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

Abstract

Field electron emission (FE) has relevance in many technological contexts. However, many 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 90 years ago. More than 60 years ago, it was shown that the 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 a work function of 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 250 and 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 inadequate 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 the 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, which may help diminish misunderstandings. It is emphasized that the correction recommended here is one of several needed to improve the presentation of theory in the FE literature and is only a first step toward higher-quality emission theory and improved methodology for current-voltage data interpretation.