Coefficient of Diffusion in Crystals of Si<sub>1-x</sub>Ge<sub>x</sub>: Role of Preexponential Factor

Abstract

In the present work the results of theoretical analysis of the process of diffusion of covalently bonded atoms (interstitial oxygen atoms) in Si1-xGex alloys are presented. The diffusion coefficient (activation energy and pre-exponential factor) was calculated by means of quantum-chemical simulations (Hartree–Fock, NDDO, PM5) and the dependences of the activation energy and pre-exponential factor on Ge atoms concentration (x) were analyzed with the use of the percolation theory. The study has revealed that the diffusivity of impurities (defects) in alloys can decrease considerably at low concentration (x<0.05) of a minor alloy component and this variation results from the fact that the pre-exponential factor depends on the concentration of component elements of the alloy. The alloy-induced decrease in the pre-exponential factor is associated with removal of the degeneracy of the number of equivalent diffusion paths. It is found that a sharp decrease in the pre-exponential factor causes experimentally observed decreases in the coefficient of diffusion of interstitial oxygen atoms and in the rate of formation of oxygen thermal donors in Si1‑xGex crystals at x~0.01.