Growth Law of Bunch Size in Step Bunching Induced by Flow in Solution

TL;DR

This study uses Monte Carlo simulations to analyze how flow speed influences the growth law of step bunching during solution growth, revealing different scaling behaviors depending on flow velocity.

Contribution

It introduces a model that captures the effect of flow speed on step bunching and identifies a transition in the growth exponent from 1/2 to 1/3.

Findings

Faster flow leads to a growth exponent of 1/2 in initial stage.

Slower flow results in a growth exponent of 1/3.

A transition interval with exponent 1/3 appears during faster flow.

Abstract

By carrying out Monte Carlo simulations,we study step bunching during solution growth. For simplicity, we consider a square lattice, which represents a diffusion field in a solution, and express the diffusion of atoms as the hopping of atoms on the lattice sites. In our model, we neglect the fluctuation along steps. An array of steps is expressed as dots on a one-dimensional vicinal face. Step bunching occurs in the case of step-down flow. In previous study (M. Sato: J. Phys. Soc. Jpn. {\bf 79} (2010) 064606), we studied step bunching with a slow flow and showed that the width of the fluctuation of step distance increases as $t^\alpha$ with $\alpha =1/3$ in the initial stage. In this paper, we carry out simulations with a faster flow. With a faster flow, the width of the fluctuation of step distance first increases as $t^\alpha$ with $\alpha=1/2$,which is larger than the exponent with a slow flow, and then an interval during which the width increases as $t^{1/3}$ appears.