The simulated device corresponds to a typical CIGS solar cell architecture:

SLG/Mo (500 nm)/p-CIGS (2 µm)/n-In₂S₃ (50 nm)/i-ZnO (100 nm)/ZnO:Al (300 nm)/metallic front grid.

This configuration reproduces standard high-efficiency CIGS devices and enables isolation of the electronic effects induced by the In₂S₃ buffer layer.

Figure 1 illustrates the functional stacking of the device layers. The molybdenum layer ensures efficient back contact, while the p-type CIGS layer acts as the primary absorber. The n-type In₂S₃ buffer layer controls junction formation and band alignment at the heterointerface. The intrinsic ZnO layer reduces leakage currents, and the ZnO:Al layer serves as a transparent conductive window. This architecture allows any performance variation to be directly attributed to modifications in the donor concentration of the In₂S₃ layer.

Figure 1.Schematic structure of the CIGS/In₂S₃ solar cell.

At thermal equilibrium, the In₂S₃/CIGS interface forms a p-n heterojunction characterized by band bending and the establishment of a built-in electric field. The relative alignment of the conduction and valence bands governs carrier separation and interfacial recombination processes [7][8].

In this study, the electron affinity and bandgap values are fixed according to literature data, leading to a constant band alignment representative of high-efficiency CIGS devices. Under these conditions, the built-in potential promotes the separation of photogenerated carriers, while buffer-layer properties mainly affect transport losses and recombination rates.

The equilibrium band alignment of the In₂S₃/CIGS heterojunction is illustrated in Figure 2, which shows the conduction and valence band profiles and the resulting built-in electric field governing carrier separation and recombination at the interface.

Figure 2 illustrates the equilibrium energy band diagram of the simulated In₂S₃/CIGS structure. The bending of the conduction band (E_C) and valence band (E_V) across the junction reflects the formation of the depletion region and the associated internal electric field. Since all band-structure parameters are kept constant in this work, performance variations arise from donor-concentration-induced changes in carrier density, conductivity and recombination within the In₂S₃ buffer layer.

Figure 2. Energy band diagram of the In₂S₃/CIGS heterojunction at equilibrium.

The numerical simulations conducted in this study are based on a consistent set of physical and electronic parameters accurately describing each layer of the CIGS solar cell. These parameters include fundamental material properties (bandgap energy, electron affinity, dielectric permittivity), geometrical characteristics (layer thickness), as well as carrier transport and recombination quantities (mobilities, carrier lifetimes, effective density of states, and interface trap density).

Table 1. Physical parameters used in the simulations for each layer.

The selected values were extracted from well-established literature sources and correspond to high-efficiency CIGS devices, while ensuring numerical stability and convergence within the ATLAS simulation environment. The simulation parameters are listed in Table 1 [3][7][9].

The interface trap density D i t was selected within realistic ranges to model partially passivated heterointerfaces, consistent with experimental data reported for high-quality CIGS devices [10][11].

The optical constants (real and imaginary parts of the complex refractive index n ˜ = n ( λ ) + i k ( λ ) ) of ZnO:Al, i-ZnO, and In₂S₃ were extracted from literature sources [12]-[14], ensuring accurate optical absorption and carrier generation modeling.

The current-voltage (J-V) characteristics were simulated under standard AM1.5G illumination (100 mW∙cm⁻²) at room temperature (300 K).

The extracted photovoltaic parameters include:

Short-Circuit Current Density (J_SC)

The short-circuit current density corresponds to the current generated per unit area when V = 0. It can be expressed as:

where I 0 ( λ ) is the incident spectral irradiance, h is Planck’s constant, c the speed of light in vacuum, E Q E ( λ ) the external quantum efficiency, and q the elementary charge.

Open-Circuit Voltage (V_oc):

The open-circuit voltage is defined at J = 0 :

where n is the diode ideality factor, k Boltzmann’s constant, T the absolute temperature, and J 0 the saturation current density.

Fill Factor (FF)

The fill factor reflects the electrical quality of the solar cell and is defined as:

where J m and V m correspond to the maximum power point.

Conversion Efficiency (η)

The power conversion efficiency is defined as:

where P m is the maximum output power and P i n the incident optical power density [15].

Series and Shunt Resistances

The series resistance R s and shunt resistance R s h were determined from the differential resistance:

evaluated near V ≈ V O C for R s , and near V ≈ 0 for R s h [16].

This approach provides a realistic estimation of resistive losses, capturing the combined effects of carrier transport, recombination, and ohmic contributions.

A single simulation campaign was performed to investigate the influence of the donor concentration N_D in the In₂S₃ buffer layer.

The donor concentration was varied from 10¹⁶ to 7 × 10¹⁸ cm⁻³ (15 values), covering low, intermediate, and high doping regimes. This range allows the exploration of the trade-off between improved electrical conductivity at moderate doping levels and enhanced recombination mechanisms at high carrier densities.

All other material parameters, including electron affinity, bandgap energy, mobilities, and interface properties, were kept constant throughout the simulations to isolate the specific impact of donor concentration on photovoltaic performance.

Table 2 summarizes the photovoltaic parameters extracted for the fifteen donor concentrations (N_D) investigated in the In₂S₃ buffer layer. The results clearly reveal a non-monotonic response of device performance as a function of doping concentration. Increasing N_D initially improves carrier collection and resistive parameters, but beyond a critical threshold, performance degradation occurs, mainly driven by a pronounced decrease in the open-circuit voltage V_OC.

This behavior reflects a trade-off between:

1) improved electrical conductivity of the buffer layer, and

2) enhanced recombination mechanisms (bulk and interface) at high doping levels, which increase the saturation current density and reduce the open-circuit voltage [15][17].

Table 2.Photovoltaic parameters as a function of donor concentration in In₂S₃.

Figure 3 shows the simulated P(V) curves for six representative donor concentrations. All curves exhibit the expected parabolic shape with a clearly defined maximum power point (MPP).

Figure 3. P-V characteristics for different donor concentrations.

A clearly non-monotonic trend is observed.

At low concentration (N_D = 10¹⁶ cm⁻³), the maximum output power reaches approximately:

at

As the concentration increases to 6 × 10¹⁶ cm⁻³, the performance significantly improves, and the maximum power reaches:

corresponding to an increase of approximately 17%. This value represents the optimal doping level for this simulation series.

Beyond this point, the performance deteriorates sharply. For N_D ≥ 2 × 10¹⁷ cm⁻³, the maximum power decreases to approximately 14 mW/cm², representing a loss of nearly 27% compared to the optimum.

Simultaneously, the voltage at maximum power V m decreases from about 0.71 V to 0.48 V, consistent with the observed reduction in V_OC.

This evolution highlights the competition between two opposing effects:

At low doping levels, limited conductivity restricts carrier extraction.At intermediate doping, improved electrical conductivity and reduced series resistance enhance carrier transport.At high doping levels, performance degradation becomes dominated by enhanced recombination mechanisms (bulk and interface), which increase the saturation current density and significantly reduce V_OC [15][17].

Thus, the improvement in P max is mainly driven by the increase in J_SC and FF, whereas the degradation is primarily governed by the reduction of V_OC.

Figure 4 presents the J-V characteristics under AM1.5G illumination, showing the systematic evolution of photovoltaic parameters with increasing donor concentration in the In₂S₃ buffer layer.

Figure 4. J-V characteristics for different donor concentrations.

The short-circuit current density initially increases from: 29.9 mA/cm² at 10¹⁶ cm⁻³, to a maximum of:

35.8 mA/cm² at 2 × 10¹⁷ cm⁻³, corresponding to an improvement of approximately 20%.

This enhancement is attributed to the increase in buffer-layer conductivity, which facilitates electron transport toward the junction and reduces resistive losses associated with the series resistance [17].

However, beyond this concentration, J_SC abruptly decreases and stabilizes around 30.1 mA/cm², indicating the onset of a dominant limiting mechanism such as enhanced recombination or unfavorable band alignment.

In contrast, the open-circuit voltage continuously decreases from 0.828 V to approximately 0.566 V, corresponding to a reduction of about 32%.

This pronounced degradation constitutes the main limiting factor at high doping levels. According to the Shockley relation, V_OC depends logarithmically on the ratio J S C / J 0 ; therefore, any increase in the saturation current density J₀ (which indicates that recombination is dominated by near-ideal mechanisms, likely radiative or diffusion-controlled processes, as supported by the extracted ideality factor close to unity) directly leads to a reduction in V_OC [15][18].

The results suggest that, at high donor concentrations:

Recombination processes become increasingly dominant,Enhanced carrier recombination reduces the quasi-Fermi level splitting under illumination,The effective built-in potential may decrease due to modifications in band bending at the heterojunction,The reduced separation of the quasi-Fermi levels ultimately results in a lower open-circuit voltage.

An analysis of the J-V curve shape reveals that:

At low doping levels, the transition around the knee region is smoother,At high doping levels, the transition becomes sharper, reflecting an improved fill factor (associated with lower R_s and higher R_sh).

However, this improvement in FF remains insufficient to compensate for the strong reduction in V_OC, confirming that V_OC is the dominant parameter controlling overall device efficiency.

Figure 5 illustrates the evolution of the open-circuit voltage as a function of donor concentration N_D (logarithmic scale). Two distinct regimes clearly emerge: a gradual decrease for N_D ≤ 7 × 10¹⁶ cm⁻³, followed by a sharp drop and eventual quasi-saturation at high concentrations.

In the low-to-moderate concentration range (10¹⁶ to 7 × 10¹⁶ cm⁻³)_,V_OC decreases almost linearly with log ( N D ) , dropping from 0.828 V to 0.751 V. This reduction primarily reflects modifications in band alignment at the In₂S₃/CIGS heterojunction, as well as a progressive increase in recombination mechanisms.

Figure 5.Open-circuit voltage as a function of donor concentration.

For N_D ≥ 7 × 10¹⁶ cm⁻³, the decrease becomes much more pronounced: V_OC reaches only 0.576 V at N_D = 2 × 10¹⁷ cm⁻³. At even higher concentrations (≥2 × 10¹⁸ cm⁻³), V_OC stabilizes around 0.566 V, indicating that recombination mechanisms have reached a quasi-steady dominant regime.

This drastic degradation of V_OC is mainly attributed to the increase in the saturation current density J₀. According to the Shockley relation, an increase in J₀ leads to a logarithmic reduction of the open-circuit voltage V_OC [16]. Several mechanisms may contribute to this increase.

Bandgap renormalization (BGN) at high doping levels may reduce the effective bandgap of In₂S₃ through many-body interactions, potentially dominating over the Burstein-Moss band-filling effect, which normally produces a blue shift [17];Enhanced bulk recombination, particularly Auger recombination at high carrier densities, which increases the recombination current and contributes to a higher J₀;Modification of the heterojunction barrier, which can alter the band alignment at the In₂S₃/CIGS interface and reduce the quasi-Fermi level splitting under illumination;Reduction of the effective built-in potential, resulting from bandgap narrowing and Fermi level shifts at high donor concentrations.

These results confirm that V_OC is the most sensitive parameter to excessive doping in the buffer layer.

Figure 6 presents the variation of J_SC as a function of donor concentration. Unlike V_OC, which continuously decreases, J_SC exhibits a non-monotonic behavior with a well-defined maximum.

Figure 6. Short-circuit current density as a function of donor concentration.

In the range 10¹⁶ to 2 × 10¹⁷ cm⁻³, J_SC increases from 29.9 to 35.8 mA∙cm⁻² (approximately 20% improvement). This enhancement is explained by:

Increased electrical conductivity of the In₂S₃ buffer layer;Reduced series resistance R_s (from 1.93 to 1.30 Ω∙cm²);More efficient extraction of photogenerated electrons.

Beyond 2 × 10¹⁷ cm⁻³, J_SC abruptly decreases and stabilizes near 30.1 mA∙cm⁻². This degradation coincides with the sharp decline in V_OC, indicating the emergence of a dominant limiting mechanism.

Several mechanisms may contribute to this behavior:

Increased bulk and interface recombination;Unfavorable modification of the band alignment at the heterojunction;Reduction of the space-charge region width, which intensifies the internal electric field and may promote carrier velocity saturation [19];Reduction of the minority carrier diffusion length in the CIGS absorber [18].

Notably, the concentration maximizing J_SC (2 × 10¹⁷ cm⁻³) is higher than the concentration maximizing overall efficiency (6 × 10¹⁶ cm⁻³). This confirms that final device performance is primarily governed by V_OC, rather than J_SC.

Figure 7 shows the evolution of the fill factor as a function of donor concentration. The FF, which reflects the squareness of the J-V curve, exhibits three distinct regimes.

1) Low concentration regime (10¹⁶ to 7 × 10¹⁶ cm⁻³)

The FF increases steadily from 67.1% to 76.2%. This improvement reflects the reduction in R_s and improved carrier transport.

2) Intermediate regime (7 × 10¹⁶ to 2 × 10¹⁷ cm⁻³)

Significant fluctuations are observed: the fill factor reaches a maximum of 78.6% at 7 × 10¹⁶ cm⁻³, followed by a decrease to 72.8% at 10¹⁷ cm⁻³, likely associated with the emergence of parasitic conduction paths, as reflected by the decrease of R_sh to 179 Ω∙cm². The fill factor then increases again to 74.3% at 2 × 10¹⁷ cm⁻³. These variations reveal a competition between resistive losses, leakage currents, and recombination processes that collectively influence the electrical quality of the heterojunction.

3) High concentration regime (≥5 × 10¹⁷ cm⁻³)

The FF reaches a high plateau (≈ 82%). This improvement results from:

Significant reduction in R_s (≈1.24 Ω∙cm²);Dramatic increase in R_sh;Reduced leakage currents.

However, despite this high FF, the overall efficiency remains limited due to the simultaneous severe degradation of V_OC. This underscores the dominant role of recombination mechanisms over purely resistive improvements.

Figure 7.Fill factor as a function of donor concentration.

Figure 8 illustrates the evolution of the power conversion efficiency as a function of donor concentration in the In₂S₃ buffer layer. This parameter, resulting from the combined contribution of J_SC, V_OC, and the fill factor (FF), represents the overall performance indicator of the photovoltaic device.

The obtained profile exhibits a characteristic bell-shaped curve, clearly revealing the existence of an optimal doping level. At low donor concentration (N_D = 10¹⁶ cm⁻³), the efficiency remains limited to 16.6%, mainly due to insufficient electrical conductivity in the buffer layer and the resulting high series resistance, which restricts carrier extraction.

As the donor concentration increases, the efficiency progressively improves and reaches a maximum value of 19.3% at N_D = 6 × 10¹⁶ cm⁻³. At this optimal concentration, the three photovoltaic parameters are well balanced:

J S C = 32.0   mA ⋅ cm − 2 , V O C = 0.765   V , F F = 78.6 % .

Figure 8.Efficiency evolution as a function of donor concentration.

Beyond this point, the efficiency gradually decreases (17.9% at 10¹⁷ cm⁻³, then 15.3% at 2 × 10¹⁷ cm⁻³) and stabilizes around 14.0% at higher concentrations (N_D ≥ 5 × 10¹⁷ cm⁻³). This corresponds to an overall loss of approximately 27% compared to the optimum.

This degradation is mainly attributed to the pronounced reduction of V_OC, resulting from the combined intensification of recombination processes and modifications of the band alignment at the heterojunction [20][21]. For low and intermediate donor concentrations, non-ideal recombination mechanisms, mainly Shockley-Read-Hall (SRH), are dominant, as suggested by the extracted ideality factors n around 1.3 - 1.2. At higher concentrations, the ideality factor approaches unity, indicating that more ideal recombination processes, such as radiative and Auger recombination, may become significant.

Recent studies on Cd-free In₂S₃ buffer layers report similar trends, where excessive doping enhances conductivity but deteriorates quasi-Fermi level splitting, ultimately limiting open-circuit voltage and overall device efficiency [22].

The optimal concentration (6 × 10¹⁶ cm⁻³) therefore represents a trade-off between improved carrier transport and controlled recombination losses.

Figure 9 shows the variation of the series resistance as a function of donor concentration.

Figure 9.Series resistance as a function of donor concentration.

Overall, R_s decreases as the donor concentration increases, from 1.93 Ω∙cm² to 1.24 Ω∙cm², corresponding to a reduction of approximately 36%. This trend is directly related to the increase in electrical conductivity of the In₂S₃ buffer layer, described by:

where n is the electron concentration and μ n the electron mobility.

Recent investigations on doped In₂S₃ thin films confirm that increasing carrier density enhances conductivity, although mobility may decrease due to ionized impurity scattering and structural disorder effects [20].

The local anomaly observed in the range 7 × 10¹⁶ to 10¹⁷ cm⁻³ (slight increase in R_s) may therefore result from transient mobility degradation or trap-assisted transport phenomena.

Although the reduction in R_s improves the fill factor, it does not compensate for the simultaneous degradation of V_OC at high doping levels. These results confirm that minimizing ohmic losses alone is insufficient to maximize efficiency without controlling recombination processes.

Figure 10 illustrates the evolution of the shunt resistance as a function of donor concentration.

At low doping levels, R_sh remains moderate (179 - 738 Ω∙cm²), indicating the presence of leakage paths associated with interface defects and trap states.

From 2 × 10¹⁷ cm⁻³ onward, R_sh increases dramatically, reaching up to 1.3 × 10⁶ Ω∙cm² at the highest concentrations. This substantial increase suggests progressive trap filling and apparent improvement in junction quality, a behavior also reported experimentally for highly doped In₂S₃ buffer layers [23].

Figure 10. Shunt resistance as a function of donor concentration.

The increase in R_sh contributes to the high fill factor (>82%) by suppressing leakage currents. However, despite this resistive improvement, the global efficiency declines due to the dominant reduction in V_OC. These findings confirm that recombination processes governing open-circuit voltage are more critical than leakage-current suppression in determining overall device performance.

The results demonstrate that the carrier concentration in the In₂S₃ buffer layer has a decisive influence on the performance of the CIGS solar cell.

An optimal compromise is identified at N_D = 6 × 10¹⁶ cm⁻³, allowing a maximum efficiency of 19.3% to be achieved. At this concentration, the improvement in electrical conductivity (reduction of R_s and increase in J_SC) still compensates for the losses induced by the progressive intensification of recombination mechanisms.

The overall analysis highlights the dominant role of the open-circuit voltage in determining the final device performance: beyond a certain doping level, the increase in recombination processes outweighs the resistive benefits, irreversibly limiting the overall efficiency of the device.