Abstract: We report on a novel approach for the Reynolds-averaged Navier-Stokes (RANS) modelling of the neutral atmospheric boundary layer (ABL), using the standard k− turbulence model. A new inlet condition for turbulent kinetic energy is analytically derived from the solution of the k− model transport equations, resulting in a consistent set of fully developed inlet conditions for the neutral ABL. A modification of the standard k− model is also employed to ensure consistency between the inlet conditions and the turbulence model. In particular, the turbulence model constant C μ is generalized as a location-dependent parameter, and a source term is introduced in the transport equation for the turbulent dissipation rate. The application of the proposed methodology to cases involving obstacles in the flow is made possible through the implementation of an algorithm, which automatically switches the turbulence model formulation when going from the region where the ABL is undisturbed to the region directly affected by the building. Finally, the model is completed with a slightly modified version of the Richards and Hoxey rough-wall boundary condition. The methodology is implemented and tested in the commercial code Ansys Fluent 12.1. Results are presented for a neutral boundary layer over flat terrain and for the flow around a single building immersed in an ABL.

Abstract: In this review paper, an overview is given of different modelling efforts for plasmas used for the formation and growth of nanostructured materials. This includes both the plasma chemistry, providing information on the precursors for nanostructure formation, as well as the growth processes itself. We limit ourselves to carbon (and silicon) nanostructures. Examples of the plasma modelling comprise nanoparticle formation in silane and hydrocarbon plasmas, as well as the plasma chemistry giving rise to carbon nanostructure formation, such as (ultra)nanocrystalline diamond ((U)NCD) and carbon nanotubes (CNTs). The second part of the paper deals with the simulation of the (plasma-based) growth mechanisms of the same carbon nanostructures, i.e. (U)NCD and CNTs, both by mechanistic modelling and detailed atomistic simulations.

Abstract: A hybrid Monte Carlofluid model is applied to simulate the wafer-temperature-dependent etching of silicon with SF6 inductively coupled plasmas (ICP). The bulk plasma within the ICP reactor volume as well as the surface reactions occurring at the wafer are self-consistently described. The calculated etch rates are validated by experiments. The calculations and experiments are performed at two different wafer temperatures, i.e. 300 and 173 K, resembling conventional etching and cryoetching, respectively. In the case of cryoetching, a physisorbed SFx layer (x = 06) is formed on the wafer, which is negligible at room temperature, because of fast thermal desorption, However, even in the case of cryoetching, this layer can easily be disintegrated by low-energy ions, so it does not affect the etch rates. In the investigated pressure range of 19 Pa, the etch rate is always slightly higher at cryogenic conditions, both in the experiments and in the model, and this could be explained in the model due to a local cooling of the gas above the wafer, making the gas denser and increasing the flux of reactive neutrals, like F and F2, towards the wafer.

Abstract: A numerical parameter study has been performed for a cylindrical atmospheric pressure dielectric barrier discharge (DBD) in helium with nitrogen impurities using a two-dimensional time-dependent fluid model. The calculated electric currents and gap voltages as a function of time for a given applied potential are presented, as well as the number densities of the various plasma species. This study shows that for the geometry under consideration the applied voltage parameters have a large impact on the electric current profiles and that the discharge current is always determined by the electron and ion conduction currents while the displacement current is nearly negligible. A relative broadening of the current profiles (compared with the duration of the half cycle of the applied voltage) with an increase in the applied frequency is obtained. Nearly sinusoidal current wave forms, usually typical for radio frequency DBDs, are observed while still operating at the frequencies of tens of kilohertz. For the setup under investigation, the Townsend mode of the DBD is observed in the entire range of applied voltage amplitudes and frequencies. It is shown that the average power density dissipated in the discharge increases with rising applied voltage and frequency. An increase in applied voltage frequency leads to an increase in the electron density and a decrease in electron energy, while increasing the voltage amplitude has the opposite effect.

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: The changes induced by exposing multi-walled carbon nanotubes (CNTs) to atomic nitrogen were analysed by high-resolution transmission electron microscopy (HRTEM), x-ray and ultraviolet photoelectron spectroscopy. It was found that the atomic nitrogen generated by a microwave plasma effectively grafts chemical groups onto the CNT surface altering the density of valence electronic states. HRTEM showed that the exposure to atomic nitrogen does not significantly damage the CNT surface.

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: 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: A one-dimensional, implicit particle-in-cell Monte Carlo collision model is used to simulate the plasma kinetic properties at a steady state in a parallel-plate direct current argon glow microdischarge under various operating conditions, such as driving voltage (301000 V) and gap size (101000 µm) at atmospheric pressure. First, a comparison between rf and dc modes is shown for the same pressure, driving voltage and gap spacing. Furthermore, the effect of gap size scaling (in the range of 101000 µm) on the breakdown voltage, peak electron density and peak electron current density at the breakdown voltage is examined. The breakdown voltage is lower than 150 V in all gaps considered. The microdischarge is found to have a neutral bulk plasma region and a cathode sheath region with size varying with the applied voltage and the discharge gap. In our calculations, the electron and ion densities are of the order of 10181023 m−3, which is in the glow discharge limit, as the ionization degree is lower than 1% . The electron energy distribution function shows a two-energy group distribution at a gap of 10 µm and a three-energy group distribution at larger gaps such as 200 µm and 1000 µm, emphasizing the importance of the gap spacing in dc microdischarges.

Abstract: A two-dimensional hybrid Monte Carlofluid model is applied to study HBr/He inductively coupled plasmas used for etching of Si. Complete sets of gas-phase and surface reactions are presented and the effects of the gas mixing ratio on the plasma characteristics and on the etch rates are discussed. A comparison with experimentally measured etch rates is made to validate the modelling results. The etch rate in the HBr plasma is found to be quite low under the investigated conditions compared to typical etch rates of Si with F- or Cl-containing gases. This allows for a higher control and fine-tuning of the etch rate when creating ultra-small features. Our calculations predict a higher electron temperature at higher He fraction, because the electrons do not lose their energy so efficiently in vibrational and rotational excitations. As a consequence, electron impact ionization and dissociation become more important, yielding higher densities of ions, electrons and H atoms. This results in more pronounced sputtering of the surface. Nevertheless, the overall etch rate decreases upon increasing He fraction, suggesting that chemical etching is still the determining factor for the overall etch rate.

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.