Extended scaling and Paschen law for micro-sized radiofrequency plasma breakdown

The single particle motion analysis and particle-in-cell merged with Monte Carlo collision (PIC/MCC) simulations are compared to explain substantial breakdown voltage reduction for helium microwave discharge above a critical frequency corresponding to the transition from the drift-dominant to the diffusion-dominant electron loss regime. The single particle analysis suggests that the transition frequency is proportional to the product of p(-m) and d(-(m+1)) where p is the neutral gas pressure, d is the gap distance, and m is a numerical parameter, which is confirmed by the PIC simulation. In the low-frequency or drift-dominant regime, i. e., gamma-regime, the secondary electron emission induced by ion drift motion is the key parameter for determining the breakdown voltage. The fluid analysis including the secondary emission coefficient, gamma, induces the extended Paschen law that implies the breakdown voltage is determined by pd, f/p, gamma, and d/R where f is the frequency of the radio or microwave frequency source, and R is the diameter of electrode. The extended Paschen law reproduces the same scaling law for the transition frequency and is confirmed by the independent PIC and fluid simulations.