Dimensional analysis on microscale gas breakdown with electric field nonuniformity and positive space charge effects

A dimensional method was employed to evaluate the microscale gas breakdown characteristics at atmospheric pressure, resulting in a universal breakdown curve applicable to different types of gases (e.g., Ar, Xe, Ne, and N 2). As the gap distance decreases, the breakdown mode transitions from ion-induced secondary electron emission to the field emission regime. In the field emission regime, the positive space charge effect becomes more significant. We discovered that incorporating the positive space charge effect in the field emission regime can be achieved by modifying the local electric field enhancement factor β. Consequently, we propose an effective electric field enhancement factor, β eff, which scales linearly with β, to accurately reproduce the breakdown curve while considering the positive space charge effect. This proposed approach significantly simplifies the numerical model. Additionally, we examined the effects of gas pressure, gap distance, cathode properties (e.g., work function and secondary electron emission coefficient), and electric field nonuniformity.