A model for the power dissipation in rf plasmas

Abstract

An analysis is made of the relations determining the electron drift velocity in the oscillating boundary between plasma and space-charge region at the electrode surface of an rf-driven parallel-plate discharge. The resulting set of equations is solved directly to yield an expression for the rf power dissipation in the plasma. Similarly, the dissipation in the space-charge region is derived from the equations for mobility-limited and free-fall movement of positive ions to the wall. This model is applied to existing data for the electrical discharge properties in a 13.56-MHz dry etch reactor. The calculated total power dissipation is shown to agree with published transfer efficiencies for the applied rf power. It appears that the electron dissipation term is dominant at high pressure and low rf power, while the ions determine the power input at low pressure and high power. The same set of equations is used to calculate the rf current wave form, the displacement of the plasma boundary with time, and the averaged plasma density. Also here, the model is in agreement with published simulations and experimental work.