Statistical Analysis of Field-Emission Currents

The current due to cold tunneling of electrons from a metallic surface exposed 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 Fowler Nordheim, Fowler-Nordheim-type equation: $I\ensuremath{\sim}{E}^{2}\mathrm{exp}(\ensuremath{-}a/E)$, where $I$ the dark current, $E$ local field, $a$ system-specific constant. In this paper, numerical approximation, rather than one given Good, presented. approximation accurate over wide range used derive effective field enhancement factor $\ensuremath{\beta}$. On basis considering fluctuations, two alternative methods for $\ensuremath{\beta}$ estimation are These allow instantaneous field-specific $\ensuremath{\beta}$, average estimate derived with methods. applicability fluctuation-based demonstrated simulation variety conditions. applied fluctuation analysis experimental measurements that were not dedicated purpose. An open-source code implementation fluctuation-derived provided, possible future opportunities experiments.