Nonparabolic band structure effect on carrier transport in semiconducting graphene nanoribbons

The band energy of graphene nanoribbon is parabolic when reaching the minimum band energy. Otherwise, it is nonparabolic. In the parabolic band structure, Fermi-Dirac integrals are employed to study the carrier statistic whereas for nonparabolic part, numerical solutions are needed. Numerical method shows Fermi energy with respect to the band edge is a function of temperature that independent of the carrier concentration in the nondegenerate regime. However, the results differ in degenerate regime. In the strongly degenerate regime, the Fermi energy is a function of carrier concentration appropriate for given dimensionality, but is independent of temperature. We also report the salient features of the saturation velocity in parabolic part of the band structure. The intrinsic velocity is found to be appropriate thermal velocity in the nondegenerate regime, increasing with the temperature, but independent of carrier concentration. Conversely in degenerate regime, this intrinsic velocity is the Fermi velocity that is independent of temperature, but depends strongly on carrier concentration.