Self-assembly of quantum dots in a thin epitaxial film wetting an elastic substrate

The evolution of quantum dots (QDs), resulting from the Asaro-Tiller-Grinfeld instability of an epitaxially strained thin solid film deposited on a solid elastic substrate, is considered. For a film that wets the substrate, a nonlocal integro-differential equation is derived that describes the evolution of QDs in the long-wave limit. The contribution of a wetting stress, that accounts for the change in wetting energy due to variation of the film thickness caused by the film deformation, is included. It is found that wetting interactions can damp the long-wave perturbations and lead to Turing-type instability. By means of a weakly nonlinear analysis, general conditions for the wetting potential are found for which the formation of spatially periodic arrays of QDs is possible. It is shown that in either the case of a two-layer or a glued-layer wetting potential, the spatially regular arrays of QDs are unstable. The numerical simulations show that the QD's evolution exhibits a power-law coarsening, with different characteristics giving different exponents.