Surface nucleation and growth in the system of interacting particles.

Recent experiments on epitaxial growth of metals on graphene have shown a strong dependence of island densities on coverage. These investigations cannot be explained by the standard mean-field nucleation theories. To understand them, we extend to higher coverage the former theory of rate equations developed for the initial state of nucleation, in a system where adsorbate interaction is included. We account for that, in the case of high coverage, the repulsive interaction influences both the attachment of monomers to clusters and the mobility of atoms. In our work we analyze the modification of the dependence of the island density on coverage, temperature and F/D ratio. In some regimes our theory results in the experimentally observed substantial growth of island density with coverage for a high deposited amount and a weak dependence on deposition rate F. We also find out the local maxima in temperature dependence of island density, as a consequence of long-range repulsive interactions.