Equilibrium Shapes of Small Three-dimensional Stranski-krastanow Islands in Epitaxially-strained Solid Lms

We determine the equilibrium morphology of a strained solid lm for the case where it wets the substrate (Stranski-Krastanow growth). Using a continuum elasticity model with isotropic surface energy and equal elastic constants in the lm and substrate, we calculate an asymptotic solution for the axisymmetric three-dimensional equilibrium shape of a small island, where the height is much less than the width. The elasticity equations are solved using an axisymmetric stress function and a Hankel transform is used to relate the island shape to the stresses. The solution to the resulting integro-diierential eigenvalue problem for the island shape is determined using a Bessel series. We nd that the width of a small three-dimensional island is almost a factor of two larger than the width of a thin two-dimensional island ridge. Our predictions of the island width compare favorably with experimental data in the GeSi/Si system.