Particle-in-cell simulations of the ionization process in microwave argon microplasmas

The importance of microwave device reliability and performance for microscale devices motivates a more fundamental understanding of breakdown mechanisms in this regime. Microwave breakdown theories predict breakdown when electron production balances electron loss. Electron production depends strongly on the ionization rate $ν i$⁠; however, previous studies either used the measured $ν i$ in macroscale gaps or the empirical formula for DC voltage, inaccurately predicting $ν i$ in microscale gaps. Alternatively, this work characterizes $ν i$ in microwave microplasmas by using particle-in-cell simulations. We calculated $ν i$ in argon gas at atmospheric pressure for 2–10 μm gaps under AC fields ranging from 1 to 1000 GHz. The behavior of $ν i$ may be separated into two regimes by defining a critical frequency $f c r$ that depends on the amplitude of the applied voltage, gap distance, and pressure. For frequency $f< f c r$⁠, the electrodes collect the electrons during each cycle and the electron number oscillates with the electric field, causing $ν i / f$ to roughly scale with the reduced effective field $E e f f / p$⁠. For $f> f c r$⁠, the phase-space plots indicate that the electrons are confined inside the gap, causing the electron number to grow exponentially and $v i / p$ to become a function of $E e f f / p$⁠. These results elucidate the ionization mechanism for AC fields at microscale gap distances and may be incorporated into field emission-driven microwave breakdown theories to improve their predictive capability.