Side view of the initial version of CNTFET

The gate electrode is actually the silicon wafer itself which is doped heavily with impurities.   The impurities cause the Fermi energy level to be closer to the conduction band or valence (depending on the type of impurity).   A Fermi level closer to the conduction band results in more electrons available for conduction, while a Fermi level closer to the valence band increases the number of holes.   In either case, the gate acts more as a metal, though it is silicon.   Image reproduced from Nanotube Field-Effect Transistor, research.ibm.com courtesy of Phaedon Avouris