A strained epitaxial film deposited on a deformable substrate undergoes a morphological instability relaxing the elastic energy by surface diffusion. The nonlinear and nonlocal dynamical equations of such films with wetting interactions are derived and solved numerically in two and three dimensions. Above some critical thickness, the surface evolves towards an array of islands separated by a wetting layer. The island chemical potential decreases with its volume, so that the system experiences a non-interrupted coarsening described by power laws with a marked dimension dependence.PACS numbers: 81.15.Aa, 68.35.Ct The dynamics of semiconductor thin films is under active scrutiny due to its importance for both fundamental science and technological applications [1,2]. Indeed, thin film elastic instabilities lead to the self-organization of nanostructures [3] potentially useful e.g. for quantum dots, wires and electronic devices with specific confinement properties [4]. A notorious experimental example is Si/Ge films on a Si substrate which exhibit a variety of structures such as pre-pyramids, pyramids, domes and huts [5,6]. Such epitaxial films experience an elastic stress due to the misfit with the substrate which is relaxed by a morphological instability similar to the Asaro-Tiller-Grinfeld thermodynamical instability in solid-liquid interfaces [7]. This instability was first observed in experiments in helium at low temperature [8] and more generally in various solid interfaces [9,10,11].Although the evolution of epitaxial films involves many complex phenomena regarding surface energy, intermixing and kinetic processes, we focus here on the main effects ruling the dynamics of the morphological instability in strained films. The dynamics is ruled here by surface diffusion driven by the interplay between isotropic surface energy and elastic energy [12,13]. When the film is infinitely thick or when the substrate is infinitely rigid, different theoretical [14,15] and numerical [16,17,18,19] approaches revealed finite-time singularities enforced by elastic stress concentration which account for experiments in thick films [8,9] where dislocations can finally develop. However, these models can not describe experiments of thin films in the Stranski-Krastanov type of growth [5,6] where the surface organizes smoothly into islands separated by a wetting layer and evolving with a coarsening dynamics under annealing [6]. A crucial issue for these systems is the wetting of the substrate by the film [20,21] which is a good candidate for regularizing the dynamics of the instability. Indeed, crack singularities were circumvented near the instability threshold by considering slope dependent wetting effects [22]. However, the interplay between elastic relaxation, surface energy and wetting interactions is still under active study [23,24] and the description of the long term dynamics of the morphological instability in a thin strained film is an open issue. In this Letter, we present a model based on continuum elasticity which we ...

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We study the step meandering instability on a surface characterized by the alternation of terraces with different properties, as in the case of Si(001). The interplay between diffusion anisotropy and step stiffness induces a finite wavelength instability corresponding to a meandering mode. The instability sets in beyond a threshold value which depends on the relative magnitudes of the destabilizing flux and the stabilizing stiffness difference. The meander dynamics is governed by the conserved Kuramoto-Sivashinsky equation, which display spatiotemporal coarsening.