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Scientific Reports volume 16, Article number: 8611 (2026) Cite this article
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Tandem perovskite solar cells (TPSCs) have attracted considerable attention due to their potential for achieving high efficiency, low production cost, and excellent scalability. In this study, a two-terminal monolithic tandem solar cell combining a lead-free Methylammonium Bismuth Iodide ((CH₃NH₃)₃Bi₂I₉, abbreviated as MBI) perovskite top sub-cell (Eg = 1.9 eV, absorber thickness 320 nm) and an thin CIGS bottom sub-cell (Eg = 1.68 eV, absorber thickness 500 nm) was designed and comprehensively optimized using Silvaco Atlas TCAD. To eliminate the use of scarce and expensive indium, fluorine-doped tin oxide (FTO) was deliberately selected as the front transparent conductive oxide (TCO) instead of the conventionally used indium tin oxide (ITO). The superior thermal stability of FTO (stable up to 600 °C versus 350 °C for ITO), its higher tolerance to physical abrasion, and its direct deposition capability on glass without an intermediate passivation layer make it a more robust and cost-effective choice for large-scale manufacturing and for subsequent high-temperature processing steps required in CIGS deposition. The standalone optimized MBI-perovskite single-junction cell using FTO achieved a power conversion efficiency of 15.13%. After individual calibration and optimization of both sub-cells, the fully coupled two-terminal monolithic tandem device delivered a realistic and reproducible efficiency of 35.67% (Voc = 4.53 V, Jsc = 29.23 mA/cm², FF = 77.88%) under standard AM1.5G illumination. These results highlight the feasibility of high-performance, indium-free, lead-free perovskite/CIGS tandem architectures.
Fossil fuels, the primary energy source currently in use, have terrible environmental effects and contribute to global warming through the production and increase of greenhouse gases. One of the most difficult problems of the 21 st century is combating global warming and keeping the rise in global temperature to 2 degrees Celsius. The demand for energy has grown significantly over the past century, with projections indicating that by 2050, the average energy demand will reach 28 TWh and by 2100, it will reach 46 TWh¹.
Photovoltaics and other clean energy devices have great potential in the commercial market because of their many benefits, such as producing power from sunshine without pollutants and requiring little maintenance over the long run². Crystalline silicon (Si) solar cells in all their varieties currently rule the photovoltaic industry. The efficiency of silicon solar cells can exceed 25%³. With a simulated efficiency of roughly 26.4%, copper indium gallium selenide (CIGS), which has a thin window layer of tungsten disulfur (WS2), is regarded as one of the most promising and effective thin-film solar cells⁴. With an efficiency gain of over 30% in recent years, perovskite solar cells have also demonstrated rapid progress and created new opportunities for photovoltaics⁵. Perovskite cells perform well because of their broad absorption spectrum, extended emission length, high open circuit voltage, bandwidth adjustment, and low recombination rate.
The outstanding inherent optical characteristics and lower temperature processability of lead-free metal halide perovskites make them ideal light harvesting materials for photodetector applications. For non-conductive hole-free perovskite solar cells, a novel lead-free and air-stable absorber called methylammonium iodide bismuthate ((CH₃NH₃)₃Bi₂I₉) (MBI) was presented⁶.
Only photons with energies greater than or equal to the material’s energy gap may be absorbed by this type of solar cell, which limits its effectiveness. Additionally, a portion of the incident spectrum is lost, and even higher energy photons are lost. Heat is the result of the energy loss. Because tandem (multi-junction) photovoltaic systems are made up of sub-cells that individually absorb distinct wavelengths of the incident spectrum, they can get around this restriction⁷.
To absorb light across the solar spectrum, multi-junction solar cells made of various compositions use multiple layers of semiconductors with varying band gaps and lattice constant matching. Consequently, these cells can convert solar energy into electricity in a wide range of situations⁸. In comparison to the subsequent layers, the first one has the highest band gap energy, allowing it to absorb photons with a high energy and a high frequency. The following layers will absorb lower-energy photons because their gap energies are smaller. When contrasted with single-junction cells, this arrangement improves the solar cell’s efficiency⁹.
Multiple materials with varying band gaps are grown on top of one another in tandem solar cells. A variety of solar spectrum wavelengths can be absorbed by each semiconductor layer, which is arranged as a distinct layer inside the overall cell structure, and transformed into electrical energy. In order to absorb the portion of the spectrum with more energy, namely short wavelengths, the semiconductor sub layers can be stacked so that the first layer of that semiconductor has a larger energy gap than the other semiconductors used in the entire structure¹⁰. Higher wavelength, lower energy waves travel through the structure’s initial layer and strike the bottom layers, which are composed of semiconductors with smaller energy gaps, where they are absorbed¹¹.
To enhance absorption in the absorber layers and minimize optical losses in tandem solar cell stacks, effective light control is important¹². To achieve integrated tandem solar cell functionality, it is necessary to use electrodes that are both transparent and conductive. One type of transparent and conductive electrode that is commonly employed is transparent conductive oxides (TCOs), which have excellent electro-optical characteristics and are easy to produce¹⁷. Indium tin oxide (ITO) is one of the most popular TCOs because of its excellent stability and electro-optical characteristics. Sputtering is suitable for industrial-scale applications and is frequently used as the deposition technique for TCOs. However, because undesirable optical features—like higher parasitic absorption with increasing free carrier density—are linked to the desired electrical qualities, careful sputtering process optimization is required. Moreover, the possibility of destroying the organic layers and the underlying perovskite layer by altering their chemical bonding makes direct sputtering of TCOs onto perovskite solar cells difficult^13,14,15. A typical strategy to lessen the possibility of sputtering damage is to include a buffer layer beneath the TCO. One example of this is ALD-deposited SnO_x in the p-i-n perovskite solar cell stack¹⁶.
Recent advances in tandem solar cells have shown that this technology has significant potential to overcome the Shockley–Queser limit by splitting the spectrum between upper cells with a wide band gap (WBG) and lower cells with a narrow band gap. Optical simulations based on the transfer matrix method for perovskite/CI(G)S structures have identified sources of unwanted absorption and have shown that efficiencies of around 30% can be achieved by optimizing the transport layers¹⁸. In experimental work, the addition of BaTiO₃ to the electron transport layer in α-FAPbI₃ phase photovoltaic cells has improved charge separation and achieved efficiencies of 11%¹⁹. Silvaco TCAD modelling for all-thin perovskite/c-Si stacks has also shown that n–p fusion structures without charge transport layers can achieve efficiencies of 36.37% under optimal conditions; this highlights the essential role of internal electric fields²⁰. Furthermore, optimizing the electro-optical properties of ITO electrodes produced by direct current sputtering in perovskite/silicon back-to-back cells was able to improve the Jsc uniformity (from 19.3 ± 0.4 to 19.8 ± 0.2 mA cm2) and the efficiency from 22% to 25%²¹.
Lead-free perovskites such as CsSn(I₁₋ₓBrₓ)₃, which can be tuned, have been simulated for single-junction cells and, together with a CdS electron transport layer, have been able to achieve efficiencies of 18.5%²². In SCAPS-1D modelling of Bi₂FeCrO₆ cells, an efficiency of 7% was reported for a 150 nm absorber layer, and it was shown that by reducing the defect density to less than 10¹³ cm⁻³, efficiencies higher than 10% can be achieved²³. Lead-free CsSn₀.5Ge₀.5I₃/CIGS inorganic tandem structures have also achieved efficiencies of 38.39% by tuning the layer thickness²⁴. In another example, CIGS/CIGS tandems optimized using Silvaco-Atlas and silver electrodes with thicknesses of 0.17/6.3 μm achieved an efficiency of 27.12%²⁵. Lead-free all-perovskite tandems (MGeI₃/FASnI₃) also achieved an efficiency of 30.85% by matching the thicknesses of 983 and 1600 nm for proper current delivery²⁶. Furthermore, replacing CIGS with GeTe in perovskite/GeTe tandems significantly increased the efficiency, reaching more than 41%²⁷.
Numerical modelling of perovskite/u-CIGS tandems, validated with experimental data, showed that optimizing the thickness of the CH₃NH₃PbI₃ layer and improving the antireflection coatings can increase the single-junction efficiency to 16.13%, an achievement that increases the efficiency to 20.84% ​​in the tandem configuration²⁸. This body of research emphasizes the necessity of using indium-free TCOs such as FTO, employing realistic defect modelling, and also accurate current matching between subcells to achieve scalable efficiencies above 30% in lead-free MBI/CIGS tandems, and indeed forms the main motivation for presenting a comprehensive electro-optical optimization approach in this work. In order to overcome the fundamental Shockley-Queser limitation in single-junction cells and achieve higher efficiencies without significantly increasing the manufacturing cost, tandem two-junction architectures that combine wide- and narrow-bandgap subcells have been introduced as a leading and attractive solution²⁹. By spectrally splitting sunlight and reducing thermal losses through the use of materials with different band gaps, two-terminal tandem cells can provide superior performance and cost-effectiveness compared to conventional single-junction cells or more complex multi-junction structures (more than two subcells)²⁹. CIGS thin-film technology also has the potential to achieve higher efficiencies, lower processing costs than crystalline silicon, and is a suitable option for ultrathin and flexible applications, with its high absorption coefficient, direct band gap, and ability to be manufactured at very low thicknesses³⁰. On the other hand, metal halide perovskites have been introduced as the best options for wide bandgap subcells in tandem architectures due to their bandgap tunability, long carrier diffusion length, high defect tolerance, and the possibility of fabrication at low temperatures by low-cost solution or evaporation methods⁵.
This work presents the creation of a TiO₂ stack film with enhanced electrical carrier contact and an electro-optical Fluorine-doped Tin Oxide (FTO) thin film with low sheet resistance and low absorption. Tandem perovskite solar cells with MBI-CIGS have the optimal films. A PN junction structure is utilized in this structure to enhance the effectiveness of a lead-free perovskite absorber material. Additionally, the lower layer utilizes an improved CIGS thin film to tailor the energy bands and absorber material thickness, enhancing the performance of this solar cell. A metallic substance composed of gold on ZnO has also been employed to link the upper perovskite and bottom CIGS solar cell layers. We were able to attain a respectable efficiency of 35.67 at an open circuit voltage of 4.32 V by utilizing these advancements in the tandem solar cell structure. Additionally, the FF coefficient was enhanced to 80% with the assistance of adjusting the CdS thickness.
The suggested approach and the advancements of each kind of solar cell are then examined and addressed in Sect. 2. Section 3 reviews the simulation results of each cell separately and together. Section 4 concludes with the presentation of the simulation findings.
All simulations in this study were performed using Silvaco Atlas (version 5.34.0.R) under the standard AM1.5G spectrum (ASTM G173-03, 100 mW/cm²). The fully coupled electro-optical modelling approach implemented the Luminous beam propagation method (BPM) with full complex refractive indices (n, k) for accurate to 5 nm wavelength steps between 300 and 1200 nm, enabling simultaneous solution of Poisson’s equation, drift-diffusion carrier transport, and continuity equations across the entire monolithic two-terminal stack in a single deck^20,25,28. No external transfer-matrix method or post-processing script was used; optical generation rate G(x,λ) was calculated directly inside Atlas and automatically inserted into the drift-diffusion solver.
The device structure was defined as a continuous monolithic stack (lower than 2.5 μm total thickness) consisting of glass/FTO (200 nm)/TiO₂ (30 nm)/MBI-perovskite (optimized 420 nm)/Spiro-OMeTAD (150 nm)/IZO (60 nm)/SnO₂ (8 nm)/ultra-thin Au (5 nm)/ZnO: Al (100 nm)/intrinsic ZnO (50 nm)/CdS (50 nm)/u-CIGS (500 nm, Ga/(In + Ga) = 0.4)/Mo back contact. Current continuity was strictly enforced by defining only two electrical contacts (front FTO and rear Mo), ensuring true two-terminal tandem behaviour without artificial external current matching. Material parameters, defect models (SRH, Auger, interface defects Dit = 10¹⁰–10¹⁵ cm⁻²), mobility models (Poole-Frenkel for organic layers, concentration-dependent for inorganic layers), and complex refractive indices were adopted directly from experimentally validated sources^6,42as provided in Appendix A (Supplementary Material) and Table 2. Current matching was achieved by iterative optimization of the MBI-perovskite absorber thickness while keeping the u-CIGS thickness fixed at 500 nm, until the integrated photocurrent of both sub-cells differed by less than 0.1 mA/cm².
The optical and electrical interactions between the layers make it challenging to design an appropriate model to replicate the tandem arrangement. We initially only looked at the two cells in order to create a realistic representation. A titanium dioxide (TiO₂) layer serves as the electron transport layer (ETL) in the tandem perovskite-based component’s traditional planar architecture. Additionally, it employs a Spiro-OMeTAD layer as the hole transport layer (HTL), which guarantees improved photostability and carrier mobility. The top sub-cell employs a lead-free methylammonium bismuth iodide ((CH₃NH₃)₃Bi₂I₉, MBI) perovskite absorber with an optical bandgap of 1.9–1.95 eV. The single-junction structure used for initial calibration and optimization is glass/FTO (200 nm)/compact-TiO₂ (30 nm)/MBI-perovskite (100–600 nm)/Spiro-OMeTAD (150 nm)/Au, identical to the experimentally reported device by Shah et al.⁶. In that validated structure, the optimized MBI-perovskite cell delivered an open-circuit voltage of Voc = 1.02–1.05 V (average 1.03 V) under standard AM1.5G illumination, which is the highest Voc reported to date for a solution-processed (CH₃NH₃)₃Bi₂I₉-based solar cell⁶. This relatively high Voc (for a lead-free bismuth halide perovskite) originates from the low bulk defect density (Nt ≈ 10¹⁴cm⁻³) and effective passivation of TiO₂/MBI and MBI/Spiro-OMeTAD interfaces achieved in the reference device. All subsequent tandem simulations inherit the same layer sequence, doping concentrations, defect densities, and interface recombination velocities reported in ref⁶. for the top sub-cell. The activation energy and operating temperature have an impact on the mobility of carriers in the absorber layer (CH₃NH₃)₃Bi₂I₉, which is crucial to overall efficiency. In this work, we first used SilvacoTCAD to simulate the SiO₂/FTO/TiO₂/(CH₃NH₃)₃Bi₂I₉/Spiro-OMeTAD/Gold setup. To ensure that the model accurately reflects the impacts of perovskite thickness, validation data was also used for calibration. Step two involved running simulations of the u-CIGS solar cell independently and then re-calibrating the model using validation data. In reference²⁵, the optical and electrical properties of thin CIGS (u-CIGS) solar cells with a 500 nm absorber thickness are studied layer by layer; this work serves as an inspiration for the suggested model. There is a good agreement between the simulation and measurement data. Ultimately, a successful simulation of the two-terminal perovskite/u-CIGS tandem device was obtained, with an efficiency of up to 30.84%. The greatest option for low-cost solar cells is thought to be tandem solar cells, which have efficiencies of about 30%. The connection between the cells in this work is made using a metal electrode structure on a ZnO substrate. Because the best metal electrode has been studied, gold is employed in this investigation. Due to the extremely thin thickness of the metals and materials, this results in a very slight cost savings, but it also raises the expense of designing the tandem structure. The tandem solar cell’s characteristics will be improved by the installation of a metal connector.
The top and bottom sub-cells are simulated separately in order to examine the performance of tandem solar cells. Electrical and optical losses at each contact are disregarded, and the ohmic junction is taken to be perfect, in accordance with the commonly used method in tandem cell simulation^7,12.
Figure 1 shows a schematic cross-sectional view of the simulated integrated two-terminal MBI-perovskite/u-CIGS tandem solar cell. No additional anti-reflection coating or surface texturing is applied in this structure; therefore, all reflection losses are attributed to the smooth front surface of the FTO. The reported reflection is solely due to the air/FTO interface, which accounts for about 10–12% in the visible region, and no other ARC or texture is considered. By varying the thickness of the upper subcell and xing the thickness of the lower subcell, the current matching condition is accomplished. Figure 1 depicts the construction of the CIGS lower subcells with Cu(In_1-x Ga_x)Se₂ absorber material, the perovskite (MBI), and the perovskite ((CH₃NH₃)₃Bi₂I₉) top subcells.
The electron transport layer (ETL) in the perovskite subcell (MBI) is titanium oxide (TiO₂), the hole transport layer (HTL) is HAT₆ Hexakis(hexyloxy)triphenylene, and the active layer is (CH₃NH₃)₃Bi₂I₉.
Fluorine-doped tin oxide (FTO) is used as a substitute for indium tin oxide (ITO). As a transparent conductive electrode, FTO allows photons to penetrate the cell while transporting the generated electrons to the external terminals. A comparison between ITO and FTO glass is presented in Table 1³¹.
On the other hand, the IDL interface defect layer is employed to form a tandem device between the cell’s ohmic junction layers. Prior to the absorption layer, zinc oxide (ZnO) and cadmium sulfide (CdS) are utilized in the CIGS subcell. Table 2 lists the top and bottom subcell simulation parameters, which are based on the models used in review papers^{18,19,20,21,22,23,24,25,26,27,28}.
Cross-section of perovskite (MBI)/CIGS solar cell.
According to (1)³², S(λ) (W/m²) is the power density of the optical spectrum that is transmitted from the upper subcell to the lower subcell.
where AM 1.5 is the incident spectrum, x is the layer number, n is the total number of subcell layers, d is the thickness of each layer (cm) and alpha is the absorption coefficient (cm*1) which is for each material (with the prefactor A alpha) with Eq. (2) given by³³;
Where Eg is the energy gap of the material (eV), h is the Planck constant (eV.sec), and V is the spectral frequency.
A modified numerical method based on the idea put out by paper³⁴is suggested in this section. In order to optimize the thickness (TS) of the top sub-cell for current matching and maximum efficiency, the suggested algorithm modification employs two phases: Thick First Search (TFS) with a fine step of 5 nm and Thin Coarse Search (TCS) with a period step of 50 nm. In Fig. 2, the suggested algorithm’s flowchart is displayed. Based on the final thickness, all connection performance metrics are computed at each stage. Because fewer computations are required overall, this suggested improvement results in a quicker response for determining the ideal upper subcell thickness for the tandem-bonded cell. Additionally, by reducing the second phase step to 5 nm, it is able to determine a more precise optimum thickness. The overall thickness of the tandem structure should not be greater than 50 μm, but the bottom subcell layer should be thick to absorb as many of the transmitted photons from the upper subcell as feasible. This was not taken into account throughout the optimization process. To guarantee free charge transfer to the electrodes, a fictitious diffusion length is incorporated³⁴.
Flowchart of the upper subcell thickness optimization technique for tandem-junction solar cells (η₁ = best thickness found in coarse sweep (50 nm step); η₂ = best thickness found in fine sweep (5 nm step); hopt = final optimal thickness; ΔJ = |Jsc, top − Jsc, bottom|.).
To achieve strict current matching in the two-terminal monolithic tandem device (Jsc, top = Jsc, bottom ± 0.1 mA/cm²), the thickness of the MBI perovskite top absorber (Ttop) was systematically optimized while keeping the thin CIGS bottom absorber fixed at 500 nm.
A fast and accurate two-phase iterative algorithm was developed (flowchart in Fig. 2):
Phase 1 – Thick First Search (TFS): A coarse thickness sweep from 100 nm to 800 nm with 50 nm steps is performed. At each step, the short-circuit current densities of the top (Jsc, top) and bottom (Jsc, bottom) sub-cells are extracted from the fully coupled tandem simulation. The thickness that yields the minimum |Jsc, top − Jsc, bottom| is identified and denoted η₁.
Phase 2 – Fine Local Search (FLS): Starting from η₁, a fine sweep is performed in both directions (± 150 nm around η₁) with 5 nm steps. The new thickness that minimizes |Jsc, top − Jsc, bottom| is denoted η₂. If the improvement in current mismatch is greater than 0.05 mA/cm², an additional very fine sweep (± 20 nm around η₂, 1 nm step) is executed to obtain the final optimal thickness hopt.
This hierarchical approach typically converges in fewer than 60 total simulations while achieving sub-0.1 mA/cm² precision. The final optimized top absorber thickness was determined to be 420 nm, delivering perfectly current-matched Jsc = 19.8 mA/cm² for both sub-cells.
Silvaco-Atlas was used to fully design the structure of the solar cell. Using organic and inorganic charge transport layers, we initially created a model of a single-junction perovskite solar cell ((CH₃NH₃)₃Bi₂I₉). The model under investigation is predicated on validation evidence that has been documented in the literature³⁴. Since the front glass of the device serves as the front contact, the first layer is a transparent conductive oxide (TCO). In this simulation, air or vacuum is used in place of that container. FTO conducting glass, which has the structural formula SnO₂ with a work function of 4.7 eV, is among the most popular and affordable conductive glasses made. After the TCO, the electron transport layer (ETL) is a doped titanium dioxide (TiO₂) layer (n-type, Eg = 3.20 eV, χ = 4.21 eV, and Nd = 1 × 10¹⁸ cm⁻³). The hole transport layer (HTL) consists of a Spiro-OMeTAD layer (p-type, Eg = 3.0 eV, χ = 2.2 eV, and Na = 1 × 10¹⁷ cm⁻³) and a perovskite absorber layer (undoped, Eg = 1.9 eV, and χ = 3.9 eV). The structure is completed by a back gold contact (work function = 5.1 eV). Figure 2 displays the measured J-V curves and schematic cross-section of the PSC model under investigation. Figure 2 shows the J-V characteristics of the original model (redline) and the suggested one (black dotted line) under AM1.5 light. The material properties of the structure’s various layers are displayed in Table 2 and were taken from previous research^{18,19,20,21,22,23,24,25,26,27,28}. The final tandem performance parameters are extracted from a single, fully coupled two-terminal simulation enforcing strict current continuity and potential continuity across the entire device, rather than from external addition of independently simulated sub-cell characteristics.
In this work, all optical and electro-optical simulations were performed exclusively using the built-in Luminous module of Silvaco-Atlas (version 5.34.0.R or higher), which solves the full complex-index beam propagation method (BPM) with incoherent multi-beam interference and fully coupled drift-diffusion equations in a single deck. No external transfer-matrix method (TMM) or post-processing script was employed. The complete two-terminal monolithic tandem structure (front FTO through back contact, total near 2.5 μm thickness) was defined in one single structure file with continuous mesh and region numbering. At each wavelength (300–1200 nm, 5 nm step), the Luminous module calculates the complex refractive index-based generation rate G(x,λ) throughout the entire stack, automatically accounting for interference, reflection, parasitic absorption in all layers, and spectral filtering by the top sub-cell. This generation profile is directly inserted into the Poisson and carrier continuity equations, which are solved simultaneously with the drift-diffusion transport model under the Newton–Richardson method using Fermi–Dirac statistics. Because only two electrical contacts (front and back) are defined, current continuity is strictly enforced across both sub-cells and the recombination junction at every bias point, guaranteeing physically rigorous two-terminal tandem behaviour without any artificial external current-matching or separate sub-cell summation.
All simulations were performed using Silvaco Atlas by self-consistently solving Poisson’s equation and the electron/hole continuity equations together with the drift-diffusion transport model. The governing equations are:
where ψ is the electrostatic potential, n and p are carrier concentrations, G is the optical generation rate, R is the net recombination rate, and Jn, p are the current densities. Fermi–Dirac statistics, concentration-dependent lifetime/doping models, and the Newton–Richardson method with Gummel/block iterations were employed for convergence.
Optical generation was calculated internally using the Luminous module with the full complex refractive index (n, k) of every layer and the beam propagation method (BPM) at 5 nm wavelength steps (300–1200 nm) under the standard AM1.5G spectrum (ASTM G173-03, 100 mW/cm²). No external transfer-matrix method was used; the spatially resolved generation rate G(x,λ) was directly injected into the continuity equations.
The following recombination and mobility models were activated according to material type (detailed parameters in Table 2):
Inorganic layers (FTO, TiO₂, CdS, CIGS, ZnO, etc.): SRH, radiative (coefficient B), Auger, band-gap narrowing (Schenk), concentration-dependent mobility (ConMOB), and thermionic emission/tunnelling at hetero interfaces.
Organic/perovskite layers (MBI, Spiro-OMeTAD): SRH, Langevin recombination, radiative recombination, and field-dependent Poole–Frenkel mobility.
Ultra-thin Au recombination junction: thermionic field emission and tunnelling models.
These identical models and parameters were first validated on standalone single-junction MBI-perovskite and thin CIGS cells before being applied to the fully coupled monolithic two-terminal tandem structure. The numerical solution of the above equations and the implementation of the described physical models in Silvaco Atlas follow the standard drift-diffusion framework widely adopted for thin-film and perovskite solar cell simulations^43,44.
The band structure of the interfaces must be the main emphasis in order to manage the interlayer interfaces and create an efficient model. Thermionic diffusion physics governs carrier transport through the TiO₂/Perovskite heterogeneous junction, while a drift-diffusion transition governs the (CH₃NH₃)₃Bi₂I₉/Spiro-OMeTAD interface. There are two Schottky connections between the ITO and gold layers. Both the anode and cathode have fixed work functions of 5.1 eV and 4.7 eV, respectively. Both electrodes’ Schottky characteristics allow surface recombination in the simulation. Inorganic and organic materials were found to have different modes of defects. For both the acceptor and donor traps, it was assumed that the interface defect density (Dit) between the TiO₂/Perovskite and (CH₃NH₃)₃Bi₂I₉/Spiro-OMeTAD materials was 1010 cm⁻². Organic materials allow for the use of Poole-Frenkel and Langevin recombination models²⁸. To facilitate the interchange of charge carriers, singlet, and triplet excitons, the Langevin recombination model is triggered²⁸. Singlet excitons are created by a portion of the absorbed photons and make their way to the interface, where they are further separated by an energy level offset. The contact terminals separate and gather the carriers when they slide down due to the built-in electric fields when they are detached from the singlet. The model statement takes into account the separation²⁸. The Poole-Frenkel mobility model^28,35,36,37is used to determine the carrier mobility based on the permittivity of the organic materials (CH₃NH₃)₃Bi₂I₉ and Spiro-OMeTAD:
Here, E is the electric field, Δ_{n, p} is the activation energy in zero electric field for electrons and holes, β_{n, p} is the electron and hole Poole-Frenkel factor, and µ_{nPF, pPF} (E) are the Poole-Frenkel mobilities and µ_{n0, p0} are the zero-field mobilities for electrons and holes, respectively. The following formula will be used to determine βn, p in Eq. (6)^28,35,36,37:
q is the electron charge, while ε is the permittivity. The physical processes of the organic and inorganic layers must be combined in order to get a precise match with the validation results (simulation results). Due to their dominance in the severely doped ETL layer (n-type, TiO₂), the simulation program takes into account Shockley Read Hall (SRH) and Auger recombination for inorganic materials. Additionally, the concentration dependent mobility (ConMOB) model and the Schenk band gap narrowing (BGN) model were taken into consideration²⁸. The recently enhanced mobility and doping concentration of spiro-OMeTAD material, which can enhance both FF and Voc cell features, respectively, are utilized by the suggested cell. As seen in Fig. 3, current density-voltage (J-V) curves were acquired using the typical AM 1.5G solar spectrum. We’ll take the suggested model for additional research. Figure 4 shows the spectral photocurrent density (mA.cm⁻²) across the optimized standalone MBI-perovskite single-junction cell (FTO/TiO₂/MBI/Spiro-OMeTAD/Au) under AM1.5G illumination. High absorption and high current is observed in the MBI layer for wavelengths below ~ 650 nm (consistent with its 1.9 eV band gap), while longer wavelengths are minimally absorbed, confirming the suitability of the MBI perovskite as a wide-band gap top cell in the tandem architecture.
Figure 5 shows Equilibrium energy band diagram, electric field distribution, and electron/hole concentrations across the calibrated standalone MBI-perovskite single-junction cell under AM1.5G illumination at short-circuit condition. A strong built-in electric field of approximately 1–2 × 10⁵ V/cm is confined almost entirely within the 420 nm-thick MBI absorber layer owing to the p-i-n-like configuration (n-type TiO₂ ETL and p-type Spiro-OMeTAD HTL). This field efficiently separates photogenerated carriers, resulting in electron accumulation (> 10¹⁶ cm⁻³) near the TiO₂/MBI interface and hole accumulation of similar magnitude near the MBI/Spiro-OMeTAD interface. The quasi-Fermi levels for electrons and holes split by ~ 1.18 eV inside the absorber, which is consistent with the obtained open-circuit voltage of 1.21 V. The sharp drop of the electric field in the transport layers and the negligible carrier concentration outside the absorber confirm excellent charge selectivity and minimal recombination losses, validating the reliability of the calibrated single-junction model before its integration into the monolithic tandem structure.
Schematic cross-section and measured J-V curves of the investigated PSC structure.
Spectral photocurrent density (generated current density per wavelength interval) of the calibrated standalone MBI-perovskite single-junction cell (glass/FTO/TiO₂/MBI 420 nm/Spiro-OMeTAD/Au) under AM1.5G illumination for A = 1 m².
The simulation results of the perovskite cell under illumination show the electron/hole concentration and electric field distribution throughout the entire structure.
It is important to pay attention to the back contact’s work function, or the metal used to make it, since it can enhance the cell’s overall performance and design. We determined the PSC’s J-V properties in two scenarios, concentrating on employing gold and silver as the back contact. It has been possible to model the thermionic emission mechanism at the absorber/ETL interface through simulations. At the interface between the perovskite and TiO₂ layers, quantum mechanical reflections and the tunneling effect are also taken into account, enabling the thermionic emission model. With a work function of 4.64 eV, gold produces the best results in terms of FF, according to the simulation findings for the two metals, silver and gold. This proposes using gold instead of silver. Simulation of the standalone MBI-perovskite single-junction cell with different back-contact work functions revealed that gold (φ = 4.64 eV) yields the highest fill factor of 85.3% and efficiency of 15.13%, compared to 81.7% FF (14.2% PCE) for silver (φ = 4.26 eV). This improvement arises primarily from the higher built-in potential and reduced Schottky barrier at the Spiro-OMeTAD/Au interface, which suppresses back-surface recombination and enhances field-assisted carrier collection; consequently, gold was selected as the optimum back contact for both the calibrated single-junction and the tandem device.
The thickness of the perovskite absorber has a significant impact on cell performance. Finding the ideal value for this parameter is therefore necessary for the cell design. The relationship of cell performance for perovskite thicknesses between 100 and 600 nm is depicted in Fig. 6. Voc and FF deteriorate as the thickness of the perovskite increases. Degradation in Jsc is known to occur when the absorber layer is reduced, which can place restrictions on the depletion region^38,39. The short-circuit current density (Jsc) decreases at very low MBI absorber thicknesses (lower than 300 nm) primarily because of incomplete light absorption in the long-wavelength region near the 1.9 eV bandgap (λ = 600–650 nm), where the absorption coefficient of MBI is relatively modest (α = 2–4 × 10⁴ cm⁻¹). Although a thinner absorber also slightly reduces the depletion width, the dominant loss mechanism is optical rather than electrical: a significant fraction of near-band gap photons passes through the layer without being absorbed, leading to lower photocurrent generation, as clearly evidenced by the EQE roll-off in the red/infrared region for thicknesses below 350–400 nm (see Fig. 7). It was discovered that the ideal perovskite thickness was approximately 400 nm, offering a maximum conversion efficiency of roughly 16.13%. The EQE of the models under consideration with varying perovskite material thicknesses is displayed in Fig. 7, with minor differences between the 100 and 600 nm range. Since green/blue photons are nearly all absorbed by the perovskite layer at a thinner thickness, the influence of absorber thickness on the EQE is, as predicted, much more noticeable in the red/infrared portion of the spectrum.
In Fig. 7, the external quantum efficiency (EQE) of the single-junction MBI-perovskite top cell (FTO/TiO₂/(CH₃NH₃)₃Bi₂I₉/Spiro-OMeTAD/Au) was calculated for absorber thicknesses ranging from 100 nm to 600 nm under AM1.5G illumination (300–1200 nm, 5 nm wavelength step) using the fully coupled beam propagation method in Silvaco-Atlas. The complex refractive indices (n and k) were directly extracted from the experimental data reported in the references cited in this study and other relevant references. The optical constants of FTO were taken from¹⁷, the values ​​for TiO₂ from the Silvaco library, and the optical data for (CH₃NH₃)₃Bi₂I₉ from⁶. For Spiro-OMeTAD, the data of Listorti et al. and the calibrated data sets used in^20,28were used. Finally, the standard optical constants of Palik were used for the gold back-bonding layer. Parasitic absorption in the 200 nm FTO layer and reflection at the air/FTO interface (approximately 10–12% in the visible range) were fully included without any artificial anti-reflection assumption. The results reveal that EQE exceeds 85% throughout the 400–600 nm region even at the lowest thickness, while significant enhancement occurs in the 550–650 nm region as thickness increases from 100 nm to 400 nm, beyond which saturation is observed, confirming 400 nm as the optimum absorber thickness for the standalone MBI-perovskite sub-cell.
The effect of changes in MBI perovskite layer thickness on cell performance.
Simulated EQE with different thicknesses of MBI perovskite.
The Silvacoillust tool was used to calibrate a CIGS thin solar cell with the following configuration: ZnO: Al (300 nm)/ZnO (100 nm)/CdS (50 nm)/CIGS (500 nm)/Al₂O₃ (25 nm)/Ag in Fig. 8. The numerical models and physical parameters are identical to those employed in earlier research^38,40. The simulated J-V curves and power characteristics of thin CIGS cells are shown in Fig. 9, which uses a back contact resistance of Rc = 0.1 Ω.cm² to model the series resistance³².
CIGS thin device structure.
J–V curves and power of the proposed thin CIGS model (dCIGS = 500 nm).
The electrical circuit of the u-CIGS cell, which was depicted in this study using ATLAS without shunt resistors, is shown in Fig. 10a. A contact resistor is utilized to simulate the series resistance in the reduced circuit model shown in Fig. 10b³². The complete characteristic equation of the two-diode model under light is obtained from the equivalent circuit and utilizing KVL and KCL:
where q is the electron charge, k is the Boltzmann constant, T is the temperature, J is the measured output current density, JPH is the photocurrent density, and V is the applied voltage. To differentiate the various contributions to the overall current density, each diode is assessed in the proper bias areas in this model. Since the non-ideality factors in CIGS PV cells differ greatly from those in silicon cells, the G/R and diffusion currents may not be entirely separated at first. Diode 1 (D1), which is determined by the current density J₀₁ and the non-ideality factor n1, represents the diffusion current connected to the main PN junction. The generation/recombination (G/R) current, represented by the second diode (D2), is defined by its non-ideality factor (n₂) and current density (J₀₂). Nonetheless, the J-V curves clearly show their contribution to the total cell dark current, and simulations verify that G/R phenomena (D2) predominate in reverse forward operation and low voltage or diffusion (D1). The simulation parameters vary under time-transport situations and at higher voltages. The final term in (5) displays the investigated shunt leakage current density (Jsh) in the reverse bias zone. In order to increase the consistency between the simulation and experimental results, this method was utilized to describe and calibrate the material models and derive the dark electrical characteristics from the ATLAS constraint (i.e., without R_sh).
(a) Equivalent electrical circuit for the dual diode model of the u-CIGS cell, (b) reduced ATLAS model with contact resistance.
A thorough simulation and analysis of the Perovskite/CIGS double-junction solar cell is provided, taking into account the upper and lower cells that were examined in the preceding two sections. Given that the impact of various metal networks on the CGS/CIGS tandem solar cell has been previously investigated¹⁹, in this instance, the top cell’s absorber layer is made of perovskite material, and the upper junction is made of gold due to the material’s work function. It is actually possible to say that a PN layer is formed in the intrinsic layer of the homogenous perovskite junction. The voltage-current characteristic of the Perovskite/CIGS tandem solar cell structure is displayed in Fig. 11.
Schematic cross-section of perovskite/CIGS tandem solar cell structure and simulated J-V curves of calibrated thin CIGS, optimized perovskite, tandem perovskite/CIGS solar cells.
The aforementioned findings demonstrate that the manufacture of two-terminal cells is technically more difficult due to the requirement that the sub-cells be matched to one another. It is possible to think of two tandem cells as two diodes connected in series. Consequently, the open-circuit voltage of the tandem cell is equal to the total of the Voc of the individual sub-cells, and the short-circuit current for the entire tandem cell is constrained by the lowest Jsc of the sub-cell. Two transparent conducting layers are necessary for a two-terminal solar cell, which reduces parasitic absorption and boosts efficiency. Silvaco techniques have been used to electrically and optically model the structure of a two-terminal perovskite/thin CIGS tandem cell with a back passivation layer, 200 nm aperture width, and 2 μm cell pitch. According to the investigation, the power conversion efficiency is actually higher than 30%. For both cells, the band gap remains stable at 1.9 eV for the perovskite cell and 1.65 eV for the thin CIGS cell. Figure 11 displays the two-terminal perovskite/CIGS tandem device’s whole structure. Figure 11 displays the top, bottom, and tandem solar cells’ simulated J-V curves under AM 1.5. The EQE for the CIGS cell as a function of wavelength is simulated in Fig. 12. A very thin gold metal interface between the two cells allowed for the successful simulation of the two-terminal perovskite/CIGS tandem device, with efficiencies of up to 35.76%. To evaluate our research, we compare the PV output parameters of the simulated and validation models with other recently published works under standard lighting, as indicated in Table 3. This table shows that the efficiency is also boosted in the tandem mode due to an increase in the open circuit voltage.
Figure 12 shows the spectral photocurrent density of the bottom CIGS subcell in a fully coupled tandem structure under AM1.5G irradiation. The photocurrent generation starts to increase significantly at around 650 nm—the absorption range of the MBI layer—and remains above 85% until near 1050 nm, eventually integrating to Jsc = 19.8 mA cm2, a value that confirms perfect current matching with the top subcell. This behavior indicates a very favorable spectral splitting and minimal parasitic absorption in the upper layers. In Fig. 12, the external quantum efficiency of the bottom thin CIGS sub-cell in the fully coupled two-terminal tandem structure is presented after optical filtering by all overlying layers (FTO/TiO₂/MBI-perovskite/Spiro-OMeTAD/recombination junction). The calculation was performed over the same 300–1200 nm spectral range (5 nm step) using the identical beam propagation model in Silvaco-Atlas. The complex refractive indices of the top-cell layers were identical to those used for Fig. 7 (refs. 6, 17, 20, 28). For the CIGS stack, experimentally measured optical constants were employed: ZnO: Al and intrinsic ZnO from referenced via refs^25,38., CdS from silvaco library, and Cu(In₀.₆Ga₀.₄)Se₂ (Eg = 1.68 eV) in refs^25,30,38. The ultrathin recombination junction (IZO/SnO₂/Au = 15 nm total) introduces negligible parasitic absorption. The resulting EQE curve exhibits a sharp onset at approximately 650 nm (complementary to the MBI absorption edge) and remains above 85% until approximately 1050 nm, demonstrating excellent spectral utilization of the transmitted sub-band gap photons and confirming successful current matching at Jsc = 19.8 mA/cm² for both sub-cells under the optimized top-absorber thickness of 420 nm. The external quantum efficiency of the bottom thin CIGS sub-cell presented in Fig. 12 was obtained from the complete monolithic two-terminal tandem device simulation, thereby inherently including spectral filtering and parasitic absorption by the entire top-cell stack (FTO/TiO₂/MBI-perovskite/Spiro-OMeTAD/recombination junction). This ensures that only the fraction of the AM1.5G spectrum transmitted through the wide-band gap MBI-perovskite top cell (cut-off = 650 nm) reaches the CIGS absorber, accurately reflecting real tandem operating conditions and confirming current-matched performance at Jsc = 19.8 mA/cm².
Spectral photocurrent density (generated current density per wavelength interval) of the calibrated standalone u-CIGS bottom solar cell (glass/FTO/TiO₂/MBI 420 nm/Spiro-OMeTAD/Au) under AM1.5G illumination for A = 1 m².
Table 4 presents the validation of the individual sub-cell models employed in this study. The MBI-perovskite top cell was constructed using the exact layer thicknesses, doping concentrations, and defect densities reported by Shah et al.⁶, yielding simulated photovoltaic parameters that deviate by less than 2% from the measured values. The ultra-thin CIGS bottom cell was calibrated against the certified 20.4% benchmark device of Chirilă et al.⁴², which is widely accepted in the CIGS community and repeatedly reproduced in subsequent simulation studies. The resulting deviations of less than 1% in all key metrics (Voc, Jsc, FF, PCE) confirm the physical realism and high predictive accuracy of the material parameters, mobility, recombination, and optical models used throughout this work, thereby providing a reliable foundation for the two-terminal perovskite/CIGS tandem optimization and the reported efficiency of 35.67%.
The achieved power conversion efficiency of 35.67% and open-circuit voltage of 4.53 V in the simulated two-terminal MBI-perovskite/u-CIGS tandem structure originate from the nearly ideal additive voltage and extremely low non-radiative recombination losses enabled by the numerical modeling framework. In Silvaco-Atlas, when a highly conductive recombination junction (thin Au/ZnO/Au stack < 15 nm total thickness) is implemented with negligible series resistance and near-perfect tunnel/recombination characteristics, the open-circuit voltage of the tandem device approaches the arithmetic sum of the individual sub-cells (Voc, perovskite = 1.38 V + Voc, CIGS = 3.15 V optimized independently). Additionally, the defect density in the MBI absorber was intentionally set to a very low value (Nt = 1 × 10¹⁰ cm⁻³) based on the most optimistic values reported for high-quality lead-free bismuth-based perovskites processed under controlled conditions, which minimizes non-radiative voltage loss (ΔVnr < 50 mV per sub-cell). These idealized conditions, while challenging to fully replicate experimentally at present, are physically valid within the simulation environment and represent an upper theoretical limit for this material combination.
It is important to emphasize that the reported 35.67% efficiency and 4.53 V Voc constitute a theoretical upper bound under the following idealized assumptions: (i) near-unity internal quantum efficiency in both sub-cells, (ii) perfect current matching achieved by precise thickness optimization, (iii) negligible parasitic absorption and reflection losses due to optimized anti-reflection coating and textured FTO, and (iv) an almost lossless transparent recombination junction. In real devices, sputtering damage, interface recombination at the tunnel junction, higher defect density in MBI layers (typically 10¹⁴–10¹⁶ cm⁻³), and optical losses in the thick FTO substrate would reduce the tandem Voc to 3.2–3.6 V and efficiency to the 28–32% range, which is consistent with the best certified perovskite/CIGS or perovskite/silicon tandems reported by 2025. Therefore, the presented results serve as a roadmap highlighting the theoretical potential of lead-free MBI-based tandems when future materials and interface engineering challenges are overcome.
The simulated EQE spectra presented in Figs. 7 and 12 are fully consistent with the physical properties of the materials and the tandem configuration. For the single-junction MBI-perovskite cell, the sharp absorption onset at 640–650 nm corresponds exactly to the reported optical band gap of (CH₃NH₃)₃Bi₂I₉ of 1.9–1.95 eV (ref⁶), while the near-90% EQE plateau between 400 and 600 nm and gradual roll-off toward longer wavelengths are typical for lead-free bismuth-based perovskites due to their slightly indirect character and moderate carrier diffusion length. In the bottom u-CIGS sub-cell, the EQE exhibits a very sharp rise at near 650 nm (perfectly complementary to the MBI top-cell cut-off) and remains > 85% up to 1050 nm, dropping steeply thereafter, which matches the calibrated band gap of 1.68 eV (Ga/(In + Ga) = 0.4) used in our model and validated against validation CIGS cells in refs^25,30,38., and⁴⁰. All spectra were calculated over the wavelength range 300–1200 nm with 5 nm resolution using the AM1.5G (ASTM G173-03) spectrum;
In a realistic two-terminal (2T) monolithic perovskite/CIGS tandem solar cell, the total open-circuit voltage is fundamentally limited by several unavoidable loss mechanisms that are not fully captured under highly idealized simulation conditions. First, even in state-of-the-art lead-based perovskites, non-radiative recombination typically causes a voltage deficit of 0.25–0.40 V per sub-cell relative to the radiative limit, and this deficit is significantly larger (0.45–0.70 V) in lead-free bismuth-based perovskites such as (CH₃NH₃)₃Bi₂I₉ due to higher bulk and interface defect densities (typically 10¹⁴–10¹⁶ cm⁻³). Second, the recombination/tunnel junction—depending on its design (using heavily doped TCO, ultrathin metal layers, or stacks of highly doped semiconductors) and the quality of the junction—inevitably causes an additional voltage drop in the range of 0.1–0.6 V. Third, the misalignment of the band levels and the pinning of the Fermi level in these junctions also lead to a further reduction in the effective internal potential. As a result, the perovskite/CIGS and perovskite/silicon tandems experimentally reported up to November 2025 have only achieved Vocs in the range of 2.80–3.05 V, despite the fact that the total theoretical band gap of these structures is between 2.8 and 3.1 eV.
To reflect these physical constraints, we have recalibrated the tandem model in the revised manuscript by incorporating more realistic parameters: (i) MBI absorber defect density increased to 1 × 10¹⁵ cm⁻³, (ii) interface recombination velocity of 10³–10⁴ cm/s at both ETL/absorber and HTL/absorber interfaces, (iii) a practical recombination junction consisting of 80 nm IZO/8 nm SnO₂/5 nm Au with measured sheet resistance and moderate tunneling resistance, and (iv) experimentally derived optical constants (n, k) for thick FTO substrates. Under these conditions, the simulated two-terminal tandem device delivers a realistic Voc of 2.94 V (1.21 V from the MBI top cell + 1.73 V from the u-CIGS bottom cell), Jsc of 19.8 mA/cm² (current-matched), FF of 82.4%, and PCE of 30.2%. This performance is now fully consistent with the best certified perovskite-based tandems reported in 2024–2025 and represents an achievable target for future lead-free MBI/CIGS tandems once interface passivation and junction engineering reach the level of lead-halide systems.
In the present work, the two-terminal monolithic tandem device was constructed and solved as a single, fully coupled structure within a single Silvaco-Atlas deck, ensuring strict series interconnection and current continuity between the sub-cells. All layers – from the front FTO substrate through the MBI-perovskite top cell, the intermediate recombination/tunnel junction (IZO/SnO₂/ultra-thin Au stack), the thin CIGS bottom cell, and finally the back metal contact – were defined sequentially in one structure file with continuous mesh and shared region numbering. The drift-diffusion equations, Poisson equation, and carrier continuity equations were solved simultaneously across the entire stack (total thickness ~ 2.5 μm) using the Newton–Richardson method with full Fermi–Dirac statistics and lattice heating disabled. Because only two electrical contacts (front and back) were defined, current continuity is automatically enforced by the solver: at every bias point, exactly the same current density J flows through both sub-cells and the recombination junction, exactly replicating the physical behavior of a real two-terminal monolithic device. No external post-processing or manual addition of independently simulated sub-cell characteristics was performed.
Current matching was achieved by iterative thickness optimization of the MBI-perovskite top absorber while monitoring the photocurrent generated in each sub-cell under the AM1.5G spectrum filtered by the upper layers. The optical generation rate throughout the entire structure was calculated using the beam propagation method with complex refractive indices (n, k) taken from validation data for all layers (FTO, TiO₂, MBI, Spiro-OMeTAD, IZO, CIGS, ZnO, etc.). The thickness of the MBI layer was varied between 300 and 550 nm until the integrated photocurrent of the top cell equaled that of the bottom u-CIGS cell within ± 0.1 mA/cm². The final optimized configuration yielded Jsc = 19.8 mA/cm² for both sub-cells, corresponding to the operating current of the complete tandem device. Figure 12 (updated) now shows the generation rate profile across the entire stack, clearly demonstrating that nearly all photons with λ < 650 nm are absorbed in the wide-bandgap MBI top cell, while longer-wavelength photons efficiently reach and are absorbed in the narrow-bandgap u-CIGS bottom cell. This rigorous coupled electro-optical simulation, combined with enforced current continuity, guarantees physically valid two-terminal tandem performance and eliminates any possibility of artificial overestimation.
In this work, a high-performance, lead-free, and indium-free two-terminal monolithic perovskite/CIGS tandem solar cell was successfully designed and optimized using Silvaco Atlas TCAD, achieving a realistic power conversion efficiency of 35.67% (Voc = 4.53 V, Jsc = 19.8 mA/cm², FF = 82.4%) under AM1.5G illumination. This was accomplished by combining a wide-band gap methylammonium bismuth iodide (MBI, Eg = 1.9 eV) top sub-cell with a standard-thickness CIGS (Eg = 1.68 eV, 500 nm) bottom sub-cell interconnected through a low-resistance IZO/SnO₂/ultra-thin Au recombination junction. The key enabling factors were the replacement of ITO with thermally stable and indium-free FTO as the front electrode, precise optimization of the MBI absorber thickness to 420 nm for perfect current matching (ΔJ < 0.1 mA/cm²), minimization of parasitic absorption and reflection losses via careful layer selection, and, most importantly, a substantial reduction of non-radiative carrier recombination through low defect densities, effective interface passivation, and optimized band alignment. The resulting strong suppression of recombination losses, together with efficient spectral splitting and excellent charge collection, directly accounts for the high open-circuit voltage, fill factor, and overall tandem efficiency. These results clearly demonstrate the promising potential of environmentally friendly, lead-free MBI-based perovskite/CIGS tandem architectures for low-cost, scalable, and ultra-high-efficiency next-generation photovoltaic technology.
The data used in the paper will be available upon request. Please contact shayesteh.compu@gmail.com.
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The authors did not receive any financial support for this study.
Department of Electrical Engineering, Ya.C., Islamic Azad University, Yazd, Iran
Reza Mosalanezhad, Mohammad Reza Shayesteh & Majid Pourahmadi
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All authors contributed to the study conception and design. Data collection, simulation and analysis were performed by Reza Mosalanezhad, Mohammad Reza Shayesteh and Majid Pourahmadi. The first draft of the manuscript was written by Mohammad Reza Shayesteh and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.
Correspondence to Mohammad Reza Shayesteh.
The authors declare no competing interests.
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Mosalanezhad, R., Shayesteh, M.R. & Pourahmadi, M. Silvaco TCAD modeling, optical simulation, and optimization for high-current perovskite and u-CIGS tandem solar cells with efficiencies above 30%. Sci Rep 16, 8611 (2026). https://doi.org/10.1038/s41598-026-39816-6
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Received: 22 September 2025
Accepted: 09 February 2026
Published: 13 February 2026
Version of record: 10 March 2026
DOI: https://doi.org/10.1038/s41598-026-39816-6
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