Modeling of Gate Bias Modulation in Carbon Nanotube Field-Effect-Transistors

The threshold voltages of a carbon nanotube (CNT) field-effect transistor (FET) are derived and compared with those of the metal oxide-semiconductor (MOS) FETs. The CNT channel is so thin that there is no voltage drop perpendicular to the gate electrode plane, which is the CNT diameter direction, and this makes the CNTFET characteristics quite different from those in MOSFETs. The relation between the voltage and the electrochemical potentials, and the mass action law for electrons and holes are examined in the context of CNTs, and it is shown that the familiar relations are still valid because of the macroscopic number of states available in the CNTs. This is in sharp contrast to the cases of quantum dots. Using these relations, we derive an inversion threshold voltage V(sub Ti) and an accumulation threshold voltage V(sub Ta) as a function of the Fermi level E(sub F) in the channel, where E(sub F) is a measure of channel doping. V(sub Ti) of the CNTFETs has a much stronger dependence than that of MOSFETs, while V(sub Ta)s of both CNTFETs and MOSFETs depend quite weakly on E(sub F) with the same functional form. This means the transition from normally-off mode to normally-on mode is much sharper in CNTFETs as the doping increases, and this property has to be taken into account in circuit design.