Nonlinearity of the radio-frequency sheath

TLDR

The study analyzes the nonlinearity of the plasma sheath at frequencies above the ion plasma frequency, deriving a fundamental relation between sheath voltage, displacement current, and time‑dependent sheath width. The authors develop a simple stepwise electron density model and a generalized model for low‑pressure discharges, using experimental data to compute the temporal evolution of sheath width. Experimental measurements in asymmetrical RF discharges confirm that the proposed models accurately describe sheath behavior.

Abstract

The nonlinearity of the plasma sheath for frequencies well above the ion plasma frequency is analyzed. The work focuses on the relation of sheath voltage and displacement current for the low-pressure discharge. The simple model of a stepwise electron density distribution within the sheath and a generalized model are derived. Both approaches result in a fundamental and general relation of sheath voltage, displacement current, and time dependent sheath width. Experiments at asymmetrical rf discharges show the models to be realistic. The temporal dependence of the sheath width is calculated from experimental data.