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Skin effect in a small symmetrically driven capacitive discharge

Thomas Mussenbrock1, Torben Hemke1, Dennis Ziegler1, Ralf Peter Brinkmann1 and Michael Klick2

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The so-called 'electrostatic' approximation postulates that the electric field can be represented by the gradient of a scalar potential, even under dynamical conditions. This assumption reduces the set of Maxwell's equations to the much simpler Poisson equation and is often employed for modeling and simulation of radio frequency driven capacitive low pressure discharges. While it is now widely acknowledged that the neglect of induction phenomena breaks down for large-area plasma sources driven at high frequencies (such as used for VLSI processing), smaller experimental devices excited at moderate frequencies (e.g. 13.56 MHz) are generally thought to be uncritical. This paper demonstrates the opposite: even small plasma reactors of the size of the Gaseous Electronics Conference reference cell exhibit a considerable skin effect in the low pressure, high density regime and render the electrostatic approximation invalid. The point is made, however, that this phenomenon is not 'fully electromagnetic' (in the sense that its analysis requires the full set of Maxwell's equations), but can be understood by means of a simplified model which assumes quasi-neutrality and may therefore be called 'magnetostatic'.


PACS

52.80.Pi High-frequency and RF discharges

52.65.-y Plasma simulation

52.50.Dg Plasma sources

Subjects

Plasma physics

Dates

Issue 2 (May 2008)

Received 23 November 2007, in final form 13 February 2008

Published 17 April 2008



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