Bulk Plasma Region Research Articles

Investigating instabilities in magnetized low-pressure capacitively coupled RF plasma using particle-in-cell (PIC) simulations

The effect of a uniform magnetic field on particle transport in low-pressure radio frequency (RF) capacitively coupled plasma (CCP) has been studied using a particle-in-cell model. Three distinct regimes of plasma behavior can be identified as a function of the magnetic field. In the first regime at low magnetic fields, asymmetric plasma profiles are observed within the CCP chamber due to the effect of E→×B→ drift. As the magnetic field increases, instabilities develop and form self-organized spoke-shaped structures that are distinctly seen within the bulk plasma closer to the sheath. In this second regime, the spoke-shaped coherent structures rotate inside the plasma chamber in the −E→×B→ direction, where E→ and B→ are the DC electric and magnetic field vectors, respectively, and the DC electric field exists in the sheath and pre-sheath regions. The spoke rotation frequency is in the megahertz range. As the magnetic field strength increases further, the rotating coherent spokes continue to exist near the sheath. The coherent structures are, however, accompanied by new small-scale incoherent structures originating and moving within the bulk plasma region away from the sheath. This is the third regime of plasma behavior. The threshold values of the magnetic field between these regimes were found not to vary with changing plasma reactor geometry (e.g., area ratio between ground and powered electrodes) or the use of an external capacitor between the RF-powered electrode and the RF source. The threshold values of the magnetic field between these regimes shift toward higher values with increasing gas pressure. Analysis of the results indicates that the rotating structures are due to the lower hybrid instability driven by density gradients and electron-neutral collisions. This paper provides guidance on the upper limit of the magnetic field for instability-free operation in low-pressure CCP-based semiconductor deposition and etch systems that use the external magnetic field for plasma uniformity control.

Numerical Study on Kinetic Effects of Driving Frequency in Atmospheric Radio Frequency Discharges Using Deep Neural Network

The particle-in-cell Monte Carlo collision (PIC-MCC) model is an essential way to investigate the kinetic behaviors of low-temperature plasmas, but usually, it is hugely time consuming in simulating atmospheric radio frequency (RF) plasmas. In this study, a deep neural network (DNN) with multiple hidden layers is developed to predict the kinetic discharge characteristics of atmospheric RF plasmas. The results obtained from the PIC-MCC model are used as the training dataset for the DNN, and the well-trained DNN is able to efficiently yield various kinetic behaviors of atmospheric RF discharges with very high precision. The validation of the results predicted by the DNN algorithm is performed by comparing them with the simulation results directly from the PIC-MCC model. Compared with the time-consuming PIC-MCC simulations, the well-trained DNN takes only 0.01 s to yield the essential kinetic characteristics of atmospheric RF discharges, which saves seven orders of magnitude of computation time compared with the traditional PIC-MCC simulation. The predicted data show that the discharge current of atmospheric RF discharges increases monotonically with the driving frequency at a given applied voltage, and as the driving frequency increases, the electric field in the sheath region is strongly enhanced with the sheath region shrinks and the bulk plasma region expanding. Additionally, the electron energy distribution function (EEDF) can be accurately predicted by DNN; moreover, as the driving frequency increases, the low-energy electrons can be transformed into medium-energy electrons, leading to a transition of the EEDF from a three-temperature distribution to a Maxwellian distribution from the DNN prediction. The study indicates that the well-trained DNN is a promising tool for plasma simulation with very high efficiency and accuracy compared with the PIC-MCC model with huge computational costs, which could provide enough kinetic results to further understand the discharge behaviors in atmospheric RF discharges.

Investigation of stochastic heating and its influence on plasma radial uniformity in biased inductively coupled Ar discharges by hybrid simulation

A bias power is usually applied in inductively coupled plasmas (ICP) to realize the separate control of the plasma density and the ion energy. In this research, a two-dimensional fluid/electron Monte Carlo hybrid model is developed to self-consistently investigate the bias effect on the stochastic heating and on the radial homogeneity in a biased argon ICP operated at low pressure (3 mTorr). The results show that the temporal evolution of the stochastic heating exhibits a plateau and a peak when the sheath collapses at high bias voltages, due to the limited sheath heating and the electron inertia. In addition, the plasma density in the diffusion chamber increases with bias voltage and bias frequency, because of the more pronounced stochastic heating both at the substrate and at the grounded wall. In the main discharge chamber, the plasma density decreases with bias voltage, due to the compression of the bulk plasma region, and this trend becomes less obvious at high bias frequency, because of the enhanced power absorption caused by the stochastic heating. Therefore, it is concluded that by tuning the bias voltage and bias frequency, the plasma radial uniformity could be modulated efficiently, which is very important for improving plasma processing.

The effects of radio frequency atmospheric pressure plasma and thermal treatment on the hydrogenation of TiO2 thin film

The effects of radio frequency (RF) atmospheric pressure (AP) He/H2 plasma and thermal treatment on the hydrogenation of TiO2 thin films were investigated and compared in this work. The color of the original TiO2 film changes from white to black after being hydrogenated in He/H2 plasma at 160 W (gas temperature ∼381 °C) within 5 min, while the color of the thermally treated TiO2 film did not change significantly even in pure H2 or He/H2 atmosphere with higher temperature (470 °C) and longer time (30 min). This indicated that a more effective hydrogenation reaction happened through RF AP He/H2 plasma treatment than through pure H2 or He/H2 thermal treatment. The color change of TiO2 film was measured based on the Commission Internationale d’Eclairage L*a*b* color space system. Hydrogenated TiO2 film displayed improved visible light absorption with increased plasma power. The morphology of the cauliflower-like nanoparticles of the TiO2 film surface remained unchanged after plasma processing. X-ray photoelectron spectroscopy results showed that the contents of Ti3+ species and Ti–OH bonds in the plasma-hydrogenated black TiO2 increased compared with those in the thermally treated TiO2. X-ray diffraction (XRD) patterns and Raman spectra indicated that plasma would destroy the crystal structure of the TiO2 surface layer, while thermal annealing would increase the overall crystallinity. The different trends of XRD and Raman spectra results suggested that plasma modification on the TiO2 surface layer is more drastic than on its inner layer, which was also consistent with transmission electron microscopy results. Optical emission spectra results suggest that numerous active species were generated during RF AP He/H2 plasma processing, while there were no peaks detected from thermal processing. A possible mechanism for the TiO2 hydrogenation process by plasma has been proposed. Numerous active species were generated in the bulk plasma region, accelerated in the sheath region, and bumped toward the TiO2 film, which will react with the TiO2 surface to form OVs and disordered layers. This leads to the tailoring of the band gap of black TiO2 and causes its light absorption to extend into the visible region.

Real-time monitoring of the plasma density distribution in low-pressure plasmas using a flat-cutoff array sensor

In the industrial semiconductor plasma processing, plasma density and its spatial distribution are critical for the understanding of discharge physics and the enhancement of the processing yield via monitoring of the status of plasma processing. Thus, real-time monitoring of plasma density and uniformity in the wafer region during wafer processing have been receiving significant attention. In this study, we developed an electrode-embedded flat-cutoff array sensor for the real-time measurement of electron density uniformity during wafer processing. We measured the spatial distribution of electron density on the wafer surface, compared it with the results measured in the bulk plasma region, and found different plasma distributions between the two where this difference can be attributed to local electron kinetics. We also performed plasma etching of amorphous carbon materials, which showed a clear correlation with the electron density distribution measured by the flat-cutoff array sensor. This indicates that the electron density distribution on the wafer surface is crucial for the process result. Thus, the array sensor developed in this study can be applied not only to measure plasma uniformity but also to predict the wafer process beforehand, making it highly significant for industrial plasma processing methods, such as virtual metrology.

Investigating the effects of electron bounce-cyclotron resonance on plasma dynamics in capacitive discharges operated in the presence of a weak transverse magnetic field

Recently, Patil et al. [Phys. Rev. Res. 4, 013059 (2022)] have reported the existence of an enhanced operating regime when a low-pressure (5 mTorr) capacitively coupled discharge (CCP) is driven by a very high radio frequency (60 MHz) source in the presence of a weak external magnetic field applied parallel to its electrodes. Their particle-in-cell simulations show that a significantly higher bulk plasma density and ion flux can be achieved at the electrode when the electron cyclotron frequency equals half of the applied radio frequency for a given fixed voltage. In the present work, we take a detailed look at this phenomenon and further delineate the effect of this “electron bounce-cyclotron resonance (EBCR)” on the electron and ion dynamics of the system. We find that the ionization collision rate and stochastic heating are maximum under resonance condition. The electron energy distribution function also indicates that the population of tail-end electrons is highest for the case where EBCR is maximum. Formation of electric field transients in the bulk plasma region is also seen at lower values of applied magnetic field. Finally, we demonstrate that the EBCR-induced effect is a low-pressure phenomenon and weakens as the neutral gas pressure increases. The potential utility of this effect to advance the operational performance of CCP devices for industrial purposes is discussed.

Observation of multilayer-structured discharge in plasma ionization breakdown

In this Letter, a multilayer-structured discharge (MSD) is reported in multipactor-coexisting plasma ionization breakdown by fully kinetic particle-in-cell simulations. The observed multilayer structure is originated by the response of ions to an electric field. It is found that the electron diffusion and multipactor discharge near the surface produce two opposite electric fields toward and away from the dielectric surface, respectively. Thus, the ions form a locally high density profile, which is followed by electron density. The lighter electrons diffuse away from the peak more quickly than the ions, resulting in an ambipolar field toward the bulk plasma region, which drives the ion density peak to propagate toward the bulk plasma. Such a process is periodically repeated, and, finally, a MSD is formed.

Two-dimensional fluid simulation of inductively coupled N2/NH3/SiH4 discharge

Low-temperature N2/NH3/SiH4 discharge is used to deposit hydrogenated silicon nitride films (SiN x H y ). In this process, the main factor influencing the improvement of film quality is the active species, such as SiH x and NH x radicals, which are responsible for surface reactions. The change in plasma chemistry under different operating conditions affects the production of active species in the bulk plasma region. In the conventional N2/NH3/SiH4 discharge for SiN x H y thin-film deposition, the information required to explain the correlation between the generation of active species and the process parameters was insufficient. In particular, it was difficult to completely understand the relationship between the generation of SiH x and NH x radicals using the experimental results based on the measured thin-film properties. Therefore, a numerical model was prepared to understand the mechanism of each radical. To improve the efficiency of material processing and enhance process controllability, an inductively coupled plasma N2/NH3/SiH4 model was introduced and investigated. This work provides an overview of the generation of each active species in the N2/NH3/SiH4 discharge. In particular, the effects of the gas pressure and N2/NH3/SiH4 gas mixture ratio are discussed. Moreover, the principle of the N2/NH3/SiH4 plasma process for the production of active species (N, NH x , SiH x , amino-silane complexes) was analyzed; it was found that the generation density of specific particles is affected by the spatial distribution of electrons based on the pressure and gas composition ratio.

A Comprehensive Circuit Modeling Approach for Self-Sustained Capacitively Coupled Microwave Plasmas

A circuit modeling approach for self-sustained capacitively coupled microwave plasmas is introduced and validated in this article. The model solves the particle balance equation using a novel circuit optimization scheme to calculate the plasma parameters like electron density, sheath thickness, and electron temperature for a given input power, operating frequency, gas type, and pressure. While the existing models capture the ohmic loss in the bulk plasma region, the proposed model also takes into account power required to sustain plasma which proves to be considerable for higher electron densities. The model is rigorously validated using experimental results from two cases—one resonant and one non-resonant—both with self-sustained microwave plasma. As the post-processing results, other discharge parameters like sheath and plasma voltages as well as plasma reduced field are calculated. The proposed modeling approach can substantially simplify design and analysis of capacitively coupled microwave plasmas.

Investigations on the effect of process parameters on the growth of vertically oriented graphene sheet in plasma‐enhanced chemical vapour deposition system

AbstractA multistage numerical model comprising the plasma kinetics and surface deposition sub‐models is developed to study the influence of process parameters, namely, total gas pressure and input plasma power on the plasma chemistry and growth characteristics of vertically oriented graphene sheets (VOGS) grown in the plasma‐enhanced chemical vapour deposition system containing the Ar + H2 + C2H2 reactive gas mixture. The spectral and spatial distributions of temperature and number densities, respectively, of plasma species, that is, charged and neutral species in the plasma reactor, are examined using inductively coupled plasma module of COMSOL Multiphysics 5.2 modelling suite. The numerical data from the computational plasma model are fed as the input parameters for the surface deposition model, and from the simulation results, it is found that there is a significant drop in the densities of various plasma species as one goes from the bulk plasma region to the substrate surface. The significant loss of the energetic electrons is observed in the plasma region at high pressure (for constant input power) and low input power (for constant gas pressure). At low pressure, the carbon species generate at higher rates on the catalyst nanoislands surface, thus enhancing the growth and surface density of VOGS. However, it is found that VOGS growth rate increases when input plasma power is raised from 100 to 300 W and decreases with further increase in the plasma power. A good comparison of the model outcomes with the available experimental results confirms the adequacy of the present model.

Investigations into growth of whistlers with energy of energetic electrons

Runaway electrons have great significance in fusion plasmas as they are considered to be responsible for the excitation of instabilities and for damage to the first wall components. The threshold for the generation of the runaway electron population in tokamaks strongly depends on the toroidal magnetic field and bulk electron temperature. The presence of these runaway electrons with a critical density and magnetic field value are correlated with the magnetosonic whistler activity. The Rosenbluth condition applies to the destabilization of upper hybrid modes, that remains mostly stable in large-scale tokamaks like Joint European Tokamakand International Thermonuclear Experimental reactor. On the other hand, whistlers with a frequency in the lower hybrid range are more likely to be destabilized in a lower magnetic field and temperature, along with the whistlers’ excitation threshold. The process of destabilization of whistlers by energetic electrons thus has a finite overlap between fusion and basic plasma devices, and the outcome from the latter can be scalable to fusion machines. We report that in the linear large volume plasma device, the destabilization of quasi-longitudinal whistlers, driven by the reflected particles from the mirror, takes place in the bulk plasma region i.e. away from the mirror in the energetic belt region, and follows the frequency ordering of . Our explanation involves an alternate limit of quasi-linear analysis, commonly employed for recovering the instability threshold of runaways scattering off whistlers in fusion plasmas, and the growth rate due to the reflected particle is proportional to the inverse square root of electron temperature, where the reflected particle fraction is (Sharma and Vlahos 1984 Astrophys. J. 280 405). The measurements required to obtain the energy scaling of runaway electrons with whistler instability are critical for large devices but remain scarce. We have emphasized the analytic correlation between the two regimes in these investigations.

Experimental study of the influence of gas puff locations on H-mode boundary plasmas with argon seeding on EAST

To investigate the optimal scenario of impurity seeding to obtain divertor plasma detachment for target protection, experiments with Ar&D2 seeding from two different poloidal locations, the upper outer (UO) divertor target and lower outer (LO) target, were carried out on EAST. Partial energy detachment (the electron temperature near the strike point T e,spt ⩽ 10 eV) were obtained with Ar&D2 mixture puffing from the UO target and, for the first time, from the LO target into H-mode plasmas in the upper single null (USN) configuration. The peak heat flux q t on the UO target was significantly reduced (by ∼80%). The rollover of ion flux density j s did not appear probably due to insufficient momentum loss, which is independent of the puff locations. The poloidal asymmetries of particle and heat fluxes on the targets have also been investigated. The UO-dominant asymmetry of particle flux was reversed, while the UO-dominant asymmetry of heat flux was mitigated but not reversed. The plasma confinement dropped by only 14% and 8.2% in the LO-puff case and UO-puff case, respectively, during detachment. The high level of C may contributed greatly to the higher radiation in the bulk plasma region and the greater decline in W MHD in the LO-puff case.

Electron dynamics in radio frequency magnetron sputtering argon discharges with a dielectric target

We demonstrate a self-consistent and complete description of electron dynamics in a typical electropositive radio frequency magnetron sputtering (RFMS) argon discharge with a dielectric target. The electron dynamics, including the electron power absorption dynamics in one radio frequency (RF) period, is studied via a fully kinetic 2d3v particle-in-cell/Monte Carlo collision (PIC/MCC) electrostatic simulation. The interplay between the fundamental plasma parameters is analyzed through their spatiotemporal dynamics. Due to the influence of magnetic trap on the electron transport, a spatially dependent charging that perturbs the electric potential is observed on the dielectric target surface, resulting in a spatially dependent ion energy distribution along the target surface. The E × B drift-to-discharge current ratio is in approximate agreement with Bohm diffusion. The electron power absorption can be primarily decoupled into the positive Ohmic power absorption in the bulk plasma region and the negative pressure-induced power absorption near the target surface. Ohmic power absorption is the dominant electron power absorption mechanism, mostly contributed by the azimuthal electron current. The power absorption due to electron inertial effects is negligible on time-average. Both the maximum power absorption and dissipation of electrons appear in the bulk plasma region during the second half of the RF period, implying a strong electron trapping in magnetron discharges. The contribution of secondary electrons is negligible under typical RFMS discharge conditions.

Two-dimensional fluid simulation of pulsed-power inductively coupled Ar/H2 discharge

In low-temperature Ar/H2 discharge used for material processing, the main factor influencing the film quality is the active species responsible for surface reactions, such as hydrogen atoms or hydrogen ions. The changes in plasma chemistry with the operating conditions affect the production of active species in the bulk plasma region. In conventional Ar/H2 discharge using continuous-wave plasma, there is not enough information to explain the correlations between the active species generation and process parameters. In particular, it is difficult to investigate the relationship between the generation of H x (x = 1, 2) ions using the ratio of Ar to hydrogen as an operating variable, and an additional control parameter is required to research the occurrence of each active species. To improve the efficiency of material processing and enhance process controllability, an inductively coupled plasma Ar/H2 pulsed-power model (source pulsing) was introduced and investigated in this study. This work provides an overview of the generation of each active species in pulsed Ar/H2 discharge and discusses the effects of the Ar/H2 gas mixture ratio, duty cycle, and pulse frequency. In addition, it presents an analysis of the principle of the Ar/H2 pulsed-plasma process for the production of active species, demonstrating that the generation densities of specific ions and neutral particles can be controlled.

The influence of electron recombination rate on the plasma characteristics in rf argon capacitive discharge

This work investigates the effect of the electron surface recombination coefficient (Ks) on radio-frequency discharge characteristics. This investigation is performed by a fluid model with the drift–diffusion approximation. The simulation results show that when the electron recombination rate is larger, the plasma density is lower in the plasma bulk region. It is found that the cycle-averaged electron and ion fluxes decrease adjacent to the electrode, while the electric potential increases in the bulk plasma region as Ks increases from 0.60 to 2.38. Moreover, the reduction in the electron density in the bulk region leads to decrease in the electron power dissipation in this region. The results also show that the electron ohmic heating and pressure heating, which play a crucial role in sustaining the discharge, can be both reduced in the sheath regions with increasing the electrons recombination rate. Finally, it is observed that the plasma characteristics can significantly be changed depending on the electrode surface properties.

Effects of electrode gap on radio-frequency discharge characteristics with a hollow electrode

In this paper, the effects of electrode gap on the discharge characteristics in low-pressure argon radio frequency (RF) discharge with a hollow electrode were investigated by a two-dimensional particle-in-cell/MCC model. The results show that the time-averaged electric field, electron density, sheath potential drop, and sheath thickness change with the increasing electrode gap. It is also found that the electron density varies non-monotonically with the electrode gap increasing from 4 to 12 mm due to the different intensities of the hollow cathode effect (HCE) and electron heating at different electrode gaps. The axial sheath at the bottom of the hollow electrode is found to determine the depth of the plasma in the hole and can significantly modulate the intensities of the HCE and electron heating. With the reducing electrode gap, the hole of the hollow electrode is eventually filled with the sheath, and the bulk plasma region is compressed. The results indicate that a small electrode gap is not beneficial to obtain large area plasma with high density outside the hole. Altering the electrode gap can tailor the spatial distribution of the plasma in the RF discharge with a hollow electrode and obtain an optimal electron density.

Particle Simulation Model for Self-Field Magnetoplasmadynamic Thruster

In order to clarify the discharge principle of the self-field magnetoplasmadynamic thruster (MPDT), a two-dimensional axisymmetric particle-in-cell/Monte Carlo collision (PIC/MCC) model is proposed. The spatial distribution and the collision characteristics of discharge plasma were calculated using this model. In addition, the influence of the operation parameters on the plasma was analyzed including the voltage and mass flow rate. The effectiveness of the model was verified by comparison to the experimentally induced magnetic field. It was found that the electrons were mainly accelerated by the electric field in the cathode sheath and the electric field shielding effect of plasma was obvious in the bulk plasma region. Due to the pinch effect, the charged particles were constrained near the cathode. The results of the present work implied that the PIC/MCC model provides an approach to investigate the plasma distribution and a kinetic description of particles for the discharge of the self-field MPDT.

Effects of HF frequency on plasma characteristics in dual-frequency helium discharge at atmospheric pressure by fluid modeling

On the basis of the fluid theory and the drift–diffusion approximation, a numerical model for dual-frequency atmospheric pressure helium discharge is established, in order to investigate the effects of the high frequency source (HF) on the characteristics of dual-frequency atmospheric pressure helium discharge. The numerical results showed that the electron heating rate increases with enhancing HF frequency, as well as the particles densities, electron dissipation rate, current density, net electron generation and bulk plasma region. Moreover, it is also observed that the efficient electron heating region moves when the HF frequency has been changed. The plasma parameters are not linear change with the HF frequency linearly increasing.

Electron heating in rf capacitive discharges at atmospheric-to-subatmospheric pressures

Electron heating is a fundamental and multidisciplinary phenomenon in partially ionized gases, from the planet’s ionosphere to laboratory-scale plasmas. Plasmas produced at ambient or reduced pressures have recently shown potential for scientific and industrial applications. However, electron heating, which is strongly coupled to the physicochemical properties of these plasmas, has been poorly understood. We experimentally found the rapid structural transition from non-local to local electron heating in collisional radio-frequency discharges at atmospheric-to-subatmospheric pressures. As the gas pressure decreased from 760 to 200 Torr, the time-averaged electron density increased from 1.3 × 1012 to 1.3 × 1013 cm−3, and the electron temperature decreased from 2.5 to 1.1 eV at the maximum allowable discharge current in the abnormal α-mode in the plasma bulk. The spatiotemporal evolution of the electron temperature clearly shows that the electron temperature increases uniformly throughout the bulk plasma region during sheath expansion and collapse at 760 Torr, but the electron heating weakens with sheath collapse as the gas pressure decreases.

Study on Effect of Neutral Gas Pressure on Plasma Characteristics in Capacitive RF Argon Glow Discharges at Low Pressure by Fluid Modeling

For capacitively coupled radio frequency argon glow discharges at low pressure, based on the drift-diffusive approximation, a 1-D fluid model of the plasmas is established. The electrons and ions continuity equations and Poisson equation are simultaneously solved until a periodic steady state is achieved. Our results show that the electrons are accelerated by strong electric fields in the sheaths, resulting in more ohmic heating. These strong fields may be caused by low electron convection in bulk plasma region even when gas pressure increases due to the sheath thickness and the electrons’ temperatures all decrease. Thus, a local peak of the dissipation near the boundary between the sheath regions and the bulk plasma region is observed due to a higher local electron temperature in the sheath regions. Subsequently, the peak of the net power absorption grows in the bulk plasma region, since the electron thermal convection and dissipation contribute significantly and the electron density reaches the maximum. Finally, the ionization and excitation rates are clearly enhanced in the sheath regions compared to the bulk plasma region due to electron heating that has small changes in the bulk plasma region.