Scaling of local interface width of statistical growth models

TL;DR

This paper compares methods for estimating roughness and dynamic exponents in statistical growth models, highlighting limitations of small-scale analysis and proposing a more reliable method for dynamic exponent estimation.

Contribution

It introduces an improved method for calculating the dynamic exponent z from local roughness scaling, validated through numerical simulations of various growth models.

Findings

Small-scale roughness scaling estimates are unreliable for alpha.

The proposed method accurately estimates the dynamic exponent z.

Evidence of Edwards-Wilkinson behavior in certain 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.