A data-driven model for the field emission from broad-area electrodes

Abstract

Electron emission from cathodes in high field gradients is a quantum tunneling effect. The 1928 Fowler–Nordheim field emission (FE) equation and the 1956 Murphy–Good FE equation have traditionally been key in describing cold field emissions, offering estimates for emitters for almost a century. Nevertheless, applying FE theory in practice is often constrained by the lack of data on the distribution and geometry of the emission sites. Predictions become more challenging with an uneven electric field distribution at the cathode surface. Consequently, FE formulations are frequently calibrated using current–voltage data after test, limiting their efficacy as true predictive models.

This study develops an alternative model for field emission using a data-driven predictive approach based on (1) vast experimental data, (2) electrostatic simulations of the cathode surface, and (3) detailed material and geometry properties, which together overcome these limitations. The objective of this work is to develop and harness this comprehensive dataset to train a machine learning model capable of providing precise predictions of the cathode current in order to further the understanding and application of field emission phenomena. More than 259 h of experimental data have been processed to train and benchmark some of the well-known machine learning models. After two stages of optimization, a coefficient of determination $>98\text{\%}$ is achieved in the prediction total field emission current using ensemble models.