One method involves providing a substrate comprised of first and second semiconductor materials, performing an etching process through a hard mask layer to define a plurality of trenches that define first and second portions of a fin for a FinFET device, wherein the first portion is the first material and the second portion is the second material, forming a layer of insulating material in the trenches, performing a planarization process on the insulating material, performing etching processes to remove the hard mask layer and reduce a thickness of the second portion, thereby defining a cavity, performing a deposition process to form a third portion of the fin on the second portion, wherein the third portion is a third semiconducting material that is different from the second material, and performing a process such that a post-etch upper surface of the insulating material is below an upper surface of the third portion.