Modelling of dual-frequency capacitive discharges

We discuss electron heating mechanisms in the sheath regions of dual-frequency capacitive discharges, with the aims of identifying the dominant mechanisms and supplying closed-form expressions from which the heating power can be estimated. We show that the heating effect produced by either Ohmic or collisionless heating is much larger when the discharge is excited by a superposition of currents at two frequencies than if either current had acted alone. This coupling effect occurs because the lower frequency current, while not directly heating the electrons to any great extent, strongly affects the spatial structure of the discharge in the sheath regions. From these results it follows that the ion flux cannot generally be independent of the low-frequency current density, and hence that separate control of the ion energy and flux must be a more complicated procedure than is sometimes suggested.