Abstract: In this computational study, a gliding arc plasma reactor with a reverse-vortex flow stabilization is modelled for the first time by a fluid plasma description. The plasma reactor operates with argon gas at atmospheric pressure. The gas flow is simulated using the k-ε Reynolds-averaged Navier–Stokes turbulent model. A quasi-neutral fluid plasma model is used for computing the plasma properties. The plasma arc movement in the reactor is observed, and the results for the gas flow, electrical characteristics, plasma density, electron temperature, and gas temperature are analyzed.

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: 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 use of microfluidic devices in the field of plasma-liquid interaction can unlock unique possibilities to investigate the effects of plasma-generated reactive species for environmental and biomedical applications. So far, very little simulation work has been performed on microfluidic devices in contact with a plasma source. We report on the modelling and computational simulation of physical and chemical processes taking place in a novel plasma-microfluidic platform. The main production and transport pathways of reactive species both in plasma and liquid are modelled by a novel modelling approach that combines 0D chemical kinetics and 2D transport mechanisms. This combined approach, applicable to systems where the transport of chemical species occurs in unidirectional flows at high Péclet numbers, decreases calculation times considerably compared to regular 2D simulations. It takes advantage of the low computational time of the 0D reaction models while providing spatial information through multiple plug-flow simulations to yield a quasi-2D model. The gas and liquid flow profiles are simulated entirely in 2D, together with the chemical reactions and transport of key chemical species. The model correctly predicts increased transport of hydrogen peroxide into the liquid when the microfluidic opening is placed inside the plasma effluent region, as opposed to inside the plasma region itself. Furthermore, the modelled hydrogen peroxide production and transport in the microfluidic liquid differs by less than 50% compared with experimental results. To explain this discrepancy, the limits of the 0D–2D combined approach are discussed.

Abstract: In recent years there has been growing interest in the use of plasma technology for CO2 conversion. To improve this application, a good insight into the underlying mechanisms is of great importance. This can be obtained from modeling the detailed plasma chemistry in order to understand the chemical reaction pathways leading to CO2 conversion (either in pure form or mixed with another gas). Moreover, in practice, several plasma reactor types are being investigated for CO2 conversion, so in addition it is essential to be able to model these reactor geometries so that their design can be improved, and the most energy efficient CO2 conversion can be achieved. Modeling the detailed plasma chemistry of CO2 conversion in complex reactors is, however, very time-consuming. This problem can be overcome by using a combination of two different types of model: 0D chemical reaction kinetics models are very suitable for describing the detailed plasma chemistry, while the characteristic features of different reactor geometries can be studied by 2D or 3D fluid models. In the first instance the latter can be developed in argon or helium with a simple chemistry to limit the calculation time; however, the ultimate aim is to implement the more complex CO2 chemistry in these models. In the present paper, examples will be given of both the 0D plasma chemistry models and the 2D and 3D fluid models for the most common plasma reactors used for CO2 conversion in order to emphasize the complementarity of both approaches. Furthermore, based on the modeling insights, the paper discusses the possibilities and limitations of plasma-based CO2 conversion in different types of plasma reactors, as well as what is needed to make further progress in this field.

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: Self-organized striated structure has been observed experimentally and numerically in CF4 plasmas in radio-frequency capacitively coupled plasmas recently (Liu et al 2016 Phys. Rev. Lett. 116 255002). In this work, the striated structure is investigated in a capacitively coupled oxygen discharge with the introduction of the effect from the secondary electron emission, based on a particle-in-cell/Monte Carlo collision model. As we know, the transport of positive and negative ions plays a key role in the formation of striations in electronegative gases, for which, the electronegativity needs to be large enough. As the secondary electron emission increases, electrons in the sheaths gradually contribute more ionization to the discharge. Meanwhile, the increase of the electron density, especially in the plasma bulk, leads to an increased electrical conductivity and a reduced bulk electric field, which would shield the ions' mobility. These changes result in enlarged striation gaps. And then, with more emitted electrons, obvious disruption of the striations is observed accompanied with a transition of electron heating mode. Due to the weakened field, the impact ionization in the plasma bulk is attenuated, compared with the enhanced ionization caused by secondary electrons. This would lead to the electron heating mode transition from striated (STR) mode to gamma-mode. Besides, our investigation further reveals that gamma-mode is more likely to dominate the discharge under high gas pressures or driving voltages.

Abstract: Electrical breakdown by the application of an electric field occurs more easily in hot gases than in cold gases because of the extra electron-species interactions that occur as a result of dissociation, ionization and excitation at higher temperature. This paper discusses some overlooked physics and clarifies inaccuracies in the evaluation of the effective ionization coefficients and the critical reduced breakdown electric field of CO2 at elevated temperature, considering the influence of excited states and ion kinetics. The critical reduced breakdown electric field is obtained by balancing electron generation and loss mechanisms using the electron energy distribution function (EEDF) derived from the Boltzmann transport equation under the two-term approximation. The equilibrium compositions of the hot gas mixtures are determined based on Gibbs free energy minimization considering the ground states as well as vibrationally and electronically excited states as independent species, which follow a Boltzmann distribution with a fixed excitation temperature. The interaction cross sections between electrons and the excited species, not reported previously, are properly taken into account. Furthermore, the ion kinetics, including electron–ion recombination, associative electron detachment, charge transfer and ion conversion into stable negative ion clusters, are also considered. Our results indicate that the excited species lead to a greater population of high-energy electrons at higher gas temperature and this affects the Townsend rate coefficients (i.e. of electron impact ionization and attachment), but the critical reduced breakdown electric field strength of CO2 is only affected when also properly accounting for the ion kinetics. Indeed, the latter greatly influences the effective ionization coefficients and hence the critical reduced breakdown electric field at temperatures above 1500 K. The rapid increase of the dissociative electron attachment cross-section of molecular oxygen with rising vibrational quantum number leads to a larger electron loss rate and this enhances the critical reduced breakdown electric field strength in the temperature range where the concentration of molecular oxygen is relatively high. The results obtained in this work show reasonable agreement with experimental results from literature, and are important for the evaluation of the dielectric strength of CO2 in a highly reactive environment at elevated temperature.

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 packed bed dielectric barrier discharge plasma reactor is computationally studied with a fluid model. Two different complementary axisymmetric 2D geometries are used to mimic the intrinsic 3D problem. It is found that a packing enhances the electric field strength and electron temperature at the contact points of the dielectric material due to polarization of the beads by the applied potential. As a result, these contact points prove to be of direct importance to initiate the plasma. At low applied potential, the discharge stays at the contact points, and shows the properties of a Townsend discharge. When a high enough potential is applied, the plasma will be able to travel through the gaps in between the beads from wall to wall, forming a kind of glow discharge. Therefore, the inclusion of a so-called ‘channel of voids’ is indispensable in any type of packed bed modelling.

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 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: Packed bed plasma reactors (PBPRs) are gaining increasing interest for use in environmental applications, such as greenhouse gas conversion into value-added chemicals or renewable fuels and volatile pollutant removal (e.g. NOx, VOC, K), as they enhance the conversion and energy efficiency of the process compared to a non-packed reactor. However, the plasma behaviour in a PBPR is not well understood. In this paper we demonstrate, by means of a fluid model, that the discharge behaviour changes considerably when changing the size of the packing beads and their dielectric constant, while keeping the interelectrode spacing constant. At low dielectric constant, the plasma is spread out over the full discharge gap, showing significant density in the voids as well as in the connecting void channels. The electric current profile shows a strong peak during each half cycle. When the dielectric constant increases, the plasma becomes localised in the voids, with a current profile consisting of many smaller peaks during each half cycle. For large bead sizes, the shift from full gap discharge to localised discharges takes place at a higher dielectric constant than for smaller beads. Furthermore, smaller beads or beads with a lower dielectric constant require a higher breakdown voltage to cause plasma formation.