The Transition to Paschen’s Law for Microscale Gas Breakdown at Subatmospheric Pressure

Abstract

The decrease in electronic device size necessitates greater understanding of gas breakdown and electron emission at microscale to optimize performance. While traditional breakdown theory using Paschen’s law (PL), driven by Townsend avalanche, fails for gap distance d ≲ 15 μm, recent studies have derived analytic equations for breakdown voltage when field emission and Townsend avalanche drive breakdown. This study derives a new analytic equation that predicts breakdown voltage V B within 4% of the exact numerical results of a previously derived theory and new experimental results at subatmospheric pressure for gap distances from 1–25 μm. At atmospheric pressure, V B transitions to PL near the product of pressure and gap distance, pd, corresponding to the Paschen minimum; at lower pressures, the transition to PL occurs to the left of the minimum. We further show that the work function plays a major role in determining which side of the Paschen minimum V B transitions to PL as pressure approaches atmospheric pressure while field enhancement and the secondary emission coefficient play smaller roles. These results indicate that appropriate combinations of these parameters cause V B to transition to PL to the left of the Paschen minimum, which would yield an extended plateau similar to some microscale gas breakdown experimental observations.