“Migration energy” for impurity diffusion in crystalline solids: A closer look

Ramanarayanan, Panchapakesan; Srinivasan, Balaji; Cho, Kyeongjae; Clemens, Bruce M.
December 2004
Journal of Applied Physics;12/15/2004, Vol. 96 Issue 12, p7095
Academic Journal
Point defect mediated diffusion of impurities in crystalline materials involves a sequence of several processes, which are repeated in varying combinations a multiple number of times. The concept of “activation energy” has been borrowed from simple chemical reactions, where the reactants are postulated to form an activated complex before decomposing into products. While ideas such as the smallest rate (or the rates of a select few “important” processes) being the rate determining step and hence the overall activation energy may be applicable in the case of chemical reactions that are sequential, such ideas are shown to be too simplistic to be applicable to describe diffusion in the crystalline phase. In this paper, we present a systematic scheme to arrive at the macroscopic activation energy in terms of the energy barriers for the constituent microscopic processes. We apply this scheme to the case of vacancy mediated diffusion of impurities in a diamond lattice. We present results of numerical verification of the scheme performed by kinetic Monte Carlo simulations based on the energy barriers obtained using the density functional theory within the local density approximation. We then present observations on the dependence of the macroscopic “migration energy” on the energy barriers for the constituent microscopic processes. As an illustration of how the energy barriers for the microscopic processes can be affected, we present first principles calculation of the effect of biaxial strain on these energy barriers.


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