Simulation-Based Model of Randomly Distributed Large-Area Field Electron Emitters

Johannes Bieker,Stefan Wilfert,Helmut F Schlaak,Richard G Forbes

doi:10.1109/jeds.2019.2940086

Abstract

With a large-area field electron emitter (LAFE), it is desirable to choose the spacings of individual emitters in such a way that the LAFE-average emission current density and total current are maximised, when the effects of electrostatic depolarization (mutual screening) are taken into account. This paper uses simulations based on a finite element method to investigate how to do this for a LAFE with randomly distributed emitters. The approach is based on finding the apex field enhancement factor and the specific emission current for an emitter, as a function of the average nearest neighbor spacing between emitters. Using electrostatic simulations based on the finite element method, the influence of neighboring emitters on a reference emitter being placed at the LAFE centre is investigated. Arrays with 25 ideal (identical) conical emitters with rounded tops are studied for different emitter densities and applied macroscopic fields. A theoretical average spacing is derived from the Poisson Point Process Theory. An optimum average spacing, and hence optimum emitter density, can be predicted for each macroscopic field.

Highlights

Field electron emitters are important for vacuum electron sources and already find applications, e.g., as cathodes in vacuum gauges [1]–[3] or X-Ray sources [4], [5]
SUMMARY In summary, in this work a model for large-area field electron emitter (LAFE) with randomly distributed emitters has been presented. This model combines a fitting function for field enhancement factor (FEF) with information about average emitter spacing obtained from the distribution of nearest-neighbor separations
By means of simulations and modelling, that a similar effect applies to random emitter arrays

Summary

Introduction

Field electron emitters are important for vacuum electron sources and already find applications, e.g., as cathodes in vacuum gauges [1]–[3] or X-Ray sources [4], [5]. Large-area field emitters (LAFEs) are commonly used. Detailed field electron emission (FE) measurements of cathodes with in-situ deposited gold nanocones have been presented recently [6]. These LAFEs are fabricated using asymmetric etching of low-cost, ion-track polymer membranes and subsequent electro-deposition. There are two main options to increase and optimize the total emission current of the LAFE: decreasing the emitter apex radii to obtain higher field enhancement, or alternatively optimizing the emitter density and the electrostatic interactions between the emitters. Decreasing the emitter apex radii is technologically not easy due to the fabrication process. Attention here is concentrated on optimizing the emitter density

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Discussion

Conclusion