Critical temperature for mound formation in molecular-beam epitaxy

The results of an analytic calculation of the surface current and selected mound angle as a function of the Ehrlich-Schwoebel step barrier E(B) and substrate temperature T are presented for a model of epitaxial growth on bcc(100) and fcc(100) surfaces. Depending on the sign of E(B) and the magnitude of the prefactor for diffusion over a step, various scenarios are possible, including the existence of a critical temperature T-c for mound formation above which (for a positive step barrier) or below which (for a negative step barrier) quasi-layer-by-layer growth will be observed. For the case of Fe/Fe(100) deposition our calculation implies an upper bound for T-c which is consistent with experiment. The weak parameter dependence of our estimates for the mound angle confirms and explains the good agreement found in previous estimates assuming different values of the step barrier. We also clarify the transition to layer-by-layer growth at low and high temperature including the effect of a finite diffusion length on reentrant behavior at low temperature.