Quantum-Mechanical Investigation of Field-Emission Mechanism of a Micrometer-Long Single-Walled Carbon Nanotube

A quantum-mechanical simulation is carried out to investigate the charge distribution and electrostatic potential along a $1\mu \mathrm{m}$ long (5,5) single-walled carbon nanotube under realistic field-emission experimental conditions. A single layer of carbon atoms is found sufficient to shield most of the electric field except at the tip where strong field penetration occurs. The penetration leads to a nonlinear decrease of potential barrier for emission, which is equally responsible for the low threshold voltage besides the well-known geometrical field enhancement factor.