Quantum dot self-assembly in growth of strained-layer thin films: A kinetic Monte Carlo study

We use Monte Carlo (MC) simulations to study island formation in the growth of thin semiconducting films deposited on lattice-mismatched substrates. It is known that islands nucleate with critical nuclei of about one atom and grow two dimensionally until they reach a critical size ${s}_{c},$ when it is favorable for the islands to become three dimensional. We investigate the mechanism for this transition from two-dimensional (2D) to three-dimensional (3D) growth. Atoms at the edge of 2D islands with the critical size ${s}_{c}$ become mobile as a result of strain and are promoted to the next level. Edge atoms of the resulting island remain highly strained and are promoted to the higher layers in quick succession. This process of depletion is rapid and occurs at a sharply defined island size. We discuss why this leads to the uniformity seen in self-assembled quantum dots in highly mismatched heteroepitaxy. The results of the MC simulations, although done in $(1+1)$ dimensions, should be applicable to $(2+1)$ dimensions.