Size calibration of strained epitaxial islands due to dipole-monopole interaction

Irreversible growth of strained epitaxial nanoislands has been studied with the use of the kinetic Monte Carlo (KMC) technique. It has been shown that the strain-inducing size misfit between the substrate and the overlayer produces long range dipole-monopole (d-m) interaction between the mobile adatoms and the islands. To simplify the account of the long range interactions in the KMC simulations, use has been made of a modified square island model. An analytic formula for the interaction between the point surface monopole and the dipole forces has been derived and used to obtain a simple expression for the interaction between the mobile adatom and the rectangular island. The d-m interaction was found to be longer ranged than the conventional dipole-dipole potential. The narrowing of the island size distributions (ISDs) observed in the simulations was shown to be a consequence of a weaker repulsion of adatoms from small islands than from large ones which led to the preferential growth of the former. Furthermore, similar to the unstrained case, the power-law behavior of the average island size and of the island density on the coverage has been found. In contrast to the unstrained case, the value of the scaling exponent was not universal but strongly dependent on the strength of the long range interactions. Qualitative agreement of the simulation results with some previously unexplained behaviors of experimental ISDs in the growth of semiconductor quantum dots was observed.