We calculate the film coverage N on a model fractal substrate embedded in a two-dimensional space. We define a nominal thickness d as that which would be present on a flat surface exposed to the same vapor. The result of our analysis is N ∝ d 2- D over the range of film thickness corresponding to the fractal scaling behavior of the substrate; a plausible deviation is observed outside this range. The result is consistent with general arguments yielding N ∝ d 3- D in our three-dimensional world.
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Cheng et al. (1989) studied this question.
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