Interaction between islands in kinetic models of epitaxial growth of quantum dots

In the present paper, for the first time, the influence of interactions between 3D islands during epitaxial growth of quantum dots by Stranski-Krastanov mechanism is considered in the frames of kinetic models. The contribution of interaction energy between nanoclusters into the free energy of the system in the process of islands formation is estimated. In this approximation, critical thickness of transition from 2D to 3D growth, surface density and size distribution function of quantum dots are calculated with the help of the original model. The results of the work show that considering the interactions between islands is essential for precise evaluation of characteristics of the ensemble of quantum dots. Moreover, it is shown that neglecting this contribution leads to the prediction of higher surface densities and smaller sizes of quantum dots, which is the traditional problem of theoretical models. Accounting for the new factor gives unexpected result for the dependence of surface density of islands on deposition rate. These results are of paramount importance from the point of view of device applications of quantum dot heterostructures.