Growth Kinetics on Nanoscale: Finite Diffusion Permeability of Interfaces

Abstract

Growth kinetic is either diffusion or interface reaction controlled process, characterized by parabolic or linear relationships, respectively. The well known diffusion paradox, predicting infinitely fast diffusion kinetics at short times (distances) for diffusion control will be discussed and resolved, by showing that the diffusion permeability across the interface should be finite at the very beginning of the process. Thus one can arrive at an atomistic interpretation of the interface transfer coefficient, K, and at linear growth kinetics even if there is no extra potential barrier present at the interface, usually assumed in the interpretation of interface reaction control. It is also shown that this phenomenon is a typical nanoeffect: after a certain diffusion distance (lying between 0.01 and 300 nm, depending on the composition dependence of the diffusion coefficient) the finite permeability of the interface will not restrict the growth and normal diffusion control will be observed.