Sudden nucleation versus scale invariance of InAs quantum dots on GaAs

InAs quantum dots (QDs) self-assembled on GaAs(001) at the early stage of growth show scale invariance of the island size distribution, which have been interpreted in the framework of the Mulheran and Blackman theory. The central concept is the capture zone of the growing nucleus properly identified by the Voronoi' cells. We show that the volume distribution of the quantum dots well overlaps the area distribution of the associated Voronoi' cells determined experimentally. Moreover, we evidence that scale invariance takes place in a restricted range of coverage and, basically, thanks to a very fast nucleation process. By comparison between experimental data and numerical simulations of the growth, we determine the spatial correlation length among QDs. The key conditions for scale invariance to occur are pointed out, thus defining the range of validity of the model for application to other systems.