It was recalled that point defect mediated diffusion of impurities in crystalline materials involved a sequence of processes which were repeated many times in various combinations. The concept of activation energy had been borrowed from simple chemical reactions, where reactants were posited to form an activated complex before decomposing into products. Whereas such ideas, as the lowest rate being the rate-determining step and a consequent overall activation energy, were applicable to sequential chemical reactions, they were shown to be too simplistic to be applicable to diffusion in a crystalline phase. Here, a systematic scheme was presented for arriving at a macroscopic activation energy in terms of the energy barriers for constituent microscopic processes. This scheme was applied to the case of vacancy-mediated diffusion of impurities in a diamond lattice. The results were presented, of numerical verification of the scheme performed by kinetic Monte Carlo simulations based upon the energy barriers obtained via density functional theory within the local density approximation. Observations on the dependence of the macroscopic migration energy upon the energy barriers for the constituent microscopic processes were then presented. As an illustration of how the energy barriers for the microscopic processes could be affected, first-principles calculation were made of the effect of biaxial strain upon these energy barriers.

“Migration Energy” for Impurity Diffusion in Crystalline Solids - a Closer Look. P.Ramanarayanan, B.Srinivasan, K.Cho, B.M.Clemens: Journal of Applied Physics, 2004, 96[12], 7095-107