Stable island arrays by height-constrained Stranski-Krastanov growth

In the Stranski-Krastanov system, the lattice mismatch between the film and the substrate causes the film to break into islands. During annealing, both surface energy, and elastic energy drive the islands to coarsen: Some islands enlarge and others shrink, keeping the total island volume constant. The islands produced this way are usually uneven in size and spacing. Motivated by several related studies, we suggest that stable, uniform islands should form when a stiff ceiling is placed at a small gap above the film. After contacting the ceiling, the islands are constrained to grow laterally and remain coherent with the substrate, preventing further stress relaxation. In fact, we show that the role of elasticity is reversed: With the ceiling, the total elastic energy stored in the system increases as the islands coarsen laterally. On the other hand, the total surface energy decreases as the islands coarsen. Consequently, the islands select an equilibrium size to minimize the combined elastic energy and surface energy. We estimate the equilibrium island size by analyzing an idealized model.