Overhangs in the solid-on-solid model

Within the framework of a solid-on-solid model we have derived expressions for [110] and [010] step free energies of a simple square (001) surface. We show that at elevated temperatures overhangs in the steps cannot be ignored. With increasing temperature, the free energy curves of [110] and [010] steps nicely collapse onto each other. This means that (1) the two-dimensional equilibrium shape of an ad-atom island or vacancy island will exhibit a perfectly circular shape at elevated temperatures and (2) the step free energies vanishes at the same temperature leading to an isotropic thermal roughening of the (001) surface.