Nucleation and step-edge barriers always destabilize step-flow growth of a vicinal surface

We consider the effect of nucleation on a one-dimensional stepped surface, finding that step-flow growth is metastable for any strength of the additional step-edge barrier. The surface is made unstable by the formation of a critical nucleus, whose lateral size is related to the destabilization process on a high-symmetry surface. Arguments based on a critical nucleus of height two, which suggest the existence of a fully stable regime for small barrier, fail to describe this phenomenon.