Effects of grains' features in surface roughness scaling

TL;DR

This study investigates how grain features influence surface roughness scaling in growth models, revealing a crossover behavior and providing estimates for grain size and surface roughness exponents across different surface morphologies.

Contribution

It introduces a detailed analysis of local roughness scaling with grain features, highlighting the crossover at a characteristic length and its relation to grain size and shape.

Findings

The local roughness exponent pprox 1 explains height differences at grain borders.

The crossover length r_c estimates average grain size across models.

Different  values in KPZ growth relate to surface sharpness and cliffs.

Abstract

We study the local and global roughness scaling in growth models with grains at the film surfaces. The local roughness, measured as a function of window size r, shows a crossover at a characteristic length r_c, from a rapid increase with exponent \alpha_1 to a slower increase with exponent \alpha_2. The result \alpha_1\approx 1 is explained by the large height differences in the borders of the grains when compared to intragrain roughness, and must not be interpreted as a consequence of a diffusion dominated intragrain dynamics. This exponent shows a weak dependence on the shape and size distribution of the grains, and typically ranges from 0.85 for rounded grain surfaces to 1 for the sharpest ones. The scaling corrections of exactly solvable models suggest the possibility of slightly smaller values due to other smoothing effects of the surface images. The crossover length r_c provides a reasonable estimate of the average grain size in all model systems, including the cases of wide grain size distributions. In Kardar-Parisi-Zhang growth, very different values of \alpha_2 are obtained, ranging from 0.4 for the films with smoothest surfaces to values in the range 0.1\lesssim \alpha_2 \lesssim 0.2 for systems with large cliffs separating the grains. Possible applications to real systems which show this crossover with similar exponents are discussed.