Self organized array of quantum nanostructures via a strain induced morphological instability

Motivated by the work of Li et al. [1], we have studied the strain induced morphological instability at the submonolayer coverage stage of heteroepitaxial growth on a vicinal substrate with regularly spaced steps. We have performed a linear stability analysis and determined for which conditions of coverage a flat front is unstable and for which conditions it is stable. For low coverages the instability will cause the front to break in an array of islands. Assuming that the fastest growing mode of the instability determines the properties of the array, we make an estimation of the islands sizes and aspect ratios as well as an estimation of the separation length between islands of the array formed when the dominant mechanism for transport of matter is diffusion of particles along the growing front. These estimations are given as functions of the terrace width and coverage. Since these ones are experimentally controllable parameters, our results could be used to tailor the spontaneous formation of quantum nanostructures.