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Effects of grains' features in surface roughness scaling

T. J. Oliveira·F. D. A. Aarao Reis
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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 α_1 to a slower increase with exponent α_2. The result α_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 α_2 are obtained, ranging from 0.4 for the films with smoothest surfaces to values in the range 0.1\lesssim α_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.

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T. J. Oliveira, F. D. A. Aarao Reis. 2007-03-19. Effects of grains' features in surface roughness scaling. https://arxiv.org/abs/cond-mat/0703504

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