Many experimental measurements have been done on GNR conductance. In this paper, analytical model of GNR conductance is presented. Moreover, comparison with published data which illustrates good agreement between them is studied. Conductance of GNR as a one-dimensional device channel with parabolic band structures near the charge neutrality point is improved. Based on quantum confinement effect, the conductance of GNR in parabolic part of the band structure, also the temperature-dependent conductance which displays minimum conductance near the charge neutrality point are calculated. Graphene nanoribbon (GNR) with parabolic band structure near the minimum band energy terminates Fermi-Dirac integral base method on band structure study. While band structure is parabola, semiconducting GNRs conductance is a function of Fermi-Dirac integral which is based on Maxwell approximation in nondegenerate limit especially for a long channel.

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Bilayer Graphene Nanoribbon (BGN) Carrier statistic in the non-degenerate and the degenerate limit is presented. Two dimensional BGN through AB configuration with width less than De-Broglie wave length can be understood as a one dimensional (1D) device. Based on the 1D behavior offered model illustrates exponential function of normalized Fermi energy which explains carrier concentration on low carrier regime. However on zero to 3kBT distance from and within conduction or valence bands high concentration of carriers sensitively depends on normalized Fermi energy which is independent of temperature as well. Since a BGN field effect transistor (BGNFET) can be shaped by using graphene bilayers with an external controllable voltage which is perpendicular to the layers in gates.

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