Jingwen Xu’s research while affiliated with Wuhan University of Technology and other places

Capacitively coupled plasmas (CCPs) are widely used in plasma processing applications, where efficient power coupling between the radio frequency (RF) source and the plasma is crucial. In practical CCP systems, impedance matching networks (IMNs) are employed to minimize power reflection. However, the presence of coaxial cables can significantly impact plasma impedance and matching performance. We develop a comprehensive simulation framework for the IMN design of CCPs, fully considering the effects of RF coaxial cables. The model self-consistently couples a distributed transmission line (TL) model, a lumped-element circuit model, and an electrostatic particle-in-cell model. This coupled model is used to investigate the impact of coaxial cables on matching performance under various discharge conditions and cable configurations. The simulation results indicate that the optimal power transmission efficiency was achieved after 6 matching iterations. The power coupled to the CCP increased from 2.7 W before matching to 180.9 W, and the reflection coefficient ultimately decreased to 0.003. The results also reveal that neglecting the cables will lead to a decrease in the power dissipated in the CCP. The proposed method demonstrates effectiveness in achieving impedance matching for different gas pressures (75–300 mTorr) and cable lengths. It can be concluded that the matching speed is faster for an appropriate cable length. This work provides valuable insights into the role of TLs in CCP impedance matching and offers a practical tool for optimizing power delivery in realistic CCP systems with RF coaxial cables.

In the study of electronegative CF4 capacitively coupled plasmas (CCP), plasma modulation is typically achieved by varying parameters such as pressure and voltage. In this work, the particle-in-cell/Monte Carlo (PIC/MC) method is used to simulate modulation of CF4 CCP with injection of anions (F⁻) ion beam (FB). The results demonstrate that FB injection effectively enhances the dissociation collision process between F⁻ ions and neutral molecules, thus altering the densities of electrons and ions. An effective modulation of the characteristic parameters of the plasma of CF4 can be achieved by controlling the current and energy of FB. Particularly noteworthy is the transition of the heating mode from the DA mode to the dissociation mode as the FB current increases to 0.038 A (energy fixed at 10 keV) or when the FB energy exceeds 10 keV (current fixed on 0.038 A). This transition is attributed to the generation of a substantial number of electrons through dissociative collisions. This approach provides insight into the controlled modulation of plasma characteristics in CF4 CCP, offering potential applications in various plasma-based technologies.

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.

Capacitively coupled plasma (CCP) tools are crucial for etching, deposition, and cleaning processes in the semiconductor industry. A comprehensive understanding of their discharge characteristics is vital for the advancement of chip processing technology. In this study, the influence of external circuitry on the breakdown process was investigated under the CF4 discharge system, with a particular focus on challenges presented by the nonlinear nature of the plasma. The results demonstrated that the external circuit significantly affects the discharge process by altering the electric field distribution as well as modifying the electron density and temperature of the plasma. By incorporating the matching circuit, stable discharge was achieved at reduced voltage levels. During breakdown, a substantial increase in the capacitance of the discharge chamber is induced by the formation of the sheath, which alters the amplitude of the electrical signal within the external circuit. The breakdown characteristics are significantly influenced by the capacitance of the matching network. Breakdowns with distinctive characteristics can be achieved by selectively choosing different capacitors. Furthermore, a shift in the CF4 discharge mode at different pressures under the external circuit model and the alteration in the discharge mode affect the electrical properties of the plasma in the matched circuit. These findings could be used to optimize the discharge of CCP and its applications, including surface treatment, material synthesis, and environmental remediation.

Micro-discharges have many excellent characteristics, such as generation of high-density and non-equilibrium plasmas at atmospheric pressure. In this paper, we used an implicit particle-in-cell/Monte Carlo collision method for three-dimensional velocities in a one-dimensional space combined with the secondary electron emission model to study the characteristics of micro-discharges driven by dual radio frequency (RF) power. The effect on plasma parameters was observed by varying the voltage of the RF power, the frequency, and the gas pressure of the discharge. Since the electrode spacing is very small in micro-discharges, the voltage change will affect the characteristics of micro-discharges. In addition, the plasma density increases with the frequency and the discharge mode changes at different frequencies. Finally, the influence of gas pressure on the characteristics of micro-discharges cannot be ignored. When the air pressure decreases, the ion flux reaching the electrodes is significantly increased, and the energy distribution of ions increases in the high-energy portion.

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.

A fully self-consistent second order accuracy model for coupling a generalized external circuit and a one-dimensional bounded electrode-driven plasma was proposed in this paper. The plasma was embedded in the circuit as a non-linear element with a potential difference. Based on Kirchhoff's voltage law and the definition of current, the problem of solving the generalized external circuit was transformed into an initial value problem of a set of first-order ordinary differential equations which can be discretized numerically by the second-order backward differential formula. The charge conservation equation at the electrode plate was coupled to the above equation, and the voltage, current, and surface charge density at the next moment were solved by a differential equation solver. Dirichlet boundary conditions of Poisson's equation were obtained through the surface charge density σ0 of the generalized external circuit equation and the plasma density ρ of the Particle-in-Cell(PIC) model. The spatial distribution of plasma potential was solved by using the second-order central difference scheme. The obtained potential at the electrode plate can be used as the Robin boundary condition of the system of generalized external circuit equations. In this model, the loose coupling between the generalized external circuit and plasma was realized by the boundary condition, and the system was fully self-consistent based on the charge conservation law and energy conservation law. We simulated the capacitively coupled plasmas (CCP) under different external circuits as the example and verified the performance of the model. This model can be used to study the influence of different external circuit structures and parameters on plasma discharge, and can be used for any plasma sources driven by electrodes, like CCP, some vacuum electronic devices, and Z-Pinches.