Thickness-dependent surface energy and formation of epitaxial quantum dots

•Nucleation and growth of germanium quantum dots on a silicon surface (100) is considered.•Thickness-dependent surface energies are calculated.•Growth model is constructed, taking into account thickness-dependent surface energies.•Evolution of surface density and average size of quantum dots is determined. Numerous theoretical and experimental studies show that during epitaxial growth according to the Stranski-Krastanow mechanism in systems mismatched by the lattice constant, the change in the surface energy of the system during nucleation and further growth of quantum dots, plays the most important role. In particular, this factor determines the equilibrium and critical thicknesses of the transition from two-dimensional to three-dimensional growth, and also affects other kinetic characteristics of the ensemble of nanoclusters, including the nucleation rate, surface density, and average size of the islands. Recent theoretical studies have made it possible to determine that the surface energy in this process depends on the thickness of the material deposited on the substrate. In this paper, we construct a kinetic model of the formation and coherent growth of two-dimensional layers and quantum dots in mismatched epitaxial systems, taking into account the dependence of the specific surface energies on the thickness of the deposited material. In this approximation, we calculate the basic parameters of the formed array of nanoislands. Experimental studies were also carried out on the growth of two-dimensional layers and quantum dots of germanium on the silicon (100) surface. The results of experimental investigations confirm the proposed theoretical model.