Height and roughness distributions in thin films with Kardar-Parisi-Zhang scaling

TL;DR

This study analyzes height and roughness distributions in thin films modeled by KPZ dynamics, finding that roughness distributions are more reliable indicators of KPZ scaling than height distributions, especially in finite-size systems.

Contribution

It provides detailed measurements of height and roughness distributions in KPZ models, highlighting the robustness of roughness distributions for identifying KPZ scaling in experimental conditions.

Findings

Height distributions show finite-size effects and limited accuracy.

Roughness distributions exhibit good data collapse and characteristic KPZ features.

Roughness distributions are more reliable than height distributions for testing KPZ scaling.

Abstract

We study height and roughness distributions of films grown with discrete Kardar-Parisi-Zhang (KPZ) models in a small time regime which is expected to parallel the typical experimental conditions. Those distributions are measured with square windows of sizes $8\leq r\leq 128$ gliding through a much larger surface. Results for models with weak finite-size corrections indicate that the absolute value of the skewness and the value of the kurtosis of height distributions converge to $0.2\leq |S|\leq 0.3$ and $0\leq Q\leq 0.5$, respectively. Despite the low accuracy of these results, they give additional support to a recent claim of KPZ scaling in oligomer films. However, there are significant finite-size effects in the scaled height distributions of models with large local slopes, such as ballistic deposition, which suggests that comparison of height distributions must not be used to rule out KPZ scaling. On the other hand, roughness distributions of the same models show good data collapse, with negligible dependence on time and window size. The estimates of skewness and kurtosis for roughness distributions are $1.7\leq S\leq 2$ and $3\leq Q\leq 7$. A stretched exponential tail was found, which seems to be a particular feature of KPZ systems in 2+1 dimensions. Moreover, the KPZ roughness distributions cannot be fitted by those of $1/f^{\alpha}$ noise. This study suggests that the roughness distribution is the best option to test KPZ scaling in the growth regime, and provides quantitative data for future comparison with other models or experiments.