Nowadays scientists and technologists have been replacing fossil fuels with renewable energy sources such as photovoltaic solar energy in order to deal with the discharge of greenhouse gases that resulting climate change on the earth [1] - [3] whereas photovoltaic conversion system provides renewable and eco-friendly energy [4] . Past few years CdTe [5] , CIGS [5] - [7] and CZTS have gained interest as an application in photovoltaic solar cells and these materials have conversion power efficiency between 16% - 20% to date [4] [8] which making them conventional semiconductor materials. But the existence of harmful elements like In and Ga in CIGS has raised global concern and on the other hand, CZTS has been increased interest due to its low cost, non-toxic, eco-friendliness nature [9] - [13] and including application in solar cell [14] [15] . The CZTS thin films have a high level of optical absorption coefficient (>10⁴ cm⁻¹) [6] [7] [16] [17] as well as p-type conductivity and a direct band gap.

In 2010, Persson et al. investigated the electrical structures and optical features of Kesterite (KS) and Stannite (ST) types Cu₂ZnSnS₄ and Cu₂ZnSnSe₄ where they found direct band gap and high absorption coefficient (>10⁴ cm⁻¹) for KS-type using density functional theory [18] . In 2015, Kong et al. investigated the electronic and optical properties of Kesterite and Stannite Cu₂ZnSnS₄ using the DFT theory where they reported that the optical properties of CZTS weak dependency of Cu, Zn cation ordering and these materials have higher potentiality for photovoltaics due to their large light absorption coefficient [19] . In 2015, AN Rosli et al. suggested that the band structure of KS-Type CZTS where they found the band gap of KS-type CZTZ has been shown semiconductor nature [20] . Compared to the pristine structure, doping with different atoms is an appropriate approach to develop the physicochemical properties [21] . However, to convert light energy into photoelectricity and improve the photovoltaic solar cell’s properties, the p-n junction must be improved [22] . In 2020, N. Manavizadeh et al. investigated the effect of Bi-doping on CZTS using density functional theory, and they reported that the Bi-doped structure had a high absorption coefficient (>10⁴ cm⁻¹) in the visible region but the pure structure did not have this [23] . Using thermal evaporation method, M. Marzougiet et al. studied the structural, optical properties of Na-doping on CZTS and they found direct band gap with absorption coefficient in the UV-region at 5% Na-doping concentration on CZTS [24] . Using DFT, C. Tablero et al. studied the effect of the oxygen isoelectronic substitution in CZTS and they reported O-doped CZTS has an electrical structure that includes a sub-band towards the CB. This deeper band is comprised of the Sn-5s and O-2p orbitals [25] .

The quantum mechanical approach enables us to make more accurate predictions regarding the behavior of particles when we attempt to interact with them. We are inspired to perform such a theoretical investigation utilizing the quantum mechanical approach based on DFT to analyze the structural, electronic and optical properties of the CZTS compounds. As far as we are aware, theoretical and experimental research has been done by single doping but double doping in CZTS compound and their structural, electronic and optical properties are still unknown to us. Therefore, we are interested to dope Ba at Zn-site and to dope Si at Sn-site resulting the Cu₂Zn_1−xBa_xSn_1−ySi_yS₄ compound and to characterize the structural, electronic, and optical characteristics of Cu₂Zn_1−xBa_xSn_1−ySi_yS₄ compounds using the DFT based calculation. Moreover, Ba and Si have been chosen for their semiconductor nature, which might increase the useability of the Cu₂Zn_1−xBa_xSn_1−ySi_yS₄ compound as an absorber layer in solar cells.

To investigate the structural, electronic and optical properties of Cu₂Zn_1−xBa_xSn_1−ySi_yS₄ (where x, y = 0.00, 0.25, 0.50, 0.75, 1.00), the CASTEP (Cambridge Serial Total Energy Package, Material Studio 2017) code was used to execute quantum mechanical approach density functional theory (DFT) [26] - [29] simulation which was based on a nonlocal ultrasoft pseudopotential [30] that indicate the presence of firmly bonded core electrons and to illustrate the electron-ion interaction. To find the exchange correlation, the Perdew-Burke-Ernzerhof (PBE) [31] form of the generalized gradient approximation (GGA) was used with a plane-wave cut-off energy of 500 eV to get comprehensive solution along with default medium level of self-consistent field (SCF) tolerance in the program [32] . To conduct the computation, we constructed a supercell measuring 2 × 1 × 1, and The BFGS algorithm [33] was employed to optimize the crystal structure through the minimization of both total energy and internal forces. The KS-type Cu₂Zn_1−xBa_xSn_1−ySi_yS₄ compounds, where x and y represent doping concentration, have been studied using a Monkhorst Pack scheme [34] . The calculations were performed using a 2 × 4 × 2 k-point mesh size. We selected 1000 cycles, which is sufficient to optimize every structure. The structural parameters of the CZTS (pure and doped) were calculated using the Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm with energy change per atom less than 2 × 10⁻⁵ eV, residual force less than 0.05 eV/Å, stress below 0.1GPa, and atom displacement during geometry optimization less than 0.002Å.

In order to find the structural stability, the formation energy is obtained by using the formula [35] :

$\begin{array}{l}{E}_{for}=E_{{\text{Cu}}_{\text{2}}{\text{Zn}}_{1-\text{x}}{\text{Ba}}_{\text{x}}{\text{Sn}}_{1-\text{y}}{\text{Si}}_{\text{y}}{\text{S}}_4}-(E_{\text{Cu}}\times 2+E_{\text{Zn}}\times \left(1-\text{x}\right)+E_{\text{Ba}}\times \text{x}\\ +E_{\text{Sn}}\times \left(1-\text{y}\right)+E_{\text{Si}}\times \text{y}+E_{\text{S}}\times 4)\end{array}$ (1)

whereas $E_{{\text{Cu}}_{\text{2}}{\text{Zn}}_{1-\text{x}}{\text{Ba}}_{\text{x}}{\text{Sn}}_{1-\text{y}}{\text{Si}}_{\text{y}}{\text{S}}_4}$ determined the ground state energy of the structures, E_Cu, E_Zn, E_Ba, E_Sn, E_S determines the energy of Cu, Zn, Ba, Sn, Si, S atoms respectively.

To get optical properties, the complex dielectric function is represented as

$\epsilon \left(\omega \right)={\epsilon }_1\left(\omega \right)+i{\epsilon }_2\left(\omega \right)$ (2)

The real portion of dielectric constant ε₁(ω) affects light polarization and absorption within a material under external electric field impact. The imaginary portion of dielectric constant ε₂(ω) represents the loss of molecular polarization due to variations in the external electric field. Dielectric function reveals solid’s band structure and spectral information [36] .

Refractive index can be expressed as a frequency-dependent complex function,

$N\left(\omega \right)=n\left(\omega \right)+i\kappa \left(\omega \right)$ (3)

where n(ω) represents the refractive index and k(ω) represents the extinction index. These values have been determined by analyzing the real and imaginary parts of the dielectric function, as mentioned previously [37] .

In the present work, the structural, electronic, and optical properties of Cu₂Zn_1−xBa_xSn_1−ySi_yS₄ compounds have been studied using GGA-PBE functional via DFT analysis. The optimized structural calculation for pure and doped CZTS compound shows that pure and fully doped (x, y = 1) CZTS compound crystallized in tetragonal structure. There are some structural deviations from tetragonal structure in the case of doped structures for x, y = 0.25, 0.5, and 0.75. The change in lattice parameters due to doping has been shown for 0% and 100% doping concentration, the crystal structure remained the same that is tetragonal crystal structure. The electronic band gaps have been increased gradually with the increase of doping concentration in the CZTS compound. The highest band gap has been found for Cu₂BaSiS₄ by 1.117 eV for fully doped CZTS compound. The obtained results for band gap identified that the present studied CZTS compounds are potential candidate as semiconductor. For all the doping concentration, the absorption coefficient is high (>10⁴ cm⁻¹) in UV-region as result these structures might be used as an absorber layer in UV detector. All the structures have a photoconductive nature with minimal loss function, making them potentially suitable for application in optoelectronic devices (OE). Refractive index and reflectivity indicate significant photon energy loss, which can be enhanced by modifying experimental work. The studied compound is promising, and it should be realized experimentally to verify the theoretical observations.

Data sharing is not applicable to this article as no datasets were generated or analyzed during the current study. (The article describes entirely theoretical research.)