Christoph Hollenstein, Alan Howling, Laurent Fabien Hubert Sansonnens
Electromagnetic wave propagation effects can give rise to important limitations for processing uniformity in large area, radio-frequency (rf) capacitive plasma reactors. The electromagnetic wavefield solution is derived for a capacitive, high-frequency, cylindrical reactor with symmetric or asymmetric electrode areas containing a uniform plasma slab. It is shown that only two distinct electromagnetic modes are necessary and sufficient to determine the electromagnetic fields everywhere within the reactor except close to the sidewalls. The first mode gives rise to the interelectrode rf voltage standing wave effect associated with high frequencies in large area reactors, and the second mode gives rise to the telegraph effect associated with asymmetric electrode areas, which necessitates the redistribution of rf current along the plasma to maintain rf current continuity. This work gives a unified treatment of both effects which have previously been studied separately, experimentally and theoretically, in the literature. The equivalent circuit of each mode is also derived from its respective dispersion relation. Examples of this electromagnetic wavefield solution show that both modes can cause nonuniformity of the plasma rf potential, depending on the reactor geometry, excitation frequency and plasma permittivity and sheath width, which has consequences for large-area plasma processing.