Strain relaxation mechanisms and local structural changes inSi1−xGexalloys

Abstract

In this work, we address issues pertinent to the understanding of the structural and electronic properties of ${\mathrm{Si}}_{1\ensuremath{-}x}{\mathrm{Ge}}_{x}$ alloys, namely, (i) how does the lattice constant mismatch between bulk Si and bulk Ge manifest itself in the alloy system? and (ii) what are the relevant strain release mechanisms? To provide answers to these questions, we have carried out an in-depth study of the changes in the local geometric and electronic structures arising from the strain relaxation in ${\mathrm{Si}}_{1\ensuremath{-}x}{\mathrm{Ge}}_{x}$ alloys. We first compute the optimized lattice constant for different compositions (x) by fully relaxing the system and by minimizing the total energy with respect to the lattice constant at each composition, using an ab initio molecular dynamics scheme. The optimized lattice constant, while exhibiting a general trend of linear dependence on the composition (Vegard's law), shows a negative deviation from Vegard's law in the vicinity of $x=0.5.$ We delineate the mechanisms responsible for each one of the above features. We show that the radial-strain relaxation through bond stretching is responsible for the overall trend of linear dependence of the lattice constant on the composition. On the other hand, the negative deviation from Vegard's law is shown to arise from the angular-strain relaxation. More specifically, the combined effect of the local bond-angle deviations from the tetrahedral angle and the magnitudes of the corresponding peaks for the partial-angle distribution function determines the negative deviation from Vegard's law. The electronic origin of the changes in the local geometric structure due to strain relaxation is also presented in this work. In particular, the correlation between the bond charges and the bond-lengths for Si-Si, Ge-Ge, and Si-Ge pairs in ${\mathrm{Si}}_{1\ensuremath{-}x}{\mathrm{Ge}}_{x}$ alloys for different compositions is explicitly shown. Our calculation of the average coordination number as a function of composition indicates a random occupation of Si and Ge on the lattice sites, suggesting that Si and Ge atoms are fully miscible in the alloy system.