Enhanced control of the ionization rate in radio-frequency plasmas with structured electrodes via tailored voltage waveforms

Radio-frequency capacitively coupled plasmas that incorporate structured electrodes enable increases in the electron density within spatially localized regions through the hollow cathode effect (HCE). This enables enhanced control over the spatial profile of the plasma density, which is useful for several applications including materials processing, lighting and spacecraft propulsion. However, asymmetries in the powered and grounded electrode areas inherent to the hollow cathode geometry lead to the formation of a time averaged dc self-bias voltage at the powered electrode. This bias alters the energy and flux of secondary electrons leaving the surface of the cathode and consequentially can moderate the increased localized ionization afforded by the hollow cathode discharge. In this work, two-dimensional fluid-kinetic simulations are used to demonstrate control of the dc self-bias voltage in a dual-frequency driven (13.56, 27.12MHz), hollow cathode enhanced, capacitively coupled argon plasma over the 66.6–200Pa (0.5–1.5Torr) pressure range. By varying the phase offset of the 27.12MHz voltage waveform, the dc self-bias voltage varies by 10%–15% over an applied peak-to-peak voltage range of 600–1000V, with lower voltages showing higher modulation. Resulting ionization rates due to secondary electrons within the hollow cathode cavity vary by a factor of 3 at constant voltage amplitude, demonstrating the ability to control plasma properties relevant for maintaining and enhancing the HCE.