AVS 56th International Symposium & Exhibition
    Plasma Science and Technology Thursday Sessions
       Session PS-ThP

Paper PS-ThP3
Semi-analytical Model of Standing Wave and Skin Effect in Large-area RF Discharges

Thursday, November 12, 2009, 6:00 pm, Room Hall 3

Session: Plasma Science Poster Session
Presenter: M. Klick, Plasmetrex, Germany
Correspondent: Click to Email
Large area plasma coating becomes more important with increasing diameter of semiconductor wafers and thin film Si solar cells. The layer characteristics depend on the plasma, the uniformity depends mainly on the plasma sheath voltage at the substrate via the ion energy distribution and the corresponding back-etch rate. Therefore the modeling of large-area CCPs is increasingly important. In particular the skin and standing wave effects must be involved, beside the non-homogeneous distribution of chemically active species in plasma these effects are the major root causes of non-uniform interaction plasma and surrounding solid bodies.

A semi-analytic, cylindrical and 2d plasma model based on the full set of the Maxwellian equations was developed. It involves also the non-uniformity and nonlinearity of the plasma sheath as nonlinear boundary condition. It involves dynamic electron effects by a fluid model for the plasma bulk and nonlinear mechanisms by a nonlinear sheath model.

The model includes nonlinear effects and provides so the dependence of the Fourier spectrum of the local RF current on geometry, plasma density, and the electron collision rate. The ratio of the excitation frequency to the resonance frequencies of the spatial mode is found to determine the nonuniformity caused by the standing wave. The collisional skin depth can be also estimated. Thus the mean sheath voltage varying along the grounded electrode through both standing wave and skin effect can be easily calculated and understood by means of a semi-analytical model.

Both a center and edge maxima or even spatial oscillations in the mean sheath voltage at the grounded electrode can be observed. This is in agreement to experimental results of Si deposition used for comparison. It can be also shown that well-known terms as symmetry loose sense for very 'flat' RF discharge systems, they can be symmetric in the center and asymmetric near the edge.