Lead-Free Sr₃MCl₃ (M = Sb, P) Perovskite Solar Cells: from First-Principles Calculations to Recombination-Aware Device Simulations

Abstract

In this study, first-principles calculations were performed to explore structural, mechanical, electronic, carrier transport, and optical properties of strontium-based perovskites (Sr₃MCl₃ (M = Sb, P)) using density functional theory (DFT). These calculations reveal that both materials are thermodynamically and mechanically stable. Employing the GGA-PBE functional, they possess a direct-band-gap semiconductor behavior with an energy of 1.704 eV (Sr₃SbCl₃) and 1.677 eV (Sr₃PCl₃). The analysis of the density of states (DOS) further corroborates the semiconducting behavior. Carrier mobility calculations indicate that electron/hole mobilities of 89.15/110.52 cm²/V·s are achieved for Sr₃SbCl₃ and 137.16/100.60 cm²/V·s for Sr₃PCl₃. In the visible region, a light absorption coefficient above 10⁵ cm^–1 is reached for both materials, highlighting their suitability as an absorber layer (AL) in perovskite solar cells (PSCs). Considering band-to-band recombination (radiative and Auger), SCAPS-1D was used to conduct an inquiry into the photovoltaic performance of various devices, integrating different electron and hole transport layers (ETL/HTL): Ag/FTO/ETL/uniform-AL/HTL/Ni. Among all configurations examined in this study, the Ag/FTO/IGZO/uniform-AL/Cu₂O/Ni architecture achieves the highest photovoltaic performance parameters, upon optimization of AL thickness, AL-doping concentration, AL-bulk and interface defect densities, radiative recombination coefficient, and series/shunt resistances. The Sr₃SbCl₃-based PSC (Device I) attains a power conversion efficiency (PCE) of ∼25.80%, with an open-circuit voltage (V _OC) of 1.31 V, a short-circuit current density (J _SC) of 21.82 mA/cm², and a fill factor (FF) of 90.27%, whereas the Sr₃PCl₃-based PSC (Device II) achieves a PCE of approximatively 26.22%, with V _OC = 1.28 V, J _SC = 22.71 mA/cm², and FF = 90.09%. Finally, replacing the single uniform-AL with a graded-Sr₃Sb_1–x P _x Cl₃ AL (Device III), adopting linear and parabolic graded physical parameters, does not demonstrate marked improvements in device performance. Consequently, this study positions Sr₃MCl₃ (M = Sb, P) perovskites as alternatives to lead-based ALs, which can constitute a suitable pathway for real-time experimentation of PSC.

1. Introduction

In conjunction with demographic expansion, remarkable industrialization has intensified global energy demand, leading to the depletion of natural resources, climate change, and significant strain on the environment. , Therefore, the transition toward renewable energy resources is becoming an international priority. Owing to its abundance, environmental friendless, and scalability, solar energy stands out among various renewable energy options including wind and hydro. , Solar cells have the ability to directly convert solar radiation into electrical energy, providing a promising, clean, and increasingly cost-effective solution. In this context, various solar cell technologies have been studied, starting with crystalline silicon (Si) solar cells, followed by thin film (CdTe, CdS, CIGS, CIS, CZTS), organic, multijunction, tandem, and dye-sensitized solar cells. Despite their excellent performance, the indirect band gap of Si, high and complex fabrication feasibility, the deficiency of indium (In), gallium (Ga), and tellurium (Te), and the toxicity of cadmium (Cd) limit further development. Addressing these limitations, extensive efforts have been focused on the development of new alternative materials that can be applied as absorber layers in solar cells. As a result, lead (Pb) halide perovskites with the APbX₃ (A = Cs⁺, CH₃NH₃ ⁺, CH­(NH₂)₂ ⁺ and X = I^–, Br^–, Cl^–) molecular formula have emerged as revolutionary materials in solar energy owing to their exceptional optoelectronic and charge transport properties including broad and strong light absorption (>10⁵ cm^–1), tunable band gap, longer charge diffusion length (>1 μm), and high carrier mobility. , Since 2009, the PCE of lead-halide perovskite-based solar cells has increased from 3.8 to 27% today. , Nevertheless, PSCs often suffer from drawbacks such as issues of long-term stability with respect to temperature, light, humidity, and oxygen, as well as Pb toxicity, stimulating work in identifying alternative host perovskite materials. As such, there is strong interest in developing Pb-free perovskite materials that can absorb a broad spectral region of sunlight and then retain or increase this impressive PSC efficiency. − Inorganic Pb-free halide perovskites, with the A₃MX₃ general formula, where A stands for a larger size inorganic divalent cation, M for a smaller trivalent metallic cation, and X for a halogen anion, have been considered to address these needs. In fact, several candidates have been explored using DFT calculations, such as Ba₃MX₃ (M = N, P, As, Sb and X = F, Cl, Br, I), Mg₃SbBr₃, Mg₃PI₃, Sr₃PI₃, etc. − Specifically, these compounds exhibit a considerable absorption coefficient (>10⁵ cm^–1), thermodynamic stability, and an optimal band gap within the range of 0.8–2.0 eV, allowing PCEs surpassing 25%. − Thanks to these key specifications, the focus has shifted toward the design of a more efficient PSC device by integrating these compounds as either a single or a double AL between an ETL and an HTL.

Among these, because of its nontoxicity, eco-friendliness, earth abundance, and easy extraction, strontium (Sr)-based perovskites (Sr₃MX₃, where M = N, P, As, Sb, Bi; X = F, Br, I) stand out as affordable options in the A₃MX₃ category. According to the DFT calculations, they feature a cubic phase with the space group Pm3̅m (no. 221) and a direct band gap ranging from 1.15 to 1.908 eV using GGA-PBE (1.55 to 2.49 eV with HSE). − Using primarily SCAPS-1D, recent studies explored their capacity to serve as ALs in PSCs. In this regard, the combination of appropriate ETLs and HTLs was found to be the dominant factor in boosting the PCE of these emerging devices. According to recent findings by Ghosh et al., the SCAPS-1D studies on the Ag/FTO/SnS₂/Sr₃AsX₃(X = F, Cl, Br)/Au configuration without HTLs led to a maximum PCE of 20.89%. These authors also investigated the incorporation of Sr₃PI₃ in the Al/FTO/SnS₂/Sr₃PI₃/Ni structure and reported a high performance of 27.32%. Moreover, keeping the same ETL and without HTL, Harun-Or-Rashid’s and Rahman’s research teams explored a single PSC using Sr₃SbI₃ and Sr₃NCl₃ perovskites as ALs, achieving 26.93 and 18.11% as the maximum PCE, respectively. On the other hand, when employing MoO₃ as an HTL and SnS₂ as an ETL, the Sr₃SbI₃-based PSC attained an exceptional PCE of 33.25%, as demonstrated by Reza et al. Along the same lines, Gupta et al. reported a PCE of 23.55% by combining CuSCN as an HTL with SnS₂ as an ETL in the FTO/ETL/Sr₃NCl₃/HTL/FB configuration. Furthermore, using other ETLs (TiO₂, ZnO, WS₂, etc.) and HTLs (V₂O₅, MASnBr₃, CBTS, etc.), perovskite materials like Sr₃SbI₃, Sr₃NCl₃, and Sr₃BiI₃ were also assessed as a single AL to enhance the performance of PSC and achieve at most a PCE of 27.34%. − To further enhance the performance of PSC, these perovskite materials have also been incorporated as double ALs. In the study, using the FTO/SnS₂/Ca₃SbI₃/Sr₃SbI₃/Spiro-OMeTAD/Au device structure, a PCE of 32.74% was achieved. Lately, Benahmedi et al. demonstrated that PCS, incorporating both Ca₃BiI₃ and Sr₃BiI₃, achieved a PCE of 28.37%. Moreover, a high PCE of 32.46% was reported by Reza et al. when combining Sr₃PBr₃ and Sr₃NCl₃ in the Al/FTO/IGZO/Sr₃PBr₃/Sr₃NCl₃/Cu₂O/Au proposed device structure. Moreover, another efficient strategy has been widely reported to enhance the solar cell efficiency, which can be realized via the intentional introduction of a graded perovskite band gap configuration. This approach was selected based on its well-established advantages over nongraded configurations, including the creation of an internal built-in electric field that enhances carrier collection, the suppression of interfacial recombination, and improved energy level alignment at the absorber interfaces.

It has been reported that the integration of phosphorus (P) and antimony (Sb) allows for efficient, lead-free, and robust perovskite configurations. This has encouraged researchers to investigate the suitability of Sr₃MCl₃ (MP, Sb) as an AL in PSCs. Asadul Islam Shimul and collaborators explored the performance of Sr₃PCl₃-based PSC. Using ZnO as an ETL and various HTLs such as Cu₂O, CBTS, MoO₃, and CuI, their results underscore FTO/ZnO/Sr₃PCl₃/Cu₂O/Ni as the best device configuration, producing a PCE of 26.67%. In addition, this research team analyzed indium gallium zinc oxide (IGZO) as an ETL in the proposed FTO/IGZO/Sr₃PCl₃/Cu2O/Ni structure, attaining a PCE of 26.66%. In a similar vein, Rahmana et al. examined, without an HTL, various ETLs including WS₂, CdS, SnS₂, and ZnS in order to optimize Sr₃PCl₃-based PSC. Among the tested configurations, Al/FTO/SnS₂/Sr₃PCl₃/Au achieved a maximum PCE of 18.58%. On the other hand, Elboughdiri et al. conducted an in-depth analysis to evaluate the application of different ETLs (CdS, PCBM, SnS₂, and ZnO) and without an HTL in Sr₃SbCl₃-based PSC. Their simulation outcomes revealed that the FTO/SnS₂/Sr₃SbCl₃/Au-based device yielded the highest PCE of 16.63%. However, despite possessing noticeable performance approaching the Shockley–Queisser (SQ) limit of 28.64% for absorbers having a band gap of 1.7 eV, these SCAPS-1D simulations do not account for recombination losses, including radiative and Auger recombination. Saidarsan et al. reinforced this limitation by establishing that even a small change in the radiative recombination coefficient can have a significant impact on device performance. This emphasizes the requirement of incorporating realistic recombination coefficients as input parameters for SCAPS-1D simulations. In addition, despite efforts to assess the performance of Sr₃MCl₃(MP, Sb)-based PSC, to the best of our knowledge, involving both ELTs and HTLs at the same time has not been completely searched out yet through simulation. Considering these gaps, this motivated us to conduct additional research into properties of these lead-free perovskite materials and SCAPS-1D simulations by accounting for recombination losses.

Therefore, in the present study, using first-principles DFT calculations, the structural, mechanical, optical, and electrical properties of Sr₃MCl₃ (MP, Sb) perovskite materials are comprehensively investigated. Their band gap energy (Eg), effective density of states (Nc and Nv), effective masses, absorption coefficient (α), static dielectric permittivity (ε), and carrier mobilities (μ_e and μ_h) are determined. Unlike previous studies, the DFT-derived perovskite properties are used as input parameters to SCAPS-1D to simulate device performance by considering recombination losses. In conjunction with different ETLs (In₂S₃, SnS₂, IGZO, CdS, WS₂, ZnO) and various HTLs (Cu₂O, CuO, CuI, MoO₃, Spiro-MeOTAD, CBTS), Sr₃MCl₃ (MP, Sb) perovskites are integrated as single uniform-ALs (Devices I and II) or novel graded-Sr₃Sb_1–x P _x Cl₃ ALs (Device III) in Ag/FTO/ETL/AL/HTL/Ni adopting an n⁺–n–p–p⁺ device configuration. Subsequently, optimization of key parameters including AL thickness, AL-doping concentration, AL-bulk and interface defect densities, recombination rates, and series/shunt resistances is employed to enhance the efficiency of the designed PSC.

2. Computational Method

2.1. First-Principles DFT Calculations of the Perovskite Absorber Layer

The structural and optoelectronic properties of the perovskite absorber layer (AL) were investigated via first-principles DFT calculations, as implemented in the VASP. In this approach, the exchange–correlation energy was treated within the generalized gradient approximation (GGA) framework using the Perdew–Burke–Ernzerhof (PBE) functional, while valence–core interactions were described using the projector-augmented wave (PAW) method. It is worth noting that these DFT calculations performed at the GGA-PBE level are well known to systematically underestimate the material band gap (Eg) relative to experimental values. More sophisticated approaches such as hybrid functionals (e.g., HSE06) or the many-body perturbation theory (GW) provide more accurate absolute band gap values, but at significantly higher computational costs. Consequently, the PBE-derived Eg values reported in this work should be regarded as lower bounds on the true optical band gaps, and emphasis is placed on the relative trends and variations rather than on absolute values. To ensure calculation accuracy, a plane-wave cutoff energy of 520 eV was applied. The Monkhorst–Pack k-point grid of the first Brillouin zone was sampled with 6 × 6 × 6 for structural relaxations and 10 × 10 × 10 for electronic property calculations. The atoms in the cell were relaxed until the total energy change was below 10^–5 eV and residual forces on each atom were smaller than 0.01 eV/Å.

2.2. Devices Simulation via SCAPS-1D

2.2.1. Simulation Method

Device simulations were performed using a one-dimensional Solar Cell Capacitance Simulator, SCAPS-1D (version 3.3.12), developed by M. Burgelman et al. This program is a powerful numerical simulation tool that enables the in-depth understanding, design, and optimization of high-efficiency solar cells. SCAPS-1D allows researchers to model the operation of multilayered devices (up to seven layers) and to optimize photovoltaic performance parameters by solving the fundamental semiconductor equations, including the charge carrier transport (eqs and 2), continuity (eqs 3 and 4), and Poisson’s (eq ) equations, under steady-state conditions. Consequently, it can simulate essentially the current density–voltage (J–V) characteristics, energy band diagrams, external quantum efficiency (EQE), and key performance parameters including short-circuit current density (J _SC), open-circuit voltage (V _OC), fill factor (FF), and photovoltaic conversion efficiency (PCE). ,

$$\{\begin{array}{ll}{J}_n=q{D}_n\frac{\partial n}{\partial x}-q{\mu }_{n}n\frac{\partial \psi }{\partial x}& (1)\\ J_{\mathrm{p}}=-q{D}_{\mathrm{p}}\frac{\partial p}{\partial x}-q{\mu }_{\mathrm{p}}p\frac{\partial \psi }{\partial x}& (2)\end{array}$$ 1

$$\{\begin{array}{ll}\frac{\partial n}{\partial t}=\frac{1}{q}\frac{\partial J_n}{\partial x}+G_n-R_n& (3)\\ \frac{\partial p}{\partial t}=-\frac{1}{q}\frac{\partial J_{\mathrm{p}}}{\partial x}+G_{\mathrm{p}}-R_{\mathrm{p}}& (4)\end{array}$$ 2

$$\frac{\partial }{\partial x}\left({\epsilon }_0\epsilon (x)\frac{\partial \psi }{\partial x}\right)=-q(p(x)-n(x)+N_{\mathrm{D}}^{+}(x)-N_{\mathrm{A}}^{-}(x)+N_{\mathrm{t}}(x))$$ 5

In these equations, J _n and J _p represent the current densities of electrons and holes, respectively. D _n and D _p are the diffusion coefficients, while n and p denote electron and hole densities, respectively. The mobilities of electrons and holes are given by μ _n and μ_p, respectively. The electrostatic potential is represented by ψ, and q denotes the electronic charge. The electron and hole generation/recombination rates are expressed by G _n /R _n and G _p/R _p, respectively. ε and ε₀ stand for the dielectric permittivities of the medium and vacuum, respectively. N _D and N _A refer to the densities of ionized donors and acceptors, respectively, while N _t indicates the defect density. Variable x specifies the position along the device length, and t denotes time.

In this study, electron–hole pair generation rates (G _n and G _p) and the optical absorption coefficient α­(hν) of layers were described using the recent advanced E _g-sqrt version of the standard hν-E _g model implemented in SCAPS-1D, which is expressed as follows:

$$\alpha (h\nu )=({\alpha }_0+{\beta }_0\frac{E_{\mathrm{g}}}{h\nu })\sqrt{\frac{h\nu }{E_{\mathrm{g}}}-1}$$

where hν represents the photon energy, and E _g denotes the band gap, while α₀ and β₀ designate the absorption model constants (e.g., 1/cm) specific to each material.

The generation rate was then computed using the following expression:

$$G(x)=\alpha (\lambda )·{\mathrm{\Phi }}_0(\lambda )·\exp (-\alpha (\lambda )·x)$$

where Φ₀(λ) is the incident photon flux, and x is the depth within the layer.

2.2.2. Device Structure

In this study, the configuration of the perovskite-based solar cell (PSC), shown in Figure a, follows a conventional n ⁺ –n–p–p ⁺ design, which enhances charge separation and reduces recombination losses by creating multiple built-in electric fields at each junction. It consists of a sequence of layers arranged according to doping concentrations: an n ⁺-type transparent conductive oxide (FTO) layer, an n-type electron transport layer (ETL), a p-type perovskite absorber layer (AL), and a p ⁺-type hole transport layer (HTL). Silver (Ag) and nickel (Ni) were employed as the front and back metal contacts, respectively. The work functions (Φ) of Ag and Ni are 4.52 and 5.35 eV, respectively. In the Ag/FTO/ETL/AL/HTL/Ni device configuration, the ETL is selected from six common materials (In₂S₃, SnS₂, IGZO, CdS, WS₂, ZnO), while six other materials (Cu₂O, CuO, CuI, MoO₃, Spiro-MeOTAD, CBTS) are investigated to identify the most suitable HTL. The AL, positioned between the ETL and HTL, consists of a uniform Sr₃SbCl₃ perovskite (Device I), a uniform Sr₃PCl₃ perovskite (Device II), or a graded Sr₃Sb_1–x P _x Cl₃ perovskite (Device III). It is worth mentioning that the ETL and HTL materials were selected based on four key criteria: (i) widespread use in the SCAPS-1D simulation literature, (ii) appropriate band gap and band alignment with the Sr₃M­(M = Sb, P)­Cl₃ absorber layer, (iii) lead-free and nontoxic composition, and (iv) experimental availability and low fabrication costs. Subsequently, among the investigated ETL and HTL candidates, the optimal transport layers were determined through systematic calculation of the conduction band offset (CBO) at the ETL/absorber interface and the valence band offset (VBO) at the absorber/HTL interface.

1.

(a) Schematic configuration of the proposed perovskite-based solar cell (PSC). (b) Working mechanism of the Ag/FTO/ETL/AL/HTL/Ni device. (c) Energy level alignment in the proposed devices with various ETLs and HTLs.

Figure b illustrates the operating mechanism of the PSC. Upon light absorption and exciton dissociation within the perovskite AL, the AL/ETL interface blocks holes while allowing electrons to flow toward the electrode. In contrast, the HTL/AL interface efficiently transports holes while restricting electron flows. The energy level alignment of each ETL, HTL, and perovskite AL is depicted in Figure c. The simulated devices are evaluated under standard AM 1.5G illumination (1 sun) with an incident power density of 1000 W·m^–2, at room temperature (300 K), and a frequency of 1.0 × 10⁶ Hz. This default setting frequency is relevant only for alternating current (AC) simulations and does not influence the J–V or EQE measurements. In line with the recommendations of Saidarsan et al., the device characteristics are analyzed by considering band-to-band recombination (radiative and Auger). Therefore, the total recombination rate in our SCAPS-1D simulation study is expressed as the combination of all three recombination mechanisms (eq ), contributing simultaneously to carrier losses:

$$R_{\mathrm{total}}=R_{\mathrm{radiative}}+R_{\mathrm{Auger}}+R_{\mathrm{SRH}}$$ 6

where radiative and Auger electron/hole band-to-band recombination are modeled through non-zero coefficients C _r (cm³/s) and C_n /C _p (cm⁶/s), respectively, and trap-assisted Shockley–Read–Hall (SRH) recombination is accounted for through the trap densities N _t (cm^–3) introduced in the bulk and at the interfaces, along with their associated capture cross sections (σ _n/σ_p). For the FTO layer, ETL, and HTL, both C _r and C _p are set to zero, while for the perovskite absorber layer, they are set to 3.0 × 10^–11 cm³·s^–1 and 1.0 × 10^–29 cm⁶·s^–1, respectively. – The bulk and interface defects were modeled as single neutral deep-level states located at 0.6 eV above the valence band maximum (VBM). This energy level was specifically chosen to represent deep-level traps acting as dominant Shockley–Read–Hall (SRH) recombination centers within all layers and at the ETL/AL and AL/HTL heterointerfaces.

As external lumped parameters, the series resistance (R _S) and shunt resistance (R _sh) are set to 2 Ω·cm² and 5000 Ω·cm², respectively. All physical input parameters for each layer are summarized in Tables , S1 and S2 (Supporting Information). Furthermore, the interface defect parameters between the perovskite and adjacent transport layers are listed in Table .

1. Input Parameters for PSCs Based on Different Materials.

parameters	FTO	IGZO	Sr 3 SbCl 3	Sr 3 PCl 3	Cu 2 O
thickness (nm)	50	50			50
band gap, E g (eV)	3.6	3.05	1.70	1.67	2.2
electron affinity, χ(eV)	4.5	4.16	4.15	4.12	3.4
relative dielectric permittivity, εr	10	10	3.45	3.28	7.5
CB/VB effective DOS (cm–3)	2.0 × 1018/1.8 × 1019	5 × 1018/5 × 1018	7.62 × 1018/1.68 × 1019	6.56 × 1018/1.94 × 1019	2.0 × 1019/1.0 × 1019
electron mobility, μn (cm2/(V s))	100	15	89.151	137.16	200
hole mobility, μp (cm2/(V s))	20	0.1	110.52	100.6	8600
shallow uniform donor density, N D (cm–3)	1018	1018	0	0	0
shallow uniform acceptor density, N A (cm–3)	0	0	1017	1017	1018
total defect density, N t (cm–3)	1014	1014	1014	1014	1015

2. Input Parameters for Interface Defect Layers in the Simulated Devices.

	interfaces
parameter	IGZO/Sr 3 MCl 3	Sr 3 MCl 3 /Cu 2 O
defect type	neutral	neutral
capture cross section for electrons (σ n )/holes (σp) (cm2)	1.0 × 10–19	1.0 × 10–19
energetic distribution	single	single
reference for defect energy level	above the highest E V	above the highest E V
defect position above the highest E V (eV)	0.6	0.6
total defect density (cm–2)	1.0 × 1011	1.0 × 1011
working temperature (K)	300	300

3. Results and Discussion

3.1. DFT Calculation Results for the Uniform Perovskite Absorber Layer

3.1.1. Structural Properties

Analyzing the structural properties of a compound is an essential first step before exploring its other characteristics. For this purpose, the studied Sr₃MCl₃ (M = Sb, P) perovskite structures were structurally optimized to determine the lattice parameters corresponding to their lowest-energy and most stable configurations. As shown in Figure , these compounds crystallize under ambient conditions in the cubic space group Pm3̅m (No. 221). Each unit cell contains seven atoms, with Sr cations located at 3c (0.5, 0, 0.5), P/Sb cations at 1b (0.5, 0.5, 0.5), and Cl anions at 3d (0, 0.5, 0). As summarized in Table , the optimized lattice parameters for the Sr₃SbCl₃ and Sr₃PCl₃ structures are 6.32 and 6.05 Å, respectively, which are in good agreement with previously reported values. ,,,,,,

2.

(a) 2D and (b) 3D views of Sr₃MCl₃ (M = Sb, P) crystal structures.

3. Summary of Optimized Structural, Mechanical, and Electronic Parameters for Sr₃MCl₃ (M = Sb, P).

	Sr 3 PCl 3	Sr 3 SbCl 3
lattice constant (a = b=c) in Å	6.05	6.32
optimum volume V 0 in Å3	221.80	252.76
formation energy, E f (eV/atom)	–2.05	–1.93
nature of the band gap	Direct	Direct
band gap, E g (Γ–Γ) in eV	1.677, 1.694[PBE], 1.65[PBE], 1.641[PBE]	1.704, 1.70[PBE], 1.72[PBE], 1.90[PBE]
elastic constant (GPa)
C 11	80.24	65.76
C 12	10.70	8.20
C 44	16.02	12.61
C 12 –C 44	–5.32	–4.41
bulk modulus, B (GPa)	33.87	27.38
Young’s modulus, Y (GPa)	54.20	43.64
shear modulus, G (GPa)	21.97	17.67
Poisson’s ratio, ν	0.233	0.234
Pugh’s ratio (B/G)	1.541	1.550

Moreover, the relative stability of the Sr₃MCl₃ halide perovskite materials can be evaluated through their formation energies, E _f , which are calculated using the following expression (eq ): ,

$$E_f({\mathrm{Sr}}_3\mathrm{M}{\mathrm{C}\mathrm{l}}_3)=\frac{(E_{\mathrm{tot}}({\mathrm{Sr}}_3\mathrm{M}{\mathrm{Cl}}_3)-(3E_{\mathrm{s}}(\mathrm{Sr})+E_{\mathrm{s}}(\mathrm{M})+3E_{\mathrm{s}}(\mathrm{Cl})))}{7}$$ 7

Here, E _tot represents the total energy of one unit cell of Sr₃MCl₃, while E _s(Sr), E _s(M), and E _s(Cl) denote the total energies of the individual atoms in their respective pure solid forms.

According to Table , the investigated perovskites exhibit negative E _f , which underlines their energetic stability and structural robustness.

To quantify the structural robustness of Sr₃MCl₃ (M = Sb, P), the mechanical properties were assessed by computing the elastic constants from stress–strain relations, obtained using Hessian matrices along each Cartesian direction. Based on Voigt notation and cubic symmetry of the A₃MX₃ perovskite materials, only three independent elastic constants, C ₁₁, C ₁₂, and C ₄₄, are required to describe their mechanical behavior. In this case, Born and coauthors , have reported the conditions of mechanical stability, which are defined as

$$C_{11}-C_{12}>0,C_{11}+2C_{12}>0,C_{44}>0$$

As Table shows, both compounds satisfy the prescribed Born’s stability conditions, demonstrating their significant mechanical stability. Furthermore, based on the computed elastic constants C _ij , several mechanical parameters like bulk modulus (B), shear modulus (G), Young’s modulus (Y), Poisson’s ratio (ν), and Pugh’s ratio (B/G) were calculated for both compounds, as summarized in Table . These outcomes illustrate that the Sr₃PCl₃ compound possesses the highest values of B, Y, and G compared to Sr₃SbCl₃. This reveals that Sr₃PCl₃ is the stiffest material among the studied compounds, demonstrating its greatest resistance to both deformation and compression. The other critical mechanical parameters for materials are ν and B/G. According to the standard criteria reported in the ref, both perovskite materials are brittle under ambient conditions because all of them have ν less than 0.26 and B/G below 1.75.

3.1.2. Electronic Properties

A comprehensive understanding of perovskite material’s electronic properties, like band structure and density of states (DOS), are essential for exploring its practical use as an AL in solar cells.

After structural optimization, the electronic band structures of Sr₃PCl₃ and Sr₃SbCl₃ materials were examined at ambient conditions along the Γ–X–M−Γ–R–X path of the first Brillouin zone (Figure a,b). The Fermi level (E _f ) is set at 0 eV for precise band gap determination. It can be seen that, for both perovskite materials, the conduction band minimum (CBM) and valence band maximum (VBM) are located at the high-symmetry Γ point in the Brillouin zone, thereby validating their direct band gap nature. As illustrated in Table , the calculated band gap energies are 1.704 eV for Sr₃SbCl₃ and 1.677 eV for Sr₃PCl₃, highlighting the suitability of these materials for photovoltaic applications. Indeed, solar cells utilizing these perovskite materials as ALs are expected to achieve an efficiency limit of 29%, as reported by Shockley–Queisser. Additionally, replacing Sb with P slightly reduces the band gap due to the higher electronegativity of P, which raises the valence band edge. Subsequently, the total and partial density of states (TDOS and PDOS) are investigated to offer significant insights into the electronic configuration of materials and thus into individual atomic orbitals’ contribution to their band structures. Figure a,b, displays the calculated TDOS and PDOS spectra for Sr₃MCl₃ (M = Sb, P) perovskites over a limited energy range from −5 to +5 eV. The TDOS spectra indicate that both studied compounds have a semiconducting behavior.

3.

Electronic band structure with DOS for (a) Sr₃SbCl₃ and (b) Sr₃PCl₃ perovskites.

Moreover, they display distinct peaks in both the valence and conduction bands, signifying a high density of electronic states available in these regions. In fact, Sr₃PCl₃ has an effective density of states of 1.940 × 10¹⁹ electrons/eV in the valence band (N _V) and 6.563 × 10¹⁸ electrons/eV in the conduction band (N _C), whereas Sr₃SbCl₃ has an N _V of 1.680 × 10¹⁹ electrons/eV and an N _C of 7.625 × 10¹⁸ electrons/eV. On the other hand, from the PDOS spectra for both perovskite materials, the conduction band predominantly originates from Sr d-orbitals, whereas the valence band is dominated by Sb/P p-orbitals, with minor contributions from Cl. These findings indicate a robust covalent interaction between Sr–Cl and Sr–Sb/P, and its significant role in the conduction process.

It has been reported that strain technology plays a crucial role in adjusting the band gap and thus enhancing visible light absorption, which are critical for improving photovoltaic performance. ,,− For this reason, the band gap energy changes of Sr₃MCl₃ (M = Sb, P) perovskites under uniaxial and biaxial strains were evaluated within the stable range from −4 to +4%, as shown in Figure a,b. It is worth noting that, after relaxation, the direct band gap nature remains stable throughout the applied strain range.

4.

Calculated band gap energy as a function of applied uniaxial and biaxial strain for (a) Sr₃SbCl₃ and (b) Sr₃PCl₃.

As depicted in these figures, the band gap for both perovskite materials is significantly influenced in response to the amount of applied uniaxial and biaxial strains. It increases monotonically from compression to tension due to the shifting of the VBM and CBM from the Fermi level energy. , In fact, for both compounds, under uniaxial compressive strain (0 to −4%), the band gap energy can be reduced to a value of 1.45 eV, while it is reduced to 1.36 eV under biaxial compressive strain. According to Shockley and Queisser, for PSCs with these band gap values, a maximum PCE of 33% can be reached. As a result, the biggest band gap change for both perovskites is obtained when biaxial strain is applied. This suggests that biaxial strain is more effective than uniaxial strain for tuning the band gap.

For a high photovoltaic performance, the perovskite material must possess high charge carrier mobility. Therefore, using the deformation potential (DP) theory proposed by Bardeen and Shockley, the three-dimensional (3D) carrier mobility is estimated as follows (eq ):

$${\mu }_{\mathrm{e}(\mathrm{h})}^{3\mathrm{D}}=\frac{2\sqrt{2\pi }{\mathrm{\hslash }}^4\mathrm{e}{M}_{\mathit{ij}}^{3\mathrm{D}}}{3{(K_{\mathrm{B}}T)}^{3/2}{(m_{\mathrm{e}(\mathrm{h})}^{*})}^{5/2}{E}_{\mathit{ij}}^2}$$ 8

where T is the room temperature, e is the elementary charge, ℏ is reduced Planck’s constant, and K _B is the Boltzmann constant.

The carrier effective masses, m _e(h) , for electrons and holes, were respectively extracted from the curvature of the conduction and valence band edges using a quadratic fitting method (eq ):

$$m_{\mathrm{e}(\mathrm{h})}^{*}={\mathrm{\hslash }}^2{\left(\frac{{\partial }^{2}E(k)}{{\partial k}^2}\right)}^{-1}$$ 9

where E(k) is the band-edge eigenvalues and k is the wave vector.

The 3D elastic modulus, M _ij , is obtained from the variation of the total energy (E _tot) under applied uniaxial strain (eq ):

$$M_{\mathit{ij}}^{3\mathrm{D}}=\frac{1}{V_0}\left(\frac{{\partial }^2{E}_{\mathrm{tot}}}{{\partial {\epsilon }_{\mathit{ij}}}^2}\right)$$ 10

where V ₀ is the equilibrium lattice volume, and ε is the applied uniaxial strain.

The deformation potential constant, E _ij , of the CBM for electrons and VBM for holes along the transport direction under uniaxial strain, is defined as (eq ):

$$E_{\mathit{ij}}=\frac{\mathrm{d}{E}_{\mathrm{edge}}}{\mathrm{d}{\epsilon }_{\mathit{ij}}}$$ 11

where E _edge denotes the band-edge (CBM or VBM) energy.

It is important to note that a uniaxial strain (±4%) were applied to both perovskite materials, followed by lattice-constrained relaxation in order to estimate E _tot together with band-edge energies, as shown in Figure . The calculated results, as presented in Table , demonstrate that Sr₃PCl₃ exhibits the highest electron mobility, approximately 137.16 cm²/V·s, which exceeds that of Sr₃SbCl₃, around 89.15 cm²/V·s. Conversely, there is a little difference between hole mobilities (110.52 cm²/V·s vs 100.60 cm²/V·s). This difference between electron and hole mobilities can play an important role in the separation of carriers and reduce the recombination of carriers in photovoltaic applications. In addition, these higher carrier mobilities facilitate the rapid migration of photogenerated electrons and holes, which is crucial for the development of high-performance devices.

5.

Total energy–strain relationship (a, b) and the evolution of VBM and CBM positions (c, d) under uniaxial strain for Sr₃SbCl₃ and Sr₃PCl₃ perovskites.

4. Summary of Electron (m _e ) and Hole (m _h ) Effective Masses, 3D Elastic Modulus (M _ij ), Deformation Potentials (E _ij ) for CBM and VBM, and the Corresponding 3D Electron (μ_e ) and Hole (μ_e ) Mobilities for Sr₃SbCl₃ and Sr₃PCl₃ .

				E ij (ev)
perovskite	m e / m 0	m h / m 0	M ij (GPa)	CBM	VBM	μ e (cm 2 /V·s)	μ h (cm 2 /V·s)
Sr3SbCl3	0.561	0.326	6.673	4.408	7.803	89.15	110.52
Sr3PCl3	0.538	0.386	8.086	4.122	7.290	137.16	100.60

3.1.3. Optical Properties

Investigating the optical properties of Sr₃MCl₃ (M = Sb, P) perovskites is an additional crucial step to assess their suitability for optoelectronic and photovoltaic applications. Consequently, frequency-dependent dielectric function ε(ω), absorption coefficient α­(ω), reflectivity R(ω), and energy loss function L(ω) were calculated.

According to Cohen’s and Ehrenreich’s equation, , the key optical parameter ε­(ω) contains two components: a real part ε₁(ω) and imaginary part ε₂(ω), as expressed by eq :

$$\epsilon (\omega )={\epsilon }_1(\omega )+i{\epsilon }_2(\omega )$$ 12

The real part can be obtained through the application of the Kramers–Kronig transformation, while the imaginary part can be achieved using momentum matrix components. Figure a depicts the ε₁(ω) and ε₂(ω) of Sr₃SbCl₃ and Sr₃PCl₃ for energy range up to 11 eV. As we know, the real part ε₁(ω) of the dielectric function is used to gain insights into the polarization and dispersion effects. The most significant factor is its static value, ε₁(ω = 0), which represents the electronic component of the dielectric function. For Sr₃SbCl₃ and Sr₃PCl₃, the values of ε₁(ω = 0) are 3.28 and 3.45, respectively. These findings are in accordance with Pen’s model, predicting that a smaller band gap energy leads to a larger ε₁(ω = 0). Moreover, from this static value, ε₁(ω) starts to increase until reaching its maximum value. After that, it declines, generating several peaks, which indicates a significant light absorption capacity within this spectral range. It is noted that a metallic behavior, identified by a negative ε₁(ω) value, appears beyond 7.5 eV and 8.1 for Sr₃SbCl₃ and Sr3PCl₃, respectively. On the other hand, the imaginary part of the dielectric function is known to offer insights into the electronic band gap of materials, such as the interband transition energy near the Fermi level. As depicted in this figure, the values of ε₂(ω) reveal a wide absorption range, where the first prominent peaks are located at a photon energy of 2.71 eV for both materials. It is from this energy that charge carriers begin to migrate from the valence band to the conduction band. At energy values above 10 eV, both Sr₃SbCl₃ and Sr₃PCl₃ become transparent.

6.

(a) Real ε₁(ω) and imaginary ε₂(ω) parts of the dielectric function, (b) absorption coefficient α­(ω), (c) optical reflectivity R(ω), and (d) energy loss function L(ω) for Sr₃SbCl₃ and Sr₃PCl₃ perovskites.

Another key parameter is the optical absorption coefficient α­(ω), which assesses the material’s capability to absorb light energy, giving information about its potential usefulness for efficient solar cells. According to Figure b, for both perovskites, α­(ω) shows comparable features to the imaginary part of the dielectric function. α­(ω) starts to increase from an energy value of 1.5 eV until reaching its first maximum (2 × 10⁵ cm^–1) at 2.75 eV, which is indispensable for solar cell applications.

The optical reflectivity R(ω) quantifies the amount of reflected light from a material surface when it is exposed to electromagnetic radiation such as visible light. As shown in Figure c, it is clear that both Sr₃SbCl₃ and Sr₃PCl₃ have lower reflectivity in the UV–visible range and can capture the most incident photon, approving their utilities as ALs in solar cells. This aligns well with the electron energy loss function L(ω), as depicted in Figure d, which represents the energy amount dissipated by electrons while they traverse through a dielectric substrate. The highest electron loss function peaks were observed at 9.75 and 8.94 eV for Sr₃PCl₃ and Sr₃SbCl₃, respectively. In addition, considering the negligibly L(ω) in the UV–visible region underscores the significant promise of these perovskites for implementation in solar cells.

4. SCAPS-1D Simulation Results

4.1. Uniform Perovskite Absorber Layer-Based Devices

4.1.1. Optimization of Charge Transport Layers (CTLs)

According to Stolterfoht et al., the efficiency of perovskite solar cells (PSCs) is strongly influenced by the selectivity of charge transport layers (ELT and HTL), which play a key role in minimizing interfacial nonradiative recombination. The authors highlighted that the alignment of energy levels at both ETL/perovskite and perovskite/HTL interfaces is essential to maximize V _OC, thereby improving the overall device efficiency. To ensure optimal alignment, the selection of suitable materials is based on the barrier potentials for electrons (ΔE _C) and holes (ΔE _V) at perovskite/CTL interfaces. Accordingly, the conduction band offset (CBO = ΔE _C) and the valence band offset (VBO = ΔE _V) were calculated using the following eqs (eqs and ): −

$$\mathrm{CBO}={\mathrm{\Delta }E}_{\mathrm{CBO}}={\chi }^{\mathrm{abso}}-{\chi }^{\mathrm{ETL}}$$ 13

$$\mathrm{VBO}=({\chi }^{\mathrm{HTL}}+E_{\mathrm{g}}^{\mathrm{HTL}})-({\chi }^{\mathrm{abs}}+E_{\mathrm{g}}^{\mathrm{abs}})$$ 14

Here, χ represents the electron affinity, while E _g denotes the band gap energy.

Initially, six different ETLs, In₂S₃, SnS₂, IGZO, ZnO, CdS, and WS₂, were evaluated based on the structure of Ag/FTO/ETLs/ALs/Cu₂O/Ni. The calculated CBOs and the corresponding V _OC values for Devices I and II are listed in Table .

5. Correlation between CBO and V _OC at the ETLs/Perovskite Interface for Both Devices.

		WS 2	SnS 2	CdS	IGZO	In 2 S 3	ZnO
Device I	CBO (eV)	+0.20	–0.09	–0.05	–0.01	–0.45	+0.15
	V OC  (eV)	1.314	1.314	1.314	1.314	1.261	1.314
Device II	CBO (eV)	0.17	–0.12	–0.08	–0.04	–0.48	+0.12
	V OC  (eV)	1.284	1.284	1.285	1.285	1.201	1.285

A positive CBO value creates an energy barrier that hinders the flow of photogenerated electrons from the absorber to the ETL. In contrast, a negative CBO facilitates efficient electron transport, allowing photogenerated electrons to move easily from the absorber to the ETL. As shown in Table , IGZO exhibits the lowest negative CBO values for both Devices I and II, while the corresponding V _OC values remain nearly constant across all ETLs within each device, except for In₂S₃. Furthermore, Table S3 indicates that IGZO delivers superior performance, achieving PCE values of 24.28 and 24.79% for Devices I and II, respectively.

On the basis of these findings, the device structure (Ag/FTO/IGZO/ALs/HTLs/Ni) was further optimized by exploring various HTLs, including Cu₂O, CuO, CuI, MoO₃, CBTS, and Spiro-MeOTAD. The calculated VBO values, along with the corresponding V _OC and overall device performance for each HTL, are summarized in Tables and S4 (see the Supporting Information).

6. Correlation between VBO and V _OC at the HTLs/Perovskite Interface for Both Devices.

		Cu 2 O	CuO	MoO 3	Spiro-MeOTAD	CuI	CBTS
Device I	VBO (eV)	–0.254	–0.274	–0.354	–0.404	–0.654	–0.354
	V OC  (eV)	1.314	1.198	1.138	1.253	1.032	1.304
Device II	VBO (eV)	–0.190	–0.210	–0.290	–0.340	–0.597	–0.297
	V OC  (eV)	1.285	1.155	1.150	1.264	1.045	1.282

All of the evaluated HTLs exhibit negative VBO values, indicating their potential suitability. Among them, Cu₂O shows the least negative VBO, suggesting a more favorable energy level alignment, which is expected to enhance charge extraction and device performance.

Overall, these findings suggest that subsequent device optimization should focus on the Ag/FTO/IGZO/AL/Cu₂O/Ni configuration. Figure S1a,b illustrates the energy band alignments of both device configurations, highlighting the conduction band edge (E _C), valence band edge (E _V), and the quasi-Fermi levels for electrons (F_n ) and holes (F _p).

As shown in Figure S1a,b, under illumination, the single equilibrium Fermi level splits into two quasi-Fermi levels: one for electrons and another for holes, indicating the photogeneration of charge carriers. Moreover, the presence of energy barrier potentials for electrons (ΔE _C) and holes (ΔE _V) at perovskite/CTL indicates the establishment of an intrinsic electric field. These internal fields not only facilitate the separation of photogenerated electron–hole pairs within the PSC but also serve as driving forces that guide electrons toward the cathode and holes toward the anode. This mechanism is critical for enhancing the overall performance of the devices.

4.1.2. Optimization of the Uniform Perovskite Absorber Layer (AL)

The AL plays a crucial role in determining the performance of PSCs by enhancing photon absorption and facilitating efficient photogeneration of electron–hole (e–h) pairs. Achieving high power conversion efficiency (PCE) requires the AL to have a suitable band gap, optimal thickness, appropriate doping density, and low bulk and interfacial defect densities. Therefore, optimizing the perovskite AL is essential to identify effective strategies for improving device performance.

4.1.2.1. Impact of Thickness

Barbé and Tietze Max reported that both the diffusion length and lifetime of photogenerated carriers strongly influence the efficiency of solar cells. To investigate this effect in our devices, the AL thickness was varied from 0.1 to 3 μm for Device I (Sr₃SbCl₃) and Device II (Sr₃PCl₃). Figure a–d illustrates the corresponding variations in PSC performance metrics as a function of AL thickness.

8.

Effects of both N _A in AL (AL-N_A) and N _t in AL (N_t-AL) on the PSC performance parameters for (a–d) Device I and (e–h) Device II.

From Figure d, a significant efficiency improvement is observed as the AL thickness increases up to 1.2 μm. For Device I, which employs Sr₃SbCl₃ as the AL, the PCE rises from 10.50 to 24.50%, whereas Device II, using Sr₃PCl₃ as the AL, exhibits a slightly higher PCE, increasing from 11.00 to 25.00%. This enhancement for both devices can be attributed to improved light absorption, which increases the generation rate of charge carriers. As a result, J _SC also rises (Figure b), directly contributing to higher power output. Beyond 1.2 μm, the PCE saturates due to additional loss mechanisms, such as enhanced recombination and reduced carrier collection efficiency. These mechanisms can explain the slight decrease in V _OC for both devices, as shown in Figure a. Meanwhile, the FF remains almost unchanged (85.7–86.9%), which can be attributed to the fact that the charge transport and series resistance remain nearly unaffected despite the increase in absorber thickness (Figure c). Consequently, an AL thickness of 1.2 μm was selected as the ideal value for further optimization steps.

7.

Variation of (a) V _OC, (b) J _SC, (c) FF, and (d) PCEs of both fevices with AL thickness.

4.1.2.2. Impact of Doping and Bulk Defect Densities

After optimizing the AL thickness, the influence of both acceptor density N _A (AL-N_A) and bulk defect density N _t (AL-N_t) in the absorber layer (AL) on the PSC performance metrics (V _OC, J _SC, FF, and PCE) was systematically investigated for Device I (Sr₃SbCl₃) and Device II (Sr₃PCl₃). Contour plots were generated by varying AL-N_A and AL-N_t from 10¹¹ to 10²⁰ cm^–3, as shown in Figure a–h. As illustrated, both devices follow similar trends under varying AL-NA and AL-Nt, with only minor differences in their optimal responses. As shown in Figure a,e, the maximum V _OC values are nearly identical (1.31 V for Device I and 1.28 V for Device II), achieved when AL-N_A < 10¹⁶ cm^–3 and AL-N_t < 10¹⁵ cm^–3. Nevertheless, with increasing AL-N_t, V _OC gradually declines to 1.07 and 1.05 V, respectively. A similar behavior is observed for J _SC (Figure b,f): it peaks at 21.70 mA/cm² for Device I and 22.70 mA/cm² for Device II when AL-N_A ≈ 10¹⁶ cm^–3 and AL-N_t < 10¹⁵ cm^–3, beyond which it declines. FF shows a slightly different behavior (Figure c,g). For Device I, FF sustains a maximum of 86.24% at AL-N_A ≈ 10¹⁷ cm^–3 and AL-N_t < 10¹⁶ cm^–3, whereas it reaches a comparable maximum (86.01%) for Device II, only when both AL-N_A and AL-N_t remain below 10¹⁶ cm^–3. Beyond these limits, FF drops sharply. Consequently, the PCE is maximized at 24.50% (Device I) and 25.01% (Device II) under optimal conditions of AL-N_A = 10¹⁶ cm^–3 and AL-N_t < 10¹⁵ cm^–3, as illustrated in Figure d,h. Beyond these threshold values, two distinct recombination mechanisms become simultaneously dominant: (i) SRH recombination, driven by the sharp decrease in carrier lifetime with increasing AL-N_t, and (ii) Auger band-to-band recombination, which intensifies with increasing AL-N_A. The coexistence and dominance of these two recombination mechanisms under these specific conditions result in significant performance degradation, − as evidenced by the sharp decline in J _SC, V _OC, FF, and PCE observed in our simulations. Therefore, the adjusted values of AL-N_A (10¹⁶ cm^–3) and AL-N_t (10¹⁴ cm^–3) are identified as optimal parameters for maximizing device efficiencies.

4.1.2.3. Impact of Interface Defect Density

After determining the optimal thickness and the best combination of N _A and N _t in the absorber layer, attention is turned to the role of interfacial properties. The quality of the absorber layer/charge transport layer (AL/CTL) interfaces is a decisive factor for device operation, as it governs both the rectifying behavior of the junction and the overall performance of the PSC.

Since interface defect densities (N_t-interface) are difficult to quantify accurately in real devices, they are systematically varied over a wide range in the simulations. This approach allows for a qualitative assessment of the impact of interface quality on the photovoltaic parameters (V _OC, J _SC, FF, and PCE) and provides valuable insights into the sensitivity of both Devices I and II to interfacial imperfections. Accordingly, the N_t-interface values were changed from 10⁹ cm^–3 to 10¹⁵ cm^–3 at an AL thickness of 1.2 μm for both Devices I and II. The simulated J–V characteristics and the corresponding PCE for both Devices I and II are presented in Figure a–f as a function of N_t-interface density.

9.

Effect of interface defect density (N_t-interface) on PCE and J–V characteristics at the IGZO/AL and AL/Cu₂O interfaces: (a–c) Device I and (d–f) Device II.

It can be seen from Figure a,d that, under front illumination, the AL/Cu₂O interface exhibits much higher sensitivity to increasing defect density (10⁹–10¹⁵ cm^–3) compared to the IGZO/AL. At the AL/Cu₂O interface, the PCE decreases substantially from 24.62 to 19.19% (a 22% reduction) for Device I and from 25.10 to 21.67% (a 13% reduction) for Device II. On the other hand, at the IGZO/AL interface, only a marginal decline is observed, with PCE dropping from 24.62 to 24.38% (≈1% reduction) for Device I and from 25.01 to 24.50% (≈2% reduction) for Device II. These results indicate that, for both devices, (i) the front interface (IGZO/AL interface) exhibits a relatively low recombination rate of the photogenerated carriers compared to that at the rear interface (AL/Cu₂O). Previous studies have reported that the ETL/perovskite interface has a greater impact on the device parameters than the perovskite/HTL interface. This has been ascribed to the direction of illumination rather than the interface nature. , Conversely, Omer et al. reported notable sensitivity of the AL/HTL interface in other perovskite devices employing SnO₂ as an ETL and spiro-MeOTAD as an HTL, particularly when illumination is applied from the SnO₂ side. This effect was attributed to asymmetry in the electric potential near the interfaces, leading to a higher potential drop at the SnO₂ side compared to the opposite one. (ii) Device I is more sensitive to defects at the rear interface, whereas Device II demonstrates greater robustness, particularly at the AL/Cu₂O junction. Since the only difference between the two devices lies in the AL, Sr₃SbCl₃ in Device I and Sr₃PCl₃ in Device II, this contrasting behavior can be attributed to the intrinsic physical properties of the absorber material, most notably the VBO with Cu₂O (see Table ). The larger VBO in Device I (−0.254 eV) impedes hole transport and enhances recombination at the rear interface, while the smaller VBO in Device II (−0.190 eV) enables more efficient hole extraction and thereby ensures greater interfacial robustness. Moreover, as shown in Figure c,f, at the rear interface (AL/Cu₂O), both V _OC and J _SC decrease with increasing N_t-interface. However, at the front interface (IGZO/AL), as shown in Figure b,e, these parameters remain nearly constant. This confirms that the characteristics of the AL/Cu₂O interface are predominantly influenced by the defect density, significantly affecting device efficiency. Consequently, based on this analysis, an N_t-interface density of 10¹⁰ cm^–3 at both IGZO/AL and AL/Cu₂O interfaces appears to be optimal for further investigation, as it yields the best performance observed so far in both devices.

4.1.2.4. Impact of Radiative Recombination

Previous simulation studies have often neglected intrinsic recombination pathways, such as radiative and nonradiative Auger processes, even though these mechanisms are fundamental in defining the realistic efficiency limits of perovskite solar cells. In this work, we explicitly incorporate both effects to provide a more accurate assessment of device behavior under practical operating conditions. Specifically, we investigate how variations in the radiative recombination coefficient (C _r) influence key photovoltaic parameters (V _OC, J _SC, FF, and PCE) while keeping the Auger electron/hole capture coefficients (C _n /C _p) at a low value of 1.0 × 10^–29 cm⁶·s^–1 for both devices. Hence, C _r was varied from 10^–15 to 10^–1 cm³·s^–1, and its impact on both devices’ performances is presented in Figure a–d. As shown in Figure a, all performance parameters for both devices remain essentially unchanged in the range from 10^–15 to 10^–13 cm³·s^–1, with a slight decrease in V _OC from 1.406 to 1.403 V for Device I and from 1.376 to 1.374 V for Device II. However, when C _r is further increased to 10^–9 cm³·s^–1, a significant drop in V _OC is observed, decreasing from 1.40 to 1.22 V for Device I and from 1.37 to 1.19 V for Device II. This behavior originates from the fact that an increase in C _r directly enhances the thermal generation rate of carriers at equilibrium. According to the detailed balance principle, this leads to a higher rate of spontaneous photon emission, which manifests as an increase in the dark saturation current density (J ₀), ultimately reducing V _oc as expressed in eq :

$$V_{\mathrm{OC}}=\frac{n{k}_{\mathrm{B}}T}{q}\ln (\frac{J_{\mathrm{SC}}}{J_0}+1)$$ 15

where $\frac{k_{\mathrm{B}}T}{q}$ designates the thermal voltage, while n represents the diode ideality factor. Noting that n = 1 corresponds to dominant radiative (band-to-band) recombination, n = 2 indicates dominant SRH trap-assisted recombination, and intermediate values reflect mixed recombination mechanisms.

10.

Dependence of (a) V _OC, (b) J _SC, (c) FF, and (d) PCEs of both devices on the radiative recombination coefficient (C _r).

As illustrated in Figure d, the decrease in VOC is accompanied by a sharp decline in PCE, from 26.54 to 22.63% for Device I and from 27.47 to 22.98% for Device II. Meanwhile, J _SC and FF are only weakly affected, as shown in Figure b,c. These results highlight the necessity of selecting a reliable Cr coefficient from the literature to ensure physically realistic simulations. At very low defect densities and C_r values, the overall recombination rate becomes unrealistically small, which can artificially boost device performance beyond the Shockley–Queisser (SQ) limit. To avoid such artifacts, a value of 1.0 × 10^–11 cm³·s^–1 was adopted for both perovskite absorber layers in this study.

4.1.2.5. Effect of Series and Shunt Resistances

The series resistance (R _S), defined as the sum of the resistances of the functional layers (ETL, AL, and HTL) and the front and back metallic contacts in the solar cell configuration, is a key parameter limiting the PCE. In our investigation, R _S was varied from 0 to 6 Ω·cm² for both Devices I and II, while the shunt resistance (R _sh) was fixed at 5 × 10³ Ω·cm² throughout the analysis (see Figure S2a–d). Figure S2d,c shows that V _OC and J _SC remain nearly constant as R _S increases. Among the two devices, Device I exhibits the highest V _OC and lowest J _SC, compared to Device II, which displays the opposite trend. By contrast, Figure S2b,a reveals that an increase in R _S significantly reduces both FF and PCE. These findings agree with previous studies, , which have shown that elevated R _S impedes current flow and consequently degrades overall solar cell performance. Therefore, minimizing R _S is essential to mitigate its detrimental effects on FF and PCE, ultimately improving device efficiency.

Another key parameter influencing PCE is the shunt resistance (R _sh), which originates primarily from point defects and grain boundary defects in the AL film, as well as from mismatches at AL/CTL interfaces. These imperfections serve as primary pathways for charge recombination in PSCs, thereby contributing to efficiency losses. In this study, the impact of R _sh was systematically evaluated over the range from 10¹ to 10⁷ Ω·cm² while keeping R _S constant at 0.1 Ω·cm² for both optimized Devices I and II, as depicted in Figure S2e–h. As shown in Figure S2h, V _OC increases with R _sh up to approximately 10² Ω·cm² and then stabilizes with minimal change beyond 10³ Ω cm². The J _SC, presented in Figure S2g, exhibits a negligible change across the entire R _sh range for both Devices I and II. On the other hand, PCE and FF (Figure S2e–f) improve markedly as R _sh increases up to 10³ Ω cm², after which both parameters plateau. These results highlight the importance of maximizing R _sh and minimizing R _S to achieve optimal device PSC performance. Thus, R _S and R _sh were fixed at 0.1 Ω cm² and 10⁶ Ω·cm², respectively, in the optimized device configurations.

4.1.3. Comparison to Previous Studies

After optimization, a detailed roadmap for improving device performance is presented in Figure , highlighting the potential of Sr₃SbCl₃- and Sr₃PCl₃-based PSCs.

11.

Detailed roadmap for enhancing the performance of PSC devices.

Considering both radiative and nonradiative recombination and optimizing the key parameters of the AL, including AL thickness to 1.2 μm, doping density N _A to 10¹⁶ cm^–3, bulk defect density N _t to 10¹⁴ cm^–3, interface defect density N _{t‑interface} to 10¹⁰ cm^–3, series resistance R _S to 0.1 Ω cm², and shunt resistance R _sh to 10⁶ Ω·cm², the PCE can be improved to 25.80% for Device I and 26.22% for Device II. To evaluate the effectiveness of our parameter optimization, the photovoltaic performance of the optimized Devices I and II was compared with previously reported studies employing the same absorber layer (AL). Table summarizes the predicted key photovoltaic parameters (V _OC, J _SC, FF, and PCE) for both devices and compares them with earlier studies.

7. Comparison of Key Photovoltaic Parameters with Previously Reported Studies.

devices	V OC (V)	J SC (mA/cm 2 )	FF(%)	PCE(%)	refs
Device I	1.31	21.82	90.27	25.80	this study
Al/FTO/CdS/Sr3SbCl3/Au	1.32	13.51	88.05	15.71
Device II	1.28	22.71	90.09	26.22	this study
FTO/IGZO/Sr3PCl3/Cu2O/Ni	1.30	22.79	89.81	26.66
FTO/ZnO/Sr3PCl3/Cu2O/Ni	1.30	22.79	89.90	26.67
Al/FTO/SnS2/Sr3PCl3/Au	1.08	19.92	86.45	18.58

This table demonstrates that a PCE of 25.80% for Device I surpasses the theoretical performance reported in previous studies using Sr₃SbCl₃ as the AL. The improved efficiency, compared with other device configurations, is primarily attributed to the incorporation of a hole transport layer (HTL) throughout the simulations and the careful selection of the ETL. This effectively minimizes band offsets at both the HTL/AL and AL/ETL interfaces, paving the way for further advancement in this technology. In contrast, the PCE of Device II using Sr₃PCl₃ as the absorber layer, at 26.22%, is slightly lower than that reported by Shimul et al. It is important to note that neither C _r nor (C_n /C _p) values are reported by these authors, even though they are unavoidable in practical devices. The observed difference is therefore likely due to the neglect of these recombination mechanisms, which can result in artificially high PCE values of 28.25% for Device I and 30.13% for Device II (see the roadmaps in Figure ).

4.2. Graded Perovskite Absorber Layer-Based Device

Band gap grading, where the band gap is tuned through compositional variation, can improve PSC performance by extending photon absorption to longer wavelengths and mitigating interfacial carrier recombination. Such graded band gap structures may arise spontaneously through ion diffusion during fabrication or can be intentionally engineered by introducing compositional gradients. In the designed Device III (Figure ), the ETL and HTL used in Devices I and II are retained, while the uniform perovskite absorber layer (Sr₃SbCl₃ or Sr₃PCl₃) is replaced with a graded Sr₃Sb_1–x P _x Cl₃ layer (Table ). The graded band gap in the Sr₃Sb_1–x P _x Cl₃ layer is achieved by varying the antimony (Sb) and phosphor (P) content along the absorber thickness, which strongly influences both light absorption and charge carrier transport. The band gap is tuned and decreases from 1.70 eV (Sr₃SbCl₃) near the Cu₂O (HTL) layer for composition (x = 0) to 1.67 eV (Sr₃PCl₃) near the IGZO (ETL) layer for composition (x = 1). Two grading profiles, linear and parabolic, are considered. The corresponding variation of the band gap energy (E _g) with composition (x), following Vegard’s law, is expressed as (eq ):

$$E_{\mathrm{g}}(\mathrm{eV})=x{E}_{\mathrm{g}}({\mathrm{Sr}}_3\mathrm{P}{\mathrm{Cl}}_3)+(1-x)E_{\mathrm{g}}({\mathrm{Sr}}_3\mathrm{Sb}{\mathrm{Cl}}_3)-\mathrm{b}x(1-x)$$ 16

where E _g(Sr₃SbCl₃) and E _g(Sr₃PCl₃) denote the band gap energies of the pure Sb- and P-based absorbers, respectively (x = 0 and x = 1, respectively), and b is the bowing parameter, set to 0 for linear grading and 0.03 for parabolic grading (Figure ).

12.

(Left) schematic of the graded band gap PSC (Device III) and (right) dependence of the band gap energy (E _g) of Sr₃Sb_1–x P _x Cl₃ on composition parameter x.

8. Physical Parameters of Layers in the Graded Solar Cell.

parameters	FTO	IGZO	Sr 3 SbCl 3	Sr 3 Sb 1‑x P x Cl 3 (graded law)	Sr 3 PCl 3	Cu 2 O
thickness (nm)	50	50				50
band gap, E g(eV)	3.6	3.05	1.70	linear/parabolic	1.67	2.2
electron affinity, χ(eV)	4.5	4.16	4.15	linear/parabolic	4.12	3.4
relative dielectric permittivity, εr	10	10	3.45	linear/parabolic	3.28	7.5
CB/VB effective DOS (cm–3)	2.0 × 1018/1.8 × 1019	5 × 1018/5 × 1018	7.62 × 1018/1.68 × 1019	linear/parabolic	6.56 × 1018/1.94 × 1019	2.0 × 1019/1.0 × 1019
electron mobility, μn (cm2/(V s))	100	15	89.151	linear/parabolic	137.16	200
hole mobility, μp (cm2/(V s))	20	0.1	110.52	linear/parabolic	100.6	8600
shallow uniform donor density, N D (cm–3)	1018	1018	0	0	0	0
shallow uniform acceptor density, N A (cm–3)	0	0	1017	uniform	1017	1018
total defect density, N t (cm–3)	1014	1014	1014	uniform	1014	1015

As shown in Figure , varying composition x from 0 to 1 in both grading directions (left-side and right-side grading) results in a slight variation in the photovoltaic parameters. For left-side grading (Sb-rich rear → P-rich front), J _SC and PCE increase gradually from approximately 22.30 to 22.71 mA cm^–2 and from 26.01 to 26.22% (for both linear and parabolic models), respectively. This small variation originates from the gradual modulation of the conduction and valence band edges across the graded Sr₃Sb_1–x P _x Cl₃ layer, leading to smooth CBO and VBO. Such favorable band alignments facilitate charge transfer and extraction while mitigating interfacial recombination, thereby slightly improving device performance. For right-side grading (P-rich rear → Sb-rich front), J _SC and PCE also exhibit minor increases with composition (from 21.82 to 22.30 mA cm^–2 and from 25.80 to 26.00%, respectively), although the overall effect is less significant than in the left-side configuration due to less favorable band alignments at the absorber/HTL interface. At the same time, V _OC remains nearly constant in both cases, with variations below 0.02 V, confirming that grading primarily influences current collection rather than voltage. Similarly, FF decreases slightly in both configurations, reflecting recombination and transport limitations along the gradient. Overall, left-side grading provides a more favorable compromise between optical absorption and energy band alignment, whereas right-side grading yields comparatively modest improvements. Further research could focus on refining grading techniques and on investigating the long-term stability and scalability of Sr₃Sb_1–x P _x Cl₃ perovskite solar cells, with a view toward broader practical applications. Hence, the efficiency increases with P concentration, reaching its maximum for PSC with P-rich compositions (x∼1). The graded absorber did not improve the PCE compared to the uniform devices; in fact, the highest PCE was observed for one of the uniform-layer devices. Nevertheless, a more systematic study of graded absorber profiles could identify conditions under which the performance of graded Sr₃Sb_1–x P _x Cl₃-based perovskite solar cells might be enhanced.

13.

Photovoltaic parameters of Device III with graded Sr₃Sb_1–x P _x Cl₃ absorbers under left- and front-side band gap grading.

5. Strategy for Experimental Validation

While Sr₃M­(Sb,P)­Cl₃ is a novel material, our simulation study provides a theoretical roadmap to its experimental realization. To ensure the validity and feasibility of the proposed device (Ag/FTO/IGZO/Sr₃M­(Sb,P)­Cl₃/Cu₂O/Ni), the following experimental steps and controls are essential:

• 1.Growth of the perovskite film: high-purity Sr₃M­(Sb,P)­Cl₃ chloride perovskites would be synthesized using a solid-state method, solution processing, or chemical vapor deposition (CVD).
• 2.Device manufacturing and environment control: The manufacturing of the Ag/FTO/IGZO/Sr₃M­(Sb,P)­Cl₃/Cu₂O/Ni device can be accomplished layer by layer using spin coating, thermal evaporation, sputtering, screen printing, or digital materials deposition (DMD) printing, which results in a planar heterojunction structure. A glovebox with an inert environment must be used to avoid damage from oxygen and moisture.
• 3.Characterization:

• Real-time in situ monitoring techniques, such as spectroscopic ellipsometry or laser reflectivity, would be used to monitor, characterize, and control the growth of thin films during deposition processes.

• Bulk and interface defect densities must be minimized through optimized annealing atmospheres and times.

• Such a successful synthesis would be verified using X-ray diffraction (XRD) to investigate the layer quality and confirm the crystallographic phase.

• X-ray photoelectron spectroscopy (XPS) was used to validate the chemical stoichiometry and purity at the interfaces.

• Scanning electron microscopy (SEM) can be used to analyze the layer surface morphology and to obtain a cross-sectional image of the PSC device.

• Transmission electron microscopy (TEM) can be used to analyze the grain connectivity and defect density.

• Trap states and charge carrier dynamics were examined using level transient spectroscopy (DLTS).

• The acceptor density in the Sr₃M­(Sb,P)­Cl₃ layer must be verified through Hall effect or capacitance–voltage (C–V) measurements to align with our simulated values.

• 4.Device performance and evaluation: The current density–voltage (J–V) characteristics of the devices can be measured in order to extract photovoltaic parameters (PCE, V _OC, J _SC, and FF). The series and shunt resistances (R _S and R _sh) can be extracted from the slopes of the J–V curve in the open- and short-circuit conditions.

By following this strategy, it will be possible to experimentally validate our simulation predictions of the Sr₃M­(Sb,P)­Cl₃-based perovskite solar cell response, thereby contributing to the development of high-performance perovskite solar cells.

6. Conclusion

In conclusion, our study presents an in-depth investigation of the structural, mechanical, and optoelectronic properties and photovoltaic performance of the cubic crystal system of Sr₃MCl₃ (MP, Sb)-based PSC using first-principles DFT calculations in combination with SCAPS-1D simulations. All DFT calculations were carried out using the VASP code within the GGA-PBE method. Based on the obtained results, both compounds are structurally, thermodynamically, and mechanically stable. It is also found that these perovskite materials have brittle behavior. Moreover, the electronic characteristics (band structure and DOS) analysis of Sr₃MCl₃ (MP, Sb) reveals that they are semiconductors with a direct band gap. Accordingly, the computed band gap energies are 1.704 eV for Sr₃SbCl₃ and 1.667 eV for Sr₃PCl₃. By calculating the carrier mobility, it is found that the electron/hole mobilities are 89.15/110.52 cm²/V·s for Sr₃SbCl₃ and 137.16/100.60 cm²/V·s for Sr₃PCl₃.They also possess high optical absorption in the visible region, exceeding 10⁵ cm^–1, underscoring their suitability to be integrated as absorber layers (ALs) in solar cells. Then, numerical simulations were performed to investigate the performance of PSCs utilizing Sr₃MCl₃ (MP, Sb) as single uniform-ALs (Devices I and II) or a graded-Sr₃Sb_1–x P _x Cl₃ AL (Device III) with various ETLs and HTLs. This simulation study leads to finding Ag/FTO/IGZO/uniform-AL/Cu₂O/Ni device design as an optimal combination. The simultaneous variation of AL thickness, AL-doping concentration, and AL-bulk and interface defect densities yields a PCE of approximately 25.80% for Sr₃SbCl₃ and 26.22% for Sr₃PCl₃ at an optimal AL thickness of 1.2 μm. Furthermore, analyses of the influences of the radiative recombination coefficient (C _r) and series (R _S)/shunt (R _sh) resistances emphasize the necessity of appropriate input parameters (C _r = 10^–11 cm³·s^–1, R _S = 0.1 Ω cm², and R _sh = 10⁶ Ω·cm²). Finally, the use of graded-Sr₃Sb_1–x P _x Cl₃ AL-based PSC does not lead to a significant improvement in PCE. These findings offer valuable insights for future experimental and computational investigations, supporting the development of environmentally sustainable and efficient solar energy technologies.

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acsomega.6c02217.

• Energy band diagrams for (a) Device I and (b) Device II based on the optimized Ag/FTO/IGZO/AL/Cu₂O/Ni configuration (Figure S1); impact of (a–d) series resistance (R _S) and (e–h) shunt resistance (R _sh) on PCE, FF, J _SC, and V _OC for both Devices I and II (Figure S2); input parameters for different ETLs (Table S1); input parameters for different HTLs (Table S2); photovoltaic parameters of PSC with different ETLs (Table S3); and photovoltaic parameters of PSC with different HTLs (Table S4) (PDF)

The authors declare no competing financial interest.