Crossover from 2-dimensional to 3-dimensional aggregations of clusters on square lattice substrates

A Monte Carlo study on the crossover from 2-dimensional to 3-dimensional aggregations of clusters is presented. Based on the traditional cluster-cluster aggregation (CCA) simulation, a modified growth model is proposed. The clusters (including single particles and their aggregates) diffuse with diffusion step length l (1 ≤ l ≤ 7) and aggregate on a square lattice substrate. If the number of particles contained in a cluster is larger than a critical size s_c, the particles at the edge of the cluster have a possibility to jump onto the upper layer, which results in the crossover from 2-dimensional to 3-dimensional aggregations. Our simulation results are in good agreement with the experimental findings.