Abstract: This work explains the need for plasma models, introduces arguments for choosing the type of model that better fits the purpose of each study, and presents the basics of the most common nonequilibrium low-temperature plasma models and the information available from each one, along with an extensive list of references for complementary in-depth reading. The paper presents the following models, organised according to the level of multi-dimensional description of the plasma: kinetic models, based on either a statistical particle-in-cell/Monte-Carlo approach or the solution to the Boltzmann equation (in the latter case, special focus is given to the description of the electron kinetics); multi-fluid models, based on the solution to the hydrodynamic equations; global (spatially-average) models, based on the solution to the particle and energy rate-balance equations for the main plasma species, usually including a very complete reaction chemistry; mesoscopic models for plasma–surface interaction, adopting either a deterministic approach or a stochastic dynamical Monte-Carlo approach. For each plasma model, the paper puts forward the physics context, introduces the fundamental equations, presents advantages and limitations, also from a numerical perspective, and illustrates its application with some examples. Whenever pertinent, the interconnection between models is also discussed, in view of multi-scale hybrid approaches.

Abstract: In this paper, the splitting of CO2 in a pulsed plasma system, such as a dielectric barrier discharge (DBD), is evaluated from a chemical point of view by means of numerical modeling. For this purpose, a chemical reaction set of CO2 in an atmospheric pressure plasma is developed, including the vibrational states of CO2, O2, and CO. The simulated pulses are matched to the conditions of a filament (or microdischarge) and repeated with intervals of 1 μs. The influence of vibrationally excited CO2 as well as other neutral species, ions, and electrons on the CO2 splitting is discussed. Our calculations predict that the electrons have the largest contribution to the CO2 splitting at the conditions under study, by electron impact dissociation. The contribution of vibrationally excited CO2 levels in the splitting of CO2 is found be 6.4%, when only considering one microdischarge pulse and its afterglow, but it can be much higher for consecutive discharge pulses, as is typical for a filamentary DBD, when the interpulse time is short enough and accumulation effects in the vibrationally excited CO2 densities can occur.

Abstract: The conversion of methane to value-added chemicals and fuels is considered to be one of the challenges of the 21st century. In this paper we study, by means of fluid modeling, the conversion of methane to higher hydrocarbons or oxygenates by partial oxidation with CO2 or O2 in a dielectric barrier discharge. Sixty-nine different plasma species (electrons, ions, molecules, radicals) are included in the model, as well as a comprehensive set of chemical reactions. The calculation results presented in this paper include the conversion of the reactants and the yields of the reaction products as a function of residence time in the reactor, for different gas mixing ratios. Syngas (i.e. H2 + CO) and higher hydrocarbons (C2Hx) are typically found to be important reaction products.

Abstract: The chemical complexity of non-equilibrium plasmas poses a challenge for plasma modeling because of the computational load. This paper presents a dimension reduction method for such chemically complex plasmas based on principal component analysis (PCA). PCA is used to identify a low-dimensional manifold in chemical state space that is described by a small number of parameters: the principal components. Reduction is obtained since continuity equations only need to be solved for these principal components and not for all the species. Application of the presented method to a CO2 plasma model including state-to-state vibrational kinetics of CO2 and CO demonstrates the potential of the PCA method for dimension reduction. A manifold described by only two principal components is able to predict the CO2 to CO conversion at varying ionization degrees very accurately.

Abstract: In this paper, we investigate the etch process of so-called low-k organic material by means of a N2/H2 capacitively coupled plasma, as applied in the micro-electronics industry for the manufacturing of computer chips. In recent years, such an organic material has emerged as a possible alternative for replacing bulk SiO2 as a dielectric material in the back-end-of-line, because of the smaller parasitic capacity between adjacent conducting lines, and thus a faster propagation of the electrical signals throughout the chip. Numerical simulations with a hybrid plasma model, using an extensive plasma and surface chemistry set, as well as experiments are performed, focusing on the plasma properties as well as the actual etching process, to obtain a better insight into the underlying mechanisms. Furthermore, the effects of gas pressure, applied power and gas composition are investigated to try to optimize the etch process. In general, the plasma density reaches a maximum near the wafer edge due to the so-called 'edge effect'. As a result, the etch rate is not uniform but will also reach its maximum near the wafer edge. The pressure seems not to have a big effect. A higher power increases the etch rate, but the uniformity becomes (slightly) worse. The gas mixing ratio has no significant effect on the etch process, except when a pure H2 or N2 plasma is used, illustrating the synergistic effects of a N2/H2 plasma. In fact, our calculations reveal that the N2/H2 plasma entails an ion-enhanced etch process. The simulation results are in reasonable agreement with the experimental values. The microscopic etch profile shows the desired anisotropic shape under all conditions under study.

Abstract: A gliding arc (GA) plasma has great potential for CO2 conversion into value-added chemicals, because of its high energy efficiency. To improve the application, a 2D/3D fluid model is needed to investigate the CO2 conversion mechanisms in the actual discharge geometry. Therefore, the complex CO2 chemical kinetics description must be reduced due to the huge computational cost associated with 2D/3D models. This paper presents a chemistry reduction method for CO2 plasmas, based on the so-called directed relation graph method. Depending on the defined threshold values, some marginal species are identified. By means of a sensitivity analysis, we can further reduce the chemistry set by removing one by one the marginal species. Based on the socalled flux-sensitivity coupling, we obtain a reduced CO2 kinetics model, consisting of 36 or 15 species (depending on whether the 21 asymmetric mode vibrational states of CO2 are explicitly included or lumped into one group), which is applied to a GA discharge. The results are compared with those predicted with the full chemistry set, and very good agreement is reached. Moreover, the range of validity of the reduced CO2 chemistry set is checked, telling us that this reduced set is suitable for low power GA discharges. Finally, the time and spatial evolution of the CO2 plasma characteristics are presented, based on a 2D model with the reduced kinetics.

Abstract: In this work particle-in-cell/Monte Carlo collision simulations are performed to study the heating mechanism and plasma characteristics in direct current (dc) superposed radio-frequency (RF) capacitively coupled plasmas, operated both in single-frequency (SF) and dual-frequency (DF) regimes. An RF (60/2 MHz) source is applied on the bottom electrode to sustain the discharge, and a dc source is fixed on the top electrode. The heating mechanism appears to be very different in dc superposed SF and DF discharges. When only a single source of 60 MHz is applied, the plasma bulk region is reduced by the dc source, thus the ionization rate and hence the electron density decrease with rising dc voltage. However, when a DF source of 60 and 2 MHz is applied, the electron density can increase upon addition of a dc voltage, depending on the gap length and applied dc voltage. This is explained from the spatiotemporal ionization rates in the DF discharge. In fact, a completely different behavior is observed for the ionization rate in the two half-periods of the LF source. In the first LF half-period, the situation resembles the dc superposed SF discharge, and the reduced plasma bulk region due to the negative dc bias results in a very small effective discharge area and a low ionization rate. On the other hand, in the second half-period, the negative dc bias is to some extent counteracted by the LF voltage, and the sheath close to the dc electrode becomes particularly thin. Consequently, the amplitude of the high-frequency sheath oscillations at the top electrode is largely enhanced, while the LF sheath at the bottom electrode is in its expanding phase and can thus well confine the high-energy electrons. Therefore, the ionization rate increases considerably in this second LF half-period. Furthermore, in addition to the comparison between SF and DF discharges and the effect of gap length and dc voltage, the effect of secondary electrons is examined.

Abstract: The application of atmospheric pressure plasmas in medicine is increasingly gaining attention in recent years, although very little is currently known about the plasma-induced processes occurring on the surface of living organisms. It is known that most bio-organisms, including bacteria, are coated by a liquid film surrounding them, and there might be many interactions between plasma species and the liquid layer before the plasma species reach the surface of the bio-organisms. Therefore, it is essential to study the behaviour of the reactive species in a liquid film, in order to determine whether these species can travel through this layer and reach the biomolecules, or whether new species are formed along the way. In this work, we investigate the interaction of reactive oxygen species (i.e. O, OH, HO2 and H2O2) with water, which is assumed as a simple model system for the liquid layer surrounding biomolecules. Our computational investigations show that OH, HO2 and H2O2 can travel deep into the liquid layer and are hence in principle able to reach the bio-organism. Furthermore, O, OH and HO2 radicals react with water molecules through hydrogen-abstraction reactions, whereas no H-abstraction reaction takes place in the case of H2O2. This study is important to gain insight into the fundamental operating mechanisms in plasma medicine, in general, and the interaction mechanisms of plasma species with a liquid film, in particular.

Abstract: We developed a microkinetic model to reveal the effects of plasma-generated radicals, intermediates, and vibrationally excited species on the catalytic hydrogenation of CO2 to CH3OH on a Cu(111) surface. As a benchmark, we first present the mechanisms of thermal catalytic CH3OH formation. Our model predicts that the reverse water-gas shift reaction followed by CO hydrogenation, together with the formate path, mainly contribute to CH3OH formation in thermal catalysis. Adding plasma-generated radicals and intermediates results in a higher CH3OH turnover frequency (TOF) by six to seven orders of magnitude, showing the potential of plasma-catalytic CO2 hydrogenation into CH3OH, in accordance with the literature. In addition, CO2 vibrational excitation further increases the CH3OH TOF, but the effect is limited due to relatively low vibrational temperatures under typical plasma catalysis conditions. The predicted increase in CH3OH formation by plasma catalysis is mainly attributed to the increased importance of the formate path. In addition, the conversion of plasma-generated CO to HCO* and subsequent HCOO* or H2CO* formation contribute to CH3OH formation. Both pathways bypass the HCOO* formation from CO2, which is the main bottleneck in the process. Hence, our model points toward the important role of CO, but also O, OH, and H radicals, as they influence the reactions that consume CO2 and CO. In addition, our model reveals that the H pressure should not be smaller than ca. half of the O pressure in the plasma as this would cause O* poisoning, which would result in very small product TOFs. Thus, plasma conditions should be targeted with a high CO and H content as this is favorable for CH3OH formation, while the O content should be minimized.

Abstract: Plasma catalysis is gaining increasing interest for various environmental applications, but the crucial question is whether plasma can be created inside catalyst pores and under which conditions. In practice, various catalytic support materials are used, with various dielectric constants. We investigate here the influence of the dielectric constant on the plasma properties inside catalyst pores and in the sheath in front of the pores, for various pore sizes. The calculations are performed by a two-dimensional fluid model for an atmospheric pressure dielectric barrier discharge in helium. The electron impact ionization rate, electron temperature, electron and ion density, as well as the potential distribution and surface charge density, are analyzed for a better understanding of the discharge behavior inside catalyst pores. The results indicate that, in a 100 μm pore, the electron impact ionization in the pore, which is characteristic for the plasma generation inside the pore, is greatly enhanced for dielectric constants below 300. Smaller pore sizes only yield enhanced ionization for smaller dielectric constants, i.e., up to εr = 200, 150, and 50 for pore sizes of 50, 30, and 10 μm. Thus, the most common catalyst supports, i.e., Al2O3 and SiO2, which have dielectric constants around εr = 8−11 and 4.2, respectively, should allow more easily that microdischarges can be formed inside catalyst pores, even for smaller pore sizes. On the other hand, ferroelectric materials with dielectric constants above 300 never seem to yield plasma enhancement inside catalyst pores, not even for 100 μm pore sizes. Furthermore, it is clear that the dielectric constant of the material has a large effect on the extent of plasma enhancement inside the catalyst pores, especially in the range between εr = 4 and εr = 200. The obtained results are explained in detail based on the surface charge density at the pore walls,
and the potential distribution and electron temperature inside and above the pores. The results obtained with this model are
important for plasma catalysis, as the production plasma species in catalyst pores might affect the catalyst properties, and thus
improve the applications of plasma catalysis.

Abstract: The mechanism of interaction of cold nonequilibrium plasma jets with mammalian cells in physiologic liquid is reported. The major biological active species produced by an argon RF plasma jet responsible for cell viability reduction are analyzed by experimental results obtained through physical, biological, and chemical diagnostics. This is complemented with chemical kinetics modeling of the plasma source to assess the dominant reactive gas phase species. Different plasma chemistries are obtained by changing the feed gas composition of the cold argon based RF plasma jet from argon, humidified argon (0.27%), to argon/oxygen (1%) and argon/air (1%) at constant power. A minimal consensus physiologic liquid was used, providing isotonic and isohydric conditions and nutrients but is devoid of scavengers or serum constituents. While argon and humidified argon plasma led to the creation of hydrogen peroxide dominated action on the mammalian cells, argonoxygen and argonair plasma created a very different biological action and was characterized by trace amounts of hydrogen peroxide only. In particular, for the argonoxygen (1%), the authors observed a strong negative effect on mammalian cell proliferation and metabolism. This effect was distance dependent and showed a half life time of 30 min in a scavenger free physiologic buffer. Neither catalase and mannitol nor superoxide dismutase could rescue the cell proliferation rate. The strong distance dependency of the effect as well as the low water solubility rules out a major role for ozone and singlet oxygen but suggests a dominant role of atomic oxygen. Experimental results suggest that O reacts with chloride, yielding Cl2 − or ClO−. These chlorine species have a limited lifetime under physiologic conditions and therefore show a strong time dependent biological activity. The outcomes are compared with an argon MHz plasma jet (kinpen) to assess the differences between these (at least seemingly) similar plasma sources.

Abstract: Cyrogenic etching of silicon is envisaged to enable better control over plasma processing in the microelectronics industry, albeit little is known about the fundamental differences compared to the room temperature process. We here present molecular dynamics simulations carried out to obtain sticking probabilities, thermal desorption rates, surface diffusion speeds, and sputter yields of F, F2, Si, SiF, SiF2, SiF3, SiF4, and the corresponding ions on Si(100) and on SiF13 surfaces, both at cryogenic and near room temperature. The different surface behavior during conventional etching and cryoetching is discussed. F2 is found to be relatively reactive compared to other species like SiF03. Thermal desorption occurs at a significantly lower rate under cryogenic conditions, which results in an accumulation of physisorbed species. Moreover, ion incorporation is often observed for ions with energies of 30400 eV, which results in a relatively low net sputter yield. The obtained results suggest that the actual etching of Si, under both cryogenic and near room temperature conditions, is based on the complete conversion of the Si surface to physisorbed SiF4, followed by subsequent sputtering of these molecules, instead of direct sputtering of the SiF03 surface.