Numerical impedance matching via extremum seeking control of single-frequency capacitively coupled plasmas

Abstract

Abstract Impedance matching is a critical component of semiconductor plasma processing for minimizing the reflected power and maximizing the plasma absorption power. In this work, a more realistic plasma model is proposed that couples lumped element circuit, transmission line, and particle-in-cell (PIC) models, along with a modified gradient descent algorithm (GD), to study the impact of presets on the automatic matching process. The effectiveness of the proposed conceptual method is validated by using a single-frequency capacitively coupled plasma as an example. The optimization process with the electrode voltage and the reflection coefficient as the objective function and the optimized state, including plasma parameters, circuit waveforms, and voltage and current on transmission lines, is provided. These results show that the presets, such as initial conditions and objective functions, are closely related to the automatic matching process, resulting in different convergence speeds and optimization results, proving the existence of saddle points in the matching network parameter space. These findings provide valuable information for future experimental and numerical studies in this field.