Theoretical Performance of BaSnO₃-Based Perovskite Solar Cell Designs Under Variable Light Intensities, Temperatures, and Donor and Defect Densities

Abstract

Barium stannate (BaSnO₃) has emerged as a promising alternative electron transport material owing to its superior electron mobility, resistance to UV degradation, and energy bandgap tunability, yet BaSnO₃-based perovskite solar cells have not reached the efficiency levels of TiO₂-based designs. This theoretical study presents a design-driven evaluation of BaSnO₃-based perovskite solar cell architectures, incorporating MAPbI₃ or FAMAPbI₃ perovskite materials, Spiro-OMeTAD, or Cu₂O hole transport materials as well as hole-free configurations, under varying light intensity. Using a systematic device modelling approach, we explore the influence of key design variables—such as layer thickness, donor density, and interface defect concentration—of BaSnO₃ and operating temperature on the power conversion efficiency (PCE). Among the proposed designs, the FTO/BaSnO₃/FAMAPbI₃/Cu₂O/Au heterostructure exhibits an exceptionally effective arrangement with PCE of 38.2% under concentrated light (10,000 W/m², or 10 Sun). The structure also demonstrates strong thermal robustness up to 400 K, with a low temperature coefficient of −0.078% K⁻¹. These results underscore the importance of material and structural optimisation in PSC design and highlight the role of high-mobility, thermally stable inorganic transport layers—BaSnO₃ as the electron transport material (ETM) and Cu₂O as the hole transport material (HTM)—in enabling efficient and stable photovoltaic performance under high irradiance. The study contributes valuable insights into the rational design of high-performance PSCs for emerging solar technologies.

1. Introduction

Among all the existing photovoltaic technologies, perovskite solar cells (PSCs) are the brightest option. Throughout the last ten years, the power conversion efficiency of PSCs has dramatically improved from 3.5% [1] to 25.8% [2,3]. This notable advancement is primarily driven by the materials’ superior optical, electrical, and electronic characteristics. Moreover, the fabrication of PSCs is achievable through a simple and economical solution-processable approach [4,5,6]. The basic structure of PSCs involves an absorber layer (perovskite) sandwiched between two electrodes. Hybrid organic–inorganic halide-based perovskite materials are widely studied for use in PSCs, with lead-based compounds such as Methylammonium lead iodide (MAPbI₃) demonstrating superior efficiency [6]. The electron transport layer (ETL) and hole transport layer (HTL) are commonly used as interfacial buffers between the absorber layer and the electrodes. These layers serve an essential function in enabling charge carrier separation and transport to electrodes while also mitigating charge recombination [6,7]. Despite this, the successful fabrication of HTL-free PSCs has been demonstrated, attributed to the inherent dual functionality of perovskite materials, which can serve as both a light absorber and a hole conductor [8,9,10].

Although there have been significant advancements in the field of PSCs, various obstacles still prevent them from being commercially viable, especially in terms of their long-term stability and overall performance [3]. An essential component in enhancing the efficiency of PSCs is the selection of electron transport material. While titanium dioxide (TiO₂) remains the predominant ETL material [11], it exhibits certain drawbacks, such as low electron mobility, vulnerability to ultraviolet (UV) radiation-induced degradation, and the necessity for high-temperature processing, all of which can negatively impact the performance of PSCs [12,13,14]. These difficulties, including charge recombination at the interface and hysteresis effects, highlight the need for more effective electron transport materials (ETMs) [15]. Although combined ETL has been adopted to enhance the performance of TiO₂-based PSCs, the issue of low electron mobility and poor stability upon UV exposure have not been overcome [16]. Other binary oxides such as tin oxide (SnO₂) [17] and ternary metal oxides such as zinc stannate oxide (Zn₂SnO₄) [15] have been studied as alternative ETMs due to their potential advantages, including better charge transport properties, enhanced stability, compatibility with low temperatures, and scalable manufacturing processes. Consequently, exploring and developing more efficient ETMs is crucial to advancing PSCs’ performance, photostability, and commercial feasibility.

BaSnO₃ (BSO) has garnered significant attention due to its promising performance as an n-type semiconductor [18,19]. BSO is an attractive ETM option because it shares similar electronic properties with TiO₂, such as bandgap and charge transfer kinetics, while offering improved chemical stability and higher electron mobility [20]. Additionally, the optoelectronic properties of BSO can be readily modified through doping or by adjusting the relative ratios of cations, thereby allowing control over its bandgap energy, work function, and electrical resistivity [12]. Sun et al. introduced BSO as ETL in planar PSCs for the first time. By optimizing the BSO layer’s coverage, roughness, and thickness, BSO-based PSCs demonstrated nearly a 12% increase in power conversion efficiency (PCE) compared to TiO₂-based cells. Such findings have been attributed to decreased charge transfer resistance, efficient electron transfer between the perovskite and BSO, and reduced charge recombination [20]. In 2021, A. Rehman [21] conducted a simulation study using SCAPS-1D to explore MAPbI₃-based perovskite solar cells, incorporating Cu or Mo as the metal back electrode and BaSnO₃ and Cu₂O as the ETL and HTL, respectively. Following critical optimisations of device parameters such as layer thickness, the carrier concentration of each layer, the bulk defect density of the photosensitive layer, and the work function of the back electrode, the device, as simulated, reached a notable PCE of 32%. The impact of BSO on the performance of Pb-free PSCs was also investigated using SCAPS-1D software. The simulated device achieved an efficiency of 22.09%; however, by optimizing the thickness and defect density of the perovskite layer and charge transport layers, the device’s PCE improved significantly to 28.21% [22].

Recently, Kohan et al. explored a composite ETL combining c-SnO₂ and mp-BSO for PSCs, achieving a PCE of 15.54%, which is comparable to or surpasses previously reported values. Notably, the champion device, even without encapsulation, exhibited significantly enhanced thermal stability and photostability, as well as superior long-term air stability, compared to devices utilizing TiO₂ as the ETL [16]. Several investigations have focused on optimizing the efficiency of BSO-based PSCs, with various studies incorporating doping techniques as a key approach. Lanthanum (La)-doped BSO was reported as an efficient ETL for PSCs, yielding a PCE of 21.2%, compared to 19.7% for an mp-TiO₂ device, with substantial stability enhancement, retaining about 93% of the initial PCE after 1000 h of full sun exposure [23]. Zinc (Zn)-doped BSO was also optimised to enhance the overall performance of BSO-based PSCs, as it has been demonstrated that Zn dopants contribute to a reduction in charge recombination and enhance charge extraction [24].

Another approach that may improve the efficiency of BSO-based PSCs is enhancing the light intensity of the incident light as seen in concentrated photovoltaics (CPVs), a promising technology that ensures high solar cell efficiency [25,26]. Concentrated photovoltaics can direct sunlight onto a highly efficient solar cell by incorporating different optical elements, thereby magnifying the intensity of the input light. Although PSCs have not been extensively explored for CPV technology, the limited theoretical and experimental studies suggest promising prospects for such third-generation photovoltaic materials, showing good stability and achieving a notable PCE, particularly with formamidinium–cesium-based hybrid perovskites [25,27]. It is observed that upon increasing the incident light intensity, the short-circuit current density (J_SC) of the PSC increases linearly and the open-circuit voltage (V_OC) increases logarithmically. However, the power conversion efficiency (PCE)’s increasing trend is limited due to the substantial reduction in the fill factor (FF) of the device [28]. The series resistance (R_S) of the extraction material, layer interfaces, and transparent conductive electrode (TCE) is the main contributor to the FF drop [25,29]. High light intensity magnifies the production of electron–hole pairs; therefore, high charge mobility is essential in both the ETL and HTL to mitigate charge accumulation at layer interfaces and recombination. Spiro-OMeTAD, first reported by U. Bach and co-workers more than twenty years ago, is the predominant hole transport material employed in PSCs [30]. Despite its prevalence, Spiro-OMeTAD exhibits suboptimal charge mobility [31]. Additionally, the high expense and poor stability of organic HTMs hinder their suitability for the commercialisation of high-performance PSCs, as they are prone to degradation from moisture and air exposure. Consequently, inorganic materials such as CuI, Cu₂O, NiO, and CuSCN have been studied as HTMs for their inherent stability, effective hole transport performance, and low-cost processing methods [32,33,34], which could be beneficial for PSCs under high light intensity. Another factor to consider during prolonged exposure to light is the increase in temperature, which can result in the degradation of PSC performance [28]. To improve the performance of BSO-based PSCs under high light intensity, it is therefore essential to select materials that provide thermal stability.

The potential of BSO has not been fully explored, and to overcome this gap, the current manuscript focuses on a simulation-based design and performance analysis of BSO-based MAPbI₃ and MAFAPbI₃ perovskite solar cells under variable light intensity, aiming to improve device efficiency through rational architecture selection. In this context, various design parameters—including HTM choice, operating temperature, BSO layer thickness, donor concentration, and defect density—are systematically investigated to identify the optimal physical parameters to enhance PCE. This theoretical study offers valuable design insights into the underlying performance mechanisms of BSO-based devices, helping experimental researchers and engineers to optimise structural configurations and material properties and predict suitable operating conditions, such as light intensity levels and temperatures, for use in a real scenario. This enables the selection of appropriate concentrated light systems and thermally stable materials before performing time-consuming and costly experiments. This can significantly speed up the development process of designing high-performance PSCs. In addition, the study highlights the potential of BaSnO₃ as a stable and efficient electron transport layer, particularly in emerging architectures such as concentrated photovoltaics and low-cost, hole-free carbon-based solar cells.

2. Methodologies

In this study, BSO with two kinds of perovskite absorber materials (MAPbI₃ and MA_0.5FA_0.5PbI₃) is used as the ETL and analysed to evaluate device performance for both conventional planar (n-i-p) PSC structures and hole-transport-material-free carbon-based PSCs (CPSCs), configured as FTO/BSO/perovskite/Cu₂O or Spiro-OMeTAD/Au, and FTO/BSO/perovskite/C using the one-dimensional Solar Cell Capacitance Simulator (SCAPS-1D) software version 3.3.11. The SCAPS-1D software can simulate solar cells’ performance by solving Poisson’s Equation (1) and the continuity equations of electron (2) and hole (3) for semiconductors [22,35].

$${\nabla }^2\Psi ={\displaystyle \frac{q}{\epsilon }}(n-p+N_A-N_D)$$

(1)

$$\nabla {.J}_n+q{\displaystyle \frac{\partial n}{\partial t}}=+qR$$

(2)

$$\nabla {.J}_n+q{\displaystyle \frac{\partial p}{\partial t}}=-qR$$

(3)

Here, Ψ denotes the electrostatic potential, ϵ is the permittivity, R is the recombination rate, q is the charge of the electron, n and p are the concentration of free electrons and holes, N_A and N_D are donor and acceptor density, and J_n and J_p are the electron and hole current densities, respectively.

Figure 1a,b illustrate the structure of the PSCs and CPSCs that were used in this modelling study. Figure 1c depicts the energy band alignment of the layers tested in this theoretical investigation.

The fundamental material parameters used to model the proposed devices were sourced from a range of numerical and experimental investigations, as outlined in

Table 1. Input parameters of each layer.

Parameters	FTO [38]	BSO [22]	MAFAPbI3 [39]	MAPbI3 [36]	Cu2O [40]	Spiro-OMeTAD [41]
Thickness (nm)	500	50 (vary)	450	600	200	200
Bandgap, Eg (eV)	3.5	3.16	1.48	1.55	2.17	2.88
Electron affinity, χ (eV)	4	3.90	3.758	3.9	3.20	2.05
Relative permittivity,  ϵr	9	17	6.5	32	7.11	3
CB effective density of states, NC (cm−3)	2.2 × 1017	1.2 × 1019	2.2 × 1015	2.8 × 1020	2.02 × 1017	2.2 × 1018
VB effective density of states, NV (cm−3)	2.2 × 1016	1.8 × 1019	2.2 × 1017	3.9 × 1020	1.1 × 1019	1.8 × 1019
Electron mobility, μn (cm2/Vs)	20	200	2	11.8	200	2.0 × 10−4
Hole mobility, μp (cm2/Vs)	10	25	2	11.8	80	2.0 × 10−4
Donor density, ND (cm−3)	1.0 × 1019 [22]	1.0 × 1017	109	1.0 × 1013	0	0
Acceptor density, NA (cm−3)	0	0.0	109	1.0 × 1013	1 × 1018	2.0 × 1019
Defect density, Nt (cm−3)	1 × 1014	1.0 × 1015	1.0 × 1013 [42]	3.0 × 1014	1.0 × 1015 [36]	1.0 × 1015

. Other parameters were assumed to be constant in all materials; for example, the thermal velocities of electrons and holes was set as 10⁷ cm. In addition, the interface defects at the BSO/perovskite and perovskite/HTL interfaces were assumed to be single and neutral, with a total defect density of 10¹⁰ cm⁻² [36]. At the BSO/perovskite interface, the hole and electron capture cross-sections were set as 10⁻¹⁸ cm² and 10⁻¹⁹ cm², respectively, and at the perovskite/HTL interface, they were also assumed to be single and neutral with hole and electron capture cross-sections of 10⁻¹⁹ cm² and 10⁻¹⁸ cm², respectively [36]. The work functions of FTO, Au, and C have been considered as 5.1 eV, 4.4 eV [22], and 5.2 eV [37], respectively. The simulations were performed under standard test conditions at solar irradiance of 1000 W/m² within AM 1.5G solar spectrum, and operating temperature of 300 K. In addition, the performance of the devices has been evaluated by testing them under different light intensities ranging from 1000 W/m² to 10,000 W/m². Figure 2 illustrates the flowchart outlining the simulation workflow for assessing the performance of different configurations of BaSnO₃-based perovskite solar cells under different varying conditions using SCAPS-1D.

3. Results and Discussion

The performances of BSO-based PSCs that employ Cu₂O and Spiro-OMeTAD as the HTL and BSO-based CPSCs have been studied. The J-V characteristics of the six examined devices are displayed in Figure 3a. A summary of the J-V parameters can be found in

Table 2. Performance indicators of BSO-based devices.

Device Configuration	VOC (V)	JSC (mA/cm2)	FF (%)	PCE (%)
FTO/BSO/MAPbI3/Cu2O/Au	0.938997	24.686179	81.6617	18.66
FTO/BSO/MAPbI3/Spiro-OMeTAD/Au	0.908349	24.319527	82.055	18.1264
FTO/BSO/MAPbI3/C	0.827971	24.2917242	83.7692	16.8484
FTO/BSO/MAFAPbI3/Cu2O/Au	1.25416	25.677727	85.9141	27.6678
FTO/BSO/MAFAPbI3/Spiro-OMeTAD/Au	1.19698	25.63886	82.0617	25.184
FTO/BSO/MAFAPbI3/C	1.221696	25.561464	81.2788	25.382

.

MAFAPbI₃ demonstrated superior device performance compared to MAPbI₃, leading to the conclusion that it is the more appropriate absorber choice for the BSO electron transport layer. This is obviously due to the conduction band alignment between BSO and MAFAPbI₃, which facilitates better electron extraction from the absorber and transportation to the front electrode. These findings can be understood by examining the conduction band offset (CBO) at the ETL/perovskite absorber junction. The CBO is obtained by subtracting the electron affinity of the ETL from that of the perovskite absorber (CBO = χ_perovskite − χ_ETL) [43]. When the CBO is negative, a “cliff” forms at the junction, enhancing electron transport from the perovskite layer to the ETL owing to the strong electric field, thereby increasing the J_SC [44]. However, a more negative CBO lowers the activation energy (E_a) for recombination at the ETL/perovskite junction (defined as E_a = E_g − |CBO|), which, in turn, decreases the V_OC and overall cell performance [45]. MAFAPbI₃ devices recorded the highest J_SC and V_OC values, potentially due to well-aligned conduction bands, as the CBO value for these devices is −0.142 eV. Such a value results in a large E_a, which, in turn, minimises defect recombination centres at the junction sites and enhances electron transport from the perovskite absorber to the electron transport layer. In the case of MAPbI₃, the CBO of about 0 eV results in a significantly smaller E_a at the junction, which increases charge recombination and hence leads to reduced V_OC and PCE.

It is worth noting that applying Cu₂O as a stable inorganic HTL has shown promising results among different hole transport materials [21,40,46]. Similarly, this finding can be elucidated by examining the valence band offset (VBO) at the HTL/perovskite junction with respect to bandgap alignment. The VBO, along with the built-in electric field (V_bi), is affected by variations in the valence band position of the HTLs. The VBO can be expressed as ((χ_HTL + E_gHTL) − (χ_Perovskite + E_gPerovskite)) [40,43]. It is reported that a negative VBO value leads to a decrease in V_bi, which, in turn, results in V_OC reduction [47]. Therefore, the higher V_OC observed in Cu₂O-based devices is ascribed to their high charge mobilities and suitable VBO values of 0.142 eV for the MAFAPbI₃/Cu₂O interface and −0.07 eV for the MAPbI₃/Cu₂O interface, compared to −0.308 eV and −0.52 eV for the corresponding Spiro-OMeTAD-based devices. The high VBO value in the designed MAFAPbI₃/Cu₂O device is attributed to the energy barrier for electrons, which blocks electron transport through the interface. Interestingly, the hole-free carbon-based MAFAPbI₃ device shows a competitive PCE result of 25.384% due to its high V_OC value. Such a high V_OC value (1.22 V) can be attributed to the lower recombination centre and more favourable energy band alignment between MAFAPbI₃ and the carbon electrode, which provide a more stable interface and minimise losses.

The external quantum efficiency (EQE) curves of the six devices are shown in Figure 3b. Incident photons in the visible range are absorbed slightly more efficiently by devices based on MAPbI₃ compared to MAFAPbI₃. However, the latter shows better performance in near-infrared regions up to 830 nm due to the lower bandgap.

3.1. The Effect of Varying Light Intensity

The theoretical maximum efficiency of a single-junction solar cell is determined by the bandgap of the perovskite absorber. However, the electrical efficiency can be enhanced by increasing the incident light intensity [48]. A higher light intensity results in more photogenerated carriers and greater quasi-Fermi-level splitting in the absorber material [49]. Therefore, increasing the light intensity of the incident light has a major role in determining the performance indicators of solar cells, such as the J_SC, the V_OC, the FF, and the PCE, as well as the series and shunt resistances [50]. The photovoltaic performance indicators of the devices under simulation were evaluated using J-V characteristics at light intensities ranging from 1000 W/m² to 10,000 W/m², as shown in Figure 4.

Increased light intensity has noticeably influenced J_SC in all devices. It is found that J_SC increases linearly with increasing light intensity in all devices, although MAFAPbI₃-based devices have a slightly higher influence compared to MAPbI₃-based devices.

The relation between J_sc and light intensity has been further analysed, as illustrated in Figure 5.

According to the power-law dependency, illumination does not alter recombination behaviour in short-circuit conditions [50].

$$J_{sc}=P_{light}^{\alpha }$$

(4)

Here, α represents the recombination coefficient, and P denotes the power of the incident light. From the linear relation, α is calculated for both MAPbI₃ and MAFAPbI₃ as 0.99. Despite the linear increase in J_SC and the logarithmic rise recorded in V_OC with light intensity, these changes do not directly lead to an improvement in PCE. The open-circuit voltage of single-junction photovoltaic devices operating under focused illumination $V_{oc}^{\ast }$ is generally determined by the saturation current $I_0$ [29].

$$V_{oc}^{\ast }={\displaystyle \frac{kT}{q}}\mathit{ln}\left({\displaystyle \frac{I_{sc}^{\ast }}{I_0}}\right)$$

(5)

where k is the Boltzmann constant, T is the absolute temperature, q is the electron charge, and $I_{sc}^{\ast }$ is the short-circuit current under light concentration.

It is clear from Figure 5 that the fill factor of all configurations experiences a reduction with the increasing light intensity of incoming light. The fill factor value is determined by the following equation [50]:

$$FF={\displaystyle \frac{J_{max}{V}_{max}}{J_{sc}{V}_{oc}}}$$

(6)

The initial fill factor and the rate of decline vary significantly among the different configurations. Although MAFAPbI₃/Cu₂O shows the highest initial FF of 85.3, it experiences a dramatic FF reduction until the 4000 W/m² level of light intensity, then shows a steady reduction. MAPbI₃/Cu₂O- and MAPbI₃-based carbon devices demonstrate a stable FF and the smallest decline under increasing light intensity. Further, MAPbI₃/Cu₂O shows a slightly lower rate of decline compared to MAFAPbI₃-based cells. Spiro-OMeTAD-based devices initially exhibited a moderate FF, which dropped significantly with increasing light intensity up to 4000 W/m², after which it declined steadily at higher intensities.. On the other hand, MAFAPbI₃ carbon-based devices exhibit the lowest initial FF and the most significant decline, showing the least stable FF. The fill factor reduction phenomenon has been identified due to series resistance in charge transport materials, resistance at layer interfaces, and parasitic resistance in transparent conducting electrodes made from FTO [29]. The increase in charge density upon an increase in light concentration may enhance the probability of charge recombination before being extracted, which requires an absorber material with a high carrier lifetime and highly conductive charge transport materials to optimise charge extraction and collection [28].

The fill factor is the main performance indicator influencing the power conversion efficiency of solar cells, which is the fraction of output power to the input power of light. The maximum power that can be generated by solar cells can be calculated using this formula [29]:

$$P_{max}^{\ast }=I_{sc}^{\ast }{V}_{oc}^{\ast }FF$$

(7)

The different materials and configurations have a considerable effect on the PCE. Specifically, solar cells based on MAFAPbI₃ consistently show higher efficiencies compared to MAPbI₃-based cells. This finding aligns with Troughton J. et al.’s study [27], which identifies that Cs/FA mixed perovskite is better suited for exposure to high light intensities. This improvement in efficiency is attributed to the reduced presence of trap states relative to MAPbI₃, which results in its recombination rate being predominantly an outcome of bimolecular mechanisms [27]. As can be seen in Figure 5, increasing light intensity positively influences the efficiency of Cu₂O-based device. When light intensity was increased from 1000 W/m² to 10,000 W/m², the efficiency of MAPbI₃/Cu₂O increased from 25.12% to 26.74% and MAFAPbI₃/Cu₂O increased from 37.13% to 38.2%; therefore, MAPbI₃/Cu₂O showed a slightly better response to increasing light intensity. Spiro-OMeTAD-based devices remained steady with the increase in the light intensity level. Despite the lowest efficiency being recorded by MAPbI₃/C among the designed devices, it showed a positive response with increasing light intensity. Figure 6 illustrates the response of the different designed devices to the light intensities of 3000 W/m², 6000 W/m², and 9000 W/m².

3.2. The Effect of Operation Temperature

Exposure to high light intensities typically leads to temperature elevation in solar cells. Therefore, evaluating the impact of rising temperatures on the performance of PSCs is crucial for determining their suitability in CPV applications. This simulation has examined the effect of increasing temperature on the functionality of the designed PSCs and CPSCs. The operating temperature was varied from 280 K to 400 K to observe the performance of the proposed devices, while a temperature of 298 K was considered the standard measuring temperature, representing the standard room temperature. The performance of the PSCs and CPSCs was significantly influenced by prolonged exposure to sunlight, which caused notable variations in their operating temperature and consequently affected their output performance. The simulation results are displayed in Figure 6, depicting the normalised values of all PV performance indicators under different operating temperatures.

It is evident from Figure 7 that the normalised values of J_SC for all configurations significantly vary with temperature. All configurations show J_SC enhancement with elevating temperature except for MAFAPbI₃/Cu₂O and MAFAPbI₃/C. However, the reduction is negligible as when the temperature rises from 280 K to 400 K, J_sc changes from 25.681 mA/cm² to 25.667 mA/cm² and from 25.563 mA/cm² to 25.556 mA/cm² for MAFAPbI₃/Cu₂O and MAFAPbI₃/C, respectively. V_OC shows a general reduction trend with increasing temperature in all configurations. However, MAFAPbI₃/Spiro-OMeTAD reaches its maximum V_OC value of 1.198 V at 320 K and then shows a reduction. At higher temperatures, the material’s carrier concentration, charge mobility, resistance, and bandgap are significantly affected, resulting in changes to their photovoltaic (PV) parameters [21]. When the temperature increases, J_SC increases due to the thermal generation of minority carriers, while V_OC decreases due to an elevated saturation current. Temperature impacts the diffusion length of carriers, leading to higher series resistance (R_s), which, in turn, reduces both the FF and the PCE [51], as depicted in Figure 7. The relationship between FF and R_S is detailed in Equation (8) [35].

$${FF}_S={FF}_0(1-R_S)$$

(8)

Here, ${FF}_0$ indicates the fill factor without the influence of $R_S$.

Interestingly, the FF of all configurations shows a slight increase with temperature to reach its maximum value and then drops, except for in the MAPbI₃/Cu₂O solar cell, which remains constant until 300 K and then drops with increasing temperature. The PCE of the simulated devices follows the reduction trend observed in the FF. Figure 7 shows how the PCE changes with increasing temperature in all configurations. The most significant finding is that the MAFAPbI₃/Spiro-OMeTAD solar cell was the most robust as its FF and PCE continued to increase with temperature and achieved its optimum values of 82.16% and 25.2%, respectively, at 320 K. To evaluate the performance of the designed PSCs and CPSCs more comprehensively, the temperature coefficient (C_T) of the PCE of the solar cells (${TC}_{PCE})$ was calculated using Equation (9) [21].

Table 3. The temperature coefficients of the simulated solar cells.

Solar Cells	TCPCE (%)/Temperature Unit	Ref.
c-Si-based module	−0.45	[53]
a-Si-based module	−0.13	[53]
CdTe-based module	−0.21	[53]
CIGS-based module	−0.36	[53]
Organic	+0.4	[52]
DSSC	−0.79	[52]
TiO2/CsPbI2Br C-PSC	−0.23/°C at 200 °C, in reverse measurement	[52]
TiO2/CsPbI2Br C-PSC	$-0.035\mathrm{at}200°$C, in forward measurement	[52]
BSO/MAPbI3/Cu2O,	−0.112 at 400 K, simulation	[21]
BSO/MAPbI3/Cu2O	−0.341 at 400 K, simulation	This work
BSO/MAPbI3/Spiro-OMeTAD	−0.277 at 400 K, simulation	This work
BSO/MAPbI3/C	−0.292 at 400 K, simulation	This work
BSO/MAFAPbI3/Cu2O	−0.078 at 400 K, simulation	This work
BSO/MAFAPbI3/Spiro-OMeTAD	+0.0285 at 320 K, −0.04 at 400 K, simulation	This work
BSO/MAFAPbI3/C	−0.066 at 400 K, simulation	This work
TiO2/m-Al2O3/MAPbI3/C	+2.5 × 10−2 (5 °C ≤ T ≤ 25 °C) and −1.8 × 10−2 (25 °C ≤ T ≤ 75 °C)	[54]
PTAA/FA0.75Cs0.22MA0.03Pb(I0.82Br0.15Cl0.03)3	−0.11 at 80 °C	[55]
NiOx/FA0.79MA0.16Cs0.05Pb (I0.83,Br0.17)3	−0.08 at 80 °C	[55]
TiO2/FAMACsPb(I,Br)3/Spiro-OMeTAD /Au	A single ${TC}_{PCE}$ is not found at 50 °C	[56]

represents the calculated TC_PCE of the different devices stimulated in this study and others obtained from the literature [52].

$$C_T=({\displaystyle \frac{1}{{\eta }_{STC}}}{\displaystyle \frac{d{\eta }_T}{dT}}\times 100)$$

(9)

Here, η_STC is the efficiency in standard test conditions (298 K) and η_T is the efficiency at temperature T.

Compared to a previous simulation study of an optimised BSO/MAPbI₃/Cu₂O cell, which reported a ${TC}_{PCE}$ of −0.112% K⁻¹ [21], the simulated MAFAPbI₃-based solar cells in our study exhibit significantly lower ${TC}_{PCE}$ values. Despite the shortage of studies on the ${TC}_{PCE}$ of perovskite solar cells, it has been proven that they could perform well for PV applications that require high temperatures compared to other solar cells [28,52]. This finding underscores the superior photovoltaic performance stability of BSO/MAFAPbI₃-based PSCs at elevated temperatures, demonstrating their potential for enhanced operational reliability in high-temperature environments. In particular, the sample incorporating Spiro-OMeTAD as the hole transport material shows an increase in PCE up to 320 K, and at 400 K, the ${TC}_{PCE}$ exhibits only a slight reduction of 0.04% K⁻¹, highlighting its advantages for applications in high-temperature conditions.

3.3. The Impact of BSO Thickness, Donor Density, and Defect Density

It is worth noting that the designed devices have not been optimised. The electron transport material has a great influence on the performance of PSCs. The thickness, donor concentration, and defect density of BSO/perovskite interfaces were investigated in this study to determine the optimised BSO parameters. For high-performance PSCs, it is crucial that the ETL exhibits high transmittance and uniform morphology, allowing incoming photons to successfully reach the perovskite with a low recombination rate. Here, the thickness of the BSO ETL was varied from 10 to 100 nm to investigate its effect on device performance parameters, as illustrated in Figure 8.

The J_SC of all devices was unaffected by increasing the BSO thickness. Additionally, other performance indicators of the MAPbI₃-based devices remained steady and did not vary with BSO thickness. Therefore, it can be inferred that the band offset, intrinsic resistance, and defect density in the BSO layer remain constant as the thickness increases. On the contrary, a greater thickness of BSO negatively influences the V_OC, FF, and PCE of MAFAPbI₃-based devices. The V_OC decreased slightly with increasing BSO thickness, and after a thickness of 30 nm, no reduction in V_OC was observed. The decrease in FF and PCE stabilised at BSO thicknesses of 80 nm and 50 nm, respectively. From Figure 8, it can be observed that the PCE of MAFAI₃-based devices decreases by approximately 15% as the BSO thickness increases from 10 nm to 60 nm. This reduction can be mainly explained by the longer distance required for photogenerated electrons to travel in thicker ETLs, which promotes carrier recombination and consequently leads to a reduction in overall device efficiency. Therefore, a BSO thickness of 10 nm results in the best performance. However, at such low ETL thickness, it is crucial to maintain uniform full coverage to ensure good contact with the perovskite layer and to avoid direct contact with the FTO substrate.

In laboratory experiments, researchers have adopted several dopants with various concentrations to improve the donor charge density and modify the conduction band alignment of ETLs. In this study, to stimulate this impact, the donor density of BSO was varied from 10¹⁴ to 10²¹ cm⁻³, as illustrated in Figure 9.

The performance of MAPbI₃-based devices was not influenced by an increase in donor density and almost remained constant. However, the performance indicators of MAFAPbI₃-based devices were enhanced with rising doping concentrations, except for J_SC, which remained steady. From Figure 9, the performance of MAFAPbI₃-based solar cells can be optimised and enhanced at a BSO doping density of at least 10²⁰ cm⁻³. The V_OC and PCE of the BSO/MAFAPbI₃/Cu₂O device showed a direct increase with an increased donor density of BSO. Such an increase could be attributed to the shift in band offsets at the BSO/MAFAPbI₃ interface. In addition, using BSO with high doping levels enhances material conductivity, ensuring effective electron transportation [57], and reduces the depletion region in the ETL, creating a “cliff” that blocks minority carriers. This helps separate the photogenerated electron–hole pairs more efficiently and reduces charge carrier recombination [58]. On the contrary, excessive doping will increase non-radiative recombination owing to donor defect formation, which will lead to an increase in the series resistance of the PSCs and, hence, lower PCE [59]. Experimentally, the doping concentration of BSO should be optimised in order to obtain high transparency and high conductivity.

Depending on the synthesis technique, the defect density at the ETL/perovskite absorber junction can alter the device’s performance. Herein, the defect density at the BSO/perovskite junction was varied from 10⁷ cm⁻² to 10¹⁹ cm⁻², while other parameters were not changed. The result of varying the defect densities at BSO/perovskite interfaces on structured devices is illustrated in Figure 10.

It is clear that all configurations were negatively affected by increasing the defect density at the BSO/perovskite junction. The J_SC of the MAPbI₃-based devices was more negatively impacted compared to the MAFAPbI₃-based ones, as they remained constant and then dropped at a defect density of 10¹⁵ cm⁻². MAFAPbI₃-based devices showed a slight decrease in J_SC, except for the carbon-based device, which was highly affected at a defect density beyond 10¹³ cm⁻². The V_OC of MAPbI₃/C and MAFAPbI₃/Cu₂O was stable and did not account for interface defects.

At defect densities higher than 10⁸ cm⁻², MAFAPbI₃/Spiro-OMeTAD and MAFAPbI₃/C showed a reduction in V_OC, while MAPbI₃/Spiro-OMeTAD and MAPbI₃/C were more stable, only exhibiting a V_OC reduction at defect densities higher than 10¹⁴ cm⁻². The devices’ performance dependency on the interface defects at the BSO/perovskite junction has been translated into the devices’ overall PCEs.

The Cu₂O-based MAFAPbI₃ cell is the most stable and reliable device, which can withstand increasing interface defects, as well as carbon-based MAPbI₃. The PCE of the devices with Spiro-OMeTAD was significantly reduced when subjected to a higher defect interface density. To enhance the performance, the interface defect density at the BSO/MAPbI₃ interface must be limited to less than 10¹⁴ cm⁻², and it should be below 10¹⁰ cm⁻² for MAFAPbI₃/Spiro-OMeTAD and MAFAPbI₃/C devices.

The comparison of BSO-based simulated devices with varying parameters as the main contributor is highlighted in

Table 4. Optimal PCE of simulated devices under specific conditions compared to previous studies.

Parameters	Result	References
Light intensity	19.02% PCE (at 1000 Wm−2)	[60]
	38% PCE (at 10,000 Wm−2)	This work
	21% PCE (at 1000 Wm−2)	[61]
	32.04% PCE (at 1000 Wm−2)	[21]
BSO thickness	22.21% PCE (at 10 nm)	[22]
	~27% PCE (at 30 nm)	[59]
	31.24% PCE (at 100 nm)	[21]
	29% PCE (at 10 nm)	This work
BSO donor concentration	29.13% PCE (at 1021 cm−3)	[62]
	33% PCE (at 1021 cm−3)	This work
	31.24% PCE (at >1020 cm−3)	[21]
	~28% PCE (at 1020 cm−3)	[59]
BSO/perovskite interface defect density	18.59% PCE (at 1015 cm−2)	[60]
	27.6% PCE (at 1014 cm−2)	This work
	22.10% PCE (at 1014 cm−2)	[22]
	20.9% PCE (at 1010 cm−2)	[63]

.

4. Conclusions and Future Work Suggestions

In this study, the performance of perovskite solar cells employing BaSnO₃ as the electron transport layer was evaluated using MAPbI₃- and MAFAPbI₃-based perovskite absorbers. Various hole transport materials and hole-free (carbon-based) configurations were implemented and analysed under varying light intensities, temperatures, donor concentrations, and defect densities using SCAPS, a one-dimensional solar cell simulator. In normal conditions at a light intensity of 1000 W/m², MAFAPbI₃ devices demonstrated greater performance compared to the traditional perovskite absorber MAPbI₃. As light intensity increased, devices using Cu₂O showed improved performance. MAPbI₃ with a carbon-based electrode showed a promising trend with increasing light intensity, recording the smallest fill factor drop among all configurations. Such a result demonstrates that conduction band alignment, high-mobility charge transport materials, and stable thermal perovskite absorbers are essential in highly efficient and stable devices for concentrated PSC applications. All devices were negatively impacted by elevating temperature, with V_oc exhibiting an initial drop and FF decreasing with temperature beyond 300 K, except for Spiro-OMeTAD devices, which were the most robust. Decreasing the thickness and increasing the donor concentration of BSO had a substantial effect in enhancing the performance of MAFAPbI₃-based devices. The defect density at the BSO/perovskite interface also influenced devices performance; however, Cu₂O-based devices exhibited the least sensitivity to interface defects. FTO/BSO/MAFAPbI₃/Cu₂O/Au was the optimal device, showing an outstanding efficiency and stability compared to the other cells, yielding a PCE of 38.2% with a J_SC = 343.3 mA/cm², V_OC = 1.39 V, and FF = 80.17% under 10,000 W/m² light intensity. Moreover, it showed a good temperature coefficient of PCE of −0.078% K⁻¹, ensuring efficient and stable performance under high exposure to light and heat up to 400 K. At a normal light intensity (1000 W/m²), this suggested device recorded a PCE of 29% at 10 nm BSO thickness, and its PCE improved from 27% to 33% when increasing the donor concentration from 10¹⁴ cm⁻³ to 10²¹ cm⁻³. The optimal device showed a slight drop in PCE from ~28% to 27% when elevating the interface defect density from 10⁷ cm⁻² to 10¹⁹ cm⁻². For high-temperature PSC applications, Spiro-OMeTAD and BSO could be suggested as effective charge transport materials for mixed-cation MAFAPbI₃, as it exhibited a slow PCE degradation rate of −0.04% K⁻¹.

This simulation provides a valuable framework for researchers investigating the development of concentrated perovskite solar cells by highlighting the potential of adopting BSO, high-mobility hole transport materials, and mixed-cation perovskite absorber materials. Furthermore, it opens new avenues for enhancing the efficiency of low-cost, carbon-based perovskite solar cells by integrating BSO as an electron transport layer in concentrated photovoltaic (CPV) applications.

In future work, several strategies could be pursued to further improve the performance of BSO-based devices. These include employing deposition techniques that enable the formation of thin, uniform films such as spin-coating and spray pyrolysis, as well as using doping methods to tailor the conduction band level of BSO, increase donor concentration, and enhance electron transport properties. Further research includes using BSO as an efficient electron transport material for perovskite solar cells illuminated with varying light intensities.