Dynamic Simulation of Electron Emission Characteristics Based on Different Numerical Models of a Nanoscale Micro-Protrusion

It is well known that electron emission is one of the key factors to cause electrical breakdown in vacuum gaps. In previous studies, it tended to use simplified numerical models with uniform electric field on emission region to investigate the electron emission characteristics at the cathode micro-protrusion and the influence of the materials of the micro-protrusions. The objective of this article is to introduce an improved numerical model of a nanoscale micro-protrusion with nonuniform electrical field on the emission region, which could be used for micro-protrusions with various irregular geometries. The improved numerical model is used in this article to study the dynamic characteristics of the electron emission of Cu and Cr micro-protrusions under different macroscopic electric fields. First, the electric field distribution is obtained by solving Laplace equation based on finite difference method (FDM). Then, the emission current and Nottingham effect are obtained by calculating the general thermal-field (GTF) equations based on the electric field distribution. Finally, the dynamic characteristics of the electron emission current and temperature distribution are iteratively calculated considering the Joule heating and Nottingham effect. The calculation results of the improved numerical model are compared with those of the previous simplified numerical model. The results show that for Cu and Cr micro-protrusions, the Joule heating, and Nottingham effect would play different roles in the emission process. In general, it is more likely for the Cr micro-protrusions to evaporate than the Cu micro-protrusions. The results of this article may provide some useful information to further understand the vacuum breakdown initiated by electron emission.