Quantum dot molecule formation in Si-Ge heteroepitaxy on pit-patterned Si (001) substrate: A theoretical study

Quantum dot molecules refer to nanostructures consisting of four quantum dots around a central pit. These are observed to form in Si-Ge heteroepitaxy and are considered as an alternative to quantum dots for strain relaxation. Here we use numerical simulations of a continuum model of strained heteroepitaxy to show the spontaneous formation of quantum dot molecules in thick Si0.5Ge0.5 films grown on pit-patterned Si substrates. The route to their formation first involves a quantum dot in the pit, followed by removal of material from the pit to form quantum dot molecules. These molecules are formed for smaller pit widths, whereas larger pit widths tend to create a ridged surface. A mature single-walled quantum dot molecule has a typical size of about 220 nm. On reducing the wavelength of the original pit-pattern, we notice that multiple-walled quantum dot molecules form, due to the interactions with other nearby molecules. Our results broadly agree with experiment and suggest that QDM formation on patterned substrates does not necessarily have a nucleation barrier and can take place following the usual evolution of the Asaro-Tiller-Grinfeld instability.