**Materials Sciences and Applications** Vol.4 No.1(2013), Article ID:27077,7 pages DOI:10.4236/msa.2013.41008

First Principles Study of Structural and Electronic Properties of O_{x}S_{1−x}Zn Ternary Alloy

^{ }^{ }^{ }^{}

^{1}Department of Physics, University of Djillali Liabes, Sidi Bel-Abbes, Algeria; ^{2}Institute of Nono Electronic Engineering, University Malaysia Perlis, Kangar, Malaysia; ^{3}Modeling and Simulation Materials Sciences Laboratory, Sidi-Bel-Abbès University, Sidi Bel-Abbes, Algeria.

Email: ^{*}lttnsameri@yahoo.fr

Received September 6^{th}, 2012; revised October 12^{th}, 2012; accepted November 2^{nd}, 2012

**Keywords:** FP-LMTO; Ab-Initio; Approach of Zunger; Effective Mass

ABSTRACT

We perform self-consistent ab-initio calculations to study the structural and electronic properties of zinc blende ZnS, ZnO and their alloy. The full-potential muffin-tin orbitals (FP-LMTO) method was employed within density functional theory (DFT) based on local density Approximation (LDA), and generalized gradient approximation (GGA). We analyze composition effect on lattice constants, bulk modulus, band gap and effective mass of the electron. Using the approach of Zunger and coworkers, the microscopic origins of band gap bowing have been detailed and explained. Discussions will be given in comparison with results obtained with other available theoretical and experimental results.

1. Introduction

The II-VI compound semiconductors have recently received considerable interest a lot of experimental and theoretical work on this alloy’s, they were promoted much interest because of their numerous applications in optoelectronic devices such as visual displays, high-density optical memories, transparent conductors, solid-state laser devices, photodetectors, solar cells, etc. for few studies that have been done on this alloy due the difficulty in the synthesis of this material, due to the large electronegativity differences between O and S [1]. From this the purpose of this paper is to illustrate such modifications by providing original ab initio structural and electronic properties for the zinc blende (ZB) alloy with different discrete compositions, namely x = 0, 0.25, 0.50, 0.75, 1 and compare them with ZB ZnS and ZnO. The calculations were carried out within the density functional theory (DFT) [2,3]. Therefore, the main aim of the present study was to investigate the electronic and structural properties of ternary alloy in cubic phase over a wide range of compositions 0 ≤ x ≤ 1 by using the full-potential muffin-tin orbitals (FP-LMTO) method. Various quantities, including lattice parameters, bulk modulus, band gap, optical bowing and effective masses, were obtained for these alloy.

The organization of this paper is as follows: we explain the FP-LMTO computational method in Section 2. In Section 3, the results and discussion for structural and electronic properties are presented. Finally, a conclusion is given in Section 4.

2. Computational Methods

The calculations reported in this work were carried out by FP-LMTO [4,5] within the density functional theory DFT based on local density Approximation LDA [6] and generalized gradient approximation GGA [7]. In this method the space is divided into an interstitial region (IR) and non-overlapping muffin-tin (MT) spheres centered at the atomic sites. In the IR region, the basis functions are represented by Fourier series. Inside the muffin-tin spheres, the basis sets is described by radial solutions of the one-particle Schrödinger equation (at fixed energy) and their energy derivatives multiplied by spherical harmonics. The valence wave functions inside the spheres are expanded up to l_{max} = 6. The k integration over the Brillouin zone is performed using the tetrahedron method [8]. The values of the sphere radii (MTS) and the number of plane waves (NPLW) used in our calculation are listed in Table 1.

3. Results and Discussion

3.1. Structural Properties

The calculations were firstly carried out to determine the structural properties of ZB binary compounds ZnS and ZnO and alloys. To model the ZB structure alloys, we applied a 8-atom supercell. For the considered structures and at different oxygen concentrations x (x = 0, 0.25, 0.50, 0.75, 1), the structural properties were obtained by a minimization of total energy as a function of the volume for ZnS, ZnO and in the ZB structure. The bulk modulus and their pressure derivatives were obtained by a non-linear fit of the total energy versus volume according to the Birche-Murnaghan’s equation of state [9]. In Table 2, we summarize the calculated modulus and their pressure derivatives) of ZnS, ZnO compounds and alloys. Considering the general trend that the GGA usually overestimates the lattice parameters while LDA is expected to underestimates them [10], It is clear that our results are in reasonable agreement with experimental values and theoretical results. Usually, in the treatment of alloys, it is assumed that the atoms are located at the ideal lattice sites and the lattice constant varies linearly with composition x according to the so-called Vegard’s law [30].

Table 1. The plane wave number PW, energy cuttof (in Ry) and the muffin-tin radius (RMT) (in a.u.) used in calculation for binary ZnS and ZnO and their alloy in zinc blende (ZB) structure.

^{}

^{a}Ref. [16], ^{b}Ref. [20].

Table 2. Lattice constants a, bulk modulus B, and pressure derivative of bulk modulus B, for ZB ZnS, ZnO and O_{x}S_{1−x}Zn solid solutions.

^{}

^{a}Ref. [11], ^{b}Ref. [12], ^{c}Ref. [13], ^{d}Ref. [14], ^{e}Ref. [15], ^{f}Ref. [16], ^{g}Ref. [17], ^{h}Ref. [18], ^{i}Ref. [19], ^{j}Ref. [20], ^{k}Ref. [21], ^{l}Ref. [22], ^{m}Ref. [23], ^{n}Ref. [24].

(1)

where a_{AC} and a_{BC} are the equilibrium lattice constants of the binary compounds AC and BC Hence, the lattice constant can be written as:

(2)

where the quadratic term b is the bowing parameter.

Figures 1 and 2 show the variation of the calculated equilibrium lattice constant and the bulk modulus versus concentration for alloy. A slight large deviation from Vegard’s law [30] is clearly visible for the alloy. The bowing parameter determined by LDA, are obtained by fitting the calculated values respectively, is the alloy lattice constant. With a polynomial function we found an upward and downward bowing parameter equal to −0.2359 Å and 142.9979 GPa for lattice and bulk modulus. The GGA results are −0.2887 Å and 142.9981 GPa. The physical origin of this slight large deviation could be mainly due to the large size difference between the O and S atom and the mismatch of the lattice constants of ZnS and ZnO compound.

3.2. Electronic Properties

The calculations of the electronic band structure properties, magnitude of band-gap were carried out for ZnS, ZnO and in ZB structure at the equilibrium calculated lattice constants. The band-gaps calculated using the FP-LMTO method for ZB ZnS, ZnO and are listed in Table 3 for the high-symmetry

Figure 1. Composition dependence of the calculated lattice constants using the GGA (solid squares) and LDA (solid circles) for alloy compared with Vegard’s law (dashed line).

Figure 2. Composition dependence of the calculated bulk modulus using the LDA (solid squares) and GGA (solid circles) of alloy.

points Γ and X in the Brillouin zone. All energies are with reference to the top of the valence band at Γ point. The results show that ZnS and ZnO compound is a direct-gap semiconductor with the minimum of conduction band at Γ point.The calculated GGA (LDA) energy gaps of ZnS and ZnO Eg are 1.97(2.12) eV and 0.69(0.79) eV, respectively, which are in good agreement with the theoretical values as listed in Table 3. Focusing now on the electronic properties of the alloy system we obtained the direct band-gap at Γ point. Figure 3 presents the variation of the direct and indirect band gap energies as functions of the composition x for the ternary alloys. We note direct (Γ-Γ) and indirect (Γ-X) band gap not intersect because the computed band structures of the alloys using both LDA and GGA schemes indicate a direct band gap at various concentrations.

Indeed it is a general trend to describe the bandgap of an alloy A_{x}B_{1−x}C in terms of the pure compound energy gap E_{AC} and E_{BC} by the sem-empirical formula:

(3)

where E_{AC} and E_{BC} corresponds to the gap of the ZnO and ZnS for the O_{x}S_{1}_{−}_{x}Zn alloy. The calculated band gap versus concentration was fitted by a polynomial equation. The results are shown in Figure 3 and are summarized as follows

(4)

In order to better understand the physical origins of the large and composition-dependent bowing in alloy alloys, we follow the procedure of Bernard and Zunger [31] and decompose the total bowing parameter b into physically distinct contributions. The overall bowing

Figure 3. Direct and indirect band gap energies as a function of O composition using the LDA and GGA of alloy.

Table 3. Direct (Γ–Γ) and indirect (Γ–X) band gaps of ZnS and ZnO and their alloy at equilibrium volume (The energy is given in eV).

^{}

^{a}Ref. [25], ^{b}Ref. [14], ^{c}Ref. [15], ^{d}Ref. [26], ^{e}Ref. [16], ^{f}Ref. [13], ^{g}Ref. [18], ^{h}Ref. [27], ^{i}Ref. [19], ^{j}Ref. [28].

coefficient at a given average composition x measures the change in band gap according to the formal reaction.

(5)

where a_{AC} and a_{BC} are the equilibrium lattice constants of the binary compounds. which a_{eq} is the equilibrium lattice constant of the alloy with the average composition x.

We decompose reaction into three step:

(6)

, (7)

. (8)

The first contribution, the volume deformation (b_{VD}) represents the relative response of the band structure of the binary compounds AC and BC to hydrostatic pressure. The second contribution, the charge-exchange (CE) contribution b_{CE}, reflects a charge-transfer effect that is due to the different (averaged) bonding behavior at the lattice constant a. The final step measures by b_{SR}, changes due to the structural relaxation (SR) in passing from the unrelaxed to the relaxed alloy. Consequently, the total gap bowing parameter is defined as

. (9)

The general representation of the composition-dependent band gap of the alloys in terms of binary compounds gaps of the, and, and the total bowing parameter b is

(10)

where, and represents respectively the volume deformation (VD) effect, the charge exchange (CE) contribution and the structural relaxation (SR) of the alloy according to the following expressions:

, (11)

, (12)

. (13)

The addition of the three contributions (11), (12), and (13) leads to the total bowing parameter b. The computed bowing coefficients b together with the three different contributions for the band gaps as a function of the molar fraction (x = 0.25, 0.5 and 0.75) are shown in the Table 4. The calculated band gap bowing parameter exhibits a strong composition dependence, as calculated within the GGA and LDA calculations, which show a weakly composition dependent bowing parameter. The variation of the band gap bowing versus concentration shown in Figure 4. The bowing remains linear and Decreases rapidly from x = 0.25 to x = 0.75 in both approaches (GGA and LDA). The calculated GGA and LDA gap bowing for alloy ranges from 0.69 eV, 1.25 eV (x = 0.25) to −0.59 eV, −0.55 eV (x = 0.75), a negligible volume deformation term was registered for system can be correlated to the large mismatch of the lattice constants of the corresponding binary compounds between ZnS and ZnO. The charge transfer contribution b_{CE} has been found greater than. This contribution is due to the different electronegativities of the O and S or Zn atoms. Indeed, scales with the electronegativity mismatch. The contribution of the structural relaxation is small, the band gap bowing is due essentially charge exchange effect.

Table 4. Decomposition of optical bowing into VD, CE and SR contributions compared with other prediction.

Figure 4. Composition dependence of the calculated band gap bowing parameter using LDA (Solid Square) and GGA (Solid Circle).

Table 5. Electron () light hole () and heavy hole () effective masses (in units of free electron mass) at the point of the Brillouin zone of the ternary alloys under investigation compared with the available experimental and theoretical predictions.

^{}

^{a}Ref. [29], ^{b}Ref. [14], ^{c}Ref. [13],^{d}Ref. [27], ^{e}Ref. [15].

3.3. Effective Masses

It is also interesting to discuss at the end of the band structure study the effective masses of electrons and holes, which are important for the excitonic compounds. We have calculated the effective masses of electrons and holes using both LDA and GGA schemes are mentioned in Table 5. A theoretical effective mass in general turns out to be a tensor with nine components. However, for a very idealized simple case where E(k is a parabola at k = 0 (high symmetry point Γ) the effective mass becomes a scalar.

4. Conclusion

In summary, we have studied the electronic, structural properties of alloys by using the FP-LMTO method. We found a slight large deviation from Vegard’s law for the lattice constant of. The physical origin of this effect should be mainly due to the significant mismatch between the lattice constants of ZnS and ZnO compounds. Particular attention has been paid to the gap bowing, which exhibits linear behaviour versus the concentration. In addition, we have computed the effective masses of the electron (hole), which increases with the composition x. Our results are compared to other theoretical and experiment values.

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NOTES

^{*}Corresponding author.