One disclosed method includes forming a fin in a substrate by etching a plurality of fin-formation trenches, forming a layer of insulating material in the trenches, performing a densification anneal process on the layer of insulating material and, after performing the densification anneal process, performing at least one ion implantation process to form a counter-doped well region in the fin. The method also includes forming an undoped semiconductor material on an exposed upper surface of the fin, recessing the insulating material so as to expose at least a portion of the undoped semiconductor material and forming a gate structure around the exposed portion of the undoped semiconductor material.