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By developing an approximation to the first integral of the Poisson equation, one can obtain solutions for the voltage-current characteristics of a radio-frequency (rf) plasma sheath that are valid over the whole range of inertial response of the ions to an imposed rf voltage or current-specified conditions. The theory adequately reproduces the time-dependent voltage-current characteristics of the two extreme cases corresponding to the Lieberman rf sheath theory and the Metze-Ernie-Oskam theory. Contained within the approximation is a time constant which controls the amount of ion response to the rf electric field. A prescription is given for determining this ion relaxation time constant, which also determines the time-dependent ion impact energy on the electrode surface

Unified model of the rf plasma sheath