Equations of motion for epitaxial growth

A set of discrete, stochastic equations of motion which describe the epitaxial growth of a single crystal are derived beginning with a master equation description of the dynamics of a solid-on-solid model. The final set of coupled Langevin equations takes explicit account of the elementary microscopic processes of deposition, surface diffusion and desorption. The first of these contributes shot noise to the system while the last two produce configuration-dependent noise correlations. Direct numerical integration of these equations provides a formal alternative to Monte Carlo simulation of the growth process. Other applications and extensions are outlined in brief.

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