Fractal growth of epitaxial surface clusters with elastic interaction

The fractal growth of clusters adsorbed on crystal surfaces has been studied by Monte Carlo simulations. Elastic interactions between the atoms through the substrate have been included. Attractive and repulsive interaction potentials 1/r(3) have been used, including a varying cutoff for the range of interaction. As an important result we find that there exists a crossover radius beyond which the fractal dimension of the cluster corresponds to the fractal dimension of conventional two-dimensional diffusion limited aggregation. The crossover radius itself and the properties of the cluster inside that radius depend sensitively on the details of the interaction. The results have been analyzed by a scaling theory. Furthermore, we have implemented a multigrid scheme which allows for very efficient simulation of a large number of mobile atoms with long-range interaction on the surface.