Statistical Analysis of Field-Emission Currents

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 similar to E2 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 ,B. On the basis of this approximation, and considering local field and current fluctuations, two alternative methods for ,B estimation are presented. These methods allow instantaneous field-specific estimation of ,B, 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 ,B using fluctuation analysis in experimental measurements that were not dedicated for this purpose. An open-source code for the implementation of fluctuation-derived ,B estimation is provided, with an analysis of possible future experimental opportunities using dedicated experiments

Dark current spikes as an indicator of mobile dislocation dynamics under intense dc electric fields

Breakdown of metals subject to intense electric fields is a long-standing limiting factor in high-voltage applications. The mechanism leading to breakdown nucleation is not completely understood. Previously, it was suggested that breakdown can be nucleated by a critical transition in the population of mobile dislocations near the surface of electrodes. This was formulated in terms of a mean-field mobile dislocation density fluctuation (MDDF) model. Based on this model, it was proposed that prebreakdown fluctuations of the mobile dislocation density might be observed as spikes in the dark current between the electrodes. We constructed a setup in which these fluctuations were measured. The rate of fluctuations, as a function of the electric field between the electrodes, agrees with the predictions of the MDDF model, both in functional form and in absolute numerical rates. This numerical agreement was obtained using previously derived numerical parameters of the model. In addition, for each electric field, the distribution of times between current fluctuations was examined. The results indicate that each such prebreakdown fluctuation is the result of a two-step process. This characteristic, too, is in line with the MDDF model, which predicts that a characteristic prebreakdown current event is described as two separate steps in a Markov process, occurring in quick succession