Effect of Flow in Solution on Motion of Steps during Solution Growth

Abstract

We study step bunching on a vicinal face in solution growth. Assuming that steps are straight, we consider a two-dimensional diffusion filed to represent a solution and a onedimensional vicinal face. The steps are expressed as dots in the vicinal face. Taking account of a flow in a solution, we numerically solve the diffusion equation and the Navier-Stokes equation in the solution, and determine step velocities. If a flow in a solution is absent or is in the step-up direction, a vicinal face is stable. When the flow is in the step-down direction, the vicinal face is unstable and step bunching occurs. In the initial stage, small bunches are formed. Then, owing to the coalescence of small bunches, large bunches are formed.

Formation of Step Bunches Induced by Flow in Solution

“…24, we studied how the process of step bunching changes with changes in the values of some parameters. A transition from step bunching with the separation of steps to that without the separation was observed when we changed the flow rate or the strength of repulsion.…”

“…3(a)], the separation and collision of steps repeatedly occur during bunching, which is similar to the step bunching in a previous study. 24) With increasing flow rate, the frequency of the separation decreases The difference in the process of bunching is observed more clearly in a later stage. During step bunching, the step density in bunches seems to change with the bunch size, so that we see a dependence of the inclination of bunches on the bunch size.…”

“…First, we investigate how the motion of steps during step bunching changes with the flow rate. In our previous study, 24) we already showed that step bunching does not occur with a step-up flow or without a flow, so that we hereafter study step bunching …”

“…In ref. 24, we numerically solved the diffusion equation of the solute and studied the motion of steps in a one-dimensional model. In the study, we investigated the dependence of the average velocity of steps on the flow rate during step bunching.…”