Abstract: A two-dimensional self-consistent fluid model combined with the full set of Maxwell equations is employed to investigate an Ar/CF4 capacitively coupled plasma, focusing on the phase-shift effect on the plasma characteristics at various frequencies and gas mixture ratios. When the discharge is sustained by a single frequency at 13.56 MHz in an Ar/CF4 mixture with a ratio of 0.9/0.1, no obvious difference is detected between the electron densities obtained in the so-called electrostatic model (with only the static electric fields taken into account) and the electromagnetic model (which includes the electromagnetic effects). However, as the frequency increases to 60 and 100 MHz, the difference becomes distinct, due to the significant influence of the electromagnetic effects. The phase-shift effect on the plasma radial uniformity has also been investigated in a dual frequency discharge, i.e. when the top driven source is switched on with a phase difference phiv ranging from 0 to π, in the frequency range 13.56100 MHz. At low concentration of CF4 (10%), Ar+ ions are the major positive ions in the entire range of frequencies. When the frequency is low, i.e. 13.56 MHz, the Ar+ density exhibits an off-axis peak at phiv = 0 due to the edge effect, and a better uniformity caused by the phase-shift modulation is obtained at phiv = π. At 60 MHz, the Ar+ density varies from edge-peaked at phiv = 0 to uniform (i.e. at phiv = 0.53π), and finally at phiv = π, a broad maximum is observed at the centre due to the standing-wave effect. As the frequency increases to 100 MHz, the best radial uniformity is reached at 0.25π, and the maximum moves again towards the radial wall in the reverse-phase case (phiv = π) due to the dominant skin effect. When the frequency is fixed at 100 MHz, the phase-shift control shows a different behaviour at a high concentration of CF4. For instance, the ${\rm CF}_3

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.

Abstract: A fluid model is self-consistently established to investigate the harmonic effects in an inductively coupled plasma, where the electromagnetic field is solved by the finite difference time domain technique. The spatiotemporal distribution of harmonic current density, harmonic potential, and other plasma quantities, such as radio frequency power deposition, plasma density, and electron temperature, have been investigated. Distinct differences in current density have been observed when calculated with and without Lorentz force, which indicates that the nonlinear Lorentz force plays an important role in the harmonic effects, especially at low frequencies. Moreover, the even harmonics are larger than the odd harmonics both in the current density and the potential. Finally, the dependence of various plasma quantities with and without the Lorentz force on various driving frequencies is also examined. It is shown that the deposited power density decreases and the depth of penetration increases slightly because of the Lorentz force. The electron density increases distinctly while the electron temperature remains almost the same when the Lorentz force is taken into account.

Abstract: PECVD of a nanoscale SiO2 capping layer using low pressure SiCl4/O-2/Ar plasmas is numerically investigated. The purpose of this capping layer is to restore photoresist profiles with improved line edge roughness. A 2D plasma and Monte Carlo feature profile model are applied for this purpose. The deposited films are calculated for various operating conditions to obtain a layer with desired shape. An increase in pressure results in more isotropic deposition with a higher deposition rate, while a higher power creates a more anisotropic process. Dilution of the gas mixture with Ar does not result in an identical capping layer shape with a thickness linearly correlated to the dilution. Finally, a substrate bias seems to allow proper control of the vertical deposition rate versus sidewall deposition as desired.

Abstract: The formation process of a microdischarge (MD) in both μm- and nm-sized catalyst pores is simulated by a two-dimensional particle-in-cell/Monte Carlo collision model. A parallel-plate dielectric barrier discharge configuration in filamentary mode is considered in ambient air. The discharge is powered by a high voltage pulse. Our calculations reveal that a streamer can penetrate into the surface features of a porous catalyst and MDs can be formed inside both μm- and nm-sized pores, yielding ionization inside the pore. For the μm-sized pores, the ionization mainly occurs inside the pore, while for the nm-sized pores the ionization is strongest near and inside the pore. Thus, enhanced discharges near and inside the mesoporous catalyst are observed. Indeed, the maximum values of the electric field, ionization rate and electron density occur near and inside the pore. The maximum electric field and electron density inside the pore first increase when the pore size rises from 4 nm to 10 nm, and then they decrease for the 100 nm pore, due to
a more pronounced surface discharge for the smaller pores. However, the ionization rate is highest for the 100 nm pore due to the largest effective ionization region.

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: Atomistic simulation methods for the quantification of free energies are in wide use. These methods operate by sampling the probability density of a system along a small set of suitable collective variables (CVs), which is, in turn, expressed in the form of a free energy surface (FES). This definition of the FES can capture the relative stability of metastable states but not that of the transition state because the barrier height is not invariant to the choice of CVs. Free energy barriers therefore cannot be consistently computed from the FES. Here, we present a simple approach to calculate the gauge correction necessary to eliminate this inconsistency. Using our procedure, the standard FES as well as its gauge-corrected counterpart can be obtained by reweighing the same simulated trajectory at little additional cost. We apply the method to a number of systems—a particle solvated in a Lennard-Jones fluid, a Diels–Alder reaction, and crystallization of liquid sodium—to demonstrate its ability to produce consistent free energy barriers that correctly capture the kinetics of chemical or physical transformations, and discuss the additional demands it puts on the chosen CVs. Because the FES can be converged at relatively short (sub-ns) time scales, a free energy-based description of reaction kinetics is a particularly attractive option to study chemical processes at more expensive quantum mechanical levels of theory.

Abstract: Plasma-based NO_Xsynthesis<italic>via</italic>the Birkeland–Eyde process was one of the first industrial nitrogen fixation methods. However, this technology never played a dominant role for nitrogen fixation, due to the invention of the Haber–Bosch process. Recently, nitrogen fixation by plasma technology has gained significant interest again, due to the emergence of low cost, renewable electricity. We first present a short historical background of plasma-based NO_Xsynthesis. Thereafter, we discuss the reported performance for plasma-based NO_Xsynthesis in various types of plasma reactors, along with the current understanding regarding the reaction mechanisms in the plasma phase, as well as on a catalytic surface. Finally, we benchmark the plasma-based NO_Xsynthesis process with the electrolysis-based Haber–Bosch process combined with the Ostwald process, in terms of the investment cost and energy consumption. This analysis shows that the energy consumption for NO_Xsynthesis with plasma technology is almost competitive with the commercial process with its current best value of 2.4 MJ mol N⁻¹, which is required to decrease further to about 0.7 MJ mol N⁻¹in order to become fully competitive. This may be accomplished through further plasma reactor optimization and effective plasma–catalyst coupling.

Abstract: Not much about the effect of thiocyanate addition on the sulphur ripening is known, although it is used for many applications in photographic practice. Via a combination of tracer analysis and diffuse reflectance spectroscopy the effect of thiocyanate addition on the sulphur and sulphur-plus-gold ripening could be unveiled. When thiocyanate is added prior to the sulphur addition, it appears to rearrange the silver halide surface in such way that the sulphur deposition rate is enhanced, but the supply of interstitials is limited. Addition of thiocyanate after the sulphur reaction results in the formation of thiocyanate complexes with silver, from which a silver ion is more easily deposited in a surface cell of the silver sulphide clusters thus enhancing the sensitization rate. For sulphur-plus-gold sensitized emulsions it was observed that part of the gold ions could be removed out of the Ag2-xAuxS clusters by addition of thiocyanate ions and subsequent washing. Hence, it was concluded that two different types of gold ions are present in the silver sulphide clusters; 1. gold ions which are substitutional for silver (bound between sulphur and bromide ions) 2. gold ions which bridge two or three sulphur atoms. Incorporation of gold ions into silver sulphide clusters suppresses their optical absorption in diffuse reflectance spectroscopy. Since the optical absorption at 505 nm can completely be restored by addition of thiocyanate, it is assumed that the entity absorbing at this wavelength is a monomer of silver sulphide.

Abstract: The destruction of ethylene in a dielectric barrier discharge plasma is investigated by the combination of kinetic modeling and experiments, as a case study for plasma-based gas purification. The influence of the specific energy deposition on the removal efficiency and the selectivity toward CO and CO2 is studied for different concentrations of ethylene. The model allows the identication of the destruction pathway in dry and humid air. The latter is found to be mainly initiated by metastable N2 molecules, but the further destruction steps are dominated by O atoms and OH radicals. Upon increasing air humidity, the removal efficiency drops by ±15% (from 85% to 70%), but the selectivity toward CO and CO2 stays more or less constant at 60% and 22%, respectively. Beside CO and CO2, we also identified acetylene, formaldehyde, and water as byproducts of the destruction process, with concentrations of 1606 ppm, 15033 ppm, and 185 ppm in humid air (with 20% RH), respectively. Finally, we investigated the byproducts generated by the humid air discharge itself, which are the greenhouse gases O3, N2O, and the toxic gas NO2.

Abstract: A gliding arc plasma is a potential way to convert CO2 into CO and O2, due to its non-equilibrium character, but little is known about the underlying mechanisms. In this paper, a self-consistent two-dimensional (2D) gliding arc model is developed, with a detailed non-equilibrium CO2 plasma chemistry, and validated with experiments. Our calculated values of the electron number density in the plasma, the CO2 conversion and energy efficiency show reasonable agreement with the experiments, indicating that the model can provide a realistic picture of the plasma chemistry. Comparison of the results with classical thermal conversion, as well as other plasma-based technologies for CO2 conversion reported in literature, demonstrates the non-equilibrium character of the gliding arc, and indicates that the gliding arc is a promising plasma reactor for CO2 conversion. However, some process modifications should be exploited to further improve its performance. As the model provides a realistic picture of the plasma behaviour, we use it first to investigate the plasma characteristics in a whole gliding arc cycle, which is necessary to understand the underlying mechanisms. Subsequently, we perform a chemical kinetics analysis, to investigate the different pathways for CO2 loss and formation. Based on the revealed discharge properties and the underlying CO2 plasma chemistry, the model allows us to propose solutions on how to further improve the
CO2 conversion and energy efficiency by a gliding arc plasma.

Abstract: We studied the use of low current (hundreds of milliamperes) gliding arc/glow discharges for CO2 dissociation, at atmospheric pressure, in three different configurations. All of these are based on the gliding arc design with flat diverging electrodes. The discharge is mainly in the normal glow regime with contracted positive column. The CO2 gas is injected from a nozzle, at the closest separation between the electrodes. A pair of quartz glasses is placed on both sides of the electrodes, so that the gas flow is restricted to the active plasma area, between the electrodes. For two of the tested configurations, an external magnetic field was applied, to create a magnetic force, both in the direction of the gas flow, and opposite to the gas flow. In the first case, the arc is accelerated, shortening the period between ignition and extinction, while in the second case, it is stabilized (magneticallystabilized). We studied two quantities, namely the CO2 conversion and the energy efficiency of the conversion. Generally, the CO2 conversion decreases with increasing flow rate and increases with power. The energy effi­ciency increases with the flow rate, for all configurations. The magnetically-stabilized configuration is more stable and efficient at low gas flow rates, but has poor performance at high flow rates, while the non-stabilized configurations exhibit good conversion for a larger range of flow rates, but they are generally more unstable and less efficient.