Optical investigations using ultra-soft pseudopotential calculations of Si0.5Ge0.5 alloy

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Abstract

Ultra-soft pseudopotential (US-PP) calculations with a powerful package called VASP (Vienna ab initio simulation package) are used. The total density of state and the energy gap of Si0.5Ge0.5 alloy of zinc-blende structure are calculated using the band structure scheme. The energy gap is found to be indirect for the zinc-blende structure. The results of refractive index and optical dielectric constant of Si0.5Ge0.5 alloy are investigated. The results are in reasonable agreement with experimental and theoretical ones.

Introduction

Group-IV semiconductor alloys have immense potential for technological applications. Many kinds of electronic and opto-electronic devices in strained layers Si1−xGex/Si heterostructures have been realized [1]. Alloys and ordered compounds of Si–Ge may also have particular unique opto-electronic properties for applications in quantum-well intersubband technology [2]. Moreover, SiGe alloys suggest many interesting possibilities for the future. Several companies offer SiGe circuits with considerable performance advantages over conventional devices [3]. The rapid demonstration of new SiGe-based devices has preceded fundamental measurements of material parameters which influence device performance [4].

Band structure engineering is one of the most fascinating aspects of modern semiconductor physics. The formation of the semiconductor alloys causes a change in the electronic structure of semiconductors. Recently, there has been a strong revival of interest in the electronic properties of Si1−xGex alloys in the context of superlattice physics [5]. Therefore, the investigation of the electronic band structure of Si1−xGex alloys has attracted considerable interest. The existing calculations are: virtual-crystal approximation (VCA) applied with empirical pseudopotential [6], tight-binding model [7] and with self-consistent pseudopotential; other calculations were carried out with coherent potential approximation (CPA) [8], [9].

There are numerous theoretical calculations of the band gaps, with varying degrees of sophistication. Empirical pseudopotential [10], [11] calculations have been presented. These calculations require a large number of fitting parameters to obtain acceptable agreement with the experimental results [12]. This makes their usefulness limited, and the method less fundamental than the first-principles calculations. The first-principles calculations, on the other hand, are technically involved and computationally time consuming. Due to the well-known problem [13] of using ground state of density-functional theory (DFT) to calculate the electronic band structure of semiconductors and insulators, the energy gap is underestimated by as much as 50%–100%. However, the starting point of such calculations is the results of self-consistent DFT calculations, which are used to compute complex many-body corrections to the ab initio band gaps. This is a complicated and CPU-intensive process.

Shen et al. [14] have illustrated the lattice constant of Si1−xGex alloys and the bond length to be simply predicted. Equation (1) in Ref. [14] has used to calculate the average bond length for Si1−xGex alloys. On the basis of Vegard’s picture [15], the lattice constant is given simply as 4d/3. Si1−xGex alloy is one of the useful semiconductor materials to form solid solutions over the entire composition range. It is determined by x-ray diffraction and extends x-ray absorption fine-structure (EXAFS) experiments [14].

Theoretical investigation studies of pressure-induced phase transition in the SiGe alloy are presented using fully ab initio approach based on DFT and LDA [16] and first-principles pseudopotential approaches [17]. These results are noticed in comparison with the experimental value of transition pressure.

The aim of the present paper is to present a self-consistent electronic structure study for Si0.5Ge0.5 alloy. Ultra-soft pseudopotential (US-PP) calculations with a powerful package called VASP (Vienna ab initio simulation package) have been used to calculate the energy gap of the electronic properties and to investigate the optical properties of Si0.5Ge0.5 alloy. The later is based on specific relationships.

Section snippets

Computational method

The density-functional theory is applied within the local-density approximation (LDA) [18] on the plane wave basis, and we have used the Ceperley and Alder [19] exchange correlation as parametrized by Perdew and Zunger (CA–PZ) [20]. An energy cutoff 13.83 Ry is used for Si, Ge and Si0.5Ge0.5 alloy (corresponding to approximately 262 planes waves). The total energy is calculated self-consistently with a grid of 6 × 6 × 6 k points [21] in the full Brillouin zone, reduced to a smaller set

Electronic properties

Before presenting the results for Si0.5Ge0.5 alloy, we will establish the reference results for Si and Ge. Table 1 compares the calculated equilibrium lattice constants and bulk moduli of Si and Ge with experimental and theoretical results. The agreement is noticed. Having established the reliability of our computational scheme for Si and Ge, we next turn to Si0.5Ge0.5 alloy. For the calculation of Si0.5Ge0.5 alloy we adopted a zinc-blende structure.

The band structure of Si0.5Ge0.5 alloy for

Conclusion

Electronic band structure and density of state of Si0.5Ge0.5 alloy are calculated using Ultra-soft pseudopotential (US-PP) calculations with a powerful package called VASP (Vienna ab initio simulation package). It is shown that Si0.5Ge0.5 alloy is found to be a semiconductor with a small indirect band gap. The results of the optical dielectric constant and refractive index of Si0.5Ge0.5 alloy are investigated. A good agreement with experimental (structural properties) and theoretical (energetic

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