How sheath properties change with gas pressure: modeling and simulation*

Here we test a 1D collisional sheath model using particle-in-cell simulations, which include charge-neutral collisions using the direct simulation Monte Carlo method. The model was created to predict how several important sheath properties change with gas pressure: the sheath edge values of the ion velocity, relative plasma density, electric field, potential, and sheath width. Currently, there are multiple models for each property, each lacking validation. We find that numerical solutions to our model and simulations agree over a large pressure range (0.01-10,000 mTorr). Both predict the ion velocity and relative density decrease with increasing pressure, while the potential and sheath width increase. The electric field is found to remain constant in both. However, the model doesn't account for kinetic effects, like non-Maxwellian features of the electron velocity distribution and temperature gradients. We find that the former leads to small differences between the model and simulations at low pressures (<100 mTorr) and that the difference can become significant at the highest pressures (>100 mTorr). Ultimately, we derive expressions for each quantity that depend only on the pressure and adjust the coefficients to best represent the simulation data with its kinetic effects.