Ge deposition on Si(001) substrates patterned by focused ion beams is a promising route toward fabricating highly ordered quantum dots. Depending on the growth temperature $T$, remarkable orderings of the assembled islands are observed. At low $T$’s, when diffusion is limited, a metastable phase with dots nucleating in the holes prevails. At high $T$’s, when diffusion is not limited by kinetics, an equilibrium ordered phase is observed with dots nucleating on the terraces in between the pits. At intermediate $T$’s, random growth arises. Monte Carlo simulations shed light onto this phenomenon. It is shown that the average stress energy of the equilibrium ordered configuration is significantly lower than the energy of configurations with islands positioned in the pits. Random nucleation gives rise to saddle configurations between the two ordered phases.

• Received 26 July 2007

DOI:https://doi.org/10.1103/PhysRevB.77.075311