Effect of composition on vacancy mediated diffusion in random binary alloys: First principles study of the Si1−xGex system

Abstract

We present the results of a systematic study using the density functional theory (within the local density approximation) of the effect of composition on the self-diffusion of silicon and germanium in silicon–germanium alloys diffusing by a vacancy mechanism. The composition dependence of the vacancy formation energy was calculated. A database of ab initio migration energy barriers for vacancy migration in different local environments was systematically developed by considering the effect of the first nearest neighbor sites explicitly and the effect of the other sites by a mean field approximation. A kinetic Monte Carlo simulation based on the migration energy barrier database was performed to determine the dependence (on the composition) of the activation energy for the diffusion of Si and Ge in Si1−xGex. A detailed study of the variation of the correlation factor with composition and temperature in Si1−xGex was performed using the results of the kinetic Monte Carlo simulation. These analyses constitute essential building blocks to understand the mechanism of vacancy mediated diffusion processes at the microscopic level.