Facet-dependent exfoliation feasibility and optoelectronic properties of two-dimensional all-inorganic halide perovskites

Abstract

Two-dimensional (2D) all-inorganic halide perovskites exhibit promise for optoelectronic applications, yet selective exfoliation along specific crystallographic planes remains a critical challenge for performance optimization. Using first-principles calculations combined with device simulations, we systematically investigated the structural stability, exfoliation feasibility, and optoelectronic properties of 24 all-inorganic 2D perovskites derived from the (100) and (111) planes of cubic perovskites, specifically the A₂BX₄ and A₃B′₂X₉ series (A = Cs, Rb; B = Pb, Sn; B′ = Bi, Sb; X = Cl, Br, I). Our results demonstrate that (111)-derived A₃B′₂X₉ perovskites exhibit significantly lower exfoliation energies (23.1−62.1 meV/Ų) than (100)-derived A₂BX₄ counterparts (59.7−174.0 meV/Ų), attributed to weaker van der Waals interlayer coupling in the former. Rb₃Bi₂I₉ possesses an ultralow exfoliation energy of 23.1 meV/Ų, rivaling that of graphene and demonstrating exceptional potential for mechanical exfoliation of high-quality monolayers. A₂BX₄ monolayers exhibit direct band gaps, which are favorable for optoelectronic applications; whereas A₃B′₂X₉ monolayers display indirect band gaps. Among all investigated materials, monolayer Rb₂SnBr₄ emerges as an outstanding candidate, featuring an ideal direct band gap of 1.34 eV (HSE06) that perfectly matches the Shockley−Queisser limit for single-junction solar cells. SCAPS-1D device simulations further predict that optimized Rb₂SnBr₄-based solar cells can achieve a remarkable theoretical power conversion efficiency of 27.10% under defect densities below 10¹⁴ cm⁻³. This work establishes that (111) plane cleavage is optimal for synthesizing exfoliable 2D perovskites, while (100) plane orientation enables superior direct band gap characteristics for photovoltaic applications, providing critical design principles for crystallographic plane engineering in halide perovskite devices.

Graphical abstract

Keywords

2D perovskites / Lead-free perovskites / Exfoliation feasibility / Density functional theory

1 Introduction

Halide perovskite materials have demonstrated promising potential in the photovoltaic field owing to their unique optoelectronic properties [1,2]. The high visible-light absorption capacity, tunable band gap, and low-cost fabrication processes enable efficient photovoltaic conversion in perovskite solar cells [3]. The halide perovskite is represented by the formula ABX₃, where the A-site is typically occupied by monovalent cations, the B-site by bivalent cations, and the X-site by halide anions. B-site cation and X-site anion form the corner-sharing octahedra framework, which induces excellent optoelectronic properties to halide perovskites; it simultaneously introduces inherent structural instability [4,5]. The halide perovskites are susceptible to degradation caused by light exposure, moisture, and temperature fluctuations, resulting in structural decomposition or performance deterioration [6,7]. Specifically, light irradiation triggers photogenerated carrier recombination within the perovskite lattice, generating reactive free radicals that catalyze material decomposition [8]. Moisture can accelerate hydrolysis reactions, promoting phase transformation of halide perovskites from crystalline to amorphous states and consequently diminishing optoelectronic performance [9]. Thermal fluctuations induce thermal expansion or contraction of the perovskite lattice, increasing structural defect density and further compromising stability [10,11].

In optoelectronic applications, two-dimensional (2D) and quasi-2D perovskite structures have demonstrated unique advantages [12,13]. Transitioning from three-dimensional (3D) to 2D or quasi-2D structures is a feasible strategy for addressing the structural instability of halide perovskites under ambient conditions. By introducing spacer layers to construct layered architectures, the stability of halide perovskites would substantially be enhanced; meanwhile, the excellent optoelectronic properties are simultaneously retained [14,15]. During this phase transition, exfoliation energy (E_exf) emerges as a critical physical parameter that quantifies the energy required to separate a single-layer 2D structure from the 3D lattice [16,17]. Lower exfoliation energy indicates weaker interlayer interactions, thereby facilitating the 3D-to-2D structural transition and simultaneously promoting material flexibility and processability [18,19]. Furthermore, by precisely controlling the chemical composition and thickness of spacer layers, one can systematically modulate exfoliation energy and crystallographic orientation, enabling customized structural design of 2D and quasi-2D perovskites [20,21]. Such rational design not only optimizes the optoelectronic properties of the material but also permits targeted adjustment to accommodate specific device applications [22].

To explore the novel monolayer halide perovskites, we systematically calculated the exfoliation energies of cubic perovskites along different crystallographic planes. We constructed 24 all-inorganic 2D perovskites derived from the (100) and (111) crystallographic planes of cubic perovskite, encompassing two representative monolayer perovskites: A₂BX₄ (A = Cs, Rb; B = Pb, Sn; X = Cl, Br, I) and A₃B′₂X₉ (A = Cs, Rb; B′ = Bi, Sb; X = Cl, Br, I). Employing first-principles calculations, we computed their exfoliation energies and identified relatively low exfoliation energies. Notably, the A₂BX₄-type materials exhibited higher exfoliation energies compared to their A₃B′₂X₉-type counterparts, providing valuable theoretical guidance for experimental exfoliation procedures. Based on HSE06 functional results, Rb₂SnBr₄ was predicted to possess a direct band gap of 1.34 eV, which aligns with the theoretical optimum band gap (~1.34 eV) for single-junction solar cells according to the Shockley−Queisser limit, providing critical theoretical insights for enhancing photovoltaic conversion efficiency. Furthermore, device simulations using SCAPS-1D predict a remarkable power conversion efficiency (PCE) of 27.10% for Rb₂SnBr₄-based solar cells. These findings not only highlight the potential of these novel 2D materials but also provide theoretical guidance for optimizing optoelectronic performance through crystallographic plane engineering.

2 Computational methods

All density functional theory calculations were carried out based on the projector augmented wave method using the Vienna Ab initio Simulation Package [23]. The generalized gradient approximation was adopted by employing the Perdew−Burke−Ernzerhof (PBE) exchange-correlation functional [24]. The plane-wave energy cutoff was set to 400 eV. Considering that the PBE functional typically underestimates the band gap of semiconductors, the Heyd-Scuseria-Ernzerhof hybrid functional (HSE06) was also employed to compute the electronic band structures [25]. For the monolayer A₂BX₄ and A₃B′₂X₉ perovskites, a vacuum spacing of approximately 20 Å was introduced along the out-of-plane direction to avoid artificial interlayer interactions. Structural relaxations were performed until the total energy and atomic forces converged to 10⁻⁸ eV and 10⁻² eV/Å, respectively. The Brillouin zone was sampled using a Γ-centered Monkhorst-Pack grid with a k-point spacing of about 0.03 Å⁻¹. The phonon structures are calculated based on the finite-displacement method using the PHONOPY package with the 3 × 3 × 1 supercells [26]. Post-processing and visualization were performed using the VASPKIT, SUMO, and VESTA software packages [27–29].

The photovoltaic device performance was simulated using the Solar Cell Capacitance Simulator (SCAPS-1D) software to evaluate the theoretical power conversion efficiency. SCAPS-1D solves the governing equations consisting of the Poisson equation and the carrier continuity equations [30,31]. The Poisson equation is expressed as:

(1){\mathrm{\nabla }}^2\psi =\frac{q}{\epsilon }\left(n-p+N_{\mathrm{A}}-N_{\mathrm{D}}\right),

where \psi is the electrostatic potential, N_{\mathrm{D}} and N_{\mathrm{A}} represent the donor and acceptor concentrations, respectively. The carrier continuity equations for electrons and holes are given by:

(2)\mathrm{\nabla }\cdot J_n-q\frac{\mathrm{\partial }n}{\mathrm{\partial }t}=qR,

(3)\mathrm{\nabla }\cdot J_p+q\frac{\mathrm{\partial }p}{\mathrm{\partial }t}=-qR.

Here, J_n and J_p denote the electron and hole current densities, respectively, and R is the total recombination rate. The current densities are described within the drift–diffusion formalism, which includes contributions from both the electric field and carrier concentration gradients:

(4)J_n=qn{\mu }_{n}E+q{D}_n\mathrm{\nabla }n,

(5)J_p=qp{\mu }_{p}E-q{D}_p\mathrm{\nabla }p,

where D_n and D_p denote the electron and hole diffusion coefficients, respectively.

3 Result and discussion

These 2D perovskite structures were constructed according to the cubic perovskite (space group Pm-3m). We first relaxed the crystal lattice of cubic CsPbI₃ and obtained the lattice parameter of 6.29 Å. Subsequently, bulk structures corresponding to the (100) and (111) crystallographic planes were generated using matrix transformation in VESTA. This structural design ensured crystallographic consistency while allowing systematic chemical substitution. The elemental compositions of the constructed layered structures derived from different crystallographic planes are illustrated in Fig. 1. For the bulk structure cleaved along the (100) surface, the 2D perovskites also consist of the typical corner-sharing BX₆ octahedra. This cleavage naturally yielded a Ruddlesden−Popper structure with the chemical formula A₂BX₄, in which the octahedral layers are separated by rock-salt-type AX layers. By introducing sufficient vacuum layers, a monolayer perovskite A₂BX₄ can be obtained, as shown in Fig. 1a. In contrast, cleavage along the (111) surface presents a more complex scenario due to the presence of a threefold rotational symmetry axis. Along this direction, the perovskite lattice can be viewed as alternating layers of corner-sharing octahedra and A-site cations. For the (111) cleavage, the substitution of bivalent cations with trivalent cations at the B-site is necessary to maintain charge neutrality and preserve the integrity of the octahedral framework. Therefore, the compound accommodates the 3:2:9 stoichiometry while retaining the fundamental perovskite connectivity. After adding vacuum layers, a monolayer perovskite A₃B′₂X₉ was obtained as illustrated in Fig. 1b.

We constructed two representative categories of perovskite systems derived from different crystallographic planes, yielding a total of 24 all-inorganic 2D halide perovskite structures. After full structural relaxation, the lattice constants exhibit clear compositional trends, most notably driven by the ionic-size effect of the halide anions, in the order I > Br > Cl. The optimized B-X bond lengths of A₂BX₄ and A₃B′₂X₉ type single-layer perovskite are summarized in Fig. 2. The B-X bond lengths predicted for the A₂BX₄ and A₃B′₂X₉ halides reveal systematic compositional trends that reflect the structural anisotropy inherent to these layered frameworks. For a fixed A- and B-site cation, both the in-plane and out-of-plane bond distances increase monotonically from chloride to bromide to iodide, consistent with the halogen ionic radius sequence. In A₂BX₄ compounds, the Pb-X bonds are longer than the corresponding Sn-X bonds, whereas substitution of Cs⁺ with the smaller Rb⁺ leads to a modest contraction of both in-plane and out-of-plane bond length. In contrast, the A₃B′₂X₉ phases display shorter B-X bond length for Sb³⁺ relative to Bi³⁺, reflecting the expected cation-size effect within the dimerized octahedral units. Notably, the A₂BX₄ family exhibits longer out-of-plane than in-plane bonds, whereas the opposite anisotropy appears in the A₃B′₂X₉ materials, highlighting the distinct bonding environments associated with corner-sharing layers versus face- or edge-sharing dimers. These systematic variations indicate the sensitivity of local coordination environments to both halide chemistry and cation substitution, providing a structural basis for understanding the compositional tuning of optoelectronic properties in low-dimensional halide materials.

Exfoliation energy serves as a crucial quantitative descriptor for evaluating the mechanical exfoliation feasibility of layered materials, offering essential criteria for identifying promising candidates with potential for experimental synthesis [32,33]. In this study, the exfoliation energies were computed using two distinct approaches: (i) the rigid-shift method and (ii) the energy-difference method, which are illustrated in Fig. 3. The first approach defines the exfoliation energy as the energy required to separate one or more atomic layers from the bulk structure, corresponding to the energy difference between the pre- and post-exfoliation states [34]. Specifically, a seven-layer bulk configuration was constructed, and the uppermost layer was gradually detached from the remaining six-layer slab. During the separation process, when the total energy either increased steadily or approached a constant value, the monolayer was considered completely exfoliated. The detailed expression for the exfoliation energy is given in Eq. (6):

(6)E_{\text{exf}}=\frac{E_n-E_0}{a\times b\times \sin \left(\gamma \right)},

where E₀ represents the total energy of the seven-layer slab structure before exfoliation, E_n denotes the total energy of the system after the uppermost monolayer is separated by 6 Å from the underlying six-layer slab. The distance of 6 Å corresponds to the point where the total energy increases only slightly or remains nearly constant, indicating that the monolayer has been fully exfoliated. The term a × b × sin(γ) refers to the area of a single unit cell in the two-dimensional material, where a, b, and γ are the lattice parameters of the slab model. However, the first approach to calculating exfoliation energy suffers from significant inaccuracies. Jung et al. found that this method neglects surface reconstruction and atomic relaxation effects [16]. To address this issue, they reported a more rigorous formulation of the exfoliation energy through analytical deduction. In this refined method, the complex effects of surface reconstruction and atomic relaxation are not necessary. Consequently, the exfoliation energy can be rigorously defined as the energy difference between the ground-state energy per layer of the bulk material and that of the isolated monolayer, as expressed in Eq. (7):

(7)E_{\text{exf}}=\frac{E_{\text{bulk}}/m-E_{\text{monolayer}}}{a\times b\times \sin \left(\gamma \right)},

where E_bulk represents the ground-state energy per layer of the bulk material, m represents the number of layers, E_monolayer denotes the total energy of the fully relaxed isolated monolayer, and a × b × sin(γ) refers to the surface area of the monolayer. Given that exfoliation primarily involves breaking weak interlayer interactions, where energetic contributions are substantially larger than entropic effects at typical processing temperatures, we assessed exfoliation feasibility based on static 0 K energy differences, neglecting vibrational entropy.

To evaluate the exfoliation feasibility, we calculated the exfoliation energies of 24 layered perovskite structures using two different methods, which are shown in Fig. 4. One can see that the exfoliation energies obtained from the energy-difference method are significantly lower compared to those from the rigid-shift approach, except for Sn-based A₂BX₄ compounds. This can be ascribed to the fact that the energy-difference method rigorously accounts for the surface reconstruction and structural relaxation of the isolated monolayer (neglected in the rigid-shift approach), which stabilizes the exfoliated layer and consequently yields a lower, physically more accurate energy value [16]. In the rigid-shift approach, a finite-thickness slab is taken as the initial state. Since the slab contains two unrelaxed surfaces, its energy is higher than that of an ideal bulk. For Sn-based systems, surface polarization associated with the active lone-pair electrons of the Sn²⁺ cation leads to an elevated slab energy. Consequently, extracting one additional layer from an already unstable, high-energy slab requires a relatively smaller incremental energy. By contrast, the energy-difference method adopts a bulk crystal as the reference. The bulk crystal provides the optimal octahedral coordination and the strong Sn-X bonding, resulting in an absolute energy minimum. For materials with strong bulk bonding and high surface energy, the energy-difference method, which disrupts a perfect bulk to create an isolated monolayer, predicts a higher exfoliation energy than the rigid-shift method applied to slabs with pre-existing surfaces. The additional cost stems from the energy required to generate new surfaces in the former case. This finding reveals the rigorous nature of the energy-difference approach, which accounts for the full thermodynamic expense of exfoliation from pristine bulk and thereby exposes the remarkably strong interlayer interactions in Sn-based materials driven by strong ionic character and lone-pair effects.

In the following sections, we employ the energy-difference method to analyze the exfoliation feasibility of these 24 materials. For the A₂BX₄-type 2D perovskites, the calculated exfoliation energies range from 59.7 to 174.0 meV/Ų, with Cs₂SnI₄ exhibiting the lowest value of 59.7 meV/Ų and Rb₂SnCl₄ showing the highest energy of 174.0 meV/Ų. A clear trend of exfoliation energies is observed with respect to halide anions, i.e., for the same A- and B-site cations, the exfoliation energy decreases in the order of Cl, Br, and I. Taking the Cs₂PbX₄ as an example, the estimated exfoliation energy decreases from 126.6 meV/Ų of Cs₂PbCl₄ to 84.1 meV/Ų of Cs₂PbI₄, corresponding to a 50.6% reduction. This trend can be attributed to the effect derived from the ionic radius, where smaller halide ions result in a more compact crystal lattice and stronger interlayer van der Waals interactions. Moreover, the A-site cation also plays a significant role in the exfoliation energy. The Rb-based perovskites generally exhibit higher exfoliation energies than their Cs-based counterparts. For instance, the exfoliation energy of Rb₂PbI₄ is predicted to be 103.6 meV/Ų, which is 23.2% higher than that of Cs₂PbI₄; and the estimated 134.9 meV/Ų of Rb₂PbBr₄ is 27.4% higher than that of Cs₂PbBr₄. This trend is consistent with the halide anion effect described above. In both cases, a smaller ionic radius leads to a more compact lattice. The smaller ionic radius of Rb⁺ (compared to Cs⁺) induces significant lattice contraction and reduces the interlayer spacing, thereby enhancing the interlayer Coulombic interactions and resulting in a higher exfoliation energy. Notably, the influence of the B-site cation on exfoliation energies is complex. For both Cs- and Rb-based compounds, lead iodides show a higher exfoliation energy than the tin iodides, whereas the lead chlorides exhibit a lower value than the tin chlorides.

For the A₃B′₂X₉-type 2D perovskites, the exfoliation energies are significantly lower than those of A₂BX₄-type perovskites. The exfoliation energies are estimated to range from 23.1 to 62.1 meV/Ų, indicating that the A₃B′₂X₉-type structures are more favorable for exfoliation from their bulk prototypes. This enhanced exfoliation feasibility arises from the unique layered configuration formed by (111) surface cleavage, which results in weaker interlayer coupling compared to the ionic dipole interactions in the A₂BX₄ structures [35]. In this configuration, the octahedral layers are held together predominantly by weak van der Waals forces, rather than strong ionic interactions [36]. The decreasing tendency of exfoliation energies influenced by the halide anions remains evident in the A₃B′₂X₉ series. Taking the Cs₃Bi₂X₉ as an example, the exfoliation energies decrease from 59.0 meV/Ų of Cs₃Bi₂Cl₉ to 34.9 meV/Ų of Cs₃Bi₂I₉, corresponding to a 69.1% decrease. Moreover, the B′-site cation effect also plays a crucial role in exfoliation energies. The Sb-based materials generally exhibit higher exfoliation energies than their Bi-based counterparts. For instance, Cs₃Sb₂I₉ (36.4 meV/Ų) is 4.3% higher than Cs₃Bi₂I₉ (34.9 meV/Ų), and Rb₃Sb₂Cl₉ (62.1 meV/Ų) exceeds Rb₃Bi₂Cl₉ (54.4 meV/Ų) by 14.2%. Remarkably, Rb₃Bi₂I₉ exhibits the lowest exfoliation energy (23.1 meV/Ų) among all the studied compounds, which is substantially lower than that of most conventional layered materials.

Compounds with exfoliation energies below 100 meV/Ų are generally regarded as having good mechanical exfoliation feasibility for practical applications. Based on this criterion, our calculated results indicate that all A₃B′₂X₉-type perovskites exhibit excellent exfoliation potential, with values ranging from 23.1 to 62.1 meV/Ų. Within the A₂BX₄ series, iodide-containing compounds display relatively lower exfoliation energies, among which Cs₂PbI₄ (84.1 meV/Ų), Rb₂SnI₄ (88.3 meV/Ų), and Cs₂SnI₄ (99.7 meV/Ų) fall below the threshold of 100 meV/Ų, suggesting promising prospects for experimental synthesis. For comparison, the exfoliation energies of graphene, MoS₂, and h-BN are approximately 20−50 meV/Ų, 34 meV/Ų, and 50 meV/Ų, respectively [37,38]. The low exfoliation energy of these A₂BX₄ and A₃B′₂X₉ perovskites highlights the excellent interlayer cleavage characteristics and mechanical exfoliation feasibility, suggesting their strong potential for the experimental realization of high-quality 2D monolayers. These findings clearly demonstrate that crystallographic orientation would be a key determinant governing the strength of interlayer interactions and the ease of exfoliation. In particular, A₃B′₂X₉-type perovskites derived from the (111) surface, owing to their exceptionally low exfoliation energies, constitute a highly promising library of exfoliable 2D semiconductor candidates, offering valuable theoretical guidance for future experimental synthesis and device applications.

We further investigate the electronic properties of these monolayer perovskites. Since the conventional PBE functionals are known to underestimate the band gaps of semiconductors, we employed the screened hybrid functional HSE06 for band structure correction and validation. The computational results reveal a strong structural dependence of the electronic properties. Specifically, A₂BX₄-type perovskites derived from the (100) surface exhibit direct band gap characteristics, whereas A₃B′₂X₉-type perovskites originating from the (111) surface display indirect band gaps. In A₃B′₂X₉, the octahedra often form low-dimensional connected motifs, leading to non-uniform band dispersion arising from B′-s or p and X-p hybridization across different k-points. As a result, the valence-band maximum (VBM) and conduction-band minimum (CBM) tend to appear at different high-symmetry points. Meanwhile, the interlayer coupling strength and stacking configuration further modulate the dispersion of the valence and conduction bands and thus shift the band-edge positions; weaker interlayer coupling typically promotes carrier localization and suppresses band dispersion, thereby enhancing the indirect-gap character [39]. In addition, the relatively low crystallographic symmetry of these structures can induce band folding and lift band degeneracies, making it more common for the band-edge extrema to deviate from the Γ point. The corresponding band gaps are illustrated in Fig. 5. The A₂BX₄-type perovskites derived from the (100) surface exhibit the direct band gap characteristics, which are highly advantageous for light-emitting and photovoltaic applications. The calculated HSE06 band gaps of these representative perovskite systems range from 0.96 to 3.30 eV, demonstrating a broad tunability of electronic properties. The halide anions play an essential role in the band gap. For instance, the band gaps are predicted to be 3.37 eV for Cs₂PbCl₄, 2.83 eV for Cs₂PbBr₄, and 2.36 eV for Cs₂PbI₄, respectively. This trend can be attributed to the variation in energy levels of halogen p-orbital, e.g., the 3p orbital of Cl lies at a lower energy than the 5p orbital of I, resulting in a downshift of the VBM and consequently a wider band gap. The influence of B-site cations is also significant to their electronic properties. The Sn-based perovskites exhibit smaller band gaps compared to their Pb-based counterparts. For instance, the band gap of Cs₂SnI₄ (1.06 eV) is significantly smaller than that of Cs₂PbI₄ (2.36 eV), and Rb₂SnI₄ (0.96 eV) has a much lower band gap than Rb₂PbI₄ (2.29 eV). This reduction primarily arises from the higher energy level of the Sn 5s-orbital compared with the Pb 6s-orbital, as well as the stronger reducing nature of the Sn²⁺ cation, which elevates the CBM and thus narrows the band gap. The effect of A-site cations is relatively minor but still observable. In most cases, Rb-based compounds exhibit slightly smaller band gaps than their Cs-based analogs, likely due to the smaller ionic radius of Rb⁺, which induces lattice contraction and stronger structural confinement.

In contrast to the A₂BX₄ family, the A₃B′₂X₉ perovskites derived from the (111) crystallographic plane usually exhibit the indirect band gap nature, with HSE06 band gaps ranging from 2.22 to 4.17 eV, which are overall larger than those of the A₂BX₄ counterparts. The indirect band gap originates from the unique layered structure formed upon (111) surface cleavage, where the VBM and CBM reside at different k-points in the Brillouin zone. Although such an indirect gap may hinder radiative recombination, it remains advantageous for optoelectronic applications, e.g., ultraviolet photodetection, owing to the enhanced carrier separation efficiency. An obvious halide-dependent band gap modulation can also be observed for these A₃B′₂X₉ layered materials. Taking the Cs₃Bi₂X₉ compounds as an example, the band gap decreases from 4.17 eV for chloride to 2.74 eV for iodides, corresponding to a 52.2% reduction. A similar trend is found in the Rb₃Bi₂X₉ as well, where the band gap decreases from 4.10 eV of Rb₃Bi₂Cl₉ to 2.72 eV of Rb₃Bi₂I₉, showing a 50.7% decrease. This notable tunability can be attributed to the distinct coordination environment of halide anions and the stronger quantum confinement effect inherent to the (111)-derived layered structures, both of which significantly affect the electronic coupling between B′-X bonds. The influence of the B′-site cation is also remarkable. Sb-based compounds generally exhibit smaller band gaps than their Bi-based counterparts. This difference can be rationalized by the electronic configuration of the cations, where the Sb³⁺ cation possesses a more active 5s² lone pair compared to the 6s² pair of the Bi³⁺ cation, resulting in a higher VBM position and consequently a reduced band gap. In contrast, the A-site cation shows an inconspicuous effect on the electronic properties. The band gap differences between Rb- and Cs-based A₃B′₂X₉ structures are typically less than 0.1 eV, indicating that the A-site cation primarily serves to maintain structural stability rather than directly modulating the electronic structure.

From the perspective of photovoltaic applications, the HSE06 band gap of Rb₂SnBr₄ is 1.34 eV (as shown in Fig. 5a), which is remarkably close to the theoretical optimum band gap for a single-junction solar cell (~1.34 eV according to the Shockley−Queisser limit) [40]. This band gap allows the material to efficiently absorption of the visible and near-infrared solar spectrum while minimizing thermalization losses, thereby enabling theoretical high power conversion efficiency. In addition, iodide compounds exhibit smaller band gaps, e.g., 1.06 eV of Cs₂SnI₄ and 0.96 eV of Rb₂SnI₄. Although these values are closer to the band gap of silicon, they may result in excessive near-infrared transmission losses. In contrast, the 1.34 eV band gap of Rb₂SnBr₄ lies precisely within the optimal spectral window for solar energy utilization, theoretically allowing for a power conversion efficiency exceeding 30%. We note that spin-orbit coupling (SOC) plays an essential role in the electronic properties of heavy-metal-based compounds. To assess SOC effects in these monolayer halide perovskites, we calculated the band gap differences at the PBE level with and without SOC inclusion; the results are illustrated in Fig. S1. For Pb- and Bi-based compounds, SOC induces substantial band gap reductions of approximately 0.5~0.8 eV, whereas for Sn- and Sb-based compounds, the differences are considerably smaller (0.1–0.3 eV). Furthermore, developing high-performance lead-free perovskite optoelectronic materials is crucial for advancing commercial applications. Notably, Bi-based monolayers already exhibit excessively large band gaps (> 2 eV) at the PBE level. Therefore, we further evaluated the optoelectronic properties of these monolayer perovskites using both PBE and HSE06 approaches.

We then investigate the electronic band structure of monolayer Rb₂SnBr₄, which is shown in Figs. 6a and 6b. The monolayer Rb₂SnBr₄ exhibits a direct band gap, with both the VBM and CBM located at the M point. The partial density of state (DOS) reveals that the upper valence band edge is primarily composed of antibonding states between Sn 5s and Br 4p orbitals, with the Br 4p orbitals being the dominant, consistent with the characteristic electronic structure of halide perovskites. The lower conduction band is mainly derived from Sn 5p orbitals, with minor contributions from Br 4p orbitals. The A-site Rb⁺ cation contributes negligibly to the band edge, exhibiting only a weak contribution from Rb 5s orbitals in the higher conduction band region (above 6 eV). This indicates that the A-site Rb⁺ cation primarily serves to stabilize the crystal structure and maintain charge neutrality. In addition to having a suitable bandgap, the charge carrier mobility plays a crucial role in determining the efficiency of photovoltaic materials. Carrier transport behavior is largely governed by the effective masses of photo-generated electrons and holes (m_e and m_h). These effective masses can be obtained by applying a parabolic fitting to the band dispersion near the CBM and VBM, and are evaluated using the following expression:

(8)\frac{1}{m^{\ast }}=\frac{1}{{\hslash }^2}\cdot \frac{{\mathrm{\partial }}^{2}E\left(k\right)}{{\mathrm{\partial }k}^2},

where E(k) denotes the band-structure eigenvalue, \hslash is the reduced Planck constant, and k represents the wave vector. The calculated m_e and m_h for monolayer Rb₂SnBr₄ are as low as 0.089 and 0.122 m₀, respectively, which are quite small and comparable to those reported for MAPbI₃. In this monolayer perovskite, the VBM is dominated by the antibonding interaction between the lone-pair ns² orbital of the B-site cation and the p-orbital of the X-site anion, which facilitates long-range diffusion of photoexcited carriers.

To further evaluate the photovoltaic potential of monolayer Rb₂SnBr₄, we calculated its frequency-dependent absorption coefficient, as depicted in Fig. 6c. The material exhibits a sharp absorption edge in the visible region with an absorption coefficient (α) rapidly reaching the order of 10⁵ cm⁻¹, which is characteristic of direct band gap semiconductors and indicates superior light-harvesting capability. Notably, its absorption profile in the visible range is comparable to that of the prototypical MAPbI₃ and significantly stronger than that of other lead-free candidates such as Cs₂AgBiBr₆ and Cs₃Bi₂I₉. Based on the calculated band gap and absorption spectrum, we estimated the theoretical power conversion efficiency using the Spectroscopic Limited Maximum Efficiency (SLME) method, as shown in Fig. 6d. The SLME of Rb₂SnBr₄ increases rapidly with film thickness. It can approach ~27% at a typical thickness of 0.5 μm and will reach a saturation value exceeding 30% at a thickness of approximately 1 μm. This theoretical efficiency is remarkably higher than that of Cs₂AgBiBr₆ and Cs₃Bi₂I₉, and competes well with the renowned MAPbI₃, suggesting that Rb₂SnBr₄ is a highly promising candidate for high-efficiency, lead-free perovskite solar cells.

Having established the superior electronic and optical properties of monolayer Rb₂SnBr₄, we further evaluated its potential in practical photovoltaic applications. Numerical simulations were carried out to assess the photovoltaic performance of 2D perovskite solar cells with the device structure FTO/ETL/Rb₂SnBr₄/HTL/Au. The Rb₂SnBr₄ absorber layer is sandwiched between the n-type electron transport layers (ETLs) and the p-type hole transport layers (HTLs). All simulations were conducted under AM 1.5G illumination (1 sun) at a temperature of 300 K, and the parameters are specified in Table S1.

The photovoltaic performances of four typical device configurations were systematically investigated by tuning the thicknesses of the ETL and HTL in the range of 0.5−1.5 Å, while maintaining the acceptor concentration and defect density at 1 × 10 [18] and 1 × 10 [15] cm⁻³, respectively. The corresponding simulated photovoltaic parameters are summarized in Table 1. The device employing PCBM as the ETL and PATT as the HTL exhibits the highest power conversion efficiency (PCE) of 27.1%, primarily attributed to its remarkably high short-circuit current density (J_SC = 41.66 mA/cm²) and the highest open-circuit voltage (V_OC = 1.03 V). However, this device shows a relatively moderate fill factor (FF = 63.3%), indicating potential resistive or interfacial losses. This trend is also evident in the current density−voltage (J−V) curves shown in Fig. 6f. In contrast, the TiO₂/PEDOT:PSS and SnO₂/Spiro-MeOTAD based devices deliver significantly higher fill factors of 85.03% and 87.15%, respectively, suggesting more efficient charge extraction and reduced recombination losses. Although their J_SC values are lower (31.21−31.98 mA/cm²), the SnO₂/Spiro-MeOTAD device achieves a competitive PCE of 26.03%, benefiting from its superior FF. The ZnO/Cu₂O based device exhibits the poorest performance, with the lowest V_OC (0.87 V), J_SC (24.71 mA/cm²), and PCE (16.43%), indicating unfavorable band alignment and increased carrier recombination at the interfaces.

The performance of perovskite solar cells is intrinsically governed by the quality and dimension of the absorber layer. Figure 7a illustrates how variations in the thickness and bulk defect density of Rb₂SnBr₄ absorber determine the key photovoltaic parameters: PCE, V_OC, J_SC, and FF. As the absorber thickness increases from 0.5 to 1.5 μm and the defect density varies from 10¹³ to 10¹⁷ cm⁻³, the contour plots reveal how changes in light‐absorption capacity and nonradiative recombination pathways ultimately shape the device performance. This visualization clarifies the causal relationship between structural parameters and photovoltaic responses. As shown in Fig. 7a, the PCE exhibits a high sensitivity to the defect density. In the high-defect domain (n_t > 10¹⁶ cm⁻³), the efficiency is severely suppressed below 15% regardless of the film thickness. This degradation is primarily attributed to Shockley−Read−Hall recombination, which reduces the carrier lifetime and diffusion length [41]. Conversely, reducing the defect density to 10¹³ cm⁻³ leads to a substantial enhancement in performance, yielding a theoretical PCE exceeding 27%.

Regarding the thickness dependence, J_SC increases monotonically with thickness (Fig. 7a), benefiting from enhanced photon absorption in the long-wavelength region. However, V_OC is predominantly determined by the defect density and remains relatively insensitive to thickness variations (Fig. 7a). This suggests that suppressing non-radiative recombination centers is more critical than thickness optimization for maximizing voltage output. Consequently, an optimized configuration is identified with a thickness of approximately 1.2 μm and a defect density lower than 10¹⁴ cm⁻³, where the trade-off between light harvesting and carrier collection is balanced.

To further minimize resistive losses, we investigated the impact of the thickness of the ETL and HTL. Figure 7b displays the device performance variations with ETL and HTL thicknesses ranging from 0.05 to 0.5 μm. The simulated results indicate a clear trend: maximizing efficiency requires decreasing the thickness of ETL and increasing the HTL. As observed in Fig. 7b, increasing the thickness of either the ETL leads to a gradual decline in PCE, V_OC, and FF. This reduction can be attributed to two primary mechanisms: (1) increasing the transport-layer thickness leads to higher series resistance, which limits charge extraction and degrades carrier collection efficiency; (2) a thicker layer enhances parasitic absorption, particularly in the front-side transport layer, thereby decreasing the photon flux incident on the absorber. Consequently, employing ultra-thin transport layers is essential to maintain low resistive losses and minimize optical attenuation. HTL thickness exerts a negligible influence on V_OC and FF; however, incremental HTL thickening systematically elevates J_SC, thereby translating into measurable PCE gains. These findings indicate that a concurrent reduction of ETL thickness and expansion of HTL would be a rational approach for efficiency optimization.

With stringent control over crystal quality (n_t ≈ 10¹³ cm⁻³) and geometric optimization (1.2 μm thickness), the Rb₂SnBr₄-based solar cell is capable of delivering a theoretical PCE as high as 27.10%. This value enables monolayer Rb₂SnBr₄ in competition with top-performing lead-free perovskites, validating its prospect as a sustainable and high-performance alternative for future photovoltaics.

4 Conclusions

In summary, we systematically investigated exfoliation viability and optoelectronic performance across 24 distinct all-inorganic 2-D halide perovskites through first-principles calculations. These structures represent the two dominant classes, i.e., A₂BX₄ and A₃B′₂X₉, cleaved from the (100) and (111) terminations of the cubic perovskite lattice, respectively. The calculated exfoliation energies and electronic structures clearly indicate the decisive influence of crystal-plane orientation on the physical properties of these materials. The A₃B′₂X₉ materials derived from the (111) plane exhibit significantly lower exfoliation energies than the A₂BX₄ materials from the (100) plane. Notably, Rb₃Bi₂I₉ shows an exceptionally low exfoliation energy of 23.1 meV/Ų, comparable to or even lower than that of graphene, highlighting the great potential of the A₃B′₂X₉ series for obtaining high-quality monolayers via mechanical exfoliation. The A₂BX₄ perovskites from the (100) plane exhibit direct band gaps, which are highly favorable for optoelectronic and photovoltaic applications, whereas the A₃B′₂X₉ perovskites from the (111) plane display indirect band gaps. Rb₂SnBr₄ is predicted to possess an ideal direct band gap of 1.34 eV at the HSE06 level, which closely matches the theoretical optimum band gap of single-junction solar cells according to the Shockley−Queisser limit. Furthermore, device simulations using SCAPS-1D predict that monolayer Rb₂SnBr₄-based solar cells can achieve a remarkable power conversion efficiency of 27.10% under optimized conditions. Therefore, the (111) plane enables facile exfoliation while the (100) plane yields superior optoelectronic properties. These results demonstrate that deliberate crystallographic engineering can simultaneously deliver exfoliation and optoelectronic performance, offering a universal blueprint for next-generation 2D optoelectronic materials.

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