The formation of surfaces by diffusion limited annihilation

Abstract

Computer simulations have been carried out in two and three dimensions to explore the formation of surfaces by diffusion limited annihilation of an initially smooth surface by mobile particles. From simulations carried out on two-dimensional strips of width l lattice units we find that the asymptotic variance in the surface height (ξ) scales with l according to ξ∼[ln(l)]1/2. For three-dimensional systems with a square cross section of size l×l lattice units we find that ξ quickly reaches a limiting value which is essentially independent of l(ξ∼l°). A variety of two-dimensional simulations were also carried out for other geometries. The results of these simulations indicate that diffusion limited annihilation processes cannot be used to produce sharply defined grooves by etching through an inert mask.