Kinetic simulations of capacitively coupled plasmas driven by tailored voltage waveforms with multi-frequency matching

Abstract Impedance matching is crucial for optimizing plasma generation and reducing power reflection in capacitively coupled plasmas (CCP). Designing these matchings is challenging due to the varying and typically unknown impedance of the plasma, especially in the presence of multiple driving frequencies. Here, a computational design method for IMNs for CCPs is proposed and applied to discharges driven by tailored voltage waveforms (TVW). This method is based on a self-consistent combination of Particle In Cell/Monte Carlo Collision (PIC/MCC) simulations of the plasma with Kirchhoff's equations to describe the external electrical circuit. Two Foster second-form networks with the same structure are used to constitute an L-type matching network, and the matching capability is optimized by iteratively updating the values of variable capacitors inside the IMN. The results show that the plasma density and the power absorbed by the plasma continuously increase in the frame of this iterative process of adjusting the matching parameters until an excellent impedance matching capability is finally achieved. Impedance matching is found to affect the DC self-bias voltage, whose absolute value is maximized when the best matching is achieved. Additionally, a change in the quality of the impedance matching is found to cause an electron heating mode transition. Poor impedance matching results in a heating mode where electron power absorption in the plasma bulk by drift electric fields plays an important role, while good matching results in the classical $\alpha$-mode operation, where electron power absorption by ambipolar electric fields at the sheath edges dominates. The method proposed in this work is expected to be of great significance in promoting TVW plasma sources from theory to industrial application, since it allows designing the required complex multi-frequency IMNs.