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. 2026 Sep 23;21(1):465. doi: 10.1186/s11671-026-04914-x

Numerical simulation and performance optimization of InPbI3 perovskite solar cells

Paulinah Oyindamola Fasanmi 1,✉, Bonginkosi Vincent Kheswa 1, Hmoud Al-Dmour 2
PMCID: PMC13601422  PMID: 42776434

Abstract

In this study, InPbI3-based perovskite solar cells were numerically analyzed using the SCAPS-1D simulation tool. The device architecture, FTO/WS2/InPbI3/CuI, was modeled and systematically optimized. The investigation focused on the influence of parameters such as the thicknesses of the hole transport layer (HTL), electron transport layer (ETL), and absorber layer, as well as the acceptor dopant concentration in the perovskite, donor dopant concentration in the ETL, interface defect densities, series and shunt resistances, operating temperature, and metal work function on device performance. Following optimization, the solar cell achieved a power conversion efficiency (PCE) of 30.86%, a fill factor (FF) of 83.95%, a short-circuit current density (Jsc) of 37.94 mA/cm2, and an open-circuit voltage (Voc) of 0.9688 V. The attained PCE surpasses previously reported efficiencies for InPbI3-based perovskite devices, highlighting InPbI3 as a highly promising material for advancing high-efficiency perovskite photovoltaics.

Keywords: Perovskite solar cell, InPbI3, HLTs, SCAP-1D, Simulation

Introduction

The emission of greenhouse gases, climate disruption, environmental pollution, and global warming, among other issues, have been identified as consequences of the use of fossil fuels such as coal, gas, and oil. These fuels have been the predominant sources of power for generations. However, apart from their inability to continuously meet the growing global energy demand, they have generated numerous environmental and health problems [1, 2]. Scientists have therefore proposed alternative renewable energy sources, one of which is solar energy. Solar energy is now regarded as a highly promising substitute for fossil fuels due to its cost-effectiveness, abundance, and sustainability [3–5].

One method of harvesting solar energy is through solar cells, which convert solar radiation into electrical energy via the photovoltaic effect. Silicon solar cells are fully developed and commercialized, but they face several drawbacks, including high production costs, relatively low power conversion efficiency, and complex manufacturing processes [6–8]. Halide perovskites, with the molecular structure ABX3, where A is an organic or inorganic cation with a valency of 1, B is a metal cation with a valency of 2, and X is a halide ion such as chloride (Cl⁻), fluoride (F⁻), bromide (Br⁻), or iodide (I⁻), have emerged as promising materials for photovoltaic applications [9–16]. These materials provide a wide range of light-absorbing properties that enable the fabrication of more efficient and stable solar cells [17]. They exhibit strong light absorption and suitable energy band gaps [18, 19].

Recently, lead-based perovskites have been extensively studied because they are recognized as outstanding semiconducting materials for photovoltaic applications. Their defect tolerance contributes to high efficiency and strong photoluminescence [20, 21]. Under ambient conditions, lead halide perovskites demonstrate relatively better stability, making them excellent candidates for light-absorbing layers [22, 23].

Pinzón et al. [24] conducted a theoretical investigation of inverted p-i-n all-inorganic perovskite solar cells (PSCs) utilizing CsPbI3 and CsPbI2Br as absorber layers, employing SCAPS-1D software. The study compared the performance of various PSC architectures incorporating different inorganic materials as hole-transport layers (HTLs) and electron-transport layers (ETLs). The results indicated that CuI and ZnO were the most effective HTL and ETL materials, respectively. Device performance was further enhanced by optimizing hole mobility in CuI, as well as absorber thickness, doping density, and defect density. Under optimized conditions, maximum efficiencies of 26.5% and 20.6% were achieved for CsPbI₃- and CsPbI₂Br-based PSCs, respectively. Khatoon et al. analyzed the efficiencies of single-, double-, and triple-absorber-layer PSCs [25]. They first simulated single-junction PSCs based on CsPbI2Br and CsPbIBr2. Next, they studied bilayer PSCs with CsPbI₂Br and CsPbIBr₂ as absorbers, optimizing their performance. Finally, they simulated a triple-layer PSC using CsPbI₂Br, CsPbIBr₂, and MAPbI₃. Optimization across all devices included absorber thickness, defect density, and interface defect density. The reported efficiencies were 29.92% for the triple-layer PSC, 20.62% for the bilayer PSC, and 7% for the single-junction PSC. They concluded that well-aligned multiple absorber layers can pave the way for highly efficient PSCs.

In another study [18], the structure FTO/ITO/CH₃NH₃PbI₃/PEDOT: PSS/Au, with an initial power conversion efficiency of 13.94%, was investigated for performance enhancement. Several materials were proposed as ETLs and HTLs. Among the ETLs, ZnO and TiO₂ were the most effective, while CuSCN was identified as the most suitable HTL. By optimizing the absorber thickness to 1 μm, the efficiency improved to 25.02% [26]. Employed three distinct PSC structures: a double electron transport layer (DETL) composed of TiO₂ and ZnO, a double hole transport layer (DHTL) consisting of MoOx and Spiro-OMeTAD, and a double active layer (DAL) comprising MAPbI₃ and CsPbI₃. Simulation results demonstrated a remarkable efficiency of 20.52% for the heterojunction DAL structure, surpassing the efficiencies of 19.8% and 18.5% achieved with the DHTL and DETL configurations, respectively.

This research aims to optimize another Pb-based PSC structure, in which InPbI₃ is used as the active absorber layer [21]. Previously investigated the structural, electronic, optical, mechanical, and photovoltaic properties of InPbI₃ using a multiscale modeling approach that combined density functional theory (DFT), SCAPS-1D simulations, and machine learning techniques. DFT calculations confirmed that InPbI₃ exhibits a stable cubic perovskite structure with a direct bandgap of 1.23 eV, strong visible-light absorption, and favorable mechanical, dynamic, and thermal stability. Optical spectra revealed high absorption, suitable dielectric response, and low reflectivity, key attributes for solar harvesting. SCAPS-1D simulations of the FTO/ZnO/InPbI₃/Cu structure yielded a peak efficiency of 24.45%, with Jsc of 35.81 mA/cm², Voc of 0.843 V, and FF of 81.01%, following optimization of absorber thickness, doping level, and defect density. Sensitivity to series and shunt resistances, along with thermal stability up to 380 K, further supports the material’s practical viability.

Nevertheless, the efficiency of the InPbI₃-based PSCs remain below the Shockley-Queisser limit, indicating significant room for improvement. Given the limited research on InPbI₃-based PSCs, this study investigates in detail the design and performance optimization of an InPbI₃-based devices. We present an optimized structure of FTO/WS₂/InPbI₃/CuI. Notably, the only prior work on InPbI₃ did not include an HTL layer. Thus, our combination of HTL and ETL represents a novel approach. We examined the effects of HTL, ETL, and absorber thicknesses, acceptor dopant density of the absorber, donor dopant density of the ETL, interface defect densities, series and shunt resistances, operating temperature and back electrode work function on key performance metrics (Voc, Jsc, FF, and PCE). The selection CuI as HTL was based on its wide band gap, favorable energy alignment and good electrical properties, along with thermal and chemical durability [27, 28]. It equally demonstrates excellent hole extraction, charge mobility, electron blocking, and recombination reduction. Its tunable carrier concentration and low thermal conductivity further enhance its suitability as an HTL [29, 30]. WS₂ was selected as the ETL due to its bandgap alignment with InPbI₃. This research is expected to advance the development of InPbI₃ PSCs.

Numerical simulation

The design and optimization of the perovskite solar cell structure FTO/WS₂/InPbI₃/CuI (depicted in Fig. 1), was performed using the SCAPS-1D software. SCAPS-1D (Solar Cell Capacitance Simulator in One Dimension) is widely used for simulating thin-film solar cell structures [31, 32]. It is a well-established tool for accurate calculations and analyses of the electrical properties of solar cells, including quantum efficiency, generation and recombination rates, band alignment, and current-voltage (J-V) characteristics such as Voc, Jsc, fill factor (FF), and power conversion efficiency (PCE) [33]. The software was developed at the Department of Electronics and Information Systems (ELIS), University of Ghent, Belgium, specifically for thin-film solar cell simulations [34]. The InPbI₃-based perovskite solar cell was simulated under standard 1-sun AM 1.5G illumination conditions at 300 K with an incident power density of 1000 W/m². The SCAPS-1D simulation framework fundamentally relies on four sets of equations: the Poisson equation, the continuity equations, the charge-transport equations, and the absorption coefficient equation.

Fig. 1.

Fig. 1

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Schematic layout of the FTO/WS2/InPbI3/CuI solar cell structure

The Poisson equation (Eq. 1) describes the behavior of the electrical potential (φ) and how different types of electrical charges are distributed within the solar cell. The elementary charge constant is denoted as q, with a value of 1.602 × 10− 19 C. Meanwhile, ϵ0, ϵr, NA/ND, ρp, ρn and p(x) and n(x) represent the absolute dielectric constant, the relative dielectric constant of each layer’s material, acceptor doping density, donor doping density, hole charge density, electron charge density, hole density distribution, and electron density distribution (as functions of thickness x), respectively [31, 35].

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The continuity equation expresses the spatial derivatives of the hole current density (Jp) and the electron current density (Jn) with respect to the position variable x. It is presented in Eqs. 2 and 3, where G denotes the carrier generation rate and R represents the carrier recombination rate.

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Equations 4 and 5 represent the charge transport equations. The parameter µp denotes the mobility of holes, while µn denotes the mobility of electrons. The diffusion coefficients for electrons and holes are represented by Dn and Dp, respectively

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The absorption coefficients are calculated in the SCAPS-1D software using several available design models. The optical absorption coefficient for PSCs is expressed mathematically in Eq. 6, where h = 6.62607015 × 10− 34 JHz− 1 is Planck’s constant, A and B are material-dependent constants, Eg denotes the band gap of the absorber layer, and ν represents the incident photon frequency [31, 35].

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Results and discussion

Initial performance of unoptimized solar cell structure

The baseline parameters employed in simulating the unoptimized FTO/WS₂/InPbI₃/CuI solar cell structure are summarized in Tables 1 and 2, with all values sourced from the literature. Before optimization, the device exhibited a power conversion efficiency (PCE) of 27.58%, a fill factor (FF) of 81.63%, a short-circuit current density (Jsc) of 38.04 mA/cm², and an open-circuit voltage (Voc) of 0.8881 V. Notably, this initial PCE already surpassed the highest reported efficiency for InPbI3-based perovskite solar cells in the literature (24.45%) [21], underscoring the strong potential of our device architecture.

Table 1.

Initial values of the properties of HTL, ETL, InPbI3, and FTO

Parameters Symbols FTO WS2 InPbI3 CuI
Thickness x (µm) 0.05 0.05 1.2 0.35
Band gap Eg (eV) 3.6 1.8 1.23 3.1
Electron affinity Χ (eV) 4.5 3.95 3.714 2.1
Dielectric permittivity ℇr 10 13.6 5.05 6.5
Effective DoS at CB Nc (cm− 3) 2 × 1018 1 × 1018 7.905 × 1018 2.2 × 1019
Effective DoS at VB Nv (cm− 3) 1.8 × 1019 1 × 1018 1.423 × 1019 1.8 × 1019
e thermal velocity V th, n (cms− 1) 1 × 107 1 × 107 1 × 107 1 × 107
hole thermal velocity V th, h (cms− 1) 1 × 107 1 × 107 1 × 107 1 × 107
Electron mobility µn (cm2/V/s) 100 5 × 101 60 1 × 102
hole mobility µp (cm2/V/s) 20 5 × 101 40 4.39 × 101
Shallow uniform donor density ND (cm− 3) 1 × 1017 1 × 1018 0 0
Shallow uniform acceptor density NA(cm− 3) 0 0 1 × 1017 1 × 1018
Defect density Nt (cm− 3) 1 × 1014 1 × 1014 1 × 1014 1 × 1014
References [21] [30] [21] [36]
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Table 2.

Interface parameters [21]

Interface WS2/InPbI3 InPbI3/CuI
Total defect density 1 × 1010 1 × 1010
Capture cross-section holes σh (cm− 2) 1 × 10− 19 1 × 10− 19
Capture cross-section electrons σe (cm− 2) 1 × 10− 19 1 × 10− 19
Energy with respect to reference Er (eV) 0.6 0.6
Working temperature (K) 300 300
Reference for defect energy level Above VB maximum Above VB maximum
Type of defect Neutral Neutral
Energetic distribution Single Single
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Device optimization

Optimization of the hole transport layer thickness

In this work, the thickness of the hole transport layer (HTL, CuI) was systematically optimized by varying it between 0.04 μm and 2 μm, while maintaining constant thicknesses for the absorber layer (InPbI3) and the electron transport layer (WS2). The outcome of this optimization is presented in Fig. 2, which illustrates the influence of CuI thickness on Voc, Jsc, fill factor (FF), and power conversion efficiency (PCE). The analysis revealed that all four parameters remained essentially unchanged across the range of CuI thicknesses investigated. These findings are consistent with the report of Utsho et al. [37], with the maximum PCE obtained at a CuI thickness of 0.04 μm. Evidently, the HTL thickness exerts negligible influence on device performance. This behavior can be attributed to the fact that the perovskite absorber and the ETL are primarily responsible for photon absorption, with the majority of photogenerated carriers formed before light reaches the HTL. Consequently, variations in HTL thickness do not influence carrier generation. CuI possesses high hole mobility and conductivity, enabling efficient hole extraction even at very thin layers (≈ 0.04 μm). Increasing its thickness beyond this value does not enhance charge transport, as the conductivity is already sufficient. Moreover, the band alignment between CuI and the absorber remains favorable across different thicknesses, ensuring effective hole transfer without introducing energy barriers or recombination centers. Unlike absorber layers, HTLs are not intended to absorb photons. Their role is strictly electrical, facilitating charge extraction, and thus their optical properties remain unaffected by changes in thickness [38–40].

Fig. 2.

Fig. 2

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Variation of HTL thickness (µm)

Optimization of the perovskite (absorption) layer thickness

The thickness of the active absorption layer greatly influences the efficiency of perovskite solar cells (PSCs). Carrier recombination before arrival at the electrode can result from an excessively thick absorption layer. In contrast, an extremely thin absorption layer can reduce photon absorption [41]. It therefore becomes imperative to optimize the thickness of the perovskite layer. To optimize the perovskite layer, the thicknesses of the HTL was maintained at its optimal value, while WS2 (ETL) thickness was kept at its initial value. The thickness of the InPbI3 absorption layer was varied from 0.06 μm to 3 μm for the structure FTO/WS2/InPbI3/CuI to investigate its impact on the efficiency and output of the solar cell. Figure 3 illustrates how the variation in the InPbI3 layer affects PCE, FF, Jsc, and Voc. It is observed that, for all structures, the PCE increased as the thickness of the InPbI3 layer approached 1.32 μm after which it began to decrease. An exceedingly thick absorption layer can lead to increased carrier recombination before they reach the electrode. In contrast, a reduction in photon absorption can result from an extremely thin absorption layer.

Fig. 3.

Fig. 3

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Variation of perovskite (InPbI3) layer thickness

FF and Voc for all structures decrease consistently as the thickness of the InPbI3 layer increases. While the FF is likely to have decreased due to internal power dissipation and increased series resistance, the Voc may have decreased due to increased recombination at higher absorption layer thickness [30]. The Jsc increased rapidly as the InPbI3 layer increased from 0.06 μm to 1.32 μm beyond which it remained fairly constant. The result of optimization of the absorber layer thickness is in consonance with the observation of [4, 17].

Quantitatively, the maximum PCE obtained for the solar cell structure was 27.58% which was the same result obtained for the initial performance of the unoptimized structure. The optimum InPbI3 layer thickness for our structure is 1.32 μm.

Optimization of the perovskite layer acceptor dopant density

The acceptor dopant density (ADD) is an essential parameter in the perovskite solar cell because the introduction of acceptor atoms into the perovskite layer significantly enhances the carrier transport characteristics of the device, therefore improving the overall efficiency of the solar cell [41]. The ADD of the structure FTO/WS2/InPbI3/CuI with was optimized by varying it from 1017 cm− 3 to 1020 cm− 3. The other parameters were kept either at their optimal values or initial values. The effects of the optimization on the PCE, FF, Jsc, and Voc are depicted in Fig. 4. We observed Voc and PCE increased consistently as the ADD increased from 1017 cm− 3 to 1020 cm− 3, Jsc remained fairly constant while FF increased as ADD approached 7.14 × 1016 beyond which it remained constant. The highest PCE obtained after the optimization of the perovskite layer ADD was 29.66%. The PCE value was obtained at optimum InPbI3 layer ADD of 1 × 1018 cm− 3. Optimization of the perovskite layer acceptor dopant density significantly improved the solar cell output. This is because introducing acceptor atoms into the absorber layer improves the carrier transport capability of the device by altering the band structure, resulting in an improved device performance [41]. The result of this optimization is similar to the reports of [41, 42].

Fig. 4.

Fig. 4

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Variation of perovskite layer acceptor dopant density

Optimization of the thickness of the ETL layer

The responsibility of the electron transport layer (ETL) is to extract and transport electrons from the absorber layer, which is a perovskite layer, to the cathode. The ETL usually has a significant effect on the efficacy of the perovskite solar cell [16]. In this study, the optimization of the ETL layer (WS2) was achieved by varying the thickness of the layer in our structure from 0.04 μm to 2 μm. The thickness of the HTL and absorber layer, as well as the value of the InPbI3 ADD, were all kept at the optimal values determined in the previous sections. The effect of the optimization of the thickness of the WS2 layer on the Voc, Jsc, FF, and PCE is shown in Fig. 5.

Fig. 5.

Fig. 5

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Variation of ETL thickness

It is observed that the Voc and Jsc somewhat decreased as the thickness of the ETL layer increased, while FF increased consistently as the ETL layer thickened [43]. Got similar results for Voc, Jsc in his findings. On the other hand, PCE increased as the thickness of the WS2 layer approached 1.3 μm then it decreased with further increase in thickness of the layer. A similar trend was reported in literature [44]. The decrease in the Jsc and the Voc with increasing ETL thickness could be because ETL partially absorbs light as the layer thickens [30, 40]. After optimizing the thickness of the ETL layer, a PCE of 30.81% was obtained for our solar cell structure FTO/WS2/InPbI3/CuI. at ETL thickness of 1.3 μm.

Optimization of the ETL donor dopant density

Figure 6 illustrates the effect of the optimization of the donor dopant density (DDD) of the ETL layer on the performance of our solar cell. To obtain better perovskite solar cell efficacy, the ETL DDD was varied from 1 × 1017 to 1 × 1020 cm− 3, while maintaining other parameters at their optimal or initial values. It was observed that FF and PCE increased sharply as the DDD increased to 7.14 × 1018 cm− 3. Further increments had little effect on the two parameters. Voc decreased, while Jsc increased as the donor dopant density of the ETL increased from 1 × 1017 to 1 × 1020 cm− 3. According to [45], who gave a similar report, the behavior of these key performance metrics can be ascribed to an increase in electron conductivity at elevated donor dopant density levels, which results in a reduction in resistance to electron flow from the absorber layer. The optimal donor dopant density of WS2 was pinned at 7.24 × 1018 cm− 3. At this value, the PCE of the solar cell increased to 31.20% for the solar cell configuration FTO/WS2/InPbI3/CuI.

Fig. 6.

Fig. 6

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Variation of ETL donor dopant density

Combined effect of interfacial total defect density on solar cell performance

The interfacial defect density quantifies the concentration of structural imperfections located at the junctions between adjacent layers. In this context, the parameter is specifically evaluated at the interface between the electron transport layer and the active layer (WS2/InPbI3) and the interface between the active layer and the hole transport layer (InPbI3/CuI). The interfacial total defect density serves as a critical indicator of recombination and interfacial losses, functioning as trap states that capture charge carriers within the solar cell [46, 47]. In order to study the effect of the interfacial defect densities of the layers on the solar cell performance, the densities for the two interfaces were varied from 1010 to 1018 cm− 3. The result obtained is illustrated in Fig. 7. At interfacial densities of 1010 for both interfaces, the performance matrices namely, PCE, FF, Voc and Jsc attained maximum but as the densities increased, the values of the four parameters clearly decreased. Hence the interfacial total densities for the two interfaces were maintained as 1010 cm− 3 with PCE remaining as 31.20%.

Fig. 7.

Fig. 7

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Effect of interfacial total defect density

Combined effect of series and shunt resistances on solar cell performance

The series resistance (Rs) has a great influence on the efficacy of the perovskite solar cell. It arises from various contact points in the solar cell, including different interfaces and front and back contacts. At zero series resistance, the device would perform most efficiently. It is however, impossible to achieve a zero Rs in a real scenario but since device performance decreases as Rs increases, it is important to keep the Rs at the barest minimum [30, 48]. The shunt resistance (Rsh) on the other hand is a very important indicator of recombination incidences and the occurrence of pinholes [41]. Defects in materials and contact interfaces that are not uniform may result in unintended current paths that are not in contact with the active region of a perovskite solar cell. The shunt resistance pertains to these unintended current paths. Increased shunt resistance helps to diminish current leakages through these paths, thereby improving the overall performance of the solar cell [30, 49]. To investigate the effect of Rs and Rsh on the efficiency of our PSC solar cell configuration, they were varied from 1 to 5 Ω cm2 and 1 × 102 to 1 × 109 Ω cm2 respectively. The thicknesses of the HTL, ETL, and InPbI3 layers, the ETL donor dopant density, the InPbI3 acceptor dopant density and the interfacial total defect densities were all kept at their optimal values discussed in the previous sections. Figure 8 shows the combined impact of Rs and Rsh on Voc, Jsc, FF, and PCE of our solar cell configuration. It is observed that the PCE and FF of the solar cell is maximum when the Rs is kept low and Rsh is high. These conditions reduces resistive losses and leakage currents. In essence, increasing the Rs leads to reductions in both PCE and FF due to enhanced voltage drops and inefficient charge transport. In the same vein, a decrease in Rsh results in significant decrease in PCE, Voc and FF, due to elevated recombination and leakage pathways. Jsc is particularly sensitive to Rs, declining as resistance rises, while device stability improves with higher Rsh. Voc is strongly dependent on Rsh and remains relatively unaffected by Rs. However as Rsh decrease below 1011, there is a sharp decline in Voc. Thus, optimal device performance is achieved by minimizing Rs and maximizing Rsh, underscoring the importance of reducing resistive losses and suppressing leakage channels.

Fig. 8.

Fig. 8

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Variation of series and shunt resistances

An increase in series resistance (Rs) causes notable reductions in fill factor (FF), power conversion efficiency (PCE), and short-circuit current density (Jsc) because charge collection is impeded and the effective voltage is diminished. While Rs cannot be completely eliminated, it must be constrained to the lowest possible value to limit performance degradation. In contrast, higher shunt resistance (Rsh) has a beneficial impact by suppressing leakage currents. This improvement in Rsh enhances the open-circuit voltage (Voc), FF, and overall PCE, thereby strengthening device efficiency. For our device, Rs and Rsh were kept at 1 and 1012 Ω cm2 yielding a PCE of 29.86%.

Effect of temperature on device performance

The impact of temperature on the performance of a solar cell cannot be overemphasized. The temperature at which solar devices operate is dependent on the geographical locations, among other factors. It is imperative, therefore, to investigate the temperature at which a solar cell performs optimally. To investigate the effect of operating temperature on our device, the temperature was varied between 280 K and 400 K, while keeping other parameters at their optimal values. Figure 9 shows the variation of Voc, Jsc, FF, and PCE with increasing temperature. While the Jsc increased slightly and slowly as temperature increased, Voc, FF, and PCE decreased consistently with increasing temperature. This trend is consistent with the literature [39], and it supports previous research ascribing loss of efficiency to mechanisms that are thermally activated, such as defect rise within material and a reduction in diffusion length of charge carriers, which increase the losses due to resistance and recombination [29].

Fig. 9.

Fig. 9

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Variation of operating temperature

The optimum temperature of our device FTO/WS2/InPbI3/CuI, is taken as 280 K. At this temperature, the PCE of the solar cell increased to 30.86%, the highest PCE obtained for our structure. While solar cells can realistically operate at temperatures between 300 and 400 K, simulations at 280 K reflect their ideal performance, characterized by a wider bandgap, lower recombination losses, and higher open-circuit voltage. This condition effectively represents the theoretical maximum efficiency.

Effect of back electrode work function

The effect of the back-contact metal work function on the current-voltage (IV) characteristics of the FTO/WS2/InPbI3/CuI solar cell was systematically investigated by varying the electrode work function between 4.8 eV and 5.9 eV. The corresponding influence on the device parameters open-circuit voltage (Voc), short-circuit current density (Jsc), fill factor (FF), and power conversion efficiency (PCE) is presented in Fig. 10. The variation in work function exhibited negligible impact on Voc and Jsc, whereas FF and PCE showed a modest increase as the work function rose from 4.8 to 4.88 eV, beyond which both parameters stabilized. The maximum PCE attained under this variation was 30.86%, consistent with the highest efficiency observed in the operating-temperature study. This outcome indicates that metals with work functions exceeding 4.88 eV, such as Au, W, Ni, Pt, and Se, are suitable candidates for the back electrode in the simulated device. Among these, Au provides the most favorable compromise between performance and scalability, rendering it particularly advantageous for large-scale implementation and making it a suitable choice as back contact electrode for our proposed structure. When the back-contact work function surpasses approximately 5.0 eV, the interface approaches Ohmic behavior, thereby reducing the hole-extraction barrier and mitigating interfacial recombination. Consequently, the fill factor improves significantly, accompanied by an enhancement in PCE. In contrast, the open-circuit voltage remains largely unaffected, as it is predominantly governed by the absorber bandgap and bulk recombination processes [50, 51].

Fig. 10.

Fig. 10

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Effect of metal work function on device performance

Optimized J–V characteristics and quantum efficiency

The optimized J–V profile alongside the quantum efficiency (QE) spectrum of our simulated solar cell device FTO/WS₂/InPbI₃/CuI, is presented in Figs. 11 and 12 respectively. The J–V curve illustrates the correlation between the applied voltage and the resulting current density, whereas the QE spectrum quantifies the effectiveness with which incident photons absorbed in the active layer are converted into photocurrent [47]. Elevated quantum efficiency was observed within the spectral range of 350 to 900 nm. ranging from 95% to 100% of QE with respect to wavelength, underscoring its superior photon-to-current conversion capability. The parameters indicating the performance of the InPbI3-based perovskite solar cell are power conversion efficiency of 30.86%, fill factor of 83.95%, open-circuit voltage of 0.9688 V and short-circuit current density of 37.94 mA/cm².

Fig. 11.

Fig. 11

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J–V curve for FTO/WS2/InPbI3/CuI solar cell structures

Fig. 12.

Fig. 12

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Curve of quantum efficiency versus wavelength

Generation and recombination profile study

A generation-recombination study is essential in order to evaluate charge carrier generation and electron-hole pair recombination. The number of electron produced and the point of production is determined through the generation profile. Electron-hole recombination resulting from structural defects can be assessed through the recombination profile [47]. Larger thicknesses of active layers result in higher charge carrier formation because of the highest amount of light absorption [52]. The generation and recombination rate of our device is illustrated in Fig. 13. It is observed that electron generation rate as high as about 5.5 × 1021 occurred at approximately 1.1 μm, while a higher rate 6.2 × 1021 occurred at approximately 2.6 μm. Correspondingly, the peak recombination (4.3 × 1021) was observed at 2.6 μm, consistent with the generation profile.

Fig. 13.

Fig. 13

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Generation and recombination profile

Energy band alignment study

The energy band diagram illustrates the spatial organization of energy levels across the layered architecture of the solar cell. Seamless interfacial transitions between layers are critical in minimizing energy losses, ultimately enhancing overall device performance and power conversion efficiency. Consequently, band alignment emerges as a decisive factor in determining photovoltaic behavior. The orientation and continuity of energy bands exert a profound influence on the efficiency of perovskite solar cells and must be rigorously examined during the optimization process [52, 53]. Energy band diagrams of our solar cell are illustrated in Figs 14 and 15. CuI with a direct band gap of 3.1 eV is a wide-band semi-conductor serving as the hole transport layer. It facilitates hole extraction to the back contact but Inhibits electrons. InPbI3 with a band gap of about 1.23 eV, serves as the absorber layer and is suitable for visible light absorption and charge carrier generation. Similarly, WS2 a transition metal dichalcogenide serve as the electron transport layer with an ideal bad gap of 1.8 eV. It allows electron transport from the absorber to the window layer (FTO), but keeps holes out. The FTO (Fluorine doped SnO2) with wide band gap oF 3.5 eV Served as the window layer. It is suitable for minimal absorption in the visible range. As a result of excellently aligned energy band, electrons are able to migrate easily to the WS2 layer and the to the FTO, while the holes move towards the CuI layer and exit via the back electrode.

Fig. 14.

Fig. 14

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Simulated energy band diagram

Fig. 15.

Fig. 15

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Energy band diagram

Optimized performance of solar cell structure

Following systematic optimization of the proposed perovskite solar cell architecture, the device achieved a power conversion efficiency (PCE) of 30.86%, a fill factor (FF) of 83.95%, an open-circuit voltage (Voc) of 0.9688 V, and a short-circuit current density (Jsc) of 37.94 mA/cm2. The optimized parameters are summarized in Table 3. The optimal thicknesses of the CuI, WS2, and InPbI3 layers were determined to be 0.04 μm, 1.32 μm, and 1.30 μm, respectively. The perovskite absorber exhibited an optimal acceptor dopant density (ADD) of 1 × 1018 cm− 3, while the electron transport layer (ETL) demonstrated an optimal donor dopant density (DDD) of 7.24 × 1018 cm− 3. Furthermore, the interfacial total defect density was minimized to 1 × 1010 cm− 2. The series resistance (Rs) and shunt resistance (Rsh) were optimized to 1 Ω·cm2 and 7.14 × 1010 Ω·cm2, respectively. The optimal operating temperature was identified as 280 K, with gold (Au) functioning as the effective back electrode. Among the investigated parameters, the acceptor dopant density of the absorber, ETL thickness, donor dopant density of the ETL, and operating temperature were found to exert the most significant influence on device performance.

Table 3.

Optimized parameters of HTL, ETL and InPbI3

Parameters WS2 InPbI3 CuI
Thickness (µm) 1.3 1.32 0.04
ND (cm− 3) 7.24 × 1018 0 0
NA(cm− 3) 0 1 × 1018 -
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Comparison of the study with Pb-based previous studies

In this section, the performance metrics of our device, FTO/WS2/InPbI3/CuI/Au, is compared with the only recent literature on InPbI3 and other Pb-based perovskite solar cells, since there is limited work done on InPbI3 using SCAP ID. As depicted in Table 4, it is observed that we obtained a higher PCE with our proposed device compared to preceeding studies.

Table 4.

Comparison of this study with previous Pb-based study

Solar cell structures Voc (V) Jsc (A/cm2) FF (%) PCE (%) References
FTO/WS2/InPbI3/CuI/Au 0.9688 37.94 83.95 30.86 This study
FTO/ZnO/InPbI3/Cu 0.843 35.81 81.01 24.45 [21]
FTO/ZnO/CS0.07/FA0.05/MA0.08/Pb(IBr)3/Spiro-OMeTAD/Pd 1.39 25.37 84.74 29.84 [54]
FTO/SnO2/MAPbI3/NiOx/Au 0.9995 22.98 74.57 17.49 [55]
FTO/TiO2/CsPbCl3/MoO3/Au 1.30 23.02 87.72 26.29 [56]
FTO/STO/FAPbI3/Spiro-OMeTAD/Au 0.98 28.34 30.91 22.58 [14]
ITO/WS2/MAPbI3/CuInSe2/Au 0.88 26.91 80.85 19.33 [57]
FTO/SnO2/CsPbCl3/Cu2O: Zn(7%)/Au 1.567 17.48 88.45 24.23 [58]
FTO/MAPbI3/CuI/Back contact 1.0654 24.66 59.15 15.54 [59]
ITO/SnO2/Rb0.02(FA0.95Cs0.05)0.98PbI2.91Br0.03Cl0.03/Spiro-OMeTAD/Ag 1.12 23.65 79.8 22.42 [60]
FTO/SnO2/MAPbI3/CuSCN/Back Contact 1.0084 30.086 72.39 21.96 [61]
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Conclusion

In this study, InPbI3-based perovskite solar cells were investigated numerically using SCAP-1D simulation software. Optimization was carried out for the solar cell structure FTO/WS2/InPbI3/CuI, by investigating the effects of varying the thicknesses of the HTL, ETL, and absorber layer, acceptor dopant density of the absorber layer, donor dopant density of ETL, interfacial total defect densities, series and shunt resistances, operating temperature and back contact work function On the performance of the solar cell. The optimization yielded power conversion efficiency (PCE) of 30.86%, a fill factor (FF) of 83.95%, an open-circuit voltage (Voc) of 0.9688 V, and a short-circuit current density (Jsc) of 37.94 mA/cm2. The PCE obtained exceeds the previously reported PCE for InPbI3-based perovskite solar cell. This study serves as a baseline for studies involving InPbI3, seeing that very little has been done on the improvement of its performance as a perovskite layer in solar cells. Although we have worked to make our simulation as realistic as possible, certain limitations might remain, signifying that predictive accuracy may differ from actual fabrication.

Acknowledgements

Authors would like to acknowledge Prof Burgelman of the University of Gent, Belgium for the SCAP-1D software used in this work.

Nomenclature

WS2

Tungsten disulfide

InPbI3

Indium Lead Iodide

CuI

Copper (I) Iodide

Author contributions

P.O. Fasanmi carried out the simulations, data analysis, and wrote the original draft; B.V. Kheswa and H. Al-Dmour reviewed and edited the original draft. All authors read and approved the final manuscript.

Funding

The authors declare that there was no funding involved in this work.

Data availability

The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.

Declarations

Consent for publication

Not applicable (as the results of studies does not involve any human or animal).

Ethics approval

Not applicable (as the results of studies do not involve any human or animal).

Consent to participate

Not applicable (as the results of studies do not involve any human or animal).

Competing interests

The authors declare no competing interests.

Footnotes

Publisher’s note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

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Associated Data

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Data Availability Statement

The datasets generated during and/or analysed during the current study are available from the corresponding author on reasonable request.

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