The studied solar cell, like any other perovskite solar cell, consists of a stack of thin films deposited on a substrate, as shown in Figure 2. The central element of this architecture is the perovskite absorber layer, whose essential function is to capture solar radiation and generate electron-hole pairs [4]. In this study, the absorber layer is a triple-cation perovskite with the structure: Cs_0.05FA_0.79MA_0.15 PbI_2.45Br_0.55. The Cs⁺-MA⁺-FA⁺ mixture optimizes the lattice tolerance factor, stabilizing the cubic or tetragonal α-phase, which is essential for efficient light absorption. Cs⁺ reinforces the lattice rigidity and prevents the transition to non-photoactive phases (such as δ-FAPbI₃), while MA⁺ and FA⁺ maintain a slightly distorted geometry favorable for carrier transport [14]-[16].

Figure 2.Structure of the studied cell.

The optimal operation of the perovskite sub-cell within a perovskite/CIGS architecture relies on effective spectral complementarity with the CIGS sub-cell. To this end, the perovskite bandgap must be judiciously adjusted to ensure high transparency in the near-infrared region, typically between 700 and 1200 nm, thereby allowing the transmission of photons to the underlying CIGS sub-cell [17]. Under solar illumination, the perovskite absorber enables electrons from the valence band to move to the conduction band, leaving holes behind.

Figure 3.Band diagram and operational mechanism.

The generated electron-hole pair (see Figure 3) rapidly dissociates into free charges, as the exciton binding energy in perovskite is relatively low (a few tens of meV at room temperature) [18]. These charges must then be selectively extracted using transport layers: the electron transport layer (ETL, here SnO₂), which facilitates the transfer of photogenerated electrons to the electrode while acting as a barrier against their recombination with holes, and the hole transport layer (HTL, here Spiro-OMeTAD), which collects the positive charges. For these processes to be efficient, energy level alignment is crucial: the LUMO (lowest unoccupied molecular orbital) level of the ETL must be lower than that of the absorber, while the HOMO (highest occupied molecular orbital) level of the HTL must be higher than that of the perovskite [19]-[21]. Meeting these conditions promotes selective extraction and efficient transport of charge carriers to the contact electrodes, the rear in Au and the front in ITO.

The operation of a solar cell is governed by the generation, transport, and recombination of charge carriers, processes described by Poisson’s Equation (1) and the continuity equations for electrons (2) and holes (3). In this study, these equations are solved numerically using the SCAPS-1D software, which is widely recognized for modeling thin-film photovoltaic devices, particularly perovskite cells [19].

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

For the numerical simulations, SCAPS-1D receives as input the numerical model of our solar cell (see Table 1), constructed from a critical analysis of the literature to faithfully reproduce the experimental electrical behavior reported by Alanazi et al. (2020) [12] with a maximum relative error set at 0.5%. This model integrates all the physical and electronic parameters of the different layers, including thicknesses, doping levels, mobilities, defect densities, electron affinities, bandgaps, etc. Based on these inputs, the software numerically solves Poisson’s equation and the carrier continuity equations (see Equations (1) (2) and (3). As output, it provides the device’s electrical characteristics, namely the open-circuit voltage (Voc), short-circuit current density (Jsc), fill factor (FF), power conversion efficiency (PCE), etc. The software thus provides a rigorous framework for quantitatively analyzing the influence of input parameters on the device’s electrical performance.

To reconcile model accuracy with numerical feasibility, several simplifying assumptions were adopted. Interface defect densities are assumed to be constant and spatially homogeneous, while the bandgap (E_g) and electron affinity (χ) are considered invariant. Carrier mobilities are treated as uniform and isotropic across all layers. The optical absorption process is modeled within a strictly one-dimensional framework, without accounting for scattering phenomena. The device temperature is fixed at 300 K, and the illumination spectrum corresponds to the AM1.5G standard. These approximations, widely accepted in the literature, allow the analysis to focus on the dominant electrical and optical mechanisms while maintaining relevant correspondence with experimental devices [22].

Table 1.Numerical model of the studied cell [23]-[29].

The validation of the numerical model for the studied solar cell is performed by comparing its electrical performance with that of the actual cell reported by Alanazi et al. (2020) [12] (see Figure 4 and Table 2). This step ensures the simulation results remain coherent, realistic, and representative of the real behavior of the experimental device.

The comparison between experimental results and simulated data reveals a remarkable degree of agreement, confirming the robustness and reliability of the adopted numerical model. The near-perfect overlap of the current-voltage curves presented in Figure 4 demonstrates that the simulation faithfully reproduces the experimental behavior of the cell across all operating regimes, thereby validating the coherence of the implemented physical parameters. This qualitative observation is supported by a quantitative analysis of the photovoltaic parameters summarized in Table 2.

The use of relative error enables moving beyond a simple visual comparison to conduct a more rigorous model validation. The simulated open-circuit voltage coincides exactly with the experimental value (1.08 V), reflecting an adequate description of recombination mechanisms. Similarly, the short-circuit current and the fill factor exhibit only marginal deviations on the order of 0.13%, indicating precise modeling of carrier absorption, transport, and collection phenomena, as well as internal resistances. The simulated conversion efficiency is strictly identical to the measured value, confirming that SCAPS-1D consistently accounts for all physical processes governing the device’s operation. Under these conditions, the numerical model can be considered a reliable predictive tool for the analysis and optimization of the studied solar cell.

Figure 4.Experimental and simulated J-V curves.

Table 2.Experimental and simulated characteristics.

3.1.1. Influence of the Absorber Layer Thickness

Figure 5 analyzes the impact of the triple-cation perovskite absorber thickness, ranging from 200 to 1250 nm, on the electrical performance of the studied solar cell.

The study reveals a marked dependence of photovoltaic performance on the absorber layer thickness. The power conversion efficiency (PCE, Figure 5(d)) increases continuously as the thickness increases from 200 to 1250 nm, rising from 14.40% to 18.87%. This improvement is primarily driven by the growth of the short-circuit current density (Jsc, Figure 5(b)), which increases from 16.02 to 23.93 mA·cm⁻². This trend indicates increasingly efficient photon absorption until a quasi-saturated regime is established for thicknesses above 800 - 900 nm, beyond which the current reaches a plateau.

Concurrently, the fill factor (FF, Figure 5(c)) decreases significantly, dropping from 81.51% to 70%. This degradation is attributed to the intensification of bulk recombination and the progressive deterioration of carrier transport within a larger active volume, a phenomenon accounted for in the recombination model implemented in SCAPS-1D. When the thickness exceeds the effective carrier diffusion length, charge extraction becomes less efficient.

Figure 5.Variation of electrical performance as a function of absorber thickness.

The open-circuit voltage (Voc, Figure 5(a)) exhibits a non-monotonic evolution. After a slight decrease between 200 and 500 nm, it gradually increases to reach 1.13 V at 1250 nm. This U-shaped trend reflects the competition between enhanced carrier generation (favorable for Voc) and increased recombination losses (which tend to reduce it).

Although the maximum efficiency is achieved at 1250 nm, the performance saturation beyond 800 nm leads to the identification of an optimal range between 800 and 1000 nm, offering a balanced compromise between efficiency, electrical stability, and loss control. From an experimental perspective, this range is compatible with commonly used perovskite deposition techniques (e.g., multi-layer spin-coating, blade coating, or slot-die coating), while thicknesses approaching 1250 nm present greater technological and structural challenges [30]-[32]. Consequently, the thickness is set to 1000 nm for the remainder of the study to investigate the combined influence of doping and defect density on electrical performance.

3.1.2. Influence of Doping and Total Defect Density

The heatmaps in Figure 6 highlight the cross-influence of the acceptor doping, varying from 10¹³ to 1.5 × 10¹⁵ cm⁻³, and the absorber defect density, ranging between 10⁹ and 10¹⁶ cm⁻³, on photovoltaic performance.

The results reveal a high sensitivity of photovoltaic performance to the absorber defect density (N_t). For low to moderate values (N_t ≤ 10¹⁴ cm⁻³), the efficiency (η, Figure 6(a)), open-circuit voltage (Voc, Figure 6(b)), and fill factor (FF, Figure 6(d)) remain high and stable, with efficiencies exceeding 24%. Conversely, when N_t reaches 10¹⁵ - 10¹⁶ cm⁻³, all parameters degrade significantly as a direct consequence of intensified non-radiative Shockley-Read-Hall recombination, which reduces carrier lifetime.

Figure 6.Variation of performance as a function of doping and total defect density.

The open-circuit voltage (Voc, Figure 6(b)) exhibits a marked dependence on acceptor doping (N_a) when the defect density remains low. Increasing N_a strengthens the internal electric field and reduces the saturation current, thereby improving Voc. At high defect densities, this beneficial trend is radically reversed: Voc drops sharply, particularly for low doping levels, revealing the dominance of bulk recombination mechanisms. The short-circuit current density (Jsc, Figure 6(c)) remains largely insensitive to doping as long as N_t ≤ 10¹⁴ cm⁻³, indicating efficient carrier collection. However, as N_t increases, Jsc decreases noticeably due to the reduced diffusion length and increasingly inefficient collection a phenomenon accentuated at low doping levels. This degradation marks a clear reversal of its initial stability.

The fill factor (FF, Figure 6(d)) evolves similarly to the efficiency. It retains high values for low defect densities, then deteriorates sharply at high N_t, under the effect of increased saturation current and recombination around the maximum power point. Even at low N_t, excessive doping (N_a ≳ 10¹⁵ cm⁻³) slightly degrades the FF, indicating an optimal compromise between doping and charge transport.

An optimal regime emerges for N_t ≤ 10¹³ - 10¹⁴ cm⁻³ and N_a between 10¹⁴ and 10¹⁵ cm⁻³, enabling efficiencies close to 25% (η, Figure 6(a)). This optimum is consistent with the state-of-the-art for high-performance perovskites [33]. Conversely, doping levels above 10¹⁵ cm⁻³ induce increased structural degradation and ionic instability, in agreement with trends observed in simulations [34]. The following section focuses, for a representative N_t of 10¹³ cm⁻³, on the joint analysis of doping and electron mobility, as the latter can become a limiting factor when dopant concentrations increase.

3.1.3. Influence of Doping and Carrier Mobility

Figure 7 illustrates the combined impact of the acceptor concentration, varying from 10¹³ to 1.5 × 10¹⁵ cm⁻³, and the charge carrier mobility (electrons and holes), ranging between 1 and 5 cm²·V⁻¹·s⁻¹, on the electrical performance of the studied solar cell.

In triple-cation perovskite solar cells, the ratio of electron to hole mobilities is generally close to unity (μ_n/μ_p ≈ 1) [35]. Consequently, the simulations performed here were configured with symmetric variations of electron and hole mobilities, imposing μ = μ_n = μ_p, in order to realistically replicate ambipolar charge transport within the absorber layer.

Figure 7.Variation of performance as a function of doping and carrier mobility.

The open-circuit voltage (Voc, Figure 7(b)) depends strongly on the acceptor concentration and increases with doping, reaching approximately 1.147 V for N_a = 1.5 × 10¹⁵ cm⁻³. This trend is attributed to the reduction of the reverse saturation current. However, an increase in mobility induces a slight reduction in Voc, a phenomenon explained by a faster redistribution of carriers towards the interfaces, where interfacial recombination becomes predominant when interface quality is limited. The short-circuit current density (Jsc, Figure 7(c)) remains practically constant around 24.4 mA·cm⁻², indicating photon absorption close to saturation within the studied parameter domain. Concurrently, the fill factor (FF, Figure 7(d)) increases with mobility and reaches about 88% for intermediate doping levels, reflecting reduced transport losses and more efficient charge extraction, whereas excessive doping deteriorates this parameter.

Overall, an optimal operating domain is identified for acceptor concentrations on the order of N_a ≈ 10¹³ - 10¹⁴ cm⁻³ combined with a carrier mobility μ ≥ 3 cm²·V⁻¹·s⁻¹, enabling the concurrent optimization of the conversion efficiency η, open-circuit voltage Voc, and fill factor FF. This parameter range is fully compatible with current experimental capabilities [36][37]. Therefore, the reference parameter set, defined by a mobility μ = 3 cm²·V⁻¹·s⁻¹ and a defect density N_t = 10¹³ cm⁻³, is adopted for the continuation of the study, which focuses on the joint optimization of doping and absorber layer thickness, aiming to identify an optimal compromise between efficient collection of photogenerated charges and the minimization of recombination losses.

3.1.4. Influence of Doping and Thickness

Figure 8 illustrates the combined impact of acceptor concentration (N_a), ranging from 10¹³ to 1.5 × 10¹⁵ cm⁻³, and absorber layer thickness, ranging from 200 nm to 1200 nm, on the photovoltaic performance of the studied solar cell.

Figure 8.Variation of electrical performance as a function of doping and thickness.

The power conversion efficiency (η, Figure 8(a)) increases significantly with absorber thickness, driven directly by the increase in photogenerated current density, and then evolves more slowly at greater thicknesses, reflecting the approach of an optical saturation regime. The short-circuit current density (Jsc, Figure 8(c)) shows a rapid increase with thickness up to approximately 800 - 1000 nm, beyond which the gain becomes marginal due to the near-complete absorption of the incident spectrum. Its dependence on N_a concentration remains generally weak over the considered range.

The open-circuit voltage (Voc, Figure 8(b)) increases significantly with Na, reflecting the improvement of the internal electric field and the effective reduction of recombination losses as the doping level promotes better charge separation. Voc also increases with thickness, although this dependence is less pronounced than that observed with doping. The fill factor (FF, Figure 8(d)) generally decreases as thickness increases, a behavior consistent with increased transport losses and recombinations in a thicker absorber; this degradation becomes more pronounced for high Na values, where resistive and recombination effects are intensified.

The efficiency η thus results from a compromise between the increase in Jsc and Voc and the progressive penalty on FF. Although the maximum η value is achieved for thicknesses near the upper limit of the studied range and for high doping levels, a value of η = 24.3% obtained for an absorber thickness of 1000 nm and a concentration of N_a = 10¹⁴ cm⁻³ appears as an optimal condition considering the overall device constraints. This configuration indeed offers an efficiency substantially equivalent to the maximum value while providing a better compromise in terms of operational stability, technological deposition limitations, doping control, and manufacturing cost.

The effectiveness of this approach highlights the decisive role of the absorber in improving perovskite device performance. However, despite these advances, interfaces often constitute critical zones where energy losses are concentrated, as interfacial defects and poor energy level alignment between the absorber and the charge transport layers promote non-radiative recombinations that limit the open-circuit voltage and overall conversion. The following section is therefore devoted to the analysis and optimization of these interfaces, in order to enhance their energetic alignment and limit residual interfacial recombination.

3.2.1. Evaluation of Functional Layer Band Alignment

Reducing recombination at the ETL/perovskite/HTL interfaces constitutes a critical lever for optimizing the extraction and collection of photogenerated charge carriers. The efficiency of this process depends directly on the band alignment, which must ensure both efficient electron injection and selective hole extraction. Thus, a valence band offset (VBO) between 0 and −0.2 eV at the HTL/perovskite interface promotes hole extraction without creating a limiting barrier, while a conduction band offset (CBO) from 0 to +0.3 eV between the ETL and the perovskite constitutes a moderate “spike,” suitable for blocking recombination while allowing efficient electron collection [38]. The analytical expressions for these energy offsets are recalled below:

where χ H T L and χ E T L denote the electron affinities of the hole transport layer (HTL) and electron transport layer (ETL), respectively, χ a b s that of the perovskite absorber, and E g the bandgap of each material.

Based on the parameters considered in this study, the estimated VBO yields a value of −0.40 eV. Such a valence band offset, significantly below the optimal limit of −0.2 eV, corresponds to a pronounced cliff at the HTL/perovskite interface. While this cliff may facilitate hole transfer to some extent, it simultaneously increases the probability of interfacial recombination via deep states located near this interface. An excessively negative VBO typically leads to a decrease in Voc and a deterioration of the HTL’s selectivity, which reduces the overall cell efficiency [39].

Similarly, the calculated conduction band offset yields CBO = −0.1 eV. This negative value indicates the presence of a cliff at the ETL/perovskite interface, inducing a collection barrier likely to favor electron recombination, particularly under strong illumination. Although a moderate cliff (≈−0.1 eV) still allows acceptable electron transport, it remains detrimental for maximizing Voc and reducing resistive losses associated with interfacial transfer [39].

Figure 9.Energy band diagram of the studied solar cell.

Figure 9 highlights that the cell’s performance is primarily limited by poor energetic alignment at the interfaces. At the SnO₂/perovskite interface, the negative CBO (≈−0.1 eV) creates an electron cliff that promotes electron accumulation and increases interfacial recombination, directly penalizing the open-circuit voltage [40]. At the perovskite/Spiro-OMeTAD interface, the strongly negative VBO (≈−0.40 eV) corresponds to a pronounced valence band cliff, reducing the hole contact selectivity and intensifying recombination losses, with a simultaneous degradation of Voc and the fill factor.

The quasi-flat bands within the bulk of the perovskite confirm that the limitations are dominated by interfaces rather than bulk transport. Therefore, performance optimization requires a controlled repositioning of the CBO towards [0; +0.3] eV and the VBO towards [0; −0.2] eV, a prerequisite for reducing recombination and maximizing device efficiency [41].

3.2.2. Optimization of the CBO via the SnO₂ Layer

The previous analysis highlighted a negative CBO (≈−0.1 eV) at the ETL/perovskite interface. To optimize the band alignment, a parametric study was conducted by varying the electron affinity of SnO₂ (3.8 - 4.0 eV) and of the absorber (3.85 - 4.1 eV), the effects of which on the cell performance are presented in Figure 10.

Figure 10.Simulation of the influence of the electron affinity of the SnO₂ layer and that of the absorber on the electrical performance of the perovskite solar cell.

The open-circuit voltage (Voc) remains largely independent of χ_ETL but decreases sharply with increasing χ_abs (from 1.16 V to 0.93 V), worsening the negative CBO (≈–0.1 eV) and promoting interfacial recombination. The short-circuit current (Jsc) increases significantly with χ_abs, while the influence of χ_ETL is marginal, indicating better electron extraction. The fill factor (FF) is mainly controlled by χ_ETL: it improves rapidly from 3.9 eV onward, reaching an optimal plateau of 86% - 88%. The overall efficiency (η) results from a trade-off between these parameters. It increases slightly with χ_ETL but decreases strongly with χ_abs, dropping from 25% to 19%. Thus, the global optimum is achieved for χ_abs ≈ 3.85 - 3.9 eV and χ_ETL ≈ 3.9 - 4.0 eV, leading to CBO values between −0.15 eV and 0 eV.

However, considering the experimental constraints related to material stability and the reproducibility of deposition processes, a pragmatic choice is to set χ_abs ≈ 3.9 eV and χ_ETL ≈ 4.0 eV (CBO ≈ −0.1 eV). This configuration, validated by the observed trends, will serve as the basis for the remainder of the study, which is dedicated to optimizing the valence band offset (VBO) through engineering of the Spiro-OMeTAD hole transport layer.

3.2.3. Optimization of the VBO via the Spiro-OMeTAD Layer

Figure 11.Simulation of the influence of the HTL bandgap and its electron affinity on the electrical performance of the perovskite solar cell.

The analysis is based on Equation (4), considering a perovskite characterized by χ_abs = 3.9 eV and E_g,abs = 1.6 eV. A dual parametric sweep of the HTL’s electron affinity (χ_HTL from 2.1 to 2.4 eV) and its optical bandgap (E_g,HTL from 2.7 to 3.4 eV) is performed to identify configurations satisfying the optimal energy condition of −0.2 ≤ VBO ≤ 0 eV. This approach allows delineation of an interfacial stability zone ensuring efficient hole extraction while limiting recombination. The complete set of results is presented in Figure 11.

The open-circuit voltage (Voc) increases monotonically with the HTL bandgap (E_g,HTL), reaching a plateau around 1.4 V for high values (≈3.2 - 3.4 eV). This trend reflects a reduction in interfacial recombination due to improved valence band alignment. A higher HTL electron affinity (χ_HTL) also improves Voc by limiting electron leakage.

The short-circuit current (Jsc) remains globally stable, as it is mainly governed by generation and transport within the perovskite. However, a slight decrease appears at high bandgaps, caused by an increased hole extraction barrier. The effect of χ_HTL on Jsc is marginal.

The fill factor (FF) exhibits a non‑monotonic behavior, with an optimum at intermediate bandgaps (≈2.9 - 3.1 eV), reflecting a trade‑off between selectivity and ease of hole extraction. Bandgaps that are too low increase recombination, while those that are too high raise the series resistance.

The efficiency (η) is maximized for χ_HTL ≈ 2.3 - 2.4 eV and E_g,HTL ≈ 3.1 - 3.2 eV, where band alignment is optimal. The remainder of the study will focus on interface passivation by fixing χ_HTL = 2.4 eV and E_g,HTL = 3.1 eV. Figure 12 confirms the significant reduction of the VBO (from an initial −0.40 eV) at the perovskite/Spiro‑OMeTAD interface, promoting hole extraction. The CBO at the perovskite/SnO₂ interface remains unchanged at −0.1 eV, a value considered as a slight, beneficial spike. The performance gain therefore arises essentially from the optimization of the perovskite/Spiro‑OMeTAD interface.

Figure 12.Energy band diagrams of the studied solar cell before and after optimization.

3.2.4. Optimization via Interface Passivation of the Solar Cell

Figure 13 highlights the critical influence of interfacial defect density on the performance of the perovskite solar cell, revealing a marked asymmetry between the ETL/perovskite and perovskite/HTL interfaces.

Voc remains stable at 1.40 V up to 10¹¹ cm⁻² at the SnO₂/Perovskite interface, then drops sharply to 1.18 V at 10¹⁴ cm⁻². At the Perovskite/Spiro-OMeTAD interface, it decreases only moderately to 1.33 V, showing much better tolerance on the HTL side.

Jsc remains nearly constant (24.425 mA/cm²) for the HTL interface, while it decreases slightly above 10¹² cm⁻² on the ETL side. The fill factor (FF) exhibits opposite behaviors: it collapses to 82% for SnO₂/Perovskite at high defect densities, but increases to 89% for Spiro-OMeTAD.

Figure 13.Simulation of the influence of interface defect density on the electrical performance of the perovskite solar cell.

Finally, the overall efficiency η is strongly degraded by defects at the SnO₂/perovskite interface: it drops from 29.5% to only 23.5% when the defect density exceeds 10¹¹ cm⁻², whereas it remains close to 29% for the interface with the HTL, even at 10¹³ cm⁻². By adopting Nit (ETL/perovskite) = 10¹⁰ cm⁻² and Nit (perovskite/HTL) = 10¹² cm⁻², the electrical parameters obtained, presented in Table 3, show a complete and substantial improvement in the performance of the triple-cation perovskite cell after optimization. The power conversion efficiency increases from 17.56% to 29.37%, corresponding to a relative improvement of 67.25%.

Table 3. Experimental and simulated characteristics.