Optimization of lead-free BiFeO₃ perovskite solar cells for efficient solar-energy conversion in futuristic green technologies

Abstract

The adverse effects of global warming and our dependence on hazardous energy sources, like coal and petroleum, have shifted focus toward solar energy, a sustainable and clean solution. Perovskite materials, particularly BiFeO₃, are attracting attention as absorber layers due to their multifunctional properties. This study employs COMSOL to simulate 1D TiO₂/BiFeO₃/Spiro-OMeTAD solar cells with ideal ohmic contacts at different operating temperatures. Results demonstrate that the short-circuit current density increases with the BiFeO₃ thickness, and efficiency peaks at an optimal thickness. However, the maximum efficiency of 10.88% is achieved (in TiO₂/BiFeO₃/Spiro-OMeTAD) when the electron-transport layer's density of states in the valence and conduction bands (N_CN_V) is ∼2 × 10¹⁶ cm⁻³, while TiO₂/SnS/BiFeO₃/Spiro-OMeTAD shows the maximum efficiency of 20.99% at the SnS layer thickness of 700 nm. Moreover, an increase in BiFeO₃'s bandgap enhances the open-circuit voltage (V_oc) but reduces the fill factor. On the other hand, BiFeO₃'s N_CN_V has no significant impact on efficiency but shows inverse coupling with V_oc. Additionally, increasing BiFeO₃'s electron affinity improves the fill factor, while increasing TiO₂'s and Spiro's electron affinities enhances the V_oc and power output, respectively. This work provides insights for optimizing material properties and device parameters in experimental applications and highlights the potential of BiFeO₃-based perovskites for next-generation photovoltaics.

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1. Introduction

The global energy crisis can be addressed by solar energy, which is a sustainable, non-polluting, and inexhaustible source of energy.^1–3 For this purpose, the materials extensively studied for photovoltaic (PV) applications are organic, inorganic or hybrid perovskite solar cells (PSCs). Since 2009, these PSCs have demonstrated robust improvement in power conversion efficiency (η), increasing from 3.8% to approximately 26%.^4–6 PSCs have been identified as next-generation PV technology, surpassing the conventional solar cell; however, perovskites (PVKs) exhibiting strong ferroelectric (FE) response are particularly preferred.⁷ Conventional solar cells are based on crystalline silicon (c-Si) technologies and operate through a single p–n junction mechanism with fixed material interfaces and well-defined efficiency limits determined by the Shockley–Queisser limit. They rely on established material and design parameters and have long served as performance benchmarks for evaluating emerging solar technologies. The inherent spontaneous polarization of FE materials facilitates the separation of the photogenerated electron–hole pairs without the development of the conventional n-type and p-type depletion regions. There are many factors that influence the PV nature of FE materials, including the Schottky barrier effect, bulk PV effect, and domain wall theory.^8–10 Specifically, the alignment of domains within the FE material induces polarization, which further produces the depolarization field. When the built-in field and depolarization field are aligned in the same direction, it promotes the efficient separation of electrons and holes.¹¹ The spontaneous polarization arises from the off-center and non-centrosymmetric displacement of positive and negative ions in the ABO₃ structure of FE materials.^12,13 Various PVK materials have been reported thus far, including BaTiO₃, Bi₄Ti₃O₁₂, and PZT.^14–17 However, the key limitation associated with these materials is their large bandgap (E_g), often exceeding 3 eV, which is not feasible for solar energy conversion under sunlight. This large E_g results from the high electronegativity difference between the B-site and oxygen atoms. Therefore, reducing the E_g is crucial to improve the η of FE materials in PV applications. Hence, bandgap engineering through the substitution of an appropriate metal cation at the B-site can alter both the FE response and E_g of FE materials. Thus, a completely new FE material for PV applications is needed, one having both high induced polarization and a small E_g. For this purpose, BiFeO₃ (BFO) has emerged as the potential candidate, as it not only fulfils these requirements but also is non-toxic.

BFO, a multiferroic material (rhombohedral symmetry, R3c space group), retains its multiferroicity above or at room temperature (RT), with a Curie temperature (T_C ∼ 1103 K) and a G-type antiferromagnetic Néel temperature (T_N ∼ 643 K). BFO is widely employed in magneto-electric, optoelectronic, multistate memory, and spintronic devices, due to its quite high remnant polarization (∼100 µC cm⁻²), which enables it to efficiently separate photogenerated electron–hole pairs.^18–23 At RT, BFO is stable and exhibits both magnetic and electric responses spontaneously, with a lower direct/indirect E_g (2.1–2.8/1.07 eV) and a high absorption coefficient (∼10⁵ cm⁻¹ at 400 nm).^24–32 The thin films of BFO exhibit lower series resistance, which promotes the enhanced collection of photogenerated charge carriers.³³ Notably, the switching of the photocurrent is achieved by simply switching the direction of spontaneous polarization. These properties render BFO a potential candidate among the other conventional PVK materials for optical and FE enhancements. Despite their large open circuit voltage (V_oc), BFO-based solar cells have a lower η than commercial Si-based cells. The highest experimentally reported η for BFO is 10% so far, though it can be improved by tuning the FE response and E_g.^34,35 There are many reasons for this low η, but the major limiting factors include high leakage currents and low magnetization, possibly due to oxygen vacancies, high volatilization of Bi, valence fluctuations in Fe ions, or the presence of secondary phases.^36–40 These factors lead to η values below the theoretical limits; however, BFO is the best choice for researchers because its ferroelectric and non-centrosymmetric natures enable polarization-driven charge separation through bulk and domain-wall photovoltaic effects.^41,42 Many strategies i.e. substitution or composite formation, have been done to resolve issues like conductivity, leakage current, and magnetization.^43,44 However, these approaches often lead to structural defects or secondary-phase occurrence.^45–49 In parallel, researchers are trying hard to improve these factors via a controlled synthesis process and the insertion of an electron-transport layer (ETL) or a hole-transport layer (HTL) across the BFO layer. Though effective, these layers result in interface defects and ultimately reduce the overall η of the solar cell. Recently, HTL-free solar cells have been proposed, which have fewer defects and are low in cost.⁵⁰ In BFO-based solar cells, TiO₂ has been widely employed as an ETL, owing to its ease of synthesis, low cost, excellent crystalline stability, anisotropic growth behavior, and efficient electron-transport characteristics.⁵¹

Extensive studies have been conducted by both experimental and theoretical groups, such as Kim et al. (2020), De Los et al. (2020), Karthick et al. (2020), Kumar et al. (2021), Sebastian et al. (2021), Singh et al. (2021) and Hossain et al. (2023).^52–58 However, no significant attention has been paid to the application of the most advanced mathematical-based solver to simulate BFO-based solar cells. In this study, we make use of the most advanced COMSOL Multiphysics simulation software to simulate the 1D TiO₂/BFO/Spiro-OMeTAD heterojunction solar cell—a novel approach that has not been explored for the enhancement of device performance. This software allows us to vary multiple factors simultaneously, offering deep insights to improve η. The software is based on the finite element method (FEM), which solves Poisson's equation and drift-diffusion partial differential equations using semiconductor physics. It allows the coupling of more than one physics simultaneously, enabling 3D simulation of complex devices. Based on advanced mathematical methods, the accuracy of this software can be estimated by comparing the simulated output values, which normally show a difference of only 1.50% and 2.40% from the experimental data.⁵⁹ The sole purpose of this simulation-based study is to optimize the parameters efficiently, improving the overall performance of the cell. Excellent optimization of parameters affords improved output results from the device, and advanced tools of simulation enable this process. This includes the optimization of the doping type, doping level, carrier concentration, defect type, defect density, layer thickness, metal contacts, etc. Once the parameters are optimized, we simulate the solar cell to find out its output characteristics, including current density–voltage (J–V) and power–voltage (P–V) curves for the determination of η and other quantities.

2. Numerical modeling

In this study, the COMSOL Multiphysics software was employed as a robust tool to analyze the underlying causes of low η in solar cells. While earlier investigations primarily utilized 1D or 2D simulation frameworks to study the basic characteristics of similar devices, the present work implements a 3D COMSOL-based model to capture realistic spatial effects and provide more accurate performance predictions. It forecasts the electrical behavior and internal physical mechanics of the structure as a physics-based 2D and 3D device simulator. It achieves this by solving fundamental equations, including Poisson's equation and carrier continuity equations, which establish a relationship between electrostatic potential and carrier densities.⁶⁰ For charge-transport analysis, the Drift-Diffusion Model emerges as the most effective and computationally efficient approach. Poisson's equation, which relates the electrostatic potential to the local space charge density, is expressed as (eqn (1)):

∇.(ε∇Ψ) = −ρ (1)

where, Ψ denotes the electrostatic potential, ε represents the local permittivity, and ρ signifies the local space charge density.⁶¹ The steady-state continuity equations (eqn (2) and (3)) for electron and hole transport are described as follows:where, J⃑_n and J⃑_p represent the current densities for the electrons and holes, respectively, and G_n and G_p denote the generation rates of charge carriers. R_n and R_p represent the total recombination rates in Gaussian and tail states, respectively, whereas the electron charge is represented by q.⁶² The term G, governing the rate of photogenerated electron–hole pairs, was incorporated in COMSOL to simulate light absorption across the active layer and is expressed as G = αI₀e^−αx. Here, α is the absorption coefficient, I₀ represents the incident light intensity, and x is the penetration depth. In the Drift-Diffusion model, the current densities are related to the quasi-Fermi levels, as follows (eqn (4) and (5)):

J⃑_n = −qµ_nn∇ϕ_n (4)

J⃑_p = −qµ_pp∇ϕ_p (5)

where, µ_n and µ_p denote the mobilities of electrons and holes, respectively, while ϕ_n and ϕ_p represent the quasi-Fermi levels. Using the Boltzmann approximation, the quasi-Fermi levels are further linked to the electrostatic potential and carrier concentrations, as follows (eqn (6) and (7)):where, T is the lattice temperature, k_B is the Boltzmann constant, and n_i represents the effective intrinsic carrier concentration.⁶³ The electrical properties of the device are computed based on the defined physical structure and applied bias conditions. This involves discretizing the governing equations (Poisson's equation and carrier continuity equations) over a finite element grid, which divides the simulation domain into a set of nodes and grid points. By solving these equations across the grid, the carrier transport mechanisms within the structure are accurately modeled. This finite-element approach enables a comprehensive simulation of the solar cell's performance.⁶⁴

The simulation of the TiO₂/BiFeO₃/Spiro-OMeTAD solar cell was performed in COMSOL using a systematic approach. First, the 1D geometry of the device, including the TiO₂ electron-transport layer, BiFeO₃ absorber, and Spiro-OMeTAD hole-transport layer, was defined with precise thicknesses. Material properties, such as the bandgap, electron affinity, carrier mobility, and permittivity, were assigned based on reported values. Ideal ohmic contacts were applied at the electrodes, and a fine mesh was generated throughout the solar cell structure, with increased density at the interfaces between the TiO₂/BiFeO₃ and BiFeO₃/Spiro-OMeTAD layers to accurately capture variations in the carrier concentration and the electric field. The semiconductor physics module solved the coupled Poisson, continuity, and drift-diffusion equations to model charge transport and carrier generation. Illumination with the AM1.5 solar spectrum provided the photo-generation rate in the absorber layer, and a cross-sectional area of 4 × 10⁻¹² m² was used. Steady-state simulations were performed for varying thicknesses, transport-layer properties, and operating temperatures. Finally, current density–voltage (J–V) characteristics were extracted, ensuring a thorough evaluation of the device performance.

3. Device simulation and methodology

3.1. Solar absorption and solar spectrum

The solar spectrum represents the distribution of solar energy across different wavelengths. Fig. 1(a) shows that solar irradiance increases sharply to a peak of about 1.6 Wm⁻² nm⁻¹ at 460 nm. Beyond this point, it gradually declines up to 2500 nm due to the combined effects of the decreasing solar blackbody emission intensity at longer wavelengths and the absorption by atmospheric gases, such as water vapor, oxygen, and carbon dioxide. This demonstrates the wavelength-dependent nature of solar irradiance, where shorter wavelengths exhibit stable intensity and longer wavelengths show a progressive decrease.⁶⁵ The refractive index (n) and extinction coefficient (k) are critical parameters that define a material's optical properties, both of which exhibit wavelength-dependent variations. The n parameter initially increases with the wavelength due to the dispersion phenomenon, where light bending intensifies as it interacts with the material, and for wavelengths beyond 0.4 µm, n begins to decrease, stabilizing at longer wavelengths (above 1 µm), as shown in Fig. 1(b). In contrast, k initially decreases with increasing wavelength, particularly beyond 0.3 µm. This behavior arises from the electronic transitions within the material, reflecting its distinct interaction with incident light, and beyond 0.5 µm, k stabilizes, indicating minimal further absorption. The interplay of n and k demonstrates their influence on light transmission, reflection, and absorption in the material.⁶⁶ The generation of electron–hole (e/h) pairs is governed by the interaction of incident light with the material, and when photons are absorbed, electrons transition from the valence band to the conduction band, creating e/h pairs.⁶⁷ In Fig. 1(c), the arc length indicates the total thickness of the optimized layers in this solar cell device. The e/h pair generation is maximum within the 100 to 500 nm arc length, approximately, signifying the high absorption and carrier generation. Beyond 500 nm, the generation rate declines and stabilizes, implying less pair generation for longer arc lengths. This behavior underscores the critical role of arc length in maximizing the photo-generated carrier densities.⁶⁸

Fig. 1 (a) Solar spectrum, (b) n and k dependence on wavelength, (c) generation rate of e/h pairs inside the layers of solar cell, and (d) Shockley-Read-Hall recombination rate within the device.

After generation, the Shockley–Read–Hall (SRH) recombination occurs, a process which involves electron–hole recombination facilitated by material defects or impurities and also exhibits wavelength-dependent characteristics. At smaller arc lengths, the SRH recombination peaks, reaching a maximum value of approximately 1.3 × 10²⁶ (1/m³ × s) at around 100 nm, as shown in Fig. 1(d). With increasing arc length, the SRH recombination rate declines sharply, highlighting its sensitivity to changes in the arc length. This reduction is attributed to variations in the carrier concentrations and the density of trapping centers that modulate the recombination dynamics. The observed trends emphasize the critical interplay between recombination mechanisms and material properties under varying spectral conditions.⁶⁹

3.2. Energy band structure

Fig. 2(a and b) presents the architecture of a multi-layer PV cell comprising TiO₂/BFO/Spiro-OMeTAD as its primary constituents, and each layer in this design is chosen for its unique properties to optimize solar-light absorption, charge separation, and efficient carrier transport, ultimately enhancing the device's power-generation efficiency.⁷⁰ The operation of this device is supported by the material-specific characteristics and semiconductor physics, both of which have been extensively studied and validated in this study. The TiO₂ layer, positioned at the top, serves as the ETL due to its wide E_g and high electron mobility. These properties render TiO₂ highly transparent to sunlight, allowing most incident photons to penetrate the underlying BFO layer for absorption.

Fig. 2 (a) Solar cell's schematic, (b) schematic with energy levels, (c) energy-level variations vs. arc length, and (d) energy-band alignment of the TiO₂/BFO/Spiro-OMeTAD heterojunction solar cell for the transportation of charge carriers.

Materials with increased thickness exhibit enhanced absorption of low-energy photons due to their large penetration depth. Conversely, high-energy photons, such as those in the near-ultraviolet spectrum, exhibit high absorption coefficients, resulting in reduced penetration depths. Fig. 2(c) shows the conduction band level (E_c) and the Fermi level for electrons (E_fn), indicating that energy remains constant as the material thickness increases, up to approximately 75 nm. Beyond this threshold, the energy begins to rise, reaching a value of 2.88 eV, and for thinner materials, the absorption of higher-energy photons predominates due to their shorter penetration depths. In contrast, low-energy photons in the near-infrared region exhibit lower absorption coefficients, allowing deeper penetration into the material. The relationship between the Fermi level for holes (E_fp) and the valence band level (E_v) demonstrates that the carrier energy initially starts at low negative values and gradually increases, reaching zero as the energy levels align. The E_g energies of the studied materials vary significantly: spiro materials exhibit the highest E_g energy, followed by BFO with an intermediate E_g, and TiO₂ with the lowest E_g energy. These variations highlight the distinct electronic properties of these materials at varying thicknesses.⁷¹ The observed trends suggest a direct correlation between the material thickness and E_g energy: as the thickness increases, the E_g energy also rises. This behavior underscores the influence of material geometry on its optical and electronic properties, emphasizing the importance of thickness-dependent optimization for tailored PV or optoelectronic performance.

Moreover, TiO₂ effectively facilitates electron transport to the top contact while minimizing electron–hole recombination, a critical factor for maintaining charge separation. The BFO layer, a multiferroic PVK with an E_g of 2.2 eV, acts as the main light-absorbing component of the device. BFO absorbs photons across a significant portion of the visible spectrum, leading to the generation of excitons upon photoexcitation.³⁴ The FE properties of BFO aid in separating these excitons, directing electrons toward the TiO₂ and holes toward the bottom HTL, Spiro-OMeTAD, and this transportation is shown in Fig. 2(d). Spiro-OMeTAD, positioned at the bottom of the cell, works as the HTL, facilitating hole transport from the BFO layer to the bottom contact.⁷² By ensuring efficient hole transport and suppressing recombination with electrons, this layer supports sustained charge separation and a steady flow of electric current. The functionality of this PV cell is governed by the principles of semiconductor band theory, particularly the energy-band alignment among the layers. The alignment between BFO and Spiro-OMeTAD supports downward hole transport, while the wide E_g of TiO₂ prevents electron recombination, directing electrons toward the top contact.

Although a dedicated interfacial recombination analysis was not presented as a separate section, its impact is inherently embedded within the simulated current–voltage characteristics and directly contributes to the observed current saturation behavior. The interfacial regions between adjacent layers were modeled under charge-neutral conditions, with a surface charge density of 0 C cm⁻², thereby eliminating artificial fixed charges and maintaining electrostatic equilibrium across the junctions. To accurately describe recombination dynamics at these interfaces, the SRH trapping mechanism was employed, assigning both electron and hole surface recombination velocities of 1000 cm s⁻¹. These parameters fall within the experimentally reported ranges for perovskite and oxide-based heterojunctions, ensuring physically consistent interfacial kinetics. The trap energy level was positioned at the midgap, corresponding to a neutral defect state with zero offset from the intrinsic Fermi level, thereby representing symmetric recombination for electrons and holes. Furthermore, the interface continuation feature in COMSOL Multiphysics was enabled to preserve numerical convergence and physical continuity across the heterointerfaces, ensuring reliable simulation of interfacial charge transport and recombination phenomena.

The properties of TiO₂, BFO, and Spiro-OMeTAD enable effective photon absorption, charge carrier separation, and transport within the multi-layer PV cell. Careful band alignment and material selection, as supported by extensive research in PV technology, contribute to a highly efficient system capable of converting solar energy into electricity with reduced recombination losses. The optimized input parameters for the TiO₂, BFO, and Spiro-OMeTAD materials, assuming the ideal ohmic front and back contacts, are tabulated in Table 1.

Table 1 Initial parameters of the materials used for the respective layers in 1D TiO₂/BFO/Spiro OMeTAD PSC

Material properties	TiO2	BFO	Spiro-OMeTAD
Thickness (nm)	80	50	40
Energy bandgap (eV)	3.2	2.5	3
Electron affinity (eV)	3.9	3.3	1.9
Relative permittivity	9	6	3
C.B effective density of states ‘NC’ (cm^−3)	1 × 10^20	5 × 10^18	1 × 10^20
V.B effective density of states ‘NV’ (cm^−3)	2 × 10^20	5 × 10^18	1 × 10^20
Electron mobility ‘µn’ (cm^2 V^−1 s^−1)	20	80	2
Hole mobility ‘µh’ (cm^2 V^−1 s^−1)	25	25	1 × 10^−2
Electron lifetime, SRH, (ns)	1	1	5
Hole lifetime, SRH, (ns)	1	1	5
Ref.	73	74	75

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4. Results and discussion

4.1. Effect of BFO's thickness on PV performance

The absorbing layer, such as BFO, acts as the active region of the solar cell and helps to generate the photo-induced charge carriers, which further migrate towards their respective electrodes. For this, the thickness of the absorbing layer is very crucial because as the thickness increases, the absorption of light may increase, ultimately enhancing the photo-induced charge carriers. But, on the other hand, after this optimum thickness is achieved, the performance of the solar cell may decrease because of the increase in the internal resistance and defect density. Fig. 3(a) presents a schematic illustration to visualize the effect of the thickness of the absorbing layer, and it is obvious that increasing the thickness of this layer beyond its optimal value may increase the number of defects, as depicted by the small circle. Fig. 3(b) shows the J–V characteristics of the solar cell for different BFO thicknesses, where J_sc increases with increasing BFO thickness. At 50 nm, J_sc is around 3.69 mA cm⁻², while at 1850 nm, it reaches approximately 9.004 mA cm⁻², indicating improved charge collection for thicker layers. The sharp decline occurs at different voltages, with the thinner layers dropping at around 1.6–2.0 V and the thicker layers at around 1.3 V, suggesting that increased thickness lowers V_oc due to the higher recombination losses. Fig. 3(c) shows P–V curves for different BFO thicknesses, where the maximum power density increases with thickness. Thinner layers peak around 1.6–2.0 V, while thicker layers peak near 1.3–1.5 V, showing that increasing the thickness enhances power generation, but excessive thickness may cause recombination losses, affecting efficiency.

Fig. 3 (a) Schematic of the effect of the absorbing layer's thickness on the performance of the solar cell, (b) J–V curve and (c) P–V curve of the TiO₂/BFO/Spiro-OMeTAD solar cell, and the effect of BFO's thickness variation on (d) J_sc, V_oc, P_max, and (e) %FF and %efficiency.

Fig. 3(d) presents the variation in J_sc, V_oc, and P_max at different thicknesses of BFO, and it shows that by varying the thickness from 50 to 1850 nm, the J_sc exhibits a steady increase with thickness, rising from 3.697 mA cm⁻² at 50 nm to a maximum of 9.004 mA cm⁻² at 1850 nm. This behavior is a result of the enhanced photon absorption as thickness increases, which facilitates the generation of a greater number of charge carriers, and the contribution of longer-wavelength photons becomes significant at larger thicknesses, further boosting J_sc. Furthermore, V_oc decreases from 2.178 V at 50 nm to 1.994 V at 1400 nm, then remains constant up to 1850 nm. This indicates that increasing the BFO thickness initially increases the recombination losses, but beyond 1400 nm, its impact stabilizes. On the other hand, the P_max of 53.485 W at 50 nm increases to 104.5 W at 631 nm and then declines to 95.79 W at 1850 nm. The rise in P_max up to 631 nm results from the optimal photon absorption and minimal recombination losses, and beyond this thickness, higher recombination rates and defect densities limit the charge-carrier generation, reducing P_max. Moreover, Fig. 3(e) shows the fill factor (FF) and efficiency (η) dependence on the BFO thickness, and FF gradually decreases from 66.39% (at 50 nm) to 53.40% (at 1850 nm). Conversely, as the BFO thickness increases, the η of the solar cell reaches a maximum at an optimal thickness and decreases beyond this point. At 50 nm, the η is 5.34%, increasing to a peak value of 10.101% at 500 nm. Beyond this optimal thickness, the η decreases to 9.579% at 1850 nm. The increase in η up to the optimal thickness is attributed to the enhanced photon absorption, particularly for photons with longer wavelengths, leading to improved charge-carrier generation. However, beyond 500 nm, the η decreases due to the increased recombination rates, which reduce charge-carrier lifetimes and limit charge-carrier generation.⁷⁶ All the output characteristics for different BFO thicknesses are listed in Table 2.

Table 2 Designed device (1D TiO₂/BFO/Spiro-OMeTAD) performance parameters with varying thickness of the absorber layer (BFO)

BFO's thickness (nm)	Jsc (mA cm^−2)	Voc (V)	Pmax (W)	FF (%)	Efficiency (%)
50	3.697	2.179	53.485	66.392	5.349
500	7.578	2.127	101.018	62.676	10.102
950	8.373	2.024	100.957	59.571	10.095
1400	8.758	1.994	98.319	56.295	9.831
1850	9.004	1.992	95.794	53.405	9.5793

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4.2. Effect of the ETL's thickness variation on the PV performance

A thinner ETL is best for achieving the maximum output yield of solar cells. An increase in the layer thickness may cause hindrance to the incident light that must reach the absorbing layer, and secondly, the increase enhances the series resistance of the solar cell. Fig. 4(a) presents the schematic illustration of the working mechanism of the solar cell having a thinner ETL, and it is clear that the incident light can reach the active region of the solar cell easily. But, if the ETL is thicker, it stops the incident light, as depicted in Fig. 4(b). Fig. 4(c) illustrates the J–V response at different ETL thicknesses, ranging from 10 to 150 nm, and J_sc decreases with increasing ETL thickness. The sharp J_sc drop occurs at 1.6 V for all thicknesses, indicating relatively high resistance and recombination losses for thicker ETLs. The P–V response is used to determine the P_max of solar cells, as shown in Fig. 4(d), and the power peaks at around 100.95 W at an ETL thickness of 10 nm and decreases to 56.76 W at 150 nm. Thinner layers achieve high power, while thicker layers exhibit reduced output due to increased resistance; P declines sharply within the 1.6–2.0 V range. It is observed that a thinner ETL improves electron transport and light absorption, maximizing current density, while thicker layers hinder these processes by increasing resistance and reducing light penetration.

Fig. 4 Schematic of the effect of the ETL's thickness on the performance of solar cells: (a) thinner ETL and (b) thicker ETL. (c) J–V curve and (d) P–V curve of the TiO₂/BFO/Spiro-OMeTAD solar cell. Effect of the ETL's thickness variation on (e) J_sc, V_oc, P_max, and (f) %FF and %efficiency.

Fig. 4(e) shows the variation in J_sc, V_oc, and P_max at different thicknesses of ETL. J_sc decreases from 7.57 to 4.420 mA cm⁻², and similarly, the V_oc decreases (from 2.126 to 2.063 V) as thickness increases (from 10 to 150 nm), suggesting that the V_oc is sensitive to the ETL thickness, with optimal performance achieved by the thinner layer. Thinner ETL layers help maintain better voltage due to efficient charge transport, while thicker layers introduce more resistance, resulting in a reduced value of voltage. Moreover, P_max decreases (101.01 to 56.76 W) with increasing ETL thickness due to the increased recombination and resistive losses. Fig. 4(f) depicts the variation in %FF and η. FF decreases from 62.67% at 10 nm to its lowest at 45 nm, then gradually increases to 62.23% at 150 nm. This suggests that a moderate ETL thickness increases the resistance and recombination rate, but thicker layers stabilize FF. On the other hand, a consistent decline can be seen in the overall η as the ETL thickness increases. This is because thinner ETLs ensure efficient charge transport, minimal recombination, and better light penetration, while thicker layers impede performance due to the increased resistance, increased recombination rate, and reduced photon absorption by the active layer.⁷⁷ The detailed numerical values for these output characteristics for different ETL thicknesses are listed in Table 3.

Table 3 Designed device (1D TiO₂/BFO/Spiro-OMeTAD) performance parameters with varying thickness of the ETL (TiO₂)

TiO2's thickness (nm)	Jsc (mA cm^−2)	Voc (V)	Pmax (W)	FF (%)	Efficiency (%)
10	7.578	2.126	101.017	62.673	10.101
45	6.295	2.101	80.035	60.492	8.003
85	5.466	2.084	69.559	61.028	6.955
115	4.876	2.074	62.335	61.619	6.233
150	4.420	2.063	56.76	62.230	5.676

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4.3 Effect of HTL's thickness variation on the PV performance

The effect of shunt resistance in solar cell's performance is remarkable, specially it affects the V_oc, and it can be understood in this sense, as HTL thickness increases it provides unwanted paths to the internal current and due to which shunt resistance decreases and it ultimately reduces the V_oc, as shown in Fig. 5(a and b). Furthermore, the J–V and P–V characteristics at different HTL thicknesses, ranging from 50 to 150 nm, were examined to determine the J_sc, V_oc, and P_max, as shown in Fig. 5(c) and (d), respectively. J_sc remains nearly constant before sharply dropping, while P increases, before a sharp decline at 1.6 V; both parameters show minimal variation across different HTL thicknesses. Fig. 5(e) presents the variation in J_sc, V_oc, and P_max, and J_sc increases from 7.57 mA cm⁻² at 10 nm to 7.74 mA cm⁻² at 150 nm due to the improved charge collection and reduced carrier recombination with increasing HTL thickness, enhancing the current extraction efficiency. On the other hand, V_oc exhibits a gradual decrease (from 2.1268 to 2.1058 V) with increasing HTL thickness (from 10 to 150 nm), likely resulting from an energy level mismatch and the shunt resistance in the thicker layers. Moreover, P_max increases as the thickness increases, peaking at 103.45 W at an HTL thickness of 150 nm, and may saturate after this optimal thickness is achieved. Furthermore, FF improves with increasing HTL thickness up to the optimum range, and finally, η increases steadily from 10.10% to 10.34%, as shown in Fig. 5(f). These findings underscore the critical role of HTL-thickness optimization in achieving a balance between efficient charge transport and resistive losses, and a properly tuned HTL thickness enhances the overall device performance, achieving the maximum η and power output for PSCs.⁷⁸ Table 4 presents a comprehensive overview of all these output characteristics for different HTL thicknesses.

Fig. 5 (a and b) Schematic of the effect of thicker and thinner HTLs on the performance of solar cells. (c) J–V curve and (d) P–V curve of the TiO₂/BFO/Spiro-OMeTAD solar cell. Effect of the HTL's thickness variation on (e) J_sc, V_oc, P_max, and (f) %FF and %efficiency.

Table 4 Designed device (1D TiO₂/BFO/Spiro-OMeTAD) performance parameters with varying thickness of the HTL (spiro)

Spiro's thickness (nm)	Jsc (mA cm^−2)	Voc (V)	Pmax (W)	FF (%)	Efficiency (%)
50	7.578	2.126	101.019	62.676	10.102
150	7.624	2.121	101.638	62.823	10.163
80	7.668	2.116	102.304	63.037	10.230
115	7.707	2.111	102.912	63.248	10.291
150	7.741	2.105	103.457	63.464	10.345

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4.4. Effect of BFO's DOS in the conduction and valence bands (N_CN_V) on the PV performance

It is important to study the density of states (DOS) in the conduction and valence bands, because it is directly linked to the carrier's transportation and recombination process. Fig. 6(a) shows the higher DOS at conduction band, reflecting the greater probability of intra-band transition, which is non-radiative emission of energy and this happens beyond an optimal level, but its probability is lesser under the optimum range of DOS. Similarly, the higher DOS in the valence band leads to a greater probability of intra-band transitions, as shown in Fig. 6(b). Fig. 6(c) shows that as N_CN_V increases from 2 × 10¹⁷ to 2 × 10²⁰ cm⁻³, J_sc remains nearly constant, but the V_oc at which it sharply drops shifts to lower values, indicating an increase in the recombination and a reduction in the charge-extraction efficiency. Fig. 6(d) illustrates the P–V characteristics. P initially rises, peaks, and then declines at higher voltages. The shifting peak suggests that higher N_CN_V values influence the recombination dynamics, impacting the optimal operating voltage and reducing the overall power extraction.

Fig. 6 (a and b) Schematic of the higher and lower density of states (DOS) in the conduction & valence bands (N_CN_V) within the BiFeO₃ (BFO) layer. (c) J–V curve and (d) P–V curve of the TiO₂/BFO/Spiro-OMeTAD solar cell. Effect of BFO's N_CN_V on (e) J_sc, V_oc, P_max, and (f) %FF and %efficiency.

In Fig. 6(e), although J_sc slightly increases from 8.158 mA cm⁻² to 8.185 mA cm⁻², V_oc significantly decreases from 1.99 V to 1.235 V, resulting in a reduction in P_max from 87.21 W to 59.117 W. The decrease in V_oc with an increase in the effective density of states strongly confirms their inverse relationship, highlighting a fundamental trade-off in device performance. This occurs because the higher density of states enhances recombination losses, which reduces the built-in potential and the V_oc, while the slight improvement in J_sc due to increased carrier generation cannot compensate for the major voltage drop, leading to a decrease in the maximum power.⁷⁹ In Fig. 6(f), the FF increases from 53.68% to 58.47%, indicating improved charge extraction and reduced resistive losses at higher N_CN_V values. However, η decreases from 8.72% to 5.91%, mainly due to the significant drop in V_oc and P_max, which outweighs the benefits of the FF improvement. This suggests that an excessive increase in N_CN_V leads to increased recombination, negatively impacting overall performance. Table 5 presents the influence of N_CN_V variations on the overall device performance, showing trends in the electrical characteristics and η as the density of states increases.

Table 5 Designed device (1D TiO₂/BFO/Spiro-OMeTAD) performance parameters with varying density of states of BFO in the conduction and valence bands (N_CN_V)

BFO's NCNV (cm^−3)	Jsc (mA cm^−2)	Voc (V)	Pmax (W)	FF (%)	Efficiency (%)
2 × 10^17	8.158	1.991	87.216	53.721	8.721
2 × 10^18	8.177	1.517	68.468	55.187	6.846
2 × 10^19	8.185	1.375	61.854	54.954	6.185
2 × 10^20	8.185	1.235	59.117	58.476	5.911

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4.5. Effect of ETL's DOS in the conduction and valence bands (N_CN_V) on the PV performance

Fig. 7(a) illustrates the J–V characteristics for different TiO₂ density of states (N_CN_V). As N_CN_V increases from 2 × 10¹⁵ to 2 × 10¹⁸ cm⁻³, J_sc remains stable at lower voltages but drops sharply at higher voltages. Higher N_CN_V shifts the cutoff point, affecting the V_oc and indicating changes in charge transport and recombination. Fig. 7(b) presents the P–V characteristics for varying TiO₂’N_CN_V. P increases, peaks, and then declines. A higher DOS shifts the peak position and alters the maximum power, highlighting its effect on the solar cell performance.

Fig. 7 Effect of the density of states within the conduction and valence bands (N_CN_V) in the electron-transport layer (TiO₂) on the solar cell performance. (a) J–V curve and (b) P–V curve of the TiO₂/BFO/Spiro-OMeTAD solar cell. Effect of TiO₂'s N_CN_V on (c) J_sc, V_oc, P_max, and (d) %FF and %efficiency.

Fig. 7(c) shows the variations in J_sc, V_oc, and P_max. As N_CN_V increases from 2 × 10¹⁵ cm⁻³ to 2 × 10²⁰ cm⁻³, J_sc decreases from 8.194 mA cm⁻² to 7.6 mA cm⁻² and then stabilizes, due to the saturation of the charge carrier transport. V_oc increases from ∼1.35 V to ∼2.1 V, indicating improved band alignment with minimal effect at higher N_CN_V, while P_max increases from ∼60.87 W to ∼108.87 W and then levels off as the recombination counteracts further gains. Moderate N_CN_V values enhance performance, but excessive values lead to saturation. Fig. 7(d) shows the variation of FF and η with the N_CN_V in TiO₂. FF increases from 54% to 66%, stabilizing or presenting a slight decline afterward due to improved charge transport. Moreover, η follows a similar trend, rising from 6.08% to 10.88%, then plateauing as further increases no longer significantly enhance performance.⁸⁰ The improvement is due to the reduced recombination loss and better carrier collection, although excessively high values lead to diminishing returns. Table 6 highlights the impact of the ETL's N_CN_V variations on the solar cell performance, showcasing key trends and dependencies.

Table 6 Designed device (1D TiO₂/BFO/Spiro-OMeTAD) performance parameters with varying density of states of TiO₂ in the conduction and valence bands (N_CN_V)

TiO2's NCNV (cm^−3)	Jsc (mA cm^−2)	Voc (V)	Pmax (W)	FF (%)	Efficiency (%)
2 × 10^15	8.194	1.357	60.871	54.727	6.087
2 × 10^16	7.713	2.108	108.877	66.940	10.887
2 × 10^17	7.750	2.115	105.899	64.575	10.589
2 × 10^18	7.670	2.119	104.556	64.315	10.455
2 × 10^19	7.668	2.120	103.353	63.552	10.335
2 × 10^20	7.668	2.114	101.784	62.781	10.178

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4.6. Effect of BFO's electron affinity (χ) on the PV performance

The energy-band alignment is crucial for the efficient operation of solar cells; any discontinuity or misalignment can lead to erroneous results. Therefore, ensuring proper energy-band alignment across the three layers requires careful optimization of the electron affinity. χ refers to the energy difference between the vacuum energy level and the conduction band minimum of a material. It governs the energy-band alignment at the heterojunction interfaces and significantly affects charge transfer and recombination dynamics within the solar cell. Therefore, its optimization is essential for achieving efficient carrier transport and high device performance. For the influence of varying the χ values of the absorber layer (BFO) on the operation performance of the solar cell, J–V characteristics show, in Fig. 8(a), that J_sc remains nearly constant, while the V_oc drop shifts with χ. At 3.3 eV, the drop starts around 0.9 V, at 3.4 eV around 1.0 V, and at 3.5 eV beyond 1.2 V, showing that higher χ improves charge transport, reducing voltage losses. In Fig. 8(b), the P–V characteristics display that P increases with the voltage, peaks, and then declines, with the highest peak occurring at 3.3 eV, while 3.4 eV and 3.5 eV show lower peaks, indicating that lower χ values favor maximum power output.

Fig. 8 (a) J–V curve and (b) P–V curve of the TiO₂/BFO/Spiro-OMeTAD solar cell. Effect of BiFeO₃ (BFO)'s electron affinity on (c) J_sc, V_oc, P_max, and (d) %FF and %efficiency.

Furthermore, Fig. 8(c) presents the variations in J_sc, V_oc, and P_max at different χ values, and it is clear that J_sc increases slightly from 8.171 mA cm⁻² at 3.3 eV to 8.179 mA cm⁻² at 3.5 eV, indicating improved charge extraction with higher χ values. V_oc first decreases from 1.81 V at 3.3 eV to 1.77 V at 3.4 eV, then increases to 1.83 V at 3.5 eV, suggesting an initial rise in recombination at 3.4 eV before the improvement in band alignment at 3.5 eV improves voltage. P_max continuously decreases from 78 W to 55 W, implying that increasing χ introduces losses that outweigh the gains in charge transport, reducing overall device performance. However, FF decreases significantly from 55.40% to 38.98%, indicating that higher χ negatively impacts charge extraction and increases resistive losses. Similarly, η declines from 8.50% to 5.80%, which follows the trend of decreasing P_max shown in Fig. 8(d). This η reduction is directly linked to energy-band misalignment, leading to compromised charge extraction and an increased recombination rate.⁷⁶ In the end, all the output characteristics with varying BFO's electron affinities are listed in Table 7.

Table 7 Designed device (1D TiO₂/BFO/Spiro-OMeTAD) performance parameters with varying electron affinity of BFO

BFO's affinity (eV)	Jsc (mA cm^−2)	Voc (V)	Pmax (W)	FF (%)	Efficiency (%)
3.3	8.170	1.808	78.317	52.987	7.831
3.4	8.176	1.770	65.361	45.147	6.536
3.5	8.179	1.834	53.127	35.411	5.312

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4.7. Effect of TiO₂'s electron affinity (χ) on the PV performance

The performance of a solar cell is significantly influenced by the χ of the TiO₂ layer, and the variations in this parameter impact key electrical characteristics. Fig. 9(a) shows the J–V characteristics for different χ values of TiO₂ (3.5 eV to 3.7 eV). The sharp drop in J occurs around 1.6 V, indicating the turn-off point. The overall J_sc remains relatively stable before this V_oc, suggesting minimal impact of χ on the current generation until a critical voltage is reached. Fig. 9(b) illustrates the P–V curve for different TiO₂ electron affinities, where P rises, peaks, and then drops sharply. The peak power remains nearly constant, indicating the minimal impact of the electron affinity on the power output. However, slight differences may be attributed to changes in charge transport and recombination dynamics within the device.

Fig. 9 (a) J–V curve and (b) P–V curve of the TiO₂/BFO/Spiro-OMeTAD solar cell. Effect of the electron affinity of TiO₂ on (c) J_sc, V_oc, P_max, and (d) %FF and %efficiency.

Fig. 9(c) depicts the variations in J_sc, V_oc, and P_max with changing χ values. J_sc fluctuates within a narrow range of 8.1685 to 8.1700 mA cm⁻², showing a peak around 3.6 eV, while dipping at intermediate values, which indicates that specific electron affinities enhance charge extraction, improving current generation. V_oc follows the same pattern as J_sc, ranging between 1.49 V and 1.53 V, reaching its maximum at 3.6 eV. This behavior suggests that band alignment at these electron affinities optimally supports voltage generation. P_max remains relatively stable, fluctuating slightly between 48.801 W and 48.785 W, as the compensatory effects of J_sc and V_oc balance the overall power output. The observed trends indicate that optimizing electron affinity is crucial for enhancing solar cell performance without significantly affecting power stability. Fig. 9(d) indicates the variation of FF and η with TiO₂'s electron affinity. FF ranges between 39.90% and 38.90%, reaching its highest values around 3.5 eV, and similarly, η peaks at 4.884% for 3.5 eV. When χ is optimal, the conduction band alignment enhances electron flow, reducing recombination losses and thereby increasing η. These findings emphasize the critical role of optimizing TiO₂'s χ to balance energy alignment, minimize recombination, and enhance charge transport, to achieve superior solar cell performance.⁸¹ Finally, the output values with varying electron affinities of TiO₂ are listed in Table 8.

Table 8 Designed device (1D TiO₂/BFO/Spiro-OMeTAD) performance parameters with varying electron affinity of TiO₂

TiO2's affinity (eV)	Jsc (mA cm^−2)	Voc (V)	Pmax (W)	FF (%)	Efficiency (%)
3.5	8.168	1.497	48.801	39.903	4.880
3.6	8.169	1.634	48.794	36.531	4.879
3.7	8.169	1.534	48.785	38.909	4.878

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4.8. Effect of Spiro's electron affinity (χ) on the PV performance

Fig. 10(a) illustrates the J–V curve, where J_sc remains constant (8.167 mA cm⁻²) up to 0.6–1.1 V before decreasing to near-zero at higher voltages. This is attributed to the better energy-level alignment, enhancing photon-to-electron conversion. Fig. 10(b) demonstrates the P–V curve, with P increasing to a peak (78.32 W) as χ rises from 1.5 to 1.9 eV. Fig. 10(c) presents the variation in J_sc, V_oc, and P_max for different χ values of Spiro, and it is observed that J_sc increases from 8.167 to 8.169 mA cm⁻² with rising χ, due to the improved symmetry in the energy levels and the enhanced charge carrier flow across the device. On the other hand, V_oc initially increases then slightly decreases as χ increases, attributable to the minimized bandgap mismatches between the absorber and HTL layers, which slightly diminish the charge-separation efficiency. However, P_max improves linearly from 48.78 to 78.32 W. These enhancements result from the improved energy-level alignment between the HTL and the PVK layer, which minimizes energy losses and charge-transport efficiency. Similarly, FF and η increase as shown in Fig. 10(d), and FF increases from 34.11 to 53.13%, while η increases from 4.878% at χ = 1.5 eV to 7.832% at χ = 1.9 eV. These results highlight the critical role of the HTL electron affinity in optimizing the performance of PSCs.⁸² In the end, Table 9 presents a comprehensive overview of all the above-mentioned output characteristics with varying electron affinities of Spiro-OMeTAD.

Fig. 10 (a) J–V curve and (b) P–V curve of the TiO₂/BFO/Spiro-OMeTAD solar cell. Effect of Spiro's electron affinity on (c) J_sc, V_oc, P_max, and (d) %FF and %efficiency.

Table 9 Designed device (1D TiO₂/BFO/Spiro-OMeTAD) performance parameters with varying electron affinity of Spiro

Spiro's affinity (eV)	Jsc (mA cm^−2)	Voc (V)	Pmax (W)	FF (%)	Efficiency (%)
1.5	8.168	1.750	48.789	34.113	4.878
1.6	8.169	1.845	55.760	36.978	5.576
1.7	8.169	1.849	62.733	41.514	6.273
1.8	8.169	1.925	70.483	44.799	7.048
1.9	8.169	1.804	78.326	53.136	7.832

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4.9. Effect of operating temperature on the PV performance

The operating temperature of a solar cell significantly influences its performance, primarily by intensifying phonon vibrations, which, in turn, increase internal resistances, such as the cell's series resistance. Elevated temperatures also raise the likelihood of collisions between charge carriers and lattice ions, thereby amplifying recombination losses. Fig. 11(a) shows that an increase in the temperature of the device enhances the random motion of charge carriers inside the layers of solar cells, and at low temperatures, the random motion reduces, as shown in Fig. 11(b).

Fig. 11 (a) Higher temperature and (b) lower temperature effect on the device's internal environment. (c) J–V curve and (d) P–V curve of the TiO₂/BFO/Spiro-OMeTAD solar cell. Effect of temperature on (e) J_sc, V_oc, P_max, and (f) %FF and %efficiency.

Furthermore, Fig. 11(c and d) shows the J–V and P–V characteristics at different operating temperatures, ranging from 290 to 310 K, for the determination of J_sc, V_oc, and P_max of the solar cell. Both J and P show a slight decline with temperature, but they sharply decrease at the V of 0.6 V. In Fig. 11(e), J_sc exhibits minimal variation with temperature changes, although a slight decrease is observed at higher temperatures. Similarly, V_oc reduces from 1.57 to 1.48 V as temperature increases from 290 to 310 K, and this decline is attributed to bandgap narrowing and an increase in the reverse saturation current, both of which negatively impact the device's ability to maintain a high V_oc at elevated temperatures. Moreover, P_max declines from 49.67 to 43.69 W, due to diminished FE polarization and increased recombination losses at higher temperatures, which collectively limit the charge-extraction efficiency. However, FF initially decreases and then increases to 36.01% as the temperature increases from 290 to 295 K, stabilizing thereafter, as shown in Fig. 11(f). This transient improvement is linked to enhanced carrier mobility and reduced series resistance, which temporarily offset the adverse effects of higher recombination rates. The η value of the solar cell slightly decreases from 4.96% to 4.36% with increasing temperature, as shown in Fig. 11(f). This is attributable to the intrinsic narrow bandgap properties and moderate FE behavior of the PVK material, which mitigate significant performance degradation under thermal variations.⁸³ Finally, all the output characteristics with varying temperatures of the operating device are tabulated in Table 10.

Table 10 Designed device (1D TiO₂/BFO/Spiro-OMeTAD) performance parameters with varying operating temperatures

Temperature (K)	Jsc (mA cm^−2)	Voc (V)	Pmax (W)	FF (%)	Efficiency (%)
290	8.1687	1.5709	49.674	38.711	4.967
300	8.1695	1.7772	46.644	32.126	4.664
310	8.1699	1.5709	45.221	35.235	4.522
320	8.1690	1.4849	43.690	36.017	4.369

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4.10. Effect of SnS's thickness on the PV performance of the TiO₂/SnS/BFO/Spiro-OMeTAD solar cell

Fig. 12(a) shows the J–V characteristics of the TiO₂/SnS/BFO/Spiro-OMeTAD solar cell for different SnS absorber thicknesses. J_sc increases with the thickness due to enhanced photon absorption and efficient charge generation. However, at higher thicknesses, a noticeable voltage drop occurs near the open-circuit region, indicating increased recombination and reduced carrier-collection efficiency in the thicker absorber layer. Fig. 12(b) presents the P–V characteristics for varying SnS absorber thicknesses. The output power increases with the thickness up to 700 nm, indicating enhanced light absorption and efficient charge-carrier extraction, which result in increased P_max. However, at 1000 nm, a noticeable voltage drop occurs near the maximum power region, leading to a decline in the power output. This reduction is primarily due to the increased series resistance, longer carrier transport paths, and enhanced recombination in the thicker absorber layer, which collectively lower the overall conversion efficiency. Fig. 12(c) shows the variation of J_sc, V_oc, and P_max with different SnS thicknesses. J_sc increases steadily from 31.02 to 31.98 mA cm⁻² as the thickness rises from 100 nm to 700 nm, which is attributed to the enhanced optical absorption and a high generation rate of charge carriers within the active region. However, at 1000 nm, J_sc slightly drops to 31.45 mA cm⁻² due to enhanced bulk recombination and limited carrier diffusion in the thicker layer. The V_oc remains nearly constant around 0.80–0.81 V throughout the thickness range, showing that it is primarily governed by the built-in potential and interface quality rather than the absorber thickness. P_max follows a similar trend to J_sc, increasing from 196.16 to 209.95 W up to 700 nm, indicating efficient charge extraction and minimal resistive losses. Beyond this point, it decreases to 155.68 W at 1000 nm because of the increased series resistance and recombination effects, which reduce the overall power conversion capability.

Fig. 12 (a) J–V curve and (b) P–V curve of the TiO₂/SnS/BFO/Spiro-OMeTAD solar cell. Effect of SnS's thickness on (c) J_sc, V_oc, P_max, and (d) %FF and %efficiency.

Fig. 12(d) illustrates the variation of FF and η with the SnS absorber thickness. Both parameters show a gradual improvement as the thickness increases from 100 nm to 700 nm, where the FF rises from 77.41% to 81.06% and the efficiency reaches its peak value of 20.99%. This enhancement is attributed to improved light absorption, efficient charge separation, and reduced recombination within the optimal thickness range. However, at 1000 nm, the FF drops sharply to 61.56%, and the efficiency decreases to 15.56%, mainly due to the increased series resistance, enhanced recombination losses, and limited carrier diffusion in the overly thick absorber layer. These results confirm that 700 nm is the optimum SnS thickness for achieving maximum device performance.

5. Conclusion

Global warming and our reliance on hazardous energy sources have intensified the search for environmentally friendly energy alternatives. Among these, solar energy has emerged as a cost-effective, sustainable, and clean solution to meet the rising energy demands of the world's growing population. For decades, researchers have been exploring suitable materials to enhance the stability, cost-efficiency, and performance of solar cells. In this context, perovskite materials, particularly BiFeO₃, have gained significant attention as absorber layers due to their multifunctional properties, including room-temperature ferroelectricity and strong permanent polarization, which eliminate the need for conventional p–n junctions. This study employs COMSOL simulation software to model 1D TiO₂/BiFeO₃/Spiro-OMeTAD and 1D TiO₂/SnS/BiFeO₃/Spiro-OMeTAD solar cell configurations, assuming ideal ohmic front and back metal contacts. Key parameters, such as the thickness and electron affinities of BiFeO₃, TiO₂, and Spiro-OMeTAD layers; the density of states in the valence and conduction bands of BiFeO₃ and TiO₂; and the operating temperature, were systematically varied to evaluate their impact on the cell's photovoltaic performance. The results demonstrate that the short-circuit current density increases linearly (from 3.697 to 9.004 mA cm⁻²) with the BiFeO₃ thickness (from 50 to 1850 nm), and efficiency reaches a maximum (10.101%) at an optimal thickness of nearly 600 nm. However, efficiency decreases (from 4.881% to 4.876%) with increased TiO₂ thickness (from 10 to 150 nm), while power output and efficiency steadily rise (ranging from 101 to 103.45 W and 10.15% to 10.35%) with the thickness of the hole-transport layer (ranging from 10 to 150 nm). For the SnS layer's thickness, at 700 nm, the device showed a maximum efficiency of 20.99% in the TiO₂/SnS/BiFeO₃/Spiro-OMeTAD configuration. The density of states in BFO has a decreasing impact on efficiency and reduces the open-circuit voltage (from 1.99 to 1.235 V), confirming the inverse relation between them, while an increase in the density of states in the ETL leads to an increase in efficiency (from 6.08% to 10.88%). Additionally, increasing the electron affinity of BiFeO₃ (from 3.3 to 3.5 eV) decreases the fill factor (from 52.987% to 35.411%), while increasing the electron affinity of TiO₂ (3.5 to 3.7 eV) enhances the open-circuit voltage (1.49 to 1.63 V), and increasing that of Spiro improves the power output (48.78 to 78.32 W). However, a rise in the device's operating temperature (from 290 to 310 K) reduces the overall efficiency (from 4.96% to 4.36%) of the solar cell. This study aids the optimization of material properties and device parameters for experimental purposes and highlights the potential of BiFeO₃-based perovskite materials as potential candidates for next-generation photovoltaic applications.

Conflicts of interest

The authors declare that there are no financial or any other types of conflicts of interest to be declared for this submission.

Data availability

Data will be made available on request.

Acknowledgements

The authors acknowledge partial support from University of the Punjab, Lahore, Research Grant for the year 2024–25.

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