### Abstract

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Atomistic simulations of strain distributions in quantum dot nanostructures
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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.