Electrostatic Breakdown at the Nanoscale

Abstract

We all experience the occasional electric shock when grabbing a doorknob. Similarly, such an electric shock can cause catastrophic damage in mechanical systems. The small spark that is seen to 'jump' through the air is actually the portion of the air that became electrically conductive, which is formally described as electrical breakdown. The breakdown of air is characterized by the formation of a large amount of free electrons, which are the result of ionization of the air under the influence of a static electric field.

To mitigate the risk of electrostatic breakdown in large scale systems, Paschen's law is generally used to predict these breakdown conditions. Such conditions include the voltage, distance and gas pressure. In MEMS and NEMS, significant deviations in breakdown voltage are seen which are attributed to an increase of secondary electron emission, caused by the high electric fields that are present in such systems. It has also been shown that the geometry of such systems can influence breakdown.

To achieve a better understanding of both the deviations from the classical theory and the effects of geometry, a Particle-in-Cell method has been implemented in Python. The computational method aims to capture the two-dimensional nature of this effect, to determine the vulnerability of given two dimensional topologies to electrostatic breakdown, and provide a computationally efficient risk assessment tool that can be used in the design phase of said systems.
The model has been validated by simulating various conditions that have also been investigated experimentally, and it has been shown that these results correspond. Since the model is not subject to the difficulties of experimental work, it can in the future be used to investigate various relations that attempt to describe the increase of secondary emission, and arbitrary topologies can be analysed to determine specific areas that are at high risk of breakdown.