Extraction of emission parameters for large-area field emitters, using a technically complete Fowler-Nordheim-type equation

TL;DR

This paper identifies and corrects a widespread misuse of the Fowler-Nordheim equation in large-area field emitter research, proposing a complete, correction-factor-based equation to improve accuracy and reporting practices.

Contribution

It introduces a comprehensive FN-type equation with correction factors for accurate emission parameter extraction from LAFE data, replacing misleading simplified equations.

Findings

The simplified FN-type equation overestimates current density by large factors.

A complete FN-type equation with correction factors improves emission parameter estimation.

Guidelines for experimental data analysis and reporting practices are proposed.

Abstract

In papers on cold field electron emission from large area field emitters (LAFEs), it has become widespread practice to publish a misleading Fowler-Nordheim-type (FN-type) equation. This equation over-predicts the LAFE-average current density by a large highly-variable factor thought to usually lie between 1000 and 1000 000 000. This equation, although often referenced to FN's 1928 paper, is a simplified equation used in undergraduate teaching, does not apply unmodified to LAFEs, and does not appear in the 1928 paper. Technological LAFE papers often do not cite any theoretical work more recent than 1928, and often do not comment on the discrepancy between theory and experiment. This usage has occurred widely, in several high-profile American and UK applied-science journals, and in various other places. It does not inhibit practical LAFE development, but can give a misleading impression of potential LAFE performance to non-experts. This paper shows how the misleading equation can be replaced by a conceptually complete FN-type equation that uses three high-level correction factors. One of these, or a combination of two of them, may be useful as an additional measure of LAFE quality; this paper describes how to estimate factor values using experimental data. Suggestions are made for improved engineering practice in reporting LAFE results. Some of these should help to prevent situations arising whereby an equation appearing in high-profile applied-science journals is used to support statements that an engineering regulatory body might deem to involve professional negligence.