We present first a compatibility equation for the misfit strains induced in alloyed quantum dots (QDs) by the mismatch in the lattice constants or the thermal-expansion coefficients of their alloying elements and show that it imposes some restrictions on the alloy composition profiles from a theoretical point of view. We then solve the strain field in embedded alloyed QDs induced by the nonuniform misfit strains. It is found that the induced field is uniform if the misfit strains satisfy the compatibility equation, but not otherwise. Finally, we consider the energy of nucleation of a circular prismatic dislocation loop to relieve the misfit strain and calculate the critical size of a dislocation-free alloyed QD. We show that this size is much larger when the alloy composition meets the restrictions imposed by the strain compatibility equation than when it does not.

• Received 17 July 2006

DOI:https://doi.org/10.1103/PhysRevB.74.195328