Kinetic Monte Carlo simulation of shape transition of strained quantum dots

The pyramid-to-dome transition in GexSi1-xon Si(100) initiated by step formation on pyramidal quantum dots is atomistically simulated using a multistate lattice model in two-dimensions incorporating effective surface reconstructions. Under quasiequilibrium growth conditions associated with low deposition rates, the transition occurs at island size ncfollowing √ nc∼ x-1.69independent of temperature and deposition rate. The shape transition is found to be an activated process. Results are explained by a theory based on simple forms of facet energies and elastic energies estimated using a shallow island approximation. An asymptotic scaling relation nc1/d∼ x-2for x→0 applicable to d=2 or 3 dimensions is derived. The shape transition energy barrier can be dominated by the interface energy between steep and shallow facets.