Deposition, diffusion, and aggregation of atoms on surfaces: A model for nanostructure growth.

Abstract

We propose a model that describes the diffusion-controlled aggregation exhibited by particles as they are deposited on a surface. The model, which incorporates deposition, particle and cluster diffusion, and aggregation, is inspired by recent thin-film-deposition experiments. We find that as randomly deposited particles diffuse and aggregate they configure themselves into a wide variety of fractal structures characterized by a length scale ${\mathit{L}}_{1}$. We introduce an exponent \ensuremath{\gamma} that tunes the way the diffusion coefficient changes with cluster size: if the values of \ensuremath{\gamma} are very large, only single particles can move, if they are smaller, all clusters can move. The introduction of cluster diffusion dramatically affects the dynamics of film growth. We compare our results with those of several recent experiments on two-dimensional nanostructures formed by diffusion-controlled aggregation on surfaces, and we propose several experimental tests of the model. We also investigate the spanning properties of this model and find another characteristic length scale ${\mathit{L}}_{2}$ (${\mathit{L}}_{2}$\ensuremath{\gg}${\mathit{L}}_{1}$) above which the system behaves as a bond percolation network of the fractal structures each of length scale ${\mathit{L}}_{1}$. Below ${\mathit{L}}_{2}$, the system shows similarities with diffusion-limited aggregation. We find that ${\mathit{L}}_{1}$ scales as the ratio of the diffusion constant over the particle flux to the power 1/4, whereas ${\mathit{L}}_{2}$ scales with another exponent close to 0.9.