Asymptotic derivation of the glued-wetting-layer model and contact-angle condition for Stranski-Krastanow islands

We derive a generic mathematical model for Stranski-Krastanow island morphologies in strained solid films. We show that a class of boundary-layer transition models for the material properties across the film/substrate interface reduce to the ``glued-wetting-layer'' model in the limit of small transition-layer thickness. Our results provide an explicit derivation of the zero-contact angle condition for Stranski-Krastanow islands with isotropic properties. The glued-wetting-layer model is used to calculate a typical Stranski-Krastanow morphology and these results are combined with a specific boundary-layer transition model to determine a detailed solution for the wetting layer and the corner region. A consequence of our results is the equivalence of Stranski-Krastanow morphologies calculated from boundary-layer models in the limit of vanishing boundary-layer thickness.