Discrete Electron Emission

TL;DR

This paper investigates the discrete nature of electron charge in space-charge limited emission, providing models and simulations to better understand electron spacing and emission scaling laws at the mesoscale.

Contribution

It introduces simplified models and scaling laws that account for the discrete charge effects in electron emission, advancing beyond mean-field approximations.

Findings

Derived scaling laws for electron emission under space-charge effects

Compared simplified models with computer simulations

Highlighted importance of charge discreteness in mesoscale emission

Abstract

Analysis of space-charge effects on electron emission typically makes some assumption of continuity and smoothness, whether this is continuity of charge as in the classical derivation of the Child-Langmuir current, or the mean-field approximation used in particle-in-cell simulations. However, when studying the physics of electron emission and propagation at the mesoscale it becomes necessary to consider the discrete nature of electronic charge to account for the space-charge effect of each individual point charge. In this paper we give an extensive analysis of some previous work on the distribution of electrons under space-charge limited conditions. We examine the spacing of electrons as they are emitted from a planar surface, We present simplified models for analysis of such conditions to derive scaling laws for emission and compare them to computer simulations.