One method disclosed herein includes, prior to forming an isolation region in a semiconducting substrate for the device, forming a doped well region and a doped punch-stop region in the substrate, introducing a dopant material that is adapted to retard diffusion of boron or phosphorous into the substrate to form a dopant-containing layer proximate an upper surface of the substrate, performing an epitaxial deposition process to form an undoped semiconducting material above the dopant-containing layer, forming a plurality of spaced-apart trenches that extend at least partially into the substrate, wherein the trenches define a fin for the device comprised of at least the undoped semiconducting material, forming at least a local isolation insulating material in the trenches, and forming a gate structure around at least the undoped semiconducting material, wherein a bottom of a gate electrode is positioned approximately level with or below a bottom of the undoped semiconducting material.