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. Understanding the processes underlying the growth of thin films has led to widespread interest, both from the physical and technological points of view. Equilibrium ("thermodynamic") models have been developed and applied with some success to the film-substrate system. However, recent dramatic improvements in experimental techniques--such as scanning tunneling microscopy--permit investigation of atomic details of the embryonic "sub-monolayer" stages of nanostructure film growth, and recent experimental work has recognized the importance of out of equilibrium (kinetic) effects on the determination of the observed morphologies. Addressing such out-of-equilibrium effects is important if one is to be able to control the morphology of submonolayer nanostructures. There exists some recent research on out-of-equilibrium models for example, models such as percolation have been developed to describe surface deposition. However percolation assumes that the deposited particles do not diffuse after being deposited, when in fact not only diffusion but also aggregation of the diffusing particles takes place. There also exist models of diffusing particles that aggregate, but such "cluster-cluster aggregation" (CCA) models do not incorporate the possibility of continual injection of new particles via deposition. Other models have been proposed, but cluster diffusion has never been included, nor has the percolation threshold been studied. The model we introduce is defined as follows: a Deposition. Particles are deposited at randomly-chosen positions of the surface at a flux F per lattice site per unit time. b Diffusion. A cluster of connected particles is chosen at random and moved North, East, South or West by one lattice constant per unit time with a probability proportional to its mobility, which is give n by D8 = D1 s -v, where s is the number of particles in the cluster, D1 is the diffusion constant of the monomers and 7 characterizes how the mobility of a cluster depends on its size. 0960-0779/94/$07.00 @ 1994 Elsevier Science All rights reserved SSD1