The breakdown of SF6 gas at low pressure is of vital importance to both aerospace and microelectronics industries. However, the breakdown characteristics of SF6 in direct current at low pressure are still seldom studied. In this work, one-dimensional implicit particle-in-cell/Monte-Carlo collision algorithm is used to study the entire direct current breakdown process of low-pressure SF6. The ion-molecule collision, recombination, and external circuit are considered in the model. According to the results, the breakdown process can be divided into three stages: pre-breakdown stage, breakdown stage, and post-breakdown stage. In the pre-breakdown stage, the cathode sheath is not yet formed so the constant electric field exists in the entire area. In the breakdown stage, the formation mechanism of the cathode sheath is analyzed and the electrodes as a whole changes from capacitive to resistive, sharing the voltage with the external resistance. In the post-breakdown stage, the continued growth of positive ions leads to the formation of a thin anode sheath, which further causes the negative plasma potential, different from electropositive gas. The energy production terms including heating power and secondary electron emission (SEE) power are equal to the energy loss terms including collision loss power and boundary loss power, where collision loss power and boundary loss power are almost equal, while SEE power is negligible. In the final, plasma parameters gradually evolve to 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.
Radiofrequency (RF) coaxial cables are one of the vital components for the power sources of capacitively coupled plasmas (CCPs), by which the RF power is transferred to excite the plasma. Usually, the cables can be treated as transmission lines (TLs). However, few studies of TLs in CCP power sources were conducted due to the nonlinear coupling between TLs and the plasma. In this work, we developed a numerical scheme of TLs based on the Lax–Wendroff method and realized the nonlinear bidirectional coupling among the lumped-element model, transmission line model, and electrostatic particle-in-cell model. Based on the combined model, three discharge patterns were found, including weak matching state, normal state, and over matching state. The great differences among the three patterns indicated that the TLs could change the impedance matching of the device and significantly affect the plasma properties.
The breakdown process of capacitively coupled plasma (CCP) in the presence of a matching network is rarely studied, even though it is the indispensable part of the most laboratory and industrial devices of CCP. Based on the method of Verboncoeur, the solution method of the general “L”-type match circuit coupled with a particle-in-cell/Monte Carlo code is deduced self-consistently. Based on this method, the electrical breakdown process of CCP is studied. Both the plasma parameters and the electric parameters of the matching network during the breakdown are given and analyzed. In the pre-breakdown phase, the entire circuit can be considered as a linear system. However, the formation of the sheath during breakdown significantly enhanced the capacitance of the discharge chamber, which changed the electric signal amplitude of the external circuit. With the stabilization of plasma, the equivalent capacitance of CCP increases, which continues to change the electrical signal until the steady-state is reached. Accompanied by plasma stabilization is the appearance of high-order harmonics of discharge current caused by the gradually oscillating CCP capacitance. The breakdown characteristics can be obviously affected by the capacitance of the matching network. In the case of a breakdown zone, some breakdowns with special characteristics can be obtained by choosing the different capacitors. These works might be a reference for understanding the interaction between the plasma and the external circuit during the breakdown process and how to modulate the gas breakdown by controlling the external circuit.
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