Elongated Quantum Dots of Ge on Si Growth Kinetics Modeling with Respect to the Additional Energy of Edges

In this paper refining of mathematical model for calculation of parameters of selforganised quantum dots (QDs) of Ge on Si grown by the method of molecular beam epitaxy (MBE) is done. Calculations of pyramidal and wedge-like clusters formation energy were conducted with respect to contributions of surface energy, additional edge energy, elastic strain relaxation, and decrease in the atoms attraction to substrate. With the help of well-known model based on the generalization of classical nucleation theory it was shown that elongated islands emerge later than pyramidal clusters. Calculations of QDs surface density and size distribution function for wedge-like clusters with different length to width ratio were performed. The absence of special geometry of islands for which surface density and average size of islands reach points of extremum that was predicted earlier by the model not taking into account energy of edges was revealed when considering the additional contribution of edge formation energy. (paper)