Skin effect in a small symmetrically driven capacitive discharge

Abstract

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’.