Growth of quantum dot crystals in amorphous matrix on rippled substrates

The formation of quantum dot crystals by multilayer deposition has been reported and explained satisfactorily only in crystalline materials, so far. Here we demonstrate a method for the growth of quantum dot crystals in amorphous matrices. The ordering of the positions of quantum dots is induced by the deposition of a multilayer on a periodically rippled substrate at an elevated substrate temperature. During the deposition, the quantum dots self-arrange following the morphology of the substrate. The result is a formation of well ordered lattice of Ge quantum dots in amorphous silica matrix. We have investigated the ordering of the dots by grazing-incidence small-angle X-ray scattering and we found that the distance of the dots in the multilayer interfaces close to the rippled surface indeed equals the ripple period. However, in more distant interfaces the dot-dot distance approaches the value for non-rippled substrate and the dot ordering is slightly less pronounced. This finding confirms the beneficial influence of the rippled substrate on the ordering of quantum dots in an amorphous matrix.