Electromagnetic field nonuniformities in large area, high-frequency capacitive plasma reactors, including electrode asymmetry effects

Abstract

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.

Electromagnetic sources of nonuniformity in large area capacitive reactors

“…In conclusion, the only electromagnetic fields which propagate into a reactor with symmetric electrodes are associated with the standing wave [1,3] of the first even quasi-TEM mode [2]. For any given radius, the sheath rf voltage amplitudes of this mode are the same at the top and bottom electrodes, and have the same radial dependence.…”

“…The lowest order even mode is in fact the quasi-TEM mode already considered above. Furthermore, none of the higher order even modes can propagate because the rf vacuum half-wavelength is longer than the electrode gap [2]. These evanescent modes satisfy the boundary conditions imposed by discontinuities at the slit and sheath/plasma interface at r = R and are called edge-localized modes [3].…”

“…The intuitive equivalent circuit for the standing wave effect in Fig. 4(a) can be derived from the dispersion relation for the first even quasi-TEM mode [2].…”

“…The mathematical treatment is given in a recently submitted paper by Sansonnens et al [2]. It is shown that two electromagnetic modes are necessary and sufficient to determine the electromagnetic fields everywhere within the reactor except close to the sidewalls.…”

“…This result applies to all parallel-plate reactors, whether cylindrical or rectangular. These two modes give rise to the interelectrode rf voltage standing wave effect [1][2][3][4][5][6][7][8] and the telegraph effect [1,[9][10][11][12]. The interelectrode rf voltage standing wave effect is associated with high frequencies in large reactors where the reactor size is larger than about a tenth of the vacuum wavelength of the rf excitation.…”