We investigate the formation and the coarsening dynamics of islands in a strained epitaxial semiconductor film. These islands are commonly observed in thin films undergoing a morphological instability due to the presence of the elasto capillary effect. We first describe both analytically and numerically the formation of an equilibrium island using a two dimensional continuous model. We have found that these equilibrium island-like solutions have a maximum height h0 and they sit on top of a flat wetting layer with a thickness hw. We then consider two islands and we report that they undergo a non-interrupted coarsening that follows a two stage dynamics. The first stage may be depicted by a quasi-static dynamics, where the mass transfers are proportional to the chemical potential difference of the islands. It is associated with a time scale tc that is function of the distance d between the islands, and leads to the shrinkage of the smallest island. Once its height becomes smaller than a minimal equilibrium height h * 0 , its mass spreads over the entire system. Our results pave the way for a future analysis of coarsening of an assembly of islands.PACS numbers: 81.15. Hi, 68.35.Ct, 81.10.Aj, 47.20.Hw Understanding the dynamics of coarsening and its effect on self-organisation is a central question in nonequilibrium physics and solid-state physics since its experimental discovery by Ostwald at the end of the 19th century [1] and the seminal theoretical papers of LishitzSlyosov and Wagner [2,3] in the late 60's, see also [4]. Coarsening is a general phenomena in which the natural size of a pattern increases with time in a continuous manner over a large range of time scales [5][6][7][8]. From a more applied point of view, coarsening has a significant impact on properties of matter such as the size of grains in polycrystalline solids, the hardening of metallic alloys, foam dynamics, sintering, sand dunes, etc. We focus here, on the fundamental aspect of coarsening of strained semiconductor quantum dots, such as the gallium-aluminumnitride or silicon-germanium islands [9][10][11][12][13][14][15][16][17][18][19][20][21]. These islands are extensively under scrutiny both for their present and promising applications in electronics or optics, as for example single photons emitters, and for their insights into the fundamental processes of epitaxial growth. The properties and potential applications of quantum dot assembly are indeed crucially dependent on the amount of coarsening, that may critically affects the size homogeneity of such structures [20]. Moreover, the coarsening of such islands seems to be out of the classical description of Ostwald coarsening and requires more investigation.The formation of self-organized semi-conductor quantum dots results from the Stranski-Krastanov growth mode [22]. In this scheme, growth initially proceeds as planar layers, that transform above a given critical thickness h c , into islands separated by a wetting layer. These islands enable a partial relaxation of the elastic stress of t...

We focus in this work on the effect of the surface energy anisotropy on an elastically strained semiconductor film and in particular on its role on the coarsening dynamics of elastically strained islands. To study the dynamics of a strained film, we establish a one-dimensional nonlinear and nonlocal partial differential equation which takes into account the elastic, capillary, wetting, and anisotropic effects. We first construct an approximate stationary solution of our model using a variational method and an appropriate ansatz. This stationary solution is used to compute the chemical potential dependence on the island height. In particular, we find that the surface energy anisotropy increases the convexity of the chemical potential and this is shown to have an effect on the driving force for the coarsening. Second, we study the coarsening dynamics of an islands pair by means of numerical simulations. We find that the presence of the surface energy anisotropy may increase or decrease the coarsening time of the system. We show that this phenomenon depends on the initial heights of island pairs. We thus highlight that the driving force for the coarsening is due to the variation of the chemical potential with respect to the islands height and that two different regimes are possible.

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