Shali Yang

A two-dimensional axisymmetric particle-in-cell/Monte Carlo collision model with self-consistent external circuit coupling is developed to investigate the influence of non-uniform magnetic fields on low-pressure capacitively coupled plasma (CCP) in a gaseous electronics conference reference cell. The model incorporates a direct implicit kinetic scheme and an anisotropic susceptibility tensor to accurately describe magnetized particle transport and plasma-circuit interactions. Argon discharges at 25 mTorr driven by a 13.56 MHz radio-frequency (RF) source are studied under different magnetic-field strengths. The results show that weak magnetic fields primarily modify the spatial plasma distribution, shifting the density peak from the discharge center toward regions of strong radial magnetic field, while producing only limited density enhancement. At the highest magnetic-field strength investigated here, strong electron confinement significantly increases the electron residence time, shifts the dominant power-absorption region from the powered sheath to the grounded sheath, and produces a marked nonlinear increase in the plasma density. Furthermore, the magnetic field reduces sheath thickness, lowers the discharge impedance, and slightly decreases the negative direct current self-bias. Ion flux distributions become more uniform and shift toward the electrode edge, while ion energy and angular distributions become increasingly concentrated. Under strong magnetic confinement, multimodal ion energy distribution functions emerge, reflecting enhanced ion interaction with RF sheath oscillations. These findings reveal the strong coupling among magnetic confinement, sheath dynamics, and external circuit behavior in magnetized CCP, providing insight into plasma control strategies for advanced semiconductor processing applications.

In this work, the influences of the direct current blocking capacitor, stray capacitance, and stray resistance in the external circuit on the self-bias driven by tailored voltage waveform (TVW)-driven asymmetric capacitive discharges are investigated using a one-dimensional three-velocity particle-in-cell/Monte Carlo collision model coupled with an external circuit. Under a zero-initial-phase sinusoidal TVW drive with an amplitude ratio of 3:2:1, a dc self-bias voltage is generated and can be significantly modulated by the blocking capacitor, stray resistance, and stray capacitance. The approximate adjustment ranges of each external circuit parameter, as well as an optimized combination of circuit parameters under specific discharge conditions are presented. Based on bias control using a single external component, combined control of multiple external circuit parameters enables a wider tuning range of plasma density, ion flux, and ion energy at the boundary. In addition, the mechanisms responsible for the formation of positive and negative self-bias voltages at different pressures are discussed. These results may provide insight and a theoretical reference for the engineering design of bias control in electrical asymmetric capacitively coupled plasma systems.

A computational method based on the particle-in-cell/Monte Carlo (PIC/MC) algorithm is developed to simulate the breakdown characteristics of low-pressure, radio-frequency (RF) driven capacitive discharges. The simulation framework incorporates key procedures such as initialization, breakdown determination, and a voltage–pressure scanning strategy, enabling efficient and accurate calculation of breakdown curves. To balance reliability and computational cost, a combined criterion based on electron avalanche growth and critical electron density is adopted for breakdown identification. Using this approach, breakdown curves under different electron surface emission conditions are investigated, revealing clear boundary effects. The results indicate that ion-induced secondary electron emission (SEE) primarily influences the high-voltage region of the curve, whereas electron-induced SEE and reflection coefficients significantly extend the breakdown region toward lower pressures and voltages. Furthermore, increases in driving frequency and gap distance both substantially expand the low-pressure breakdown region, with the drift-diffusion branch becoming more pronounced. At frequencies beyond a certain threshold, the low-pressure breakdown curve transitions from closed to open, accompanied by a voltage span exceeding 100V — a behavior associated with the transition from RF-driven plasma to multipactor discharge under sub-millitorr conditions. In the high-pressure, high-voltage regime, the breakdown behavior remains consistent with Paschen’s law, while the drift-diffusion branch exhibits clear scaling with gap distance.

This study employs 1D particle-in-cell/Monte Carlo collision simulations to systematically investigate the modulation of capacitively coupled plasma by a unidirectional electron beam under tunable magnetic field gradients. The results reveal a remarkable sensitivity of electron beam injection to both the orientation and intensity of the magnetic field gradient, enabling precise tailoring of plasma properties. Critically, the contribution of injected electrons to the discharge is maximized when their cyclotron radius matches the electrode gap, yielding peak plasma density. Furthermore, while ion bombardment energy remains stable under optimal beam injection, the ion flux exhibits significant modulation, demonstrating a decoupling between energy and flux control. These findings establish magnetic field gradients as a powerful tool for real-time plasma tuning in applications requiring dynamic control of density and ion flux.

To ensure a robust tokamak start-up, electron cyclotron heating (ECH) assisted plasma initiation has been proposed. In this study, a zero-dimensional (0D) model studying tokamak start-up assisted by ECH has been redeveloped. To validate the reliability of the model, an ohmic start-up discharge in deuterium plasma with carbon and oxygen impurities has been simulated. The results were benchmarked against a reference model and showed favorable agreement. Based on the established 0D model, it has been enhanced by the integration of the ECH module for studying ITER start-up discharge. Compared with pure ohmic heating, the simulation results demonstrate that ECH assisted start-up not only achieves plasma breakdown more efficiently, but also significantly enhances key parameters, increasing the electron density by 9% and plasma current by 50% under the same simulation time. An analysis has also been conducted regarding the influence of ECH on the ionization states of impurities. It was found that carbon and oxygen impurities could achieve higher ionization states at the same gas pressure with ECH-assisted discharge, consequently prompting a faster impurity burn-through. In addition, the ITER start-up has been conducted under different injected ECH power. The results demonstrate that overall energy balance remains favorable for the discharge despite the increased loss related to impurities under higher injected ECH power, and the ECH power absorption efficiency is also improved.

Extinction is an inevitable process in the discharge of capacitively coupled plasma and frequently occurs many times in some special discharges, such as pulse-driven discharges. However, this indispensable process has rarely been studied in detail. In this study, based on the particle-in-cell/Monte-Carlo collision algorithm, this process is demonstrated and studied. The extinction evolution of electron density, energy under different external circuit, voltage decay time, and different pressure are first given and analyzed. The whole extinction process may take the slow diffusion of electrons, which can take hundreds of microseconds and even milliseconds, and will take much longer time under high pressure. Longer decay time of rf voltage will shorten the extinction. Three-body recombination cannot be ignored at 20 mTorr lower pressure. Furthermore, the effects of the voltage suddenly changes from a high sustaining voltage (pre-voltage) of 200 V to lower extinction voltage (post-voltage) are observed. The plasma will extinguish at a much faster speed under the lower post-voltage of several volt than directly switched off. The extinction process driven by different post-voltages under different background pressures was also examined. There is a minimum sustaining voltage at the middle pressure of about 100 mTorr, and post-voltage (several volts to tens of volts) to minimize the extinction time. These results may provide a reference for optimizing the radio-frequency (rf) power sources of the rf pulse-driven plasma sources to reduce extinction time.

In this study, a one-dimensional particle-in-cell/Monte Carlo collision model was employed to simulate capacitively coupled plasma discharges driven by tailored voltage waveforms and modulated with electron beam (EB) injection. The electrical asymmetry introduced by tailored voltage waveform leads to distinct plasma behaviors depending on the EB injection side. The effects of injection location, EB current, and electron energy on plasma characteristics were systematically investigated. Injection from the powered electrode significantly enhances plasma density and produces striped ionization structures in the sheath, resulting from the combined effects of the ionization energy threshold and sheath acceleration. As the electron energy increases, injection from the grounded side becomes more effective, eventually yielding higher densities due to longer electron trajectories and enhanced ionization. Increasing the EB current density from 0.5 to 2.0 A/m2 results in more uniform ionization in the bulk while maintaining an expanded but stable sheath. Moreover, the maximum ion energy at the grounded electrode decreases with increasing EB current, offering potential for ion energy control in plasma processing.

In this study, a one-dimensional particle-in-cell/Monte Carlo collision model is developed to investigate the effects of harmonic number and magnetic field variation on electron beam modulation discharges. The results show that increasing the harmonic number leads to greater voltage waveform asymmetry, which enhances sheath expansion on the powered electrode side. This enables more effective electron acceleration, resulting in higher plasma density, elevated electron temperature near the powered sheath, and the formation of a self-bias voltage. Additionally, under a fixed harmonic number, increasing the magnetic field strength initially increases the plasma density due to extended electron paths that enhance ionization. However, at stronger fields, the electron Larmor radius decreases, leading to more localized ionization near the injection side and reduced overall density. The ion energy distribution function at the powered electrode becomes narrower with decreasing peak energy, while that at the grounded electrode shows an increasing and broadened energy spectrum. These findings provide guidance for optimizing plasma density and ion energy control in plasma processing applications.

This study explores the combined effects of electron beam (EB) injection and magnetic field gradients on argon capacitively coupled plasma driven by tailored voltage waveforms, using a one-dimensional implicit particle-in-cell/Monte Carlo collision model. Simulation results show that applying a positive magnetic field gradient enhances plasma density and suppresses the asymmetry induced by EB injection and waveform excitation. As the gradient increases, electron confinement improves, leading to more localized ionization during the sheath expansion phase and a broader enhancement in plasma uniformity. In contrast, a negative magnetic field gradient intensifies density asymmetry by restricting the EB to the powered side, concentrating ionization near the injection region. Additionally, the ion energy distribution function (IEDF) becomes increasingly monoenergetic at the powered electrode, while the grounded electrode exhibits a multi-peaked profile due to sheath dynamics. These findings provide insights into magnetic-field-assisted control of plasma properties and offer promising strategies for tuning IEDF in plasma processing applications.

The magnetic field can effectively affect the properties of capacitively coupled plasma (CCP) modulated by electron beam injection, leading to improved discharge performance. In this study, a one-dimensional particle-in-cell/Monte Carlo collision model is used to simulate electron beam injected CCP under various magnetic fields. At a pressure of 20 mTorr, increasing the magnetic field from 0 to 50 G initially caused the plasma density to increase and then fall, with a peak density observed at 20 G. This is because the gyroradius of the injected electrons in the magnetic field is comparable to the electrode gap. When the pressure is increased, this effect is significantly weakened due to the disruption of the electrons’ gyration. Additionally, the electron energy distribution is significantly impacted by increasing the magnetic field. An increase in the magnetic field reduces the maximum ion energy and significantly enhances ion flux at the powered electrode. At the grounded electrode, when the maximum cyclotron radius of the injected electrons is comparable to the electrode spacing, the ion flux reaches its maximum. Further increasing the magnetic field results in a decrease in ion flux. This is crucial for semiconductor etching processes aiming to reduce electrode damage and improve etching efficiency. It also provides new insights for plasma research.