Theoretical approaches to collective diffusion on stepped surfaces

Abstract

We study collective diffusion of adsorbed particles on stepped surfaces using analytic andnumerical techniques. We employ the Langmuir lattice gas model where the distribution ofadatoms on the surface is solely determined by the difference in adsorption energy of atomson terraces and along step edges. For the system in equilibrium, we consider the masterequation approach for collective diffusion across the steps within the dynamic mean fieldapproximation. We demonstrate that results obtained for the collective diffusion coefficientDc(Θ) are sensitive to the choice of relevant slow variables for inhomogeneous systems such asstepped surfaces. Next, we consider diffusion across steps in situations where the system isnot in equilibrium such as during spreading or ordering. To this end, we consider aphenomenological theory using balance between particle fluxes across a stepped surfacewithin the linear response theory. This allows us to derive expressions for effective diffusioncoefficients in the limit of large and small coverages, where the results agree well withDc(Θ) in the corresponding limits.