Model calculation for the field enhancement factor of carbon nanotube

To estimate the apex field enhancement factor associated with carbon nanotube on a planar cathode surface, the simple model of floated sphere between parallel anode and cathode plates was studied. When the anode-cathode distance d is much larger than the height h of carbon nanotube, the field enhancement factor of carbon nanotube was given as the following expression β0=h∕ρ+3.5 with the image method, which is a little than the early work of Miller. Finally, the influence of the anode-cathode distance on the enhancement factor was also discussed and the expression of enhancement factor of carbon nanotube should be modified to be β=h∕ρ+3.5+A(h∕d)3, where A is the constant. This shows a much weaker influence of the relatively smaller anode-cathode distance on the field enhancement factor of carbon nanotube than that estimated earlier. Thus, we can lower the threshold voltage to some extent by the decrease of the anode-cathode distance. The higher aspect ratio of carbon nanotube and the lower anode-cathode distance (still larger than a few times of the height of carbon nanotube) are the main factors leading to the stronger field at the apex.