Revisiting Surface Diffusion in Random Deposition

TL;DR

This paper analytically and numerically investigates how surface diffusion influences the surface roughness in a random deposition model, revealing the transition from random-like to correlated growth as layers increase.

Contribution

It derives an analytical expression for diffusion probabilities and studies their impact on surface morphology, providing new insights into diffusion effects in surface growth models.

Findings

Surface diffusion causes initial random deposition-like behavior.

Correlation effects dominate as the number of layers increases.

Surface roughness saturates due to diffusion-induced correlations.

Abstract

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.