Most plasma sources have to undergo a breakdown process, during which, energy is injected, and particles are ionized. However, we still know little about this fast evolution process. In this work, a one-dimensional direct implicit particle-in-cell/Monte-Carlo collision (PIC/MCC) program is used to study the breakdown process of a capacitively coupled plasma (CCP) driven by dual radio frequencies. The results show that the breakdown process can be divided into three phases: the pre-breakdown, transition, and post-breakdown phases. In the pre-breakdown phase, the plasma density and heating power grow exponentially. The electric field can penetrate the whole discharge region without any shielding, resulting in a higher-than-average electron energy. Secondary electron emission is critical to grow the electron numbers under these discharge conditions. During the transition phase, the formation of sheaths maximizes the electron generation rate and heating power. The formation of sheaths also causes a drastic change in the electrical characteristics of CCP devices. In the post-breakdown phase, the plasma parameters gradually evolve until a steady state is reached. The decreasing rate of generation and the increasing rate of particle loss gradually equalize. The trends of the power gain and plasma loss are similar to the curves for the particle generation and loss rates, and a dynamic equilibrium is finally reached in the last steady state.

Impedance matching can maximize the absorbed power transferred to the plasma load and minimize the reflected power, making it critical and indispensable for capacitively coupled plasmas (CCPs). The external circuit usually interacts with the plasma nonlinearly, so the global simulation of the external circuit and plasma and the matching design is very challenging. In this work, an a priori model was proposed to match the plasma impedance and the external circuit impedance for single-frequency CCPs. By calculating the plasma impedance and the matching network, the matching parameters were iteratively updated to find the best matching parameters. By adjusting the capacitance and the inductance of the circuit by numerical simulations, the reflection coefficient can be significantly reduced. At the same time, the plasma power absorption efficiency will be significantly improved. The universality of the method was demonstrated by choosing different initial circuit, discharge, and plasma parameters. The proposed method provides an effective matching design reference for CCPs.

The electrical characteristics of the Gaseous Electronics Conference reference cell at low pressures are investigated using a two-dimensional electrostatic implicit particle-in-cell/Monte Carlo collision model in cylindrical coordinates. The coupling between the complex reactor geometry and the external circuit is included via an equivalent capacitance calculated from the electric energy density and the charge conservation equation. The results of this model are compared with experimental measurements and other model calculations and show agreement. The plasma series resonance effect, closely related to electron heating, is observed in this numerical simulation of a strongly asymmetric reactor at low pressures. The plasma kinetics of the capacitively coupled discharge and details of the external circuit response, including electrical waveforms and higher-order harmonics, are discussed at different pressures, which provides important insights for understanding the power coupling mechanisms in capacitively coupled discharges.