View of AB-INITIO STUDY OF ELECTRONIC STRUCTURE AND ELASTIC PROPERTIES OF ZNS

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ACCENT JOURNAL OF ECONOMICS ECOLOGY & ENGINEERING Peer Reviewed and Refereed Journal (International Journal) ISSN-2456-1037

Vol. 05,Special Issue 02, (IC-IRSHEM-2020) February 2020, Available Online: www.ajeee.co.in/index.php/AJEEE

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AB-INITIO STUDY OF ELECTRONIC STRUCTURE AND ELASTIC PROPERTIES OF ZNS Saroj Dhaka¹, Garima², and H. S. Mund³

1Rajguru College, Kabari Dungri, Sherawtpura Mundota, Kalwad, Amer, Jaipur, Rajasthan-303701, India

2III/74, Gandhi Nagar, Jaipur, Rajasthan-302015, India

3Department of Physics, Kamla Rai College, Gopalganj (J. P. University, Chapra), Bihar-841428, India

Abstract:- The electronic structure and elastic properties of ZnS have been reported in this paper using the linear combination of atomic orbitals (LCAO) method within the framework of density functional theory. Different exchange-correlation functionals are taken into account within the local density approximation and generalized gradient approximation.

The energy bands, density of states, lattice parameters, elastic constants, shear modulus, Young’s modulus, Poisson’s ratio and bulk modulus along with pressure derivative of the bulk modulus have computed by calculating the ground state energy of ZnS.

Keywords:- Band structure, Equation of state, LCAO method.

PACS:- 71.20.-b, 64.30.Ef, 71.15.Mb.

1. INTRODUCTION

Zinc sulfide (ZnS) is an imperative semiconducting compound of the II-VI group with a broad and direct bandgap at room temperature. It has large industrial applications in modern technologies such as high-density optical memories, photodetectors, solar cells, projection television, blue-light diodes, and electro-luminescence [1-6, 9-12]. The physical and mechanical applications are widely achieved by the structural and elastic properties of ZnS.

In the present work, the electronic properties like energy bands, density of state (DOS) and elastic properties (such as elastic constants, shear modulus, Young’s modulus, Poisson’s ratio), lattice parameters, bulk modulus and it’s pressure derivative of ZnS semiconducting compound have investigated using local density approximation (LDA) and generalized gradient approximation (GGA) scheme under density functional theory (DFT) within LCAO model.

2. COMPUTATIONAL DETAILS

The quantum mechanical CRYSTAL17 package based on the LCAO approach, in which the crystalline orbitals are expanded over the Gaussian basis sets of the atomic orbital’s have been employed for the present computations [7]. A variety of schemes, namely Hartree–Fock (HF), DFT with LDA and GGA, second-order corrected GGA (SO-GGA), hybridization of DFT and HF (known as B3LYP), etc. employed within this code.

In present calculations, the performance of different exchange-correlation effects is taken into account using the LYP, PWGGA, and PBE functional under the GGA scheme, while PZ and VWN useful used under LDA scheme. For the calculations, self-consistency has been achieved using 12x12x12 k points in the irreducible Brillouin zone. The minimum ground state SCF energy (-2177.7697 a.u.) has found for the PWGGA functional within GGA scheme.

3. RESULTS AND DISCUSSION

The structural parameters and elastic properties, like lattice constants, bulk modulus and pressure derivative of bulk modulus have been calculated by performing the structural optimization of the cubic phase of ZnS using different functional of LDA and GGA schemes by fitting the Murnaghan equation of states [8] to the total energies. The obtained results from various DFT schemes are given in Table 1, along with the available experimental and theoretical studies.

The minimum ground state SCF energy has found for the PWGGA functional within the GGA scheme using the equilibrium lattice parameter 5.4943 Å. The band structure, DOS and Compton profile anisotropies are obtained using the equilibrium lattice parameter within the PWGGA scheme. The total energy variation as a function of volume using PWGGA scheme for cubic ZnS is shown in Fig. 1. The total and partial density of states

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along-with electron dispersion curves (energy bands) along the high symmetry directions in the Brillouin zone are shown in Figs. 2 and 3 within PWGGA scheme.

Figure 1. Energy volume curves for ZnS using DFTPWGGA scheme.

Figure 2. Total and partial DOS of ZnS using PWGGA scheme.

Table 1. The calculated lattice constant a (in Ǻ), bulk modulus B (in GPa), pressure derivative of bulk modulus (Bʹ), elastic constants Cij (in GPa), shear modulus G (in GPa), Young’s modulus E (in GPa), Poisson’s ratio σ and Band gap (Eg in eV) along-with the available experimental and theoretical data.

The band structure calculation shows that valence band maximum and conduction band minimum are to be found at the Γ point in the first Brillouin zone, which confirms it as the direct band gap semiconductor with a band gap 2.09 eV. The calculated band gap results are tabulated in Table-1 with the earlier results, which show that calculated band gaps are smaller than experimental band gaps due to the underestimation band gap of LDA and GGA. From DOS, a sharp peak arises in valance region near to -6 eV manly due to p

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orbitals of S, while below the Fermi level between -5 eV to 0 eV the DOS arises due to hybridization of Zn sp and d orbitals with sp orbitals of S.

In conduction region, most of DOS arises due to the hybridization of sp orbitals of Zn with the p-orbitals of S. Thus, ZnS have covalent bonding characteristics. The earlier reported data verify the computed/calculated results. In real and momentum space, the electron density is one of the essential ground state property to characterize material properties [13, 14]. The Compton Profiles (CPs) have been calculated along [100], [110] and [111] directions to compute the anisotropy in momentum density. Fig. 4 shows the anisotropic CPs along [100]–[110], [100]–[111] and [110]–[111]. It is found that anisotropy in the high momentum densities side (pz≥4.0 a.u.) is almost negligible due to the dominancy of core electrons in this part whose contribution cancels while taking the directional differences.

The trend of anisotropies can be understood based on energy bands and degenerate states in the vicinity of EF in the particular branch of the Brillouin zone. The oscillations in anisotropies depend upon of degenerate states and crossovers in the energy bands at Fermi energy. From Fig. 4, the maximum anisotropy is found between [100] and [110] directions at 𝑝𝑧 = 0.8 a.u. The present anisotropy data are in reasonable agreement with the available data [15]. The anisotropy along [110]-[111] can be explained on the basis of extheistence of degenerate states along Γ-L [111] and Γ-X [110] branches as shown in Fig. 3. At the Γ point, more degenerate states are found along Γ-X branch then Γ-L branch.

Figure 3. Band structure along high symmetry direction of Brillouin zone within PWGGA scheme.

Figure 4. PWGGA scheme based Compton profile anisotropies of ZnS, which calculated along with the principal directions [100], [110] and [111].

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4 5. ACKNOWLEDGMENT

The author is thankful to Prof. Dovesi for providing the CRYSTAL17 code.

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