Scaling laws for AC gas breakdown in microscale gaps

Abstract

For microscale gaps, DC breakdown voltage is described theoretically and through simulation by accounting for field emission generated electrons and the subsequent ionization of neutral gas and ion-induced secondary electron emission. Here, we extend DC microscale breakdown theory to AC. Particle-in-cell (PIC) simulations show that breakdown voltage V varies linearly with gap distance d independent of frequency and the ion-induced secondary electron coefficient γSE for d≲4μm, where field emission dominates breakdown over ionization and avalanche. For d≳4μm and γSE=0, DC breakdown voltage increases linearly with d; for γSE=0.05, DC breakdown voltage decreases to a minimum before beginning to increase at larger gap distances. For AC fields with γSE=0.05, V behaves similarly to the DC case with the decrease corresponding to secondary emission occurring at higher voltages and larger gap distances with increasing frequency. At 10 GHz and γSE=0.05, V resembles that of the DC case with γSE=0 up to ∼8 μm, suggesting that increasing the frequency effectively changes the number of ions striking the electrodes and the resulting electrons released. Phase space plots showing electron and ion velocities as a function of position across the gap show that electrons and ions are increasingly trapped within the gap with increasing frequency, reducing the number of ions that can strike the cathode and the subsequent secondary emission. Incorporating the resulting effective secondary emission coefficient for AC microscale gaps yields a simple phenomenologically based modification of the DC microscale gas breakdown equation.