A mathematical model of the modified Paschen’s curve for breakdown in microscale gaps

Source abstract

Traditionally, Paschen’s curve has been used to describe the breakdown voltage for gaseous ionization between two electrodes. However, experiments have shown that Paschen’s curve, which is based on Townsend effects, is not necessarily accurate in describing breakdown between electrodes spaced less than 15 μm apart. In this regime, electron field emission plays a significant role in the breakdown phenomenon, and recently an alternative mathematical description that accounts for ion-enhanced field emission was proposed to describe the breakdown voltage in small gaps. However, both Paschen’s curve and the small gap equation only work in certain regimes, and neither predicts the transition that occurs between Townsend and field emission effects—the so-called modified Paschen’s curve. In this work, a single, consistent mathematical description of the breakdown voltage is proposed that accounts for both Townsend ionization and ion-enhanced field emission mechanisms. Additionally, microscale breakdown experiments have been conducted in atmospheric air. The proposed formulation is compared to the present experiments and other atmospheric air experiments in the literature and describes the transition region in the breakdown curve. The proposed formulation represents a mathematical model for the modified Paschen’s curve.