Graphene Nanoribbon Fermi Energy Model in Parabolic Band Structure

Graphene nanoribbon (GNR) has possibility to overcome the carbon nanotube chirality challenge as a nanoscale device channel. Because of one dimensional behavior of GNR, carrier statistic study is attractive. More research work has been done on carrier statistic study of GNR especially in Boltzmann approximation (Nondegenerate regime). Based on quantum confinement effect to improve the fundamental studies in degenerate regime we focused on, parabolic part of GNR band energy. Our method demonstrates that the band energy of GNR near to the minimum band energy is parabolic. In this part of the band structure, Fermi-Dirac integrals are sufficient for carrier concentration study. Similar to any other one dimensional device in nondegenerate regime Fermi energy shows temperature dependent behavior, on the other hand normalized Fermi energy with respect to the band edge is function of carrier concentration in the degenerate regime. However band structure is not parabolic in other parts of the band energy and numerical solution of GNR Femi-Dirac integrals are needed.