Kink-formation kinetics and submonolayer density of magic two-dimensional islands in molecular beam epitaxy

The nucleation and growth of compact two-dimensional islands having a regular shape and edges consisting of atomically straight kink-free segments is studied analytically and with kinetic Monte Carlo (KMC) simulations. In the analytical model the islands grow by a cyclic process of deposition of single atomic rows along the island edges. Two ends of an incomplete row are the kink sites where adatoms incorporate into the crystal. Adatoms attached to the island edge are able to migrate along the edge and detach back to the terrace before reaching the kinks. Completion of the rows corresponds to a sequence of the magic island sizes. It is assumed that a one-dimensional nucleus of the next atomic row (a pair of kinks) forms when two adatoms meet each other at the edge of the magic island. It follows from the model that at certain growth conditions the island density is independent of the deposition flux and increases with the increasing growth temperature. The predictions of the analytical model are in good agreement with results of KMC simulations. Computer simulations also show that the island size distribution gradually changes with the increasing detachment probability from the monomodal distribution with a peak around the mean island size to a sequence of monotonously decreasing peaks at magic sizes.