Heterogeneous Nucleation of Quantum Dot Molecules in Heteroepitaxy*

We develop a theoretical model to elucidate the heterogeneous nucleation of quantum dot molecules (QDMs) in heteroepitaxial growth of strained thin films. We show that critical size and energy barrier for nucleation of a QDM (two islands ``strain bonded'' by a pit in between) are reduced relative to those for isolated strained islands on flat surface. This is caused by an attractive strain-induced interaction between the islands and the pit. Consequently, islands prefer to heterogeneously nucleate next to a pit forming QDMs. For a fixed pit size, island-island interaction is shown to increase with increasing island size, giving rise to a self-limiting effect to prevent the island from further lateral growth (perpendicular to the pit edge), so that the islands elongate along the pit edge to form a ``mature'' structure of QDM. Our theory explains the most salient features of experimental results of QDMs.