Continuum Modeling of cyclic growth in Ge/Si(001) heteroepitaxy

We present a continuum approach able to tackle both elastic and plastic relaxation (via insertion of misfit dislocations) during deposition of Ge on Si(001). Our model is based on a suitable definition of chemical potential, accounting for both surface- and elastic-energy contribution. Material is added to the system by an external flux and is allowed to redistribute along the profile of the growing film by a diffusion equation, mobility being restricted to the free-surface region only. At different stages of deposition, an attempt is made to insert a dislocation in the system. In case the energy is lowered by the presence of the defect, the contribution to the chemical potential of the dislocation stress field is superimposed to that originated by lattice misfit in further evolution. The procedure is iterated, possibly leading to the insertion of several dislocations. Our simulations predict cyclic growth, i.e. oscillations in Ge- islands shape and aspect ratio, as observed experimentally [F. K. LeGoues et al., Phys. Rev. Lett. 73, 300 (1994)].