Interpreting the empirical field emission equation for large area field emitters

TL;DR

This paper investigates the interpretation of the Fowler-Nordheim plot parameters for large area field emitters, revealing that the slope depends on both the enhancement factor and emitter density changes, affecting emission area calculations.

Contribution

It introduces a shielding model to analyze the validity of assumptions in interpreting LAFE emission characteristics, highlighting the combined influence on the slope and emission area.

Findings

Slope includes contributions from enhancement factor and emitter density rate.

Emission area relates to both slope and intercept in LAFE.

Standard interpretation is valid when emitter spacing exceeds height.

Abstract

Both single emitters and large area field emitters (LAFE) are generally characterized using the slope and intercept of a Murphy-Good (or Fowler-Nordheim) plot which are used to extract the field enhancement factor and the emission area. Using a shielding model that has been developed recently for a LAFE, the validity of the underlying assumption is investigated. It is found that in case of a LAFE, the slope has contributions from the enhancement factor {\it as well as} the rate at which the effective number of super-emitters changes with the applied field. As a consequence, the emission area is related to both the slope and the intercept in a LAFE. When the mean spacing in a LAFE is much larger than the height of emitter, the usual interpretation of the slope and intercept are recovered.