An empirical relationship for ionization coefficient for microscale gaps and high reduced electric fields

Abstract

The importance of gas discharges for numerous applications with increasingly small device size motivates a more fundamental understanding of breakdown mechanisms. Gas breakdown theories for these gap sizes unify field emission with the Townsend avalanche, which depends on Townsend's first ionization coefficient [Formula: see text]; however, the ratio of the electric field E to gas pressure p for microscale gas breakdown exceeds the range of validity for the typical empirical equation. While some studies have used particle-in-cell simulations to assess [Formula: see text] in this range, they only examined a narrow range of experimental conditions. This work extends this approach to characterize ionization in microscale gaps for N2, Ar, Ne, and He for a broader range of pressure, gap distance d, and applied voltage V. We calculated [Formula: see text] at steady state for [Formula: see text] and p  = 190, 380, and 760 Torr. As expected, [Formula: see text] is not a function of reduced electric field [Formula: see text] for microscale gaps, where the electron mean free path is comparable to d and [Formula: see text] is high at breakdown. For [Formula: see text], [Formula: see text] scales with V and is independent of p. For [Formula: see text], [Formula: see text] approaches the standard empirical relationship for [Formula: see text] and deviates at higher levels because the ionization cross section decreases. We develop a more rigorous semiempirical model for [Formula: see text], albeit not as universal or simple, for a wider range of d and p for different gas species that may be incorporated into field emission-driven breakdown theories to improve their predictive capability.