Statistical Analysis of Field-Emission Currents

Sagy Lachmann, Marek Jacewicz, Iaroslava Profatilova, Jan Paszkiewicz, Walter Wuensch, Yinon Ashkenazy*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


The current due to cold tunneling of electrons from a metallic surface exposed to high electric fields, regularly named "dark current,"is commonly described in modern literature using an analytical approximate solution provided by Murphy and Good [Phys. Rev. 102, 1464 (1956)]. This expression, which corrects earlier work by Fowler and Nordheim, is a Fowler-Nordheim-Type equation: I∼E2expâ (-A/E), where I is the dark current, E is the local electric field, and a is a system-specific constant. In this paper, a numerical approximation, rather than the analytical one given by Murphy and Good, is presented. This approximation is accurate over a wide range of fields, and is used to derive the effective field enhancement factor β. On the basis of this approximation, and considering local field and current fluctuations, two alternative methods for β estimation are presented. These methods allow instantaneous field-specific estimation of β, rather than the average estimate derived with current methods. The applicability of fluctuation-based methods is demonstrated by numerical simulation in a variety of conditions. The methods are applied to estimate β using fluctuation analysis in experimental measurements that were not dedicated for this purpose. An open-source code for the implementation of fluctuation-derived β estimation is provided, with an analysis of possible future experimental opportunities using dedicated experiments.

Original languageAmerican English
Article number024007
JournalPhysical Review Applied
Issue number2
StatePublished - Aug 2021

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© 2021 authors. Published by the American Physical Society. Published by the American Physical Society under the terms of the ""Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.


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