Methods of forming a semiconductor structure having FinFET's and planar devices, such as MOSFET's, on a common substrate by a damascene approach, and semiconductor structures formed by the methods. A semiconductor fin of the FinFET is formed on a substrate with damascene processing in which the fin growth may be interrupted to implant ions that are subsequently transformed into a region that electrically isolates the fin from the substrate. The isolation region is self-aligned with the fin because the mask used to form the damascene-body fin also serves as an implantation mask for the implanted ions. The fin may be supported by the patterned layer during processing that forms the FinFET and, more specifically, the gate of the FinFET. The electrical isolation surrounding the FinFET may also be supplied by a self-aligned process that recesses the substrate about the FinFET and at least partially fills the recess with a dielectric material.