Scaling laws near percolation during three-dimensional cluster growth: A Monte Carlo study

We have developed a Monte Carlo code to simulate various types of three-dimensional cluster growth that can be found experimentally. These simulations include the possibility of atomic diffusion and cluster coalescence, and reproduce the growth from nucleation to percolation, with simple hypotheses and few free parameters. We used them to study the scaling behavior of percolation in various cases of granular growth. We first defined a thickness of transition t(trans) at which islands on the substrate are on an average composed of two coalescing clusters. We show that the thickness of transition always follows scaling laws as a function of the deposition rate. The scaling exponent depends on the type of growth: it is 0.16 when there is no cluster coalescence during the growth, and 0.29 when there is a fast coalescence. A scaling transition between these two values is observed when varying the coalescence duration of clusters. These scaling laws are also valid for the thickness at which percolation is reached, and can be useful tools to extract information about growth mechanisms during granular growth experiments.