Diffusion-controlled deposition on surfaces: Cluster-size distribution, interface exponents, and other properties

The diffusion-controlled deposition of particles onto surfaces has been simulated in two and three dimensions. The deposits generated in these simulations are substantially larger than those used in earlier work and allow the geometric scaling relationships which characterize the surface deposits to be more precisely determined. Several of these geometric scaling relationships are investigated in this paper. All of our results are consistent with the idea that surface deposits generated by diffusion-limited particle deposition have a fractal-like structure with a fractal dimensionality ($D$) equal to that of clusters generated by the Witten-Sander model for diffusion-limited aggregation. Our results are also consistent with the relationships between the cluster-size-distribution exponent ($\tau$), the fractal dimensionality and the Euclidean dimensionality ($d$) [$\tau =1+\frac{\mathrm{}(d-1\mathrm{})\mathrm{}}{D}$] recently obtained by Rácz and Vicsek. Results are also presented for the way in which the size of the old-growth-new-growth interface depends on the size of the old growth.