Effect of screening on the emissivity of field electron emitters based on carbon nanotubes

The effect of screening on the emissivity of a field cathode built around a carbon nanotube array is analyzed. A numerical method of solving the Laplace equation for intricate-shape cathodes is developed that makes it possible to relate the amplification factor to the nanotube spacing in arrays containing as many as 225 emitters. Mutual screening of the tubes, which shows up in the dependence of the field amplification factor on the average emitter spacing, is studied numerically. The optimal spacing between the tubes that provides an emission current maximum density at a given applied voltage is determined. The role of edge effects in carbon nanotube screening is established.