Statistics of second layer nucleation in heteroepitaxial growth

Statistics of second layer nucleation in heteroepitaxial growth is analysed theoretically. It is assumed that strain can influence the step permeability and atom detachment from two-dimensional (2D) islands. Both effects promote the island-on-island nucleation, however with increasing growth temperature the step permeability decreases, whereas detachment of atoms from the strained 2D island increases. This favours three-dimensional (3D) growth at low and high temperatures, but at the moderate temperatures layer-by-layer growth prevails. It is shown that transition from layer-by-layer to 3D growth enhances temporal fluctuations of the second layer island appearance, so that they change nonmonotonously and stay considerable in the temperature range of interest.