Directed self-organization of quantum dots

We devise a nonlinear dynamical model of the growth of strained islands on a pattern. We study the morphological instability of a thin film that develops with a characteristic wavelength in the presence of an external forcing due to an underlying patterned substrate with another wavelength. We find in some conditions that the islands can form in well-organized arrays located on either the peaks or valleys of the pattern depending on the film thickness and ratio of the two characteristic wavelengths. These results are rationalized by a kinetic phase diagram and correlated with the morphology when the islands and the wetting layer grow. We find that the islands may be ordered and homogeneous when their coarsening is significantly slowed down, in agreement with experimental observations reported in the literature.