Recent experiment on carbon NT p-channel FETs with a long channel (3 µm)@footnote 1@ is analyzed theoretically. They observed saturation of drain current (I@sub d@) as a function of drain voltage (V@sub d@), which plays a crucial role in digital applications. Two possible mechanisms can make the carrier acceleration by V@sub d@ ineffective and bring about the I@sub d@ saturation: (1) Coulomb repulsion from other carriers forming a self-consistent spatial distribution, leading to channel pinch-off; (2) phonon scattering due to a large field created by V@sub d@, leading to carrier velocity saturation. Since the former causes the saturated current I@sub dsat@ to depend quadratically on gate voltage (V@sub g@) and the latter linearly, two mechanisms are distinguishable. Noticing the quadratic dependence in their measurement, we argue that the Coulomb-induced pinch-off formation was the mechanism in these long-channel NT FETs. The maximum field was about 10 kV/cm and the velocity saturation for holes still did not occur. This field is comparable to that of electrons in silicon. |I@sub d@|-V@sub g@ characteristics did not show a sharp rise at the onset of strong inversion, during the transition from accumulation to inversion, as V@sub g@ was increased. This is significantly different from the familiar behavior of metal-oxide-semiconductor FETs. In NT FETs, I@sub d@ was practically zero for a wide range V@sub g@ = 3 to 40 V beyond accumulation. We argue that a high Schottky barrier for electrons existed at the source/drain metal-semiconductor contact and the electron flow was blocked in the inverted case although the hole flow was not in the accumulated case. Making Ohmic contact to both p- and n-NTs is mandatory for complementary circuitry, and will have to be explored for future electronics. @FootnoteText@ @footnote 1@C. Zhou, J. Kong, and H. Dai, Appl. Phys. Lett. 76, 1597 (2000).