Calculation of the auto-bias voltage for RF frequencies well above the ion-plasma frequency

A model is presented which describes the coupling of the two RF sheaths in the high-frequency regime for a reactor with different electrodes. The sheaths are coupled by the current-balance equation and the assumption of a harmonic potential difference between the two electrodes. In contrast with most existing models, no assumption is made for either the displacement current or the potential drops across the sheaths. The sheath dynamics are due to an oscillating, step-like electron density profile. The calculations show that the sheaths react nonlinearly to the applied potential. The auto-bias voltage and averaged ion-impact energy coincide reasonably well with experimental data for different reactor types only if one demands that the time-averaged conduction currents flowing towards the electrodes vanish