On diffusion theory in inhomogeneous media: Thin-film source of diffusant

Using asymptotic methods in the theory of differential equations, the original solution of the atomic diffusion problem in the semi-infinite inhomogeneous medium has been obtained for the thin-film (instantaneous) source of diffusant and arbitrary coordinate dependence of the diffusion coefficient. We have mathematically estimated the applicability of this solution and compared it numerically with the known exact solution for a particular case of the exponential coordinate dependence of the diffusion coefficient and a trivial case of the constant diffusion coefficient. Based on our analysis, the ranges of annealing times and depths of diffusant penetration for which the suggested approach proves to be correct have been established.