Cluster size distribution in self-organised systems.

We present a study on the scaling phenomena, both in dimension and density, of self-organised islands. Starting from the Family Meakin (FM) model, our work analyses the exponent values of the power-law part of the distribution and how they are modified by some growth parameters (i.e., temperature and alloy composition). The FM model applies to a variety of physical systems when three-dimensional objects form on a two-dimensional substrate. By scanning electron microscopy, we acquired and digitised images evidencing the surface morphology and the island distribution. A computer program performed a statistical analysis of the cluster dimensions. Our investigation applied the method to clusters of Si1xGex alloys grown by MBE in different conditions. We used a modified FM model introducing the diffusion of impinging atoms and small islands near the growing surface, to explain our experimental data. The whole procedure allows choosing suitable ranges of the growth parameters to obtain controlled cluster-size distribution.