Modeling and calculation of field emission enhancement factor for carbon nanotubes array.

To estimate the apex field enhancement factor associated with carbon nanotubes (CNTs) array on a planar cathode surface, the image model of floated sphere between parallel anode and cathode plates was proposed. Firstly, the field enhancement factor of individual CNT was given as the following expression, beta0=h/rho+3.5, where h is the height and rho is the radius of CNTs. Then the field enhancement factor of CNTs array was discussed and the above expression was modified to be beta=h/rho+3.5-W, in which W is the function of the intertube distance R and represents the coulomb field interaction between the CNTs. All results show that the intertube distance of CNTs array critically affects the field emission. When the intertube distance is less than the height of tube, the field enhancement factor will decrease rapidly with decreasing the intertube distance. According to the calculated results and considering the field emission current density, the filed emission is optimal theoretically when the intertube distance is comparable with the height of CNTs.