The Electrical Field in a Capacitively Coupled RF Discharge: An Advanced Algebraic Approximation
Ralph Peter Brinkmann
Abstract: The electric field in a radio-frequency driven capacitively coupled plasma (RF-CCP) is studied, taking dynamic (finite electron mass) and thermal (finite electron temperature) effects into account. Under the assumption that the ratios of the electron Debye length to the minimum plasma gradient length (typically the sheath thickness) and of the RF frequency to the electron plasma frequency are small but finite, a systematic asymptotic expansion of an electron fluid model is carried out up to quadratic order inclusively. An expression for the electric field is obtained which yields i) the space charge field in the sheath, ii) the generalized Ohmic and ambipolar field in the plasma bulk, and iii) a smooth interpolation for the transition in between. The model may be viewed as an extension to the well-known step model introduced by Godyak.
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