One illustrative method of forming a TFET device includes forming a first semiconductor material that extends for a full length of a drain region, a gate region and a source region of the device, masking the drain region while exposing at least a portion of the gate region and exposing the source region, forming a second semiconductor material above the gate region and above the source region, forming a third semiconductor material above the second semiconductor material and above the gate region and above the source region, the third semiconductor material being doped with an opposite type of dopant material than in the first semiconductor material, masking the drain region, and forming a gate structure above at least a portion of the exposed gate region.