Emittance of a field emission electron source

An analytical formula of the emittance of a field emitter is given. In contrast to thermal and photoemission, such a formula contains complexity due to the multidimensional nature of the source. A formulation of emittance is given for oneand three-dimensional 3D field emitters. The 3D formulation makes use of the point charge model of a unit cell emitter coupled with a trajectory analysis to follow electrons to an evaluation plane where emittance is determined. The single tip theory is extended to an array and the resulting theory predicts the emittance of a Spindt-type square array of emitters 0.2 cm on a side producing 2000 A /cm2 is 23 mm mrad. Theory compares favorably with experimental measurements in the literature from ungated and gated sources. The impacts of several complications are estimated: the effects of a gate for modulating the emitter; the influence of space charge within the unit cell on the beam; and constraints imposed by modulation frequency, emitter dimensions, and rise/fall time requirements for turning a beam on and off, as determined by the array’s RLC characterization. © 2010 American Institute of Physics. doi:10.1063/1.3267288