Numerical test of the damping time of layer-by-layer growth on stochastic models

TL;DR

This study uses Monte Carlo simulations to analyze how diffusion interval affects island separation and damping time in layer-by-layer growth models, confirming theoretical predictions.

Contribution

It introduces modified stochastic models with diffusion within an interval and numerically verifies the relationship between damping time and island separation.

Findings

Damping time scales as rac{4}{3} of mean separation in WV model.

Damping time scales as the square of mean separation in Family model.

Numerical results agree with recent theoretical predictions.

Abstract

We perform Monte Carlo simulations on stochastic models such as the Wolf-Villain (WV) model and the Family model in a modified version to measure mean separation $\ell$ between islands in submonolayer regime and damping time $\tilde t$ of layer-by-layer growth oscillations on one dimension. The stochastic models are modified, allowing diffusion within interval $r$ upon deposited. It is found numerically that the mean separation and the damping time depend on the diffusion interval $r$, leading to that the damping time is related to the mean separation as ${\tilde t} \sim \ell^{4/3}$ for the WV model and ${\tilde t} \sim \ell^2$ for the Family model. The numerical results are in excellent agreement with recent theoretical predictions.