The energy band alignment of the proposed device is evaluated using the bandgap and electron affinity values listed in Table 1. The conduction band minimum (CBM) and valence band minimum (VBM) positions of each layer are determined using the electron affinity rule. Energy band alignment of the PSC device structure is illustrated in Fig. 2.

PCBM has E_g of about 2.0 eV and a χ of 3.9 eV, giving a CBM near −3.9 eV and a VBM around −5.9 eV. Likewise, C₆₀ exhibits a E_g ~1.7 eV with the same χ value of 3.9 eV, resulting in a CBM of about −3.9 eV and a VBM near −5.6 eV. The Cs₂BiAgI₆ absorber layer has a E_g of 1.6 eV and a χ of 3.9 eV, corresponding to a CBM of about −3.9 eV and a VBM near −5.5 eV.

The conduction band alignment among PCBM, C₆₀, and Cs₂BiAgI₆ is therefore nearly ideal, with an almost-zero conduction band offset. Such a negligible offset provides a barrier-free pathway for electron extraction from the absorber to the ETL side, thereby facilitating efficient electron transport and suppressing interfacial carrier accumulation. In addition, the small valence band offset between C₆₀ and Cs₂BiAgI₆ [ΔE_v = 0.1 eV] helps maintain carrier selectivity and reduces back-transfer losses.

Although CdTe is traditionally used as an absorber material on thin-film solar cell, in the present study, it is employed as a hole-transport layer due to its favorable electronic properties. It has an E_g of about 1.5 eV and a χ of 3.9 eV. That gives a CBM near −3.9 eV and a VBM around −5.4 eV. The energy band alignment analysis reveals a small valence band offset (~0.1 eV) between Cs₂BiAgI₆ and CdTe, which enables efficient hole extraction across the interface. Moreover, the nearly flat conduction band alignment (ΔE_c ≈ 0) helps to block electron backflow and suppress interfacial recombination. In addition, CdTe exhibits relatively high hole mobility and p-type conductivity, which further enhances hole transport toward the back contact. These characteristics make CdTe a suitable HTL candidate in the proposed device architecture despite its conventional use as an absorber material.

Overall, the band structure of the proposed device shows favorable energy-level matching at both the ETL/absorber and absorber/HTL interfaces. The near-flat CB alignment promotes efficient electron collection through PCBM/C₆₀. Whereas the small VB offset between Cs₂BiAgI₆ and CdTe enables effective hole transport. Such a favorable band alignment is expected to reduce interfacial recombination and contribute to the enhanced photovoltaic performance of the simulated perovskite solar cell.

The study examined how the thickness of the ETL layer affects device performance, with the ITO layer fixed at 50 nm, the absorber layer at 2 μm, and both PCBM and CdTe at 200 nm. The ETL thickness varied from 100 nm to 600 nm in 100 nm steps.

Fig. 3 shows the obtained solar cell performance as a function of the C₆₀-electron transport layer (ETL) thickness. As the thickness increases from 100–600 nm, we observe a modest rise in the (J_sc) value, shifting from 23.74 to 23.81 mA/cm². In contrast, the (V_oc) value remains relatively unchanged, as illustrated in Fig. 3a,b. From a carrier-transport perspective, the C₆₀ layer facilitates selective electron extraction while blocking holes due to its favorable conduction-band alignment with the absorber. Increasing the ETL thickness can improve interfacial coverage and reduce defect-assisted recombination at the absorber/ETL interface. This leads to a marginal improvement in electron collection efficiency, which explains the slight increase in Jsc. However, since the conduction band alignment is already nearly ideal (ΔE_c ≈ 0), further increases in ETL thickness do not significantly enhance charge separation, resulting in minimal variation in V_oc. At the same time, increasing ETL thickness introduces additional series resistance, which limits further performance gains. This behavior is consistent with drift-diffusion transport models, where carrier extraction efficiency depends on both interface quality and layer resistance.

Furthermore, the fill factor (FF) increases from 86.06% to 86.19% as the thickness increases. Additionally, the rise in ETL thickness affects the efficiency (Eff), which varies from 22.10% to 22.22%, as shown in Fig. 3c,d.

Efficiency is a function of J_sc, V_oc, and FF. The slight increases in J_sc and FF, combined with stable V_oc, lead to a slight improvement in overall efficiency. This indicates that moderate thickening of the C₆₀-ETL enhances performance, but beyond a certain point, gains plateau or may even reverse due to resistive losses. Thicker ETLs can improve quality and charge extraction, but at the cost of increased series resistance [20,21,22]. Performance benefits are modest, suggesting the system is nearing an optimal ETL thickness. Further thickening could eventually harm performance.

The study investigated how HTL layer thickness influences device performance, with the ITO fixed at 50 nm, the absorber layer at 2 μm, and both PCBM and C₆₀ at 200 nm. The HTL thickness was varied from 100 nm to 600 nm, in 100 nm increments.

Fig. 4 illustrates the effect of varying the thickness of the CdTe hole transport layer (HTL) from 100 to 600 nm on solar cell performance. The J_sc remains constant at 23.76 mA/cm² throughout this range, as observed in Fig. 4a. This indicates that changes in CdTe-HTL thickness have minimal impact on photon absorption or charge carrier generation. This makes sense, as the HTL primarily affects hole transport rather than light absorption, which is dominated by the absorber layer. From a carrier dynamics perspective, the primary role of the HTL is to facilitate efficient hole extraction and transport while blocking electrons. The small valence band offset (~0.1 eV) between Cs₂BiAgI₆ and CdTe enables efficient hole transfer across the interface, minimizing energy barriers for hole transport. As the HTL thickness increases, a slight improvement in V_oc is observed, as shown in Fig. 4b. This behavior can be attributed to reduced interfacial recombination and improved hole selectivity, which enhances the quasi-Fermi level splitting. Additionally, a thicker HTL can improve the built-in electric field distribution near the back contact, contributing to more efficient carrier extraction.

The FF improves slightly from 85.92% to 86.21%. As a result, the Eff experiences a minor enhancement, increasing from 21.90% to 22.21%, as depicted in Fig. 4c,d. The results indicate that HTL thickness optimization primarily influences recombination dynamics and carrier selectivity rather than photogeneration, leading to gradual improvements in V_oc, FF, and overall efficiency.

The study examined how the thickness of the absorber layer affects device performance, with the ITO fixed at 50 nm and both PCBM and C₆₀ at 200 nm, as well as the CdTe at 200 nm. The absorber layer thickness was varied from 100 nm to 2 μm, in 100 nm steps.

Fig. 5 presents the impact of varying the thickness of the Cs₂BiAgI₆ absorber layer, ranging from 100 nm to 2 μm, on the performance metrics of the solar cell. As shown in Fig. 5a, the J_sc initially increases from 24.97 mA/cm² to a peak of 25.32 mA/cm² at thicknesses of 300–400 nm. Beyond this point, J_sc declines, reaching 23.43 mA/cm² at 900 nm, followed by a slight recovery to 23.76 mA/cm² at greater thicknesses. The initial increase in J_sc suggests improved light absorption due to greater material volume. However, beyond a certain thickness of 400 nm increased recombination and poor charge transport likely reduce carrier collection, resulting in a drop in J_sc.

Fig. 5b illustrates that the V_oc consistently increases with thickness, starting at 0.79 V and reaching up to 1.08 V. This behavior may be associated with improved junction operation and reduced effective recombination losses under the optimized device configuration.

Fig. 5c shows that the FF initially drops from 81.67% to a minimum of 67.27% at 400 nm, but then improves to a peak of 86.09% at 2 μm. Consequently, the power conversion efficiency (Eff), shown in Fig. 5d, follows a similar trend, dropping from 16.13% to a minimum of 15.29% at 300 nm before increasing to a maximum of 22.13% at 2 μm thickness. What emerges here is a fairly typical trade-off. Increasing the absorber thickness does help with light harvesting, but it also starts to push against the limits of transport charge. In the case of Cs₂BiAgI₆, this balance becomes even more sensitive because of its indirect bandgap and only moderate absorption.

So, the improvement at larger thickness is not really about the material suddenly performing better optically. It has more to do with how the device is put together. With favorable band alignment and efficient transport layers. It enables improved carrier extraction and reduced recombination, ultimately leading to enhanced overall device efficiency. For that reason, the peak efficiency observed at 2 μm should be understood as the outcome of overall structural optimization. It does not provide evidence that Cs₂BiAgI₆ intrinsically behaves like a highly absorbing direct-bandgap perovskite.

From a practical perspective, achieving such thickness may introduce challenges, including increased bulk defect density and enhanced recombination losses during fabrication. Therefore, the results obtained in this work should be considered as an optimized theoretical scenario. Future experimental studies may explore alternative strategies, such as light trapping or optical enhancement techniques, to achieve similar performance with reduced absorber thickness.

Based on the simulation results discussed in the previous sections, the optimal thicknesses of the individual layers in the solar cell structure were determined to maximize device performance. The finalized configuration includes an indium tin oxide (ITO) layer with a thickness of 50 nm, a PCBM electron-transport layer of 600 nm, a C₆₀ interlayer also at 600 nm, a Cs₂BiAgI₆ perovskite absorber layer of 2 μm, and a CdTe hole transport layer of 600 nm. This carefully engineered layer structure balances efficient light absorption, charge carrier separation, and transport, resulting in high overall device performance.

Fig. 6 presents the current density-voltage (J-V) characteristics of the optimized solar cell under standard illumination conditions. Key performance indicators obtained from the simulation include a J_sc of 23.23 mA/cm², a V_oc of 1.08 V, a R_s of 0.25 Ω·cm², and a R_sh of 7123 Ω·cm². The device also exhibited a high FF of 86.35% and an Eff of 22.33%. These values indicate strong photovoltaic performance and efficient charge carrier dynamics within the cell.

The use of Cs₂BiAgI₆ as a lead-free double perovskite absorber offers significant advantages in terms of environmental safety and material stability compared to conventional lead-based perovskites. Its optimal thickness (2 μm) ensures sufficient photon absorption across the solar spectrum, while the PCBM and C₆₀ layers effectively facilitate electron transport and reduce interfacial recombination. CdTe, widely recognized for its high hole mobility, serves as an efficient hole-transport layer, thereby further enhancing carrier extraction. The low series resistance and high shunt resistance values indicate minimal resistive losses and leakage currents, which contribute to the high fill factor observed. Altogether, these results highlight the potential of the proposed structure for high-efficiency, lead-free solar cells, demonstrating both strong performance metrics and environmentally sustainable material choices.

Fig. 7 illustrates the quantum efficiency (QE) spectrum of the optimized solar cell under standard operating conditions. The QE remains consistently high across a broad wavelength range, demonstrating strong photon-to-electron conversion efficiency. Specifically, in the spectral range of 200–733 nm, the device exhibits a nearly constant quantum efficiency of approximately 96%, indicating effective light absorption and carrier collection in this region. Beyond 733 nm, the QE sharply declines and reaches zero at around 788 nm, marking the cutoff wavelength beyond which the device no longer responds to incident photons.

The high and steady quantum efficiency observed between 200 and 733 nm confirms the excellent optical absorption and charge carrier extraction capabilities of the active layers, particularly the Cs₂BiAgI₆ absorber in combination with the transport layers. The strong QE in the visible and near-UV region implies that most photons in this range are successfully converted into electrical current, which significantly contributes to the high J_sc observed.

The abrupt decline in QE after 733 nm dropping to zero by 778 nm, suggests that photons with wavelengths longer than this threshold do not possess sufficient energy to overcome the bandgap of the absorber material. This behavior aligns with the expected spectral response of perovskite-based absorbers, where the absorption edge is determined by the material’s bandgap. The sharp cutoff indicates minimal sub-bandgap absorption or parasitic losses, which is favorable for efficient device operation. Overall, the QE spectrum reinforces the effectiveness of the material selection and layer design in maximizing light harvesting and charge collection, particularly within the high-intensity portion of the solar spectrum.

One of the inherent limitations of Cs₂BiAgI₆ is its relatively weak absorption in the near-infrared (NIR) region, primarily due to its indirect bandgap nature. As a result, a significant portion of the solar spectrum remains unutilized, which limits the achievable photocurrent density.

To address this limitation, advanced photonic strategies, such as the incorporation of upconversion materials, have been proposed in recent studies [23]. Rare-earth-doped phosphors, such as NaYF₄:Yb³⁺, Er³⁺, and NaYF₄:Yb³⁺, Tm³⁺, are capable of converting low-energy NIR photons into higher-energy visible photons through nonlinear optical processes. These converted photons can then be effectively absorbed by the perovskite layer, thereby enhancing the device’s spectral response.

Although the present study is based on numerical simulation and does not explicitly include upconversion layers, the integration of such materials represents a promising direction for future work to overcome the intrinsic absorption limitations of Cs₂BiAgI₆ and further improve device efficiency.

The simulated energy band diagram of the optimized PSC is shown in Fig. 8. It includes the conduction band edge E_c, valence band edge E_v, and the quasi-Fermi levels for electrons E_fn and holes E_fp along the device thickness.

The band diagram reveals clear discontinuities at the material interfaces, confirming the formation of a multilayer heterojunction structure. At the front side of the device, the conduction band alignment between the ETL layers (PCBM/C₆₀) and the Cs₂BiAgI₆ absorber provides a favorable pathway for electron transport toward the front contact. The small conduction band offset reduces potential barriers for electron extraction and minimizes interfacial recombination losses.

Within the Cs₂BiAgI₆ absorber layer, noticeable band bending is observed, indicating the presence of a built-in electric field across the junction. This internal electric field facilitates the separation of photogenerated carriers, driving electrons toward the ETL side while holes move toward the CdTe layer.

At the absorber/HTL interface, the valence band alignment between Cs₂BiAgI₆ and CdTe enables efficient hole extraction toward the back contact. Meanwhile, the conduction band discontinuity acts as an electron-blocking barrier, suppressing electron back transfer and reducing recombination at the rear interface.

Furthermore, the separation between the electron and hole quasi-Fermi levels inside the absorber confirms effective carrier separation under illumination conditions. Overall, the simulated band structure demonstrates that the proposed device architecture provides favorable energy-level alignment for efficient charge transport and enhanced photovoltaic performance.

The quasi-Fermi level splitting observed in the absorber region corresponds to the photovoltage generated in the device and reflects the capability of the proposed structure to maintain efficient carrier separation.

As shown in Table 2, previously reported different double perovskite solar cells generally exhibit relatively low efficiencies due to intrinsic limitations such as indirect bandgap characteristics and weak absorption. In contrast, the proposed device achieves a significantly higher efficiency of 22.33%.

This improvement is primarily attributed to the optimized double-heterojunction architecture, which enhances charge separation and reduces recombination losses. The incorporation of a bilayer ETL (PCBM/C₆₀) improves electron extraction and transport, while the CdTe layer provides efficient hole extraction due to favorable band alignment. Additionally, absorber thickness optimization plays a key role in improving overall device performance. These results demonstrate the effectiveness of the proposed design strategy in overcoming the limitations of lead-free double perovskite materials.