  A static variational model for shape formation in heteroepitaxial crystal
growth is considered. The energy functional takes into account surface energy,
elastic misfit-energy and nucleation energy of dislocations. A scaling law for
the infimal energy is proven. The results quantify the expectation that in
certain parameter regimes, island formation or topological defects are
favorable. This generalizes results in the purely elastic setting from [Goldman
and Zwicknagl (2014)]. To handle dislocations in the lower bound, a new variant
of a ball-construction combined with thorough local estimates is presented.
