Effects of grains' features in surface roughness scaling

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.