Interplay between morphological and shielding effects in field emission via Schwarz-Christoffel transformation

TL;DR

This paper analyzes how morphological changes and electrostatic shielding effects influence field emission in large area emitters, using an analytical model with Schwarz-Christoffel transformation to understand their interplay.

Contribution

It introduces an analytical model to study the combined effects of morphology and proximity on the field enhancement factor in LAFEs.

Findings

Tradeoff between morphological and proximity effects explains FEF reduction.

Analytical expression for FEF near apex considering shape and distance.

Insights into behavior of LAFEs at small inter-emitter distances.

Abstract

It is well known that sufficiently strong electrostatic fields are able to change the morphology of Large Area Field Emitters (LAFEs). This phenomenon affects the electrostatic interactions between adjacent sites on a LAFE during field emission and may lead to several consequences, such as: the emitter's degradation, diffusion of absorbed particles on the emitter's surface, deflection due to electrostatic forces and mechanical stress. These consequences are undesirable for technological applications, since they may significantly affect the macroscopic current density on the LAFE. Despite the technological importance, these processes are not completely understood yet. Moreover, the electrostatic effects due to the proximity between emitters on a LAFE may compete with the morphological ones. The balance between these effects may lead to a non trivial behavior in the apex-Field Enhancement Factor (FEF). The present work intends to study the interplay between proximity and morphological effects by studying a model amenable for an analytical treatment. In order to do that, a conducting system under an external electrostatic field, with a profile limited by two mirror-reflected triangular protrusions on an infinite line, is considered. The FEF near the apex of each emitter is obtained as a function of their shape and the distance between them via a Schwarz-Christoffel transformation. Our results suggest that a tradeoff between morphological and proximity effects on a LAFE may provide an explanation for the observed reduction of the local FEF and its variation at small distances between the emitter sites.