Traveling waves of step density and solution supersaturation in the assigned diffusion layer thickness model of step bunching

Abstract

Step bunching in crystal growth from solutions is investigated theoretically in the approximation of nonstationary mass transfer in a diffusion layer of assigned thickness. It is shown that this model is described by a set of equations including a diffusion equation for a diffusion layer, a one-dimensional step motion equation, the boundary conditions relating these equations, and the boundary condition at the diffusion layer boundary. This set of equations has solutions in the form of coupled traveling periodical and soliton-like waves of density steps n and relative supersaturation σ on the growing surface and in volume of the diffusion layer. The parameters obtained for traveling n and σ agree with experimental data on step bunches in KDP crystal growth.