Generalization of scaling laws for gas breakdown to account for pressure

摘要

Summary form only given. The increasing importance of electronics miniaturization has motivated research into the behavior of breakdown voltage for microscale and nanoscale gaps1-4; however, the traditional Paschen's law for predicting gas breakdown fails for smaller gaps1. Recent studies have developed analytic and numerical approaches to predict these deviations at atmospheric pressure1,2; however, the analytic expressions2 are only valid at atmospheric pressure and cannot be used to predict or explain recent breakdown studies at sub-atmospheric pressures down to vacuum3,4 or deviations from Paschen's law at higher pressures.5 In this presentation, we will generalize previously derived expressions2 for breakdown voltage at atmospheric pressure to derive simplified scaling laws valid for any pressure up to the Meeks criterion for streamer discharge. We will compare these results to particle-in-cell simulations, numerical solutions, and experiments3,4. The implications of these expressions for predicting breakdown voltage as a function of pressure and the significance for understanding deviations from the traditional Paschen's law will be discussed.