Statistical Analysis of Field-Emission Currents,Physical Review Applied

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Statistical Analysis of Field-Emission Currents
Physical Review Applied ( IF 3.8 ) Pub Date : 2021-08-04 , DOI: 10.1103/physrevapplied.16.024007
Sagy Lachmann ₁ , Marek Jacewicz ₂ , Iaroslava Profatilova ₃ , Jan Paszkiewicz ₃ , Walter Wuensch ₃ , Yinon Ashkenazy ₁

Affiliation

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 \sim E^{2} \exp ﻿ (- 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