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Using a multiscale approach combining continuum model with first-principles calculation, we develop a quantitative theoretical model for heterogeneous nucleation and the growth of a quantum dot molecule-a few islands "strain bonded" by a pit in heteroepitaxy of thin films, in contrast to homogeneous nucleation and growth of isolated strain islands on the surface. We show that the critical size and energy barrier for island nucleation next to a pit is substantially reduced with the increasing pit size, but the reduction approaches an upper bound of ~85% and ~72% for the size and barrier, respectively. Our model also predicts a self-limiting effect on island growth, resulting from an intriguing interplay between island-pit attraction and island-island repulsion, that drives the island size to increase linearly with the pit size, which explains a long-standing puzzle of experimental observation.

Quantitative Model of Heterogeneous Nucleation and Growth of SiGe Quantum Dot Molecules