Designing a large area field emitter for uniform electron emission

Obtaining uniform emission from a large area field emitter (LAFE) is a challenge that has proved difficult to overcome, both theoretically and experimentally. We use an approximate analytical formula for the apex field enhancement factor (AFEF) of individual emitters to design a LAFE with uniform electron emission, either by optimizing the location of identical emitters or by optimizing the height of individual emitters placed at fixed locations. The optimized parameters (the location or height) are then fed into COMSOL to check for uniformity in the AFEF, a quantity that determines the emitted current. The AFEFs obtained from COMSOL are found to be nearly identical, thereby validating the semi-analytical design technique. For larger LAFEs containing thousands of emitters, the semi-analytical method can be used for designing the LAFE and estimating the current in the optimized configuration.