Mechanics of quantum-dot self-organization by epitaxial growth on small areas

Energetic arguments are used to understand the mechanics of Stranski-Krastanow epitaxial systems constrained to grow on a finite area of a substrate. Examples include selective area epitaxy and growth on patterned substrate features as raised mesa and etched pits. Accounting only for strain energy, (isotropic) surface energy, wetting layer potential energy, and geometric constraints, a rich behavior is obtained, whereby equilibrium configurations consist of a single island, multiple islands, or no islands, depending on the size of the growth area. It is shown that island formation is completely suppressed in the case of growth on a sufficiently small area. These behaviors are in stark contrast to growth on an indefinitely large area, where the same model suggests that the minimum free energy configuration of systems beyond the wetting layer transition thickness is a single island atop a wetting layer. The constraint of growing on a finite area can suppress island coarsening and produce minimum energy configurations with multiple self-organized islands of uniform size and shape.