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

Abstract

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.

Morphologies and kinetics of a dewetting ultrathin solid film

“…19, following Ref. 20, the partial differential equation ͑PDE͒-based model is developed, which allows to predict the wavelength of the fastest growing cosinelike perturbation of the film surface ͑also called the normal perturbation͒, assuming surface diffusion and the two-layer wetting potential. [20][21][22][23][24] The model also enables computation of the dynamical, faceted morphologies.…”

Multiscale Pattern Generation in Viscoelastic Polymer Films by Spatiotemporal Modulation of Electric Field and Control of Rheology

“…Pattern formation in thin polymer fi lms by exploiting the instabilities engendered by the intermolecular forces, residual stresses, [30][31][32] contact forces, [33][34][35][36][37][38][39][40][41][42] lithographically induced self assembly (LISA), [43][44][45] and externally applied electric fi eld has been extensively studied. Rapid miniaturization of the technological devices has made these patterns useful in a variety of mesoscale product or processes such as coatings, micro-adhesives, microelectronics, micro/nanofl uidic devices, and superhydrophobic surfaces.…”

Dewetting of a Solid Monolayer

“…Spontaneous breakup of the film into dots can be analyzed within the frame of continuum models including an effective wetting potential, with surface energy [4], and elastic effects [5]. Moreover, the nonlinear dynamics of the edges of these layers [2,6,7] may also lead to the periodic formation of holes behind the dewetting rim.…”