A perovskite solar cell is composed of a stack of thin films, with a typical thickness ranging from a few hundred nanometers to a few micrometers, deposited on a substrate, as schematically illustrated in Figure 1. Its operating principle is based on the absorption of incident light radiation by the perovskite active layer, which generates free charge carriers in the form of electron-hole pairs, which are subsequently extracted by selective contacts. The perovskite layer, located at the core of the device architecture, constitutes the main photoactive element [14]. When incident sunlight in the visible range reaches this layer, electrons are excited from the valence band to the conduction band, generating holes simultaneously. The exciton binding energy in perovskite materials is on the order of a few tens of meV at room temperature [15]. The photogenerated electrons and holes are selectively transported by a hole transport layer (HTL) and an electron transport layer (ETL), positioned on either side of the perovskite layer [16]. These charge carriers diffuse towards the contact electrodes of the photovoltaic device, namely the transparent conducting electrode and the counter-electrode, where they are extracted, enabling the conversion of light energy into electrical energy [17].

(a) (b)

Figure 1. (a) Image of a perovskite solar cell [13]; (b) Structure of a perovskite based solar cell.

The simulation tools developed by research communities are currently available under both free and commercial licenses. Among the most widely used freely accessible simulation platforms are AFORS-HET (Automat FOR Simulation of HET erojunctions), ASA (Amorphous Semiconductor Analysis), AMPS-1D (Analysis of Microelectronic and Photonic Structures), and SCAPS-1D (Solar Cell Capacitance Simulator) [18].

SCAPS-1D is a one-dimensional numerical simulation code operating in a Windows environment, developed by the team of Marc Burgelman within the Department of Electronics and Information Systems (ELIS) at Ghent University, Belgium. Its development was initially based on modeling work dedicated to CdTe and Cu (In, Ga) Se₂ solar cells [17][18]. SCAPS-1D is used to simulate thin-film perovskite solar cells as it solves the fundamental charge transport equations and analyzes the influence of material physical parameters on photovoltaic performance. It thus constitutes an effective tool for modeling interfaces, defects, and recombination mechanisms for optimizing the structure and efficiency of photovoltaic devices.

Numerous studies have shown that the results provided by SCAPS-1D exhibit excellent agreement with experimental data [19]-[21], as well as with those obtained from the AMPS-1D software.

SCAPS-1D enables a detailed analysis of the main electrical and optoelectronic characteristics of photovoltaic devices, including J-V, C-V, and C-f characteristics, and external quantum efficiency (EQE), under both illuminated and dark conditions [22]. The model explicitly incorporates defect related mechanisms responsible for charge carrier recombination. In this context, the charge carrier recombination rate, denoted as R, is given by Equation (1) [23]:

Given that n is the free carrier density, p is the hole concentration, n j e is the intrinsic carrier density, and τ n is the electron lifetime, the generation of charge carriers resulting from the optical excitation of the material is described quantitatively by Equation (2) [23]:

where Φ is the photon flux density per unit area and time, α x is the absorption coefficient, Φ ( z 0 ) is the flux density at an initial depth z 0 , and z represents the penetration depth of the flux.

For reproducibility, the following additional SCAPS-1D parameters were used; front contact work function (ITO) = 4.7 eV, back contact work function (Au) = 5.1 eV (typical for high work function metals); interface defect density at both ETL/perovskite and perovskite/HTL interfaces 1 × 10¹⁰ cm⁻² (neutral, single energy level at mid gap, capture cross sections 1 × 10⁻¹⁹ cm⁻² for electrons and holes, based on common practice in perovskite SCAPS modeling) [24]; absorber bulk defect model (single neutral acceptor) like defect at mi gap with total density N_t = 1 × 10¹³ cm⁻³ as given in Table 1 (capture cross sections 1 × 10¹⁵ cm⁻² for both carriers); temperature = 300 K (standard room temperature). The absorption coefficient of CH₃NH₃PbI_3-xCl_x was modeled using the built-in optical model of SCAPS-1D with a constant absorption coefficient of 1 × 10⁵ cm⁻¹ above bandgap, consistent with literature values for this material.

SCAPS-1D simulation software (version 3.2.0.9) was employed for the numerical modeling of the device. The considered perovskite solar cell architecture adopts the following multilayer configuration: TCO/ETL/Perovskite/HTL. The conclusions drawn from this study are specifically valid for the architecture ITO/Y-TiO₂/CH₃NH₃PbI_3-xCl_x/Spiro-OMeTAD and may not be directly transferable to other perovskite compositions (e.g., mixed cations or lead-free perovskites) or alternative charge transport layers (e.g., inorganic HTLs like NiO_x or different ETLs like SnO₂). Table 1 summarises all the input parameters associated with the different layers of the cell, namely the transparent conductive oxide layer, the electron transport layer, the absorber layer, and the hole transport layer, composed of ITO, Y-TiO₂, CH₃PbI_3-xCl_x, and Spiro-OMeTAD, respectively.

Table 1. Electrical parameters [13][21][25]-[27].

SCAPS-1D is employed for the modeling and analysis of thin-film solar cells, primarily developed for research applications, incorporating various buffer layer architectures. The simulation environment provided by SCAPS-1D provides access to detailed results, including current-voltage characteristics under both dark and illuminated conditions, as well as their evolution as a function of temperature. Furthermore, the software facilitates the extraction of the internal electric field, spatial profiles of free and trapped carrier concentrations, recombination mechanisms, and the associated electron and hole current densities as a function of position within the device [22]. The determination of the electrical parameters of the cell using SCAPS-1D is based on the coupled numerical solution of three fundamental equations governing charge transport in semiconductors: Poisson’s Equation (3) and the continuity Equations for electrons (4) and holes (5) [28].

where ε 0 and ε r are the dielectric constants of vacuum and the relative dielectric constant, respectively; n and p are the free carrier concentrations (electrons and holes), respectively; N D + and N A − denote the ionized donor and acceptor concentrations, respectively; ρ p and ρ n represent the charge densities of holes and electrons, respectively; J n and J p are the electron and hole current densities, respectively; R n and R p are the electron and hole recombination rates, respectively; and G n and G p are the electron and hole generation rates, respectively

The validation of our model using SCAPS-1D is based on several essential aspects to ensure that the simulation accurately reflects physical and experimental reality. The J-V curves under AM1.5G illumination enable the evaluation of the electrical performance of a solar cell by measuring several key parameters. The short-circuit current density ( J S C ) represents the maximum current generated at zero voltage, while the open-circuit voltage ( V O C ) corresponds to the maximum voltage under no current flow. The fill factor (FF) quantifies the quality of the J-V curve, and the power conversion efficiency (PCE) indicates the overall performance of the cell. Furthermore, all simulations are performed under AM 1.5 illumination, with an incident power of 1000 W/m². Table 2 presents the values of the electrical parameters. The baseline device (without intentional variations of thickness, doping, or mobility) was reproduced directly using the material parameters reported by [13] as listed in Table 1, without any additional calibration or fitting. The excellent agreement between our simulated J-V curve and the experimental reference from [13] (Figure 2) confirms that the input parameter set accurately captures the reference device behavior.

Table 2. Values of the electrical parameters.

The electrical parameters of our model show excellent agreement with those reported by Zhou and colleagues (Table 2) [13]. Furthermore, the current density-voltage characteristics curves are in good accordance (Figure 2).

The hole mobility of the absorber layer in a perovskite solar cell governs the transport and collection efficiency of photogenerated charge carriers, thereby directly influencing the current density, fill factor, and overall device performance. Investigating its variation as function of doping enables the identification of the optimal doping level that enhances charge separation and the internal electric field while limiting recombination and carrier diffusion. The coupling between hole mobility ( μ p ) and the acceptor doping concentration ( N A ) of the absorber layer governs the stable operating regime of the solar cell. Low doping level result in an insufficient internal field, making the device performance highly sensitive to transport limitations and recombinations [12]. Conversely, high doping reduces the influence of μ p but accentuates intrinsic recombinations, thereby capping performance. An intermediate doping level ensures an optimal trade-off between carrier transport and the internal electric field, characterized by a low sensitivity of the electrical parameters. We varied the hole mobility between 2 × 10⁻⁴ cm²/V∙s and 10⁻² cm²/V∙s, and the doping concentration between 3 × 10¹⁷ cm⁻³ and 3 × 10¹⁸ cm⁻³. Figure 3 highlights the combined influence of the absorber layer doping and hole mobility on the electrical performance and overall electrical stability of the device. Overall, the device performance is primarily governed by these factors. The results show that the open-circuit voltage ( V O C ) is strongly influenced by doping: it increases almost continuously from 0.90 V to 1.08 V as the doping concentration rises from 3 × 3 × 10¹⁷ cm⁻³ to 3 × 10¹⁸ cm⁻³. In contrast, hole mobility has a negligible effect, with variations limited to a few millivolts, underscoring the dominant role of the internal field and recombinations [12]. Conversely, the fill factor is largely governed by mobility and device architecture; it increases from 75% - 77% at low doping to 86% - 87% at high doping, reflecting a reduction in resistive losses [29]. The short-circuit current density systematically decreases with increasing doping due to enhanced recombination [30]. The efficiency, therefore, results from a trade-off between the increase in open-circuit voltage and fill factor and the decrease in short-circuit current density, reaching a plateau of 16.4% with an optimized HTL [31]. Optimal stability is achieved for intermediate to high doping concentrations (1 × 10¹⁸ cm⁻³ to 3 × 10¹⁸ cm⁻³) with hole mobility being the key parameter for operational robustness [12].

Figure 3. Influence of hole mobility as a function of absorber layer doping on cell stability.

The hole mobility ( μ p ) and the thickness of the perovskite absorber layer are two critical parameters for optimizing the performance of perovskite solar cells. Hole mobility determines the efficiency of photogenerated charge transport and extraction, while the thickness of the absorber layer directly controls light absorption and carrier generation. Figure 4 illustrates the combined influence of hole mobility ( μ p ) and active layer thickness on the electrical parameters of the perovskite solar cell (PSC). Overall, it is observed that all electrical parameters of the perovskite solar cell (PSC) depend strongly on thickness, but very little on hole mobility ( μ p ) within the studied range. The results show that performance is primarily governedby thickness, whereas ( μ p ) exerts a negligible influence over the investigated range of 10⁻³ cm²/V∙s to 10⁻² cm²/V∙s 1. The open-circuit voltage ( V O C ) increases slightly with thickness due to improved absorption and a relative reduction in recombinations (Figure 4(a)). The short-circuit current density ( J S C ) (Figure 4(b)) and the fill factor (FF) (Figure 4(c)) reach their maximum values for an optimal thickness between 0.06 and 0.07 µm, reflecting a trade-off between photon absorption and bulk recombination within the absorber. Concerning the power conversion efficiency ( η ) (Figure 4(d)), it exhibits a maximum of approximately 15% within this same thickness range. Based on our analysis in this section, we can conclude that the performance of the perovskite solar cell (PSC) is primarily controlled by the absorber thickness, and hole mobility ( μ p ) has very little influence on the performance of the perovskite solar cell (PSC) over the studied interval. Optimal performance is achieved for a thickness of approximately 0.06 to 0.07 µm. Beyond this value, recombination phenomena limit performance. These results indicate that optimization of the active layer constitutes the key determining parameter for improving the overall device efficiency.

Figure 4. Influence of hole mobility as a function of absorber layer thickness on cell stability.

Figure 5 illustrates the impact of absorber doping concentration (CH₃PbI_3-xCl_x) on the performance of perovskite solar cells with and without a hole transport layer (HTL). Overall, a decrease in the performance of the perovskite solar cell is observed in the absence of the hole transport layer. The electrical parameters of both device configurations exhibit a similar trend. Increasing the doping concentration generally enhances the overall efficiency through an increase in open-circuit voltage and fill factor, despite a gradual decrease in short-circuit current density due to enhanced recombination [27][28]. The efficiency increases at low to moderate doping levels and then stabilizes, with devices incorporating an HTL maintaining superior performance owing to more selective charge extraction [30][31]. The open-circuit voltage increases and subsequently saturates, dominated by recombination processes within the absorber layer [31], while the short-circuit current density decreases as a result of Shockley-Read-Hall (SRH) recombination. The fill factor improves with increasing doping concentration, with the HTL ensuring a selective back contact and superior overall device performance.

Figure 5. Influence of doping variation on electrical parameters.

In this section, we analyze the performance of the perovskite solar cell with and without the hole transport layer while varying the absorber thickness from 100 nm to 2000 nm. The comparison between architectures with and without a hole transport layer (HTL) highlights the central role of the absorber in determining photovoltaic performance. The efficiency (Figure 6(a)) increases rapidly with absorber thickness in both cases, but only the architecture incorporating an HTL reaches a plateau near 22%, whereas the perovskite solar cell without a hole transport layer remains limited to 8% - 9%. This underscores the importance of selective hole extraction and the reduction of interfacial recombination [32]-[34]. The open-circuit voltage (Figure 6(b)) is significantly penalized in the absence of an HTL (0.52 V at 1600 nm), while it stabilizes around 1.12 V with an HTL, a consequence of improved band alignment and suppression of interface defects [35]. The short-circuit current density (Figure 6(c)) reaches 25 mA·cm⁻² with the hole transport layer compared to 23 - 24 mA·cm⁻² without the hole transport layer, reflecting more efficient charge collection [36]. Finally, the fill factor (Figure 6(d)) remains substantially higher with an HTL due to reduced resistive losses and more ideal diode behavior [35]-[38]. The optimal thickness (approximately 800 nm) is fully exploited only in the architecture incorporating an HTL, in agreement with recent high-efficiency devices [39]-[41].

Figure 6. Influence of thickness variation on electrical parameters.