There have been extensive studies on the field electron emission from carbon nanotubes both theoretically [1-3] and experimentally [4-7] since the large apex ratio of carbon nanotubes provides the possibility of achieving strong field-emission current. For bulk emitters and weak emission current, the quasi-equilibrium hypothesis works quite good and leads to the standard Fowler-Nordheim (FN) theory. However for carbon nanotubes, which have much less atoms than the bulk emitters, the non-equilibrium effect will be important, especially when the emission current is strong. On the other hand, the current saturation has been observed experimentally in field emission from carbon nanotubes [4-6], which has been considered as a direct evident of FN theory violation. To simulate the single-walled carbon nanotubes (SWCNT) in realistic FE experimental conditions, a multi-scale strategy is used [9,10]. The key point is to divide the quantum region into subregions. Each sub-region and its adjacent's form a subsystem that is simulated by the modified neglect of diatomic overlap (MNDO) semiempirical quantum mechanical method. The electronic structure of the total quantum region is obtained by Yang's divide-and-conquer method [8]. The simulation can be accelerated by a tabulate of electron density matrix of a subsystem of SWCNT in various electrostatic fields. This tabulate method will be reported elsewhere.
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