Ion energy distribution transitions in capacitive discharges caused by abnormal dc self-bias formation induced by very-low-frequency voltage waveform tailoring

Based on particle-in-cell/Monte Carlo collision (PIC/MCC) simulations of geometrically symmetric capacitive argon discharges driven by a high-frequency sinusoidal voltage, the ion energy distribution (IED) on the powered electrode is demonstrated to transition from a multimodal to a quasi-single-peak distribution by adding a very-low-frequency tailored voltage waveform (TVW) and varying its peak-to-peak voltage. This transition is controlled by an abnormal dc self-bias transition. A theory developed in this work reveals that the dc self-bias transition is attributed to temporal charge dynamics and shows good agreement with the results of a time-dependent transmission line model and PIC/MCC plasma simulations. At low-voltage amplitudes, the charging effect of the external blocking capacitor causes multiple sheath collapses per fundamental period of the very-low-frequency TVW. This reduces the total uncompensated charge in the discharge and enhances the ratio of the maximum net charge in both sheaths as well as the discharge symmetry, leading to a very-low dc self-bias and a multimodal structure of the IED. As the voltage amplitude is increased, the sheath adjacent to the bottom powered electrode collapses only once per cycle of the TVW, giving rise to a large charge asymmetry, which leads to a strong dc self-bias and a quasi-single-peak structure of the IED.