Comparing Continuum and Particle-in-Cell Simulations at Microscale

Accurately assessing electron emission and gas breakdown at microscale-and even nanoscale-is vital due to decreasing electrical device size. While Paschen's law (PL) characterizes DC gas breakdown due Townsend avalanche (TA), it fails at microscale when the stronger electric fields decrease the potential barrier at the cathode, allowing electrons to tunnel from the electrode into the gap due to field emission (FE) [1]. This deviation from PL is characterized through various theories, simulations, and experiments. Many simulations are conducted using XPDP1, a 1d/3v particle-in-cell code modified to account for FE effects. However, running these simulations with a nonzero secondary emission coefficient and/or a gap distance greater than ~10 mm at atmospheric pressure is computationally unfeasible. Thus, we compare XPDP1, theory [1], and experiments [2] to the continuum simulation SOMAFOAM [3], which simulates low-temperature plasmas over a finite-volume. DC breakdown results with no secondary emission agree well with theory and simulation for no secondary emission; however, disagreements between theory and SOMAFOAM arise with nonzero secondary emission. SOMAFOAM predicts a lower breakdown voltage than XPDP1 and theory and shows a smoother transition to PL. The differences between the simulations, including computational efficiency, ionization coefficient, and chemistry, will be discussed, along with plans for extending these analyses to RF fields.