Optimal epitaxially-strained islandsdeposited on deformable substrates Paolo Piovano Faculty of Mathematics, University of Vienna, Austria In this talk the problem of characterizing the equilibrium shape of multilayer islands of thin films deposited on deformable substrates is considered both in the Stranski-Krastanow (SK) and Volmer-Weber (VW) modes. SK differs from VW for the presence of a layer of film atoms that always wets the substrate. We refer to the model introduced in [2] for which the island shape is the results of two competing mechanisms. On one hand, the lattice mismatch between the film and the substrate generate large stresses, and corrugations are created because film atoms move to release the elastic energy. On the other hand, the flat profile is preferable to minimize the surface energy. Regularity results for the film profile are established by extending ideas developed in [1] to include the VW mode and the case of (possibly) different elastic properties for the film and the substrate, and by employing regularity results introduced for transmission problems. As a byproduct of the analysis, geometrical conditions on the wetting angle, i.e., the angle formed by the film profile and the substrate surface, are provided. In particular, the validity of the Young-Dupr´e equation is assessed for solid islands in the context of linear elasticity. References [1] Fonseca I., Fusco N., Leoni G., Morini M., Equilibrium configurations of epitaxially strained crystalline films: existence and regularity results. Arch. Ration. Mech. Anal. 186 (2007), 477–537. [2] Spencer B.J., Asymptotic derivation of the glued-wetting-layer model and the contact-angle condition for Stranski-Krastanow islands. Phys. Rev. B 59 (1999), 2011–2017.
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