Scaling of local interface width of statistical growth models

Abstract

We discuss the methods to calculate the roughness exponent alpha and the dynamic exponent z from the scaling properties of the local roughness, which is frequently used in the analysis of experimental data. Through numerical simulations, we studied the Family, the restricted solid-on-solid (RSOS), the Das Sarma-Tamborenea (DT) and the Wolf-Villain (WV) models in one- and two dimensional substrates, in order to compare different methods to obtain those exponents. The scaling at small length scales do not give reliable estimates of alpha, suggesting that the usual methods to estimate that exponent from experimental data may provide misleading conclusions concerning the universality classes of the growth processes. On the other hand, we propose a more efficient method to calculate the dynamic exponent z, based on the scaling of characteristic correlation lengths, which gives estimates in good agreement with the expected universality classes and indicates expected crossover behavior. Our results also provide evidence of Edwards-Wilkinson asymptotic behavior for the DT and the WV models in two-dimensional substrates.

To appear in Surface Science

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• Optimal detrended fluctuation analysis as a tool for the determination of the roughness exponent of the mounded surfaces
• Domain formation in the deposition of thin films of two-component mixtures
• Modeling of nonequilibrium surface growth by a limited mobility model with distributed diffusion length
• Thin film deposition with time varying temperature
• Surface roughness evolution in a solid-on-solid model of epitaxial growth
• Anomalous roughening in competitive growth models with time-decreasing rates of correlated dynamics
• Effects of the growth kinetics on solute diffusion in porous films
• Transition from compact to porous films in deposition with temperature activated diffusion
• Interface Collisions