One illustrative method disclosed herein includes, among other things, forming a first fin having first and second opposing sidewalls and forming a first sidewall spacer positioned adjacent the first sidewall and a second sidewall spacer positioned adjacent the second sidewall, wherein the first sidewall spacer has a greater height than the second sidewall spacer. In this example, the method further includes forming epitaxial semiconductor material on the fin and above the first and second sidewall spacers.