Electrostatic shielding versus anode-proximity effect in large area field emitters

TL;DR

This paper investigates how the anode-proximity effect can counteract the shielding effect in large area field emitters, providing a model to predict local electric field enhancements and supporting findings with numerical simulations.

Contribution

It introduces a line charge model to accurately predict apex field enhancement factors in large area emitters considering anode proximity effects.

Findings

Anode proximity significantly enhances local electric fields even at large distances.

The model accurately predicts apex enhancement factors in large area emitters.

Numerical simulations support the theoretical predictions.

Abstract

Field emisison of electrons crucially depends on the enhancement of the local electric field around nanotips. The enhancement is maximum when individual emitter-tips are well separated. As the distance between two or more nanotips decreases, the field enhancement at individual tips reduces due to the shielding effect. The anode-proximity effect acts in quite the opposite way, increasing the local field as the anode is brought closer to the emitter. For isolated emitters, this effect is pronounced when the anode is at a distance less than three times the height of the emitter. It is shown here that for a large area field emitter (LAFE), the anode proximity effect increases dramatically and can counterbalance shielding effects to a large extent. Also, it is significant even when the anode is far away. The apex field enhancement factor for a LAFE in the presence of an anode is derived using the line charge model. It is found to explain the observations well and can accurately predict the apex enhancement factors. The results are supported by numerical studies using COMSOL Multiphysics.