An investigation of the effect of surface diffusion in random deposition model was made by analytical methods and reasoning. For any given site, the extent to which a particle could diffuse was decided by the morphology in the immediate neighbourhood of the site. An analytical expression was derived to calculate the probability of a particle at any chosen site to diffuse to a given length, from first principles. This method may become particularly important in cases where obtaining the continuum limit and solving the corresponding differential equation may not be feasible. Numerical simulation of surface diffusion in random deposition model with varying extents of diffusion were performed and their results were interpreted in the light of the analytical calculations. Systems with surface diffusion showed an initial random deposition-like growth up to monolayer deposition, then a deviation due to correlation effects and eventual saturation. An explanation for this behaviour was discussed and the point of departure from the linear form was estimated analytically.

Revisiting Surface Diffusion in Random Deposition. B.Mal, S.Ray, J.Shamanna: The European Physical Journal B, 2011, 82[3-4], 341-7