Yu-Ru Zhang

Comparison of electrostatic and electromagnetic simulations for very high frequency plasmas

A two-dimensional self-consistent fluid model combined with the full set of Maxwell equations is developed to investigate an argon capacitively coupled plasma, focusing on the electromagnetic effects on the discharge characteristics at various discharge conditions. The results indicate that there exist distinct differences in plasma characteristics calculated with the so-called electrostatic model (i.e., without taking into account the electromagnetic effects) and the electromagnetic model (which includes the electromagnetic effects), especially at very high frequencies. Indeed, when the excitation source is in the high frequency regime and the electromagnetic effects are taken into account, the plasma density increases significantly and meanwhile the ionization rate evolves to a very different distribution when the electromagnetic effects are dominant. Furthermore, the dependence of the plasma characteristics on the voltage and pressure is also investigated, at constant frequency. It is observed that whe...

Fluid simulation of the phase-shift effect in hydrogen capacitively coupled plasmas: I. Transient behaviour of electrodynamics and power deposition

A two-dimensional self-consistent fluid model coupled with the full set of Maxwell equations is established to investigate the phase-shift effect on the transient behaviour of electrodynamics and power deposition in a hydrogen capacitively coupled plasma. The effect has been examined at 13.56?MHz and 100?MHz, respectively, because of the different phase-shift modulation when the electromagnetic effects are dominant. The results indicate that the spatiotemporal distributions of the plasma characteristics obtained for various phase-shift cases are obviously different both in shape and especially in absolute values. Indeed, when the phase difference varies from 0 to ?, there is an increase in the electron flux, thus the power deposition becomes more pronounced. At the frequency of 13.56?MHz, the axial electron flux in the bulk plasma becomes uniform along the z-axis, and the radial electron flux exhibits two peaks within one period at the reverse-phase case, whereas the oscillation is less pronounced at the in-phase case. Furthermore, in the very high frequency discharge, the radial electron flux is alternately positive and negative with four peaks during one period, and the ionization mainly occurs in the sheath region, due to the prominent power deposition there at a phase difference equal to ?.

Fluid simulation of the phase-shift effect in hydrogen capacitively coupled plasmas: II. Radial uniformity of the plasma characteristics

A two-dimensional fluid model, including the full set of Maxwell equations, has been developed and applied to investigate the effect of a phase shift between two power sources on the radial uniformity of several plasma characteristics in a hydrogen capacitively coupled plasma. This study was carried out at various frequencies in the range 13.56?200?MHz. When the frequency is low, at 13.56?MHz, the plasma density is characterized by an off-axis peak when both power sources are in-phase (??=?0), and the best radial uniformity is obtained at ??=??. This trend can be explained because the radial nonuniformity caused by the electrostatic edge effect can be effectively suppressed by the phase-shift effect at a phase difference equal to ?. When the frequency rises to 60?MHz, the plasma density profiles shift smoothly from edge-peaked over uniform to centre-peaked as the phase difference increases, due to the pronounced standing-wave effect, and the best radial uniformity is reached at ??=?0.3?. At a frequency of 100?MHz, a similar behaviour is observed, except that the maximum of the plasma density moves again towards the radial edge at the reverse-phase case (??=??), because of the dominant skin effect. When the frequency is 200?MHz, the bulk plasma density increases significantly with increasing phase-shift values, and a better uniformity is obtained at ??=?0.4?. This is because the density in the centre increases faster than at the radial edge as the phase difference rises, due to the increasing power deposition Pz in the centre and the decreasing power density Pr at the radial edge. As the phase difference increases to ?, the maximum near the radial edge becomes obvious again. This is because the skin effect has a predominant influence on the plasma density under this condition, resulting in a high density at the radial edge. Moreover, the axial ion flux increases monotonically with phase difference, and exhibits similar profiles to the plasma density. The calculation results illustrate that the radial uniformity of the various plasma characteristics is strongly dependent on the applied frequency and the phase shift between both power sources, which is important to realize, for controlling the uniformity of the plasma etch and deposition processes.

Phase-shift effect in capacitively coupled plasmas with two radio frequency or very high frequency sources

A two-dimensional fluid model was built to study the argon discharge in a capacitively coupled plasma reactor and the full set of Maxwell equations is included in the model to understand the electromagnetic effect in the capacitive discharge. Two electrical sources are applied to the top and bottom electrodes in our simulations and the phase-shift effect is focused on. We distinguish the difference of the phase-shift effect on the plasma uniformity in the traditional radio frequency discharge and in the very high frequency discharge where the standing wave effect dominates. It is found that in the discharges with frequency 13.56 MHz, the control of phase difference can less the influence of the electrostatic edge effect, and it gets the best radial uniformity of plasma density at the phase difference π. But in the very high frequency discharges, the standing wave effect plays an important role. The standing wave effect can be counteracted at the phase difference 0, and be enhanced at the phase difference ...

Computational study of plasma sustainability in radio frequency micro-discharges

We apply an implicit particle-in-cell Monte-Carlo (PIC-MC) method to study a radio-frequency argon microdischarge at steady state in the glow discharge limit, in which the microdischarge is sustained by secondary electron emission from the electrodes. The plasma density, electron energy distribution function (EEDF), and electron temperature are calculated in a wide range of operating conditions, including driving voltage, microdischarge gap, and pressure. Also, the effect of gap size scaling (in the range of 50-1000 μm) on the plasma sustaining voltage and peak electron density at atmospheric pressure is examined, which has not been explored before. In our simulations, three different EEDFs, i.e., a so-called three temperature hybrid mode, a two temperature α mode, and a two temperature γ mode distribution, are identified at different gaps and voltages. The maximum sustaining voltage to avoid a transition from the glow mode to an arc is predicted, as well as the minimum sustaining voltage for a steady glow discharge. Our calculations elucidate that secondary electrons play an essential role in sustaining the discharge, and as a result the relationship between breakdown voltage and gap spacing is far away from the Paschen law at atmospheric pressure.

Electromagnetic effects in high-frequency large-area capacitive discharges: A review

In traditional capacitively coupled plasmas, the discharge can be described by an electrostatic model, in which the Poisson equation is employed to determine the electrostatic electric field. However, current plasma reactors are much larger and driven at a much higher frequency. If the excitation wavelength λ in the plasma becomes comparable to the electrode radius, and the plasma skin depth δ becomes comparable to the electrode spacing, the electromagnetic (EM) effects will become significant and compromise the plasma uniformity. In this regime, capacitive discharges have to be described by an EM model, i.e., the full set of Maxwells equations should be solved to address the EM effects. This paper gives an overview of the theory, simulation and experiments that have recently been carried out to understand these effects, which cause major uniformity problems in plasma processing for microelectronics and flat panel display industries. Furthermore, some methods for improving the plasma uniformity are also ...

Bulk plasma fragmentation in a C4F8 inductively coupled plasma: A hybrid modeling study

A hybrid model is used to investigate the fragmentation of C4F8 inductive discharges. Indeed, the resulting reactive species are crucial for the optimization of the Si-based etching process, since they determine the mechanisms of fluorination, polymerization, and sputtering. In this paper, we present the dissociation degree, the density ratio of F vs. CxFy (i.e., fluorocarbon (fc) neutrals), the neutral vs. positive ion density ratio, details on the neutral and ion components, and fractions of various fc neutrals (or ions) in the total fc neutral (or ion) density in a C4F8 inductively coupled plasma source, as well as the effect of pressure and power on these results. To analyze the fragmentation behavior, the electron density and temperature and electron energy probability function (EEPF) are investigated. Moreover, the main electron-impact generation sources for all considered neutrals and ions are determined from the complicated C4F8 reaction set used in the model. The C4F8 plasma fragmentation is explained, taking into account many factors, such as the EEPF characteristics, the dominance of primary and secondary processes, and the thresholds of dissociation and ionization. The simulation results are compared with experiments from literature, and reasonable agreement is obtained. Some discrepancies are observed, which can probably be attributed to the simplified polymer surface kinetics assumed in the model.

Effects of reactor geometry and frequency coupling on dual-frequency capacitively coupled plasmas

In dual-frequency (DF) capacitively coupled plasma discharges, the effect of reactor geometry on the plasma density is investigated by means of a two-dimensional self-consistent fluid model combined with a power supply computation module. The results indicate that by enlarging the inter-electrode gap or by blocking the electrode with dielectric materials, the plasma density becomes more uniform along the radial direction due to the suppressed edge effect. Different approaches of the connections of the DF sources show that the distribution of plasma density is mostly confined within the blocked high-frequency (HF)-driven electrode region. Considering the asymmetry electrode shape effect, a higher plasma density could be obtained by connecting the HF source on a smaller electrode. When considering the two methods of source coupling, the DF sources applied individually on opposite electrodes may produce a higher density in comparison with the sources applied on the same electrode.

Nonlocal electron kinetics and spatial transport in radio-frequency two-chamber inductively coupled plasmas with argon discharges

A two-chamber inductively coupled plasma (ICP) system, in which an expansion region with large volume is attached to a main ICP (driver region with a small vessel), is investigated. In order to give a comprehensive knowledge of this kind of plasma source, the axially and radially resolved measurements of the electron density, effective electron temperature, and electron energy probability function (EEPF) for an argon discharge are systematically conducted by means of Langmuir probe for various powers and gas pressures. Moreover, a hybrid model within COMSOL Multiphysics is employed to validate the experimental results. It is found that the diffusion combined with the nonlocal electron kinetics plays a predominant role in two-chamber ICPs. Along the axial direction, both the electron density and the electron temperature peak at the center of the driver region and they decline towards both sides. The depletion of high-energy tails of EEPFs with axial distance demonstrates the cooling mechanism for energetic...

Equivalent circuit effects on mode transitions in H2 inductively coupled plasmas

It is well known experimentally that the circuit matching network plays an important role in the mode transition behavior of inductively coupled plasmas. To date, however, there have been no reports of numerical models being used to study the role of the matching circuit in the transition process. In this paper, a new two-dimensional self-consistent fluid model that couples the components of an equivalent circuit module is developed to investigate the effects of the equivalent circuit on the mode transition characteristics of an inductively coupled, hydrogen plasma. The equivalent circuit consists of a current source, impedance matching network, reactor impedance, and plasma transferred impedance. The nonlinear coupling of the external circuit with the internal plasma is investigated by adjusting the matching capacitance at a fixed input current. The electron density and temperature as well as the electromagnetic fields all change suddenly, and the E to H mode transition occurs abruptly at a certain matching capacitance as the impedance matching of the external circuit is varied. We also analyze the fields and the plasma characteristics during the transition process, especially for the case of the capacitive E mode.