Growth and percolation of thin films: A model incorporating deposition, diffusion and aggregation

We propose a model for describing diffusion-controlled aggregation of particles that are continually deposited on a surface. The model, which incorporates deposition, diffusion and aggregation, is motivated by recent thin film deposition experiments. We find, that the diffusion and aggregation of randomly deposited particles "builds" a wide variety of fractal structures, all characterized by a common length scale L₁. This length L₁ scales as the ratio of the diffusion constant over the particle flux to the power 1/4. We compare our results with several recent experiments on two-dimensional nanostructures formed by diffusion-controlled aggregation on surfaces.