Macroscopic description of the diffusion of interstitial impurity atoms considering the influence of elastic stress on the drift of interstitial species

Abstract

The diffusion equation for non-equilibrium interstitial impurity atoms taking into account their charge states and drift of all mobile interstitial species in the built-in electric field and in the field of elastic stress is obtained. The obtained generalized equation is equivalent to the set of diffusion equations written for the interstitial impurity atoms in each individual charge state. Due to a number of characteristic features the generalized equation is more convenient for numerical solution than the original system of separate diffusion equations. On this basis, the macroscopic description of stress-mediated impurity diffusion due to a kick-out mechanism is obtained. It is supposed that the interstitial impurity atom makes a number of jumps before conversion to the substitutional position. At the same time, local equilibrium prevails between substitutionally dissolved impurity atoms, non-equilibrium self-interstitials, and interstitial impurity atoms. Also, the derived equation for impurity diffusion due to the kick-out mechanism takes into account all charge states of interstitial impurity atoms as well as drift of interstitial species in the electric field and in the field of elastic stress. Moreover, this equation exactly matches the equation of stress-mediated impurity diffusion due to the generation, migration, and dissociation of the equilibrium ‘impurity atom–self-interstitial’ pairs.