Unified model of the rf plasma sheath: Part 2, Asymptotic connection formulae

Abstract

A previously-developed approximation to the first integral of the Poisson equation enables one to 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 reproduced the time-dependent voltage-current characteristics of the two extreme cases corresponding to the Lieberman rf sheath theory and the Metze-Ernie-Oskam theory. In this paper the sheath model is connected to the plasma bulk description, and a prescription is given for the ion relaxation time constant, which determines the time-dependent ion impact energy on the electrode surface. It appears that this connected model should be applicable to those high density, low pressure plasmas in which the Debye length is a small fraction of the ion mean free path, which itself is a small fraction of the plasma dimension.