  For carbon nanotube transistors, as for graphene, the electrical contacts are
a key factor limiting device performance. We calculate the device
characteristics as a function of nanotube diameter and metal workfunction.
Although the on-state current varies continuously, the transfer characteristics
reveal a relatively abrupt crossover from Schottky to ohmic contacts. We find
that typical high-performance devices fall surprisingly close to the crossover.
Surprisingly, tunneling plays an important role even in this regime, so that
current fails to saturate with gate voltage as was expected due to "source
exhaustion".
