Nonlocal transport models of the self-consistent potential distribution in a plasma sheath with charge transfer collisions

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Abstract
Plasma sheaths are often assumed to be collision free; however, high-voltage cathode sheaths are typically thicker than the mean free path for charge transfer collisions at pressures encountered in glow discharge processing equipment (greater than 10 mTorr). In this paper, the potential distribution in a plasma sheath is determined by solving Poisson’s equation self-consistently using a kinetic theory nonlocal ion transport model for charge transfer collisions. The relationship between the potential distribution, ion flux, and thickness of a plasma sheath is presented for arbitrary values of the sheath thickness relative to the mean free path for charge transfer. The results may be used to estimate the ion flux from measurements of the sheath thickness and potential drop across the sheath. Ion energy distribution functions and a one-parameter approximation to the numerically determined potential distribution are also presented. These results apply to rf discharges in a time-averaged sense when the ion sheath transit time is much longer than the rf cycle time, and they apply to high-voltage cathode sheaths in ‘‘abnormal’’ dc and low-frequency rf discharges. The present model is compared to earlier self-consistent sheath models, including the collision-free approximation, the local mobility model, and a nonlocal fluid approximation known as the viscous drag model.