Consider faceting of a crystal surface caused by strongly anisotropic surface tension, driven by surface diffusion and accompanied by deposition (etching) due to fluxes normal to the surface. Nonlinear evolution equations describing the faceting of 1+1 and 2+1 crystal surfaces are studied analytically, by means of matched asymptotic expansions for small growth rates, and numerically otherwise. Stationary shapes and dynamics of faceted pyramidal structures are found as functions of the growth rate. In the 1+1 case it is shown that a solitary hill as well as periodic hill-and-valley solutions are unique, while solutions in the form of a solitary valley form a one-parameter family. It is found that with the increase of the growth rate, the faceting dynamics exhibits transitions from the power-law coarsening to the formation of pyramidal structures with a fixed average size and finally to spatiotemporally chaotic surfaces resembling the kinetic roughening.
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.
Articles you may be interested inGeneric role of the anisotropic surface free energy on the morphological evolution in a strained-heteroepitaxial solid droplet on a rigid substrate Morphological evolution in a strained-heteroepitaxial solid droplet on a rigid substrate: Dynamical simulations Phase-field modeling of stress-induced surface instabilities in heteroepitaxial thin films J. Appl. Phys. 98, 044910 (2005); 10.1063/1.1996856Effect of a cap layer on morphological stability of a strained epitaxial film This paper investigates effects of surface stress and wetting layers on the morphological instability of a growing epitaxially strained dislocation-free solid film. Linear stability analysis of the planar film shows that the film, unstable due to lattice mismatch, is affected differently by surface stress for a film under compression than for one under tension and depends on whether the relative stiffness of the film to the substrate is less than or greater than ͑1−2͒ −1 ; here is Poisson's ratio. The presence of a wetting layer has the capacity to substantially stabilize the planar film. The critical thickness of the film below which the film is stable depends on the bulk elastic properties of film and substrate and increases with increase of the wetting potential.
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