Step bunching in crystal growth from solutions: Model of nonstationary diffusion layer, numerical simulation

Step bunching in crystal growth from solutions is investigated theoretically in the approximation of assigned diffusion layer thickness. This model is described by a set of equations including a two-dimensional diffusion equation for a diffusion layer, a one-dimensional step motion equation, the boundary condition on the growing surface relating these equations, and the boundary condition at the diffusion layer boundary. This set of equations has solutions in the form of coupled traveling step density wave n and relative supersaturation wave σx on the growing surface. The amplitude, the wavelength and the propagation velocity depend on the degree of deviation of growth parameters from the “equilibrium” ones for which the bunch amplitude tends to zero. The parameters obtained for traveling n and σx agree with available experimental data on step bunches in KDP crystal growth.