AB-INITIO STUDY OF STRUCTURAL, ELECTRONIC AND OPTICAL PROPERTIES OF ZnX (X = Te, S and O): APPLICATION TO PHOTOVOLTAIC SOLAR CELLS

The purpose of this research is to investigate the structural, electronic, and optical properties of ZnX compounds, particularly those with X = Te, S


I. INTRODUCTION
Zinc monochalcogenides (ZnX: X = O, S, Se and Te) are considered the prototype of II-VI semiconductors and can crystallize in either the zinc-blende (z) or wurtzite (w) type structures.The ZnX-z phases are optically isotropic, while the ZnX-w phases are anisotropic, with c serving as the polar axis [1].Due to their optical properties, ZnX phases are considered prime candidates for use in optical devices, such as visual displays, high-density optical memories, transparent conductors, solid-state laser devices, photodetectors, and solar cells [1].Thus, understanding the optical properties of these materials is crucial in designing and analyzing ZnX-based optoelectronic devices [1].ZnO, with a wide direct band-gap of approximately 3.37 eV at room temperature, is a typical semiconductor used for optoelectronic applications.It also possesses transparent properties in visible light and is non-toxic since zinc is abundant in the earth [2].
ZnS, ZnSe, and ZnTe are part of a family of IIB-VIA compounds that crystallize in the cubic zinc-blende structure at ambient pressure and have direct energy band-gaps [3].These wide band-gap semiconductors are of significant interest since they are capable of emitting light even at room temperature [4].Zinc Telluride (ZnTe) is of particular interest due to its low cost, high optical absorption coefficient, and suitability for use in PV applications [5].It has also made extensive contributions to the field of microelectronics and optoelectronics applications [6].Researchers have conducted various studies to investigate the electronic, structural, and dynamic properties of zinc-based semiconductors, such as Agrawal et al., who used ab-initio to calculate these properties [7].D. Bahri et al. investigated the structural, electronic, and optical properties of ZnTe cubic zinc-blende phase with the space group F-43m [8].J. Serrano et al. used ab-initio to study the network dynamics of ZnO [9].P. Walter et al. calculated the electronic energy band structures of ZnTe and ZnSe using the experimental pseudo-voltage method, which included spin-orbit coupling [10].
The focus of current research is on investigating the structural, electronic, and optical properties of ZnX (X = Te, S, and O) for potential photovoltaic applications, using the Density Functional Theory and GGA/PBE gradient approximation.

II. COMPUTATIONAL DETAILS
In this research, we utilized the CASTEP software [11] to analyze the structural, electronic, and optical characteristics of ZnX compounds, where X denotes Te, S, and O.The compounds have a space group of (216 F-43m, 186 P-63mc, 186 P-63mc), respectively.Through our assessments, we determined that (8×8×8) BZ k-point cell densities and planar wave discontinuities of 750 eV for ZnTe, 850 eV for ZnS, and 800 eV for ZnO were adequate.In general, the
GGA approach is preferred over LDA because LDA tends to underestimate the lattice parameters and cell volume, whereas GGA overestimates them.To approximate the GGA method, we used the Perdew-Burke-Ernzerhof [12] approach to estimate the band gap.We conducted geometric optimization with a precision of 1 × 10 -5 eV/atom and we used the Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm to relax at the lowest energy levels, with force, pressure, and displacement values set at 0.001 eV/A, 0.05 GPa, and 5.0× 10 -4 Å, respectively.We examined the electronic structures and other optical properties using total and partial densities of states, such as TDOS and PDOS, to achieve a more refined geometry.
Ⅲ. RESULTS AND DISCUSSIONS a. Structural Properties In the first stage of our study, we performed calculations to determine the equilibrium structural parameters of ZnX (X = Te, S, and O), including the lattice constant a0, size modulus B0, and its first derivative B0'.The crystal structure of ZnX (X = Te, S, and O) is shown in Fig. 1.We focused on investigating the structural properties of ZnX and optimizing the lattice constants, and the results are presented in Table 1.The accuracy and validity of our research are confirmed by comparing our findings with existing theoretical and experimental data (as shown in Table 1).Our calculations show that the lattice constant a0 is 6.28 Å for ZnTe, 5.62 Å for ZnS, and 3.25 Å for ZnO.These values are slightly larger than the experimentally recorded values of 6.1 Å [13], 5.41 Å [13], and a = 3.249 Å, c = 5.204 Å [9], respectively.However, this discrepancy can be attributed to the difference in the atomic radii of ZnTe, ZnS, and ZnO, as well as the larger total energies, lattice relaxation constants, volume coefficients, and ground state energy of each material.We have optimized the structures of ZnTe, ZnS and ZnO at different pressure by fitting the Murnaghan equation of state [14], which gives the variation of the total energy as a function of the volume and given by: where V 0 , B and B′ are the volume at equilibrium, the bulk modulus and its derivative.The modulus of compressibility and its pressure derivative B 0 ' written as follows: The fits of our data regarding the relative lattice constant a 0 (Å), bulk modulus B 0 (GPa) and the volume are given in Table 1.

b. Electronic properties
The band structure and the total density of states (TDOS) and partial density of states (PDOS) calculated with optimized values were utilized to examine the electronic properties of ZnX (X = Te, S and O).The band-gap energy, particularly, provided insights into the bonding nature.The PBE-GGA approximation was used in the calculations.The computed band-gap of the three compounds revealed that all were semiconducting in nature, as illustrated in Fig. 3.In addition, the direct band-gap values for ZnX (X = Te, S and O) were 2.436, 2.698, and 1.721 eV, respectively.The conduction and valence bands were situated above and below the Fermi level.Both the bottom of the conduction band and the top of the valence band were located at the same point k (G -G), confirming that ZnX (X = Te, S and O) is a direct band-gap.All the calculated band-gap values for ZnX (X = Te, S and O) at 0 GPa are presented in Table 2.All values shown in Table 2 are consistent with theoretical and experimental data reported in other references that employ the PBE-GGA approximation.It is worth noting that the calculated band-gaps were lower than experimental values, which is attributed to the known Kohn-Sham DFT calculation error.The relatively higher band-gap energy of ZnTe, ZnS and ZnO compounds suggests that these compounds could potentially exhibit enhanced optical properties.

c. Density of States
To better understand the band and optical properties of ZnX (X = Te, S and O), it is important to investigate the electronic density of states (DOS) [29] and its relationship with the band structure.In this study, the DOS was determined and its connection with the band structure was examined.The chemical bonding of ZnX was illustrated by counting single atoms using partial DOS (PDOS) and all atoms using total DOS (TDOS).The electronic DOS is a crucial electronic property as it provides a deeper understanding of the band structure.Fig. 4 shows the TDOS and PDOS obtained using the GGA-PBE approximation, with the Fermi level taken as the energy origin.The electron configuration of Zn, Te, S, and O were 3d24s2, 3s23p6, 4s24p65s2, and 2s22p4, respectively.There are two regions, BV and BC, on both sides of the Fermi level: the BV region, dominated by Te-p, S-p, and O-p states, is centered between -5 eV and 0 eV for all three compounds.The second region, BC, centered between 0 eV and 5 eV, is dominated by Zn-s-p, Te-s-p, and S-s-p states.These results are consistent with previous reports.

d. Optical Properties
The investigation of photonic properties is crucial for the studied compounds, as they have potential applications in photovoltaic devices and the semiconductor industry.To describe the optical properties of these materials, the transverse dielectric function ε(ω) [30] is used.The frequency-dependent dielectric constants have been calculated using the following formula: The dielectric function is characterized by the real and imaginary parts, ɛ1(ω) and ɛ2(ω), respectively [31].The real part of ɛ1(ω) corresponds to the dispersion of incident photons by the material, while the imaginary part of ɛ2(ω) represents the energy absorbed by the material.The complex dielectric function ɛ(ω) is made up of two contributions: intraband and interband transitions [31].The contribution from intraband transitions is significant only for metals.The interband transitions can be further divided into direct and indirect transitions.In this study, the indirect interband transitions, which involve phonon scattering and contribute minimally to ɛ(ω), were neglected.
The complex dielectric function components were utilized to determine other optical parameters, including reflectivity R, refractive index n, optical conductivity σ, and absorption ⍺ [32].The equations used to calculate these parameters are as follows: = Ɛ₂  (6) Fig. 5 through 9 depict various optical properties of ZnX (X = Te, S and O), including reflection spectra, absorption spectra, imaginary and real parts of the dielectric function, and photoconductivity.

Reflectivity R
The reflectivity R of a compound ZnX (where X = Te, S, or O) can be accurately predicted using computational tools such as the CASTEP program.For example, CASTEP simulations have shown that ZnTe exhibits a high reflectivity of approximately 96% in the infrared region, which makes it a promising material for infrared detectors and solar cells.Similarly, ZnS and ZnO have been found to exhibit high reflectivity in the visible and ultraviolet regions, respectively, with values reaching up to 87% and 96%.By tuning the composition and morphology of ZnX compounds, researchers can manipulate their reflectivity to suit specific applications.For instance, by growing ZnO thin films with a specific orientation, researchers can achieve high reflectivity of visible light while maintaining transparency.
Our analysis, as presented in Fig. 5, reveals that the reflectivity peaks of ZnTe, ZnS, and ZnO compounds increase at low energy (up to 7 eV), and decrease significantly at high energy (below 20 eV), as the forbidden bandwidth reduces.

Absorption A
The absorption, denoted by A, is an important optical property of materials that describes the amount of light absorbed by the material.The absorption of ZnX compounds, where X can be Te, S, or O, can be accurately predicted using computational tools such as the CASTEP program.The results have shown that ZnTe has a high absorption coefficient of approximately 25 × 10 4 cm -1 in the mid-infrared region, making it a promising material for mid-infrared detectors and emitters.Similarly, ZnS and ZnO have been found to exhibit high absorption in the ultraviolet and visible regions, respectively, with values reaching up to 3 × 10 5 cm -1 .By understanding the absorption properties of ZnX compounds, researchers can design materials with specific absorption properties for various optoelectronic applications.
According to our study, when more electrons can be easily excited from the valence band to the conduction band, less energy is required, resulting in a redshift at the absorption edge.In this scenario, the probability of valence band electron guide transitioning to the excited state increases, leading to an obvious increase in the number of absorption peaks.Our findings, presented in Fig. 6, indicate that the maximum transmittance for ZnX (X = Te, S, and O) occurs in the energy regions between 0 eV and 5 eV, which are located in the infrared region.

Refractive index
The refractive index, denoted by n, is an important optical property that characterizes how light propagates through a material.The refractive index of ZnX compounds, where X can be Te, S, or O, can be accurately predicted using computational tools such as the CASTEP program.We have shown that the refractive index of ZnTe is approximately 2.5 in the mid-infrared region, making it a promising material for applications such as infrared lenses and waveguides.Similarly, ZnS and ZnO have been found to exhibit high refractive indices in the ultraviolet and visible regions, respectively, with values reaching up to 2 and 1.9.By understanding the refractive index of ZnX compounds, researchers can design materials with specific optical properties for various optoelectronic applications.

Dielectric function
The dielectric function, denoted by ε, is an important optical property that characterizes the response of a material to an external electric field.The simulation results using CASTEP have shown that the dielectric function of ZnTe is approximately 12 in the mid-infrared region, making it a promising material for applications such as infrared detectors and emitters.Similarly, ZnS and ZnO have been found to exhibit high dielectric functions in the ultraviolet and visible regions, respectively, with values reaching up to 9 and 5.By understanding the dielectric function of ZnX compounds, researchers can design materials with specific optical properties for various optoelectronic applications.

Conductivity
The conductivity, denoted by σ, is an important electronic property that characterizes the ability of a material to conduct electric current.The conductivity of ZnX can be accurately predicted using computational tools such as the CASTEP program.The simulation results have shown that ZnTe has a high electrical conductivity of approximately 7 S/m at room temperature, making it a promising material for applications such as solar cells and thermoelectric devices.ZnS and ZnO materials exhibit moderate to high electrical conductivity, respectively, with values reaching up to 9 and 5 S/m.
Finally, based on the current findings, it can be inferred that the ZnX (X = Te, S and O) materials show promising potential as suitable options for optical and photovoltaic devices.IV.Application to the substrate Cu(In,Ga)Se2 solar cells The conventional method of fabricating Cu(In,Ga)Se 2 (CIGS) thin-film solar cells involves the use of a substrate configuration that incorporates a CdS buffer layer and a doped ZnO or ITO window layer.This configuration has demonstrated conversion efficiencies exceeding 22% [29].The exceptional optoelectronic properties of ZnX (X = Te, Se, S …etc) buffer layers have led to increased attention as a potential alternative to CdS buffer layers in recent years [33].It is widely believed that the buffer layers play a critical role in preventing shunting through the TCO/CIGS interface, and they should possess suitable properties that help to minimize carrier recombination at the buffer/CIGS interface [34].For example, the efficiency of CIGS solar cells decreases significantly due to severe shunting when a conventional ZnO/TCO is directly deposited onto the CIGS layer [35].According to some studies, the buffer layer demonstrated a higher level of electrical resistance compared to the top contact layer, which is highly conductive [30].In this study, the use of ZnTe and ZnS as buffer layers in the substrate CIGS solar cell, along with the incorporation of the ZnO layer as a window layer, were investigated.
IV.1.Device settings and simulation process Fig. 10 shows schematic of the substrate n++-ZnO/n-ZnS/p-Cu(In,Ga)Se2 and n++-ZnO/n-ZnTe/p-Cu(In,Ga)Se 2 solar cell hetero-structures.To study the transport physics of these structures, the SCAPS-1D software solution solves the dipolar issues of the device using the Poisson equation and continuity equations for both electrons and holes.The SCAPS-1D simulator provides a software environment that can accurately replicate the behavior of a real solar cell [32,36].Typically, the simulation process for a solar cell would require following the steps outlined in Fig. 11 through a series of screen-shots.The initial screenshot, labeled (a), displays the standard information input panel of the SCAPS-1D graphical user interface.This panel provides access to input buttons that enable the user to specify the simulation model and view the device's operating conditions, structure, and material parameters.The device simulation utilizes DOS mode.One particular layer's structure and material parameters, along with optical properties and defects, are displayed in screenshot (b).The results of light J-V characteristics in the form of a curve and axes are shown in screenshot (c).The simulation uses AM1.5 illumination spectrum with an incident power of 100 mW/cm 2 .Table 3 summarizes the input parameters of each layer, including thickness, permittivity constant, band gap, electron affinity, electron/hole mobility, effective density of states in conduction/valence band, donor/acceptor concentration, defect concentration, and absorption coefficient within a range of 320 -1100 nm wavelength.The thermal velocity recombination for holes/electrons at front and back contacts is 1.0 × 10 7 cm/s.
All data that have been previously calculated using CASTEP are being considered in the simulation.

IV.2. Effect of CIGS absorber thickness on solar cell performance
In an attempt to determine the most favorable thickness for a high-performance substrate CIGS solar cell that employs ZnTe and ZnS buffer layers, the thickness of the CIGS absorber was modified.

Case of ZnO/n-ZnS/p-CIGS/Mo solar cell structure
It is desirable to reduce the thickness of the absorber layer, d(CIGS), in order to lower costs while still maintaining high performance.ZnTe and ZnS buffer layers can help achieve this goal due to the abundance of these materials.In the calculations, the thickness of the buffer layers is fixed at 100 nm.As shown in Fig. 12, the short-circuit current density (Jsc), open circuit voltage (Voc), Fill Factor (FF), and power conversion efficiency (η) are all affected by the thickness of the CIGS absorber layer.For absorber thicknesses up to 4 µm, Jsc remains around 32.1 mA/cm 2 and Voc is above 0.61 Volt.However, for the thinnest CIGS absorber layer, there is a slight reduction in Voc which may be due to an increased influence of recombination at the Mo back contact layer, resulting in a smaller effective minority carrier lifetime.The fill factor slightly increases but remains above 79% for all absorber thicknesses greater than 4 µm.The short-circuit current density and open circuit voltage show a strong dependence on the absorber thickness, Jsc increases from 29.12 mA/cm 2 to 32.08 mA/cm 2 as the CIGS absorber thickness varies from 1 to 4 µm.For devices thinner than 1 µm, current loss may be due to optical and/or electrical losses.The losses in Jsc and Voc mainly contribute to the conversion efficiency losses.The optimum thickness for the CIGS absorber layer is greater than 4 µm, which results in a maximum conversion efficiency of 15.6% with FF = 78.5%,Voc = 0.61 Volt and Jsc = 32.1 mA/cm 2 .2. Case of ZnO/n-ZnTe/p-CIGS/Mo solar cell structure Fig. 13 presents the performance of ZnO/ZnTe/CIGS/Mo solar cell as a function of CIGS absorber thickness.It shows that the recorded efficiency is 14.66% and 16.58% at the CIGS thickness of 1 µm and 4 µm, respectively.A comparison of these results with the 16.12% efficiency at 2 µm reveals that decreasing the absorber thickness by 1 µm leads to an 11.58% drop in efficiency, whereas increasing it by 1 µm results in only a 3.8% increase in efficiency.This trend continues to hold for absorber thicknesses more than 2 µm.These findings support the theoretical assumption that a thickness of around 2 µm is sufficient to absorb most of the incident light.However, reducing the absorber layer thickness below this value would bring the back contact too close to the depletion region, which would facilitate electron capture by the back contact during the recombination process.The open circuit voltage (Voc) and short circuit current density (Jsc) increase with the thickness of the absorber layer, primarily due to the longer wavelengths' absorption, which contributes to electron-hole pair generation.When d(CIGS) is greater than 4 µm, the maximum Fill Factor of 79.5% is obtained.The highest efficiency of approximately 16.58%, with FF = 79.5%,Voc = 0.61 Volt, and Jsc = 34.05mA/cm 2 can be achieved when d(CIGS) is approximately 4 µm.

III. CONCLUSIONS
The use of computational tools like CASTEP provides a powerful tool for the design and optimization of such materials, enabling the development of advanced optoelectronic devices.In this paper, the electronic structure and optical properties of ZnX systems were studied using the first principles of the ultra-smooth pseudovoltage method of density functional theory and the generalized gradient approximation method using the CASTEP tool.The search showed the following results: The network parameters took different values; Therefore, it is possible to deposit them on different substrates.The binary alloy is interesting, because it has a wide bandgap (2.436 eV, 2.698 eV, 1.721 eV) for ZnTe, ZnS and Zn0, respectively.From the results obtained, the structural, physical and optical properties are in close agreement with the available theoretical and experimental data which indicate the accuracy of the proposed calculation scheme.The properties of pure ZnX (X = Te, S, O) materials indicate that these materials have great potential for use in solar cells.The outcomes of the calculation reveal that although the efficiency grew alongside the absorber thickness, d(CIGS), the pace of this increase was much less beyond 2 µm.The result concludes that the CIGS absorber layer's ideal thickness is likely to exceed 4 µm.ORCID Faiza Benlakhdar, https://orcid.org/0009-0003-1131-6289

Figure 2 .
Figure 2. Total energy versus volume for ZnX (X = Te, S and O) compounds.

Figure 5 .
Figure 5. Reflectivity R as a function of energy of ZnTe, ZnS and ZnO compounds calculated using GGA-PBE approximation.

Figure 6 .
Figure 6.Absorption A as a function of energy of ZnTe, ZnS and ZnO compounds calculated using GGA-PBE approximation

Figure 7 .
Figure 7. Refractive index as a function of energy of ZnTe, ZnS and ZnO compounds calculated using GGA-PBE approximation.

Figure 8 .
Figure 8. Dielectric function as a function of energy of ZnTe, ZnS and ZnO compounds calculated using GGA-PBE approximation.

Figure 9 .
Figure 9. Conductivity as a function of energy of ZnTe, ZnS and ZnO compounds calculated using GGA-PBE approximation.

Figure 12 .
Figure 12.Solar cell performance using ZnS buffer layer as a function of the p-CIGS thickness.

Figure 13 .
Figure 13.Solar cell performance using ZnTe buffer layer as a function of p-CIGS thickness.

Table 2 .
Calculated band-gap value of ZnX at 0 GPa.

Table 3 .
Settings for ZnO, ZnTe, ZnS and Cu(In,Ga)Se2 layers used in the simulation.