So what we have done is perform, for the first time, a detailed modeling of the nanotube transistor for different electron densities [as opposed to just modeling what an individual electron does]. And we found some surprising results.
Of course, voltage- and current-wise, the more voltage you apply to the gate, the higher the current. But we found that the mobility--the ratio of the electron velocity to the applied field--depends rather strongly on density, which was a surprise. The more density you have, the more carriers you have; but when their density becomes very high, they begin to slow down. Their mobility goes down a lot, by as much as 400 percent.
EET: How did you come to that conclusion?
Avouris: With our theoretical model. Imagine electrons moving in the channel and behaving like a particle. They have an effective mass, a certain ability to move [mobility], and they collide with phonons [get scattered by lattice vibrations]. What we found was that as the density of electrons increases, initially the mobility goes up to a maximum, then it drops. This is due to the electron monotonically increasing the effective mass, and initially increasing and then decreasing the scattering time.
EET: Why does it behave in this way?
Avouris: As you raise the bias voltage on the gate of a nanotube [transistor] channel, you initially fill up the first conduction band with electrons. Then there is a strong drop in mobility as you begin filling the second conduction band and hence open an additional channel for scattering.
EET: So is this an advantage or disadvantage compared with silicon?
Avouris: There has been an interest in [harnessing] negative-differential mobility as a way of doing electronics and logic, but we are not proposing that here. We are just studying the transport in the nanotube transistor channel as a phenomenon.
EET: So you are defining the operating regions of the nanotube transistor. What is so different about the operating regions of nanotube transistors?
Avouris: The interesting thing is not just that mobility is dependent on density. For low densities, velocity initially goes up with increasing drain field; then you hit the negative-differential resistance regime, where velocity decreases with an increasing field. Above this critical density, you don't see the usual saturation of the transistor [as you do for silicon transistors], where the velocity reaches a value and stops. For nanotube transistors with high electron density, velocity just keeps increasing. Saturation is the normal limit to operating silicon transistors in the diffusion regime, but in nanotube transistors you only see saturation-like behavior for conditions of low density and before you reach negative-differential mobility.
This is why some groups have reported seeing saturation and others have not. We think the conflicting reports can be ex- plained by the [lack of knowledge] that mobility depends on density, and that saturation only occurs at low densities.
EET: So some groups, because they were operating their nanotube transistors at high densities, did not find saturation?
Avouris: [Correct.] At high densities, there is no saturation in sight. Recently we [at IBM] demonstrated light-emitting nanotubes that operated in the high-density regime, where the excess energy in the channel was released as photons.