Observation of Nonlinear Standing Waves Excited by Plasma-Series-Resonance-Enhanced Harmonics in Capacitive Discharges

It is well-recognized that in a very high frequency (VHF) capacitive discharge, standing wave effects come into play that compromise the plasma uniformity. Here we present the first experimental evidence of nonlinear standing waves excited by plasma-series-resonance-enhanced harmonics in low pressure, VHF, parallel plate, capacitively coupled plasmas. Spatial structures of the harmonics of the magnetic field, measured by a magnetic probe, are in very good agreement with simulations based on a nonlinear electromagnetics model. At relatively low pressure, the nonlinear sheath motion generates high-order harmonics that can be strongly enhanced near the series resonance frequencies. Satisfying certain conditions, such nonlinear harmonics induce radial standing waves, with voltage and current maxima on axis, causing center-high plasma density. Excitation of higher harmonics is suppressed at higher pressures, due to more frequent electron momentum transfer collision with the background gas, resulting in improved plasma uniformity.