Nonlinear Evolution Equation of a Step with Anisotropy in a Diffusion Field for the Two-Sided Model

Abstract

The nonlinear evolution equation for the fluctuation of a terrace edge with anisotropy in step stiffness during step flow growth is derived in the two-sided model where adatoms can be incorporated into the step from the upper terrace as well as from the lower terrace. It is shown by reductive perturbation method based on the linear stability analysis that (1) up to ε³ order in the smallness parameter of instability the nonlinear evolution equation reduces to the closed Kuramoto–Sivashinsky (KS) equation with extra coefficients compared with the one-sided model and (2) the nonlinear evolution equation up to ε⁵ order is also derived in order to take into account the anisotropy in step stiffness in the lowest order. The nonlinear evolution equation is numerically calculated for various parameters included. It is also shown that the asymmetry of attachment into a step and the Gibbs–Thomson effect with anisotropy in step stiffness bring about various growth patterns of the step from chaotic growth to periodic growth and further to an inclined straight step mode with a single peak.