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

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 the mean separation l between islands in a submonolayer regime and the damping time t* of layer-by-layer growth oscillations in one dimension. The stochastic models are modified, allowing for diffusion within interval r upon deposition. It is found numerically that the mean separation and the damping time depend on the diffusion interval r, leading to the fact that the damping time is related to the mean separation as t* approximately l(4/3) for the WV model and t* approximately l(2) for the Family model. The numerical results are in excellent agreement with recent theoretical predictions.