Comparison of a consistent theory of radio frequency sheaths with step models

In order to find analytically tractable models for the electrode sheath of a capacitively coupled rf discharge, step models are used in the Literature, describing the electron density by a step function oscillating with the radio frequency omega (omega(pi)much less than omega much less than omega(pe)) Comparison of the results of these step models with the results of numerical calculations shows similar current-voltage characteristics for symmetric discharges. On the other hand, distinct deviations in the spatial behavior of field and potential for a single sheath are observed. We discuss the deviations of the step models and show that they arise from systematic errors in the boundary conditions which are due to misinterpretations of the asymptotic two scale formalism. On the basis of a systematic two scale theory, we develop an improved step model with correct boundary conditions. (C) 1998 American Institute of Physics. [S0021-8979(98)02707-8].