Quantum Transport in Nanowires and Nanographene

Transport in nanowires and nanographene with emphasis on nanotubes is reviewed from classical to quantum, low-field to high-field, nondegenrate to degenerate, scattering limited to ballistic, and beyond. Nonequilibrium Arora distribution function (NEADF) is shown to be an outgrowth of the Fermi-Dirac statistics by inclusion of the energy gained in a mean free path (mfp). NEADF is highly asymmetric with electrons changing equilibrium random phase to extreme nonequilibrium unilateral phase in a towering electric field. The drift response to the electric field is shown to be limited to the unilateral intrinsic velocity appropriate for twice the carrier concentration as electrons transfer from −x-direction to +x-direction in the presence of an extremely high electric field in the −x-direction. An electron temperature for degenerate statistics is defined to make it compatible with nondegenrate statistics. The intrinsic velocity giving saturation is shown to be independent of the scattering-limited or ballistic mobility. Optical phonon emission may lower the saturation velocity. In a low-field domain, the mobility may become size-dependent and is ballistic when injection from the ohmic contacts is considered.