Dark-to-Arc Transition in Air for Planar Electrodes with Microscale Gaps

Electrical breakdown at threshold voltages predicted by Paschen's law occurs due to electron avalanches created by electron impact ionization and secondary electron emission from the electrodes. For a typical gas discharge, breakdown marks the end of the Townsend dark discharge regime and is followed by the normal glow regime where the current stays constant over a long range of voltages. For such a discharge, the electrode sheath is sustained by secondary electrons and the sheath thickness corresponds to the electrode gap at Stoletov's point for a given gas pressure
¹
. At microscale electrode gaps, quantum tunneling of electrons from the cathode, termed field emission, becomes significant thereby reducing the breakdown voltage. This follows the modified Paschen curve
²
. However, breakdown in some configurations, namely planar electrodes, is not followed by the normal glow regime, but transitions directly into the arc regime where the current spikes to high values
³
.