1D PIC-DSMC Simulations of Breakdown in Microscale Gaps

An explicit electrostatic particle-in-cell (PIC) code with complex boundary conditions and direct simulation Monte Carlo (DSMC) particle collisions is utilized to investigate one dimensional direct current breakdown between two electrodes separated by air at STP. The simulation model includes Auger neutralization and cold field electron emission from the cathode as well as electron-neutral elastic, ionization, and excitation interactions. The simulated breakdown voltages at various electrode gap sizes are compared to experimental data and the Paschen curve. It is found that cold field electron emission can explain the breakdown voltage deviation from the Paschen curve measured for small gaps. Breakdown in large gaps proceeds over multiple ion transit timescales as electrons created via Auger neutralization of ions at the cathode quickly stream across the gap, creating new ions which accelerate towards the cathode and release another "pulse" of electrons. If the resultant pulse of electrons is larger than the initial pulse, then this process can build up a significant quasi-neutral plasma in the gap and the voltage drop across the gap will occur primarily across the (thin) sheath. Breakdown is accelerated if the electric field at the cathode surface is large enough for significant cold field emission flux, which increases the plasma density and decreases the Debye length and thus the sheath size, further increasing the electric field and cold field emission flux from the cathode surface. Breakdown in air pressure gaps was found to be sensitive to the differential scattering cross section for electron-neutral interactions. Isotropic scattering of elastic collisions results in lower breakdown voltages at moderate gaps (several mean free paths) and higher breakdown voltages for large gap sizes compared to when more accurate forward-biased scattering distributions are used. The dependence of breakdown voltage on the scattering distribution is due to a competition between increased backscattering resulting in a larger effective path length across the gap versus changes in the electron energy distribution function.