Dataset and article "Exploring optoelectronic, optical thin films, mechanical and thermal transport properties of bromide double perovskites Rb2Ag(Ga/In)Br6 for photovoltaic and thermoelectric applications"

Exploring optoelectronic, optical thin films, mechanical and thermal transport properties of bromide double perovskites Rb 2 Ag(Ga/In)Br 6 for photovoltaic and thermoelectric applications I. Benkaddour a , A. Haddou b , Y.A. Khachai b , N. Baki b , F. Chiker b , H. Khachai b,* , R. Khenata c,** , N. Metadjer b , S. Bin-Omran d , A. Shankar e , Saleem A. Khan f a Ecole Sup´ erieure des Sciences de l’Aliment & des Industries Agroalimentaires-(ESSAIA), Algeria b Laboratory for the Study of Materials and Optical Instrumentations-Faculty of Exact Sciences, Djillali Liab` es University, 22000, Sidi Bel Abb` es, Algeria c Laboratoire de Physique Quantique de la Mati` ere et de Mod´ elisation Math´ ematique, Universit´ e de Mascara, 29000, Mascara, Algeria d Department of Physics and Astronomy, College of Science, King Saud University, P.O. Box 2455, Riyadh, 11451, Saudi Arabia e Condensed Matter Theory Research Lab, Department of Physics, Kurseong College, Darjeeling, 734203, India f New Technologies Research Centre, University of West Bohemia, CZ-301 00, Pilsen, Czech Republic ARTICLE INFO Keywords: FP-LAPW Double perovskites Optoelectronics Thermoelectric properties Figure of merit Renewable energy ABSTRACT Lead-free double halide perovskites like Rb 2 Ag(Ga/In)Br 6 have demonstrated themselves potential candidates in solar cell research owing to their environmental friendliness, stability, and exceptional performance. This study comprehensively analyzes the structural, mechanical, optoelectronic and optical coating features, as well as thermodynamic and thermoelectric properties of two Rb 2 AgGaBr 6 and Rb 2 AgInBr 6 compounds. Using the Wien2k code with GGA +mBJ exchange-correlation potentials, we confirm their structural stability in cubic phase Fm-3m and identifying them as direct band gap semiconductors (Γ → Γ) of 0.38 eV and 1.0644 eV, respectively. Then, optical analysis reveals broad absorption bands across visible and ultraviolet wavelengths, making them suitable for photovoltaic absorbers. Finally, the thermoelectric investigations under varying temperatures show favourable properties, such as a high Seebeck coefficient with poor electronic thermal conductivity. This also yields exceptional value (0.96 and 0.994 for Rb 2 AgGaBr 6 , Rb 2 AgInBr 6 , respectively) of figure of merit (ZT) at room temperature and chemical potential μ - μ 0 =- 0.09eV near the Fermi energy level, enhancing their potential for thermoelectric applications. These findings underscore the versatility and promising future of Rb 2 Ag(Ga/In)Br 6 as important semiconductors processing for optoelectronic, thermoelectric, and mechanical devices. 1. Introduction To address the growing demand for clean and renewable energy, it is essential to investigate various classes of the novel materials with enhanced efficiencies, stabilities and environmental friendliness. Among them the lead based perovskites have attracted significant interest due to their diverse characteristics, including optical properties [1], photoluminescence [2,3], applications in photovoltaic technology and solar cells [4,5], high energy conversion efficiency [6,7], and thermoelectric power energy [8]. The stability and toxicity issues associated with lead have hindered the commercialization of lead-based perovskite photovoltaic devices. Therefore, in recent years, experts in this field share a crucial goal: to elucidate the growing interest in lead-free perovskites materials known for their structural flexibility and substitutability, offering the potential to improve performance while resolving lead-related issues for useful in solar cells applications [9–11] and optoelectronic devises [12]. Since, thanks to the efforts of researchers, lead-free perovskites are now considered promising candidates among solar cell materials because of their ability to overcome problems associated with lead-based hybrid perovskites. Double halide perovskites were introduced in 1975 by R. Haegele and colleagues when they synthesized perovskite fluorides Rb 2 KFeF 6 and Rb 2 NaFeF 6 [13]. The Halogened double perovskites, denoted by the * Corresponding author. ** Corresponding author. E-mail addresses: [email protected] (H. Khachai), [email protected], [email protected] (R. Khenata). Contents lists available at ScienceDirect Materials Science in Semiconductor Processing journal homepage: www.elsevier.com/locate/mssp https://doi.org/10.1016/j.mssp.2024.108974 Received 11 April 2024; Received in revised form 13 August 2024; Accepted 30 September 2024 Materials Science in Semiconductor Processing 185 (2025) 108974 Available online 3 October 2024 1369-8001/© 2024 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY license ( http://creativecommons.org/licenses/by/4.0/ ). chemical formula A 2 B ´ B X 6 , represent an innovation within the perovskite family, where, A, B, and ´ B correspond to different cations and X is an anion. The double perovskites have great potential for the technological applications owing to their excellent optoelectronic properties, which includes high optical absorption and optical conductivity. Particularly, most of these perovskites suffer from stability issues or lack in the required electronic and optical properties. Therefore, it is necessary to explore suitable combination of B and ´ B cations to achieve a stable material with desired electronic and optical properties. There is substantial evidence supporting the substitution of the Pb 2+ ion of the perovskites with a monovalent B + and trivalent ´ B 3+ cations to achieve a halide based double perovskite (A 2 B ´ B X 6 ; A + =Cs, Rb, K, Na; B + =Cu, Ag, Au, In; ´ B 3+ =Bi, Sb, In, Ga; X:Cl, Br, I) [14]. Furthermore, halide perovskites exhibit exceptional stability and offer a wider range of active light absorbers. The in-depth exploration of double perovskites, especially Cs 2 AgBiCl 6 and Cs 2 AgBiBr 6 , contained both synthesis and comprehensive studies. The findings indicate that these compounds exhibit notable chemical stability [15]. However, both double perovskites display an extended indirect bandgap which a drawback for photovoltaic applications [16]. The available experimental and theoretical results suggest Cs 2 AgSbCl 6 is promising candidate for the light absorbing, particularly when conjugated with TiO 2 , giving an alternative for the development of the solar cell devices out of perovskite free from lead [17]. Conversely, theoretical studies on K 2 AgBiCl 6 and K 2 AgBiBr 6 revealed their band gap of 2.3 eV and 1.5 eV, respectively with robust absorption in the visible range. Despite these favourable characteristics, their indirect band gap limits their use in solar cell devices [18]. Inspired by these studies, we have undertaken a theoretical investigation of the structural and mechanical stability along with elastic constants and also the optical response of the material including thinfilm coating of newly developed double perovskites Rb 2 Ag(Ga/In)Br 6 . The themodynamic and thermoelectric behaviours are also studied for these lead-free halide alloys. The full-potential linearized augmented wave [19,20] method based computational tool known as wien2k [21] within the framework of density functional theory [22,23] is used to perform the calculation here. The generalized gradient potential approximated by Perdew–Burke and Ernzerhof (GGA-PBE) [24] combined with the modified Becke–Johnson formalism (mBJ) [25] is used to correct effect of electron exchange correlation functional. The mBJ enables to describe the electronic properties of the semiconducting materials with precise energy band gap [26–28]. The advantages and the novelty in studying the optoelectronic, optical thin films and thermoelectric properties of lead free Rb 2 Ag(Ga/In) Br 6 double perovskites, are as follows: firstly, we have extended our attention to the study of the optical characteristics of these compounds and also their thin film structures. The theoretical simulation is used to analyze the film deposition technique and their synthetic modification to vary the properties of thin films structures. We have also treated the effect of the thickness of each layer by analyzing their optical thin films spectra like Transmittance, Reflectance and Absorbance. Further we performed the influence of the substrate by using a layer on glasses substrate or freely suspended layer, the obtained results may make them as potential candidates in new thin films photovoltaic (PV) technology for single-junction and tandem PV applications. Secondly, we further present a first-principles study of thermoelectric parameters for use in thermo power energy devices. 2. Computational frameworks We have utilized the density functional theory (DFT) [22,23] based the full-potential linearized augmented wave method [19,20] as integrated in the Wien2k code [21] to perform the computations of Rb 2 Ag (Ga/In)Br 6 . In the FP-LAPW method [19,20], the space is partitioned into the non-overlapping spheres with maximum possible size so-called muffin-tins (MTs) centered at atomic sites and the interstitial region outside the MT spheres. The potentials inside the MT spheres and interstitial regions are approximated as follows V(r)=⎧ ⎪ ⎨ ⎪ ⎩ ∑ lm Vlm(r)Ylm(r)Inside Muffin −Tins ∑ k VkeiKr Interstitial region (1) And the basis functions are given by the following expression ϕ(r)=⎧ ⎪ ⎪ ⎨ ⎪ ⎪ ⎩ ∑ lm [Alm Ul(r)+Blm ˙ Ul(r)] Ylm(r)r<R α 1  Ω √∑ G CGExp [i(G+K)r]r>R α (2) The coefficients Blm and Alm are determined to ensure the continuity in value and derivative of the basis functions across the muffin-tin boundary. The problem of energy dependence of the basis set that arises in linearized APW approach is corrected by including a fixed set of suitable MT radial functions Ul and their energy derivatives ˙ Ul in FPLAPW method which are the solutions of the Schr¨ odinger equation: {−d2 dr2+l(l+1) r2+V(r)− El}r˙ Ul(r)=r Ul(r)(3) Similarly, the modified Becke–Johnson potential (mBJ) [25] approach consists of a Becke-Roussel potential combined to a modified version of the BJ exchange potential that can be read as: υ TB−mBJ x, σ (r)=c υ BR x, σ (r)+(3c−2)1 π  5 6 √ t σ (r) ρ σ (r) √(4) Where, vBR xc is the Becke-Roussel (BR) potential [29], designed to model the Coulomb potential created by the exchange hole, ρσ =∑N σ i=1Ψi, σ  2 is the spinσ electron density, and t σ is the kinetic-energy density. The parameter c in Eq. (4) is given by: c= α +β(1 Vcell) 1 / 2 (5) Here, V cell is the volume of the unit cell. The experimental band gaps available for a set of materials are used to determine the parameters α = −0.012 and β =1.023 Bohr ½ using the least-squares fitting method. Since, to proceed the present simulations, the wave functions inside the atomic sphere were expanded with angular momentum l max =10. The expansion of the wave functions into plane waves is controlled by the plane wave cutoff in the interstitial region. This cutoff is identified through the product R MT K max , where R MT is the smallest muffin-tin sphere radius and K max is the magnitude of the largest wave vector. In this work R MT K max =7.5 was used. The modified tetrahedron integration scheme was used for k-space integration. The external and internal geometries of Rb 2 Ag(Ga/In)Br 6 were optimized using 1000 k-points in the irreducible Brillouin zone (IBZ) distributed according to a (10 ×10 ×10) Monkhorst-Pack scheme [30] while the self-consistencies of the ground state energies were obtained by setting the energy convergence criteria to 10 −4 Ry. When examining optical and thermoelectric properties, a set of 2000 k-points were used. The thin film structures are designed using the optical matrix approach as incorporated in optical thin-film design program [31,32], where a 2 ×2 matrix containing the layer thickness and refractive index is used to represent each layer. The transport phenomena were analysed using the semi-classical Boltzmann transport equation [33–35], implemented in the BoltzTrap code [36,37]. The elastic character of the cubic sample are estimated by using the elast code as designed by Morteza Jamal and interfaced in wien2k package [38]. Additionally, we have evaluated the temperature and pressure dependence of thermodynamic parameters for halide perovskites using the Quasi-harmonic model integrated in the Gibbs2 software program I. Benkaddour et al. Materials Science in Semiconductor Processing 185 (2025) 108974 2 [39–41]. The projector-augmented wave method [42] as incorporated in Vienna Ab initio simulation package (VASP) [43,44] is employed for the calculation of the energy of formation. To be consistent with Wien2K code, the PBE-GGA is used for exchange-correlation functional [24]. The energy cut-off is adopted as 400 eV. 3. Results and discussion 3.1. Structural property and stability A self-consistent total energy calculation was carried out for various lattice parameters of each Rb 2 Ag(Ga/In)Br 6 compound and the resulting energy values were subsequently subjected to interpolation through the Birch-Murnaghan equation of state [45,46], as displayed in Figs. 1 and 2, to optimize the crystal structure and derive the optimized lattice constants (a 0 ). Some of the double perovskites are also stable in Fm3m space group of cubic structure [47]. It’s important to highlight that not all halogenated double perovskites are inherently stable compounds and hence, in the present study, the stability of the samples are verified from the octahedral factor ( μ ) and Goldsmith tolerance factor (t) by using Eqs. (6) and (7) [48,49]. Here, r Rb , r B =(r Ag +r (In/Ga) )/2, and r Br represents the ionic radii of Rb, Ag, (Ga/In) and Br, respectively. The computed values of μ and t, fall within the range of 0.81 <t <1.11 [50], 0.825 <t <1.059 [51], and 0.41 < μ <0.90 [48], which establishes the stable nature of the sample crystal in the cubic structure, ideal configuration for the double perovskites. t=(rRb +rBr)  2 √*(rB+rBr)(6) μ =rB rBr (7) The unit cell structure of Rb 2 Ag(Ga/In)Br 6 containing a total of 10 atoms as illustrated in Fig. 3, exhibits a distinctive feature of identical Wyckoff positions. Gourav et al. [52] recently discussed the stability of Rb 2 Ag(Ga/In)Br 6 in detail with respect to the tolerance factor, formation energy and phonon band structure of Rb 2 Ag(Ga/In)Br 6 where no imaginary frequencies were found throughout the entire BZ thus provide a strong base to further investigate the uncovered properties. In DFT the formation energy plays the key role for understanding the relative stability of different atomic substitution in crystal structures. The formation energy of Rb 2 Ag(Ga/In)Br 6 is calculated according to Equation (8): HRb2Ga/InBr6 f=E(Rb2(Ga/In)Br6)− 2E(Rb)− E(Ag)− E(Ga /In)− 6E(Br) (8) where E(Rb 2 Ag(Ga/In)Br 6 ) is the total ground state energy of Rb 2 Ag (Ga/In)Br 6 and E(Rb), E(Ag), E(Ga/In) and E(Br) are the total ground state energies of individual Rb, Ag, Ga/In and Br atoms in their stable configuration. The calculated negative formation energies of (−2.765 eV and −2.795 eV) of Rb 2 Ag(Ga/In)Br 6 are in agreement with Ref. [52]. In the present samples in the A 2 BB’X 6 model, the constituent atoms are located at the Wyckoff positions of A =Rb at 8c(0.25, 0.25, 0.25), B =Ag at 4a(0, 0, 0) and B’=(Ga/In) at 4b(0.5, 0.5, 0.5), whereas the position of X =Br is at 24e (x, 0, 0). Here, the position of Br in x as determined from the internal relaxation is in agreement with the experimental report of 0.25 [53]. The final output of the structural optimization yields the cubic phase of the samples with optimized lattice constants (as presented in Table 1), in close agreement with the previous Fig. 1. Unit cell crystal structure of the perovskite structure for the two studied compounds Rb 2 Ag(B’ =Ga/In)Br 6 . Fig. 2. Total energy as a function of volume fitting curve regarding Rb 2 AgGaBr 6 crystal structure. Fig. 3. Total energy as a function of volume fitting curve regarding Rb 2 AgInBr 6 crystal structure. I. Benkaddour et al. Materials Science in Semiconductor Processing 185 (2025) 108974 3 theoretical values from various research studies [52,54,55]. 3.2. Mechanical properties In a cubic lattice, the elastic tensor C ij is defined by the three independent elastic constants, namely C 11 which defines the material’s resistance to shear deformation, C 12 associated with shear stress and C 44 pertains to its resistance against shear stress. The evaluated elastic moduli C ij of Rb 2 Ag(Ga/In)Br 6 compounds are plotted in Fig. 4. The stability criteria (C 11 +2C 12 >0, C 11 >0, C 44 >0, and C 11 -C 12 >0) established by Born-Huang’s theory [56,57] is followed by the studied samples as summarized in Table 2, predicting the mechanically stable nature of Rb 2 Ag(Ga/In)Br 6 . Furthermore, certain elastic parameters such as bulk modulus (B), shear modulus (G), and Young’s modulus (Y) also can be derived from these independent elastic tensors to understand the mechanical behaviour of the samples as given by Eqs. (8)–(20) [58–60]. The calculated high bulk modulus of Rb 2 Ag(Ga/In)Br 6 suggests that these crystals possess robust structural strength. Shear modulus, which measures the stiffness of material as given by Eqs. 9–11, where, in accordance with Hills [61], G V , G R , and G stand for the Voigt [62], Reuss [63] and the average shear moduli, respectively. The computed values of shear modulus indicate that Rb 2 AgInBr 6 possesses the higher shear modulus value of 10.47 GPa, signifying its greater stiffness compared to Rb 2 AgGaBr 6 , which has a shear modulus of 8.05 GPa. According to Pugh’s criterion, for a ductile material B/G >1.75 and defines its ability to deform readily whereas below this threshold indicates its brittle nature [64]. A higher Young’s modulus value corresponds to increased material strength, as determined by Eq. (13). The elevated Young’s modulus value of 27.35 GPa for Rb 2 AgInBr 6 underscores its superior strength when compared to the compound Rb 2 AgGaBr 6 , which has a Young’s modulus of 21.85 GPa. The Poisson ratio calculated by Eq. (14) is anticipated to fall within the range of 0.25–0.50, with values of 0.1, 0.25, and 0.33 indicating covalent, metallic, and ionic bonding, respectively. The estimated values for sample under consideration fall within the range of 0.31–0.36 indicating their inherent nature of ionic bonding [65–67]. Cauchy pressure Cp =C 12 – C 44 also confirm the ductile behaviour of the samples as supported by Pugh’s criterion. The Zener anisotropy factor [68], which measures the dimensional stability, is defined as Eq. (15). The calculated values for Rb 2 AgGaBr 6 and Rb 2 AgInBr 6 are 1.93 and 0.56, respectively, which clearly demonstrate the anisotropic nature of these materials. The shear modulus C ′ as expressed by Eq. (16) is another essential parameter that contributes to understanding the stability of a structure. Material stability necessitates condition C’ >0, hence the positive values obtained for C ′ affirm the elastic stability of these compounds. Internal deformations within a compound can be explored through a parameter known as the Kleinman parameter (ζ) [69], which elucidates the stretching of bonds in relation to their bending, as defined by Eq. (17). A ζ value of zero signifies a reduction in bond bending, whereas a ζ value of one signifies a reduction in bond stretching. The tabulated values validate the presence of bond Table 1 Equilibrium structural parameters a, bulk modulus B, and its derivative B’ (GPa) calculated by GGA, tolerance factor t f , octahedral factor μ for the compounds Rb 2 Ag (Ga/In)Br 6 and compared to other theoretical work values Ref (a¼[52],b¼[54],c¼[55]). Compound a(Å) V 0 (Ǻ 3 ) B(GPa) B’t f μ Rb 2 AgInBr 6 Present work 11.0741 2291.1931 25.1464 5.1469 0.92 0.50 Other work (a) 10.79 –20.16 –0.98 0.45 Other work (c) 10.90 –29.20 –0.91 – Rb 2 AgGaBr 6 Present work 10.8214 2137.8946 27.3047 5.5122 0.94 0.45 Other work (a) 10.76 –22.16 –0.98 0.44 Other work (b) 11.77 –29.352 –0.91 – Fig. 4. Elastic constants C 11 , C 12 , and C 44 for Rb 2 Ag(Ga/In)Br 6 . Table 2 Elastic constants C11, C12, and C44 (in GPa), bulk modulus B (in GPa), shear modulus G (in GPa), and Young’s modulus Y (in GPa), Poisson’s ratio ν , Cauchy’s pressure CP (in GPa), Pugh ratio B/G, anisotropy A, Kleinman parameter (ζ), Lam´ e constants (λ, μ ), stiffness modulus M and melting temperature Tm (in K) for Rb 2 Ag(Ga/In)Br 6 .Others Works Ref (a¼[52], b¼[54], c¼[55]). Elastic Parameters Rb 2 AgGaBr 6 Rb 2 AgInBr 6 C 11 32.68 (44.12) a , (31.607) b 43.2, (37.68) c C 12 21.83(13.81) a , (28.225) b 13.7, (11.18) c C 44 10.49(11.17) a , (10.109) b 8.28, (9.89) c Cp =C 12 -C 44 11.4, (2.64) a 5.29,(1.29) c B 25.45(22.16) a ,(29.352) b 23.45,(20.16) c Y 21.85,(18.787) b 27.35 G 8.05 10.47 G V 8.46 10.89 G R 7.64 10.05 ν 0.36(0.393) b 0.31 A 1.93 0.56 B/G 3.16 2.24 Tm 746.17 ±300 808.36 ±300 μ 8.05 10.47 λ20.08 16.46 C’5.43 14.82 C 11 -C 12 10.85 29.63 C 11 +2C 12 76.34 7034 M 36.18 37.41 ξ1.1 0.6 I. Benkaddour et al. Materials Science in Semiconductor Processing 185 (2025) 108974 4 stretching in these compounds. Another noteworthy mechanical parameter is the Lam´ e constants (λ, μ ), which serve to characterize the anisotropy of a material predicated by Eqs. (17) and (18). In the case of isotropic materials, λ =C 12 and μ =C’. The Lam´ e coefficients determined for Rb 2 Ag(Ga/In)Br 6 are provided in Table 2, corroborating the findings from the anisotropic parameter A and indicating that these materials exhibit anisotropic characteristics. In Table 2, the melting temperature for the herein studied cubic sample crystals using the C 11 dependent Eq. (20) as proposed by Fine et al. [70] with 87 % coefficient of determination as presented. The ability of a material to withstand the deformation against a shear stress is measured by the stiffness modulus (M) given by Eq. (21). Therefore, a material with increased rigidity and enhanced resistance against deformation due to shear stress is linked to its improved M. This finding further supports the conclusion that Rb 2 Ag (Ga/In)Br 6 is mechanically stable and resistant to softening, making it a promising candidate for experimental preparation. B=(C11 +2C12) 3(9) Gv=1 5(C11 −C12 +3C44)(10) GR=5(C11 −C12)C44 3(C11 −C12)+4C44 (11) G=GV+GR 2(12) Y=9BG (3B+G)(13) ν =3B−2G 2(3B+G)(14) A=2C44 C11 −C12 (15) Cʹ=C11 −C12 2(16) ξ=(C11 +8C12) (7C11 −2C12)(17) λ=Y. ν (1+ ν )(1−2 ν )(18) μ =Y 2(1− ν )(19) Tm=[553+(5.911)C11 ]±300 K(20) M=(1− ν ).Y (1+ ν )(1−2 ν )(21) 3.3. Electronic properties We explore the electronic properties of studied materials through DFT utilizing the PBE-GGA together with mBJ methods. The energy band structure and the total and partial density of states (DOS) offer a valuable insight into the physical attributes of these materials and electronic properties. These calculations are essential for identifying the exact ground state electronic behaviour of the samples. In Figs. 5 and 6, it is evident that the highest level of valence band and the lowest level of conduction band align perfectly along the same Γ-symmetry point of the Brillouin zone (BZ) indicating that both Rb 2 AgGaBr 6 and Rb 2 AgInBr 6 are semiconductor materials with direct energy band gap (Γ → Γ) of 0.38 eV and 1.0644 eV, respectively, using PBE-GGA +mBJ methods, which predicts exact band gap with accurate band profile than that using only PBE-GGA approximation where we found a zero band gap for both the studied compounds respectively. Further it’s worth highlighting that the estimated band gap of these two components falls within the ideal range for visible light absorption. The direct band gap natures of the materials predict the enhanced efficiency for optoelectronic applications as compared to the indirect band gap materials. The band gaps for other works have been also reported in the same range [54,55](as listed in Table 3). To understand the potential movement of the electrons from the valence region to conduction region and the individual contributions of the constituent elements, we performed the mBJ +GGA method to derive their total and partial DOS as plotted in Figs. 7 and 8. In these figures, the Rb states are in the deep energy level giving a negligible contribution to the electronic transitions from valence to conduction region. However, in the present hybrid model double perovskites, the contributions of the p,d-states of (In/Ga) are minor in the region close to Fermi energy level. According to Figs. 7 and 8, we observe that the highest level of valence band is constituted of Ag-d mixed with Br-p states whereas (Ga/In)- s states contribute to the lowest conduction region. Consequently, the transitions occur from the mixed valence states (Ag-d and Br-p) to the s-(Ga/In) dominated conduction region which is also accountable of the phenomena occurs in the optical response curve and thermoelectric behaviour of Rb 2 Ag(Ga/In)Br 6 as discussed in next section. Fig. 5. Rb 2 AgGaBr 6 band structure estimated using the mBJ +GGA calculation. I. Benkaddour et al. Materials Science in Semiconductor Processing 185 (2025) 108974 5 3.4. Electron charge density distribution To gain deeper insights into the chemical bonding characteristics of the examined materials, we have generated charge density contour plots in the crystallographic planes (100) and (110), as depicted in Fig. 9 (B’ =Ga/In) and (X =Br). Within the halide perovskite structure (A 2 BB’X 6 =Rb 2 Ag(In/Ga)Br 6 ), a consistent observation is made regarding the ionic nature of the A-X bond, while the B-X or B ′ -X bonds consistently exhibit covalent characteristics, aligning with findings in existing literature [71,72]. Examining the (100) plane, the overlapping regions between Ag and Br atoms indicate the presence of covalent bonds, corresponding to AgBr 6 octahedra. Similarly, in the (110) plane, the overlapping areas between (In/Ga) and Br atoms also affirm the existence of covalent bonds, corresponding to BBr 6 octahedra. The non-overlapping and symmetrically spherical charge distributions around Rb atoms suggest ionic bonds between Rb and Br. It’s crucial to note that the double halide perovskite Rb 2 Ag(Ga/In)Br 6 demonstrates a mixed ionic-covalent nature, positioning it as a promising candidate for photocatalytic degradation. 3.5. Optical properties Several domains in which the incident light interacts with the matter are interesting for their commercial use. The investigation of the response of the materials against incident photon radiation is also a powerful tool to understand its electronic properties and atomic structure [73]. This requires an analysis of essential characteristics, including the frequency dependent absorption coefficient α ( ω ), optical conductivity σ ( ω ), complex refractive index n( ω ), reflectivity R( ω ), and other properties associated with the interaction of light with the double perovskites. In fact, the understanding of the complex dielectric function ( ε ( ω ) = ε 1 ( ω ) +i ε 2 ( ω )) also enables us to analyze these properties using different equations as mentioned in Refs. [74,75]. Since, it requires a dense mesh of K-points to estimate the accurate optical properties in the present work we have used 2000 K-points to perform the integration in the BZ. The variation of the real ε 1 ( ω ) and the imaginary ε 2 ( ω ) parts of ε ( ω ) within the energy range of 0–26 eV of incident photon energy for Rb 2 AgGaBr 6 and Rb 2 AgInBr 6 is depicted in Figs. 10 and 11. From these figures, one can estimate the static dielectric constants as presented in Table 4, which are also in close agreement with those obtained in other theoretical studies [54,55]. The static values of ε 1 (0) are 4.617and 3.665 for Rb 2 AgGaBr 6 and Rb 2 AgInBr 6 , respectively. These values exhibit an upward trend as shown in Fig. 10a, reaching peaks at 5.32 arb. unit (1.56 eV) for Rb 2 AgGaBr 6 and 4.56 arb. Unit (2.29 eV) for Rb 2 AgInBr 6 . At resonance, Fig. 6. Rb 2 AgInBr 6 band structure estimated using the mBJ +GGA calculation. Table 3 Gap values for the two compounds Rb 2 AgGaBr 6 and Rb 2 AgInBr 6 compared to other values (a¼[54]; b¼[55]). Compound E g (eV) Present work Other works PBE-GGA (PBE-GGA +mBJ) Theo. (GGA +mBJ) Rb 2 AgGaBr 6 0.0 0.38 1.28 a Rb 2 AgInBr 6 0.0 1.0644 1.32 b Fig. 7. Rb 2 AgGaBr 6 densities of states (TDOS, PDOS) using the mBJ +GGA. Fig. 8. Rb 2 AgInBr 6 densities of states (TDOS, PDOS) using the mBJ +GGA. I. Benkaddour et al. Materials Science in Semiconductor Processing 185 (2025) 108974 6 there is maximal dispersion of incident light energy, followed by a slight decrease as energy deviates from the resonance levels. Additionally, the dispersion of light alters with increasing energy. It is noteworthy that the substitution of Ga appears to have a more pronounced effect compared to In. Thus, the choice of cation plays a pivotal role in influencing optical applications. The refractive index n( ω ) also plays a key role to determine the transparency of a system. As the incident energy increases, there is a corresponding rise in dispersion, ultimately reaching 2.148 for Rb 2 AgGaBr 6 and 1.914 for Rb 2 AgInBr 6 , as depicted in Fig. 10b. In Fig. 11a, where the incident photon energy dependent ε 2 ( ω ) is presented, which also reflect the optical absorption and optical band gap of the alloy. Here, it is clear that up to 1.047eV and 0.30 eV, no absorption phenomena occurs for In and Ga based sample which also implies that the optical band gaps are equivalent to the electrical bandgap. The variation of extinction coefficient k( ω ), which also measures the absorption of light by the matter also follow synonymous type of variation with ε 2 ( ω ) and attains it maximum values of value 11.85arb.unit and 11.71 arb. unit for Rb 2 AgGaBr 6 and Rb 2 AgInBr 6 at 1.25 eV and 1.26 eV, respectively. The absorption of the photon energy denoted by ε 2 ( ω ) which can be derived from ε 1 ( ω ) using the Kramer-Kronig relation [76] also Fig. 9. Electron Density Distributions (100), (100) of Rb 2 AgB’Br 6 (where B’ =Ga/In) using the mBJ +GGA. Fig. 10. Real part of dielectric function (a), refractive index n( ω ) (b), reflectivity R (c) and loss (d) of Rb 2 AgInBr 6 and Rb 2 AgGaBr 6 compounds as functions of energy. Fig. 11. Imaginary part of dielectric function (a), extinction coefficient k( ω ) (b), optical conductivity (c), and absorption coefficient (d) of Rb 2 AgInBr 6 and Rb 2 AgGaBr 6 compounds as functions of energy. Table 4 Static values of the real part of the dielectric function, refractive index, and reflectivity for the compounds Rb 2 AgGaBr 6 and Rb 2 AgInBr 6 compared to Others studies (a¼[54]; b¼[55]). Rb 2 AgGaBr 6 Rb 2 AgInBr 6 Present work Other work Present work Other work ε 1 (0) 4.617 3.18 a 3.665 3.24 b  n (0) 2.148 1.78 a 1.914 1.80 b  R (0) 0.133 0.07 a 0.098 0.082 b  I. Benkaddour et al. Materials Science in Semiconductor Processing 185 (2025) 108974 7 provides the insight into the optical band gap from its threshold value which can be determined by drawing a tangent in its frequency dependent curve. There are absorption peaks at approximately 167.5 ×10 4 cm⁻ 1 at 19.8 eV for Rb 2 AgInBr 6 and peaks at 173.2 ×10 4 cm⁻ 1 at 19.8 eV for Rb 2 AgGaBr 6 , as depicted in Fig. 11d. Consequently, both Rb 2 AgGaBr 6 and Rb 2 AgInBr 6 are well-suited for optoelectronic devices in visible and UV regions, making them particularly valuable for solar cells operating in the visible region. Reflectivity spectra (R( ω )) and optical loss function (L( ω )) are also significant parameters, with lower values indicating superior optical materials. R( ω ) offers insights into the surface characteristics of the compounds. The calculated values of R( ω ) as presented in Fig. 10d, indicates their values 0.133 arb. unit for Rb 2 AgGaBr 6 and 0.098 for Rb 2 AgInBr 6 at zero energy. One can note that these values increase as photon energy rises, reaching a maximum of 0.30 arb. unit (21.97eV) for Rb 2 AgGaBr 6 and 0.27arb.unit (20.93eV) for Rb 2 AgInBr 6 . The loss of incident photon energy due to electronic transition can be measured by the loss function [77,78]. In the L( ω ) spectra of Rb 2 Ag (Ga/In)Br 6 as presented in Fig. 10c does not reflect any reflection for the photon energy up to their energy band gap. The prominent peaks of 4.2 arb. unit and 3.5arb.unit for both Rb 2 AgGaBr 6 and Rb 2 AgInBr 6 respectively, observed at about 22eV. As the energy levels rise, loss peaks become apparent, peaking at 3.59 arb. unit for Rb 2 AgInBr 6 at 22.9 eV and 4.27 arb. unit for Rb 2 AgGaBr 6 at 22.92 eV, respectively. These materials are benefitted with their very low amplitude of reflectivity and loss function for the design of the absorption layers in the solar cells. The careful analysis of the optical conductivity spectra ( σ ) (Fig. 11c) suggest the maximum amplitude of σ 5899.4 ×10 15 cm⁻ 1 and 5638.9 ×10 15 cm⁻ 1 at 9.33 eV for Rb 2 AgGaBr 6 and Rb 2 AgInBr 6 , respectively. 3.6. Optic of thin films In the context of semiconductors and dielectrics, the predominant absorption mechanism arises from the interaction of light with electrons [79,80]. For semiconductors, there exists a minimum energy (band gap) that separates the conduction and valence regions and the transition of electrons between these two bands constitute the primary source of absorption. However, the absorption of a photon in the material occurs when its energy corresponds to the energy needed to excite an electron from allowed lower energy to another higher energy states. In the absence of energy matching between the incident photon and the required excitation energy, no excitation occurs, rendering the material transparent to such specific radiation. To determine the optics of the thin layers of the studied perovskites Rb 2 AgGaBr 6 and Rb 2 AgInBr 6 , we conducted this study using the optical matrix method based on the Abel` es method. As a result, one can find a variety of physical approaches as well as the mathematical modelas to characterize the optical spectra of the thin-film structures in the literature [81–86]. In this method, a square matrix [M] as implemented in optical thin film design program [87–89] is used to design a thin layer of an absorbing material which also requires the extension coefficient and the refractive index of the material as described in section 3.5. In this process, a 2 ×2 matrix can be used to describe the optical response, such as transmission (T), absorption (A), and reflection (R) of each thin layer of the absorbing material. These optical responses depend on the optical constants k and n as well as the layer thickness (d). Here, the frequency dependent complex reflective index is obtained by using FP-LAPW calculations [90–95] and the obtained transmission, absorption, and reflection spectra are analysed by varying the layer thickness from 600 nm to 1300 nm for the incident wavelength of 100–1400 nm. While preparing the layer sample, two different approaches were inducted. Firstly, it was suspended on a transparent substrate (for glass n =1.5, k =0), and later involves a self-supporting layer (for air n =1 and k =0). The variation of absorbance spectra (A%) as function of wavelength as shown in Fig. 12 reflects better absorbance of Rb 2 AgGaBr 6 film as compared to Rb 2 AgInBr 6 by 85 %. Here, both the film samples prepared through layer suspended on a transparent substrate as well as free-standing layer show the spectral radiation in the visible (400 nm–800nm) to UV (200 nm–400nm) range. Further increase in the incident radiation in the infrared (IR) region, the absorbance spectra decreased rather sharply for Rb 2 AgInBr 6 . The higher values of absorbance of Rb2AgGaBr6 film in the incident photon of visible to UV region make this semiconductor a suitable candidate for device fabrication of solar cell. Furthermore, one can also remark that the peaks in the absorption spectra shift towards long wave length indicating the lowering of optical energy band gap with the increase of layer thickness. Similarly, the transmittance spectra (T%) of thin film structures of both the sample alloys obtained by using two estimated process of deposition (free standing layer and layer on glass substrates) and with the variation of films thickness are presented in Fig. 13. A careful analysis of the plot also reveal a comparatively low amplitude of transmittance for a wide range of electromagnetic spectrum (UV–Visible–NIR) for thicker films (for d =900 nm and d =1300 nm) in Rb 2 AgGaBr 6 . This phenomenon Fig. 12. Absorbance spectra of Rb 2 Ag(Ga/In)Br 6 thin films of different thicknesses, presented for both standalone and glass-supported layers. I. Benkaddour et al. Materials Science in Semiconductor Processing 185 (2025) 108974 8 also can be regarded as the good absorbing nature of the material for solar radiation. The reflectance spectra (R%) against the wavelength for at different layer thickness 200 nm and 800 nm of Rb 2 AgGaBr 6 and Rb 2 AgInBr 6 thin films samples estimated using two processes of deposition are illustrated in Fig. 14. From the graphs, it could be clearly seen that at all studied thicknesses both films have poor reflectance values in the case of samples on glass substrates than the free-standing layers process. It can be concluded that this material can cause a reflection of ~20 % and 35 % of the total incident photon radiation and hence they can be used as an anti-reflection coating on the reflecting surfaces of window glasses, camera lense, video screen as well as solar cell devices to protect the cell and reduce the loss from reflection from the cell surfaces. 3.7. Thermal properties The ab initio calculations are successful to estimate the result close to the experiments and predict the exact structure and electronic properties of the solids, however, their efficiency is limited to 0 K temperature. Hence, to overcome this limitation, we have used the Gibbs program [39–41] to study the thermodynamical properties of the sample at high pressure and temperature using Debye’s quasi-harmonic approximation [96]. In this approach, the variation of the volume of the crystal and its compressibility module (bulk modulus B 0 ), thermal expansion coefficient ( α V ), thermal capacity and the Debye temperature at different pressure are measured with respect to temperatures from 0 to 800 K for Rb 2 Ag(Ga/In)Br 6 compounds. Calculating these quantities through Fig. 13. Transmittance spectra of Rb 2 Ag(Ga/In)Br 6 thin films with varying thicknesses, shown for both standalone and glass-mounted layers. Fig. 14. Reflectance spectra of Rb 2 Ag(Ga/In)Br 6 thin films of different thicknesses, displayed for both standalone and glass-supported layers. I. Benkaddour et al. Materials Science in Semiconductor Processing 185 (2025) 108974 9 [43] G. Kresse, G. Furthmüller, J. Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set, Comput. Mater. Sci. 6 (1996) 15–50. [44] G. Kresse, G. Furthmüller, J. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set, Phys. Rev. B 54 (1996) 11169–11186. [45] F. Birch, J. Appl. Phys. 9 (4) (1938) 279–288. [46] F.D. Murnaghan, Proc. Natl. Acad. Sci. U.S.A. 30 (1944) 244. [47] F. Bachhuber, J. von Appen, R. Dronskowski, P.S. Nilges, T.A. Pfitzner, R. Weihrich, Ang. Chemie. Interna. Edit. 53 (2014) 11629. [48] V.M. Goldschmidt, The laws of crystal chemistry, Naturwissenschaften 14 (21) (1926) 477–485. [49] C. Li, X. Lu, W. Ding, L. Feng, Y. Gao, Z. Guo, Acta Crystallogr., Sect. B: Struct. Sci. 64 (2008) 702. [50] F. Ji, G. Boschloo, F. Wang, F. Gao, Sol. RRL 7 (2023) 2201112, 1-23. [51] C.J. Bartel, C. Sutton, B.R. Goldsmith, R. Ouyang, C.B. Musgrave, L. M. Ghiringhelli, M. Scheffler, Sci. Adv. 5 (2) (2019) eaav0693, 1-9. [52] Mukaddar S. k Gourav, R. Krishnamoorthy, G. Saurabh, Int. J. Quant. Chem. 122 (2022) 26910. [53] H.S. Kim, C.R. Lee, J.H. Im, K.B. Lee, T. Moehl, A. Marchioro, S.J. Moo, R. Humphry Baker, J.H. Yum, J.E. Moser, M. Gr¨ atzel, N.G. Park, Sci. Rep. 2 (2012) 591. [54] M. Kibbou, Z. Haman, I. Essaoudi, A. Ainane, J. Solid State Chem. 317 (Part A) (2023) 123698. [55] N.A. Kattan, Q. Mahmood, Ghazanfar Nazir, Adeela Rehman, N. Sfinaf, Murefahmana Al-anazy, Shakeel Ahmad Sofi, Manal Morsi, Mohammed A. Amin, Material today communications 34 (2023) 105166. [56] T.M. Bhat, D.C. Gupta, RSC Adv. 6 (83) (2016) 80302–80309. [57] G.V. Sin’Ko, N.A. Smirnov, J. Phys. Condens. Matter 14 (29) (2002) 6989–7005. [58] M.J. Mehl, B.M. Klein, A. Dimitri Papaconstantopoulos, Intermetallic Compounds: Principle and Practice. I. Principles, John Wiley and Sons, Hoboken, New Jersey, 1995, pp. 195–210. [59] Challapalli Suryanarayana, Mechanical behavior of emerging materials, Mater. Today 15 (11) (2012) 486–498. [60] E. Schreiber, O.L. Anderson, N. Soga, J.F. Bell, N. Y.: McGraw-Hill 42 (1975) 747–748. [61] R. Hill, Proc. Phys. Soc. A. 65 (5) (1952) 349–354. [62] W. Voigt, Lehrbuch der Kristallphysik" (Textbook of Crystal Physics), BG Teubner, Leipzig und Berlin, 1928. [63] A. Reuss, ZAMMZeitschrift fur Angewandte Mathematik und Mechanik 9 (1929) 49–58. [64] S.F. Pugh, London Edinburgh Philos Mag J Sci. 45 (367) (1954) 823–843. [65] S.A. Dar, V. Srivastava, U.K. Sakalle, V. Parey, J. Electron. Mater. 47 (7) (2018) 3809–3816. [66] B. Mayer, H. Anton, E. Bott, Intermetallics 11 (1) (2003) 23–32. [67] J. Haines, J.M. Leger, G. Bocquillon, Annu. Rev. Mater. Res. 31 (1) (2001) 1–23. [68] S. Yalameha, Z. Nourbakhsh, D. Vashaee, Comput. Phys. Commun. 271 (2022) 108195. [69] L. Kleinman, Phys. Rev. 128 (1962) 2614. [70] M.E. Fine, L.D. Brown, H.L. Marcus, Scripta Metalurgica 18 (1984) 951–956. [71] M. Wuttig, C.F. Sch¨ on, M. Schumacher, J. Robertson, P. Golub, E. Bousquet, C. Gatti, J.Y. Raty, Adv. Funct. Mater. 32 (2) (2022) 2110166. [72] M. Saeed, I. Ul Haq, S. Ur Rehman, A. Ali, W. Ali Shah, Z. Ali, Q. Khan, I. Khan, Opt Lett. 19 (3) (2021) 030004. Article in Chinese. [73] S. Adachi, J. Appl. Phys. 61 (1987) 4869. [74] H. Jin, J. Im, A.J. Freeman, Phys. Rev. B 86 (2012) 121102. [75] M.A. Hadi, R.V. Vovk, A. Chroneos, J. Mater. Sci. Mater. Electron. 27 (2016) 11925. [76] V.B. Bobrov, S.A. Trigger, G.J.F. van Heijst, P.P.J.M. Schram, EPL 90 (2010) 10003. [77] S. Saha, T.P. Sinha, A. Mookerjee, Phys. Rev. B 62 (2000) 8828. [78] A.H. Reshak, Z. Charifi, H.J. Baaziz, Solid State Chem. 183 (2010) 1290. [79] M.L. Cohen, J. Chelikowsky, Electronic structure and optical properties of semiconductors. Series on Solid State Science second ed., 75, Springer-Verlag, Berlin, Heidelberg, 1989. Springer. [80] P.T. Yu, M. Cardona, Fundamentals of Semiconductors, Springer-Verlag, Berlin, Heidelberg, 1996. [81] F. Abeles, Investigations on the propagation of sinusoidal electromagnetic waves in stratified media: application to thin films, Ann. Phys. 5 (1950) 596–640. [82] P.H. Berning, Theory and calculations of optical thin films, in: G. Hass (Ed.), Physics of Thin Films, 1, Academic Press, New York, NY, USA, 1963, pp. 69–121. [83] O.S. Heavens, Measurement of optical constants of thin films, in: G. Hass, R. E. Thun (Eds.), Physics of Thin Films, 2, Academic Press, New York, NY,USA, 1964, pp. 193–238. [84] H.E. Bennett, J.M. Bennett, Measurement of optical constants of thin films, in: G. Hass, R.E. Thun (Eds.), Physics of Thin Films, 4, Academic Press, New York, NY, USA, 1967, pp. 1–96. [85] M.H. Francombe, R.W. Hoffman (Eds.), Physics of Thin Films, 6, Academic Press, New York, NY, USA, 1967, pp. 151–204. [86] J.A. Dobrowolski, Numerical methods for optical thin films, Opt Photon. News 8 (6) (1997) 24–33. [87] A. Piegari, F. Flory, Optical thin films and coatings: from materials to applications, in: Electronic and Optical Materials Book, second ed., Woodhead Publishing Series, 2018. ISBN: 978-0-08-102073-9. [88] R.R. Willey, Practical design and production of optical thin films, in: Revised and Expanded Willey Optical, second ed., MARCEL DEKKER, INC., NEW YORK, 2002. ISBN: 0-8247-0849-0. [89] H.A. Macleod, Thin-Film Optical Filters, fourth ed., Thin Film Center Inc., Tucson, Arizona, USA, 2018. A TAYLOR & FRANCIS BOOK, ISBN13: 978-1-138-198241. [90] F. Chiker, N. Baki, Y.A. Khachai, H. Khachai, R. Miloua, R. Khenata, S. Bin Omran, A. Bouhemadou, M.B. Kanoun, S. Goumi-Said, Crystals 12 (10) (2022) 1397. [91] W.A. Drouni, N. Baki, F. Chiker, Y.A. Khachai, H. Khachai, R. Miloua, R. Khenata, R. Ahmed, A. Bouhemadou, S. Bin Omran, Eur. Phys. J. Plus 138 (2023) 255. [92] Z. Derkaoui, Z. Kebbab, R. Miloua, N. Benramdane, Solid State Commun. 149 (2009) 1231–1235. [93] R. Miloua, Z. Kebbab, F. Chiker, K. Sahraoui, M. Khadraoui, N. Benramdane, Opt. Lett. 37 (2012) 449–451. [94] R. Miloua, Z. Kebbab, F. Chiker, M. Khadraoui, K. Sahraoui, A. Bouzidi, M. Medles, C. Mathieu, N. Benramdane, Opt Commun. 330 (2014) 135–139. [95] F. Boukabrine, F. Chiker, R. Miloua, Z. Kebbab, R. Khenata, D. Prakash, S Bin Omran, K. Verma, Opt. Mater. 54 (2016) 200–206. [96] P. Debye, Ann. Phys. 39 (4) (1912) 789. [97] A.T. Petit, P.L. Dulong, Ann. Chem. Phys. 10 (1819) 395–413. [98] J. Zhang, Transport Studies of the Electrical, Magnetic and Thermoelectric Properties of Topological Insulator Thin Films, Springer Theses, 2016, p. 99. [99] J.R. Sootsman, D.Y. Chung, M.G. Kanatzidis, Angew. Chem. Int. Ed. 48 (46) (2009) 8616–8639. [100] F. Aslam, H. Ullah, M. Hassan, Mater. Sci. Eng. B 274 (2021) 115456. [101] M. Wolf, R. Hinterding, A. Feldhoff, Entropy 21 (2019) 1058. I. Benkaddour et al. Materials Science in Semiconductor Processing 185 (2025) 108974 16