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The theoretical link between voltage loss, reduction in field enhancement factor, and Fowler-Nordheim-plot saturation

Forbes, Richard (2017) The theoretical link between voltage loss, reduction in field enhancement factor, and Fowler-Nordheim-plot saturation Applied Physics Letters, 110 (13), 133109. 133109-1-133109-4.

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Abstract

With a large-area field electron emitter, when an individual post-like emitter is sufficiently resistive, and current through it is sufficiently large, then voltage loss occurs along it. This letter provides a simple analytical and conceptual demonstration that this voltage loss is directly and inextricably linked to a reduction in the field enhancement factor (FEF) at the post apex. A formula relating apex-FEF reduction to this voltage loss was obtained in the paper by Minoux et al. [Nano Lett. 5, 2135 (2005)] by fitting to numerical results from a Laplace solver. This letter derives the same formula analytically, by using a “floating sphere” model. The analytical proof brings out the underlying physics more clearly and shows that the effect is a general phenomenon, related to reduction in the magnitude of the surface charge in the most protruding parts of an emitter. Voltage-dependent FEF-reduction is one cause of “saturation” in Fowler-Nordheim (FN) plots. Another is a voltage-divider effect, due to measurement-circuit resistance. An integrated theory of both effects is presented. Both together, or either by itself, can cause saturation. Experimentally, if saturation occurs but voltage loss is small (<20 V, say), then saturation is more probably due to FEF-reduction than voltage division. In this case, existing treatments of electrostatic interaction ("shielding") between closely spaced emitters may need modification. Other putative causes of saturation exist, so the present theory is a partial story. Its extension seems possible and could lead to a more general physical understanding of the causes of FN-plot saturation.

Item Type: Article
Divisions : Faculty of Engineering and Physical Sciences > Electronic Engineering
Authors :
NameEmailORCID
Forbes, RichardR.Forbes@surrey.ac.ukUNSPECIFIED
Date : 11 March 2017
Identification Number : 10.1063/1.4979320
Copyright Disclaimer : Copyright 2017 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. The following article appeared in Applied Physics Letters, 110, 133109 and may be found at R.G. Forbes, Appl. Phys. Lett. 110, 133109 (2017); doi: 10.1063/1.4979320
Depositing User : Clive Harris
Date Deposited : 13 Jun 2017 09:21
Last Modified : 17 Aug 2017 09:26
URI: http://epubs.surrey.ac.uk/id/eprint/841351

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