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Effects of grains’ features in surface roughness scaling

2007; American Institute of Physics; Volume: 101; Issue: 6 Linguagem: Inglês

10.1063/1.2710286

1520-8850

Tiago J. Oliveira, F. D. A. Aarão Reis,

Stochastic processes and statistical mechanics

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 rc, from a rapid increase with exponent α1 to a slower increase with exponent α2. The result α1≈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 one 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 rc 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 α2 are obtained, ranging from 0.4 for the films with smoothest surfaces to values in the range 0.1≲α2≲0.2 for systems with large cliffs separating the grains. Possible applications to real systems which show this crossover with similar exponents are discussed.