Equilibrium shape diagram for strained Ge nanocrystals on Si(001)

We introduce a chemical-thermodynamic model to explain the formation and annealing behavior of Ge nanocrystalline islands grown on Si(001). Assuming the nanocrystals are essentially large adsorbed molecules, we propose a simple free energy expression for islands of different shapes interacting with each other via the substrate on which they reside. Nanocrystal growth, disappearance, and shape transitions are all consonant with a near-equilibrium system constrained by mass conservation and characterized by interisland repulsions. We construct an equilibrium shape diagram from experimentally determined free energy differences between island shapes and use it to resolve several anomalies that have been noted for the Ge on Si(001) system.