Comments on the continuing widespread and unnecessary use of a defective emission equation in field emission related literature

TL;DR

This paper critiques the widespread use of a defective emission equation in field emission literature, emphasizing the importance of the more accurate Schottky-Nordheim barrier model to avoid significant errors and uphold scientific integrity.

Contribution

It highlights the persistent use of an outdated, physically inaccurate emission equation, and advocates for adopting the more precise Schottky-Nordheim model in research and review processes.

Findings

Elementary equation underestimates LECD by a factor of 250-500.

Most FE theorists prefer the Schottky-Nordheim barrier model.

Many papers spread errors due to outdated equations and lack of awareness.

Abstract

Field electron emission (FE) has relevance in many different technological contexts. However, many related technological papers use a physically defective elementary FE equation for local emission current density (LECD). This equation takes the tunneling barrier as exactly triangular, as in the original FE theory of 90 years ago. More than 60 years ago, it was shown that the so-called Schottky-Nordheim (SN) barrier, which includes an image-potential-energy term (that models exchange-and-correlation effects) is better physics. For a metal-like emitter with work-function 4.5 eV, the SN-barrier-related Murphy-Good FE equation predicts LECD values that are higher than the elementary equation values by a large factor, often between around 250 and around 500. By failing to mention/apply this 60-year-old established science, or to inform readers of the large errors associated with the elementary equation, many papers (aided by defective reviewing) spread a new kind of "pathological science", and create a modern research-integrity problem. The present paper aims to enhance author and reviewer awareness by summarizing relevant aspects of FE theory, by explicitly identifying the misjudgment in the original 1928 Fowler-Nordheim paper, by explicitly calculating the size of the resulting error, and by showing in detail why most FE theoreticians regard the 1950s modifications as better physics. Suggestions are made, about nomenclature and about citation practice, that may help to diminish misunderstandings.