Space-Charge Limited Current from a Finite Emitter in Nano- and Microdiodes

TL;DR

This paper numerically investigates space-charge limited current in nano- and micro-scale vacuum diodes with finite emitters, revealing limitations of classical models and proposing new relations for small emitters.

Contribution

It introduces a detailed molecular dynamics simulation of charge dynamics in finite-area emitters, extending classical models to nanoscale regimes.

Findings

Classical Child-Langmuir law has limited applicability for sub-micron emitters.

New simple relations are proposed for space-charge limited flow from small emitters.

Simulation results highlight the importance of finite emitter size in diode behavior.

Abstract

We simulate numerically the classical charge dynamics in a microscopic, planar, vacuum diode with a finite emitter area and a finite number of electrons in the gap. We assume electrons are emitted under space-charge limited conditions with a fixed potential applied to the diode. The Coulomb interaction between all electrons is included using the method of molecular dynamics. We compare our results to the conventional two-dimensional Child-Langmuir and explain how it is limited in applicability for sub-micron diameter emitters. Finally, we offer some simple relations for understanding space-charge limited flow from very small emitters.