Abstract: In this paper, some modelling approaches to describe direct current (dc) magnetron discharges developed in our research groups will be presented, including an analytical model, Monte Carlo simulations for the electrons and for the sputtered atoms, a hybrid Monte Carlo-fluid model and particle-in-cell-Monte Carlo collision simulations. The strengths and limitations of the various modelling approaches will be explained, and some characteristic simulation results will be illustrated. Furthermore, some other simulation methods related to the magnetron device will be briefly explained, more specifically for calculating the magnetic field distribution inside the discharge, and for describing the (reactive) sputtering.

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: The reproducible temporal separation of ion signals generated from a single multi-element droplet, observed in previous studies, was investigated in detail in this work using an ICPTOFMS with high temporal resolution. It was shown that the signal peak intensities of individual elements temporally shift relative to each other only for droplets moving through the plasma off-axis. The magnitude of these shifts correlated with the vaporization temperatures of the analytes and depended on the radial position of the droplets as well as on the thermal properties and velocity profiles of the carrier gases of the ICP. The occurrence of the signal shifting was explained by a spatial separation of analytes already present in the vapor phase in the ICP from a yet unvaporized residue of the droplet. This separation is most likely driven by anisotropic diffusion of vaporized analytes towards the plasma axis and a radial velocity gradient. The proposed explanation is supported by modeling of the gas velocities inside the ICP and imaging of the atomic and ionic emissions produced from single droplets, whose patterns were sloping towards the center of the torch. The effects observed in these studies are important not only for the fundamental understanding of analyteplasma interactions but have also a direct impact on the signal intensities and stability.

Abstract: An inductively coupled plasma, connected to a sampling cone of a mass spectrometer, is computationally investigated. The effects of the sampler orifice diameter (ranging from 1 to 2 mm) and distance of the sampler cone from the load coil (ranging from 7 to 17 mm) are studied. An increase in sampler orifice diameter leads to a higher central plasma temperature at the place of the sampler, as well as more efficient gas transfer through the sampler, by reducing the interaction of the plasma gas with the sampling cone. However, the flow velocity at the sampler position is found to be independent of the sampler orifice diameter. Moreover, by changing the sampler orifice diameter, we can control whether only the central gas or also the auxiliary gas can exit through the sampler. Finally, with the increasing distance of the sampler from the load coil, the plasma temperature at the place of the sampler decreases slightly, which might also have consequences for the ion generation and transport through the sampling cone.

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.