Band energy effect on carrier velocity limit in graphene nanoribbon

Many studies on low-energy limit indicate that band energy of graphene nanoribbon research (GNR) is linear while it illustrates parabolic characteristic with square root approximation model near the Fermi point (k = 0) and non-parabolic characteristic when wave vector is far away from Fermi point . We report that in parabolic and non-parabolic conditions charge transport is controlled by the saturation velocity similar to the conventional one-dimensional device. Also, we claim that at narrower bandwidth the intrinsic velocity approaches saturation faster because wider widths have lighter effective mass, which leads to higher average velocity. The intrinsic velocity is approximated to be thermal velocity in nondegenerate regime and Fermi velocity in degenerate regime, which depends on carrier concentration. Even in very high electric field, because of quantum emission, the saturation velocity can be lower than the intrinsic velocity.