Faceting instability in the presence of wetting interactions: A mechanism for the formation of quantum dots

A mechanism for the formation of quantum dots on the surface of thin solid films is proposed, not associated with the Asaro-Tiller-Grinfeld instability caused by epitaxial stresses. This mechanism, free of stress, involves instability of the film surface due to strong anisotropy of the surface energy of the film, coupled to wetting interactions between the film and the substrate. According to the mechanism, the substrate induces the film growth in a certain crystallographic orientation. In the absence of wetting interactions with the substrate, due to a large surface-energy anisotropy, this orientation would be thermodynamically forbidden and the surface would undergo a long-wave faceting (spinodal decomposition) instability. We show that wetting interactions between the film and the substrate can suppress this instability and qualitatively change its spectrum, leading to the damping of long-wave perturbations and the selection of the preferred wavelength at the instability threshold. This creates a possibility for the formation of stable regular arrays of quantum dots even in the absence of epitaxial stresses. This possibility is investigated analytically and numerically, by solving the corresponding nonlinear evolution equation for the film surface profile, and analyzing the stability of patterns with different symmetries. It is shown that, near the instability threshold, the formation of stable hexagonal arrays of quantum dots is possible. With the increase of the supercriticality, a transition to a square array of dots or the formation of spatially localized dots can occur. Different models of wetting interactions between the film and the substrate are considered and the effects of the wetting potential anisotropy are discussed. It is argued that the mechanism can provide a new route for producing self-organized quantum dots.