Band Structure Effect on Carbon Nanotubes Carrier Drift Velocity

A single wall Carbon nanotube (SWCNT) is a sheet of graphite (called graphene) rolled up into a cylinder. Band structure of carbon nanotube (CNT) is obtained from the graphene band structure. It has been shown the band energy of CNT near to the minimum band energy is parabolic. However it’s not parabolic in other regions. In the parabolic band structure Fermi-Dirac Integrals for carrier study are sufficient, because tabulated solutions are available. On the contrary, for non-parabolic condition density of state and carriers velocity proportion of numerical integrals those are different from Fermi integrals. The carrier statistics to all degeneracy level is presented and its limits obtained. In the nondegenrate regime the results reproduce what is expected from, the Boltzmann statistics. However, the results differ in degenerate regime. The Fermi energy with respect to the transformed conduction band edge is a function of carrier concentration. Given density of state the carrier concentration is obtained based on the Numerical method as an alternative for Fermi – Dirac integrals that we call it Carbon nanotube Fermi integral. Fermi energy with respect to band edge is function of temperature that independent of the carrier concentration in the nondegenrate regime. In the other strongly degenerate, the Fermi energy is a function of carrier concentration appropriate for given dimensionality, but is independent of temperature. On the other hand in no degenerate regime for total part of the band structure carrier velocity limit has been presented.