The elastic relaxation energy and equilibrium aspect ratio of self-organized pyramidal quantum dot

The formation of dislocation-free three-dimensional island by heteroepitaxial growth of lattice-mismatched materials is used to produce quantum dots. The equilibrium shape of these islands results from the competition between surface and elastic energies. The system Ge/Si has been studied in detail. The elastic relaxation energy of the islands has been calculated within a continuum elasticity theory using finite element method, and the fitted function of relaxation factor with respect to aspect ratio, and functional relation between the aspect ratio and the volume of the deposited material when the epitaxial system is at equilibrium state has been obtained. The results obtained show that equilibrium aspect ration is increased with increasing QDs volume.