Abstract: This chapter discusses modeling efforts for plasma-based CO2 conversion, which are needed to obtain better insight in the underlying mechanisms, in order to improve this application. We will discuss two types of (complementary) modeling efforts that are most relevant, that is, (i) modeling of the detailed plasma chemistry by zero-dimensional (0D) chemical kinetic models and (ii) modeling of reactor design, by 2D or 3D fluid dynamics models. By showing some characteristic calculation results of both models, for CO2 splitting and in combination with a H-source, and for packed bed DBD and gliding arc plasma, we can illustrate the type of information they can provide.

Abstract: The electrical asymmetry effect is realized by applying multiple frequency power sources
(13.56 MHz and 27.12 MHz) to a capacitively biased substrate electrode in a specific inductively
coupled plasma reactor. On the one hand, by adjusting the phase angle θ between the multiple
frequency power sources, an almost linear self-bias develops on the substrate electrode, and
consequently the ion energy can be well modulated, while the ion flux stays constant within a
large range of θ. On the other hand, the plasma density and ion flux can be significantly
modulated by tuning the inductive power supply, while only inducing a small change in the self-
bias. Independent control of self-bias/ion energy and ion flux can thus be realized in this specific
inductively coupled plasma reactor.

Abstract: A pulsed microwave surfaguide discharge operating at 2.45 GHz was used for the conversion of molecular nitrogen into valuable compounds in several gas mixtures: N2 :O2 , N2 :O2 :CO2 and N2 :CO2 . The ro-vibrational absorption bands of the molecular species were monitored by a Fourier transform infrared apparatus in the post-discharge region in order to evaluate the relative number density of species, specifically NO production. The effects of specific energy input, pulse frequency, gas flow fraction, gas admixture and gas flow rate were studied for better understanding and optimization of the NO production yield and the corresponding energy cost (EC). By both the experiment and modelling, a highest NO yield is obtained at N2 :O2 (1:1) gas ratio in N2 :O2 mixture. The NO yield reveals a small growth followed by saturation when pulse repetition frequency increases. The energy efficiency start decreasing after the energy input reaches about 5 eV/molec, whereas the NO yield rises steadily at the same time. The lowest EC of about 8 MJ mol−1 corresponding to the yield and the energy efficiency of about 7% and 1% are found, respectively, in an optimum discharge condition in our case.

Abstract: Since the onset of pattern transfer technologies for chip manufacturing, various strategies have been developed to circumvent or overcome aspect ratio dependent etching (ARDE). These methods have, however, their own limitations in terms of etch non-idealities, throughput or costs. Moreover, they have mainly been optimized for individual in-device features and die-scale patterns, while occasionally ending up with poor patterning of metrology marks, affecting the alignment and overlay in lithography. Obtaining a better understanding of the underlying mechanisms of ARDE and how to mitigate them therefore remains a relevant challenge to date, for both marks and advanced nodes. In this work, we accordingly assessed the neutral transport mechanisms in ARDE by means of experiments and multiscale modeling for SiO₂etching with CHF₃/Ar and CF₄/Ar plasmas. The experiments revealed a local maximum in the etch rate for an aspect ratio around unity, i.e. the simultaneous occurrence of regular and inverse reactive ion etching lag for a given etch condition. We were able to reproduce this ARDE trend in the simulations without taking into account charging effects and the polymer layer thickness, suggesting shadowing and diffuse reflection of neutrals as the primary underlying mechanisms. Subsequently, we explored four methods with the simulations to regulate ARDE, by varying the incident plasma species fluxes, the amount of polymer deposition, the ion energy and angular distribution and the initial hardmask sidewall angle, for which the latter was found to be promising in particular. Although our study focusses on feature dimensions characteristic to metrology marks and back-end-of-the-line integration, the obtained insights have a broader relevance, e.g. to the patterning of advanced nodes. Additionally, this work supports the insight that physisorption may be more important in plasma etching at room temperature than originally thought, in line with other recent studies, a topic on which we recommend further research.

Abstract: Secondary electron emission is an important process that plays a significant role in several plasma‐related applications. As measuring the secondary electron yield experimentally is very challenging, quantitative modelling of this process to obtain reliable yield data is critical as input for higher‐scale simulations. Here, we build upon our previous work combining density functional theory calculations with a model originally developed by Hagstrum to extend its application to metallic surfaces. As plasmonic effects play a much more important role in the secondary electron emission mechanism for metals, we introduce an approach based on Poisson point processes to include both surface and bulk plasmon excitations to the process. The resulting model is able to reproduce the yield spectra of several available experimental results quite well but requires the introduction of global fitting parameters, which describe the strength of the plasmon interactions. Finally, we use an in‐house developed workflow to calculate the electron yield for a list of elemental surfaces spanning the periodic table to produce an extensive data set for the community and compare our results with more simplified approaches from the literature.

Abstract: technologies have been expanding, and one of the most exciting and rapidly growing
applications is in biology and medicine. Most biomedical studies with DBD plasma systems are performed in vitro, which include cells grown on the surface of plastic well plates, or in vivo, which include animal research models (e.g. mice, pigs). Since many DBD systems use the biological target as the secondary electrode for direct plasma generation and treatment, they are sensitive to the surface properties of the target, and thus can be altered based on the in vitro or in vivo system used. This could consequently affect biological response from plasma treatment. Therefore, in this study, we investigated the DBD plasma behavior both in vitro (i.e. 96-well flat bottom plates, 96-well U-bottom plates, and 24-well flat bottom plates), and in vivo (i.e. mouse skin). Intensified charge coupled device (ICCD) imaging was performed and the plasma discharges were visually distinguishable between the different systems. The geometry of the wells did not affect DBD plasma generation for low application distances (≤ 2 mm), but differentially affected plasma uniformity on the bottom of the well at greater distances. Since DBD plasma treatment in vitro is rarely performed in dry wells for plasma medicine experiments, the effect of well wetness was also investigated. In all in vitro cases, the uniformity of the DBD plasma was affected when comparing wet versus dry wells, with the plasma in the wide-bottom wells appearing the most similar to plasma generated on mouse skin. Interestingly, based on quantification of ICCD images, the DBD plasma intensity per surface area demonstrated an exponential one-phase decay with increasing application distance, regardless of the in vitro or in vivo system. This trend is similar to that of the energy per pulse of plasma, which is used to determine the total plasma treatment energy for biological systems. Optical emission spectroscopy performed on the plasma revealed similar trends in radical species generation between the plastic well plates and mouse skin. Therefore, taken together, DBD plasma intensity per surface area may be a valuable parameter to be used as a simple method for in situ monitoring during biological treatment and active plasma treatment control, which can be applied for in vitro and in vivo systems.

Abstract: In this study we report on a 2D fluid model of a gliding arc discharge in argon. Despite the 3D nature of the discharge, 2D models are found to be capable of providing very useful information about the operation of the discharge. We employ two modelsan axisymmetric and a Cartesian one. We show that for the considered experiment and the conditions of a low current arc (around 30 mA) in argon, there is no significant heating of the cathode surface and the discharge is sustained by field electron emission from the cathode accompanied by the formation of a cathode spot. The obtained discharge power and voltage are relatively sensitive to the surface properties and particularly to the surface roughness, causing effectively an amplification of the normal electric field. The arc body and anode region are not influenced by this and depend mainly on the current value. The gliding of the arc is modelled by means of a 2D Cartesian model. The arcelectrode contact points are analysed and the gliding mechanism along the electrode surface is discussed. Following experimental observations, the cathode spot is simulated as jumping from one point to another. A complete arc cycle is modelled from initial ignition to arc decay. The results show that there is no interaction between the successive gliding arcs.

Abstract: 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 when the voltage is low, the difference between these two models becomes more obvious than at higher voltages. As the pressure increases, the plasma density profiles obtained from the electromagnetic model smoothly shift from edge-peaked over uniform to a broad maximum in the center. In addition, the edge effect becomes less pronounced with increasing frequency and pressure, and the skin effect rather than the standing-wave effect becomes dominant when the voltage is high.

Abstract: The aim of this work consists of the evaluation of atmospheric pressure dielectric barrier discharges for the conversion of greenhouse gases into useful compounds. Therefore, pure CO2 feed flows are administered to the discharge zone at varying discharge frequency, power input, gas temperature and feed flow rates, aiming at the formation of CO and O2. The discharge obtained in CO2 is characterized as a filamentary mode with a microdischarge zone in each half cycle of the applied voltage. It is shown that the most important parameter affecting the CO2-conversion levels is the gas flow rate. At low flow rates, both the conversion and the CO-yield are significantly higher. In addition, also an increase in the gas temperature and the power input give rise to higher conversion levels, although the effect on the CO-yield is limited. The optimum discharge frequency depends on the power input level and it cannot be unambiguously stated that higher frequencies give rise to increased conversion levels. A maximum CO2 conversion of 30% is achieved at a flow rate of 0.05 L min−1, a power density of 14.75 W cm−3 and a frequency of 60 kHz. The most energy efficient conversions are achieved at a flow rate of 0.2 L min−1, a power density of 11 W cm−3 and a discharge frequency of 30 kHz.

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: Using Brownian dynamics simulations, we investigate the dynamics of colloids confined in two-dimensional narrow channels driven by a nonuniform force Fdr(y). We considered linear-gradient, parabolic, and deltalike driving-force profiles. This driving force induces melting of the colloidal solid (i.e., shear-induced melting), and the colloidal motion experiences a transition from elastic to plastic regime with increasing Fdr. For intermediate Fdr (i.e., in the transition region) the response of the system, i.e., the distribution of the velocities of the colloidal chains õi(y), in general does not coincide with the profile of the driving force Fdr(y), and depends on the magnitude of Fdr, the width of the channel, and the density of colloids. For example, we show that the onset of plasticity is first observed near the boundaries while the motion in the central region is elastic. This is explained by: (i) (in)commensurability between the chains due to the larger density of colloids near the boundaries, and (ii) the gradient in Fdr. Our study provides a deeper understanding of the dynamics of colloids in channels and could be accessed in experiments on colloids (or in dusty plasma) with, e.g., asymmetric channels or in the presence of a gradient potential field.