Shielding in ungated field emitter arrays

Abstract

Cathodes consisting of arrays of high aspect ratio field emitters are of great interest as sources of electron beams for vacuum electronic devices. The desire for high currents and current densities drives the cathode designer towards a denser array, but for ungated emitters, denser arrays also lead to increased shielding, in which the field enhancement factor β of each emitter is reduced due to the presence of the other emitters in the array. To facilitate the study of these arrays, we have developed a method for modeling high aspect ratio emitters using tapered dipole line charges. This method can be used to investigate proximity effects from similar emitters an arbitrary distance away and is much less computationally demanding than competing simulation approaches. Here, we introduce this method and use it to study shielding as a function of array geometry. Emitters with aspect ratios of 102–104 are modeled, and the shielding-induced reduction in β is considered as a function of tip-to-tip spacing for emitter pairs and for large arrays with triangular and square unit cells. Shielding is found to be negligible when the emitter spacing is greater than the emitter height for the two-emitter array, or about 2.5 times the emitter height in the large arrays, in agreement with previously published results. Because the onset of shielding occurs at virtually the same emitter spacing in the square and triangular arrays, the triangular array is preferred for its higher emitter density at a given emitter spacing. The primary contribution to shielding in large arrays is found to come from emitters within a distance of three times the unit cell spacing for both square and triangular arrays.