Fluid simulation of the bias effect in inductive/capacitive discharges
Computer simulations are performed for an argon inductively coupled plasma (ICP) with a capacitive radio-frequency bias power, to investigate the bias effect on the discharge mode transition and on the plasma characteristics at various ICP currents, bias voltages, and bias frequencies. When the bias frequency is fixed at 13.56 MHz and the ICP current is low, e.g., 6 A, the spatiotemporal averaged plasma density increases monotonically with bias voltage, and the bias effect is already prominent at a bias voltage of 90 V. The maximum of the ionization rate moves toward the bottom electrode, which indicates clearly the discharge mode transition in inductive/capacitive discharges. At higher ICP currents, i.e., 11 and 13 A, the plasma density decreases first and then increases with bias voltage, due to the competing mechanisms between the ion acceleration power dissipation and the capacitive power deposition. At 11 A, the bias effect is still important, but it is noticeable only at higher bias voltages. At 13 A, the ionization rate is characterized by a maximum at the reactor center near the dielectric window at all selected bias voltages, which indicates that the ICP power, instead of the bias power, plays a dominant role under this condition, and no mode transition is observed. Indeed, the ratio of the bias power to the total power is lower than 0.4 over a wide range of bias voltages, i.e., 0–300 V. Besides the effect of ICP current, also the effect of various bias frequencies is investigated. It is found that the modulation of the bias power to the spatiotemporal distributions of the ionization rate at 2 MHz is strikingly different from the behavior observed at higher bias frequencies. Furthermore, the minimum of the plasma density appears at different bias voltages, i.e., 120 V at 2 MHz and 90 V at 27.12 MHz.