Disclosed herein are various methods of forming isolation structures on FinFETs and other semiconductor devices, and the resulting devices that have such isolation structures. In one example, the method includes forming a plurality of spaced-apart trenches in a semiconducting substrate, wherein the trenches define a fin for a FinFET device, forming a layer of insulating material in the trenches, wherein the layer of insulating material covers a lower portion of the fin but not an upper portion of the fin, forming a protective material on the upper portion of the fin, and performing a heating process in an oxidizing ambient to form a thermal oxide region on the covered lower portion of the fin.