Nonlinear sheath motion and stochastic heating in a capacitive RF discharge

Low pressure (<100 mTorr) capacitive r.f. discharges are widely used in the electronics industry. It has been shown that stochastic heating by the oscillating sheaths is a major energy deposition mechanism. An analytical model of the sheath motion predicts that the heating rate is sensitively dependent on the detailed shape of the non-sinusoidal sheath motion. An experimental procedure has been developed for detrermining this sheath motion. A high frequency response, Langmuir probe measures the sheath potential throughout the sheath region, as a function of position and time. The probe-discharge system can be modeled as a non-linear capacitive voltage divider. Incorporating the non-linear sheath motion into this circuit model yields a set of equations that are solved numerically, and the resulting waveforms are compared with the experimental observations both in magnitude and harmonic content. The parameters describing the sheath motion can then be varied to match the experimentally observed potential. The results indicate good agreement between the theoretically predicted and experimentally observed sheath motion. The differences between the theory and experiment are discussed