Vacancy-mediated diffusion in disordered alloys: Ge self-diffusion inSi1−xGex

Abstract

A model is proposed for vacancy mediated diffusion in disordered alloys, with particular application to Ge self-diffusion in ${\mathrm{Si}}_{1\ensuremath{-}x}{\mathrm{Ge}}_{x}.$ We argue that if the vacancies formation energies (VFE) have a strong dependence on the configuration of nearest neighbor (NN) atoms, there will be preferential diffusion paths for some concentrations. For ${\mathrm{Si}}_{1\ensuremath{-}x}{\mathrm{Ge}}_{x}$ we show that the VFE vary linearly from 2 to 3 eV as the number of NN Ge atoms varies from 4 to 0. Thus, the equilibrium population of the various kinds of vacancies changes significantly with x, and the diffusion proceeds by paths that do not necessarily resemble the concentration of the alloy.