One method disclosed includes, among other things, forming an initial fin structure comprised of portions of a substrate, a first epi semiconductor material and a second epi semiconductor material, forming a layer of insulating material so as to over-fill the trenches that define the fin, recessing a layer of insulating material such that a portion, but not all, of the second epi semiconductor portion of the final fin structure is exposed, forming a gate structure around the final fin structure, further recessing the layer of insulating material such that the first epi semiconductor material is exposed, removing the first epi semiconductor material to thereby define an under-fin cavity and substantially filling the under-fin cavity with a stressed material.