ASYMPTOTIC PROPERTIES OF THIN FILM GROWTH MODELS THROUGH THE ROUGHNESS DISTRIBUTION METHOD WITH AND WITHOUT NOISE REDUCTION TECHNIQUES

Abstract

Conventionally, the asymptotic property of a growth model is identified via the scaling of interface width. This method requires large-scale simulations to minimize finite-size effects on the results. The multiple hit noise and the long surface diffusion length noise reduction techniques ( NRTs) have been used to promote the asymptotic behaviors of the growth models. Lately, an alternative method involving comparison of roughness distribution in the steady state has been proposed. In this work, firstly, the roughness distribution of the (2+1)-dimensional ballistic deposition (BD), Das Sarma-Tamborenea (DT), Wolf-Villain (WV), Larger Curvature (LC), and Family (F) models, without the NRTs, are calculated. Next, the noise reduced DT, WV, and LC models are studied in order to investigate the effects of the NRTs on the roughness distributions. In the steady state, our results indicate that the NRTs do not seem to have any impact on the roughness distribution of the DT model, but it significantly changes the roughness distributions of the LC and WV models to the normal distribution curves. Furthermore, we found that the finite substrate size does not strongly affect the roughness distributions of the noise reduced DT, LC, and WV models. Secondly, the effects of the NRTs on the height distributions of the LC, WV, and DT models are also studied. Qualitative characterization of the height distributions can be done via skewness and kurtosis calculation. The result shown that oscillating skewness and kurtosis are characteristic of layer-by-layer growth mode at early growth time of the films grown with the noise reduced LC, WV, and DT models. In the steady state, both NRTs slightly affect the height distributions of the LC and WV models and their skewness and kurtosis are approximately the same. The NRTs have strong effect on the height distribution of the DT models at the steady state. Finally, we found that the finite size effects on the height distributions of the films grown with the LC and F models are very weak, but the finite substrate size does strongly affect the height distribution of the BD model.