  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. Using the method, the probabilities for
different diffusion lengths are calculated and their dependence on system size
and the number of deposited layers is studied. 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. Thus, a clearer understanding of the diffusion process and the
effect of diffusion length on surface roughness is obtained. Systems with
surface diffusion show nearly random deposition-like behaviour upto monolayer
deposition. Their interface widths, in a logarithmic plot, are initially
linear, as in random deposition. With increase in the number of layers,
correlation effects between neighbouring columns become dominant. The interface
deviates from its initial linear growth and eventually becomes saturated. An
explanation for this behaviour is discussed and the point of departure from the
linear form is estimated analytically.
