Computer simulation for the roughness and fractal properties of film surfaces

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Abstract
Physical properties of films deposited on substrates and the fractal nature of film shapes have been topics of widespread interest. However, the fractal property of the roughness of film surfaces is little studied. In this paper we investigate, by computer simulation, the fractal behavior of one-dimensional random surfaces, as a first approach to this topic. Here, random surfaces are shaped by depositing unit-square particles one by one at random on segments divided into unit cells, and we plot the surface lengths of clusters formed on the segments against the areas. As a result, we have obtained evidence that the clusters exhibit two typical fractal dimensions (1.46 and 1.86).