A Comparative Study of High-Efficiency Lead-Free Cs₃Bi₂X₉ (X = Cl, Br, I)-Based Solar Cells

Abstract

Lead halide-based perovskite solar cells have gained significant attention from academia and the photovoltaic industry due to their exceptional optical and electrical characteristics. The primary problem with Pb-based perovskite pertains to its toxicity and solubility in water within the external environment. These concerns regarding hazards to the environment are constraining the application of lead-based perovskite in both consumer and industrial contexts. To offer a viable alternative to lead-based hazardous perovskite solar cells, we examined an inverted (p-i-n) perovskite structure with three distinct absorber layers based on cesium bismuth halides (Cs₃Bi₂I₉, Cs₃Bi₂Cl₉, Cs₃Bi₂Br₉) and conducted a comparative analysis utilizing SCAPS-1D software (version 3.3.08). The comparison analysis of our design against starting parameters indicated that the optimal power conversion efficiency (PCE) of 10.01% was recorded for Cs₃Bi₂I₉, 7.56% for Cs₃Bi₂Br₉, and 4.34% for Cs₃Bi₂Cl₉. Following careful optimization of the thickness of charge-transport layers (CTLs), doping concentrations of CTLs, and all three absorber layers, the overall efficiencies of the three inverted structures were enhanced from 10.01% to 14.08% for Cs₃Bi₂I₉, from 4.34% to 5.28% for Cs3Bi2Cl9, and from 7.56% to 11.05% for Cs₃Bi₂Br₉, respectively. The other performance enhancement, open-circuit voltage, increased from 1.08 V to 1.37 V for Cs₃Bi₂I₉, from 1.26 V to 1.47 V for Cs₃Bi₂Cl₉, and from 1.20 V to 1.47 V for Cs₃Bi₂Br₉. This comparative analysis of proposed perovskite devices demonstrates that Cs₃Bi₂X-based perovskite devices possess significant potential to replace conventional hazardous solar cells in the renewable and clean energy sectors.

1. Introduction

The energy requirements are escalating swiftly due to industrialization and commercialization in both developed and underdeveloped countries [1,2]. Conventional methods of power generation utilizing coal, gas, and gasoline are inadequate to address the energy issue intensified by population growth, and these resources are finite and will deplete over time [3]. Conventional energy sources are limited and negatively affect human health by increasing carbon emissions, which contribute to global warming and worsen diseases such as asthma and cardiovascular conditions [4]. It is imperative to identify alternate methods, such as renewable energy sources (solar, wind, biogas, etc.), for power generation to address the energy problem. Among all renewable energy sources, solar cells are a prominent contender for ecologically sustainable and cost-effective power generation [5,6]. The need for solar cells has expanded over time; nonetheless, a primary worry is the elevated cost of manufacturing solar cells for large-scale integration. Perovskite solar cells are considered a leading prospect in the solar cell market due to their expected lowered manufacturing costs in the near future [6,7].

The chemical composition of the perovskite material is ABX₃, where X represents halogen atoms (anions, e.g., chlorine (Cl), bromine (Br), and iodine (I)), B represents divalent cations (lead (Pb²⁺), tin (Sn²⁺), bismuth (Bi²⁺), etc.), and A represents monovalent cations such as methylammonium cation (CH₃NH₃⁺ or MA⁺), formamidinium cation (HC(NH₂)₂⁺ or FA⁺), and caesium (Cs⁺). In the crystalline structure of perovskite, the A ion is mostly surrounded by eight three-dimensional configurations formed by corner-sharing octahedral BX₆ units [8,9]. The chemical structure of perovskite is derived from calcium titanium oxide (CaTiO₂), discovered in 1839 [10]. Perovskite solar cells exhibit enhanced optical and electrical characteristics, including elevated absorption coefficients, robust carrier mobility, prolonged carrier lifetimes, significant binding energy, and adjustable band gaps, in comparison to conventional solar cells. Perovskite solar cells will continue to increase in efficiency over time, reaching 30%, and will soon be able to undergo additional modifications from an industrial perspective [10,11,12].

Recent studies indicate that mixed perovskite solar cells (Sn-Pb based) are considered efficient for tandem solar cells due to their suitable band gap values [13,14]. Pb-based organic–inorganic perovskite solar cells have attracted significant interest due to their high-power conversion efficiency values, reaching up to 25.8%. However, the large-scale commercialization of these Pb-based perovskites remains constrained by their toxic characteristics and water solubility [15]. Thus, it is essential to identify alternative, environmentally friendly candidates from the functional group, such as Sn, Ge, and Bi, to replace the toxic characteristics of Pb-based perovskite. Nonetheless, the inadequate stability resulting from suboptimal oxidation states and elevated defect rates (both surface and interfacial) in tin-based perovskite presents a significant challenge that restricts the efficiency of pure tin-based perovskite for large-scale integration [16,17].

Suboptimal oxidation is the unfavourable and spontaneous transition of tin (Sn) from its stable +2 oxidation state (Sn²⁺) to the +4 oxidation state (Sn⁴⁺) within the perovskite crystal lattice. This instability generates Sn⁴⁺ impurities and a significant concentration of tin vacancies, which serve as flaws that critically undermine the material’s electrical characteristics and long-term stability. Similarly, the suboptimal efficiency is the resulting constraint in the performance of the photovoltaic response. The elevated defect density resulting from inadequate oxidation causes substantial energy losses, mainly by diminishing the open-circuit voltage and total power output, hindering the device from attaining its theoretical efficiency potential.

To enhance the stability of perovskite layers, various heterovalent materials are incorporated through compositional and interfacial engineering in experimental studies. Notably, Bi³⁺ and Sb³⁺ have demonstrated relatively superior stability, garnering significant interest from researchers [18,19]. Furthermore, Bi³⁺ exhibits optoelectronic properties comparable to those of Pb²⁺, attributable to its strong ionic radius and electronic band structure [20,21]. Cs₃Bi₂X₉ is a prominent candidate for researchers in the field of Bi-based perovskite solar cells, attributed to its superior efficiency and enhanced stability [22].

In this study, we simulated and optimized the performance of three perovskites (Cs₃Bi₂I₉, Cs₃Bi₂Cl₉, and Cs₃Bi₂Br₉) using the SCAPS-1D (Solar Cell Capacitance Simulator -1 Dimension) simulation tool. The primary objective of this research is to compare the performance of these three perovskites through key performance analyses, including variations in the thickness of the hole-transport layer and electron-transport layer, doping concentrations of charge-transport layers, and the three absorber layers. Common charge-transport layers, including Spiro-OMeTAD and TiO₂, were employed in simulation models for three distinct inverted (P-i-N) structures. To the best of our knowledge, a comprehensive analysis and performance optimization of these three absorber layers has not been reported in simulation studies. Initially, the control devices were simulated without any parametric optimization of performance parameters, resulting in suboptimal efficiency and other performance metrics. Following the careful optimization of the thickness of the hole-transport layer and electron-transport layer, as well as the acceptor density (doping concentration of hole-transport layer, donor density of hole-transport layer and absorber layers), the performance parameters (open -circuit voltage V_OC, short-circuit current (J_SC), fill factor (FF), power conversion efficiency (PCE)) exhibited significant enhancement compared to control structures. Additionally, it was observed that the optimization of performance parameters was crucial for the improvement of optical properties, specifically quantum efficiency (%) across all optimized structures. A detailed comparison of performance parameters of perovskite devices was performed to identify optimized performance and device characterization. This comparative analysis and performance optimization of three perovskite structures (Cs₃Bi₂I₉, Cs₃Bi₂Cl₉, and Cs₃Bi₂Br₉) presents significant theoretical and practical implications for laboratory fabrication.

2. Mathematical Modelling and Device Simulation Setup

The mathematical modelling and design of our proposed perovskite solar cells were carried out using a well-established simulation software known as SCAPS-1D. This simulation software, which may create up to seven layers, was created by Gent University in Belgium [23]. This simulation tool was originally employed for the design and simulation of single junction solar cells; however, it has since been expanded to include the design of perovskite and tandem solar cells. Coupled fundamental equations are generally employed in SCAPS-1D for the simulation as well as for analysis of the proposed solar cells: (1) the Poisson equation, (2) the equation of continuity for electrons, and (3) the equation of continuity for holes. The equations are computed in SCAPS-1D to ascertain the optical (quantum efficiency) and electrical (J-V analysis) properties of perovskite solar cells [24,25,26,27,28,29]. The mathematical equations defining the coupled modelling and simulations of the proposed solar cell are presented below.

$${\displaystyle \frac{d}{dx}}\left(-\epsilon (x){\displaystyle \frac{d\psi }{dx}}\right)=q[p\left(x\right)-n\left(x\right)+{\mathrm{N}}_{\mathrm{D}}^{+}\left(\mathrm{x}\right)-{\mathrm{N}}_{\mathrm{A}}^{-}\left(\mathrm{x}\right)+{\mathrm{p}}_{\mathrm{t}}\left(\mathrm{x}\right)-n_t\left(\mathrm{x}\right)]$$

(1)

$${\displaystyle \frac{d{p}_n}{dt}}=G_P-{\displaystyle \frac{p_n-p_{n0}}{{\tau }_p}}+p_n{\mu }_p{\displaystyle \frac{d\xi }{dx}}+{\mu }_p\xi {\displaystyle \frac{d{p}_n}{dx}}+D_p{\displaystyle \frac{d^2{p}_n}{d{x}^2}}$$

(2)

$${\displaystyle \frac{d{n}_p}{dt}}=G_n-{\displaystyle \frac{n_p-n_{p0}}{{\tau }_n}}+n_p{\mu }_n{\displaystyle \frac{d\xi }{dx}}+{\mu }_n\xi {\displaystyle \frac{d{n}_p}{dx}}+D_p{\displaystyle \frac{d^2{n}_p}{d{x}^2}}$$

(3)

$$J=J_n+J_p$$

(4)

$$J_n=D_n{\displaystyle \frac{dn}{dx}}+{\mu }_n\times n{\displaystyle \frac{d\varnothing }{dx}}$$

(5)

$${ J}_p=D_p{\displaystyle \frac{dn}{dx}}+{\mu }_p\times p{\displaystyle \frac{d\varnothing }{dx}}$$

(6)

These equations illustrate the following key parametric values: $G_P$—generation rate of hole; $G_n$—generation rate of electron; τ_n—electron lifetime; τ_p—hole lifetime; D—diffusion coefficient; q—electronic charge; ψ—electrostatic potential; μ_n—electron mobility; μ_p—hole mobility; n(x)—concentration of free electrons; p(x)—concentration of free hole; n_t(x)—concentration of trapped electrons; p_t(x)—concentration of trapped holes; N_D⁺(x)—ionized acceptor concentrations; $J_n$— electron current density; $J_p$ —hole current density; and N_A⁻(x)—ionized donor concentrations, where ξ is the electric field and x is thickness. Additionally, $D_n$ and $D_p$ are the diffusion coefficients for free electrons and holes.

In our simulation, we selected the inverted structure (p-i-n) for the design of the proposed perovskite devices widely known as an inverted structure. In this arrangement, the letters signify the order of the functional layers: a p-type hole-transport layer (HTL), an intrinsic (i) perovskite absorber layer, and an n-type electron-transport layer (ETL). This configuration is different from the traditional n-i-p (or “standard”) structure. The “p” layer (e.g., NiOₓ, PEDOT:PSS, Spiro-OMeTAD, etc.) is initially deposited on the substrate to selectively extract holes, followed by the deposition of the “n” layer (e.g., TiO₂, PCBM, C₆₀, etc.) on top of the perovskite to selectively extract electrons. The designation “intrinsic” for the perovskite layer signifies that its principal role is light absorption and charge creation, rather than intentional doping for charge transfer. This p-i-n configuration is frequently used due to its low-temperature manufacturing, reduced hysteresis, and compatibility with flexible substrates and tandem cell applications. Therefore, the p-i-n structural arrangements are as follows: 1- (FTO/Spiro-OMeTAD/Cs₃Bi₂I₉/TiO₂), 2- (FTO/Spiro-OMeTAD/Cs₃Bi₂Cl₉/TiO₂), and 3- (FTO/Spiro-OMeTAD/Cs₃Bi₂Br₉/TiO₂). The work function energies (5.1 eV and 4.4 eV) for the back and FTO metal electrodes were applied to all three perovskite structures in our study.

Table 1. Essential simulation parameters for the SCAPS-1D modelling of Cs₃Bi₂X₉ (X = I, Cl, Br)-based perovskite solar cells.

Parameters	FTO Glass	TiO2	Cs3Bi2I9	Cs3Bi2Cl9	Cs3Bi2Br9	Spiro-OMeTAD
Thickness (nm)	400	50	500	500	500	500
Eg (eV)	3.5	3.260	2.030	2.55	2.2	3.170
Χ (eV)	4.0	4.1	3.55	3.6	3.6	2.1
εr	9	10	9.68	9.6	9.680	3
NC (cm−3)	1.1 × 1019	2.2 × 1018	4.98 × 1019	4.98 × 1019	4.98 × 1019	2.5 × 1018
NV (cm−3)	1.8 × 1018	1.8 × 1019	2.11 × 1019	2.11 × 1019	2.11 × 1019	1.8 × 1019
μe (cm2/Vs)	2 × 101	2 × 101	4.3	4.3	4.3	2 × 10−4
μp (cm2/Vs)	1 × 101	1 × 101	1.7	1.7	1.7	2 × 10−4
Electron thermal velocity (cm/s)	107	107	107	107	107	107
Hole thermal velocity (cm/s)	107	107	107	107	107	107
ND (cm−3)	1 × 1018	1 × 1017	1 × 1019 (variable)	1 × 1019 (variable)	1 × 1019 (variable)	-
NA (cm−3)	-	-	-	-	-	1 × 1020
Total Defect density Nt (cm−3)	1 × 1015	1 × 1015	1 × 1015	1 × 1015	1 × 1015	1 × 1015

and

Table 2. Simulation parameters for defect states at the FTO/hole-transport layer (HTL), HTL/perovskite, and perovskite/electron-transport layer (ETL) interfaces.

Parameters	FTO/Hole-Transporting Layer	Hole-Transporting Layer/Perovskite	Perovskite/Electron-Transporting Layer
Defect type	neutral	neutral	neutral
σn (cm−2)	1 × 10−19	1 × 10−19	1 × 10−19
σp (cm−2)	1 × 10−19	1 × 10−19	1 × 10−19
Energy distribution	single	single	single
Energy level with respect to Ev (eV)	0.600	0.600	0.600
Reference for defect Energy level Et	Above the highest EV	Above the highest EV	Above the highest EV
Nt (cm−2)	1 × 1015	1 × 1015	1 × 1015

present the material and interface properties for the FTO, TiO₂, Spiro-OMeTAD, and perovskite layers (Cs₃Bi₂X₉) utilized in our simulation. The values, along with the standard thickness ranges, were obtained from published literature [27,28,29,30,31,32,33,34,35,36]. The “trap density measure quantifies material imperfections that might entrap and liberate charge carriers. This process results in energy loss by recombination, substantially affecting the efficiency of the solar cell. The examination of our device was conducted under conventional testing circumstances (300 K temperature, 1000 W/m² illumination).

Figure 1a,b presents the device representation of our three inverted perovskite structures along with their proposed band gap alignment diagram. The parametric values for all perovskite, charge-transporting layers, and interfacing layers were obtained from reputable literature sources and are listed in Table 1 and Table 2 [27,28,29,30,31,32,33,34,35,36], as discussed earlier. The thermal velocities of electrons and holes were standardized at 10⁷ cm/s. The absorption coefficient values for all perovskite and charge-transporting layers utilized the default standardized built-in values from SCAPS-1D. The absorption coefficient values of SCAPS-1D were determined using a prominent mathematical equation for absorption coefficients, as presented below [37]:

$$\alpha \left(\mathsf{\lambda }\right)= \left(A+{\displaystyle \frac{B}{hv}}\right)\sqrt{hv-E_g}$$

(7)

In the equation above, A and B are arbitrary constants; h represents Planck’s constant; ν denotes the optical frequency of photons; and Eg signifies the band gap energy of perovskite materials. The thickness and doping concentrations of perovskite and other charge-transporting layer parameters were utilized in the initial stage without optimization.

3. Results and Discussion

3.1. Electrical J-V and Optical QE (%) Analysis for Perovskite Devices

The electrical and optical characteristics of the perovskite photovoltaic devices were examined via J-V and QE methodologies under standardized testing settings. The device architecture, characterized by the layer configuration of FTO Glass (400 nm)/TiO₂ (50 nm)/Perovskite (500 nm)/Spiro-OMeTAD (500 nm), was simulated utilizing the parameters specified in Table 1 and Table 2. The performance parameters obtained from device simulations are listed in

Table 3. J-V characteristic (performance parameters) for all perovskite devices.

Device	Open-Circuit Voltage (V)	Short-Circuit Current (mA.cm−2)	Fill Factor (%)	Power Conversion Efficiency (%)
Cs3Bi2I9	1.08	10.84	85.37	10.01
Cs3Bi2Cl9	1.26	4.12	83.50	4.34
Cs3Bi2Br9	1.20	7.91	79.50	7.56

, while the graphical representations of the J-V and QE analyses are shown in Figure 2. Cs₃Bi₂I₉ exhibited the highest performance parameters, achieving a power conversion efficiency of up to 10.01%, open-circuit voltage of 1.08 V, short-circuit current of 10.84 mA.cm⁻², and fill factor of 85.37%. In contrast, Cs₃Bi₂I₉-based perovskite demonstrated intermediate performance with a power conversion efficiency of up to 7.56%, open-circuit voltage of 1.20 V, short-circuit current of 7.91 mA.cm⁻², and fill factor of 79.50%. Cs₃Bi₂Cl₉ showed the lowest performance parameters, with a power conversion efficiency of up to 4.34%, open-circuit voltage of 1.26 V, short-circuit current of 4.12 mA.cm⁻², and fill factor of 83.50%. The Cs₃Bi₂Cl₉ perovskite exhibited distinct behaviour at a higher open-circuit voltage of 1.26 V compared to the other two devices, although other performance parameters were significantly degraded. The higher short-circuit current value of the Cs₃Bi₂I₉-based device is attributed to lower recombination currents in comparison to the other two perovskite devices [38]. A comparable trend was observed in the fill factor value for the Cs₃Bi₂I₉-based device, attributed to reduced series resistance and recombination rates [39]. The performance parameters of all devices were calculated without optimizing thickness, doping concentrations, and layer defects. The optimized results, along with graphical representations, are presented in the subsequent section. The analysis of optical properties indicated a similar trend across the visible light spectrum from 300 nm to 900 nm (Cs₃Bi₂I₉ > Cs₃Bi₂Br₉ > Cs₃Bi₂Cl₉). The quantum efficiency of Cs₃Bi₂I₉ indicates superior absorption capability and enhanced charge carrier generation across the light spectrum, resulting in improved performance parameters relative to other Cs-based perovskite devices [40].

The higher quantum efficiency value of the Cs₃Bi₂I₉-based perovskite device also justifies our electrical analysis results and performance parameters. The tentative comparison between all Cs-based perovskite devices can be analyzed from Table 3.

Based on our best investigation, we concluded that Cs₃Bi₂Cl₉ had the lowest QE (%) against the light spectrum between 300 and 900 nm, which resulted in poor performance characteristics and absorption. This performance degradation is attributed to inadequate surface morphology, increased surface defects, reduced carrier lifetime, and carrier diffusion issues [41].

3.2. Impact of Hole-Transport Layer Thickness Variation on Performance Parameters of Devices

The thickness of the hole-transport layer was varied from 100 nm to 600 nm to assess its effect on the performance parameters of all three perovskite devices, while maintaining constant values for other parameters in the simulation analysis. The results are shown in Figure 3. No significant changes in open-circuit voltage were observed with variations in hole-transport layer thickness across all devices, exhibiting behaviour similar to that of short-circuit, see Figure 3a,b. In the case of short-circuit current, degradation was observed with variations in the thickness of the hole-transport layer ranging from 100 nm to 600 nm. The decline in short-circuit current was linked to increased recombination currents; as the thickness of the hole-transport layer increased, the devices experienced elevated recombination rates and diminished charge carrier mobility towards the electrode [42,43,44]. In the case of fill factor (see Figure 3c), a minor degradation was observed with variations in the thickness of the hole-transport layer for all perovskite devices, attributed to increased series resistance associated with greater hole-transport layer thickness [45,46]. The PCE (See Figure 3d) of all devices decreased as a result of the decline in short-circuit current and fill factor values with increased thickness of the hole-transport layer for Cs₃Bi₂I₉ (10.41% to 9.84%), Cs₃Bi₂Br₉ (8.09% to 7.50%), and Cs₃Bi₂Cl₉ (4.93% to 4.27%), respectively. Figure 3 illustrates the graphical representations of the variation in thickness of the hole-transport layer on the performance parameters for all three perovskite devices. The optimized thickness value was determined to be 100 nm for all perovskite structures based on simulation results [47].

3.3. Impact of Thickness of Electron-Transport Layer on Performance Parameter of Cs-Based Perovskite

The thickness of the electron-transport layer significantly influences the performance parameters of a specific perovskite device. The electron-transport layer thickness of all perovskite samples ranged from 10 nm to 70 nm, and performance parameters were subsequently analyzed. It was observed that as the thickness of the electron-transport layer increased, the values of open-circuit voltage for all devices tended to degrade significantly. We attributed these open-circuit voltage losses to inadequate diffusion lengths and the limited carrier extraction capability of charge carriers at the tentative electrode [48,49,50]. Surprisingly, no significant degradation was observed in short-circuit current with respect to the variation in electron-transport layer thickness across all perovskite devices. Similar degradation was observed in terms of fill factor (%), with consistent degradation noted as the thickness of the electron-transport layer increased. The consistent degradation was attributed to increased series resistance, which further leads to elevated recombination rates in perovskite structures [51]. The power conversion efficiency of perovskite devices is primarily influenced by the open-circuit voltage, fill factor, and short-circuit current density. The ultimate power conversion efficiency decreased from 10.31% to 9.89% for Cs₃Bi₂I₉, from 7.84% to 7.55% for Cs₃Bi₂Br₉, and from 4.46% to 4.31% for Cs₃Bi₂Cl₉. Figure 4 presents graphical representations for three perovskite devices. Our simulation analysis indicates that the optimized thickness for the electron-transport layer in all devices is approximately 10 nm, which demonstrates superior performance parameters across varying thicknesses.

3.4. Impact of Acceptor Density of Hole-Transport Layer on Performance Parameters

To assess the overall impact of acceptor density in the hole-transport layer on all perovskite devices, we varied its value from 10¹⁵ cm⁻³ to 10²⁰ cm⁻³ at the logarithmic scale, while maintaining constant values for other structural parameters. Simulation results were subsequently computed. The simulation results and the effect of varying acceptor density in the hole-transport layer on performance parameters are presented in Figure 5a–d. We observed a slight increase in open-circuit voltage values, as shown in Figure 5a for Cs₃Bi₂I₉, while the open-circuit voltage values for Cs₃Bi₂Cl₉ initially increase and then become constant. In contrast, Cs₃Bi₂Br₉ exhibited a more significant increase with variations in the acceptor density of the hole-transport layer. This improvement in open-circuit voltage for Cs₃Bi₂Br₉ is attributed to the enhanced electric field at the hole-transport layer/perovskite interface, which facilitates greater charge accumulation or extraction from the absorber layer, resulting in a lower dark saturation current [52,53]. No significant changes were observed in the short-circuit current with respect to variations in acceptor density of the hole-transport layer across all devices, see Figure 5b. Our observations indicate significant improvement in the variation in acceptor density of the hole-transport layer for fill factor (%) across all devices, as shown in Figure 5c, which may contribute to the reduction of overall series resistances (layers and metal contacts) in the devices [54]. The observed enhancement was consistent across the devices, leading to tentative improvements in the power conversion efficiency values for all structures (Figure 5d): Cs₃Bi₂I₉ (8.94% to 10.14%), Cs₃Bi₂Cl₉ (3.85% to 5.04%), and Cs₃Bi₂Br₉ (6.59% to 8.74%). Our observations indicate that the optimized acceptor density for the hole-transport layer in all perovskite structures is approximately 10²⁰ cm⁻³. This value demonstrates significant improvements compared to the control doping concentration of 10¹⁸ cm⁻³. When the doping concentration in the hole-transport layer reached 10²⁰ cm⁻³, higher performance was observed. However, further increases in acceptor density may result in reduced hole mobility due to the generation of deep Coulomb trap states [55,56]. Figure 5 illustrates the impact of varying doping concentration on the performance parameters of the devices.

3.5. Impact of Donor Density Variation N_D (cm⁻³) of Electron-Transport Layer on Performance Parameters

The acceptor density of the electron-transport layer was varied from 10¹⁵ cm⁻³ to 10²⁰ cm⁻³ on a logarithmic scale to assess its impact on the performance of all three perovskite structures, as shown in Figure 6a–d. The performance parameters, excluding short-circuit current (see Figure 6b), of all devices improved with increased donor density of the electron-transport layer [57,58]. The open-circuit voltage increased for all devices as a function of electron-transport layer doping density, respectively. A similar trend was observed regarding FF improvements, attributed to increased doping concentration in the electron-transport layer, which tentatively enhanced FF values for all perovskite structures by reducing series resistance (layers and interface) in perovskite devices. Additionally, a significant electric field was established at the perovskite/electron-transport layer interface, which likely inhibited interfacial recombination and altered the movement of charge carriers towards the electrodes [59,60]. The enhancements in open-circuit voltage (see Figure 6a) and fill factor (see Figure 6c) values resulting from increased donor concentration in the electron-transport layer tentatively elevated the PCE (see Figure 6d) of all structures: from 9.95% to 12.39% for Cs₃Bi₂I₉, from 4.27% to 5.25% for Cs₃Bi₂Cl₉, and from 7.32% to 9.32% for Cs₃Bi₂Br₉. Simulation results indicated that a doping concentration of 10²⁰ cm⁻³ in the electron-transport layer was optimized, leading to improved performance parameters for all perovskite devices [61,62]. Figure 6 illustrates the relationship between the doping (donor) concentration of the electron-transport layer and the performance parameters, including open-circuit voltage, short-circuit current, fill factor, and power conversion efficiency.

3.6. Impact of Doping Concentration N_D (cm⁻³) of Absorber Layer on Performance Parameters of Devices

The doping concentration of the absorber layer is crucial for enhancing device performance. Consequently, we simulated the proposed perovskite structures while varying the doping concentration of the absorber layer from 10¹⁶ cm⁻³ to 10¹⁹ cm⁻³, and we computed the corresponding performance parameters. The results are shown in Figure 7a–d. We observed that increasing the doping concentrations of the absorber led to a degradation in the open-circuit voltage values of all devices (Figure 7a). The increased open-circuit voltage losses were attributed to a greater number of vacancy defects resulting from variations in deep doping concentration within the absorber layer of all devices [63]. Literature studies indicate that vacancy defects can alter the nature of the absorber layer from n-type to p-type as doping concentration increases, establishing a direct relationship between vacancy defects and open-circuit voltage losses [64,65]. The decline in open-circuit voltage associated with increased doping concentration in absorber layers can be explained using the following mathematical equation:

$${ V}_{oc}=n\times V_{T}ln\left(1+{\displaystyle \frac{I_G}{I_0}}\right)$$

(8)

In the equation presented above, n represents the ideality factor, V_T denotes the thermal voltage, I₀ signifies the dark saturation current, and I_G indicates the light-generated current. An increase in doping concentration results in a corresponding rise in dark saturation current, which, according to the equation, leads to a degradation of open-circuit voltage. A similar trend was observed in the short-circuit current (Figure 7b) degradation of Cs₃Bi₂I₉ with varying doping concentrations, indicating a general mechanism. However, the other two devices, Cs₃Bi₂Cl₉ and Cs₃Bi₂Br₉, exhibited atypical behaviour, as short-circuit current values improved with changes in doping concentration, representing a special case. The fill factor values of Cs₃Bi₂Cl₉ and Cs₃Bi₂Br₉ (see Figure 7c) tended to degrade with increasing doping concentration within both absorber layers due to the transformation from n-type to p-type, also referred to as vacancy defects. The overall PCE for Cs₃Bi₂Cl₉ and Cs₃Bi₂Br₉ improved, whereas Cs₃Bi₂I₉ exhibited degradation at higher doping concentrations, indicating a generalized trend. The graphical representation of these performance parameters is provided in Figure 7. Our calculations indicate a recommended doping concentration of 10¹⁹ cm⁻³ for Cs₃Bi₂Cl₉ and Cs₃Bi₂Br₉, and 10¹⁶ cm⁻³ for Cs₃Bi₂I₉.

The power conversion efficiency (see Figure 8a) of Cs₃Bi₂I₉ increased from 10.01% to 14.08% following parameter optimization, while Cs₃Bi₂Cl₉ improved from 4.34% to 5.28%, and Cs₃Bi₂Br₉ rose from 7.56% to 11.05%. The optimized performance parameters of perovskite devices, as shown in

Table 4. Optimized Performance Parameters for all the perovskite devices.

Devices	Open-Circuit Voltage (V)	Short-Circuit Current (mA.cm−2)	Fill Factor (%)	Power Conversion Efficiency (%)
Cs3Bi2I9	1.37	11.39	89.62	14.08
Cs3Bi2Cl9	1.45	4.07	88.84	5.28
Cs3Bi2Br9	1.47	8.5	88.30	11.05

, demonstrate that all devices exhibited superior performance relative to the initial unoptimized perovskite structure. Similar improvements were observed in the J-V curve and QE, indicating that the optical and electrical properties have been altered compared to unoptimized perovskite structures.

4. Conclusions

A comparative investigation of the performance of three cesium-based perovskite solar cells (Cs₃Bi₂I₉, Cs₃Bi₂Cl₉, and Cs₃Bi₂Br₉) was performed using a series of simulations. In this study, three inverted perovskite structures were proposed for simulations and performance optimization analysis: FTO/Spiro-OMeTAD/Cs₃Bi₂I₉/TiO₂, FTO/Spiro-OMeTAD/Cs₃Bi₂Cl₉/TiO₂, and FTO/Spiro-OMeTAD/Cs₃Bi₂Br₉/TiO₂. Parametric optimization for perovskite devices is essential for enhancing performance and achieving improvements. In our simulation and modelling, we varied key layer parameters, including the thickness of charge-transport layers, absorber layers, and the doping concentrations of electron-transport layers, hole-transport layers, and all three absorber layers, to enhance device performance. A significant enhancement in PCE values was observed for all three perovskite structures when compared to unoptimized configurations. The power conversion efficiencies increased from 10.01% to 14.08% for Cs₃Bi₂I₉, from 4.34% to 5.28% for Cs₃Bi₂Cl₉, and from 7.56% to 11.05% for Cs₃Bi₂Br₉. The optical properties were enhanced across the visible spectrum following the optimization of the parametric values for all devices. Cs₃Bi₂I₉ exhibited superior performance in terms of power conversion efficiency and quantum efficiency values relative to the other two Cs-based perovskite devices. The comparison of the electrical and optical performances of perovskite devices, following parametric optimization, reveals the following trend: Cs₃Bi₂I₉ > Cs₃Bi₂Br₉ > Cs₃Bi₂Cl₉. This study’s concept and simulation analysis may significantly aid in the design of environmentally friendly perovskite solar cells, in contrast to toxic Pb-based perovskite alternatives. This work represents a significant advancement in the design of environmentally friendly and cost-effective perovskite, with implications for both theoretical and laboratory research in the future.