Spatial distribution of elastic deformations in Ge/Si structures with quantum dots

A method is developed for calculating the elastic deformation in coherently strained heterostructures on the basis of the valence force field (VFF) model using the Green’s function of the “atomistic” elastic problem. The spatial distribution of the elastic deformations in a Ge/Si system with pyramidal Ge quantum dots buried in a Si matrix is investigated theoretically. The deformation distribution in and around the pyramids is determined. Near quantum dots, the region near the tip of the pyramid is most strongly intensely. Inside quantum dots the region of the vertex is most relaxed, and the most strained section lies on the contour of the pyramid base. Compression occurs in the plane of the pyramid base inside quantum dots, and stretching occurs along the vertical direction. The picture is reversed near quantum dots: stretching occurs in the lateral direction and compression in the vertical direction. It is shown that the local deformations and their spatial distribution are essentially independent (to within the scaling) of the size of the quantum dots for 10–15 nm pyramid bases.