Modeling and simulation for the field emission of carbon nanotubes array

To optimize the field emission of the infinite carbon nanotubes (CNTs) array on a planar cathode surface, the numerical simulation for the behavior of field emission with finite difference method was proposed. By solving the Laplace equation with computer, the influence of the intertube distance, the anode-cathode distance and the opened/capped CNT on the field emission of CNTs array were taken into account, and the results could accord well with the experiments. The simulated results proved that the field enhancement factor of individual CNT is largest, but the emission current density is little. Due to the enhanced screening of the electric field, the enhancement factor of CNTs array decreases with decreasing the intertube distance. From the simulation the field emission can be optimized when the intertube distance is close to the tube height. The anode-cathode distance hardly influences the field enhancement factor of CNTs array, but can low the threshold voltage by decreasing the anode-cathode distance. Finally, the distribution of potential of the capped CNTs array and the opened CNTs array was simulated, which the results showed that the distribution of potential can be influenced to some extent by the anode-cathode distance, especially at the apex of the capped CNTs array and the brim of the opened CNTs array. The opened CNTs array has larger field enhancement factor and can emit more current than the capped one.