Continuum modeling of Ge/Si heteroepitaxy in the presence of misfit dislocations

The interplay between elastic and plastic relaxation during the growth of heteroepitaxial systems is investigated. A continuum model for the growth dynamics, including both deposition and surface diffusion, is developed and applied to Ge/Si(001). The material transfers are defined according to the tendency toward free energy minimization, as given by the balance between surface energy, including substrate wetting contributions, and strain relaxation. Dislocations are introduced in the growing film based on an energetic criterion. The predicted evolution is in agreement with experimental data. A cyclic growth process, observed in the literature, is reproduced by the simulations.