Features of the stress-strain state of Si/SiO$_2$/Ge heterostructures with germanium nanoislands of a limited density

Within the elastic continuum model, with the use of the finite-element method, the stress-strain state of silicon-germanium heterostructures with semispherical germanium islands grown on an oxidized silicon surface is calculated. It is shown that as the density of islands is increased to limiting values, in the SiGe structure with open quantum dots the value and spatial distribution of the elastic-strain fields significantly change. The results of theoretical calculation allow the heterostructure portions with the maximum variation in the stress-strain state to be determined. The position of such a portions can be controlled by changing the density of islands.