Determination of Ionization Frequency in Microwave Discharges at Microgaps

The continuing reduction of device size in electronics increases the importance of accurately predicting microwave breakdown voltage at microscale¹, where the ionization frequency ν differs from the ionization coefficient used to assess DC breakdown². Previous studies determined ν at microwave frequencies by modifying the DC equation³; however, this is inaccurate. A comprehensive assessment of ν with gap distance, electric field, and frequency is required to improve the accuracy of AC breakdown theories³, particularly at smaller gaps where the breakdown electric fields can be strong². Here, we use particle-in-cell simulations to characterize ν for atmospheric pressure argon plasmas in 2-10 µm gaps at 1-1000 GHz. For f<f_cr (critical frequency), ν/f scales with the reduced electric field. For f >f_cr, ν becomes a function of the reduced electric field, which agrees with previous results at larger gaps. For f<f_cr, the electrodes collect the electrons during each cycle, causing the electron number to oscillate over time. For f >f_cr electrons are confined in the gap, leading to exponential growth in the electron number.

1. Y. Fu, et al., Plasma Res. Express 2, 013001 (2002).

2. H. Wang, et al., J. Appl. Phys. 132, 073302 (2022).

3. M. U. Lee, et al., Eur. Phys. J. D 71, 94 (2017).