Electric field enhancement in field-emission cathodes based on carbon nanotubes

The problem of determining the field enhancement factor in field-emission cathodes based on carbon nanotubes (CNTs) is considered. The electrostatic problem of finding the field enhancement factor for nanotubes with different shapes of the tip as a function of the angle the nanotube makes with the cathode surface and of the interelectrode spacing is solved. The dependence of the electric field enhancement factor on the spacing between vertically oriented nanotubes constituting an array is derived. Making allowance for this dependence gives an optimal value of the surface density of nanotubes in the array at which the emission current density is maximal. The I-V characteristic of CNT-based cathodes is studied with regard to the statistical straggling of their orientation angles. This I-V characteristic is compared with the characteristic obtained with regard to the statistical straggling of the CNT geometrical parameters.