Second Layer Nucleation in Thin Film Growth

We study the second layer nucleation on top of islands emerging during epitaxial growth of thin films. By employing kinetic Monte Carlo simulations we determine the critical island radius $R_c$ upon which small stable nuclei form in the second layer. We find that the dependence of $R_c$ on the additional step edge barrier $\Delta E_s$ (Schwoebel barrier) is not in accordance with existing theories. Scaling arguments are presented which explain how $R_c$ depends on $\Delta E_s$ as well as on adatom diffusion rates and on the incoming atom flux. Based on the theory, the occurrence of smooth layer-by-layer growth as opposed to rough multilayer growth is discussed.