Abstract
A recent analytical model for large area field emitters [D. Biswas and R. Rudra, Phys. Plasmas 25, 083105 (2018)], based on the line charge model (LCM), provides a simple approximate formula for the field enhancement on hemiellipsoidal emitter tips in terms of the ratio of emitter height to pairwise distance between neighboring emitters. The formula, verified against the exact solution of the linear LCM, was found to be adequate, provided that the mean separation between emitters is larger than half the emitter height, h. In this paper, we subject the analytical predictions to a more stringent test by simulating (i) an infinite regular array and (ii) an isolated cluster of 10 random emitters, using the finite element software COMSOL v5.4. In the case of the array, the error in the apex field enhancement factor (AFEF) is found to be less than 0.25% for an infinite array when the lattice constant c ≥ 1.5h, increasing to 2.9% for c = h and 8.1% for c = 0.75h. For an isolated random cluster of 10 emitters, the error in large AFEF values is found to be small. Thus, the error in the net emitted current is small for a random cluster compared to a regular infinite array with the same (mean) spacing. The LCM thus provides a reasonable analytical tool for optimizing a large area field emitter.
Highlights
Large area field emitters (LAFEs) are promising as a high brightness source of cold electrons
For the random cluster under consideration, the error in net emission current density is a nominal 15.5% at a macroscopic field of 17.5 MV/m, while for the infinite array having c = h, the roughly 3% error in the line charge model (LCM)-apex field enhancement factor (AFEF) shifts the current density by a factor of 2
The analytical predictions of the line charge model for large area field emitters have been the subject of investigation in this paper
Summary
Large area field emitters (LAFEs) are promising as a high brightness source of cold electrons They have been investigated for around four decades, as patterned arrays of pointed emitters or clusters of nanotubes or nanorods. An isolated hemiellipsoid with its axis aligned along an external macroscopic field E0zhas a projected line charge distribution [along the emitter (Z) axis] that is linear.. It is necessary to subject Eq (1), obtained using linear LCM, to more stringent tests such as by comparing its predictions with numerical (finite element) simulations where the projected charge density does not have constraints of linearity. Rather than studying just the error in the apex field enhancement factor of individual emitters in the cluster, we shall compute the error in the net emitted current so that emitters in close proximity do not get a disproportionately large weight in deciding the error in LCM prediction. We shall discuss the implications of our results in designing large area field emitters
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