Space Charge Effects in Field Emission: One Dimensional Theory

TL;DR

This paper develops a one-dimensional theoretical model to analyze how space charge influences field emission currents, providing exact solutions and methods to relate the model to real 3D structures.

Contribution

It introduces a modified classical 1D Child-Langmuir model that accurately captures space charge effects in field emission and connects it to periodic 3D structures.

Findings

Exact solutions for space charge effects in 1D field emission.

Method to relate 1D model to 3D periodic structures.

Insights into current dependence on space charge in field emission.

Abstract

The current associated with field emission is greatly dependent on the electric field at the emitting electrode. This field is a combination of the electric field in vacuum and the space charge created by the current. The latter becomes more important as the currentdensity increases. Here, a study is performed using a modified classical 1D Child-Langmuir description that allows for exact solutions in order to characterize the contributions due to space charge. Methods to connect the 1D approach to an array of periodic 3D structures are considered.