Optimizing a CIGS Thin-Film Solar Cell with SILVACO ATLAS: Effects of Optical Bandgap and Absorber Electron Affinity

Alioune Ngom¹, Youssou Gning¹, Mamadou Lamine Samb^1*, Aly Toure¹, Moussa Toure¹, Ahmed Mohamed-Yahya²

¹Department of Physics and Chemistry, University Iba Der Thiam of Thies, Thies, Senegal.
²Applied Research Unit for Renewable Energies, University of Nouakchott, Nouakchott, Mauritania.

DOI: 10.4236/msce.2025.1310001                

Abstract

This study uses TCAD numerical simulation to evaluate how key absorber parameters in Cu(In, Ga)Se₂ (CIGS) thin-film solar cells influence device performance, with the objective of identifying low-material, cost-effective optimization strategies. While crystalline-silicon (c-Si) still dominates the market despite its indirect bandgap and the thick wafers it requires, the CIGS pathway, featuring a direct, composition-tunable bandgap and a high absorption coefficient, on glass or flexible polymer substrates, offers a compelling alternative. The device investigated adopts the stack Al/ZnO/CdS/CIGS/Mo/PET and is simulated in SILVACO ATLAS (drift-diffusion transport coupled to Poisson and carrier-continuity equations) under conditions close to STC (AM1.5G, 27˚C, 1000 W·m⁻²). Parameter sweeps cover the absorber optical bandgap $g\in \left[1.14,1.50\right]$ eV, electron affinity $\chi \in \left[4.0,4.8\right]$ eV, and CIGS thickness $d\in \left[0.1,3.0\right]$ μm, with p-type doping fixed at 1 × 10¹⁶ cm⁻³. The results show that the short-circuit current density $J_{sc}$ is nearly invariant with respect to $E_g$ and $\chi$ once the absorber is sufficiently thick ($d\ge 0.3\mu \text{m}$ ); a deviation appears at $d=0.1\mu \text{m}$ , attributed to stronger optical losses (residual transmission) and less efficient carrier collection. In contrast, the open-circuit voltage $V_{oc}$ increases markedly with $E_g$ over the investigated range (consistent with a reduced effective saturation current), which in turn raises the fill factor $FF$ and the power-conversion efficiency η. The electron affinity $\chi$ has little influence on $J_{sc}$ (except for $d<0.3\mu \text{m}$ ), but it systematically impacts $V_{oc}$ , $FF$ , and η\etaη via band alignment at the buffer/absorber interface. Within our parameter window, a maximum efficiency of about 27.05% is achieved for $E_g\approx 1.50\text{eV}$ with $d=3.0\mu \text{m}$ , where gains in $V_{oc}$ and $FF$ compensate the near-invariance of $J_{sc}$ . Moreover, electron-affinity windows of $\chi \approx 4.0\text{-}4.2\text{eV}$ and $\chi \approx 4.6\text{-}4.8\text{eV}$ are shown to be favorable across 0.1 - 3.0 μm. These findings suggest that joint engineering of composition (Ga content) to tailor $E_g$ and of band alignment (through $\chi$ and the CdS/CIGS/ZnO interfaces) is a robust route to boost CIGS efficiency while minimizing material usage.

Keywords

CIGS Thin-Film Solar Cells, Optical Bandgap, Electron Affinity, Band Alignment (CdS/CIGS), Open-Circuit Voltage, Fill Factor, Power-Conversion Efficiency

1. Introduction

The global photovoltaic market remains largely dominated by crystalline-silicon (c-Si) solar cells, a mature, industrialized technology known for reliability, high field efficiencies, and long service lifetimes. Silicon is abundant, low-toxicity, and low-cost, and it can be readily doped with boron or phosphorus. Nevertheless, intrinsic limitations, an indirect bandgap ($E_g\approx 1.12\text{eV}$ ) and a low absorption coefficient (~104 cm⁻¹), necessitate thick wafers (≥100 μm) to efficiently absorb the solar spectrum, which raises material and energy consumption and, ultimately, costs [1].

These constraints have fueled growing interest in thin-film technologies, which aim to reduce material usage and manufacturing costs while maintaining competitive performance [2]. Among them, Cu(In, Ga)Se₂ (CIGS) stands out for its high absorption coefficient and direct, composition-tunable bandgap (≈1.04 - 1.68 eV with gallium content), as well as its compatibility with diverse substrates (glass, flexible polymers) and multiple deposition routes (co-evaporation, sputtering, PLD, screen printing), enabling flexible and Cd-free architectures [2]-[6]. These attributes motivate the performance optimization of CIGS thin-film devices, the focus of the present study.

The objective here is to quantify the influence of two key absorber parameters, the optical bandgap $E_g$ and the electron affinity $\chi$ , on the main figures of merit: short-circuit current density $J_{sc}$ , open-circuit voltage $V_{oc}$ , fill factor $FF$ , and power-conversion efficiency $\eta$ . To this end, we numerically simulate a laboratory-grade CIGS device using TCAD SILVACO-ATLAS, solving Poisson and carrier-continuity equations coupled through the drift-diffusion transport model [3] [7] [8].

The paper is organized as follows. Section 2 revisits the electrical modeling and the characteristic parameters of CIGS cells (equivalent circuit, $J\left(V\right)$ relation, $J_{sc}$ , $V_{oc}$ , $FF$ , and $\eta$ ). Section 3 details the materials, device structure, method, and simulation settings. Section 4 presents the results, followed by their analysis and discussion.

2. Modeling and Electrical Parameters of CIGS Thin-Film Solar Cells

2.1. Equivalent Electrical Circuit

A CIGS solar cell is a p-n heterojunction (p-type CIGS absorber, n-type buffer layer, and TCO window). Its electrical behavior is classically modeled by a two-diode equivalent circuit comprising a photogenerated current source ($I_{ph}$ ), a series resistance ($R_s$ ), and a shunt resistance ($R_{sh}$ ), as shown in Figure 1 [9] [10].

Figure 1. Equivalent electrical circuit of a CIGS thin-film solar cell.

In this framework, $R_s$ aggregates ohmic losses due to the sheet resistance of the transparent conducting oxide (i-ZnO/ZnO:Al), interfacial resistances, the back contact (Mo/CIGS), and the bulk resistivity of the active layers, whereas $R_{sh}$ accounts for leakage currents that partially short the junction (pinholes, percolation along grain boundaries, deep defects, metallic impurities) [9] [11]. The two diodes represent distinct recombination pathways (space-charge region vs. quasi-neutral regions), which enables faithful reproduction of the dark and illuminated J-V characteristics and of the impact of $R_s$ and $R_{sh}$ on the fill factor (FF) and the power conversion efficiency (PCE) [8]-[10].

2.2. Electrical Parameters

2.2.1. Current Density-Voltage Characteristic $J\left(V\right)$

The current density delivered by a CIGS thin-film solar cell under load, within the two-diode model, is written as:

$\begin{array}{c}J=J_{ph}-J_{01}\left\{\exp \left[\frac{q\left(V+R_{s}J\right)}{n_1{k}_{B}T}\right]-1\right\}\\ -J_{02}\left\{\exp \left[\frac{q\left(V+R_{s}J\right)}{n_2{k}_{B}T}\right]-1\right\}-\frac{V+R_{s}J}{R_{sh}}\end{array}$ (1)

where $J_{01}$ and $J_{02}$ are the saturation current densities (A·cm⁻²), $n_1$ and $n_2$ are the diode ideality factors, $R_s$ and $R_{sh}$ are the (area-normalized) series and shunt resistances (Ω·cm²), J is the current density (A·cm⁻²), q the elementary charge (C), $k_B$ the Boltzmann constant (J·K⁻¹), T the temperature (K), V the terminal voltage, and $J_{ph}$ the photogenerated current density (A·cm⁻²) [11]. The J-V characteristic is measured under standard test conditions (STC), typically AM1.5G spectrum, $T=25˚\text{C}$ , and irradiance $G=1000\text{W}\cdot {\text{m}}^{-2}$ [12].

2.2.2. Short-Circuit Current Density $J_{sc}$

The short-circuit current density, measured at $V=0$ , ideally equals the photocurrent ($J_{sc}\approx J_{ph}$ ). It depends on irradiance and spectrum, optical absorption and reflection, device thickness/quality, and minority-carrier diffusion lengths. A general expression is:

$J_{sc}=q{\displaystyle {\int }_0^{{\lambda }_g}{I}_O\left(\lambda \right)\frac{\lambda }{hc}EQE\left(\lambda \right)\text{d}\lambda }\approx q{\displaystyle {\int }_0^{{\lambda }_g}{I}_O\left(\lambda \right)\frac{\lambda }{hc}\text{d}\lambda }\left(\text{if}EQE\simeq 1\right)$ (2)

where $I_O\left(\lambda \right)$ is the spectral irradiance (W·cm⁻²·nm⁻¹), $h$ is Planck’s constant (J·s), $c$ is the speed of light in vacuum (m·s⁻¹), $\lambda$ is the wavelength (m), and ${\lambda }_g$ is the cutoff wavelength associated with the absorber’s optical bandgap [11].

Here $EQE\left(\lambda \right)$ is the external quantum efficiency (electrons collected per incident photon; $0\le EQE\le 1$ ), i.e., the fraction of incident photons at wavelength $\lambda$ that generate carriers collected at the external circuit.

In (2), we assume $EQE\left(\lambda \right)\approx 1$ and negligible front-side reflection $R_{front}\left(\lambda \right)\approx 0$ . This first-order simplification is reasonable for an optically optimized device (e.g., low-reflectance TCO window with an anti-reflective coating and/or surface texturing), for which nearly all above-bandgap photons generate carriers that are actually collected. Formally, writing $EQE\left(\lambda \right)=IQE\left(\lambda \right)\left[1-R_{front}\left(\lambda \right)\right]A\left(\lambda \right)$ we adopt the upper-bound approximation $IQE\to 1$ , $R_{front}\to 0$ , and $A\left(\lambda \right)\to 1$ for $\lambda <{\lambda }_g$ .

Where:

$IQE\left(\lambda \right)$ : the internal quantum efficiency,

$R_{front}\left(\lambda \right)$ : the front-side spectral reflectance,

$A\left(\lambda \right)$ : the spectral absorptance of the device,

${\lambda }_g$ : the bandgap wavelength of the absorber.

2.2.3. Open-Circuit Voltage $V_{oc}$

At open circuit, $J=0$ . In the single-diode effective approximation one obtains:

$V_{oc}=\frac{n{k}_{B}T}{q}\cdot \ln \left(\frac{J_{SC}}{J_o}+1\right)$ (3)

where n is the (effective) ideality factor, typically $1\le n\le 2$ [13].

2.2.4. Fill Factor (FF)

The fill factor is defined by

$FF=\frac{P_m}{J_{sc}{V}_{oc}}=\frac{J_m{V}_m}{J_{sc}{V}_{oc}}$ (4)

with ($J_m,V_m$ ) the current density and voltage at the maximum-power point. The fill factor can be written as:

$FF=F{F}_{id}\cdot \left(1-\frac{V_{OC}}{R_{Sh}{J}_{SC}}-\frac{J_{SC}{R}_S}{V_{OC}}+\frac{R_S}{R_{Sh}}\right)$ (5)

where $F{F}_{id}$ is the ideal fill factor of the cell [11] [12].

2.2.5. Power-Conversion Efficiency

The efficiency is the ratio of the maximum electrical power density to the incident optical power density:

$\eta =\frac{P_m}{P_{in}}=\frac{J_{sc}{V}_{oc}FF}{P_{in}}$ (6)

where $P_{in}$ is the incident irradiance (e.g., 100 mW·cm⁻² under STC) [11] [14].

3. Numerical Simulation

3.1. Materials, Structure, and Method

3.1.1. Materials

The thin-film solar cell under study consists of a polyethylene terephthalate (PET) substrate, a molybdenum (Mo) back contact, a Cu(In, Ga)Se₂ (CIGS) absorber, a CdS buffer layer, a ZnO window (transparent conducting oxide, TCO), and two aluminum metal fingers deposited on the TCO to collect the front-side current [3] [4] [15].

3.1.2. Structure

The stack is Al/ZnO/CdS/CIGS/Mo/PET, in a substrate configuration (front-side illumination through the TCO window and Al grid). The structural schematic is shown in Figure 2 [3] [5] [16].

3.1.3. Method

We investigate, by numerical simulation, the influence of two key absorber parameters, optical bandgap $E_g$ and electron affinity $\chi$ on the photovoltaic figures of merit (short-circuit current density $J_{sc}$ , open-circuit voltage $V_{oc}$ , fill factor $FF$ , and efficiency $\eta$ ). Calculations are performed using SILVACO ATLAS, by solving Poisson’s equation and the carrier continuity equations coupled with the drift-diffusion transport model [7] [8].

3.1.4. Simulation Parameters

Layer thicknesses follow the reference device specifications from our laboratory when available; the remaining parameters are taken from the literature [3] [7] [8]. A parametric analysis is conducted over the following ranges:

• CIGS bandgap $E_g$ from 1.14 to 1.50 eV;

• Electron affinity $\chi$ from 4.0 to 4.8 eV;

• CIGS thickness from 0.1 to 3.0 μm.

Unless stated otherwise, the absorber doping is fixed at 1 × 10¹⁶ cm⁻³, a value retained from our previous simulations.

Figure 2. Schematic of the simulated CIGS cell structure (substrate configuration).

Numerical convergence. We verified convergence by refining the mesh (halving $\Delta x$ and $\Delta y$ in ZnO/CdS/CIGS and near the electrodes), reducing the voltage sweep step (vstep: 20 mV → 10 mV → 5 mV), and doubling the spectral discretization (120 → 240 wavelengths). Deviations in $V_{oc}$ , $J_{sc}$ , FF, and $J_0$ remained <0.5% (or <0.3 mA·cm⁻² for $J_{sc}$ and <0.3 percentage point for FF. The time per bias point reported by ATLAS ranges from 0.01 to 0.05 s with the final setup.

Table 1 and Table 2 present the optoelectronic and geometric parameters (Table 1), as well as the defect parameters in the various layers (Table 2).

Table 1. Material properties (input parameters used in the simulations).

Materials	CIGS	CdS	ZnO
Optical bandgap $E_{g300}$ (eV)	1.14 - 1.5	2.4	3.3
Thickness $d$ (µm)	0.1 - 3 µm	0.1	0.8
Electron affinity $\chi$ (eV)	4.0 - 4.8	4.5	4.1
Relative dielectric permittivity ${\epsilon }_r$	13.6	10	9
Effective electron state density $N_{C300}$ (cm−3)	2.2. × 1018	2.2. × 1018	2.2. × 1018
Effective hole state density $N_{V300}$ (cm−3)	1.8 × 1019	1.8 × 1019	1.8 × 1019
Electron mobility ${\mu }_n$ (cm2·V−1·s−1)	100	100	100
Hole mobility ${\mu }_p$ (cm2·V−1·s−1)	25	25	25
Electron lifetime ${\tau }_n$ (s)	1 × 10−7	1 × 10−7	1 × 10−7
Hole lifetime ${\tau }_p$ (s)	1 × 10−7	1 × 10−7	1 × 10−7
Acceptor concentration $N_A$ (cm−3)	6. × 1016	-	-
Donor concentration $N_D$ (cm−3)	-	1. × 1018	1. × 1018

Table 2. Defect properties.

Materials	CIGS	CdS	ZnO
Gaussian defect concentration (cm−3)	$N_{DG}=1.\times {\text{10}}^{14}$	$N_{DA}=1.\times {\text{10}}^{15}$	$N_{DA}=1.\times {\text{10}}^{15}$
Gaussian defect concentration (cm−3)	0.1	0.1	0.1
Peak energy $E_{GA}$ and $E_{GD}$ (eV)	0.6	1.2	1.65
Electron capture cross section ${\sigma }_n$ (cm2)	1. × 10−17	1. × 10−17	1. × 10−17
Hole capture cross section ${\sigma }_p$ (cm2)	1. × 10−15	1. × 10−15	1. × 10−15

4. Results and Discussion

4.1. Effect of the Absorber Optical Bandgap

The optical bandgap of the CIGS absorber is given by:

$E_g=1.04+0.64x-0.15x\left(1-x\right)$ (7)

where $x=\text{Ga}/\left(\text{In}+\text{Ga}\right)$ is the gallium content [7].

This relation shows that the CIGS bandgap is tunable from 1.04 to 1.68 eV. By varying $x$ from 0.2 to 0.8, we obtained bandgap values in the 1.14 - 1.50 eV range. In what follows, we analyze how $E_g$ affects the $J\left(V\right)$ characteristic, the short-circuit current density, the open-circuit voltage, the fill factor, and the cell efficiency.

4.1.1. Effect of Absorber Bandgap on the Current-Voltage Characteristic

Figure 3 shows the current-density evolution as a function of voltage for different absorber bandgap values.

Figure 3. Current-density-voltage characteristics for different absorber bandgaps in CIGS.

Figure 3 shows that all J-V curves intersect the current axis at the same point ($J_{sc}=31.15\text{mA}\cdot {\text{cm}}^{-2}$ ), while they cross the voltage axis at different values: 0.61 V, 0.67 V, 0.73 V, 0.79 V, 0.87 V, and 0.98 V. In other words, the short-circuit current remains identical, whereas the open-circuit voltage increases with the absorber bandgap $E_g$ . Under the present simulation conditions, the bandgap does not affect $J_{sc}$ but raises $V_{oc}$ , consistent with a reduced effective saturation current. To substantiate these trends, we examine the effect of $E_g$ separately on $J_{sc}$ and $V_{oc}$ [17].

4.1.2. Effect of Absorber Bandgap on the Short-Circuit Current

As outlined above, Figure 4 reports $J_{sc}$ versus $E_g$ for several absorber thicknesses. Over our parameter range, $J_{sc}$ is nearly invariant with $E_g$ , with minor scatter attributable to thickness-dependent optical losses [17].

Figure 4. Short-circuit current density versus CIGS absorber bandgap for different thicknesses.

Figure 4 shows that for absorber thicknesses between 0.3 and 3 μm, the short-circuit current density remains essentially unchanged as the bandgap $E_g$ is varied from 1.14 to 1.50 eV. In contrast, for a very thin absorber (0.1 μm), $J_{sc}$ changes appreciably, indicating increased optical losses (residual transmission) in an under-thick layer. Hence, over the explored range, $E_g$ has no significant impact on $J_{sc}$ once the absorber is sufficiently thick, while thickness-dependent optics accounts for the deviation at 0.1 μm. The optimum $J_{sc}$ occurs around 0.3 - 0.5 μm, consistent with the integral form of $J_{sc}$ (Equation (2)) and its dependence through EQE [6].

4.1.3. Effect of Absorber Bandgap on Open-Circuit Voltage

Figure 5 shows the variation of the open-circuit voltage as a function of the optical bandgap of the absorber layer, for different thickness values.

Figure 5. Variation of the open-circuit voltage as a function of the optical bandgap of the CIGS absorber, for different thickness values of the layer.

Figure 5 indicates that the open-circuit voltage $V_{oc}$ increases for all thicknesses from 0.1 to 3 μm as $E_g$ rises from 1.14 to 1.50 eV. This trend is attributed to the decrease in effective saturation current with wider bandgap, which, according to Equation (3), yields a larger $V_{oc}$ [18].

4.1.4. Effect of Absorber Bandgap on the Fill Factor (FF)

Figure 6 shows the variation of the fill factor as a function of the optical bandgap of the absorber layer, for different thickness values.

Figure 6. Variation of the fill factor as a function of the optical bandgap of the CIGS absorber, for different absorber thickness values.

From Figure 6, the fill factor improves as $E_g$ increases within 1.14 - 1.50 eV for thicknesses of 0.1 - 0.3 μm. The rise is particularly pronounced (81.9435% → 84.3659%) at 0.3 μm when $E_g$ changes from 1.14 to 1.26 eV. This $FF$ enhancement mainly reflects the dependence of $F{F}_{id}$ , while first-order resistive corrections remain unchanged (Equation (4), Equation (5)).

For ${\chi }_{\text{CIGS}}=4.45\text{eV}$ , the saturation currents simulated under STC are $J_0\left(n=1\right)=1.18\times {10}^{-14}\text{A}\cdot {\text{cm}}^{-2}$ and $J_0\left(n=2\right)=2.16\times {10}^{-8}\text{A}\cdot {\text{cm}}^{-2}$ , consistent with the observed trends in $V_{oc}$ and FF.

4.1.5. Effect of Absorber Bandgap on Efficiency

Figure 7 depicts how the optical bandgap of the CIGS absorber influences the solar cell efficiency for different values of layer thickness.

Figure 7. Variation of the conversion efficiency as a function of the optical bandgap of the CIGS absorber, for different absorber thickness values.

Figure 7 shows that the efficiency η increases (from 14.63% to 27.05%) as $E_g$ grows from 1.14 to 1.50 eV for thicknesses between 0.1 and 3 μm. The gain results from stable $J_{sc}$ (except at 0.1 μm) together with increasing $V_{oc}$ and $FF$ . Therefore, a moderate widening of the absorber bandgap can enhance CIGS device performance.

In summary, the bandgap does not significantly affect $J_{sc}$ beyond 0.3 μm, but it raises $V_{oc}$ , $FF$ , and $\eta$ . Targeting $E_g\approx 1.50\text{eV}$ is thus a sound optimization route [19] [20].

Because optical effects (front-side reflection, residual transmission, and surface losses) are not explicitly modeled here, the integral in (2) tends to overestimate $J_{sc}$ and, consequently, the efficiency $\eta$ . The magnitude of this bias depends on the actual $R_{front}\left(\lambda \right)$ and $EQE\left(\lambda \right)$ of the device.

4.2. Effect of the Absorber Electron Affinity

The electron affinity of a semiconductor is the energy required to lift an electron from the conduction band edge to the vacuum level:

$\chi =E_0-E_c$ (8)

where $E_0$ is the vacuum energy and $E_c$ the conduction-band edge.

We now examine how $\chi$ affects the $J\left(V\right)$ characteristic, short-circuit current, open-circuit voltage, fill factor, and efficiency.

Experimentally, the target electron-affinity range can be reached by tuning the Ga fraction $x=\text{Ga}/\left(\text{Ga}+\text{In}\right)$ during co-evaporation/three-stage selenization (Ga-grading), since for $\text{Cu}\left({\text{In}}_{1-x}{\text{Ga}}_x\right){\text{Se}}_2$ the electron affinity follows $\chi \left(x\right)\approx 4.61-1.162x+0.034x^2\text{eV}$ , and recent work demonstrates such control via engineered Ga profiles [21] [22].

For context between 2023 and 2025, SCAPS-1D modeling studies project CIGS efficiencies above 24%, e.g., 24.43% with a p-Si BSF [23], >31% with an Sb₂S₃ BSF [24], and 24.61% with a CuAlO₂ BSF [25]. On the experimental side for single-junction devices, the best cells reported over the same period remain below 24% (~23% - 23.6% under STC), which underscores the value of the optimizations investigated here (increasing $E_g$ , reducing $J_0$ , and engineering the BSF/contacts) to bring real-world performance closer to the simulated potential.

4.2.1. Effect of Electron Affinity on the Current-Voltage Characteristic

Figure 8 reports the current-density as a function of voltage for several values of the absorber $\chi$ in CIGS.

Figure 8. Current-density-voltage characteristics for different electron affinities of the CIGS absorber.

Figure 8 shows that all J-V curves intersect the current axis at the same point () as the electron affinity $\chi$ is swept from 4.0 to 4.8 eV. In contrast, the voltage-axis intercept varies: about 0.69 V at $\chi =4.0\text{eV}$ , 0.68 V at $\chi =4.2$ or 4.4 eV, and 0.67 V at $\chi =4.6$ or 4.8 eV. Hence, $\chi$ does not materially affect $J_{sc}$ in our range, whereas $V_{oc}$ generally decreases with increasing $\chi$ (with a slight leveling at the upper end). To confirm these trends, we analyze $J_{sc}$ and $V_{oc}$ versus $\chi$ separately [26].

4.2.2. Effect of Electron Affinity on Short-Circuit Current

Figure 9 illustrates the variation of the short-circuit current density as a function of the electron affinity of the CIGS absorber layer, for different absorber thickness values.

Figure 9. Evolution of the short-circuit current density as a function of the electron affinity of the CIGS absorber, for various thickness values.

Figure 9 shows that $J_{sc}$ remains unchanged for absorber thicknesses between 0.3 and 2 μm as $\chi$ varies from 4.0 to 4.8 eV. For a very thin absorber (0.1 μm), $J_{sc}$ is constant from 4.0 to 4.2 eV, then changes as $\chi$ increases from 4.2 to 4.8 eV. Thus, the influence of $\chi$ on $J_{sc}$ emerges only when the absorber is too thin (<0.3 μm), where band alignment and thickness-dependent optics weigh more heavily on carrier collection [9].

4.2.3. Effect of Electron Affinity on Open-Circuit Voltage

Figure 10 shows the evolution of the open-circuit voltage as a function of the electron affinity of the absorber layer, for various thickness values.

As shown in Figure 10, $V_{oc}$ decreases for all thicknesses (0.1 - 3 μm) as $\chi$ rises from 4.0 to 4.6 eV, followed by a slight recovery toward 4.8 eV. This behavior is consistent with an increase in effective saturation current $J_0$ when the band alignment deteriorates (e.g., a conduction-band cliff), which reduces $V_{oc}$ via Equation (3); when the offset approaches a more favorable regime (e.g., a small spike), interface recombination drops and $V_{oc}$ recovers [10] [27].

Figure 10. Evolution of the open-circuit voltage as a function of the electron affinity of the CIGS absorber for various thickness values.

4.2.4. Effect of Electron Affinity on the Fill Factor

Figure 11 shows the variation of the fill factor as a function of the electron affinity of the absorber layer, for various thickness values.

Figure 11. Evolution of the fill factor as a function of the electron affinity of the CIGS absorber for various thickness values.

From Figure 11, the fill factor improves for $\chi$ 4.0 → 4.2 eV and 4.6 → 4.8 eV, while it degrades within 4.2 → 4.6 eV, across all thicknesses (0.1 - 3 μm). This response reflects the combined evolution of $V_{oc}$ (setting $F{F}_{id}$ ) and resistive losses (first-order in $R_s$ and $R_{sh}$ , Equation (4), Equation (5)). A less favorable offset in the 4.2 - 4.6 eV window enhances interface recombination (apparent rise of $J_0$ ), thereby lowering $FF$ ; near 4.0 - 4.2 and 4.6 - 4.8 eV, a better alignment mitigates losses and raises $FF$ .

4.2.5. Effect of Electron Affinity on Efficiency

Figure 12 shows the evolution of the conversion efficiency as a function of the electron affinity of the absorber layer, for various thickness values.

Figure 12. Evolution of the conversion efficiency as a function of the electron affinity of the CIGS absorber for various thickness values.

Figure 12 shows that the efficiency $\eta$ increases when $\chi$ goes from 4.0 to 4.2 eV and from 4.6 to 4.8 eV, but declines between 4.2 and 4.6 eV, for all thicknesses (0.1 - 3 μm). This mirrors the behavior of $FF$ and $V_{oc}$ : the central dip is consistent with an increase of $J_0$ (recombination/leakage) in the less favorable offset region, while the 4.0 - 4.2 and 4.6 - 4.8 eV windows provide a more favorable alignment that enhances $\eta$ [10] [27].

Partial conclusion. The electron affinity affects $J_{sc}$ only for ultrathin absorbers (<0.3 μm), yet it systematically impacts $V_{oc}$ , $FF$ , and $\eta$ . For good performance, $\chi \approx 4.0\text{-}4.2\text{eV}$ and $\chi \approx 4.6\text{-}4.8\text{eV}$ appear favorable [28].

5. Conclusions

This study first reviewed the theoretical background and the two-diode equivalent circuit for CIGS cells, together with the governing equations for their electrical parameters. It then detailed the materials, the device structure, and the TCAD methodology used, SILVACO-ATLAS with drift-diffusion transport coupled to Poisson and carrier-continuity equations [7] [8]. Finally, we quantified the impact of the absorber’s optical bandgap $E_g$ and electron affinity $\chi$ on the figures of merit.

The main findings are as follows:

1) $J_{sc}$ is essentially independent of $E_g$ over 1.14 - 1.50 eV once the absorber is sufficiently thick (≥0.3 μm); a deviation appears at 0.1 μm (enhanced optical losses), while $V_{oc}$ , $FF$ , and $\eta$ increase with $E_g$ .

2) A maximum efficiency of about 27.05% is achieved for $E_g\approx 1.50\text{eV}$ with $d_{\text{CIGS}}=3\mu \text{m}$ , where the rise of $V_{oc}$ and $FF$ compensates the near-invariance of $J_{sc}$ .

3) The electron affinity $\chi$ affects $J_{sc}$ only for ultrathin absorbers (<0.3 μm); however, it systematically impacts $V_{oc}$ , $FF$ , and $\eta$ , with favorable windows around $\chi \approx 4.0\text{-}4.2\text{eV}$ and $\chi \approx 4.6-4.8\text{eV}$ across 0.1 - 3 μm.

These trends support the view that joint engineering of $E_g$ (e.g., via Ga content) and $\chi$ (band alignment at the CdS/CIGS and TCO interfaces) is a robust lever for optimizing CIGS thin-film solar cells [6] [19] [20] [27] and [28]. In the longer term, a broader comparison with other chalcogenide absorbers (e.g., Sb₂Se₃) could refine the performance-sustainability trade-offs highlighted here [29].

Abbreviations

AM1.5G: Standard solar spectrum (Air Mass 1.5 Global)

CdS: Cadmium sulfide (buffer layer, n-type)

CIGS: Cu(In, Ga)Se₂, chalcopyrite absorber (p-type)

EQE: External Quantum Efficiency

FF: Fill Factor

IQE: Internal Quantum Efficiency

J-V: Current-density-voltage characteristic

PET: Polyethylene terephthalate (substrate)

PCE: Power-conversion efficiency

PLD: Pulsed Laser Deposition

STC: Standard Test Conditions (AM1.5G, 25˚C, 1000 W·m⁻²)

TCAD: Technology Computer-Aided Design (device simulation)

TCO: Transparent conducting oxide

ZnO: Zinc oxide (window layer/TCO)

Mo: Molybdenum (back contact)

Al: Aluminum (front grid/contact)

Conflicts of Interest

The authors declare no conflicts of interest regarding the publication of this paper.

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