Ordering of epitaxial quantum dots on nanomembranes

Semiconductor nanomembranes (NMs) provide fascinating opportunities to create unique structures and electronic devices owing to their mechanical flexibility. A fascinating question is whether the growth mediated by such flexibility can lead to the formation of ordered epitaxial surface nanostructures. By using computational modeling, we investigate the energetics of ordering of SiGe quantum dots (QDs) on both Si(001) and Si(111) NMs. We calculate the interaction energies for quantum dots grown on one side and on both sides of the NM and assembled in a square lattice for the Si(001) surface and in a hexagonal lattice for the Si(111) surface. Our calculations show that for QDs grown on the Si(001) NM the interaction energy possesses a minimum at a well-defined spacing only when the QDs are positioned on both sides in a square array and aligned along the [110] direction. The predicted QD ordering, spacing, and other features are in excellent agreement with recent experimental results. For QDs grown on the Si(111) NM, our calculations predict that ordered QDs can be achieved for both one-side and both-side growth, albeit with different QD spacings. The present work suggests that semiconductor NMs are a fascinating template for the self-assembled growth of ordered QDs.