Design and Optimization of Cs₂AgBiBr₆/AgBiS₂ Two-Terminal Tandem Solar Cells for High-Efficiency Lead-Free Photovoltaics

Abstract

The ternary chalcogenide AgBiS₂ has emerged as a promising lead-free photovoltaic absorber due to its high optical absorption, tunable bandgap (∼1.3 eV), and nontoxic composition. In this work, we present a comprehensive numerical study of AgBiS₂-based thin-film solar cells using a one-dimensional solar cell capacitance simulator (SCAPS-1D). The influence of absorber thickness, defect density, bandgap variation, and charge transport layers on device performance is systematically analyzed. The optimized single-junction architectureFTO/TiO₂/AgBiS₂/Cu₂Oachieves a simulated power conversion efficiency (PCE) of 13.98% under AM1.5G illumination. Because of its high absorption, a two-terminal tandem structure combining AgBiS₂ as the bottom cell with Cs₂AgBiBr₆ (top cell) is also modeled, achieving a PCE of 23.47% after current matching. Simulations reveal that AgBiS₂ thickness and defect density critically impact both J _sc and V _oc, while Cu₂O and TiO₂ provide optimal band alignment and charge extraction. The results demonstrate the potential of AgBiS₂ as an efficient, environmentally benign absorber for next-generation tandem photovoltaics and establish theoretical design guidelines for future experimental development.

1. Introduction

Global technological advancement and urbanization require an increasing amount of energy that has led scientists to investigate renewable energy sources to reduce dependency on traditional fossil fuels. The photovoltaic industry promises to lead the renewable energy supply because of abundant solar irradiance and decreasing levelized cost of energy, with silicon solar cells primarily occupying the market. In recent decades, thin-film solar cells have emerged as solutions to further reduce costs because of their cheap fabrication process, high power conversion efficiency (PCE), and good stability. , Among these, Pb-based perovskite solar cells have had a maximum reported efficiency of 25.8% with FAPbI₃, but these materials are toxic due to the presence of Pb. The Pb-free perovskite-based materials that are currently being investigated are mainly Sn-based, which oxidize very quickly from Sn²⁺ to Sn⁴⁺ under ambient conditions.

Recently, chalcogenides have gathered a lot of attention as promising alternatives to perovskite-based solar cells because of their optimum tunable bandgap, exceptionally high absorption coefficient, and good stability. AgBiS₂, a ternary chalcogenide-based semiconductor material consisting of group I–V–VI₂ elements with a bandgap of 1–1.3 eV, was found to have an absorption coefficient of 5–8 × 10⁵ cm^–1, which is 5–10 times higher than currently researched absorbers such as perovskites, CIGS, CZTS, etc. The first AgBiS₂ solar cell was demonstrated in 2016 by Bernechea et al., who used hot injection method to synthesize a complete stack of AgBiS₂ solar cells with an indirect bandgap of 1.3 eV, yielding an efficiency of 6.31% a with the MoO₃/Polymer PTB7/AgBiS₂/ZnO/indium doped tin oxide (ITO) stack. Although investigations into different synthesis methods and DFT studies on material properties were previously investigated for this material, − this work inspired a further close investigation into AgBiS₂ absorbers. In 2022, Wang et al. reported a PCE of 9.17%, which was reported with a ITO/SnO₂/ AgBiS₂/ hole transport layer (HTL)/MoO₃/Ag stack via cation disorder engineering, which remains the highest reported efficiency until date. Despite these experimentally promising results, studies focusing on the optimum thickness, defect density, doping concentration, bandgap tuning, suitable transport layers and compatibility in a multijunction architecture etc. remain largely limited.

As single-junction solar cells are limited by the Shockley–Queisser limit, the current research direction in solar cells focuses on tandem architectures to surpass it, with 4-terminal solar cells gaining the highest reported PCE of 47.6%, as of August 2025. Because of its high absorption coefficient as well as tunable narrow band gap, we hypothesize that AgBiS₂ is an ideal candidate for the bottom subcell in 2T tandem architectures where the top subcell has a wide band gap.

Therefore, in this work, we perform a comprehensive numerical study on AgBiS₂ solar cells both as standalone single-junction and tandem with Cs₂AgBiBr₆ as top subcell. At first, we have calibrated the current–voltage characteristics of a single top subcell (Cs₂AgBiBr₆) and bottom subcell (AgBiS₂) with experimental results published in the literature. Using this calibrated environment, we have optimized AgBiS₂ by varying its thickness, electron and hole transport layers, temperature, defect density, etc. After that, we connected the bottom subcell AgBiS₂ with Cs₂AgBiBr₆ in series for 2T configuration with current matching, where the AM 1.5G solar spectrum is incident on the top subcell and the filtered spectrum from top cell is incident on the bottom subcell. Figure shows the structure of our proposed 2T cell. We have found that a standalone AgBiS₂ cell with a thickness of 400 nm with TiO₂ and Cu₂O electron transport layer (ETL) and HTL, respectively, yields a PCE of 13.98% under standard operating conditions (300 K temperature, AM 1.5G). While used as a bottom subcell in 2T tandem architecture with Cs₂AgBiBr₆, which was simulated to have a standalone PCE of 13.53%, the same stack with 350 nm thickness yields an efficiency of 23.47%. In addition, we have discussed potential challenges in achieving this theoretical upper bound result from an experimental perspective. We believe this work will contribute to further development in AgBiS₂-based standalone, as well as tandem solar cell architecture design and implementation.

1.

Proposed 2T tandem cell showing AgBiS₂ as the bottom subcell and Cs₂AgBiBr₆ as the top subcell with corresponding transport layers. The top subcell is illuminated by standard AM 1.5G and the bottom subcell absorbs the filtered spectrum from the top subcell.

2. Device Structure and Simulation Methodology

The simulations presented in this work were performed using SCAPS-1D. SCAPS-1D software (Solar Cell Capacitance Simulator One dimension) is a one-dimensional solar cell simulation program developed at the department of electronics and information systems (ELIS) of the University of Gent, Belgium. SCAPS-1D numerically solves the one-dimensional equations that govern the semiconductor material such as Poisson’s equation, carrier continuity equation, and transport equations under steady state conditions. The primary governing equations of this model include the Poisson equation, carrier continuity equation, and electron and hole current density equations respectively given by

$$\frac{{\partial }^2\mathit{\psi }}{\partial x^2}=-\frac{\partial \mathit{E}}{\partial \mathit{x}}=-\frac{\rho }{{\epsilon }_{\mathrm{s}}}=-\frac{q}{{\epsilon }_{\mathrm{s}}}[\mathit{p}-\mathit{n}+N_{\mathrm{D}}^{+}(\mathit{x})-N_{\mathrm{A}}^{-}(\mathit{x})\pm N_{\mathrm{def}}(\mathit{x})]$$ 1

$$\frac{\partial j_{\mathrm{n}}}{\partial \mathit{x}}+\mathit{G}-U_{\mathrm{n}}(\mathit{n},\mathit{p})=\mathbf{0}$$ 2

$$-\frac{\partial j_p}{\partial \mathit{x}}+\mathit{G}-U_{\mathrm{p}}(\mathit{n},\mathit{p})=\mathbf{0}$$ 3

$$j_{\mathrm{n}}=q_{\mathrm{n}}{\mu }_{\mathrm{n}}\mathit{E}+\mathit{q}{D}_{\mathrm{n}}\frac{\partial \mathit{n}}{\partial \mathit{x}}$$ 4

$$j_{\mathrm{p}}=q_{\mathrm{p}}{\mu }_{\mathrm{p}}\mathit{E}+(-\mathit{q})D_{\mathrm{p}}\frac{\partial \mathit{p}}{\partial \mathit{x}}$$ 5

where ψ is the electrostatic potential, ρ is the space charge density, N_D (N_A ) are the ionized donor (acceptor densities), j _n, j _p are the electron and hole current densities; U _n(U _p) is the net electron (hole) recombination rate; G is the electron–hole generation rate, μ_n(p) is electron (hole) mobility, and D _n(p) is diffusion coefficient of electrons (holes). SCAPS-1D software extracts the basic characteristics of the solar cell, such as the J–V Characteristics, Quantum efficiency, band diagrams, generation and recombination rates, and cell current densities.

Figure was used for this simulation. For the top cell, the double perovskite Cs₂AgBiBr₆ was used for its wide bandgap, exceptional optoelectronic properties, non toxicity and stability because of Bi³⁺ presence. , The general rule of thumb for designing a tandem structure is given by

$${\mathbf{E}}_{\mathbf{g}\text{\_}\mathbf{t}\mathbf{o}\mathbf{p}}=\mathbf{0.5}\times {\mathbf{E}}_{\mathbf{g}\text{\_}\mathbf{b}\mathbf{o}\mathbf{t}\mathbf{t}\mathbf{o}\mathbf{m}}+\mathbf{1.15}\mathbf{e}\mathbf{V}$$ 6

Equation suggests that a solar cell with a bandgap around 1.8 eV will be an ideal match in terms of bandgap with AgBiS₂, which has a bandgap of 1.3 eV. Comparing across materials, we found that 600s hydrogenated Cs₂AgBiBr₆ by Zhang et al. of bandgap 1.91 eV with experimental PCE of 4.22% would be the best match for AgBiS₂. Both top and bottom subcells were calibrated with experimental data with same transport layers to ensure validity of the simulation. Figure shows the calibration results for both Cs₂AgBiBr₆ and AgBiS₂. The calibration results are presented in Table .

2.

Calibration of simulated J–V characteristics with experimentally reported data for the top and bottom subcells. (a) Comparison between simulated and experimental J–V curves for AgBiS₂ (bottom subcell) and Cs₂AgBiBr₆ (top subcell). (b) and (c) Experimental device architectures of the Cs₂AgBiBr₆ top subcell and AgBiS₂ bottom subcell, respectively.

1. Comparison between Experimental and Simulation Data for Top and Bottom Sub-Cells.

		V oc (V)	J sc (mA/cm2)	FF (%)	PCE (%)
top subcell	experimental (Zhang et al.)	0.89 V	7.68 mA/cm2	62.00%	4.20%
	simulation	0.91 V	7.70 mA/cm2	60.14%	4.19%
bottom subcell (AgBiS2)	experimental (Bernechea et al.)	0.450 V	22.10 mA/cm2	63.00%	6.31%
	simulation	0.447 V	22.45 mA/cm2	63.27%	6.35%

In experimental TSCs, an interconnect layer with high electron mobility such as aluminum doped zinc oxide, Fluorine doped Tin Oxide (FTO), or ITO is used between top and bottom subcells to ensure high carrier transport. For this simulation, an ideal tunnel junction with no interfacial optical or electrical loss has been considered, which is also consistent with previously published literature. The bottom subcell is exposed to the filtered spectrum from the top subcell. The filtered spectrum can be calculated as

$$\mathrm{S}(\lambda )=S_{\mathrm{A}\mathrm{M}1.5\mathrm{G}}(\lambda )\exp (-{\alpha }_{\mathrm{Sn}{\mathrm{O}}_2}(\lambda )\times d_{\mathrm{Sn}{\mathrm{O}}_2})\exp (-{\alpha }_{{\mathrm{Cs}}_2\mathrm{AgBi}{\mathrm{Br}}_6}(\lambda )\times d_{{\mathrm{Cs}}_2\mathrm{AgBi}{\mathrm{Br}}_6})\exp (-{\alpha }_{\mathrm{C}{\mathrm{u}}_2\mathrm{O}}(\lambda )\times d_{\mathrm{C}{\mathrm{u}}_2\mathrm{O}})$$ 7

where AM 1.5G is the incident solar radiation on the top subcell, α­(λ) is the absorption coefficient, and d is the thickness of different layers in the top subcell. α­(λ) is calculated as follows

$$\alpha (\lambda )=A\sqrt{(h\nu -E_{\mathrm{g}})}$$ 8

where A is the model parameter taken as 10⁵ eV^–1/2, h is the Planck’s constant, and ν is the frequency of the incident radiation. The bulk and interfacial defect densities were both considered Gaussian in this simulation. Using this experimental structure as a benchmark, we further optimize this structure to generate optimum performance. For optimization, parameters such as absorber layer thickness, suitable electron and hole transport layers, defect density, doping density, and bandgap were considered. The Results and Discussion section (3.1–3.3) Supporting Information Figures and Supporting Information Note (1–3) elaborate on the results. The optimized results are shown in Figure . Table shows the simulation parameters for the Optimized structure, which have been meticulously picked from the literature. ,− It is important to outline that we focus primarily on AgBiS₂ optimization, as there are no data available in literature on numerical simulation on this absorber. The optimization of top subcell follows methodology presented in previously published SCAPS-1D simulation data. ,, The optimized results are presented in Figure . A close inspection into the quantum efficiency plots in Figure c,f elucidates the compatibility of these two stacks as AgBiS₂ dominates absorption above 650 nm wavelength.

3.

Optimized structure and output from stand-alone top and bottom subcells. (a) Optimized schematic of Cs₂AgBiBr₆ top subcell, (b) top subcell J–V characteristics, (c) top subcell QE, (d) optimized schematic of the AgBiS₂ bottom subcell, (e) bottom subcell J–V characteristics, (f) bottom subcell QE.

2. Input Parameters for Top and Bottom Subcells Used in SCAPS −1D.

	top subcell				bottom subcell
parameters	FTO	SnO2 (ETL)	Cs2AgBiBr6	Cu2O (HTL)	TiO2 (ETL)	AgBiS2 ,,,	Cu2O (HTL)
thickness (nm)	100	100	1000	100	100	60	100
bandgap (eV)	3.5	4.04	1.9	2.17	3.2	1.3	2.17
dielectric Constant	9	9	5.8	7.1	32	19.29	7.1
electron affinity (eV)	4	4.09	4.1	3.2	3.9	4.1	3.2
hole mobility (cm2/(V s))	10	2.5 × 101	1.18 × 101	80	10	0.032	80
electron mobility (cm2/(V s))	20	2.4 × 102	4.9 × 10–1	200	20	0.07	200
conduction band effective density of states (cm–3)	2.2 × 1018	1 × 1019	1 × 1016	2.02 × 1017	1 × 1019	5.184 × 1018	2.02 × 1017
valence effective density of states (cm–3)	1.8 × 1019	1 × 1019	1 × 1016	1 × 1019	1 × 1019	1.536 × 1019	1 × 1019
donor density (cm–3)	1 × 1019	1 × 1019	1 × 1018	0	1 × 1017	1 × 1010	0
acceptor density (cm–3)	0	0	1 × 1018	1 × 1018	0	1 × 1010	1 × 1018
hole thermal velocity (cm/s)	1 × 107	1 × 107	1 × 107	1 × 107	1 × 107	1 × 107	1 × 107
electron thermal velocity (cm/s)	1 × 107	1 × 107	1 × 107	1 × 107	1 × 107	1 × 107	1 × 107

3. Results and Discussion

3.1. AgBiS₂ Bottom Subcell Thickness Optimization

In this section, the thickness of the AgBiS₂ absorber layer has been optimized with ETL and HTL set at 100 nm each to ensure maximum charge extraction. As per previous literature, absorber layer thickness is a critical parameter that needs optimization to ensure that a certain solar cell structure generates maximum PCE. Figure shows the output parameters (V _oc, J _sc, fill factor (FF) and PCE) with thickness changing from 0 to 800 nm. In this simulation, illumination has been set at AM 1.5G 1000 Wm^–2 and temperature at 300 K. It was observed that the value of short-circuit current (J _sc) increases to around 30 mA/cm² with increasing thickness up to 600 nm because a thicker absorber layer can generate more photons and consequently create a higher number of electron–hole pairs. However, the possibility of recombination also increases as the charges must travel a greater length for diffusion, which explains a slight drop at a thicknesses higher than 600 nm. The value of V _oc also shows similar trends to V _oc at initial stages but does not show the drop. This can be explained by the theory of Landsberg et al. that V _oc depends on photogenerated current J _sc as well as the dark saturation current J_o. A higher J_o means there is more carrier recombination; therefore, V _oc is a measure of carrier recombination of the solar cell. The relation is given by

$$V_{\mathrm{o}\mathrm{c}}=\frac{kT}{q}\ln (\frac{J_{\mathrm{s}\mathrm{c}}}{J_0}+1)$$ 9

where kT is thermal voltage, J _sc is light-generated current density, and J ₀ the dark saturation current density. The decrease in the FF is caused by the increase in series resistance in the layer. As the thickness of the absorber layer increases, it causes an increase in the series resistance of the structure. And this increase in the series resistance decreases the FF of the structure. The equation for PCE of the solar cell, is given by

$$\eta =\frac{V_{\mathrm{o}\mathrm{c}}{J}_{\mathrm{s}\mathrm{c}}\mathrm{F}\mathrm{F}}{P_{\mathrm{i}\mathrm{n}}}$$ 10

4.

Output parameters (V _oc, J _sc, FF, and PCE) of bottom subcell AgBiS₂ with thickness variation with Cu₂O as HTL and TiO₂ as ETL.

Equation suggests that the highest PCE is dependent on the optimum values of the other three parameters, namely, V _oc, J _sc, and FF. As both V _oc and J _sc have an increasing trend in contrast to FF, which has a decreasing trend, the device was found to have the highest efficiency around 400 nm, which is determined to be the optimum thickness. This thickness represents the theoretical upper bound of device performance based on the optimum band alignment. Practical solar cell absorbers may have a higher degree of defects associated with them; therefore, taking that into consideration, the optimum thickness might vary a certain amount. In addition, optimization of deposition, annealing, and cation-disorder control may be required for achieving this target thickness.

3.2. AgBiS₂ Bottom Subcell Transport Layer Optimization

For solar cells, suitable transport layers are crucial for efficient charge extraction. To identify the suitable transport layers for AgBiS₂, we investigated different electron (PCBM, WS₂, STO, TiO₂) and hole transport materials (CuI, Cu₂O, CuSCN, and NiO). The thickness of both ETL and HTL materials has been kept as 100 nm. The corresponding transport parameters are listed in Tables and .

3. Input Parameters of Different Hole Transport Layers for the AgBiS₂ Bottom Subcell.

parameters	CuI	Cu2O	CuSCN	NiO
thickness (nm)	100	100	100	100
bandgap (eV)	2.98	2.17	3.4	3.6
dielectric constant	6.5	7.1	10	11
electron affinity (eV)	2.1	3.2	1.9	1.46
hole mobility (cm2/(V s))	2 × 10–4	80	1 × 10–1	50
electron mobility (cm2/(V s))	1.7 × 10–4	200	1 × 10–4	50
conduction band effective density of states (cm–3)	2.8 × 1019	2.02 × 1017	1.7 × 1019	1.6 × 1019
valence band effective density of states (cm–3)	1 × 1019	1 × 1019	2.5 × 1021	1.1 × 1019
donor concentration (cm–3)	0	0	0	0
acceptor concentration (cm–3)	1 × 1018	1 × 1018	1 × 1018	1.8 × 1018
electron thermal velocity (cm/s)	1 × 107	1 × 107	1 × 107	1 × 107
hole thermal velocity (cm/s)	1 × 107	1 × 107	1 × 107	1 × 107

4. Input Parameters of Different Electron Transport Layers for the AgBiS₂ Bottom Subcell.

parameters	PCBM	WS2	STO	TiO2
thickness (nm)	100	100	100	100
bandgap (eV)	2	1.8	3.2	3.2
dielectric constant	3.9	13.6	8.7	32
electron affinity (eV)	3.9	3.95	4	3.9
hole mobility (cm2/(V s))	0.2	50	6.6 × 102	10
electron mobility (cm2/(V s))	0.2	50	5.3 × 103	20
conduction band effective density of states (cm–3)	2.5 × 1021	1 × 1018	1.7 × 1019	1 × 1019
valence band effective density of states (cm–3)	2.2 × 1021	1 × 1018	2 × 1020	1 × 1019
donor concentration (cm–3)	2.93 × 1021	1 × 1018	2 × 1020	1 × 1017
acceptor concentration (cm–3)	0	0	0	0
electron thermal velocity (cm/s)	1 × 107	1 × 107	1 × 107	1 × 107
hole thermal velocity (cm/s)	1 × 107	1 × 107	1 × 107	1 × 107

For ETL optimization, the materials have been chosen keeping in mind some essential conditions for efficient carrier extraction such as (i) higher electron affinity of ETL than absorber layer to ensure the electron flow to ETL and (ii) much lower HOMO of ETL compared to the absorber to ensure there is no backflow of holes in that direction. , Figure a,b show the corresponding J–V characteristics of (PCBM, WS₂, STO, TiO₂) and their corresponding band alignments where Cu₂O has been used as HTL. Among these ETLs, PCBM shows the lowest PCE (9.86%), which may be because of low hole and electron mobilities (2 × 10^–1 cm²/(V s)). To investigate further, the energy-band block diagram of 4 different ETLs were taken into consideration, which is shown in Supporting Information Figure 1. From the band diagram, it was observed that STO and PCBM had large cliffs, which corresponded to lower PCE value. TiO₂ has the smallest cliff compared to the other 3 materials. There is also very high difference in valence band layers between the AgBiS₂ absorber and TiO₂ that ensures holes are blocked.

5.

(a) Simulated J–V characteristics of different ETLs for the AgBiS₂ bottom subcell with Cu₂O as HTL. (b) Alignment of the energy band between different ETL materials with the AgBiS₂ absorber. (c) Simulated J–V characteristics of different HTLs for the AgBiS₂ bottom subcell with TiO₂ as ETL. (d) Alignment of the energy band between different HTL materials with the AgBiS₂ absorber.

Figure c,d show the corresponding J–V characteristics of the device using 4 different HTLs ( CuI, Cu₂O, CuSCN, and NiO) where TiO₂ has been used as ETL. The response shows that the graphs are almost identical to each other with Cu₂O providing the best result, yielding a PCE of 13.98%. This result is also supported by Bernechea et al. as the positioning of HOMO (Highest Occupied Molecular Orbital) has a negligible impact on the overall performance of the AgBiS₂ NC solar cells. This similar trend of the curves may be because of similar values of their corresponding Valence Band Offset (VBO) and CBO (Conduction Band Offset) values given by

$$\mathrm{V}\mathrm{B}\mathrm{O}=E_{\mathrm{V}}(\mathrm{A}\mathrm{b}\mathrm{s}\mathrm{o}\mathrm{r}\mathrm{b}\mathrm{e}\mathrm{r})-E_{\mathrm{v}}(\mathrm{H}\mathrm{T}\mathrm{L})$$ 11

$$\mathrm{C}\mathrm{B}\mathrm{O}=E_{\mathrm{C}}(\mathrm{E}\mathrm{T}\mathrm{L})-E_{\mathrm{C}}(\mathrm{A}\mathrm{b}\mathrm{s}\mathrm{o}\mathrm{r}\mathrm{b}\mathrm{e}\mathrm{r})$$ 12

Band alignments for the selected HTLs with AgBiS₂ are shown in Figure d. The four HTLs, namely, CuI, CuSCN, Cu₂O, and NiO, have VBO values of 0.32 eV, 0.14 eV, 0.21, and 0.10 eV, respectively. This may seem as contradictory to convention as the induced electric field would be opposite, which would prevent the flow of holes from getting collected. However, according to Minemoto et al., the optimum value of VBO for good carrier transmission and band alignment is 0–0.2 eV. Although all the elements prove with a nearly identical result, the J _sc and PCE are found to be the highest in case of Cu₂O. The reason for the slight improvement of Cu₂O may be because of high hole and electron mobility of 80 cm²/(V s) and 200 cm²/(V s), respectively, which is significantly higher compared to the other HTLs.

To summarize, the simulations show that the optimized structure achieves a maximum PCE of 13.98% using Cu₂O as the HTL and TiO₂ as the ETL.

3.3. Effect of Absorber Defect Density on Top and Bottom Subcells

Defects play a crucial role in the performance of a solar cell. These defects can originate from the bulk absorber, the transport layers, as well as the interfaces between each layer. In this section, we analyze how the key performance metrics (e.g., V _oc, J _sc, FF, and PCE) of both the Cs₂AgBiBr₆ top subcell and AgBiS₂ bottom subcell vary with different defect densities. To do so, we vary the defect density from 10¹⁴ cm^–3 to 10¹⁷ cm^–3 in the corresponding absorber layers and observe a steady decline in all 4 parameters. Figure a,b show how the 4 parameters evolve with increasing defect density for the Cs₂AgBiBr₆ top sub cell and AgBiS₂ bottom sub cell, respectively. This is expected, since defects are recombination centers that create localized trap states for carriers to get trapped instead of being extracted at the contacts. This mechanism is referred to as Shockley-Read-Hall (SRH) recombination, which is one of the primary loss mechanisms in solar cells. The equation for SRH is given in eq as

$$\mathbf{R}=\frac{\mathbf{n}\mathbf{p}-{\mathbf{n}}_{\mathbf{i}}^{\mathbf{2}}}{{\mathit{\tau }}_{\mathbf{n}}(\mathbf{p}+{\mathbf{N}}_{\mathbf{v}}{\mathbf{e}}^{({\mathbf{E}}_{\mathbf{t}}/\mathbf{k}\mathbf{T})})+{\mathit{\tau }}_{\mathbf{p}}(\mathbf{n}+{\mathbf{N}}_{\mathbf{c}}{\mathbf{e}}^{({\mathbf{E}}_{\mathbf{g}}-{\mathbf{E}}_{\mathbf{t}}/\mathbf{k}\mathbf{T})})}$$ 13

In this equation, the concentrations of mobile electrons and holes are n and p, respectively, the energy level and concentration of trap defects are E _t and N _t, and the intrinsic concentration is n _i.

7.

Effect of absorber defect density on top and bottom subcells; (a) AgBiS₂ bottom subcell; (b) Cs₂AgBiBr₆ top subcell.

A similar trend is observed for the parameters except FF when interface defect densities between the absorber and corresponding transport layers of both top and bottom subcells are varied from 10¹⁴ to 10¹⁶ cm^–3. These results are presented in Supporting Information Figure S2. It is worth noting that interfacial defects, because of their position, influence the cells more than the defects in the bulk, since recombination centers at the interface cause photogenerated carriers to recombine before they can be efficiently extracted by the transport layers. This directly reduces charge collection efficiency and increases nonradiative recombination losses, leading to lower V _oc, J _sc, FF, and overall PCE. Therefore, controlling the interfacial defect density through proper band alignment, surface passivation, and optimized transport-layer deposition is essential for realizing the simulated device performance.

The best possible result is found if the defect density is kept at 10¹⁴ cm^–3. Further increases only cause strong degradation of PCE. Therefore, achieving high absorber crystallinity, minimizing bulk trap density, and implementing effective interface passivation will be necessary to approach the expected efficiency of the proposed tandem architecture.

3.4. Output Characteristics of the Proposed 2T Tandem Cell with Current Matching

Figure shows the J–V characteristics after current matching. In a 2T tandem cell, as the top and bottom subcells are connected in series, their open-circuit voltages add up, and the cell with the lowest current becomes the limiting current of the overall structure. , For our structure, Cs₂AgBiBr₆ had a lower current value (15.07 mA/cm²) compared to AgBiS₂ (15.73 mA/cm²), which received the filtered spectrum (615.72 W/m²). To match the current values, the thickness of AgBiS₂ was gradually decreased, and at a thickness of 350 nm, the optimum match (15.04 mA/cm²) was found. An ideal lossless junction was considered between them for simulation purposes. After current matching, an efficiency of 23.47% was achieved. Figure b shows the QE plot, where AM 1.5 G was incident on the top cell and filtered spectrum on the bottom cell. The figure shows a 90% absorption above 650 nm by the bottom cell, where the top cell absorption is effectively zero. Hence, the proposed 2T tandem utilizes a higher portion of the spectrum, resulting in a higher PCE. Figure c shows the current matching of the bottom subcell to the limiting top subcell by varying its thickness. The green dashed circle represents the matching point, which corresponds to a 350 nm thickness. Figure d shows a comparison between experimental results and our optimized simulated result. The top, bottom, and 2T tandem show 182.4%, 114.1%, and 216.3% increase, respectively. Table summarizes the output parameters of the 2T tandem solar cell.

6.

2T tandem output with current matching. (a) J–V characteristics curve of the top subcell Cs₂AgBiBr₆ (square), bottom subcell AgBiS₂ (circle), and 2T Tandem cell (diamond). (b) QE plots for top and bottom subcells. (c) Thickness variation of AgBiS₂ to achieve current matching with the top subcell Cs₂AgBiBr₆. (d) Bar plots to show efficiency improvement after optimization and current matching.

5. Simulated V _oc, J _sc, FF, and PCE of the 2T Tandem Solar Cell after Current Matching.

	V oc (V)	J sc (mA/cm2)	FF (%)	PCE (%)
Cs2AgBiBr6 (top)	1.36	15.07	65.15	13.33
AgBiS2 (bottom)	0.74	15.04	68.41	12.28
tandem	2.10	15.10	74.01	23.47

While current matching is the most effective approach for numerical optimization of tandem structures, practical tandem solar cells may experience additional challenges such as temperature variations between subcells and dynamic current mismatch. To address these issues, strategies such as bandgap tuning of the bottom subcell and optimization of the transparent conductive oxide (TCO) interconnect thickness may become important in addition to current matching. A summary of J–V characteristics under different bandgaps for the AgBiS₂ bottom subcell is presented in Supporting Information Figure S3.

3.5. Potential Experimental Challenges in Achieving the Simulated Performance in Cs₂AgBiBr₆/AgBiS₂ Solar Cells

It is important to note that the simulated 2T tandem cell performance assumes ideal, lossless interconnection and optimal band alignment between the absorbers and their respective transport layers. In practical devices, the interconnection is typically formed using TCOs, which, despite their high carrier transport properties, introduce additional losses due to finite diffusion lengths and recombination at the top subcell/interconnect and bottom subcell/interconnect interfaces. In practical monolithic tandem devices, the TCO recombination layer introduces additional losses through parasitic optical absorption, interfacial recombination, and contact resistance. Based on recent experimental and simulation studies, these effects are estimated to reduce the ideal tandem efficiency by approximately 2.6–3.7% − absolute, resulting in a practically attainable efficiency of ∼20–21% compared to the simulated value of 23.47%. Therefore, the reported PCE should be interpreted as a theoretical upper bound under ideal interconnection conditions. In addition, the simulation assumes a Gaussian defect distribution in between the interfacial layers in the range of 10¹⁴ cm^–3–10¹⁵ cm^–3, which is commonly adopted in SCAPS-based studies. , However, in experimental AgBiS₂ and Cs₂AgBiBr₆ absorbers, based on surface defects and lattice mismatch during fabrication, the interface may contain a higher degree of defects, which may result in a lower PCE. To examine this, we performed a defect density variation study for both subcells, as shown in Section and Supporting Information Figure S2.

Furthermore, experimentally reported AgBiS₂ solar cells typically employ much thinner absorber layers (e.g., ∼30–35 nm), , whereas the optimized structure in this study uses a significantly thicker absorber (∼400 nm). This increased thickness in simulation enhances photon absorption and carrier generation but achieving such thickness experimentally while maintaining high film quality and uniformity remains challenging. Another potential limitation could arise from material quality. The high absorption coefficient of AgBiS₂ is often achieved through cation disorder engineering; however, maintaining a controlled crystallinity and uniform cation distribution becomes increasingly difficult as film thickness increases. This may lead to structural inhomogeneity and increased recombination in experimentally fabricated thicker films. Therefore, the optimized results presented here should be interpreted as a theoretical upper bound performance achieved under favorable band alignment and optimized device parameters.

After optimization, the proposed structure of Figure is redrawn in Figure .

8.

Schematic illustration of optimized 2T TSC after current matching.

4. Conclusion

In this work, a comprehensive analysis on the prospects of a 2-terminal tandem solar cell with Cs₂AgBiBr₆ and AgBiS₂ has been performed. The standalone cells have been calibrated with experimental data to validate the simulation. The analysis has been performed primarily focusing on optimizing AgBiS₂ to achieve the maximum PCE with different transport layers, thicknesses, defects, doping density, etc. It has been observed that the AgBiS₂ solar cell provides optimal band alignment with TiO₂ and Cu₂O as electron and hole transport layers, respectively. In addition, it has been observed that the thickness at which AgBiS₂ solar cells perform best is 400 nm. On the basis of these optimizations and a suitable bandgap of 1.3 eV, it has been integrated into a 2-terminal tandem solar cell architecture with Cs₂AgBiBr₆ as the top subcell. In doing so, an optimized solar cell stack of FTO (100 nm)/TiO₂ (100 nm)/AgBiS₂ (400 nm)/Cu₂O (100 nm) has been found that yields an efficiency of 13.98%. In terms of the 2T TSC with current-matched conditions, the projected PCE reaches 23.47%, corresponding to a 216.3% improvement relative to the experimentally reported efficiencies of the individual subcells.

Overall, this study provides a material-specific device design framework for AgBiS₂ and demonstrates its potential role in lead-free tandem photovoltaics. The insights presented here can serve as a guideline for future experimental efforts and for further development of environmentally friendly, all-inorganic tandem solar-cell architectures.

The data that support the findings of this study are available throughout this manuscript and Supporting Information as Tables S1–S3 and Figures S1–S5.

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acsomega.6c02691.

• Energy-band block diagram shown for the bottom subcell AgBiS₂ with four different ETLs and Cu₂O as HTL: PCBM, STO, WS₂, TiO₂, energy-band block diagram for the top subcell Cs₂AgBiBr₆; output parameters showing variation with interfacial defect density: open-circuit voltage, short-circuit current density, FF, PCE; comparison of J–V characteristics of AgBiS₂ for different bandgaps reported in literature, with ETL and HTL kept constant; variation of simulated device parameters with change in absorber doping concentration (p-type doping); output parameters as a function of device temperature; variation of J–V characteristics for different bandgaps in the AgBiS₂ Bottom subcell; effect of doping concentration on the AgBiS₂ Bottom subcell; and calibration details for the top subcell Cs₂AgBiBr₆ and bottom subcell AgBiS₂ (PDF)

The authors declare no competing financial interest.