Abstract: One of the main issues in plasma chemistry modeling is that the cross sections and rate coefficients are subject to uncertainties, which yields uncertainties in the modeling results and hence hinders the predictive capabilities. In this paper, we reveal the impact of these uncertainties on the model predictions of plasma-based dry reforming in a dielectric barrier discharge. For this purpose, we performed a detailed uncertainty analysis and sensitivity study. 2000 different combinations of rate coefficients, based on the uncertainty from a log-normal distribution, are used to predict the uncertainties in the model output. The uncertainties in the electron density and electron temperature are around 11% and 8% at the maximum of the power deposition for a 70% confidence level. Still, this can have a major effect on the electron impact rates and hence on the calculated conversions of CO2 and CH4, as well as on the selectivities of CO and H2. For the CO2 and CH4 conversion, we obtain uncertainties of 24% and 33%, respectively. For the CO and H2 selectivity, the corresponding uncertainties are 28% and 14%, respectively. We also identify which reactions contribute most to the uncertainty in the model predictions. In order to improve the accuracy and reliability of plasma chemistry models, we recommend using only verified rate coefficients, and we point out the need for dedicated verification experiments.

Abstract: Cold atmospheric plasmas (CAPs) have attracted significant interest for their potential benefits in medical applications, including cancer therapy. The therapeutic effects of CAPs are related to reactive oxygen and nitrogen species (ROS and RNS) present in the plasma. The impact of ROS has been extensively studied, but the role of RNS in CAP-treatment remains poorly understood at the molecular level. Here, we investigate the permeation of RNS and ROS across native and oxidized phospholipid bilayers (PLBs) by means of computer simulations. The results reveal significantly lower free energy barriers for RNS (i.e. NO, NO2, N2O4) and O3 compared to hydrophilic ROS, such as OH, HO2 and H2O2. This suggests that the investigated RNS and O3 can permeate more easily through both native and oxidized PLBs in comparison to hydrophilic ROS, indicating their potentially important role in plasma medicine.

Abstract: Compared with dust-free plasmas, the existence of dust particles in plasmas may greatly influence the plasma properties. such as the plasma density, electron temperature, sheath properties, electron energy distribution function (EEDF) as well as the heating mechanism. In this work, a 1D hybrid fluid/MC model has been developed to investigate the interaction between dust and plasma in a low-pressure silane discharge sustained in a radio frequency capacitively coupled plasma, in which we assume spherical dust particles with a given radius are generated by taking the sum of the production rate of Si2H4- and Si2H5- as the nucleation rate. From our simulation, the plasma may experience definite perturbation by dust particles with a certain radius (more than 50nm) with an increase in electron temperature first, which further induces a rapid rise in the positive and negative ion densities. Then, the densities begin to decline due to the gradual lack of sufficient seed electrons. In addition, as the dust radius increases, the high energy tails of the EEDFs will be enhanced for discharge maintenance, accompanied by a decline in the population of low-energy electrons in comparison with those of pristine plasma. Furthermore, an obvious bulk heating is observed apart from the a-mode and local field reversal heating. This may contribute to the enhanced bulk electric field (also called the drift field) as a result of electron depletion via the dust. In addition, large-sized dust particles that accumulate near the sheaths tend to form two stable density peaks with their positions largely influenced by the time-averaged sheath thickness. A detailed study of the effects of the external parameters, including pressure, voltage and frequency, on the spatial distribution of dust particles is also conducted.

Abstract: Dielectric barrier discharges (DBDs) typically operate in the filamentary regime and thus exhibit great spatial and temporal non-uniformity. In order to optimize DBDs for various applications, such as in plasma catalysis, more fundamental insight is needed. Here, we consider how the millions of microdischarges, characteristic for a DBD, influence individual gas molecules. We use a Monte Carlo approach to determine the number of microdischarges to which a single molecule would be exposed, by means of particle tracing simulations through a full-scale packed bed DBD reactor, as well as an empty DBD reactor. We find that the fraction of microdischarges to which the molecules are exposed can be approximated as the microdischarge volume over the entire reactor gas volume. The use of this concept provides good agreement between a plasma-catalytic kinetics model and experiments for plasma-catalytic NH3 synthesis. We also show that the concept of the fraction of microdischarges indicates the efficiency by which the plasma power is transferred to the gas molecules. This generalised concept is also applicable for other spatially and temporally non-uniform plasmas.

Abstract: Packed bed dielectric barrier discharge (PB-DBD) plasma reactors are very promising for various plasma catalysis applications, but the exact mechanisms of plasma-catalyst interaction are far from understood, because the plasma discharge and catalyst/packing properties are mutually dependent. To better understand the effect of packing dielectric material on the electrical plasma properties, we study here a single bead DBD plasma reactor operating in dry air, with beads of different dielectric constant and for different applied voltages, by means of fluid modelling validated by optical imaging experiments. Our study reveals that the plasma in the single bead DBD reactor can manifest itself in two different modalities, i.e. (a) polar discharges at the bead poles in contact with the electrodes, and (b) a streamer discharge caused by surface ionization waves, which bridges the gas gap. Beads with high dielectric constant result in localised electric field enhancement and hence yield a reduction of the applied voltage required for plasma production. At low applied voltage, the discharge appears as polar discharges between the bead and the electrodes, and upon higher voltage it undergoes a transition into a bridging streamer discharge. The transition voltage to the streamer mode rises for beads with higher dielectric constant. These observations are important for plasma catalysis applications. A higher dielectric constant yields a higher electric field and thus higher average electron energy and density, giving rise to more reactive species, but it also yields a confined discharge near the contact points of packing beads, limiting the interaction area between the catalyst and the active plasma species. In addition, our model reveals that the dielectric bead behaves as a capacitor and traps charges, which can explain the significant occurrence of partial discharging in PB-DBDs and non-parallelogram shaped Lissajous plots. Hence, equivalent circuit modelling of PB-DBDs should take into account the role of packing beads in charge trapping as a capacitor.

Abstract: A 2d3v particle-in-cell/Monte Carlo collisions model was applied to study the influence of the magnetic field strength on the cathode sheath region of a direct current (dc) magnetron discharge. When applying a magnetic field of 520-730 G, the cathode sheath width decreases with magnetic field strength, whereas, if a stronger magnetic field is applied (i. e. from 730 to 2600 G), the sheath width increases. This is explained by studying the structure of the sheath in different magnetic field strengths in terms of the electron and ion densities. The consequences of sheath structure on the sputter deposition process are also investigated. It is found that the magnetic field strength can control the erosion profile and the sputter rate.

Abstract: In this paper, some modelling approaches to describe direct current (dc) magnetron discharges developed in our research groups will be presented, including an analytical model, Monte Carlo simulations for the electrons and for the sputtered atoms, a hybrid Monte Carlo-fluid model and particle-in-cell-Monte Carlo collision simulations. The strengths and limitations of the various modelling approaches will be explained, and some characteristic simulation results will be illustrated. Furthermore, some other simulation methods related to the magnetron device will be briefly explained, more specifically for calculating the magnetic field distribution inside the discharge, and for describing the (reactive) sputtering.

Abstract: In this paper, a simulation method is described to predict the etching behaviour of Cl2/O2/Ar inductively coupled plasmas on a Si substrate, as used in shallow trench isolation for the production of electronic devices. The hybrid plasma equipment model (HPEM) developed by Kushner et al is applied to calculate the plasma characteristics in the reactor chamber and two additional Monte Carlo simulations are performed to predict the fluxes, angles and energy of the plasma species bombarding the Si substrate, as well as the resulting surface processes such as etching and deposition. The simulations are performed for a wide variety of operating conditions such as gas composition, chamber pressure, power deposition and substrate bias. It is predicted by the simulations that when the fraction of oxygen in the gas mixture is too high, the oxidation of the Si substrate is superior to the etching of Si by chlorine species, resulting in an etch rate close to zero as is also observed in the experiments.

Abstract: Plasma modelling is an exciting subject in which virtually all physical disciplines are represented. Plasma models combine the electromagnetic, statistical and fluid dynamical theories that have their roots in the 19th century with the modern insights concerning the structure of matter that were developed throughout the 20th century. The present cluster issue consists of 20 invited contributions, which are representative of the state of the art in plasma modelling and numerical simulation. These contributions provide an in-depth discussion of the major theories and modelling and simulation strategies, and their applications to contemporary plasma-based technologies. In this editorial review, we introduce and complement those papers by providing a bird's eye perspective on plasma modelling and discussing the historical context in which it has surfaced.

Abstract: A hybrid model, called the hybrid plasma equipment model (HPEM), was used to study an inductively coupled plasma in gas mixtures of H2 or NH3 with CH4 or C2H2 used for the synthesis of carbon nanotubes or carbon nanofibres (CNTs/CNFs). The plasma properties are discussed for different gas mixtures at low and moderate pressures, and the growth precursors for CNTs/CNFs are analysed. It is found that C2H2, C2H4 and C2H6 are the predominant molecules in CH4 containing plasmas besides the feedstock gas, and serve as carbon sources for CNT/CNF formation. On the other hand, long-chain hydrocarbons are observed in C2H2-containing plasmas. Furthermore, the background gases CH4 and C2H2 show a different decomposition rate with H2 or NH3 addition at moderate pressures.

Abstract: 'Bohm diffusion' causes the electrons to diffuse perpendicularly to the magnetic field lines. However, its origin is not yet completely understood: low and high frequency electric field fluctuations are both named to cause Bohm diffusion. The importance of including this process in a Monte Carlo (MC) model is demonstrated by comparing calculated ionization rates with particle-in-cell/Monte Carlo collisions (PIC/MCC) simulations. A good agreement is found with a Bohm diffusion parameter of 0.05, which corresponds well to experiments. Since the PIC/MCC method accounts for fast electric field fluctuations, we conclude that Bohm diffusion is caused by fast electric field phenomena.

Abstract: A hybrid model, called the hybrid plasma equipment model, was used to study inductively coupled SF6 plasmas used for Si etching applications. The plasma properties such as number densities of electrons, positive and negative ions, and neutrals are calculated under typical etching conditions. The electron kinetics is analysed by means of the electron energy probability function. The plasma chemistry taking place in pure SF6 and in an Ar/SF6 mixture is also discussed, and finally the effect of the argon fraction on the plasma properties is investigated.

Abstract: 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 13.56200 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 (phgr = 0), and the best radial uniformity is obtained at phgr = π. 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 π. 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 phgr = 0.3π. 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 (phgr = π), 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 phgr = 0.4π. 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 π, 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.