Estimation of Ion Impact Energies and Electrode Self-Bias Voltage in Capacitive RF Discharges

ABSTRACTThe dependences of the electrode self-bias voltage and the ratio of ion energies on electrode area ratio are calculated for a model of capacitively coupled rf discharges. It is assumed that concentric spherical elecrodes with fluid-like radial ion flow adequately models the ion motion, that sheath impedances are dominant, and that ionization processes in the glow are due to ohmically heated electrons. Results show that the ratio of ion energies impacting the smaller electrode to those on the larger depends on the ratio of electrode areas in a more complex manner than a power law.The reason for this is that sheath impedances are more resistive or capacitive at different times in the rf cycle. The self-bias ratio is found to depend relatively little on the ionization model or the pressure but differs substantially from the “power law” result. The agreement of measurements with the model is fairly good.