Impact of pressure on perovskite MSnX₃ (M = Li, Na; X = Cl, Br, I): A density functional theory study

Abstract

This study explores the structural, electronic, and optical properties of tin-based halide perovskites, MSnX₃ (M = Li, Na; X = Cl, Br, I), under varying pressure conditions. Using volume optimization and the Perdew-Burke-Ernzerhof generalized gradient approximation (PBE-GGA) method, it analyzes these perovskites in their cubic Pm\stackrel{-}{3} m phase. The findings reveal that the lattice constants of these compounds decrease as pressure increases, with more pronounced changes observed when anions are substituted from Cl to I. The electronic analysis shows that these materials maintain their direct band gap nature under pressures, although the band gaps narrow with increasing pressure and larger anion sizes. Notably, Li/NaSnCl₃, Li/NaSnBr₃, and Li/NaSnI₃ may exhibit metallic behavior at pressures exceeding 5 GPa. Optical studies reveal significant pressure-induced enhancements in static dielectric constant and optical absorption, especially in the visible spectrum, highlighting the potential of these perovskites for solar cell applications. The refractive index increases with pressure, indicating a higher material density and enhanced optical performance. Additionally, the extinction coefficient and electron energy loss function provide insights into the energy absorption and scattering characteristics, which are crucial for improving the efficiency of optoelectronic devices. This comprehensive analysis underscores the potential of these tin-based halide perovskites for advanced optoelectronic and photovoltaic technologies.

Graphical abstract

Keywords

halide perovskites / high absorption / hydrostatic pressure / solar cell materials

1 Introduction

The effects of global warming, energy storage, and energy production have become central issues in the world today, highlighting the urgent need to shift from fossil fuels to renewable energy resources. Renewable energy technologies such as solar cells, biomass, thermoelectric (TE) devices, and photovoltaics are becoming increasingly important [1–4]. As conventional non-renewable energy sources deplete, producing electricity with solar energy will become the best option. Solar energy is abundant, accessible everywhere on Earth, and virtually inexhaustible. As solar energy does not directly contribute to environmental or climatic contamination, its importance continues to grow. Over the past 30 years, tremendous progress has been made to enhance the efficiency of semiconductor-based solar cell and to refine their design. Today, silicon remains the industry-standard material for solar photovoltaics, and researchers have been continuously working for decades to improve the efficiency of these devices [4–6].

In recent years, there has been a surge in research on novel perovskite solar cells due to their exceptional advantages, including low manufacturing costs, high efficiency, ease of application, and environmental friendliness. The ABX₃ perovskites (A = CH₃NH₃, Cs, Rb; B = Sn, Pb; X = Cl, Br, I) have been the focus of substantial experimental and theoretical studies [7–20]. Due to their higher stabilities compared to their organic counterparts, all-inorganic structures have shown remarkable potential in optoelectronic characteristics [21–27]. Bourachid et al. [28] conducted a theoretical study on the structural, electrical, and optical characteristics of inorganic lead base bromide materials APbBr₃ using the FP-LAPW method within the generalized gradient approximation (GGA) to deliberate the exchange-correlation potential. Their research on band composition suggests that all these materials exhibit semiconductor behavior, making them strong candidates for photovoltaic applications. Optical constants further support their potential as semiconductors for optoelectronic devices. Lead-based halide perovskites, in particular, are notable for their higher energy conversion efficiency. Their bright, narrow photoluminescence, which can be tuned from the UV to near-infrared range (nm), is easily adjustable through halide substitution (F, Cl, Br, I) or by varying nanocrystal size, making them appealing for displays and lighting technologies. Additionally, they can be synthesized quickly and at low cost [29]. However, these materials face challenges related to structural stability and environmental concerns [6,30–32].

According to Li et al. [33], extensive research has been conducted on the computational and synthetic aspects of lead-free (nontoxic) perovskites. However, there is a noticeable gap in the study of fabricating these perovskites, with most research efforts focusing on tin (Sn)-based materials. Among lead-free perovskites, Sn-based compounds have been the most extensively studied, and researchers have tried to deposit them onto flexible substrates. Despite this, more work needs to be done to increase the efficiency of other lead-free perovskites. The limited research on flexible lead-free perovskites indicates that they are promising materials deserving of more attention. Therefore, this presents an opportune moment to advance flexible, lead-free perovskite optoelectronics [33].

Applying high pressure to materials leads to improvements in structure and properties. Liang et al. [34] investigated the influence of high pressure on the crystal structure of methylammonium lead bromide (MAPbBr₃), a hybrid perovskite, to understand how pressure affects its structural characteristics. Their findings provide insights that could help develop more efficient materials for technological applications, eg. solar cells. Similarly, Rashid et al. [35] examined the structural, electrical, and optical characteristics of rubidium-based materials RbSnCl₃ and RbSnBr₃ using ab initio calculations, under pressures ranging from 0 to 10 GPa. At ambient pressure, these materials are direct band gap semiconductors; but as induced strain increases, the band gap narrows, eventually closing with sufficient strain. This pressure-induced strain also enhances optical absorbance and conductivity, making them more suitable for optoelectronic applications [35].

To support the practical potential of these materials, Das et al. [36] analyzed the structural, electrical, and optical characteristics of KGeCl₃ and KSnCl₃ under various pressures ranging from ambient to 8 GPa. Their results indicate that at zero strain, the compounds exhibit semiconducting behavior, but their band gap decreases as pressure rises, boosting conductivity and driving the transition from semiconductor to metallic behavior. This pressure also improves the optical properties of the materials, making them viable candidates for a range of optoelectronic devices operating in the visible and UV spectra.

Ullah et al. [37] investigated inorganic halide-based materials ASnX₃ (A = K, Rb; X = Cl, Br, I) at ambient and increased pressure. It is found that when the pressure was applied to these materials, the special effects of exchange-correlation were observed, which is very promising in terms of the optoelectronic and structural properties. These materials show higher absorption under strained conditions. Because these materials have appropriate energy bandgaps, they can be used in various optoelectronic devices [37].

Using first-principles calculations, Saikia et al. [38] examined the structural and optoelectronic properties of ABBr₃ perovskites (A = K, Na, Rb, Cs, where B = Ge, Sn) for green energy applications. All the compounds under investigation displays a direct band gap ranging from 1.00 to 1.97 eV, making them ideal candidates for use in solar cells. Additionally, across the complete ultraviolet to visible (UV–Vis) spectrum, all of the ABBr₃ compounds show substantial photo absorption.

To replace lead-based (toxic) perovskite solar cells (PSCs) with stable and environmentally friendly alternatives, Charlie et al. [39] investigated the effects of alkali metals (Li, Na, K) doping at the X sites in tin-based X–SnI₃ halide perovskites on their structural and electronic properties. These findings were then correlated with their optoelectronic efficiency. Additionally, Labrim et al. [40] explored the optoelectronic and thermo-electric characteristics of NaSnX₃ (X = Br or I) using the DFT-based Boltzmann transport theory. They applied the exchange-correlation approximation of the generalized gradient approximation (GGA) to investigate the structural, and optoelectronic physical characteristics of these compounds. The obtained outcomes corroborate the possibility that the materials under consideration could be good fits for thermoelectric and engineering applications in addition to solar ones.

According to Sharma et al. [41], NaSnCl₃ has demonstrated excellent properties when studied through the first principles techniques. Similarly, with a focus on potential uses in photovoltaic systems, Pakravesh and Izadyar [42]. focused on the structural, and optoelectronic characteristics of LiBX₃ materials (B = Ge, Sn, Pb, X = F, Cl, Br, I) in both unit cell and supercell structures.

Different from previous studies, the current research centers on the high-pressure effects on MSnX₃ (M = Li, Na; X = Cl, Br, I), offering new insights into how these materials respond to pressure, with implications for their structural and optoelectronic behavior. To enhance the performance of optical devices such as solar cells and photovoltaic characteristics, it provides a comprehensive analysis of tin-based inorganic materials, specifically LiSnCl₃, LiSnBr₃, LiSnI₃, NaSnCl₃, NaSnBr₃, and NaSnI₃ perovskites under hydrostatic pressure (0 to 5 GPa) for the first time. The calculations were performed using the recently modified Becke-Johnson (mBJ) method for perovskites [43].

2 Computational details

The perovskites MSnX₃ (M = Li, Na; X = Cl, Br, I) were studied for their structural, electronic, and optical characteristics using the DFT framework within the WIEN2k code [44] and the full-potential linearized augmented-plane wave (FP-LAPW) approach [45]. The crystal structure was optimized using the PBE-GGA generalized gradient approximation [46]. The muffin tin radii (R_MT) were chosen to ensure no charge leakage from the core for all the compounds in all structures. A plane wave cutoff value of R_MT*K_max = 7 was selected to achieve an appropriate basis set size, and a cutoff energy of −6 Ry was employed to distinguish between the core and valence states in a non-spherical region. In the entire reciprocal cell, a suitable mesh grid of 10×10×10 k-points was employed across the entire reciprocal cell to integrate the Brillouin zone.

It is worth mentioning that the Heyd-Scuseria-Ernzerhof (HSE06) method is one of the most accurate approaches for calculating band gap energies, particularly favored for its accuracy in predicting band gaps in complex materials, such as strongly correlated systems. When computational resources are available and high accuracy is essential, HSE06 is preferred [47]. However, this method is significantly more computationally demanding than standard DFT methods, resulting in longer calculation times and higher memory requirements.

The mBJ [43] method is another popular approach for calculating band-gap energies, offering a balance between accuracy and computational efficiency. For larger systems or when computational efficiency is a priority, mBJ is a practical alternative, providing better performance in predicting band gaps with reduced computational costs.

3 Results and discussion

3.1 Structural properties

The structural properties of the tin-based halide perovskites LiSnCl₃, LiSnBr₃, LiSnI₃, NaSnCl₃, NaSnBr₃, and NaSnI₃, all in cubic form with the space group Pm\overline{3}m, were investigated using a volume optimization approach, as illustrated in Fig.1. To determine these properties, the PBE-GGA method was employed. The relationship between energy and unit cell volume was modeled using Birch-Murnaghan’s equation of state [48]. The optimized plots, which depict the energy minimum (E₀) as a function of unit cell volume (V₀), are shown in Fig.1, where the ground state of each compound is marked by the minimum points on the parabolic curves.

Tab.1 summarizes the structural parameters, revealing that lattice constants, bulk modulus, and minimum volume generally increase with the size of the halide ion, though the differences between the Li and Na variants are less pronounced. The bulk modulus (B₀) remains relatively consistent across all compounds, while the minimum energy decreases in the sequence of Cl > Br > I for the halides, with a similar, albeit less pronounced trend observed for the alkali metals (Li and Na).

As shown in Tab.1, the calculated structural parameters closely align with previous theoretical results [39,42]. Notably, the substitution of the cation from Li to Na causes a relatively smaller change in both lattice parameters and bulk modulus compared to the substitution of anion from Cl to I. The bulk modulus is an important physical property that quantifies the resistance of a material to compression under applied pressure, making it crucial for predicting material behavior in various applications such as optical devices, energy storage, and materials science [49]. In this case, the larger atomic radius of iodine (I) leads to a larger lattice volume and increased compressibility.

Fig.2 illustrates the lattice constant as a function of applied pressure. For all the materials studied, the lattice constant consistently decreases as pressure increases. While the substitution of the cation from Li to Na causes a relatively minor change in the lattice constant, the substitution of Cl with I results in a more pronounced shift, highlighting the significant influence of the anion size on the structural properties.

The mechanical stability conditions for cubic structures under pressure [50] are

C_{44}- P>0,

C_{11}- C_{12}- 2P>0,

C_{11}+ 2C_{12}+P>0 .

It is verified from Tab.2 that the calculated elastic constants at both 0 and 5 GPa satisfy the required stability criteria, confirming that the materials studied are mechanically stable within the studied pressure range.

3.2 Electronic properties

For LiSnCl₃, LiSnBr₃, LiSnI₃, NaSnCl₃, NaSnBr₃, and NaSnI₃, the energy band structure and density of states (DOSs), including the total density of states (TDOSs) and partial density of states (PDOSs), were computed at both zero and high pressure using the Tran and Blaha modified Becke-Johnson potential (TB-mBJ) functional for perovskites [43]. Fig.3 depicts the band structure and TDOS of the MSnX₃ compounds. In all cases, the valence band (VB) maxima and conduction band (CB) minima are located at the “M” symmetry point, indicating a direct band gap nature.

At 0 GPa, the band gaps are 2.23 (LiSnCl₃), 1.36 (LiSnBr₃), 0.76 (LiSnI₃), 2.31 (NaSnCl₃), 1.38 (NaSnBr₃) and 0.77 (NaSnI₃). Tab.3 summarizes these energy band gaps, showing that NaSnCl₃ has the largest band gap (2.31 eV), while LiSnI₃ has the smallest band gap (0.76 eV). All the compounds exhibit a semiconductor nature, with the band gap decreasing as the anion changes from Cl to I.

This trend is attributed to the increasing ionic size moving from Cl to I, which affects the electronic structure. Band gap is also changing due to Li and Na but more change is coming due to halide elements. The band gap of all materials is a direct one which makes them highly suitable for applications in solar cells and optoelectronic devices. Additionally, band gap values of these materials at 0 GPa obtained using the TB-mBJ approximation are more accurate than the previous results [41,42,51]. This is because the optoelectronic characteristics of these compounds are intended using the TB-mBJ for perovskites approximation [43], which yields an approximation result that is closer to the experimental result.

The sections in Fig.3 illustrate the influence of pressures ranging from 0 to 5 GPa on TDOS, taking LiSnCl₃ as an example. The VB, spanning from 0 to −5.5 eV, and the CB, from 0 to 5.5 eV, are the regions that are most affected by pressure. Tab.3 demonstrates that, for ASnCl₃ and ASnBr₃, the computed energy band structures at 0 pressure are superior (i.e., wider band gaps) compared to previous theoretical data [41,42]. This improvement is largely due to the use of TB-mBJ functional designed for the perovskites. However, the reported gaps for NaSnI₃ are lower than those found in other studies [39,51], likely due to differences in the computational potentials used for electronic calculations.

These materials have not yet been experimentally studied; however, their direct energy bandgap in the right variety makes them suitable for optoelectronic applications. The location of the Fermi level is crucial for assessing the electronic stability of a compound. Further calculation on the band structures of LiSnBr₃, LiSnI₃, NaSnCl₃, NaSnBr₃, and NaSnI₃ (see the Electronic Supplementary Material, Figs. S1–S6) show that the highest peak for Li/NaSnX₃ (Cl, Br, I) that appears in the VB at both 0 and high pressure is largely attributed to the Cl atom, as seen in the figure.

In all circumstances, the X (X = Cl, Br, I) atoms contribute in an intermediate way to the development of the VB. The X anion in the Li/NaSnX₃ VB in TDOS displays prominent peaks at 0 to 5 GPa hydrostatic pressure, ranging from −2.5 to −7 eV. The largest contribution comes from X (X = Cl, Br, I) and Sn atoms in the CB, while the CB contribution rapidly rises with pressure, nearly reaching the Fermi energy level. This trend is consistently observed across all materials, as depicted in Fig.3.

Pressure fluctuations can lead to notable physical changes in materials. Fig.4 presents the variations in band gap values of the compounds studied under different pressure. The data reveal that the direct band gap nature of the compounds at the M symmetry point is maintained despite pressure changes. As pressure increases and the anion transitions from Cl to I, the energy band gap decreases monotonically. However, Fig.4 also shows a slight enhancement in the energy band gap when the cation changes from Li to Na.

When the pressure exceeds 5 GPa, the compounds Li/NaSnCl₃, Li/NaSnBr₃, and Li/NaSnI₃ are predicted to exhibit metallic behavior. These findings suggest that the perovskite crystal structures have significant potential to function as semiconducting materials, which is essential for their application in solar cell technologies.

The partial density of states (PDOSs) provide valuable insight into the specific atomic orbitals that contribute to the electronic states within a material. By analyzing the PDOS, it can be identified which atomic orbitals play a crucial role in influencing the band edges. Fig.5 illustrates the orbital contributions to the formation of valence and CBs over an energy range from − 8 to 14 eV, at ambient pressure.

Fig.5 shows the total and partial density of states at zero pressure for the compounds LiSnCl₃, LiSnBr₃ and LiSnI₃. In these materials, the VB, located below the Fermi level, is primarily composed of on Sn-5s, Sn-5p, and halide X-p states. The Sn-s orbitals and X-p states cause substantial p-d hybridization near the top of the VB, while the X-p state predominates in the lower portion of the VB. In contrast, the alkali cations A-s,p states contribute primarily to the top portion of the CB region, located above the Fermi level, with the Sn-p state playing a major role in the lower region of the CB.

Additional calculations on NaSnCl₃, NaSnBr₃, and NaSnI₃ under 0 and 5 GPa pressure are shown in the supplementary information (see Figs. S7 and S8). As pressure increases, these bands move closer together, leading to a reduction in the energy difference between the valence and CBs.

3.3 Optical properties

An examination of the frequency response of different optical constants to incident photon radiation is essential to investigate the potential of any material for solar cell applications [52]. It also reveals the interior structure of the substance. To fully comprehend if a material is suitable for higher-performance device applications, it is imperative to thoroughly investigate its optical functions. Therefore, a detailed study is conducted for the optical characteristics of the cubic perovskites LiSnCl₃, LiSnBr₃, LiSnI₃, NaSnCl₃, NaSnBr₃, and NaSnI₃ under a range of hydro-static strain from 0 to 5 GPa.

One crucial characteristic for understanding light-matter interaction is the dielectric function \epsilon (\omega ). As seen below, this function is frequency-dependent and consists of both real and imaginary components.

\epsilon (\omega )={\epsilon }_1(\omega )+\mathrm{i}{\epsilon }_2 (\omega ),

where the imaginary part is indicated by {\epsilon }_2(\omega ) while the real component is represented by {\epsilon }_1 (\omega ). The imaginary part of the dielectric is one significant characteristic that explains the optical shifts between energy levels, from conduction to VBs. The absorption of photons in crystalline compounds is described by the imaginary part of the dielectric function [53].

A useful metric for assessing the charge carrier recombination rate, and consequently, the overall efficiency of optoelectronic devices, is the static peak of the dielectric function [54]. Materials with a higher dielectric constant have lower rates of charge carrier recombination, suggesting they are more effective in optoelectronic devices. The real part and imaginary components of the dielectric factor for the pressure-induced LiSnCl₃, LiSnBr₃, LiSnI₃, NaSnCl₃, NaSnBr₃, and NaSnI₃ are shown in Fig.6 across electromagnetic energy levels of up to 40 eV.

As observed in Fig.6, the static peak of both the real and imaginary components of the materials MSnX₃ rises in the visible region with increased strain. It has been observed that compounds with larger band gaps tend to have low static dielectric constant [55]. Conversely, as the band gap narrows, the static value of the dielectric constant increases for all pressure-induced MSnX₃ halide materials, including LiSnCl₃, LiSnBr₃, LiSnI₃, NaSnCl₃, NaSnBr₃, and NaSnI₃ (see Section 3.2).

The absorption characteristics can be attributed to the close relationship between the imaginary component and the material band structure [56].

Tab.4 reveals that the static values of the real component of the dielectric constant increases when the anion is replaced from Cl to I at both 0 and high pressure. Similarly, substituting Li with Na as the cation raises these static values. However, in the high energy range (above 20 eV), the real part of all pressure-induced MSnX₃ (M = Li, Na; X = Cl, Br, I) samples approaches unity. The imaginary part of the dielectric constant for the Li\NaSnCl₃ and Li\NaSnBr₃ compounds approaches 0 at above 25 eV, while the Li\NaSnI₃ compounds approach 0 at above 20 eV in the high-energy region.

Fig.7 displays the optical conductivity spectra of MSnX₃ (X = Cl, Br, I; M = Li, Na) as a function of photon energy for induced pressures ranging from 0 to 5 GPa. As demonstrated in Fig.7, the conductivity spectrum resembles the absorption spectra, reflecting ability of the material to generate free carriers for conduction during energy absorption.

Due to the rising absorption coefficient, there is an increase in optical conductivity within the optical frequency spectrum with increasing pressure (see Fig.7). The massive interbond transitions from the VB to the CB are responsible for the noticeable peaks in the visible area. The graphic shows that threshold energies, which are finite energy values, are the source of the initial absence of a peak in the Ωσ(\omega) plots.

The absorption coefficient of MSnX₃ (M = Li, Na; X = Cl, Br, I) significantly influences solar cell efficiency, as it determines the ability of the material to capture light. As pressure increases, the threshold energy for absorption shifts, causing the absorption edge of the compound to redshift. In the visible spectrum, the absorption coefficient notably increases with substituting changes from Cl to I. Specifically, Li/NaSnCl₃ exhibits higher absorption in the high-energy UV region compared to the other compounds.

Previous studies by Ullah et al. [37] focused on K and Rb-based materials under varying pressures. However, our findings show that Li and Na-based materials, particularly Li/NaSnBr₃ and Li/NaSnI₃ under high pressure, exhibit superior absorption in the lower visible region, making them more suitable for solar cell applications. Additionally, strained compounds demonstrate enhanced absorption coefficients in the visible spectrum compared to their unstrained counterparts.

Fig.8 illustrates that the absorption capacity of these compounds improves with increased pressure, which potentially lead to higher solar cell efficiency. The results for LiSnBr₃, LiSnI₃, NaSnBr₃, and NaSnI₃ at 0 GPa align with previous predictions [40,42], emphasizing the importance of optimizing these materials for use in strained geometries to maximize their performance. Combined with the results from Fig.6, the absorption spectra shown in Fig.8 reveal that the absorption characteristics can be attributed to the close relationship between the imaginary component and the material band structure [56], where the gap moves to the low energy edge and the peaks of the imaginary part of the dielectric function notably widen with increasing pressure.

Fig.9 displays the reflectivity spectra of LiSnCl₃, LiSnBr₃, LiSnI₃, NaSnCl₃, NaSnBr₃, and NaSnI₃ at different pressures and photonic energies up to 40 eV, along with the refractive index beneath it. As the pressure rises, so does the amount of reflection, which could reduce the efficiency of the solar cell. As hydrostatic pressures increase, the reflectance of these materials increases as well, potentially weakening their performance in solar cell applications.

According to Khan et al. [57], KSnBr₃ and RbSnBr₃ have a 25% better optical efficiency than the Cl-based compounds at 0 GPa pressure, making them more suitable for future optoelectronic and photovoltaic applications. Ullah et al. [37] and Dash et al. [36] have also focused on K and Rb-based materials at both zero and high pressure. In contrast, our findings indicate that the high-pressure Li/NaSnBr₃ and Li/NaSnI₃ compounds based on Li and Na exhibit low reflectivity at lower energy levels, making them more suitable for use in optoelectronic devices.

To further reduce the reflectivity of pressure-induced MSnX₃ compounds and potentially improve absorptivity and solar cell proficiency, additional studies should be conducted in the visible energy region.

Fig.9 also shows the spectrum of refractive index as a function of the photon energy of the materials at pressures ranging from 0 and 5 GPa. The amount that light bends or refractively varies when it travels through a medium is measured by the refractive index (n) [58,59]. It is also crucial to determine the electromagnetic phase velocity of electromagnetic waves within that medium. As shown, the compounds demonstrate a higher static refractive index as pressure rises. This increase can be attributed to the reduction in volume at high pressure, which leads to an increase in the number of electronic oscillators per unit volume, thereby enhancing both the refractive index and static refractive index.

According to the photo-elasticity theory [60], variations in the refractive index under pressure are primarily caused by changes in the size of unit cell. Variations in the polarizability of ions or even individual atoms are primarily caused by changes in the number of oscillators in a unit volume or the density of the material. A substance that is under pressure immediately experiences an increase in density, which raises the refractive index of the material.

As illustrated in Fig.9, the compounds LiSnCl₃, LiSnBr₃, LiSnI₃, NaSnCl₃, NaSnBr₃, and NaSnI₃ have the highest refractive index values in the visible region at 0 pressure. The refractive index continues to decrease in the UV region until it reaches the values for Li\NaSnCl₃, Li\NaSnBr₃, and Li\NaSnI₃, respectively, at approximately 20, 17, and 15 eV. Notably, there are several erratic peaks at 30, 28, and 25 eV that persist beyond this point.

Tab.4 shows that the static values of the refractive index increase when the anion was replaced from Cl to I at both 0 and high pressure. Similarly, substituting Li with Na for the cation also raises the static values. The refractive index peaks under pressure show irregularities in the energy range of 5–30 eV. LiSnI₃ may be a superior option for optical devices such as photonic crystals and waveguides because of its relatively higher refractive index after 5 GPa [61].

The extinction coefficient and electron energy loss function L(\omega ) of the LiSnCl₃, LiSnBr₃, LiSnI₃, NaSnCl₃, NaSnBr₃, and NaSnI₃ under various applied pressures, up to 40 eV are displayed in Fig. S9. When assessing whether electrons are elastically scattering (zero energy loss) or not, the electron energy loss (EEL) is a crucial parameter. The greatest Plasmon peak is seen in all investigated substances at approximately 20 eV. While there are only minor variations in the peak height, the applied pressure causes the EEL structures to move slightly toward lower energy.

The extension coefficient of LiSnCl₃, LiSnBr₃, LiSnI₃, NaSnCl₃, NaSnBr₃, and NaSnI₃ is measured as light loss owing to scattering and absorption per unit volume. The peak values of the extension coefficient are 1.4, 1.41, 1.5, 1.43, 1.42, and 1.55 occurring at energies of 17.2, 14.6,12.5, 18.8, 13.9, and 12.6 eV under high pressure, respectively. The extinction coefficient measures the rate of decrease in transmitted and scattering photons for the material, and additional results are provided in Fig. S10.

A comparison of the extinction coefficient behavior across the compounds resembles the imaginary part, or {\epsilon }_2 (\omega ), of the dielectric function. When energy accumulates in the low-energy area, the peak altitude rises and gets redshifted.

4 Conclusions

This work investigates the structural, electronic, and optical properties of tin-based halide perovskites, specifically LiSnCl₃, LiSnBr₃, LiSnI₃, NaSnCl₃, NaSnBr₃, and NaSnI₃, under varying pressure conditions.

From the structural insights, this work shows that these perovskites, in their cubic Pm-3m phase, exhibit changes in lattice constants and bulk modulus with high pressure. The lattice constants decrease with increasing pressure, with more pronounced effects observed when changing the anion from Cl to I.

The electronic analysis shows that the perovskites maintain a direct band gap nature even under high pressure. However, the band gap decreases with increasing pressure and changes in anion size. Notably, Li/NaSnX₃ compounds (X = Cl, Br, I) may transition to metallic behavior at pressures exceeding 5 GPa, while still exhibit semiconductor characteristics suitable for optoelectronic applications.

The optical properties, including the dielectric function, optical conductivity, and absorption, reveal significant pressure-induced changes. Increased pressure enhances both the static dielectric constant and optical absorption, especially in the visible spectrum. The materials demonstrate improved optical performance with higher pressure, indicating their potential for solar cell applications. As the refractive index rises with pressure, the material density increases as well. The extinction coefficient displays significant peaks related to energy absorption and scattering, which could impact the efficiency of optoelectronic devices.

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