Quantitative model of heterogeneous nucleation and growth of SiGe quantum dot molecules*

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 use a multiscale approach combining continuum model with first-principles calculation, and 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 $\sim$85{\%} and $\sim$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.