Efficient phase-field simulation of quantum dot formation in a strained heteroepitaxial film

A Cahn-Hilliard evolution equation possessing a source term is employed to study the morphological evolution of a strained heteroepitaxial thin film, during continuous mass deposition, on a substrate with an embedded coherent island. The elastic properties and the surface energy are anisotropic, with the surface energy anisotropy being strong enough to result in missing orientations and facets. A sophisticated finite-difference/multigrid method and an implicit time integration scheme are combined to make an efficient numerical method, one which enables numerically tractable computation in both two and three dimensions. Herein we present preliminary two-dimensional results demonstrating the utility of our finite difference/multigrid algorithms. The strain localization effects produced by a buried, coherent inclusion are shown to produce laterally organized quantum dots during the morphological evolution of the film.