Equilibrium and metastable phase diagrams for island self-organization in selective area epitaxy

An energetic model is used to understand the mechanics of StranskiKrastanow epitaxial systems constrained to grow on a finite area of a substrate. The model is representative of physical systems that include selective area epitaxy and growth on patterned substrate features such as raised mesas and etched pits. By considering only strain energy, isotropic surface energy, wetting layer potential energy and the geometric constraints of the system, equilibrium configurations consisting of a single island, multiple islands or no islands can be obtained depending on the dimensions of the growth area. These results are in contrast to growth on a substrate of infinite dimensions where the minimum energy configuration of systems with deposited volumes beyond the wetting layer transition thickness is a single large island on top of the wetting layer. It is therefore concluded that growth on a finite area can suppress island coarsening and result in minimum energy configurations consisting of multiple self-organized islands of uniform size and shape. Qualitative comparisons are made to experimental results from literature, and are shown to have good agreement.