One illustrative device disclosed herein includes, among other things, an active layer positioned above a layer of insulating material, a fin positioned above the active layer, a gate insulation layer positioned on the active layer and on the fin, a conductive gate structure that is positioned around at least a portion of the fin and above at least a portion of the active layer, wherein the conductive gate structure comprises at least one work function adjusting metal layer positioned on the gate insulation layer, a first channel region defined in the fin under the conductive gate structure, and a second channel region defined in the active layer under the conductive gate structure.