Stability of strained heteroepitaxial systems in (1 + 1) dimensions

We present a simple analytical model for the determination of the stable phases of strained heteroepitaxial systems in (1 + 1) dimensions. In order for this model to be consistent with a subsequent dynamic treatment, all expressions are adjusted to an atomistic Lennard-Jones system. Good agreement is obtained when the total energy is assumed to consist of two contributions: the surface energy and the elastic energy. As a result, we determine the stable phases as a function of the main "control parameters" (binding energies, coverage, and lattice mismatch). We find that there exists no set of parameters leading to an array of islands as a stable configuration. We, however, show that a slight modification of the model can lead to the formation of stable arrays of islands.