Voltage waveform to achieve a desired ion energy distribution on a substrate in contact with plasma

A methodology is developed to determine the bias voltage waveform needed to achieve a desired (pre-selected) ion energy distribution (IED) on a substrate in contact with plasma. The approach is applicable to collisionless sheaths at all radio frequencies. It combines a circuit model with an equation for a ‘damped’ sheath potential to which ions respond. The methodology is demonstrated by computing the rf voltage waveform required to achieve a Gaussian IED with specified mean energy and energy spread on an electrode biased through a blocking capacitor. This inverse problem has multiple solutions, i.e. there exists a multitude of waveforms all producing the same IED. (Some figures in this article are in colour only in the electronic version)