Power dissipation in capacitively coupled rf discharges

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Abstract
The power dissipation in capacitively coupled rf discharges (Ar, 400 Pa) has been studied by impedance measurements in the 10–50 MHz frequency range. The article focuses on electrodeless discharge configurations in which the field-supplying electrodes are separated from the discharge volume by a dielectric wall, but the study of a classical electroded rf discharge is also included for comparison. The power share between bulk plasma and sheath regions is determined quantitatively using an equivalent circuit model which reflects the discharge structure. It depends strongly on both rf discharge current and frequency. For the electrodeless discharge configurations and equally for the electroded one, the fraction of power dissipated in the sheaths generally increases with increasing current and decreasing frequency. The sheath thickness derived from the impedance measurements decreases with frequency. It is nearly independent of the current for the electrodeless discharge configurations, but decreases with increasing current for the discharge configuration with internal metallic electrodes. A model for the power dissipation in the sheath is based on the current-voltage characteristics of a space-charge-limited ion current. It allows the calculation of the dissipated power Ps for operator set discharge conditions such as rf current, frequency, electrode area, and gas pressure, and predicts that Ps should vary with current I and frequency ω as (I/ω)5/2. The model is in good agreement with the experimental data. The contribution to the power dissipation from further processes besides the ion current in the sheath is also examined.