Investigation of structural, electronic, mechanical, & optical characteristics of Ra based-cubic hydrides RbRaX3 (X= F and cl) perovskite materials for solar cell applications: First principle study

Perovskite materials are considered the gateway of various physical applications to meet the production and consumption of energy and medical fields. Density Functional Theory (DFT) becomes the most important field in the modern era to investigate perovskite materials for various physical properties. DFT nowadays is used to explore the perovskite materials for a lot of applications like photocatalytic, optoelectronic, and photovoltaics. We discussed radium based cubic hydrides RbRaX3 (while X = F & Cl) perovskite material's electrical, optical, elastic, & physical characteristics with the help of DFT-based CASTEP code with PBE exchange-correlation efficient of GGA. The RbRaF3 & RbRaCl3 have three-dimensional nature by means of space group 221 (Pm3 m). According to electronic characteristics, the direct bandgap of RbRaF3 RbRaCl3 are 3.18eV and 2.209eV, respectively. Both compounds are brittle in nature via Poisson's ratio & Pugh's criteria. Thus, our novel RbRaX3 (X = F and Cl) compounds have excellent applications for solar cell and medical areas.


Introduction
Perovskites are well-known materials in the field of research, perovskite compounds are represented in general by ABX 3 while A and B are cations having different sizes when X is a bound anion to both [1]. Organic photovoltaics, also known as OPVs, have a substantial amount of untapped potential to meet the ever-increasing energy needs of the future [2,3]. Extensive research on inorganic-organic perovskites has led to the identification of new resources that may be used in the creation of solar systems that are both effective and economical [4,5]. In 2009, many different perovskite-based photovoltaic cells (also known as perovskite solar cells, or PSCs) were reported to have fast-rising power conversion efficiencies (PCE) [6][7][8]. Perovskites through a piezoelectric effect for detectors, lead zirconium titanate, & high-temperature perovskite super-conductors such as beryllium copper oxide are a few examples [9,10]. When exposed to a magnetic field, some perovskite groups, primarily those based on manganese, exhibit extremely high resistance of magnet, which can expressively alter electrical resistance [11]. Furthermore, perovskites have been observed in a variety of other sectors, including lasers [12], light emitting diodes (LEDs), catalysts [13], and thermoelectric materials [14]. It has recently gained popularity due to capable of serving as a solar cell absorber and has gained large attention of researchers.
Fluoro-perovskites and halide perovskites are two categories of mixes with ABF 3 and ABCl 3 stoichiometry, respectively [15]. There is a large body of study on the crystals of halide perovskites and fluoro-perovskites [16]. In general, A is alkali, alkaline, or rare earth metals. Here B is considered as a transition, post-transition, & non-transition metal while X, which is oxides and halides, is used to represent an anion [17]. It has demonstrated that it can create a variety of chemically stable rising fluorides, the most prevalent of which are strong electro-positive alkali metals and alkaline earth metals. Due to their ferromagnetic [18], non-magnetic insulating material, piezoelectric, and photoluminescence properties, complex metal fluorides have grown a lot of interest [19]. But completely unleash organic photovoltaics' latent potential; it is still necessary to synthesize highly efficient photovoltaic materials, especially hole-transport materials (HTMs) and electron-transport materials (ETMs) [20][21][22][23].
Moreover, numerous recent researches have demonstrated that the fluoro-perovskite crystals are guaranteed to have UV-Deep UV wave bands. KMgF 3 , NaSrF 3 , NaBaF 3 , and LiBaF 3 can be used to create prisms, glasses, and windows that are fully transparent and optical with little loss. Halide perovskites are grabbing the interest of research teams due to their wide range of outstanding features, possible technical uses, & the chance to add almost each component throughout the periodic table [24,25]. Following these developments, research into the thickness-dependent optical, electronic, and vibrational properties of organic and hybrid perovskites has begun to gain momentum. Recent investigations have also demonstrated that these materials' optical, vibrational, and electronic properties may differ depending on their material thickness for solar cell applications. Due to its historic launch in solar cell (SC) applications, metal hydride perovskite have recently attracted enormous attention from the research community. These materials actually have intriguing optoelectronic characteristics such as a flexible band gap, a predominate point, and strong optical absorption defect for solar cell applications [26]. Therefore, in current study, we have attempted to improve the performance of electrical, optical, elastic, & physical characteristics with the help of DFT-based CASTEP code with PBE exchange-correlation efficient of GGA. Interestingly, we have found that the performances of the radium based cubic hydrides RbRaX 3 (while X = F & Cl) perovskite materials for solar cell applications using DFT approach are significantly improved by Cl.
In this study, the structural, electrical, & optical characteristics of RbRaF 3 and RbRaCl 3 are studied. The whole energy estimation is achieved via DFT-designed GGA-PBE method, which is incorporated by CASTEP code. These compounds have great contribution for energy and medical applications.

Computational details
Both RbRaF 3 and RbRacl 3 are studied using cubic crystal structure of ternary fluoro perovskites. Both compounds belong to Pm3 m space group. In both compounds, atomic place of Rb atoms is (0.00, 0.00, 0.00) & the atomic position of F and cl atoms are (0.0, 0.5, 0.5). In RbRaF 3 and RbRaCl 3 , the atomic positions of the Ra atom are (0.5, 0.5, 0.5). The following is the elemental configuration for the atoms in question: F: 2s2 2p 5 ; Rb: 4s 2 4p 6 5s 1 and Ra: 6s 2 6p 6 7s 2 of RbRaF 3 and Cl: 3s 2 3p 5 ; Rb: 4s 2 4p 6 5s 1 and Ra: 6s 2 6p 6 7s 2 of RbRaCl 3 . To investigate the characteristics of our material, we employed the CASTEP program, which is developed on DFT [27]. The PBE functional are used to accomplish the calculations. We calculated the properties of our material using a unit cell. The characteristics of materials were calculated via geometry optimization. The total energy convergence per atom for RbRaF 3 is 5 × 10 − 6 eV/atom and for RbRaCl 3 is 1.0 × 10 − 5 eV/atom respectively. The atoms are subjected to extreme force of 0.010 eV/A and a max ionic displacement (5 × 10 − 4 ) for RbRaF 3 . In the case of RbRaCl 3, the max force and ionic displacement is set to 0.03 eV/A and 0.001 A respectively. In order to conduct an analysis of the material's band structure, k-integration was carried out on a mesh grid consisting of 8 × 8 × 8 k-points, and an energy cutoff of 230 eV was applied uniformly over the Brillouin zone. Our research outlines a method that is straightforward, economical, and kind to the natural world to prepare the effective perovskite materials discussed before. Aqueous Table 1 Lattice Parameters, Volume, and Band gaps energy of RbRaF 3 and RbRaCl 3 compounds. lead precursors that do not include halides are subjected to a hydrothermal reaction during this method [20,23]. A limited experimental or theoretic data available for RbRaF 3 & RbRaCl 3 compounds. We have made a comparison with other Rbbased fluoro perovskites and halide perovskites. Table 1 shows the values of the lattice constant and band gap of RbRaCl 3 and RbRaF 3 in comparison with other Rb-based flour-perovskites materials. Fig. 1 (a) and Fig. 1(b) shows the crystal structure of RbRaCl 3 and RbRaF 3 compounds.

Structural properties
In order to discuss the structural properties, both substances' cell geometries are improved. Murnaghan state equation is utilized to derive balanced lattice limitations though keeping the overall energy of crystals minimal [30]. The value of the optimum lattice parameter is exposed to be over geometry optimization 3.55 A 0 and 6.45 A 0 for RbRaF 3 and RbRaCl 3 respectively as mentioned in Table 1. For both compounds, there is no theoretic or experimental information available in literature. Table 2 shows the values of calculated lattice constants and lists the values of these elastic constants. Three elastic constants, C11, C12, & C44, are used to explain the mechanical characteristics of cubic symmetry crystals.
To calculate the bulk modulus, Equation (1) is used to find its values [31].
For stability, Equation (2) is helpful to check the condition as follows: [32].
In Table 2, effects of the anisotropy factor A is calculated from Equation (3), the young's modulus E is calculated from Equation (4), the possion ratio v is calculated from Equation (5), and the pugh's index ratio B/G is calculated from Equation (6), Equation (7) and Equation which are displayed as follows [33].
G v = (C 11 -C 12 +3C 44 ) / 5 G R = 5C 44 (C 11 -C 12 ) / 4C 44 +3(C 11 -C 12 ) The B/G ratio is known as Pugh's ratio if its value is less than 1.750, the material is brittle, and for values more than 1.750, the material is supposed ductile [34]. The ratio of the poison can also be used to evaluate whether a material is harsh or ductile. Poisson's ratio v is another tool for determining if a substance is harsh or ductile; if this ratio rises above the threshold of 0.26, the substance is said to be ductile [35,36]. Table 2 shows the values for both Pugh's ratio and poison's ratio for RbRaF 3 and RbRaCl 3 . Using these two indicators it can be concluded that both materials exhibit a brittle nature.

Electronic properties
When assessing the band structure of materials, the density of states, also known as DOS, is an essential component to take into consideration. Due to the existence of a bandgap at the Fermi levels, the DOS plot of RbRaF 3 demonstrates unequivocally that the material has features typical of semiconductors [37]. The Rb-d orbital is responsible for the vast bulk of the contribution that is seen in the conduction band. On the other hand, the DOS plot of RbRaCl 3 reveals semiconductor characteristics, with a bandgap located near the Fermi levels. The Rb-d orbital has the most significant impact on the conduction band, whereas the Rb-p and Ra-p orbitals have a marginal bearing on its characteristics. Fig. 2(a) shows the band structure while Fig. 2(b) depicts density of states of RbRaF 3 compounds.
For the sake of our computations, the Fermi level is placed at the peak of the valence band and for the sake of clarity, only the states with the greatest contributions are observed.
Moreover, it is possible to forecast a material's optical nature using its electrical properties [38,39]. Thus, we performed the BG and DOS calculations of RbRaF 3 and RbRaCl 3 to comprehend their optical and electrical characteristics. Fig. 3(a)-(b) show band structures and TDOS of RbRaF 3 and RbRaCl 3 respectively. The E F was fixed to 0.0 eV which coincides with the top of valence band. The calculated bandgap of RbRaF 3 and RbRaCl 3 is 3.18 eV and 2.209 eV correspondingly. At the G point in both valence band maximum and conduction band minimum are observed. RbRaF 3 & RbRaCl 3 are showing that both compounds have a direct band gap [40]. As a result, these materials may be suitable for optoelectronics, photovoltaic, and photo-thermal applications. Fig. 4 (a) shows PDOS of RbRaF 3 compounds. The p-states of the fluorine and Rb atoms, respectively, contribute significantly to the formation of the valence band as observed in Fig. 4(b). The conduction band is formed by the main role of Ra-d states & the minor involvement of Ra-s-states & Rb-p states as observed in Fig. 4(c). Moreover, Fig. 4(d) shows F-PDOS formation. Fig. 5 (a) shows PDOS of RbRaCl 3 compound. In RbRaCl 3 below the fermi level, the major contribution is due to Cl-p states and Rb-states as observed in Fig. 5(b)-(d). Above fermi level, conduction band is mostly formed due to the major contribution of Ra-d states and minor contribution of Rb-p states and Ra -states as seen in Fig. 5(c).

Optical properties
The optical properties of compounds including their reflectivity, energy loss function, relative permittivity, and index of refraction, can be utilized to define their electronic structure. These qualities are highly useful in determining the material's suitability and feasibility in nano-electronics and optoelectronics. Fig. 6(a) and (b) show the optical characteristics of RbRaF 3 and RbRaCl 3 compounds. Because all of the optical properties are interrelated, dielectric function ε (ω) is used, which is calculated by Equation (9) [41]: In the above equation, ε 1 (ω) denotes the real part while ε 2 (ω) signifies the imaginary portion of the dielectric function.
The conductivity's primary peak (Real) is 7.10 at 17.0 eV and 5.00 at 16.72 eV of RbRaF 3 and RbRaCl 3 and the imaginary part of the conductivity is 5.14 at 18.0eV and 3.49 at 17.48eV of RbRaF 3 and RbRaCl 3 . Fig. 7(a) shows that initially the conductivity of the compounds will be increased gradually and after reaching at maximum peak the conductivity start to decrease.
The main absorption peak for RbRaF 3 is 17.55 eV while for RbRaCl 3 it is 17.15 eV. Fig. 7(b) depicts that absorption has no value when 2.24 eV and 4.00 eV for RbRaF 3 and RbRaCl 3 . The absorption of the compounds increases and after the maximum peak, it starts to decrease.
The primary maximum of the refractive index (n) for RbRaF 3 is 1.76 at 5.58 eV whereas for RbRaCl 3 is 1.80 at 3.11 eV. Fig. 8(a) demonstrates that the refractive index (k) for the primary peak for RbRaF 3 is 1.39 at 17.48 eV while that for RbRaCl 3 is 1.06 at 17.10 eV. At 0.0 eV, the value of the refractive index (n) for RbRaF 3 is 1.43 whereas for RbRaCl 3 is 01.53. Refractive index (k) starts at zero at 1.56eV and 3.29 of RbRaCl 3 and RbRaF 3 . Real part of refractive index initially increases and then starts to decrease. The primary dielectric function peak (real) for RbRaF 3 appears a 2.14 and 2.07 at 0 eV of RbRaF 3 and RbRaCl 3 and the imaginary part appears at 0.0 at 1.53eV and 3.28eV of RbRaF 3 and RbRaCl 3 compounds. The major ultimate of dielectric function (for imaginary) for RbRaF 3 give the impression at 3.02 at 5.33eV while that for RbRaCl 3 , it seems at eV.
The rate of the loss function of main peak is 3.49 at 20.17 eV and 5.90 at 18.29 eV for RbRaF 3 and RbRaCl 3 as observed in Fig. 8(b). The loss function starts to rise at 4.42 eV and 2.52 eV of RbRaF 3 and RbRaCl 3 and increases gradually and decreases to zero.

Overview
In order to discuss the overview of the perovskites materials, following steps are necessary.
1. Degradation issue of CH 6 I 3 NPb perovskite needs to be studied. 2. The film quality and thickness are core problems in perovskite solar cells. 3. Perovskite materials will break down quickly due to exposure of heat, moisture and snow. 4. The material is toxic in nature. The above mentioned points are the limitations of perovskite solar cell.
In addition, two basic strategies have been discovered as ways to improve the perovskite cells' capacity to maintain their stability. The first strategy involves the addition of composite perovskite components in order to boost the perovskite's natural stability. The second strategy involves finding appropriate additive compounds that may effectively limit the perovskite materials' breakdown. This strategy has the potential to be more successful than the first.

Conclusion
In modern period, perovskite materials play an excellent role for many applications that can be used to investigate photocatalytic, optoelectronic, energy and medical applications. In this study, we investigated Rubidium-based hydride perovskite materials via firstprinciples calculations. CASTEP code is used for the investigation of RbRaF 3 and RbRaCl 3 compounds, with cutoff energy 230 eV and 8 × 8 × 8 mesh k-points. The structural, mechanical, optical, and electrical properties of RbRaF 3 and RbRaCl 3 compounds are reported. We observed that both compounds exhibit brittle nature according to the Possion ratio and Pugh ratio calculations. It is realized that both materials have direct band gaps and the band gaps' values are found to be 3.18 and 2.209 for RbRaF 3 and RbRaCl 3, respectively. The main absorption peak for RbRaF 3 is 17.55 eV while for RbRaCl 3 it is 17.15 eV. In connection to structural-electronic purpose, alloptical properties including energy loss function, absorption, reflection, & refractive index are studied. This work represents significant progress towards energy and medical applications.

Data availability statement
Data will be made available on request.

Funding information
Deanship of Scientific Research at King Khalid University Abha 61,421, Asir, Kingdom of Saudi Arabia Large Groups Project under grant number RGP.2/499/44.

Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to  influence the work reported in this paper.