Generalization of Microdischarge Scaling Laws for All Gases at Atmospheric Pressure

Abstract

The failure of traditional breakdown theories to predict breakdown voltage $V_{b}$ for microscale gaps motivates studies for more accurate approaches. We generalize scaling laws previously derived for argon at atmospheric pressure to model any gas at atmospheric pressure for gap distances from 100 nm to $30~\mu \text{m}$ and perform a matched asymptotic analysis to derive simple analytic equations for $V_{b}$ at critical limits. We obtain excellent agreement between numerical solutions, analytic equations, particle-in-cell simulations, and experimental data. Furthermore, we assess the relative contributions of field emission and Townsend discharge for gaps larger than 100 nm, demonstrating that the field emission contribution exceeds the Townsend contribution for gap distances smaller than several microns. For example, with argon, nickel electrodes, and a field enhancement factor of 55, the field emission contribution exceeds the Townsend contribution below $10~\mu \text{m}$ .