Semi-analytical theory of emission and transport in a LAFE-based diode

A large area field emitter (LAFE) typically consists of several thousands of nanoscale emitting tips. These are difficult to simulate using purely numerical methods based on finite/boundary element or finite difference methods. We show here that a semi-analytically obtained electrostatic field allows tracking of field emitted electrons of a LAFE fairly accurately using the knowledge of only the LAFE geometry. Using a single and a 9-emitter configuration, the beam parameters calculated using this method are compared with the results of tracking using fields generated by COMSOL. The net emission current, energy conservation and the transverse trace-emittance are found to be reproduced with reasonable accuracy.