Scaling law for direct current field emission-driven microscale gas breakdown

The effects of field emission on direct current breakdown in microscale gaps filled with an ambient neutral gas are studied numerically and analytically. Fundamental numerical experiments using the particle-in-cell/Monte Carlo collisions method are used to systematically quantify microscale ionization and space-charge enhancement of field emission. The numerical experiments are then used to validate a scaling law for the modified Paschen curve that bridges field emission-driven breakdown with the macroscale Paschen law. Analytical expressions are derived for the increase in cathode electric field, total steady state current density, and the ion-enhancement coefficient including a new breakdown criterion. It also includes the effect of all key parameters such as pressure, operating gas, and field-enhancement factor providing a better predictive capability than existing microscale breakdown models. The field-enhancement factor is shown to be the most sensitive parameter with its increase leading to a significant drop in the threshold breakdown electric field and also to a gradual merging with the Paschen law. The proposed scaling law is also shown to agree well with two independent sets of experimental data for microscale breakdown in air. The ability to accurately describe not just the breakdown voltage but the entire pre-breakdown process for given operating conditions makes the proposed model a suitable candidate for the design and analysis of electrostatic microscale devices.