2D Voronoi tessellation generated by lines and belts of dots

The application of the Voronoi tessellation for studying the nucleation process at the basis of thin film formation dates back to the end of nineties. In particular, Poissonian and spatial correlated nuclei distributions were investigated. The growth of stressed interfaces, however, has evidenced that elastic strain can modify the spatial distribution of nuclei giving rise to new challenges at the level of stochastic geometry. Here we report a study of a 2D nucleation of dots randomly arranged in lines and/or belts on the surface. The results are compared to the experimental case of multilayer structures of InAs quantum dots grown on GaAs(001).