Energetics of epitaxial island arrangements on substrate mesas

Self-assembly of strained epitaxial deposits (islands) grown on a substrate is a promising route to fabricate nanostructures of significance for electronic and optoelectronic devices. The challenge is to achieve specific island arrangements that are required for device functionality and high performance. This article investigates growth on a topographically patterned substrate as a means to control the arrangement of islands. By taking free energy to consist of elastic energy and surface energy, minimum energy configurations are calculated for islands on a raised substrate mesa. Configurations of one, two, and three islands at different positions on the mesa are considered to determine their relative energies as a function of mesa size, island size, mismatch strain between the island and substrate materials, surface energy, and elastic moduli. Insight is offered on the mechanisms responsible for certain physical observations such as a transition from the formation of multiple islands to a single island as mesa size is reduced.