Calculation of the size-distribution function for quantum dots at the kinetic stage of growth

A theoretical model for calculating the distribution of quantum dots in size in the case of growth according to the Stranski-Krastanow mechanism in the lattice-mismatched heteroepitaxial systems is suggested. The model is based on the general theory of the islands’ nucleation at the first-order phase transition, in which situation the role of the metastable phase is played by the overstressed wetting layer, while the elastically stressed three-dimensional islands act as nuclei of the new phase. The suggested model clarifies and generalizes a number of the results reported previously. The theory can be used at the kinetic stage of formation of quantum dots, in which case their ensemble is noninteracting. An example of calculation of the kinetics for formation of hut-shaped clusters in the heteroepitaxial Ge/Si(100) system is given.