Revisiting surface diffusion in random deposition

An investigation of the effect of surface diffusion in random deposition model is made by analytical methods and reasoning. For any given site, the extent to which a particle can diffuse is decided by the morphology in the immediate neighbourhood of the site. An analytical expression is 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 are performed and their results are interpreted in the light of the analytical calculations. Systems with surface diffusion show an initial random deposition-like growth upto monolayer deposition, then a deviation due to correlation effects and eventual saturation. An explanation for this behaviour is discussed and the point of departure from the linear form is estimated analytically