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

• Published in: Journal of applied physics 2022-08, Vol.132 (7)
• Main Authors: Wang, Haoxuan, Venkattraman, Ayyaswamy, Loveless, Amanda M., Buerke, Cameron J., Garner, Allen L.
• Format: Article
• Language: English
• Subjects: Applied physics; Electric fields; Empirical equations; Field emission; Gas breakdown; Gas discharges; Gas pressure; Ionization coefficients; Ionization cross sections; Townsend avalanche
• ISSN: 0021-8979; 1089-7550
• DOI: 10.1063/5.0098961

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 α; 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 α 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 α at steady state for 0.75 ≤ d ≤ 10 μ m and p = 190, 380, and 760 Torr. As expected, α / p is not a function of reduced electric field E / p for microscale gaps, where the electron mean free path is comparable to d and E / p is high at breakdown. For d < 2 μ m, α / p scales with V and is independent of p. For d > 10 μ m, α / p approaches the standard empirical relationship for E / p ≲ 1000 V Tor r − 1 c m − 1 and deviates at higher levels because the ionization cross section decreases. We develop a more rigorous semiempirical model for α, 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.