22nd International Symposium on Plasma Chemistry
July 5-10, 2015; Antwerp, Belgium
Global (volume-averaged) model of oxygen plasmas
E.H. Kemaneci1, J. van Dijk2 and R.P. Brinkmann1
1
2
Ruhr University Bochum, Theoretical Electrical Engineering, Bochum, Germany
Department of Applied Physics, Eindhoven University of Technology, Eindhoven, the Netherlands
Abstract: In this contribution, we investigate oxygen plasmas using a global (volumeaveraged) model. The investigation mainly focuses on the population of the vibrational
quantum levels of oxygen molecule in radio-frequency plasmas, where a ladder-like
dissociation is included in addition to the various e-V, V-V and V-T transitions. The
plasma interactions with the wall, such as recombination of oxygen atom and ozone
formation, are also investigated. Furthermore, we cover both the continuous and pulsed
power input modes, where we observe agreement with various experimental data of oxygen
plasmas in literature.
Keywords: oxygen plasma, global model, vibrational quantum levels
1. General
Oxygen plasmas are widely used for technological
purposes and scientific investigations. These plasmas
include variety of species, such as, different types of ions
and electronic energy levels of atomic and molecular
species. Additionally, the vibrational degree of freedom
of the molecules contributes to this variety with the
corresponding quantum energy levels. Although most of
these species are covered in previous studies [1-5], a
detailed and up-to-date study on the population of the
vibrational levels as well as their role in the plasmas are
still missing. In this study we address this issue by
providing a detailed investigation.
The chamber wall is also an important factor in the
plasma behaviour. For example, it is shown that the
recombination of oxygen atoms at the chamber wall plays
major role on the plasma parameters [5]. Recent studies
also reveal ozone formation at certain types of wall
materials contacting the plasma. The role of these wall
reactions are also investigated within the framework of
this contribution.
Pulse-modulated power input of the oxygen plasmas is
often preferred mostly due to the better control of the ion
wall fluxes and reduced thermal load. We also analyse
the temporal plasma chemical kinetics in the pulse-on and
pulse-off regions of the modulation period.
2. Global (volume-averaged) model
Global (volume-averaged) models are widely used in
literature to investigate oxygen plasmas [1-3, 5]. These
models are often preferred over detailed spatially-resolved
models due to the low cost in the computational load and
smaller simulation durations. Although, the main focus
of their usage is the inductively (or capacitively) coupled
plasmas, they are also employed to analyse plasmas
induced by the microwaves [6, 7]. The global models
include the particle balance equations and the electron
energy balance equation, that are both spatially averaged
over the plasma volume with the assumption of spatial
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homogeneity [8]. These equations describe the particle
densities and the electron temperature, whereas the heavyparticle temperature and the pressure are externally
provided in the model. The volume-averaged particle
balance equation of a particle i can be written as
𝒅𝒏𝒊
𝒅𝒅
= 𝑺𝒊 ,
where n i represents the density and S i represents the
source of the particle. The source term includes the
volume-averaged chemical reactions in the plasma bulk,
the wall induced reactions, as well as the transport losses
at the plasma boundary. The volume-averaged electron
energy balance equation is given by the relation
𝟑
𝒅(𝟐𝒏𝒆 𝑻𝒆 )
𝒅𝒅
= 𝑸𝒆 ,
where T e is the electron temperature and Q e is the
electron energy source. The source term includes the
absorbed power, the energy losses in the plasma bulk due
to various elastic and inelastic collisions, as well as the
energy losses at the plasma boundary.
The simulations are carried on the modular plasma
simulation platform Plasimo developed in Technical
University of Eindhoven. The set of ordinary differential
equations are iteratively solved for a given set of initial
conditions. In the iterative process Livermore Solver for
Ordinary Differential Equations (LSODA) is used.
3. Experimental comparison
The simulation results are compared with various
experimental data of oxygen plasmas in literature and we
show only two example cases here. The first case is the
electron and negative ion densities measured by Stoffels
et al. [9] on a capacitively coupled plasma. In Fig. 1, the
measured and calculated densities are shown with respect
to the pressure. The second case is the electron, negative
1
ion and atomic oxygen densities measured by Baeva et al.
[4] on a microwave waveguide plasma, sustained by
pulse-modulated power input.
The time-resolved
densities and the simulation data of this setup are shown
in Fig. 2.
In addition to the direct dissociation of the molecular
oxygen due to the electron impact, Cacciatore et al.
suggests an additional mechanism to dissociate molecular
oxygen. This mechanism excites the vibrational levels
ladder-like manner mostly due to the e-V processes.
After a pseudo level has been reached the dissociation
occurs via various vibrational processes.
5. Acknowledgements
The authors gratefully acknowledges the support by
BmBF via PluTO+.
Fig. 1. Electron and negative ion densities measured by
Stoffels et al. [9] (points) on a capacitively coupled
plasmas and the corresponding simulation data (lines).
Fig. 2. Electron, negative ion and atomic oxygen
densities measured by Baeva et al. [4] (points) on a
pulse-modulated microwave waveguide plasma and the
corresponding simulation data (lines).
4. Vibrational chemical kinetics
The vibrational quantum levels of the molecular oxygen
is created via vibrational excitation by electron impact.
The direct vibrational excitation is in general an
inefficient process. On the other hand, the resonant
vibrational excitation, in which the incident electron
firstly attaches to the molecule and forms a temporary
resonant anionic state, may effectively populate these
levels. These levels are heavily depopulated due to the V-T processes with oxygen atoms [4]. This fact is solely
responsible in their absence in the earlier oxygen plasma
models [1-5] by reducing their importance in the chemical
kinetics.
2
6. References
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