Computation of the preferential nucleation sites for Ge quantum dots on a relaxed SiGe layer

We compared directly the nucleation sites of Ge quantum dots on a relaxed SiGe buffer layer with the sites of a minimum stored energy density of the Ge dots. The computed elastic stored energy of the Ge dots encompasses the effect of both lattice mismatch and misfit dislocations. We computed the strain/stress of the misfit dislocations near a free surface by using the solution presented by Gosling and Willis [J Mech Phys Solids 1994;42:1199]. The study revealed that the intersection of the slip-planes with the free surface is the site of the maximum tensile strain, thus the Ge dots, which have a negative misfit, preferentially nucleate at that site. Our work clearly demonstrates the role of misfit dislocations in the formation of the ordered array of Ge dots. We also discuss the application of misfit dislocations for selective etching and the effects of a free surface on the displacements of the underlying misfit dislocations.