Verification of shielding effect predictions for large area field emitters

TL;DR

This study validates an analytical line charge model for large area field emitters by comparing its predictions with finite element simulations, demonstrating its accuracy for array and cluster configurations, aiding emitter optimization.

Contribution

The paper provides a rigorous validation of the line charge model against finite element simulations for large area field emitters, extending its applicability.

Findings

Error in apex field enhancement factor is less than 0.25% for array with lattice constant ≥ 1.5h.

Error increases to 8.1% for array with lattice constant 0.75h.

Small error in large AFEF for isolated random clusters, supporting the model's use.

Abstract

A recent analytical model for large area field emitters, based on the line charge model (LCM), provides a simple approximate formula for the field enhancement on hemi-ellipsoidal emitter tips in terms of the ratio of emitter height and pairwise distance between neighboring emitters. The formula, verified against the exact solution of the linear LCM, was found to be adequate provided the mean separation between emitters is larger than half the emitter height. 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. In case of the array, the error in apex field enhancement factor (AFEF) is found to be less than $0.25\%$ for an infinite array when the lattice constant $c \geq 1.5h$, 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 net emitted current is small for a random cluster compared to a regular infinite array with the same (mean) spacing. The line charge model thus provides a reasonable analytical tool for optimizing a large area field emitter.