Kinetics of second layer nucleation with permeable steps

The critical island size for second layer nucleation is a basic parameter which determines the mechanism of growth and in turn the morphology of the growing surface. When it is larger than the mean distance between the islands layer-by-layer growth takes place. In the opposite case 3D mounds are formed. The critical island size for second layer nucleation is calculated by taking into account the ability of adatoms to cross the step surrounding the island without joining the kink sites (the effect of the step permeability). We have found that the mean field approximation fails to give solution in the case of permeable steps. By making use of the probabilistic approach for derivation of the nucleation frequency on top of the first layer island we show that the critical size decreases with increasing degree of permeability. This is due to the contribution of atoms from the area surrounding the island which is especially important at the early stage of deposition where the average size of the first layer islands is small. The decrease of the critical size is steeper at higher temperatures or smaller densities of the first layer nuclei and in turn larger areas around the islands which feed the latter. The rate of growth of the first level island remains unaffected by the step permeability as the adatoms always join the step after several (or many) attempts under the condition of complete condensation. An important conclusion is that the step permeability could give rise to a transition from planar to 3D growth.