Growth of patterned surfaces
During epitaxial crystal growth a pattern that has initially been imprinted on a surface approximately reproduces itself after the deposition of an integer number of monolayers. Computer simulations of the one-dimensional case show that the quality of reproduction decays exponentially with a characteristic time which is linear in the activation energy of surface diffusion. We argue that this lifetime of a pattern is optimized if the characteristic feature size of the pattern is larger than (D/F)1/(d+2), where D is the surface diffusion constant, F the deposition rate, and d the surface dimension.
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