Studies on Optoelectronic and Transport Properties of XSnBr₃ (X = Rb/Cs): A DFT Insight

Abstract

Modern manufacturing is aiming for products that are readily available, environmentally sustainable, and energy efficient. This paper delves into the exploration of compounds meeting these criteria. Specifically, we investigate the structural, elastic, optoelectronic, and transport properties of XSnBr₃ (X = Rb/Cs) compounds utilizing the full-potential linearized augmented plane wave program (FP LAPW), a component of Wien2K software. Structural optimization is carried out through the generalized gradient approximation (GGA) approach, yielding lattice constants consistent with preceding numerical and experimental studies. The explored XSnBr₃ (X = Rb/Cs) materials exhibit ductility and mechanical stability. Notably, XSnBr₃ (X = Rb/Cs) displays a direct bandgap, signifying its semiconducting nature. The bandgap values, as determined by the modified Becke–Johnson (mBJ) approach, stand at 2.07 eV for X = Rb and 2.14 eV for XSnBr₃ (X = Rb/Cs). Furthermore, utilizing the BoltzTraP software’s transport feature, we investigate thermoelectric properties. Remarkably, XSnBr₃ (X = Rb/Cs) demonstrates impressive figures of merit (ZT) at room temperature, implying its potential to serve as a material for highly efficient thermoelectric devices. This research holds promise for contributing to the development of environmentally friendly and energy-efficient technologies.

1. Introduction

Globally, there is a rapid increase in the consumption of fossil fuels, leading to detrimental environmental impacts and the exacerbation of global warming. Due to the high cost and potential environmental hazards associated with petroleum usage, exploring alternative energy sources is crucial. To address the challenges posed by global warming, the excessive dependence on fossil fuels, and the utilization of waste heat from vehicles and industrial machinery, researchers in the field of material science are placing greater emphasis on investigating the thermoelectric properties of various alloys and compounds [1,2,3,4,5]. The conversion of waste heat into energy helps alleviate the demand for fossil fuels and mitigates its environmental impact. The dimensionless figure of merit, ZT = S²σT/κ, serves as a crucial indicator of the efficiency of thermoelectric materials. This value is determined by several key thermoelectric properties, including the Seebeck coefficient (S), which quantifies the voltage generated from a temperature gradient, the electrical conductivity (σ/τ) denoting the material’s ability to carry electrical current, and the thermal conductivity (κ/τ), which characterizes its capacity to conduct heat. In essence, ZT encapsulates the balance between the material’s ability to generate an electric potential difference from temperature variations and its capacity to maintain this difference against heat dissipation. Thus, higher ZT values correspond to superior thermoelectric materials that efficiently convert heat into electricity [6,7,8]. ZT optimization is challenging because the factors that affect ZT are inversely correlated. Discovering novel compounds with high ZT values is challenging because of the tight interdependence among all three factors: electrical structure, charge carrier concentration, and crystalline structure. Although there are several theoretical models for improving material efficiency, nanostructured engineering and the usage of superlattice or quantum well structures are the ones that have the most success [9].

Due to the adverse consequences of climate change on the environment, there has been a noticeable rise in research on materials and chemicals relevant to optoelectronic and energy conversion applications in recent decades. Numerous inorganic and organic halide perovskite materials have demonstrated excellent application potential as solar materials due to their exceptional productivity in power transformation, high carrier mobility, and other beneficial properties [10,11,12]. They have been found to have excellent applications in electrical, optoelectronic, and thermoelectric transmission. One of the most significant perovskites is the organic–inorganic hybrid CH₃NH₃PbI₃, which has wide absorption, high mobility, and other advantageous thermoelectric and optoelectronic properties [13,14,15]. There have been a few notable constraints, such as lead’s growing toxicity, which is unfavorable because of environmental considerations. Additionally, it has been shown that the organic component degrades and generates harmful compounds when used with inorganic and organic–inorganic hybrid compounds to replace the Pb atom, as well as perovskite compounds with equivalent oxidation states and lead-free replacement metal atoms [16,17]. These substitutions nonetheless demonstrate that lead-free compounds have a lower ZT, and they are only slightly more favorable for changing energy, necessitating more research in halide-based perovskite compounds.

Despite the fact that the organic component of hybrid perovskites degrades at high temperatures, inorganic halide perovskite compounds have been the subject of substantial research [18,19]. These studies are being carried out on compounds with different architectural arrangements, with the main focus being on the features of the compounds employing computer programs. They have the generic formula ABX₃, where X is a halide (Cl, Br, or I atoms), and A and B are elements from the main group [20,21]. The significance of halide perovskites with a chemical composition of ABX₃ has grown in a number of research domains because of their adaptive and highly beneficial physical characteristics in areas like photovoltaics, piezoelectricity, and optoelectronics. According to a thorough assessment of the literature, perovskites with good optoelectronic and transport capabilities include SrTiO₃, XFeO₃ (X = Ag, Zr), and LaAlO₃ [22,23,24]. Additionally, Bouadjemi investigated the magnetic and physical characteristics of NdMnO₃ using density functional theory (DFT) [25]. A new material for optical LEO operation is BaThO₃ [26]. Due to the characteristics of BiBO₃ and BiAlO₃, optoelectronic devices can gain from reduced UV area, visibility, and invisibility [27]. CsPbX₃ (X = Cl, Br, and I)’s electrical, optical, and physical properties have been discussed [28]. The Cs base material CsMO₃ (M = Ta, Nb)’s mechanical, optical, and thermodynamic properties have been identified [29]. The lattice alteration of Cs-based CsPbX₃ has allowed for computational analysis of the bandgap change. The physical properties of cubic perovskite oxides need to be confirmed, according to previous investigations [23].

As was already noted, Cs-based halide perovskites have been researched and are well known; however, as of now, not much is known about CsXO₃ (X = Ge, Sn, Pb) [30]. The chemical and physical characteristics of numerous appliances can be enhanced by switching the B site in transition metals. In order to replace lead, scientists have tried using a metal from group 14 of the periodic table, such as Sn or Ge. In this paper, first-principles computations are utilized to compare the electronic, optical, and thermoelectric attributes of perovskite Sn-halide materials XSnBr₃ (X = Rb/Cs). These perovskites may be employed in nano-optoelectronic devices, according to studies of their optical characteristics. The subsequent sections of this paper are organized as follows to provide a comprehensive exploration of the subject matter. Section 2 delves into the intricacies of the computational methodologies employed in this study, outlining the specific techniques and tools used to conduct our analyses. In Section 3 and Section 4, we extensively discuss and present the outcomes of our research. These sections offer a detailed breakdown of our findings, addressing each aspect of our investigation and drawing meaningful conclusions from our results.

2. Computational Method

The first-principles computations in the present investigation were performed using the full plane wave augmented plane wave technique [31] implementation of the WIEN2k package [32]. The generalized gradient approximation (GGA) [33], and the preferred modified Becke–Johnson (mBJ) approach [34] which is used to properly anticipate band structure computations, were utilized to explain the electronic exchange and correlation potentials. The bandgap underestimate that existed in earlier classical LDA and GGA techniques is addressed in this upgrade. The l_max value was set to 10. To calculate a converged scf, we utilized cut off energy = −6.0 Ry, R_MTK_Max = 7, and k-points = 10,000 [35]. A 21 × 21 × 21 k-mesh has been used to incorporate the Brillouin zone into the Monkhorst–Pack design. The thermoelectric properties were calculated using the BoltzTraP technique [36]. We sampled the Brillouin Zone of a 46 × 46 × 46 k-mesh, a denser mesh, to obtain more accurate findings.

3. Results and Discussion

3.1. Structural Properties

As previously noted, we improved the topologies of the under-researched compounds while taking into account their cubic structure. Figure 1 depicts their fully relaxed structure. In contrast to the ion Cs/Rb, which is placed at (0,0,0), the component atoms Ge and Br are situated at (1/2,1/2,1/2) and (1/2,1/2,0), respectively [37]. It is found that the studied compounds have a cubic Pm3m space group. To obtain the ideal lattice parameters, as illustrated in Figure 2, the Birch–Murnaghan equation of state against volume (a.u.) [38] and the PBE-GGA functional were utilized, demonstrating that when the atomic number increases, the lattice characteristics improve. From Rb to Cs, the atomic radius increases, changing the ionic bond strength, which mostly impacts the strength of the ionic bonds. The magnitudes of the lattice parameters (a₀), bulk modulus (B), and its pressure derivative (B_p) were determined and depicted in

Table 1. The evaluated lattice constant a (Å), bulk modulus B (GPa), derivative of the bulk modulus B_p, tolerance factor (τ) as well as formation energy (E_f) for XSnBr₃ (X = Rb/Cs).

HH	a (Å)	V (a.u.)3	B	Bp	Etot (Ry)	τ	Ef (eV/atom)
RbSnBr3	5.61	545.005	43.869	3.935	−7676.422	0.97	−1.662
CsSnBr3	5.82	651.515	35.041	4.014	−19,454.663	0.96	−1.690
Other Studies [42]	5.46

and found to be in good agreement with earlier reports. The equilibrium energies of the investigated compounds are found to be negative, which suggests their stability. The bulk modulus is found to decrease from RbSnBr₃ to CsSnBr₃, which arises because of the interaction of halide ions with Rb/Cs atoms. This again signifies that the compressibility of these compounds raises while their stiffness is reduced as we proceed from RbSnBr₃ to CsSnBr₃. Additionally, the tolerance factor (τ) was devised to account for the cubic structural features [39]. The examined compound is assumed to have a cubic structure if the indicator parameter’s value falls within the range of 0.95 and 1.04. Table 1 displays the predicted value of the τ, which represents the cubic structure. Additionally, the thermodynamic stability can be affected by taking the Formation energy (E_f) into account [40,41]. Table 1 displays the predicted E_f for XSnBr₃ (X = Rb/Cs). Thermodynamic stability is demonstrated by the negative formation energy.

3.2. Elastic Characteristics

Hardness, stress, and other structural deformations caused by pressure have all been studied using the elastic constant. The study of these constants is very helpful for understanding the Poisson ratio effect, Young’s modulus, Debye temperature, and melting temperature, among other topics. There are three diverse elastic components for cubic crystals: C₁₁, C₁₂, as well as C₄₄ [43]. The elastic constant tensors, or C_ij in Voigt notation, have emerged as a result of the shift in internal energy deformation in this instance. By expanding the elastic energy or stress relative to the applied strain, Taylor’s formula defines elastic tensors of any order. To define the dynamic and mechanical behavior of the alloys under study, the three second-order elastic coefficients (SOECs) C₁₁, C₁₂, and C₄₄ must be determined. The only three distinct elastic constants for cubic crystal formations, according to Hooke’s law, are C₁₁, C₁₂, and C₄₄. We may infer that C₁₁ = C₂₂ = C₃₃, C₁₂ = C₁₃ = C₂₃, and C₄₄ = C₅₅ = C₆₆ from the symmetry of the second-order elastic constant matrix. All of the eigenvalues of the elastic constant matrix are non-zero, supporting the stability of the compound. The Born-theory-based stability criteria are presented below in addition to this condition.

C₁₁ > |C₁₂|, C₁₁ > 0, and (C₁₁ + 2C₁₂) > 0 are all greater than zero [44]. Since it is expected that cubic crystals’ elastic constants are compatible with the aforementioned stability conditions, the studied XSnBr₃ (X = Rb/Cs) compounds are mechanically stable. The bulk modulus (B), a metric of compressibility resistance, specifies the solid’s resistance to volume change, whereas the shear modulus specifies the solid’s resistance to shear deformation while preserving volume [45]. Elastic structures play a significant role in the analysis and construction of materials. The computed outcomes are discovered to be consistent with past studies, as shown in

Table 2. Computed elastic properties of XSnBr₃ (X = Rb/Cs) using GGA-PBE exchange correlation functionals.

Material Property	RbSnBr3	CsSnBr3	Other Studies [42]
C11 (GPa)	61.93	63.88	58.18
C12 (GPa)	10.83	12.32	11.70
C44 (GPa)	7.62	7.14	9.27
S11 (GPa−1)	0.01710179	0.01669554
S12 (GPa−1)	−0.00246767	−0.00269933
S44 (GPa−1)	0.13123359	0.14005602
Bulk modulus, B (GPa)	27.87	29.51	27.00
Shear modulus, G (GPa)	14.79	14.59	13.53
Young modulus, E (GPa)	37.70	37.58	34.83
Poisson ratio, σ (GPa)	0.27	0.28
Pugh ratio, B/G (GPa)	1.88	2.02	2.01
Cauchy pressure CP (GPa)	3.21	5.18
Anisotropy factor (A)	0.29	0.27
Transverse sound velocity (m/s)	1706	16,585
Longitudinal sound velocity(m/s)	3204	3254
Average sound velocity (m/s)	1906	1886
Temperature ΘD (K)	199	196.6
Melting temperature $T_m$(K)	783.7	768

. The bulk modulus has been calculated using the formula B = C₁₁ + 2C₁₂/3. The good value of B is used to estimate the good crystal strength of the XSnBr₃ (X = Rb/Cs). The significant value of G, as shown in Table 2, supports their ability to subsequently flex transversely [46,47]. Young’s modulus (E) and Poisson’s ratio (σ) are calculated using the following formulas, σ = 3B 0–E/6B and E = 9BG/3B + G. Table 2 displays the expected values for E and σ. These cubic crystals’ anisotropy is measured by Zener’s anisotropy index (A) [48,49], which has the formula A = 2C₄₄/C₁₁–C₁₂. In some circumstances, the amount of elastic anisotropy (A) is helpful. If A is zero or one, the crystal represents elastic isotropy; otherwise, it represents the proportional degree of elastic anisotropy that the crystal truly contains. As a result, Table 2 interferes with the anisotropic nature of the XSnBr₃ (X = Rb/Cs). Additionally, the computed Pugh ratio (B/G) [50] and Poisson ratio interact with the examined XSnBr₃ (X = Rb/Cs) compounds’ ductility. We estimated the wave velocities V_S, V_P, and V_m from the data on the elastic characteristics of the materials and acquired them from the Navier equation shown below and summarized in Table 2.

$$V_s={\left[\frac{G_H}{\rho }\right]}^{1/2};V_s={\left[\frac{B_{H+}4/3G_H}{\rho }\right]}^{1/2}; V_m={\left[\frac{\frac{2}{V_S^3}+\frac{1}{V_P^3}}{3}\right]}^{-1/3}$$

(1)

Another method to calculate Debye temperature is to estimate it from average elastic wave velocity V_m, represented as

$${\theta }_D=\frac{h}{k}{\left[\frac{3n}{4\pi }\left(\frac{N_A\rho }{M}\right)\right]}^{1/3}{V}_m$$

(2)

Here, h, k, N_A, are Planck’s constant, Boltzmann’s constant, Avogadro’s number, respectively, while n and M are the number of atoms per formula unit and molecular mass per formula unit, respectively. The density of the compound is ρ = M/V. All computed values are represented in Table 2.

The analysis of the elastic properties of three-dimensional (3D) surfaces helps to visualize and completely explain the anisotropic behavior of the mechanical modulus as represented in Figure 3 and Figure 4 [51]. The Bulk modulus B, Young’s modulus E, and shear modulus G’s dependency on crystallographic direction can be calculated using the formulas below:

$$\begin{array}{cc}\hfill \frac{1}{B}=\left(S_{11}+2S_{12}\right)& \left(l_1^2+l_2^2+l_3^2\right) \frac{1}{E}\hfill \\ & =S_{11}-2\left(S_{11}-S_{12}-\frac{1}{2}{S}_{44}\right)\left(l_1^2{l}_2^2+l_2^2{l}_3^2+l_3^2{l}_1^2\right) \hfill \end{array}$$

(3)

$$\frac{1}{G}=S_{44}-4\left(S_{11}-S_{12}-\frac{1}{2}{S}_{44}\right)\left(si{n}^2\theta .co{s}^2\theta +0.125si{n}^4\right)\left(1-cos4\phi \right)$$

(4)

$S_{ij}$ are the contents of the elastic compliance constants’ matrix, which are acquired from the inverse of the elastic constant’s matrix $S_{ij}=C_{ij}^{-1}$ and their values are represented in matrix form below. l₁, l₂, and l₃ are the x, y and z-axis director cosines, respectively.

$$S_{ij}=\left(\begin{array}{cccccc}{S}_{11}& S_{12}& S_{12}& 0& 0& 0\\ S_{12}& S_{11}& S_{12}& 0& 0& 0\\ S_{12}& S_{12}& S_{11}& 0& 0& 0\\ 0& 0& 0& S_{44}& 0& 0\\ 0& 0& 0& 0& S_{44}& 0\\ 0& 0& 0& 0& 0& S_{44}\end{array}\right)$$

(5)

The degree of divergence from a spherical form often represents the degree of anisotropy. The linear compressibility obtained 3D directional dependency and cross-section in many reticular planes. The fact that Y and G greatly diverge from the sphere and confirm the large anisotropy of XSnBr₃ (X = Rb/Cs) supports the spherical shape of the linear compressibility. Furthermore, it is clear from Figure 3 that for both compounds under investigation, the stress along the [100], [010], and [001] axes results in the highest Young modulus value. Conversely, the maximum shear modulus value is obtained when external force is applied along the [111] direction, demonstrating both strong stiffness and weak shear deformation resistance along the [100], [010], and [001] directions.

3.3. Electronic Properties

The predicted results for the band structure are displayed in Figure 5, which demonstrate the presence of the E_F valence band VB below the Fermi energy. The bandgap is calculated taking into account a number of approximations, including GGA-PBE and mBJ. In comparison to alternative approximations, the computed bandgap taking into account mBJ is found to be 2.07 eV and 2.14 eV higher and can therefore be taken as being equivalent to the experimental value.

The elemental contribution for the studied XSnBr₃ (X = Rb/Cs) is advocated from the density of states plot (DOS) as represented in Figure 6a,b. The Fermi level, which is calibrated to be at 0 eV and can be shown to be near the valence band in both compounds on the band plots, suggests that the material is a p-type semiconductor. The valence band at the Fermi level is produced by the combination of the Rb/Cs and Sn states [52]. As shown in Figure 6a,b, the conduction band formed through the hybridization of Rb/Cs and Br with an Sn atom contribution.

Table 3. Calculated bandgap utilizing various exchange correlation functional, effective mass of electrons (m_e*) and holes (m_h*), Bader charges (employing PBE-GGA methodology) XSnBr3 (X = Rb/Cs).

HHs	GGA	mBJ	Effective Mass	Bader Charge
RbSnBr3	2.02	2.15	me* = 0.27 mh* = 0.29	Rb = 0.85 Sn = 1.06 Br = −1.52
CsSnBr3	2.07	2.14	me* = 0.26 mh* = 0.28	Cs = 0.87 Sn = 1.12 Br = −1.62
Other Studies [42]		2.20

lists the evaluated effective masses for XSnBr₃ (X = Rb/Cs) in the high symmetry primary directions of the Brillouin zone. Understanding the effective masses (m*) of carriers (holes and electrons), which are greatly impacted by resistivity, carrier mobility, and optical response of free carriers, is essential for increasing photovoltaic characteristics [53]. It can be computed from band structure E_n(k) as

$$\frac{1}{m^{\ast }}=\frac{1}{{ћ}^2}\frac{d^{2 }{E}_n \left(k\right)}{d{k}^2}$$

(6)

Table 3 records the values of the projected effective mass for the XSnBr₃ (X = Rb/Cs) compounds under investigation. The results reveal that the compounds under research have incredibly small effective masses. A lower effective mass is highly advantageous for solar materials because it facilitates the easier transmission of carriers. This could demonstrate the effectiveness of XSnBr₃ (X = Rb/Cs) in photovoltaic applications.

The electron localization function (ELF) [54] for XSnBr₃ (X = Rb/Cs) is projected on the (110) plane, as seen in Figure 7a,b. We used the ELF to look for atom-to-atom bonds in XSnBr₃ (X = Rb/Cs) compounds. Figure 7a,b imply that the Rb/Cs-Sn, Sn-Br bonding are covalent. As seen in Figure 7, the electron cloud of Br is red, suggesting accepting the electrons from the other network. The Bader charge analysis depicted in Table 3 leads to additional support for this. The fact that Br can accept electrons from Rb/Cs and Sn supports the idea that it is an ion. Switching Rb to Cs has a significant effect on Bader charges, as represented in Table 3. The Bader charge increases with the increase in atomic number and probably due to the increase in states [55].

3.4. Optical Properties

In this subsection, we highlight more details about the optical properties of the examined XSnBr₃ (X = Rb/Cs) compounds, inspired by their direct bandgaps and wide bandgaps. To obtain the precise knowledge needed for use in optoelectronic and photovoltaic applications, it is important to analyze the optical properties of the material [56]. The real ε₁(ω) and imaginary ε₂(ω) components of the complex dielectric function ε(ω) are considered for the computation of optical properties which are written as,

ε(ω) = ε₁(ω) + ε₂(ω)

Figure 8a,b represent the variation of ε₁(ω) and ε₂(ω) with photon energy. Interaction of the light with the material results in polarization, quantified by ε₁(ω), as well as the loss of energy because of light dispersion, given by ε₂(ω). At zero energy, ε₁(ω) is quantified by ε₁(0). It is noticed that with the variation of the atom Rb to Cs, ε₁(0) increases with the more polarizing nature of the larger atoms, in accordance with Penn’s model (i.e., ε₁(0) = 1 + (hω_p/E_g)) that is inversely linked to the bandgap [57]. After ε₁(0), the graph shows the variation with the number of peaks that are commonly known as relaxation peaks. These peaks are useful in the determination of the relaxation frequency. However, due to the inverse relation between the relaxation frequency and total mass of the oscillating atoms, these peaks are observed to move towards lower energy [41]. The primary peaks in the ε₁(ω) plot are observed in the visible region. By employing the relationship n²(ω) = ε₁(ω), the refractive index can be computed. As observed in Figure 8c, the n (ω) plot is similar to ε₁(ω). The calculated values of n(ω) are illustrated in

Table 4. Calculated optical properties (at zero energy) and transport properties (at 300 K) for XSnBr3 (X = Rb/Cs).

	Material Property	RbSnBr3	CsSnBr3	Other Study [42]
Optical properties	ε1(0)	5.03	4.88	5.92
	n(0)	2.24	3.08	2.43
Transport properties (300 K)	S(µVK)	249	298
	σ/τ(Ωms)−1(1017)	0.61	1.1
	k/τ (W/mKs)(1013)	0.21	0.20
	ZT	0.79	0.83

. Figure 8b represents the variation of ε₂(ω) with incoming radiation. The optical bandgap, as well as the absorption characteristics, are represented by ε₂(ω). It is noticed that no absorption is achieved up to 2.06 eV and 2.11 eV for XSnBr₃ (X = Rb/Cs) with validating the optical bandgap, which is approximately equal to the electronic bandgap. The reflectance R(ω) of the XSnBr₃ (X = Rb/Cs) over the energy range of 0 eV to 10 eV is exhibited in Figure 8d; XSnBr₃ (X = Rb/Cs) exhibits normal semiconducting properties with reflectivity less than 0.6. The measurement of reflectance at zero energy is known as absolute reflectivity, or R(0). Table 4 displays R(0)’s magnitude. After R(0), the reflectivity increases and decreases when it reaches its maximum value. The detailed investigation of optical properties reveals exceptional photoelectric capabilities, indicating enormous potential for utilization in the absorber layer of a solar cell.

3.5. Thermoelectricity

Semiclassical Boltzmann theory is used to examine the thermoelectric properties of the tested XSnBr3 (X = Rb/Cs) HHs while taking constant time relaxation time (τ) into consideration. The Seebeck coefficient (S), thermal conductivity (κ/τ), and electrical conductivity (σ/τ) are taken into account. The Seebeck coefficient (S) is regarded as a crucial consideration when examining thermoelectric (TE) qualities. Higher Figure of Merit (ZT) values, which indicate a material’s suitability for thermoelectric applications, are preferable to lower Seebeck values. The Seebeck coefficient (charge and heat) is related to the electron carriers. The Seebeck coefficient must be high for the thermoelectric performance to be optimum. It is positive for p-type materials but negative for n-type materials [58,59]. The investigated compound is p-type as evidenced from Figure 9a. S values for the investigated XSnBr₃ (X = Rb/Cs) compounds at room temperature were 249 μV/K and 298 μV/K, respectively, as indicated in Table 4. The valence electrons become less tightly bound and need less energy as the ionic scale rises from Rb to Cs. The quantity of free charge carriers increases along with electrical conductivity as well. This is due to the possibility that the potentials preserved across the sample edges may drop as the bandgap closes, and the number of free charge carriers rises at lesser exciting energies, much to how S declines as an atom moves from Rb to Cs.

Furthermore, it appears that the compounds under investigation have an outstanding thermoelectric response, which is essential considering that the ideal TE material has a Seebeck value higher than 200 μV/K [45]. The computed S is bigger than earlier reporting, as seen in Table 4. Figure 9b represents the variation of electrical conductivity with temperature change. At 300 K, they are determined to be 1.1 × 10¹⁸ Ωm⁻¹S⁻¹ and 0.61 × 10¹⁷ Ωm⁻¹S⁻¹ for RbSnBr₃ and CsSnBr₃, respectively. An increase in σ/τ as the temperature rises is a typical pattern for semiconductor materials. The high density of charge carriers in the cubic perovskite under investigation contributes to its excellent electrical conductivity. Both electronic and lattice thermal conductivities collectively constitute the thermal lattice conductivity [60]. Lattice thermal conductivity arises from phonons, whereas electronic thermal conductivity is produced by the movements of electrons and holes. Electrical and thermal conductivity are connected according to the Wiedemann–Franz law. It was discovered to be on the order of 10⁻⁵, which indicates both poor heat conductivity and strong electrical conductivity. A thermoelectric compound’s efficiency can be calculated using the ZT figure of merit [8]. Figure 9d displays the computed ZT for the investigated XSnBr₃ (X = Rb/Cs) compounds. The estimated ZT at room temperature for RbSnBr₃ and CsSnBr₃ compounds is found to be 0.79 and 0.83, respectively. Because the compounds have a high ZT, they can be employed in thermoelectric devices. According to Table 4, the computed PF is seen to be greater than in earlier reports. The XSnBr₃ (X = Rb/Cs) discovered should be further investigated for its applicability in thermoelectric devices. Finally, this study sheds light on using the proposed compound in solar cells, one of the most significant renewable energy sources [61].

4. Conclusions

The structural, magnetic, electrical, elastic, vibrational, optical, thermodynamic, and thermoelectric properties of quaternary XSnBr₃ (X = Rb/Cs) compounds are fully investigated with the use of DFT as implemented in the Wien2k code. The calculated equilibrium structure data accord well with the majority of the related theoretical and experimental literature. The volume optimization curves show that the examined compounds are stable crystal structures. These compounds’ calculated formation energy demonstrates their thermodynamic stability. The mechanical stability of XSnBr₃ (X = Rb/Cs) compounds is satisfied by the computed second-order elastic constants for these compounds. Additionally, the effects of incident electromagnetic radiations up to 10 eV on the fluctuation of optical characteristics including dielectric function, refractive index, reflectivity are investigated. The figure of merit (ZT) at room temperature is computed to be 0.79 and 0.83 for XSnBr₃ (X = Rb/Cs). As a result, XSnBr₃ (X = Rb/Cs) compounds have the potential to be cutting-edge and fascinating thermoelectric materials that can also be applied to optoelectronic and energy-harvesting systems.