Transition from droplet growth to percolation: Monte Carlo simulations and an analytical model

Depositing a metal on an oxide or carbon substrate often leads to the formation of clusters which grow like droplets and percolate into zebra-striped structures. We study this phenomenon for different dimensionalities of the clusters and the substrate with two methods: an analytical model which is a generalization of the one presented by Jeffers et al. [J. Appl. Phys., 75, 5016 (1994)] and with kinetic Monte Carlo simulations (KMCS's). These KMCS's are the first which include the coalescence duration of clusters in a deposit, so they are able to simulate the whole cluster growth during atom deposition on a surface, from nucleation to percolation. They reproduce very realistically the experimental evolution of deposits obtained by other groups studying the growth of three-dimensional (3D) clusters on a 2D substrate. We show that one can define a deposited thickness where the transition between the regime of droplet growth and percolation occurs. This deposited thickness is well defined both analytically and experimentally. The analytical model and the KMCS show that this transition thickness is proportional to (B/F)^α, where F is the deposition rate, B is inversely proportional to the cluster coalescence speed, and α depends on the dimensionality of the clusters and the substrate. The values of α extracted from the model and from the KMCS are in good agreement.