Nonlinearity of the radio-frequency sheath

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.