How sheath properties change with gas pressure: modeling and simulation

Sheaths regulate how plasma affects material surfaces, making properties of sheaths important in applications like etching and implantation. Properties that are often studied are the values of the ion velocity, plasma density, electric field, and potential at the sheath edge. Current models for each of these properties account for the effects of charge-neutral collisions, which is useful since devices operate over a range of gas pressures. However, experimental validation of these models is limited, generally to low pressures (~1 mTorr), where diagnostics like laser-induced-fluorescence and Langmuir probes work well. We design a two-fluid model to estimate each sheath property at varying pressures and test the model with1D particle-in-cell simulations. The simulations include charge-neutral collisions through the direct simulation Monte Carlo method and are a first step in validating collisional sheath models. We solve the two-fluid model numerically to compare with the simulations and find they generally agree over a wide pressure range (0.01-10,000 mTorr). Both predict the ion velocity (collisional Bohm speed), and the density relative to the bulk density decrease with increasing pressure, while the sheath potential drop and sheath width increase. The electric field is constant in both. However, the two-fluid model lacks 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), while the latter leads to larger differences at the highest pressures (>100 mTorr). We derive expressions for each property that depend only on pressure and include kinetic effects. Our simulations show that collisions modify the sheath properties as predicted by a collisional sheath model.