Effect of Multi-Frequency Excitation on Dust Particle Charging in Weakly Collisional Radio-Frequency Capacitive Discharge

A one-dimensional (1D) fluid model is developed to investigate the effect of multi-frequency excitation consisting of \(N\) consecutive harmonics on the charge of a single dust grain in a weakly collisional capacitively coupled plasma discharge. The spatial distributions of the electron density, the electrons temperature, and the charged particle flux are obtained and analyzed under the effects of the number of harmonics. It is shown that the number of harmonics considerably affects the discharge properties and the sheath thickness. In order to analyze the charge of an injected dust particle under the effect of different operating parameters, the model takes into account the electron and ion currents, as well as the effect of collisions between ions and neutral atoms. The results showed that as the number of harmonics increases, the particle charge increases in the powered sheath region while it decreases in the grounded sheath due to the electrical asymmetry effect. However, the charge remains constant in the central region where the electron temperature is constant. The present study further shows that the gas pressure and the driving frequency affect the dust charge oppositely, where an increase in pressure leads to a decrease in the dust charge, especially in the sheath regions, while the particle charge negatively increases as the driving frequency increases for all excitation waveforms.