  We theoretically model the formation of quantum dots(QDs) and quantum dot
molecules(QDMs) in silicon germanium heteroepitaxy by explicitly incorporating
the role of noise in a continuum theory for surface evolution in molecular beam
epitaxy. Using the connection between flux and noise, we explain how changing
flux can lead to a transition from QD to QDM formation, as seen in experiments.
In these systems we show a dual role of noise in nanostructure growth; one
where it promotes formation of QDMs via pit nucleation, and another where it
curtails QDM formation due to stochastic effects.
