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. Two electrodes are separated by a microscale gap with a non-uniform neutral gas distribution. For example, there may be a higher density near the anode as a result of vacuum seal failure near the anode. 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. Previously, it has been found that cold field electron emission can explain the breakdown voltage deviation from the Paschen curve measured for small gaps.1, 2 Furthermore, even in large gaps, as breakdown proceeds the plasma density becomes large enough and thus the cathode sheath thin enough that cold field emission dominates and super-exponential current growth results.3 Breakdown was found to be sensitive to the neutral gas density distribution across the gap. Specifically, if the gap is large enough that the cold field emission is negligible then gas concentrated near the cathode results in higher breakdown voltages since electrons leaving the cathode due to Auger neutralization are not yet energetic enough to ionize the high density neutral gas at the cathode. Conversely, if the gap size is of order the mean free path then gas concentrated near the anode results in smaller breakdown voltages because the electrons reaching the anode have energies near the peak of the ionization cross section near the higher density anode region. These lower breakdown voltages should be taken into account when designing vacuum electronics for failure tolerance.
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