Size-dependent reversal of the elastic interaction energy between misfit nanostructures

By exploiting a fully three-dimensional finite-element modeling of strain fields, we investigate the spatial dependence of the elastic interaction energy between misfitting nanostructures beyond the point-dipole approximation. When interacting islands are finite in size, the detailed shape of the elastic strain field around and under the islands may convert the repulsive interactions, usually experienced between equal-sized islands, into an attractive basin between a large island and a population of neighboring clusters smaller than a critical size. The results of the simulations applied to large Ge islands grown on a Si(111) substrate have significant implications for the understanding of the strain-mediated coarsening of quantum dots around the islands.