Equilibrium and Nonequilibrium Carrier Statistics in Carbon Nano-Allotropes

The integrated carrier statistics of Dirac Fermions in carbon allotropes comprising graphene nanolayer, graphene nanoribbons (GNR) and carbon nanotubes (CNTs) is described. Nonequilibrium Arora’s Distribution Function (NEADF) is the basis of transformation of randomly oriented to directed moments in the presence of an electric field, leading to saturation that is limited to the intrinsic Fermi velocity

$$ v_{Fo} \approx 10^{6} m/s $$

for carbon-based devices. In the semiconducting state, the intrinsic velocity is the saturation velocity that is substantially below

$$ v_{Fo} $$

depending on the carrier concentration. Velocity-field relation arising from NEADF is elaborated by a tanh function as a result of degeneracy temperature that rises linearly with carrier concentration in the strongly degenerate regime. Current–voltage characteristics and high-field-initiated resistance surge indicate the transformed nature of existing paradigms.