An analytical model for the growth of quantum dots on ultrathin substrates

The self-assembly of heteroepitaxial quantum dots on ultrathin substrates is analyzed within the context of small perturbation theory. Analytical expressions are derived for the dependence of the quantum dot separation on the substrate thickness. It is shown that the substrate thickness is critical in determining this separation when it is below the intrinsic material length scale of the system. The model is extended to simultaneous dot growth on both sides of the substrate. It is shown that vertically anticorrelated structures are preferred with an increase in the dot separation of 15% above that found in the one-sided case.