Field emission: calculations supporting a new methodology of comparing theory with experiment

TL;DR

This paper introduces a new methodology to compare field emission theories with experimental data by analyzing the exponent kappa in the current-voltage relationship, supported by simulations and applied to historical theories, highlighting the need for improved measurement techniques.

Contribution

The paper proposes a novel approach using the exponent kappa to distinguish between competing field emission theories, supported by simulation studies of emitter shapes.

Findings

Simulations show contribution of emission area voltage-dependence is uncertain.

Methodology favors Murphy-Good theory but remains inconclusive.

Highlights need for better experimental measurement of kappa.

Abstract

This paper presents a new methodology for making comparisons between the theory of field electron emission (FE) and experiment, and is intended as a "demonstration of concept". This methodology is based on the value of the exponent kappa that describes the power to which voltage is raised in the pre-exponential of a mathematical equation that describes (for an electronically ideal FE system) the dependence of measured emission current on measured voltage. The aim is to use experimental exponent-values kappa^expt in an attempt to decide between two alternative FE theories, for both of which allowable (but different) ranges of kappa have been established. At present, there is limited information on what contribution to the "total theoretical kappa" is made by the voltage-dependence of the notional emission area: this paper reports simulations intended to add to our knowledge about this, for four common assumed shapes of an emitter apex. The methodology is then applied to the choice between 1928/29 Fowler-Nordheim (FN) FE theory and 1956 Murphy-Good (MG) FE theory (which is a situation where it is theoretically certain that 1956 MG FE theory is "better physics" than 1928/29 FN FE theory). Like all previous attempts to reach the known correct theoretical conclusion by experimentally based argument, the outcome of the new methodology tends to favour MG FE theory, but is formally indecisive at this stage of discussion. There seems an urgent need for better methods of measuring kappa^expt and of establishing reliable experimental error limits.