Atomistic simulations of strain distributions in quantum dot nanostructures

Strain distributions around a Ge quantum dot (QD) buried in a Si spacer layer are investigated theoretically by means of classical molecular dynamics simulations using the Tersoff potential. Applying periodic boundary conditions laterally, two-dimensional superlattices of QDs are obtained. Strain distributions in systems of different size and lattice misorientation are computed in order to explain possible vertical correlations in self-organized three-dimensional QD superstructures. Generally, the strain of relaxed systems displays an oscillatory behaviour as a function of the distance from the QD. For QD systems with growth direction [001], a simple fitting function is used to describe the strain along a vertical path above the QD by an oscillation and a decay according to a power law. For QDs with the shape of a truncated pyramid, the planar strain decays by a power of approximately -3. The period of the oscillation is nearly proportional to the QD superlattice constant and decreases with increasing coordination number of the QD superlattice. In misoriented systems with a small tilt angle about the [110] axis, the region of tensile planar strain above the QD is bent in the direction opposite to the misorientation causing a vertical correlation with lateral shift. For a tilt angle ~55°, no strain oscillation is found which implies a perfect vertical correlation.