One illustrative method disclosed herein includes, among other things, forming an initial bottom spacer above a semiconductor substrate and adjacent a vertically-oriented channel semiconductor (VOCS) structure and forming a gate structure around the VOCS structure and above the initial bottom spacer. In this example, the method also includes performing at least one etching process to remove at least a portion of the initial bottom spacer that is positioned vertically under the gate structure so as to thereby result in the formation of an air gap that is positioned under the gate structure, wherein the air gap extends around at least a majority of a perimeter of the VOCS structure, and forming a replacement bottom spacer above the semiconductor substrate and adjacent the air gap.