Assessment of self-consistent analytic model for inductive RF discharge and design of uniform discharge with planar-vertical antennas

An RF discharge source with a vertical internal exciting coil was studied in OSRAM SYLVANIA recently (Godyak et al., 1995). Based on the self-consistent electron kinetic analysis presented by (Dai and Wu, 1995), a two-dimensional (2-D) (r,z) model is provided for this kind of inductively coupled discharge source. The mode analysis solves the vector and scalar potentials of the electromagnetic (EM) fields, while the kinetic analysis gives the perturbed Maxwellian distribution of electrons by solving the Boltznann-Vlasov equation. The vector potential of the EM fields, which dominates the scalar potential in inductively coupled discharge, is calculated by considering the induced space currents obtained in terms of the electron kinetic analysis. With closed-form solutions, the model provides a rigorous and fast way to compute the EM fields and electron kinetic behaviors in the sources. The theoretical results achieve good agreement with the measurements given by Godyak et al. (1995). Furthermore, in order to achieve a uniformly distributed plasma in the discharge chamber, which is desired for plasma processing, we propose a novel discharge structure with both external planar coil and internal vertical coil excitations. For a few sets of parameters, the theoretical results demonstrate the improved uniformity for excited azimuthal E-fields in the chamber.