before experiment and commercialization. The One Dimension Solar Cell Capacitance Simulator (SCAPS-1D) program which is created by Burgelman et al. [40] can be used to do the numerical calculations of PSCs [41]. SCAPS-1D software solves the charge carrier continuity Equations such as hole continuity Equation 1 and electron continuity Equation 2, the semiconductor Poisson Equation 3 in one direction, total charge transport Equation 4, electron transport Equation 5, hole transport Equation 6 and optical absorption coefficient Equation 7.

\frac{{d n}_{p}}{d t} = G_{n} - \frac{n_{p} - n_{p 0}}{τ_{n}} + n_{p} μ_{n} \frac{d ξ}{d x} + μ_{n} ξ \frac{{d n}_{p}}{d s} + D_{n} \frac{d^{2} n_{p}}{{d x}^{2}}

(1)

\frac{{d n}_{n}}{d t} = G_{p} - \frac{p_{n} - p_{n 0}}{τ_{p}} + p_{n} μ_{p} \frac{d ξ}{d x} + μ_{p} ξ \frac{{d n}_{n}}{d s} + D_{p} \frac{d^{2} p_{n}}{{d x}^{2}}

(2)

\frac{d^{2} \emptyset (x)}{{d x}^{2}} = \frac{q}{ϵ_{o} ϵ_{r}} (p (x) - n (x) + N_{D} - N_{A} + - 0.3 ρ_{p} - - 0.3 ρ_{n})

(3)

J = J_{n} + J_{p}

(4)

J_{n} = D_{n} \frac{d n}{d x} + μ_{n} n \frac{d ϕ}{d x}

(5)

J_{p} = D_{p} \frac{d p}{d x} + μ_{p} p \frac{d ϕ}{d x}

(6)

α (λ) = (A + \frac{B}{h v}) \sqrt{h v - E_{g}}

(7)

where,

ξ

is the electric field, q denotes electrical charge whose typical value is considered as

1.602 \times 10^{- 19}

ϵ_{o}

is the vacuum absolute permittivity and

ϵ_{r}

is the semiconductor relative permittivity, N_D and N_A represent donor doping density and acceptor doping density respectively, p(x) and n(x) are carrier density of hole and electron, -0.3

ρ_{p}

is the defect density of hole and -0.3

ρ_{n}

is the defect density of electron, G_n and G_p indicates electron generation rate and hole generation rate respectively, J_n and J_p are current density and hole current density of electron, respectively,

μ_{n}

and

μ_{p}

are electron and hole mobilities,

τ_{n}

and

τ_{p}

represents lifetime of electrons and holes respectively, D_p and D_n represents diffusion coefficient of free hole and electron.

v

represents optical frequency, A and B depicts arbitrary constant while E_g represents bandgap,

h

represents plank constant and

α (λ)

depicts absorption coefficient. More information about these equations can be learned from somewhere [42,43,44,45,46].

2.2. PSC structure and material charateristics

2.2.1. PSC structure

The device structure in this paper is Au/HTL/absorber layer/ETL/ITO/glass, where Au is employed as back contact having work function of 5.1eV and Cs₃Bi₂I₉ is applied as absorber or perovskite layer. The simulation is carried out with different ETLs and HTLs to obtain a novel optimized configuration. The ETLs that are simulated in this study include TiO₂, PCBM, WS₂, IGZO and C60 whereas CuO, Cu₂O, PEDOT:PSS, P3HT, CuSCN, CuSbS₂, NiO, Spiro-OMeTAD and CuI are applied as hole transport layer material.

Figure 1 shows a typical model of PSC with different layers such as ITO, ETL, absorber layer and HTL.

The band diagram of our selected configuration is showed in Figure 2, from where it can be seen that the blue curve depicts the conduction band line and red curve shows the valence band line.

2.2.2. Physical input parameters and methodology

The AM1.5 illumination spectrum is used by default in this study. The incident light power (Ps) and temperature are fixed at 1000 W/m² and 300 K, respectively. In every layer, the thermal velocities of the electrons and holes are fixed at 10⁷ cm/s. The absorption co-efficient (

α

) of ETL and HTL layers are determined in SCAPS-1D through Equation 8 [47], like in many works on PSCs,

α = A_{a} \sqrt (h v - E_{g})

(8)

where, A_a is a layer-dependent pre-factor in the simulation. The application of interface defects has schemed the design more realistic and assisted to predict the experimental behavior of the solar cell model.

PSC device investigation has been carried out in two different steps where the first step includes building up a PSC device configuration with suitable HTL and ETL for Cs₃Bi₂I₉ absorber layer. Different input attributes for nine HTL materials have been listed in Table 2 and input parameters for five ETL materials has been listed in Table 3. With these various ETL and HTL materials 45 different configurations have been simulated. After scrutinized comparison, it was found that when WS₂ as ETL and NiO as HTL were applied as charge transporting layers then the configuration (ITO/WS₂/Cs₃Bi₂I₉/NiO/Au) have showed best results with higher performance parameters. In second stage, the selected model (ITO/WS₂/Cs₃Bi₂I₉/NiO/Au) has been optimized by tuning bandgap and thickness of absorber layer, defect density of absorber layer and carrier density of ETL and HTL.

3. Results and discussion

3.1. Optimization of ETL and HTL

In this study, Cs₃Bi₂I₉ was selected as absorber layer due to its non-toxicity and better optoelectronic parameter, however it’s hard enough to match this absorber layer with appropriate ETL and HTL due to band structure of Cs₃Bi₂I₉. To obtain the best performance, simulation of the configuration (ITO/ETL/Cs₃Bi₂I₉/HTL/Au) for five different ETL materials and nine different HTL materials have been carried out.

Figure 3 shows performance parameters of different PSC configurations for different HTLs where PCBM and Cs₃Bi₂I₉ were applied as ETL and absorber layer respectively. In a similar way, Figure 4 shows performance parameters for WS₂ ETL, Figure 5 shows comparison for IGZO ETL, Figure 6 reveals performance comparison for C60 ETL as well as comparison for TiO₂ ETL can be observed in Figure 7.

After scrutinized comparison, it can be observed from these figures that when NiO and WS₂ were applied as HTL and ETL, respectively, the configuration ITO/WS₂/Cs₃Bi₂I₉/NiO/Au shows best performance characteristics. The optimized characteristics are given in From Figure 4, Figure 5, Figure 6 and Figure 7, it can be observed that the maximum 20.25% PCE can be achieved when WS₂ and NiO were employed as ETL and HTL material respectively with Cs₃Bi₂I₉ perovskite layer. Cu₂O also showed extraordinary performance with WS₂ ETL and Cs₃Bi₂I₉ absorber layer. However, as the configuration ITO/WS₂/Cs₃Bi₂I₉/NiO/Au shows best performance so further optimization was carried out for this model.

Table 4 for which improved performance characteristics were obtained. From Figure 4, Figure 5, Figure 6 and Figure 7, it can be observed that the maximum 20.25% PCE can be achieved when WS₂ and NiO were employed as ETL and HTL material respectively with Cs₃Bi₂I₉ perovskite layer. Cu₂O also showed extraordinary performance with WS₂ ETL and Cs₃Bi₂I₉ absorber layer. However, as the configuration ITO/WS₂/Cs₃Bi₂I₉/NiO/Au shows best performance so further optimization was carried out for this model.

3.2. Effect of absorber layer thickness

The light-absorbing layer thickness has a great impact on the performance of PSCs. The layer needs an optimized thickness for the collection of solar radiation basically to collect photons and facilitates the electron and hole pair generation. The photon absorption density drops hence the efficiency when there is a decrease in layer thickness from the optimized value [68]. And with the augmentation of thickness the photon absorption falls down because of the recombination of electron hole pair [69]. In this paper, the thickness of Cs₃Bi₂I₉ was varied from 400 to 5000 nm for getting optimized thickness for the model. There was change in V_OC, J_SC, FF and PCE with the variation in absorber layer thickness. These changes have been graphically represented on the Figure 8.

Firstly, it has been observed that with the extension of absorber layer thickness, the V_OC decreases from 1.4368 to 1.4279 V. The reason behind this is the recombination of charge carrier for their longer travel path. But the J_SC has been increased with the increase in absorber layer thickness. This is because of the rise in the spectral response when wavelength is longer. On the contrary the FF get reduced from 84.85% to 72.06% and the reason is the enhancement of series resistance and might be because of the charge carrier recombination along with the resistant losses. The maximum value of PCE was found 20.59% for the thickness of 400 nm which was taken as optimum thickness. For further augmentation of thickness there was drop in PCE. This is because of the charge pathway resistance and enhanced radiative recombination [70].

3.3. Effect of absorber layer band gap

The absorber layer band gap is an important parameter for the absorber layer, and it has a major impact on the effectiveness of the PSCs. In this regard, the tunability is the most important property of PSCs. The energy gap of perovskite absorber is tuned from 1.65 eV to 2.34 eV to investigate the performance of the PSC. Figure 9 reported that the maximum value of V_OC 1.4669V is obtained at 2.34 eV, J_SC of 22.88 mA/cm² at 1.65 eV, and the maximum PCE and FF of the device were found 20.9% and 88.79%, respectively at 2.1 eV.

The FF and PCE increased from 63.87% to 88.79% and 19.16% to 20.9% with the augmentation of bandgap from 1.65 to 2.1 eV. After there was a decrease in FF and PCE with increase in band gap because of lowering the band gap increases the number of electrons but the problem is the energy of the electrons wasted as heat energy. On the other hand, higher the band gap the generation of electrons drops for some of the photon’s higher energy [71]. The optimum value of bandgap was taken 2.1 eV for the maximum PCE of 20.9%.

3.4. Effect of absorber layer defect density

In order to attain the stable PV output parameters, the proper amount of defect density is important. The defect density impacts directly on the recombination and generation of electron hole pairs which also has an impact on the efficiency of the PSCs [72]. Defect density depends on the quality of the absorber layer. If the quality is poor, then this causes higher defect density. For this reason, recombination of electron hole pair increases hence reduce the efficiency of the perovskite film.

And this recombination rate depends on the diffusion length, which is affected by the bulk defect density of the PSC. Shockley-Read-Hall (SRH) recombination is the most important type of recombination in PSCs, the calculation of the diffusion length can be done by the trap assisted SRH recombination model [73]. Following two Equations (9 and 10) is used to describe SRH recombination.

R_{S R H} = \frac{n p - n_{i^{2}}}{[π (p + n + \frac{2 n_{i} \cosh (E_{i} - E_{t})}{k T})]}

(9)

τ = \frac{1}{[σ \times N_{t} \times V_{t h}]}

(10)

where, τ represents the life time of charge carriers, σ is the capture cross section of charge carriers, N_t is the defect density of the perovskite absorber layer, V_th is the thermal velocity of charge carriers.

The diffusion length,

L = \sqrt{D τ}

, where

D = \frac{k T}{e} μ

. Here, D refers to the diffusion coefficient and τ refers to the lifetime of minority carriers. In addition to that k denotes as Boltzmann’s constant, e refers to the charge of electron, T refers to the temperature, and µ denotes as mobility of charge carrier.

The defect density has an impact on the value of V_OC by the following Equation 11.

V_{o c} = \frac{k T}{q} \ln (\frac{J_{s c}}{J_{o}} + 1)

(11)

where, J_O and J_SC represent the recombination current density and short-circuit current density, respectively.

In order to get the optimum defect density, N_t of the absorber layer on the PSCs performance is analyzed by taking the values from 10¹² cm^-3 to 10¹⁷ cm^-3. Figure 10 shows with the increase in defect density all the photovoltaic parameters decrease. The V_OC drops from 1.4387 V to 1.4364 V and the J_sc from 16.364 to 15.859 mA/cm². A high density of defects can lead to a decrease in V_OC due to the increase in recombination. In devices with high defect densities, the recombination rate becomes dominant, leading to a decrease in V_OC. In addition, the increase in defect density can lead to an increase in the trap-assisted recombination rate, which can also reduce the V_OC of the device. The values PCE and FF remains almost similar up to the defect density of 10¹² cm^-3 to 10¹⁴ cm^-3 and reduce significantly after 10¹⁵ cm^-3. Therefore, the optimal defect density is taken as 10¹² cm^-3. The maximum PCE and FF is found to be 20.9% and 88.79% respectively for the defect density of 10^-12 cm^-3.

3.5. Effect of carrier density

The doping of ETL and HTL can be carried out using one of the two methods. Minority carriers can be used to accomplish the doping rate., however this method dramatically reduces the photovoltaic characteristics. On the other hand, most carriers with greatly improved PV characteristics can also achieve it. PSC performance will be improved with an intermediate level of doping density.

3.5.1. Effect of donor density of ETL

In order to find the best suitable doping concentration of ETL, the donor density for WS₂ was enhanced from 10¹⁵ cm^-3 to 10¹⁹ cm^-3. The variation of V_oc, J_sc, FF and the PCE was shown in Figure 6. The PCE and FF increased from 19.88% to 20.96% and 82.53% to 89.03%, respectively with the increase in donor density from 10¹⁵ to 10¹⁸ cm^-3. The J_sc was almost constant with the variation and there was a sudden drop after 10¹⁸ cm^-3. Additionally, the V_oc enhanced from 1.43V to 1.44V with the rise in doping concentration. The optimal value of donor density was taken as 10¹⁸ cm^-3 as the maximum PCE 20.96% was found at that value. The higher value of N_D makes it easy to extract charge and transportation of charge at the ETL/perovskite interface [74].

3.5.2. Effect of acceptor density of HTL

The variation of acceptor density of HTL(N_A) has a major influence on the performance of PSCs. Small amount of variation in acceptor concentration caused variation in the stability of the PSCs. To obtain the optimum value of N_A, the N_A was varied from 10¹⁶ cm^-3 to 10²⁰ cm^-3. There was a small increase in V_oc and J_sc from 1.4385V to 1.4388V and 16.359 mA/cm² to 16.366 mA/cm² with the increase in HTL acceptor density.

Figure 12. Effect of acceptor density of HTL(NiO) on (i) Jsc, Voc, and (ii) FF, PCE.

In addition to that the PCE and FF was improved from 20.26% to 20.96% and 86.11% to 89.03%, respectively with the augmentation of N_A. Therefore, the optimum value of N_A was taken 10²⁰ cm^-3 as the maximum PCE 20.96% was found at that value of acceptor concentration. The higher the N_A, the production of interface electric field among the PSC layer is higher. It causes the increase in electric potential. However, this growth in PCE brings a higher recombination of charge carriers, which causes an increase in dopant concentration in the absorber layer[74,75].

3.6. Comparison of initial and optimized final model

An improvement of current-voltage characteristic can be seen from Figure 13 for the optimized final model than the initial model. From the J-V characteristic curve, performance parameters of a PSC device can be understood. Here, from the J-V curve it can be observed that for the final optimized model an improved I-V curve is obtained than that of initial model.

Figure 14 depicts that the quantum efficiency in optimized final model is higher than the quantum efficiency of initial model. To obtain proper knowledge about quantum efficiency of the initial model and optimized final model, the wavelength was varied from 300 nm to 900 nm. In this wavelength range, the quantum efficiency varied due to tuning of different input attributes such as bandgap and thickness of absorber layer, carrier density and defect density of absorber material.

Quantum efficiency (QE) measures a solar cell's capacity to produce charge carriers from photon energy. From Figure 14, it’s clear that higher quantum efficiency can be obtained by tuning the PSC device in a proper way, thus higher amount of charge carriers can be produced from the absorber layer, that means generation rate would be increased. As a result, better performance can be obtained due greater generation of electron-hole pairs.

3.7. Comparison with literature

Organic spiro-OMeTAD can be fabricated in flexible and simple method of manufacture, therefore, is the material that is most frequently employed in the commercial and industrial sectors [76]. Despite this, the material is unsuitable for PSCs due to poor hole mobility, low conductivity, high manufacturing costs, and instability brought on by moisture, oxidation, and light. Additionally, TiO₂ is another popular n-type material which is most commonly used as ETL. Despite having potential for excellent photovoltaic function, photo corrosion resistance, superior thermal stability, and the 3.2eV bandgap presents a difficulty [77]. PSC configurations with these materials and lead-based perovskite shows better characteristics that is clear from table, however due to their toxicity and instability problem further improvement are required through investigating new materials to replace these toxic and instable materials.

In this study, a novel PSC model was designed and simulated that shows better performance characteristics after optimization which can be seen from Table 5. Additionally, the selected perovskite material (Cs₃Bi₂I₉) is considered much stable [85] which is introduced in the previous section. Therefore, the designed model in this present work can be considered for further experiment and commercialization.

4. Conclusions

In this paper, the modeling and performance analysis was done for the Cs₃Bi₂I₉ based PSC using SCAPS-1D. The lead-free Cs₃Bi₂I₉ was used as the absorber layer and the selection of this layer was based on the better stability and non-toxicity of this material. WS₂, PCBM, C60, TiO₂, IGZO were used as the ETL material and Cu₂O, CuSCN, CuSbS₂, P3HT, PEDOT:PSS, Spiro-OMeTAD, NiO, CuI, CuO was used as the HTL material. Total of 45 different PSC models were simulated with the combination of these HTL and ETL with the Cs₃Bi₂I₉ based absorber layer. In addition, Au was taken as the back contact material. After the numerical simulation of these models, the combination of WS₂-Cs₃Bi₂I₉-NiO was found to give the maximum PCE of 20.25%. This combination is the novel model in which WS₂ is used as ETL with Cs₃Bi₂I₉ perovskite layer. In order to enhance the performance parameters (V_OC, Jsc, FF, PCE) of the PSC and to achieve the maximum PCE, this model was scrutinized by varying the parameters like absorber layer thickness, band gap, defect density and carrier density of the ETL and HTL. The thickness of absorber layer was found to be 400 nm as optimum as PCE was maximum 20.59% at 400 nm. Thin absorber layer was found to give the good efficiency for the perovskite model. There was a significant change in the performance with the variation of absorber layer band gap. For the band gap of 2.1 eV, the PCE was the highest among others. There was found a significant increase in PCE from 20.59% to 20.9% for this bandgap. Though, the defect density has a major impact on the effectiveness of the PSCs, there was observed no such changes in the maximum efficiency with the variation of defect density. The maximum efficiency of 20.9% was found at the absorber layer dopant density of 10¹² cm^-3. There was a gradual increase in the performance parameters with the variation in carrier density. The maximum of 20.96 % PCE was obtained with the ETL donor density of 10¹⁸ cm^-3 which was the best we found in our numerical analysis. Since, higher the N_D makes the extraction of the charge easier to the ETL/ perovskite layer. The optimum acceptor density of HTL was found to be 10²⁰ cm^-3 and here also the maximum PCE was found to be 20.96%. Finally, after the full optimization the PSC attained a PCE of 20.96% which was initially found to be 20.25%.

Acknowledgement

Authors are thankful to Prof. M. Burgelman and his co-workers, Department of Electronics and Information Systems, University of Gent, Belgium for supporting with the SCAPS-1D simulation software.

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Figure 1. Model of a perovskite-based solar cell with different layers.

Figure 2. Energy band diagram for the selected configuration in this study.

Figure 3. Performance parameters for different HTLs with PCBM ETL and Cs3Bi2I9 absorber layer.

Figure 4. Performance parameters for different HTLs with WS₂ ETL and Cs3Bi2I9 absorber layer.

Figure 5. Performance parameters for different HTLs with IGZO ETL and Cs3Bi2I9 absorber layer.

Figure 6. Performance parameters for different HTLs with C60 ETL and Cs3Bi2I9 absorber layer.

Figure 7. Performance parameters for different HTLs with TiO₂ ETL and Cs3Bi2I9 absorber layer.

Figure 8. Effect of absorber layer thickness on PSC device' performance parameters (i). (J_sc, V_oc), and (ii) (FF, PCE).

Figure 9. Effect of absorber layer bandgap on (i) Jsc, Voc, and (ii) FF, PCE.

Figure 10. Effect of absorber layer defect density on (i) Jsc, Voc, and (ii) FF, PCE.

Figure 11. Effect of donor density of ETL (WS₂) on (i) Jsc, Voc, and (ii) FF, PCE.

Figure 13. Comparison of J-V characteristic curve of initial and final optimized model.

Figure 14. Comparison of capacitance of initial and final optimized model as a function of wavelength.

Table 1. Literature review on recent experimental perovskite-based solar cells performance.

Device structure	Year	PCE(%)	V_OC(V)	J_SC(mA/cm²)	FF(%)	Ref
Au/spiro-OMeTAD/ FTO/TiO2	2022	12.54	1.32	13.13	72.01	[27]
HTL/back contact /MAPbBr₃/SnO₂/ FTO	2021	25.40	1.19	25.09	84	[28]
Ag/BCP/PCBM/(Cs_0.05(FA5/MAI) _0.95Pb(I_0.9Br_0.1)₃)/PTAA/TTO/Glass	2021	23	1.16	24	82	[29]
Cu/BCP/ITUC₆₀/Cs_0.05(FA_0.92MA_0.08)_0.95Pb(I_0.92Br_0.08)₃/ PTAA/ITO	2020	22.30	1.71	24.10	81	[30]
Au/ Spiro-OMeTAD/CsSn_0.5Ge_0.5I₃/PCBM/FTO	2019	7.11	0.63	18.61	60.6	[31]
ITO/NiO_x/FASnI₃/PCBM/Ag	2018	6.70	0.60	17.53	65	[32]
Ag/PCBM/MASn_0.6Pb_0.4I_3-xBr_x/PEDOT:PSS/ITO	2017	12.10	0.78	20.65	75	[33]
Au/Spiro-OMeTAD/Cs_0.16FA_0.84Pb(I_0.88Br_0.12)₃/SnO₂/FTO	2016	18	1.02	22.40	78	[34]
Ag/BCP/PCBM/0.15 mol% Al₃+-dopedCH₃NH₃PbI₃/ Poly-TPD/FTO	2016	19.10	1.01	22.40	78	[35]
Au/spiro-OMeTAD /MASnI₃/ ZnO/ITO	2015	7.66	0.97	11.10	66	[36]
Au/SpiroOMeTAD + LiTFSI + tBP /MASnI₃/ m-TiO₂/ TiO₂	2014	6.40	0.88	16.80	42	[37]

Table 2. Input attributes for perovskite material, different electron transport layer (ETL) materials and ITO.

Parameter	Cs₃Bi₂I9 [48]	PCBM[49,50]	TiO₂ [51,52,53]	WS₂ [54]	IGZO [49]	C60 [55]	ITO [56]
Electron affinity, X (eV)	3.40	3.90	4.26	3.95	4	3.90	4.1
Relative permittivity ( $ε_{r}$ )	9.68	4	100	13.60	9	4.20	10
Thickness(nm)	1000	30	30	100	30	50	60
Bandgap, E_g (eV)	2.1	2	3.20	1.80	3.50	1.70	3.6
State density of conduction band, N_C (1/cm³)	4.98×10¹⁹	$1 \times 10^{21}$	$2 \times 10^{18}$	10⁷	$5 \times 10^{18}$	$8.0 \times 10^{19}$	$2.2 \times 10^{18}$
State density of valence band, N_V (1/cm³)	2.11×10¹⁹	$2 \times 10^{20}$	$1.8 \times 10^{19}$	10⁷	$5 \times 10^{18}$	$8.0 \times 10^{19}$	$1.8 \times 10^{19}$
AL defect density, N_t (1/cm³)	10¹⁴	$1 \times 10^{14}$	$1 \times 10^{15}$	10¹⁵	$1 \times 10^{15}$	$1 \times 10^{14}$	-
Mobility of electron, $μ_{n}$ (cm²/Vs)	10⁷	$1 \times 10^{- 2}$	$2 \times 10^{4}$	100	15	$8.0 \times 10^{- 2}$	10⁷
Mobility of hole, $μ_{p}$ (cm²/Vs)	10⁷	$1 \times 10^{- 2}$	$1 \times 10^{3}$	100	0.20	$3.5 \times 10^{- 3}$	10⁷
AD, N_A(1/cm³)	10¹⁹	-	-	-	-	-	-
DD, N_D(1/cm³)	10¹⁹	$1 \times 10^{20}$	$6 \times 10^{19}$	10¹⁸	$1 \times 10^{17}$	$2.6 \times 10^{17}$	10¹⁹

Table 3. Input attributes for different hole transport layer (HTL) materials.

Parameter	NiO [50]	CuO [57]	Cu₂O [58]	PEDOT [59]	P3HT [58]	CuSCN [58]	CuI [60,61,62,63]	Spiro-OMeTAD [64]	CuSbS₂ [65,66,67]
Relative permittivity ( $ε_{r}$ )	11.75	18.1	7.1	3	3	10	6.5	3	14.6
Bandgap, E_g(eV)	3.6	31.5	2.17	3.6	1.7	3.4	2.98	2.9	1.58
Electron affinity, X(eV)	2.1	4.07	3.2	1.57	3.5	2.1	2.1	2.2	4.2
Thickness(nm)	50	50	50	50	50	50	50	350	50
AL defect density, N_t (1/cm³)	$1 \times 10^{8}$	$1 \times 10^{13}$	$1 \times 10^{13}$	$1 \times 10^{14}$	$1 \times 10^{14}$	$1 \times 10^{8}$	$1 \times 10^{15}$	$1 \times 10^{13}$	$1 \times 10^{18}$
State density of conduction band, N_C (1/cm³)	$2.5 \times 10^{20}$	$2.2 \times 10^{19}$	$2.5 \times 10^{20}$	$2.2 \times 10^{18}$	$2 \times 10^{18}$	$2.5 \times 10^{18}$	$2.8 \times 10^{19}$	$2.5 \times 10^{18}$	$2 \times 10^{18}$
State density of valence band, N_V (1/cm³)	$2.5 \times 10^{20}$	$5.5 \times 10^{20}$	$2.5 \times 10^{20}$	$1.8 \times 10^{19}$	$2 \times 10^{19}$	$1.8 \times 10^{19}$	$1 \times 10^{19}$	$1.8 \times 10^{19}$	$1 \times 10^{18}$
Mobility of electron, $μ_{n}$ (cm²/Vs)	$1 \times 10^{- 3}$	100	200	100	$1.8 \times 10^{- 3}$	$2 \times 10^{- 4}$	$1.69 \times 10^{- 4}$	$2 \times 10^{- 4}$	49
Mobility of hole, $μ_{p}$ (cm²/Vs)	$1 \times 10^{- 3}$	0.1	8600	4	$1.8 \times 10^{- 2}$	$2 \times 10^{- 4}$	$1.69 \times 10^{- 4}$	$2 \times 10^{- 4}$	49
AD, N_A(1/cm³)	$1 \times 10^{19}$	$1 \times 10^{15}$	$1 \times 10^{19}$	$2 \times 10^{19}$	1 $\times 10^{18}$	$1 \times 10^{17}$	$1 \times 10^{18}$	$1 \times 10^{17}$	$1 \times 10^{18}$
DD, N_D(1/cm³)	-	-	-	-	-	-	-	-	-

Table 4. Optimized input attributes for the selected configuration in this study.

Parameters	ITO	WS₂	Cs₃Bi₂I₉	NiO
Electron affinity (eV)	4.1	3.95	3.4	2.1
Bandgap (eV)	3.6	1.8	2.10	3.6
Thickness (nm)	60	100	400	150
Dielectric permittivity (relative)	10	13.6	9.68	11.75
Thermal velocity of hole (cm/s)	10⁷	10⁷	10⁷	10⁷
Mobility of electron (cm²/Vs)	50	100	4.3	10^-3
CB effective density of states (cm^-3)	2.2 $\times$ 10¹⁸	2 $\times$ 10¹⁸	4.98 $\times$ 10¹⁹	$2.5 \times 10^{20}$
VB effective density of states (cm^-3)	1.8 $\times$ 10¹⁹	2 $\times$ 10¹⁸	2.11 $\times$ 10¹⁹	$2.5 \times 10^{20}$
Thermal velocity of electron (cm/s)	10⁷	2 $\times$ 10⁵	10⁷	10⁷
Mobility of hole (cm²/Vs)	75	100	1.7	10^-3
Shallow uniform DD, N_D (cm^-3)	10¹⁹	10¹⁸	10¹⁹	-
Shallow uniform AD, N_A (cm^-3)	-	-	10¹⁹	$1 \times 10^{20}$
Defect density of AL, N_t (cm^-3)	-	10¹³	10¹²	$1 \times 10^{14}$

Note: The bold attributes depicts the optimized input paramters.

Table 5. Comparison of different established model with the present model in this study.

Models	Methods	V_OC(V)	J_SC(mA/cm²)	FF(%)	PCE(%)	Ref
FTO/TiO2/Cs₃Sb₂I₉/spiro-OMeTAD/Au	Simulation	1.32	13.13	72.01	12.54	[27]
CZTSe/MAPbI₃/Cd_1-xZn_xS/FTO	Simulation	1.12	26.45	88.90	27.13	[78]
PTAA/MAPbI₃/TiO₂	Experimental	1.11	19.58	76	16.46	[79]
Spiro − OMeTAD/MAPbI₃/TiO₂	Simulation	1.27	21.87	79.58	22.13	[80]
Spiro − OMeTAD/MAPbI₃/TiO₂	Experimental	1.09	23.83	76.2	19.71	[81]
CuI /MAPbI₃/TiO₂	Simulation	1.27	21.89	83.12	23.14	[80]
CuI /MAPbI₃/TiO₂	Experimental	0.55	17.8	62	6	[82]
NiO_x/MAPbI₃/PCBM : C₆₀/Zr	Experimental	1.08	23.47	79.4	20.13	[83]
FTO/TiO2/Cs3Bi2I9/spiro-MeOTAD/Au	Simulation	1.03	21.02	73.4	11.14	[84]
FTO/TiO₂/Cs₃Bi₂I₉/NiO	Simulation	0.92	22.07	68.21	13.82	[84]
ITO/WS₂/Cs₃Bi₂I₉ /NiO/Au	Simulation	1.438	16.366	89.03	20.96	[Present work]

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Submitted:

19 May 2023

Posted:

25 May 2023

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Subject: Engineering - Mechanical Engineering

1. Introduction