Generalized method for optimizing impedance matching in capacitively coupled plasmas

Impedance matching in capacitively coupled plasma (CCP) systems is crucial. However, due to the complex nonlinear interactions between the plasma and the external circuit, identifying control parameters that enable efficient and robust power transfer remains particularly challenging. Traditional optimization methods rely on favorable initial conditions for convergence. Even when successful, they yield only a single set of control parameters and often require highly complex optimization designs due to strong coupling with the CCP load. To address these challenges, we propose a simpler yet more robust optimization method by shifting the optimization process from the control parameter space to the load’s complex impedance space. In this approach, the load impedance acts as a bridge between the new and old control parameters, decoupling the derivation of new parameters from historical trajectories. This eliminates dependence on initial conditions and enables the method to yield multiple sets of control parameters at different saddle positions. Additionally, the load impedance also acts as a bridge between the optimization algorithm and the load device, decoupling complex physical details from the optimization process, making our method remain consistent across both numerical simulations and experimental setups. In this paper, when applying the method to a numerical CCP system with an L-type matching network, it not only achieved efficient energy matching optimization within a few iterations but also identified multiple well-matched solutions.