A diffusion equation was obtained, for non-equilibrium interstitial impurity atoms, which took account of their charge states and of the drift of all mobile interstitial species in the built-in electric field and in the field of elastic stress. The resultant generalized equation was equivalent to the set of diffusion equations for the interstitial impurity atoms in each individual charge state. Due to various characteristic features, the generalized equation was more convenient for numerical solution than was the original system of separate diffusion equations. Due to this, the macroscopic description of stress-mediated impurity diffusion due to a kick-out mechanism was obtained. It was supposed that an interstitial impurity atom made a number of jumps before conversion into the substitutional position. At the same time, local equilibrium held between substitutionally dissolved impurity atoms, non-equilibrium self-interstitials and interstitial impurity atoms. The equation derived for impurity diffusion due to the kick-out mechanism also took account of all of the charge states of interstitial impurity atoms as well as of the drift of interstitial species in the electric field and in the field of elastic stress. Moreover, this equation exactly matched the equation of stress-mediated impurity diffusion due to the generation, migration and dissociation of the equilibrium so-called impurity-atom-self-interstitial pairs.

Macroscopic Description of the Diffusion of Interstitial Impurity Atoms Considering the Influence of Elastic Stress on the Drift of Interstitial Species. O.I.Velichko: Philosophical Magazine, 2008, 88[10], 1477-91