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.