Size selected growth of nanodots: effects of growth kinetics and energetics on the formation of stationary size distributions

The size selection of nanodots during the growth is studied by using a reaction kinetic model, where reaction rates depend on the dot size. The characteristic feature of the reaction rates is the energetics, where the free energy of dots has a minimum at the certain dot size. The model equations are solved by using a particle coalescence simulation method. We find phenomenologically three distinct stages of growth. First, during the initial deposition stage, distributions with high density of small dots occur. Second, there is an intermediate and short-lived stationary state, which is controlled by kinetics of growth. Third, a long-lived stationary state is obtained, with nearly Gaussian size distributions, mostly determined by the energetics of the growth but also significantly affected by the kinetics. In the final stage, size selection and narrowing of the distributions occur. It is also shown that in the final stage of growth the Fokker-Planck type continuum model describes well the evolution of the distributions and the size selection.