The Ultimate Ballistic Drift Velocity in Carbon Nanotubes

The carriers in a carbon nanotube (CNT), like in any quasi-1-dimensional (Q1D) nanostructure, have analog energy spectrum only in the quasifree direction; while the other two Cartesian directions are quantum-confined leading to a digital (quantized) energy spectrum. We report the salient features of the mobility and saturation velocity controlling the charge transport in a semiconducting single-walled CNT (SWCNT) channel. The ultimate drift velocity in SWCNT due to the high-electric-field streaming is based on the asymmetrical distribution function that converts randomness in zero-field to a stream-lined one in a very high electric field. Specifically, we show that a higher mobility in an SWCNT does not necessarily lead to a higher saturation velocity that is limited by the mean intrinsic velocity depending upon the band parameters. The intrinsic velocity is found to be appropriate thermal velocity in the nondegenerate regime, increasing with the temperature, but independent of carrier concentration. However, this intrinsic velocity is the Fermi velocity that is independent of temperature, but depends strongly on carrier concentration. The velocity that saturates in a high electric field can be lower than the intrinsic velocity due to onset of a quantum emission. In an SWCNT, the mobility may also become ballistic if the length of the channel is comparable or less than the mean free path.