# Electron power absorption in capacitively coupled neon-oxygen plasmas: a
comparison of experimental and computational results

A. Derzsi1, P. Hartmann1, M. Vass1,2, B. Horváth1, M. Gyulai1, I. Korolov2, J.
Schulze2,3, Z. Donkó1 1 Institute for Solid State Physics and Optics, Wigner
Research Centre for Physics, 1121 Budapest, Hungary
2 Department of Electrical Engineering and Information Science, Ruhr
University Bochum, 44780 Bochum, Germany
3 Key Laboratory of Materials Modification by Laser, Ion and Electron Beams,
School of Physics, Dalian University of Technology, 116024 Dalian, China
<EMAIL_ADDRESS>
###### Abstract

Phase Resolved Optical Emission Spectroscopy (PROES) measurements combined
with 1d3v Particle-in-Cell/Monte Carlo Collisions (PIC/MCC) simulations are
used to study the electron power absorption and excitation/ionization dynamics
in capacitively coupled plasmas (CCPs) in mixtures of neon and oxygen gases.
The study is performed for a geometrically symmetric CCP reactor with a gap
length of 2.5 cm at a driving frequency of 10 MHz and a peak-to-peak voltage
of 350 V. The pressure of the gas mixture is varied between 15 Pa and 500 Pa,
while the neon/oxygen concentration is tuned between 10% and 90%. For all
discharge conditions, the spatio-temporal distribution of the electron-impact
excitation rate from the Ne ground state into the Ne $\rm{2p^{5}3p_{0}}$ state
measured by PROES and obtained from PIC/MCC simulations show good qualitative
agreement. Based on the emission/excitation patterns, multiple operation
regimes are identified. Localized bright emission features at the bulk
boundaries, caused by local maxima in the electronegativity are found at high
pressures and high O2 concentrations. The relative contributions of the
ambipolar and the Ohmic electron power absorption are found to vary strongly
with the discharge parameters: the Ohmic power absorption is enhanced by both
the high collisionality at high pressures and the high electronegativity at
low pressures. In the wide parameter regime covered in this study, the PROES
measurements are found to accurately represent the ionization dynamics, i.e.,
the discharge operation mode. This work represents also a successful
experimental validation of the discharge model developed for neon-oxygen CCPs.

##  1 Introduction

Capacitively Coupled Plasmas (CCPs) represent important reactor types widely
used in plasma etching, sputtering, deposition, and cleaning processes
providing the basis for semiconductor manufacturing and biomedical
applications [1, 2, 3, 4, 5]. In such plasmas, efficient control of the
particle properties at the electrodes (e.g., the fluxes of chemically reactive
species and the ion flux-energy distribution), which determine the
plasma–surface interaction, is a basic requirement. In order to achieve
improved process control in such systems, a detailed understanding of the
electron power absorption and ionization dynamics is necessary.

The spatio-temporal distributions of the electron power absorption and the
ionization within the radiofrequency (RF) period determine the operation mode
of the discharge. In low-pressure CCPs, several different discharge operation
modes can be identified: the $\alpha$-mode and the $\gamma$-mode [6] are
typical in electropositive gases, while the drift-ambipolar (DA) mode [7] and
the striation (STR) mode [8, 9, 10, 11, 12] can be observed in electronegative
gases. In the $\alpha$-mode, the ionization, caused by energetic electrons
accelerated by electric fields during the times of sheath expansion, is
concentrated at the bulk side of the expanding sheath edge, while in the
$\gamma$-mode, the ionization, dominated by secondary electrons (SEs)
accelerated by the strong electric field inside the sheaths, is concentrated
within the sheath region. In the DA-mode, the ionization can be observed
across the whole bulk region and at the collapsing sheath edges, as it is
generated by fast electrons accelerated by the strong drift electric field in
the plasma bulk caused by the low conductivity of the plasma bulk, and by the
ambipolar electric fields at the sheath edges caused by the strong gradients
of the electron density. In the STR-mode, which develops when both positive
and negative ions can react to the fast variation of the RF electric field,
the ionization, concentrated within the bulk region, exhibits layered
structures called “striations”; these are generated as a result of the
formation of alternating space charges and the modulation of the electric
field and the energy gain of electrons in the plasma bulk. The simultaneous
presence of the ionization patterns characteristic of the different discharge
operation modes can be observed in low-pressure CCPs under specific discharge
conditions, as well as transitions between these modes by varying the external
control parameters [13, 14, 15, 16, 17, 18].

Experimental observation of the space and time-resolved plasma emission based
on Phase Resolved Optical Emission Spectroscopy (PROES) [19, 20, 21] provides
invaluable information on the electron power absorption and
excitation/ionization dynamics in low-pressure CCPs [7, 8]. For PROES
measurements, Ne is often used as a tracer gas due to its favorable
spectroscopic properties. By adding Ne in a small concentration (typically 5%
– 15%) to the background gas, and measuring the emission from a carefully
selected atomic transition (e.g., Ne
$\rm{2p^{5}(^{2}P^{o}_{1/2})3p_{0}}\rightarrow\rm{2p^{5}(^{2}P^{o}_{1/2})3s_{1}}$
with a wavelength of 585.25 nm) the spatio-temporal electron impact excitation
rate from the ground state into the upper level can be derived. This way, by
selecting an emission line resulting from an excited state with a high
electron impact excitation threshold energy, information about the dynamics of
high-energy electrons (which are typically responsible both for the excitation
and the ionization processes in the discharge) can be obtained, making PROES
an effective non-intrusive diagnostic technique. Although PROES provides
information about the spatio-temporal distribution of the electron-impact
excitation dynamics from the ground state into the selected excited atomic
state in the discharge, it is generally considered to probe the discharge
operation mode (which, in turn, is determined by the spatio-temporal
distribution of the ionization dynamics) as well.

Recently, the applicability of PROES to probe the discharge operation mode was
investigated in low-pressure CCPs operated in pure neon [22]. In this work, a
detailed comparison of computational and experimental results focusing on the
spatio-temporal distributions of the excitation and the ionization rates in
geometrically symmetric single-frequency neon CCPs has been performed in a
wide parameter regime. Particle-in-Cell/Monte Carlo Collisions (PIC/MCC)
simulations [23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34] and PROES
measurements were carried out at driving frequencies ranging from 3.39 MHz to
13.56 MHz and pressures from 60 Pa to 500 Pa, at a fixed peak-to-peak voltage
of 330 V and an electrode gap of 2.5 cm. At fixed frequencies, transitions of
the discharge operation mode from the $\alpha$-mode to the $\gamma$-mode were
observed by increasing the pressure. The electron impact excitation rates from
the ground state into the Ne $\rm{2p^{5}(^{2}P^{o}_{1/2})3p_{0}}$ state (for
which we will use the simplified notation Ne $\rm{3p_{0}}$) obtained from
PROES measurements and PIC/MCC simulations were in good agreement in all
cases. However, it was found that PROES results do not always probe the
ionization and significant $\gamma$-mode ionization can take place in the
discharge even in the cases when this is not seen in the spatio-temporal
distribution of the Ne $\rm{3p_{0}}$ excitation. This was explained by the
difference in the cross sections of the electron impact excitation into the
observed level and the ionization as a function of the electron energy [22].
Although the threshold energy of the Ne $\rm{3p_{0}}$ excitation process is
close to the one of the ionization, the shapes of the cross sections are
different within the electron energy range of the discharges studied. As a
consequence of this, it is more likely that the highly energetic SEs within
the sheaths induce ionization rather than excitation.

Due to their high relevance in material processing, oxygen CCPs have been
studied extensively, both experimentally and by simulations [35, 36, 37, 38,
39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 13, 49, 50]. In pure oxygen CCPs,
transitions between the $\alpha$-mode and the DA-mode have been found by
changing the gas pressure [13, 14], the gap distance [14, 17], the driving
frequency [13, 47], the driving voltage waveform [51, 13, 18, 46, 15, 52], and
the external magnetic field [49]. A transition from a hybrid DA-$\alpha$ mode
to a pure $\alpha$-mode was observed by increasing the driving frequency at a
constant pressure [47], as well as by increasing the pressure or the electrode
gap [14]. PIC/MCC simulations and PROES measurements showed a transition from
the DA-mode to the $\alpha$-mode in oxygen CCPs driven by tailored voltage
waveforms by changing the number of consecutive harmonics included in the
driving voltage waveform at high base frequencies [13].

In this work, we study the electron power absorption and excitation/ionization
dynamics in capacitively coupled plasmas (CCPs) operated in mixtures of neon
and oxygen. PROES measurements are combined with PIC/MCC simulations in a wide
parameter regime. The study is performed in a geometrically symmetric CCP
reactor with a gap length of 2.5 cm, at a driving frequency of 10 MHz and a
peak-to-peak voltage of 350 V. The pressure of the gas mixture is varied
between 15 Pa and 500 Pa, while the mixing ratio of neon-to-oxygen is between
10% and 90%. Transitions between different discharge operation modes are found
to be induced by changing the gas pressure and varying the neon/oxygen
concentration ratio in the discharge, as well as the development of localized
bright emission/excitation features at the edges of the bulk region at high
pressures and high O2 concentrations. The good qualitative agreement between
the PROES results and the PIC/MCC simulation results supports the validity of
the discharge model developed for neon-oxygen CCPs. While experimental
validation of simulations is of major importance for the reliability of the
simulation results, this has only been done for some inert gases [22, 53] and
electronegative gases [48], but such efforts are barely found for reactive gas
mixtures [15], which are required for process development.

The paper is structured in the following way. In section 2, the experimental
setup is presented. In section 3, the simulation method and the neon-oxygen
discharge model is described, including details on the collision processes in
section 3.1, the surface processes in section 3.2, the gas heating module in
section 3.3, the calculation of the density of $\rm{O_{2}(a^{1}\Delta_{g})}$
metastable molecules in section 3.4, the study of the electron power
absorption based on the Boltzmann term method in section 3.5, and the
simulation settings in section 3.6. The results are shown and discussed in
section 4. The conclusions are drawn in section 5.

##  2 Experimental setup and discharge conditions

The space and time resolved optical emission of the discharge is measured
experimentally, by PROES [19, 20, 21], in which the emitted light from the
selected excited atomic/molecular state is spatio-temporally resolved. From
that, the electron impact excitation rate from the ground state into the
observed level, $W_{0,i}(x,t)$, can be calculated, as introduced in [21]. In
order to perform a successful PROES measurement on a CCP, some crucial
conditions have to be fulfilled [21]: (i) Knowledge of the optical transition
rates in the gas is needed. (ii) The contribution of cascades, excitation from
metastable levels and quenching to the population of the measured excited
state need to be negligibly low. (iii) The intensity of the emitted light at
the measured line has to be high enough. (iv) No superposition with other
optical lines is tolerated within the spectral resolution of the spectrometer
or the interference filter. (v) The lifetime of the relevant excited state has
to be short enough to temporally resolve the RF period (100 ns in the current
study). All in all, the choice of the optical line to measure is critical. A
typical line that satisfies these criteria well and is, therefore, often
applied for PROES is the emission line corresponding to the Ne
$\rm{2p^{5}(^{2}P^{o}_{1/2})3p_{0}}\rightarrow\rm{2p^{5}(^{2}P^{o}_{1/2})3s_{1}}$
transition, with a wavelength of 585.25 nm and lifetime of 16.26 ns [54]. Its
threshold energy for electron impact excitation from the ground state is
18.966 eV [55].

Figure 1: Scheme of the experimental setup.

For the current measurements, our geometrically symmetric “Budapest v.3”
plasma reactor is used, which was first introduced in [22]. A sketch of the
setup is shown in figure 1. The flat disk electrodes made of 304 grade
stainless steel with identical diameters of 14.0 cm are situated within a
quartz cylinder. Their separation is 2.5 cm. The upper electrode is driven by
RF voltage, while the lower one is grounded. There is no active cooling
applied on the electrodes. The chamber can be evacuated via a turbomolecular
and a rotary pump, providing a base pressure of approximately $10^{-5}$ Pa.
The experiments are performed in a gas flow of $\approx$3 sccm set by two flow
controllers. The driving voltage is provided by a waveform generator (Juntek
JDS-2900), which is connected to a linear power amplifier (RM BLA-300) and an
impedance matching box (MFJ-949E). The voltage drop across the discharge is
measured by a high voltage probe (HP 10076A, 100:1) right at the power feeding
point, and the pressure is monitored by capacitive gauges (Pfeiffer Vacuum
CMR264 and MKS Baratron 631A).

PROES measurements are performed with a fast-gateable ICCD camera (4 Picos,
Stanford Computer Optics). The optical emission from the Ne $\rm{3p_{0}}$
state with a wavelength of 585.25 nm is measured. In order to limit the
measured light to this specific line, an interference filter is applied with a
central wavelength of 585 nm and a spectral full width at half maximum of
$\sim$10 nm. The gate width of the camera is set to 2 ns. The camera is
equipped with a Thorlabs MVTC23013 0.128x bi-telecentric lens, by which two-
dimensional pictures can be taken. The spatial resolution is approximately 150
$\rm{\mu m}$. Due to the lateral uniformity of the plasma, the data are
averaged in the direction perpendicular to the discharge axis, which reduces
the noise significantly.

##  3 Simulation method

The simulations are based on a one dimensional in space and three dimensional
in velocity space (1d3v) Particle-in-Cell/Monte Carlo Collisions (PIC/MCC)
simulation code [23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34]. This code
(named _PICit!_), recently developed in our group, is suitable to model
geometrically symmetric capacitively coupled RF discharges in various mixtures
of electropositive/electronegative gases. The particles traced in the
simulations of neon-oxygen gas mixture plasmas are electrons, Ne+ ions, fast
Ne atoms (Nef), ${\rm O_{2}^{+}}$ ions, ${\rm O^{-}}$ ions and fast ${\rm
O_{2}}$ molecules (O${}_{2}^{\rm f}$). The set of collision processes taken
into account in the neon-oxygen discharge model is based on the sets of
collision processes used previously for simulation studies of CCP discharges
operated in pure neon [22] and oxygen [51, 13, 52, 17, 50, 56], complemented
with “cross processes” between oxygen and neon species and collision processes
for fast neutrals (see section 3.1). The heating of the background gas due to
elastic collisions of fast neutrals and ions with thermal (background)
atoms/molecules, as well as heating up of the electrodes due to inelastic
collisions of plasma particles with the electrodes [57] is taken into account
in the model (see section 3.3). The complexity of the model necessitates a
relatively detailed description, which we provide below.

###  3.1 Collision processes

The elementary collision processes included in the discharge model are listed
in table 1.

Table 1:  List of collision processes for neon–oxygen mixtures.  # | Reaction | Process | References
---|---|---|---
1 | $\rm{e^{-}+Ne\longrightarrow e^{-}+Ne}$ | Elastic scattering | [58]
2 | $\rm{e^{-}+Ne\longrightarrow e^{-}+Ne}$ |  $\rm{2p^{5}(^{2}P^{o}_{3/2})3s_{2}}$ excitation | [58]
3 | $\rm{e^{-}+Ne\longrightarrow e^{-}+Ne}$ |  $\rm{2p^{5}(^{2}P^{o}_{3/2})3s_{1}}$ excitation | [58]
4 | $\rm{e^{-}+Ne\longrightarrow e^{-}+Ne}$ |  $\rm{2p^{5}(^{2}P^{o}_{1/2})3s_{0}}$ excitation | [58]
5 | $\rm{e^{-}+Ne\longrightarrow e^{-}+Ne}$ |  $\rm{2p^{5}(^{2}P^{o}_{1/2})3s_{1}}$ excitation | [58]
6 | $\rm{e^{-}+Ne\longrightarrow e^{-}+Ne}$ |  $\rm{\sum 2p^{5}3p}$ excitation | [58]
7 | $\rm{e^{-}+Ne\longrightarrow e^{-}+Ne}$ |  $\rm{\sum 2p^{5}4s}$ excitation | [58]
8 | $\rm{e^{-}+Ne\longrightarrow e^{-}+Ne}$ |  $\rm{\sum 2p^{5}3d}$ excitation | [58]
9 | $\rm{e^{-}+Ne\longrightarrow e^{-}+Ne}$ |  $\rm{\sum 2p^{5}4p}$ excitation | [58]
10 | $\rm{e^{-}+Ne\longrightarrow e^{-}+Ne}$ |  $\rm{2p^{5}(^{2}P^{o}_{1/2})3p_{0}}$ excitation | [58]
11 | $\rm{e^{-}+Ne\longrightarrow 2e^{-}+Ne^{+}}$ | Ionization | [58]
12 | $\rm{e^{-}+O_{2}\longrightarrow O_{2}+e^{-}}$ | Elastic scattering | [59]
13 | $\rm{e^{-}+O_{2}}(\textit{r}=0)\longrightarrow\rm{e^{-}+O_{2}}(\textit{r}>0)$ | Rotational excitation | [60]
14 | $\rm{e^{-}+O_{2}}(\textit{v}=0)\longrightarrow\rm{e^{-}+O_{2}}(\textit{v}=1)$ | Vibrational excitation | [60]
15 | $\rm{e^{-}+O_{2}}(\textit{v}=0)\longrightarrow\rm{e^{-}+O_{2}}(\textit{v}=2)$ | Vibrational excitation | [60]
16 | $\rm{e^{-}+O_{2}}(\textit{v}=0)\longrightarrow\rm{e^{-}+O_{2}}(\textit{v}=3)$ | Vibrational excitation | [60]
17 | $\rm{e^{-}+O_{2}}(\textit{v}=0)\longrightarrow\rm{e^{-}+O_{2}}(\textit{v}=4)$ | Vibrational excitation | [60]
18 | $\rm{e^{-}+O_{2}}\longrightarrow e^{-}+O_{2}(a^{1}\Delta_{g})$ | Metastable excitation (0.98 eV) | [60]
19 | $\rm{e^{-}+O_{2}}\longrightarrow e^{-}+O_{2}(b^{1}\Sigma_{g})$ | Metastable excitation (1.63 eV) | [60]
20 | $\rm{e^{-}+O_{2}}\longrightarrow O+O^{-}$ | Dissociative attachment | [60]
21 | $\rm{e^{-}+O_{2}}\longrightarrow e^{-}+O_{2}$ | Excitation (4.5 eV) | [60]
22 | $\rm{e^{-}+O_{2}}\longrightarrow O(^{3}P)+O(^{3}P)+e^{-}$ | Dissociation (6.0 eV) | [60]
23 | $\rm{e^{-}+O_{2}}\longrightarrow O(^{3}P)+O(^{1}D)+e^{-}$ | Dissociation (8.4 eV) | [60]
24 | $\rm{e^{-}+O_{2}}\longrightarrow O(^{1}D)+O(^{1}D)+e^{-}$ | Dissociation (9.97 eV) | [60]
25 | $\rm{e^{-}+O_{2}}\longrightarrow O^{+}_{2}+e^{-}+e^{-}$ | Ionization | [61]
26 | $\rm{e^{-}+O_{2}}\longrightarrow e^{-}+O+O(3p^{3}P)$ | Dissociative excitation (14.7 eV) | [60]
27 | $\rm{e^{-}+O^{-}}\longrightarrow e^{-}+e^{-}+O$ | Electron impact detachment | [61]
28 | $\rm{e^{-}+O^{+}_{2}}\longrightarrow O(^{3}P)+O(^{1}D)$ | Dissociative recombination | [61]
29 | $\rm{Ne^{+}+Ne\longrightarrow Ne^{+}+Ne}$ | Isotropic scattering | [62]
30 | $\rm{Ne^{+}+Ne\longrightarrow Ne^{+}+Ne}$ | Backscattering | [62]
31 |  Ne+ \+ O2 $\longrightarrow$ Ne + O${}_{2}^{+}$ | Charge transfer | [63]
32 |  Ne+ \+ O2 $\longrightarrow$ Ne+ \+ O2 | Isotropic elastic scattering | [64]
33 | $\rm{O^{+}_{2}+O_{2}}\longrightarrow O_{2}+O^{+}_{2}$ | Elastic scattering: charge exchange | [61]
34 | $\rm{O^{+}_{2}+O_{2}}\longrightarrow O_{2}+O^{+}_{2}$ | Elastic scattering: isotropic part | [61]
35 |  O${}_{2}^{+}$ \+ Ne $\longrightarrow$ O${}_{2}^{+}$ \+ Ne | Isotropic elastic scattering | [64]
36 | $\rm{O^{-}+O_{2}}\longrightarrow O^{-}+O_{2}$ | Elastic scattering | [61]
37 | $\rm{O^{-}+O_{2}}\longrightarrow O+O_{2}+e^{-}$ | Detachment | [61]
38 | $\rm{O^{-}+O_{2}^{+}}\longrightarrow O+O_{2}$ | Mutual neutralization | [61]
39 | $\rm{O^{-}+O_{2}(a^{1}\Delta_{g})}\longrightarrow O_{3}+e^{-}$ | Associative detachment | [65]
40 |  O- \+ Ne $\longrightarrow$ O- \+ Ne | Isotropic elastic scattering | [64]
41 |  O- \+ Ne+ $\longrightarrow$ O + Ne | Mutual neutralisation | [61]
42 | $\rm{Ne^{f}+Ne\longrightarrow Ne^{f}+Ne}$ | Elastic scattering |
43 | $\rm{O^{f}_{2}+O_{2}}\longrightarrow O^{f}_{2}+O_{2}$ | Elastic scattering |
44 | $\rm{Ne^{f}+O_{2}\longrightarrow Ne^{f}+O_{2}}$ | Elastic scattering |
45 | $\rm{O^{f}_{2}+Ne\longrightarrow O^{f}_{2}+Ne}$ | Elastic scattering |

Figure 2: Cross sections of electron collisions listed in table 1 (processes
1–28) as a function of the kinetic energy of the projectile: (a) Elastic
scattering between electrons and Ne atoms (processes 1), electron impact
excitation (processes 2-10) and ionization (process 11) of Ne. The red curve
(process 10) in panel (a) corresponds to the excitation from the ground state
into the Ne $\rm{3p_{0}}$ state. (b) Elastic scattering between electrons and
O2 molecules (processes 12), electron impact rotational excitation (process
13) and vibrational excitation (processes 14–17) of O2. (c) Metastable
excitation (processes 18 and 19), dissociative attachement (process 20),
electronic excitation (process 21), dissociation (processes 22–24), ionization
(process 25) and dissociative excitation (process 26) between electrons and O2
molecules, as well as detachment with O- (process 27) and dissociative
recombination with O${}_{2}^{+}$ (process 28). Figure 3: Cross sections of the
collision processes for Ne+, $\rm{O_{2}^{+}}$ and $\rm{O^{-}}$ ions, listed in
table 1 (processes 29–41), as a function of the kinetic energy (considered in
the center-of-mass frame) of the projectile: (a) Isotropic and backward
elastic scattering between Ne+ ions and Ne atoms (processes 29 and 30,
respectively), Ne+ ions and O2 molecules (processes 32 and 31, respectively),
$\rm{O_{2}^{+}}$ ions and O2 molecules (processes 33 and 34, respectively),
and isotropic elastic scattering between $\rm{O_{2}^{+}}$ ions and Ne atoms
(process 35). (b) Elastic scattering (process 36) and detachement (process 37)
between $\rm{O^{-}}$ ions and O2 molecules, mutual neutralization of
$\rm{O^{-}}$ with $\rm{O_{2}^{+}}$ (process 38) and Ne+ (process 41),
associative detachment of $\rm{O^{-}}$ with $\rm{O_{2}(a^{1}\Delta_{g})}$
(process 39) and isotropic elastic scattering with Ne atoms (process 40). Note
that the cross sections overlap in case of processes 36 and 40, as well as in
case of processes 38 and 41.

#### Electron collisions:

The collision processes between electrons and Ne atoms are elastic scattering
(process 1), excitation (processes 2–10) and ionization (process 11). Nine
electron impact Ne excitation processes are considered, including the Ne
$\rm{3p_{0}}$ excitation from the ground state (process 10), whose population
dynamics is captured experimentally by the PROES measurements. The cross
sections for the e- \+ Ne collisions are adopted from the Biagi-v7.1 dataset
[58] and are plotted in figure 2(a).

Collisions between electrons and $\rm{O_{2}}$ molecules include elastic
scattering (process 12), rotational and vibrational excitation (processes
13–17), metastable excitation (processes 18 and 19), dissociative attachment
(process 20), electronic excitation (process 21), dissociation (processes
22-24), ionization (process 25), and dissociative excitation (process 26).
Electron impact detachment of $\rm{O^{-}}$ ions (process 27) and dissociative
recombination of $\rm{O_{2}^{+}}$ ions (process 28) are also considered. The
e- \+ O2 process list and cross sections adopted are largely based on the
“xpdp1” set [60]. However, a few changes have been introduced [51]: we (i)
replace the elastic collision (process 12) cross section with the elastic
momentum transfer cross section of Biagi [59] and use, accordingly, isotropic
electron scattering, (ii) replace the original “xpdp1” cross sections for the
ionization (process 25), electron impact detachment (process 27) and
dissociative recombination (process 28) with those recommended by Gudmundsson
[61]. The cross sections for the electron impact collisions with oxygen
species are plotted in figure 2(b) (processes 12–17) and figure 2(c)
(processes 18–28).

#### Ion collisions:

For Ne+ ions, elastic collisions with Ne atoms and O2 molecules are taken into
account. In case of Ne+ \+ Ne collisions, an isotropic channel (process 29)
and a backward scattering channel (process 30) is considered and the cross
sections are taken from [62] in the functional forms
$\sigma_{29}(\varepsilon_{\rm com})=1.06\cdot 10^{-19}\varepsilon_{\rm
com}^{-0.5}$ m2 and $\sigma_{30}(\varepsilon_{\rm com})=2.8\cdot
10^{-19}\varepsilon_{\rm com}^{-0.15}(1+0.8/\varepsilon_{\rm com})^{-0.3}$ m2,
where $\varepsilon_{\rm com}$ is the value of the kinetic energy in the
ion–atom center-of-mass reference frame in units of eV.

As Ne+ \+ O2 collisions, charge transfer (process 31) and isotropic elastic
scattering (process 32) are included in the model. Process 31 is a non-
resonant charge transfer reaction that is possible as the ionization potential
of Ne is higher than that of O2. The rate coefficient of this reaction at
thermal energies was reported in [63]. Schlumbohm [66] reported a measurement
of this cross section in the energy range of 3-200 eV, and found it to be
between 3.5 $\times 10^{-20}$ m2 and 4 $\times 10^{-20}$ m2. We use a cross
section of constant 3.7$\times 10^{-20}$ m2 for this process. Process 32 is
treated with its Langevin cross section:

$\sigma_{\rm L}=\sqrt{\frac{\alpha\pi
e^{2}}{\epsilon_{0}\mu}}\frac{1}{g}=\sqrt{\frac{\alpha\pi
e}{2\epsilon_{0}}}\varepsilon_{\rm com}^{-1/2},$ (1)

where $\mu$ is the reduced mass, $g$ is the relative velocity and
$\varepsilon_{\rm com}$ is kinetic energy in the centre-of-mass frame in units
of eV. The polarizibility values are: $\alpha$(O2) = 1.562 $\times~{}10^{-30}$
m3 and $\alpha$(Ne) = 0.381 $\times~{}10^{-30}$ m3 [67]. The cross sections of
the collision processes used for Ne+ ions are shown in figure 3(a).

The $\rm{O_{2}^{+}}$ \+ $\rm{O_{2}}$ collisions can result in charge exchange
or isotropic elastic scattering (processes 33 and 34, respectively). The cross
sections for these processes are taken from Gudmundsson’s work [61]. Between
O${}_{2}^{+}$ ions and Ne atoms isotropic elastic scattering (process 35) is
considered. Similarly to process 32, this process is treated with its Langevin
cross section. The cross sections of the collision processes used for
$\rm{O_{2}^{+}}$ ions are included in figure 3(a).

For $\rm{O^{-}}$ \+ $\rm{O_{2}}$ collisions elastic scattering (process 36)
and detachment (process 37) are considered. Mutual neutralization of
$\rm{O^{-}}$ and $\rm{O_{2}^{+}}$ ions (process 38) and associative detachment
between $\rm{O^{-}}$ ions and $\rm{O_{2}(a^{1}\Delta_{g})}$ singlet delta
oxygen molecules (process 39) are also included in the model. The metastable
$\rm{O_{2}(a^{1}\Delta_{g})}$ singlet delta oxygen molecules are not traced in
the simulation, however, their density is calculated self-consistently based
on the balance of their creation, de-excitation, and diffusive transport as
discussed in section 3.4 below. The cross sections of processes 36–38 are from
[61], for process 39 the cross section is taken from [65]. As “cross-process”
between O- ions and Ne species, isotropic elastic scattering with Ne atoms
(process 40) and mutual neutralisation with Ne+ ions (process 41) is
considered. Process 40 is treated with its Langevin cross section. Process 41
is treated in a similar way as the mutual neutralisation O- \+ O${}_{2}^{+}$
$\longrightarrow$ O + O2 (process 38). Due to the lack of cross section data
for O- \+ Ne+ $\longrightarrow$ O + Ne neutralization, we use the same cross
section for process 41 as that used for process 38. The cross sections of the
collision processes used for $\rm{O^{-}}$ ions are plotted in figure 3(b).

#### Fast neutral collisions:

Figure 4: Cross sections of the collision processes for fast Ne atoms (Nef)
and fast O2 molecules (O${}_{2}^{\rm f}$), listed in table 1 (processes
42–45), as a function of the kinetic energy (considered in the center-of-mass
frame) of the projectile: elastic scattering between Nef and Ne atoms/O2
molecules (process 42/44) and elastic scattering between O${}_{2}^{\rm f}$ and
O2 molecules/Ne atoms (process 43/45). Note, that the cross section of
processes 44 and 45 are the same (see text).

A background gas atom or molecule acquiring a kinetic energy greater than a
threshold energy of $E_{\rm thr}=9\cdot\tfrac{3}{2}k_{\rm B}T$ after a
collision is considered to be a fast neutral, and is traced in the simulation
until its energy drops below $E_{\rm thr}$. Thermalization of fast neutrals
due to collisions with atoms/molecules of the background gas contributes to
the heating of the gas (see section 3.3). Elastic collisions of fast Ne atoms
(Nef) and fast O2 molecules (O${}_{2}^{\rm f}$) with background O2 molecules
and Ne atoms (processes 42–45) are considered in the model in the following
way: (i) the scattering cross sections are derived from $\sigma_{\rm V}$, the
viscosity cross section and (ii) isotropic scattering in the COM frame is
assumed. As reliable cross section data for Nef and O${}_{2}^{\rm f}$ for
neon-oxygen mixture are not available in the literature, the cross sections
are calculated for processes 42–45 based on the pair-potential between the
particles, for which the Lennard-Jones (LJ) type is assumed:

$\phi(r)=4\epsilon_{\rm LJ}\biggl{[}\biggl{(}\frac{r}{\sigma_{\rm
LJ}}\biggr{)}^{-12}-\biggl{(}\frac{r}{\sigma_{\rm
LJ}}\biggr{)}^{-6}\biggr{]},$ (2)

where the energy $\epsilon_{\rm LJ}$ and the characteristic length
$\sigma_{\rm LJ}$ can be found in tables, e.g. in [68]. The calculation of the
cross section starts with computing the scattering angle $\chi$ as a function
of the impact parameter $b$. This is done as described in [69]. Having
obtained the $\chi(b)$ function for a given LJ potential, the viscosity cross
section is computed as [70]:

$\sigma_{\rm V}=\int_{0}^{\infty}\sin^{2}(\chi)b~{}{\rm d}b.$ (3)

The $\chi(b)$ function is computed for a set of energies (in the COM frame)
and the above integral is evaluated for all these energy values, resulting in
the energy-dependent elastic scattering cross section $\sigma_{\rm
fast}(\varepsilon)=\frac{3}{2}\sigma_{\rm V}(\varepsilon)$. To obtain the LJ
parameters for the Ne–O2 ”cross collisions”, the Lorentz-Berthelot combining
rule is used [71]:

$\displaystyle\sigma_{\rm LJ}^{ab}=\frac{\sigma_{\rm LJ}^{aa}+\sigma_{\rm
LJ}^{bb}}{2},$ (4) $\displaystyle\epsilon_{\rm LJ}^{ab}=\sqrt{\epsilon_{\rm
LJ}^{aa}\,\epsilon_{\rm LJ}^{bb}},$ (5)

where $a$ and $b$ denote the interacting species. The $a\leftrightarrow b$
symmetry of these equations results in the same cross sections for Nef+O2 and
O${}_{2}^{\rm f}$+Ne collisions. These computed cross sections (for processes
42–45) are plotted in figure 4. The calculation of the cross sections of fast
neutrals was validated by comparing our results for argon gas with those given
in [70].

###  3.2 Surface processes

The surface processes taken into account in the discharge model are electron
reflection, secondary electron emission (SEE) induced by O${}_{2}^{+}$ ions
and Ne+ ions, and surface quenching of $\rm{O_{2}(a^{1}\Delta_{g})}$
metastable molecules. Constant surface coefficients are specified for these
processes. At the electrode surfaces, electrons are elastically reflected with
a probability of $\eta_{\rm{e}}=0.7$. This value is adopted based on the
findings of Schulenberg _et al._ [53]. For O${}_{2}^{+}$ ions, a SEE
coefficient of 0.015 is considered, while for Ne+ ions the SEE coefficient is
set to 0.1 [72]. The value of the surface quenching probability (surface
destruction probability), which controls the loss rate of
$\rm{O_{2}(a^{1}\Delta_{g})}$ metastable molecules, is set to $\alpha=8\cdot
10^{-4}$ in this study (see discussion in section 3.4).

###  3.3 Gas heating

The collision frequency of elementary processes is strongly dependent on the
local gas temperature (through the dependence on the background gas density).
In order to cover the wide range of discharge parameters properly, gas heating
needs to be included in the model. The coupling of the input RF electric power
to the gas heating is realised by two processes: (i) in the gas phase, ions
are accelerated by the electric field and energy is transferred to the
background gas atoms/molecules through collisions, mediated by fast neutrals,
and (ii) at the surfaces, the flux of particles interacting with the
electrodes causes them to heat up.

#### Heat transfer:

The thermal power density, $P(x)$, accumulates the excess energy transferred
to the background gas, originating from the particles accelerated by the
electric field, per unit time and volume [73]. It acts as the source term in
the steady-state heat equation, that is included in the model to calculate the
equilibrium temperature distribution in the discharge gap:

$\frac{\partial^{2}T_{\text{gas}}(x)}{\partial x^{2}}=-\frac{1}{\kappa}P(x),$
(6)

were $\kappa$ is the thermal conductivity specific to the gas mixture.

Analogously to the linear particle shape function in the PIC method, if a
collision with the background gas happens within the $i$-th grid cell, it
contributes to $P(x)$ at the neighbouring grid points in the following way:

$\displaystyle{\rm d}P_{i}$ $\displaystyle=$ $\displaystyle\frac{\Delta
E}{A\Delta x\Delta t_{\rm{H}}}\left((i+1)-\frac{x}{\Delta x}\right),$ (7)
$\displaystyle{\rm d}P_{i+1}$ $\displaystyle=$ $\displaystyle\frac{\Delta
E}{A\Delta x\Delta t_{\rm{H}}}\left(\frac{x}{\Delta x}-i\right),$

where $A$ is the surface of the electrodes, $\Delta x$ is the length of the
grid cell normal to the electrodes, and $\Delta t_{\rm{H}}$ is the time of
data collection (several RF cycles). $\Delta E$ is the energy gain of a
background gas atom/molecule due to the collision. Collisions of ions, as well
as fast neutrals with the background gas, contribute to $P(x)$. When
thermalized, the neutrals deposit all their energy to the $P(x)$ thermal
power.

#### Boundary condition:

In order to solve eq. (6), the boundary values of the temperature distribution
have to be defined. In regimes with Knudsen number (Kn) close but below unity
the “slip flow” approximation can be applied [74]. The Knudsen number is
defined as $\text{Kn}=l/\Lambda$, where $l$ is the molecular mean free path
and $\Lambda$ is the characteristic size of the system, i.e. the length of the
discharge gap in our case. The resulting boundary condition is of the third
kind, introducing a temperature jump at the electrodes as described in [75,
76]:

$T_{\text{gas}}(x=0/L)=T_{\rm wall}+\lambda\left|\frac{\partial
T_{\text{gas}}}{\partial x}\right|_{x=0/L},$ (8)

where $T_{\rm wall}$ is the temperature of the walls (i.e. the electrodes).
$\lambda$ is called the temperature jump distance, and is proportional to the
mean free path perpendicular to the electrodes, and it depends on the gas
mixture. For further details see [75]. Note that eq. (8) imposes conditions on
the slope of the temperature distribution at the boundaries. To satisfy these,
the following iterative method is used: (i) Initially the temperature jump is
neglected and wall temperatures ($T_{\rm wall}$) are used as boundary values
for the Thomas algorithm which solves eq. (6). (ii) Since the resulting
temperature distribution does not satisfy eq. (8), the right hand side of eq.
(8) is set as new boundary values to solve eq. (6) again. (iii) Step (ii) is
repeated until condition (8) is fulfilled within pre-defined tolerance limits.
The convergence of this method was demonstrated in [75].

Figure 5: Simplified geometry assumed in the model for heat convection at the
electrodes, showing the relevant quantities and a sketch of the temperature
profile.

#### Heat convection at the electrodes:

The heating of the electrode surfaces is caused by inelastic collisions of
plasma particles with the electrodes. In order to accurately describe the
experimental system, this change of wall (electrode) temperature must be
accounted for in the gas heating module, as it enters directly in eq. (8). The
equilibrium wall temperature is determined by the balance of heat influx at
the plasma side, thermal conduction of the electrode assembly, and heat
dissipation to the environment at the outer surface of the system. In our
calculations, we consider a simplified geometry of the electrode arrangement,
as compared to the experimental realisation (consisting of the electrodes,
spacers, and flanges), which is shown in figure 5. This simplification is
permissible because of the use of a calibration procedure for the effective
heat conductivity of the setting, to be revealed below. Let $\dot{q}_{0}$
denote the heat flux originating from the discharge reaching the electrode and
$T_{\infty}$ the room temperature. $k$ and $L_{\rm e}$ are the thermal
conductivity and the width of the electrode, respectively. $h$ is the
convection heat transfer coefficient of air. For the model system of figure 5,
the steady-state homogeneous heat equation inside the electrode and its
boundary conditions read:

$\displaystyle\frac{\text{d}^{2}T_{\text{elec.}}(x)}{\text{d}x^{2}}$
$\displaystyle=$ $\displaystyle 0{\rm~{}~{}~{}~{}for~{}}0<x<L_{\rm e},$ (9)
$\displaystyle-k\frac{\text{d}T_{\text{elec.}}(0)}{\text{d}x}$
$\displaystyle=$ $\displaystyle\dot{q_{0}},$ (10)
$\displaystyle-k\frac{\text{d}T_{\text{elec.}}(L_{\rm e})}{\text{d}x}$
$\displaystyle=$ $\displaystyle h\left[T_{\text{elec.}}(L_{\rm
e})-T_{\infty}\right],$ (11)

where $x=0$ represents the plasma side and $x=L_{\rm e}$ the external surface
of the electrode assembly. Eqs. (10) and (11) are boundary conditions for
boundaries at point 1. and 2. in figure 5. The solution of eq. (9) yields the
wall temperature in terms of the heat flux from the plasma, assuming equal
$\dot{q}_{0}$, $k$, and $L_{\rm e}$ values for both electrodes:

$T_{\text{wall}}=T_{\text{elec.}}(0)=T_{\infty}+\dot{q}_{0}\left(\frac{L_{\rm
e}}{k}+\frac{1}{h}\right).$ (12)

The value of $\dot{q}_{0}$ could, in principle, be calculated tracing
individual particle–surface interactions, however, an even simpler and more
precise estimation can be achieved by assuming that, in equilibrium, all
electric power absorbed by the plasma (charged plasma particles only) from the
RF field becomes finally absorbed by the electrodes and is dissipated in form
of heat. This means that the heat flux reaching one electrode is the time
average ($\langle...\rangle$) of the half of the total electrical input power
per unit area:

$\dot{q}_{0}=\frac{1}{2A}\left<\sum_{i}q_{i}W_{i}({\bf E}_{i}\cdot{\bf
v}_{i})\right>,$ (13)

where the sum runs over all charged particles $i$ with charge $q_{i}$, weight
factor $W_{i}$, velocity ${\bf v}_{i}$ and electric field at the particles’
position ${\bf E}_{i}$. Having calculated this quantity, the wall temperature
can readily be obtained from eq. (12), if $(L_{\rm e}/k+1/h)$ is known. While
this factor (that consists of three components, each characterizing different
aspects of the overall heat dissipation) could be approximated based on the
exact dimensions and material properties of the electrode constructions, we
have chosen an alternative way to determine it, using a calibration technique.
Tunable diode laser absorption spectroscopy (TDLAS) measurements were
performed in pure Ar discharges in the same experimental system. The details
of this technique are described in [53]. The measured gas temperature was then
compared with PIC/MCC results obtained for different values of the $(L_{\rm
e}/k+1/h)$ coefficient, and its value giving the best agreement was determined
and used throughout this study.

###  3.4 Oxygen metastable balance

Previous studies on oxygen CCPs have shown that at low pressures the discharge
contains more O- ions than electrons, thus it is electronegative [48, 46, 50],
which is quantified by the global parameter $\beta=\langle n_{\rm
O^{-}}\rangle/\langle n_{\rm e}\rangle$, i.e., the global electronegativity of
the discharge. The O- ion density is determined by the balance of its creation
(by means of electron impact dissociative attachment of ${\rm O_{2}}$
molecules, process 20 in table 1) and the primary loss in the gas phase due to
associative detachment in collisions with ${\rm O_{2}(a^{1}\Delta_{g})}$
metastable molecules (process 39 in table 1). In order to accurately compute
the O- ion density distribution, it is important to determine the density of
the ${\rm O_{2}(a^{1}\Delta_{g})}$ metastable species self-consistently. This
is done by modeling the balance of creation, transport, and surface de-
excitation of the ${\rm O_{2}(a^{1}\Delta_{g})}$ molecules, which are
incorporated as continuum species, described by the stationary diffusion
equation

$D\frac{\partial^{2}n_{\rm m}(x)}{\partial x^{2}}=S_{\rm m}(x),$ (14)

where $D$ is the diffusion coefficient, $n_{\rm m}(x)$ and $S_{\rm m}(x)$ are
the density and time averaged (over several RF cycles) source rate
distributions of the ${\rm O_{2}(a^{1}\Delta_{g})}$ metastables. Like in the
gas temperature calculation module, here we aim only for the stationary
solution of the transport equation and assume that it does not depend on the
actual time-evolution, which, on the other hand, can be significantly slower
than the relaxation of other plasma parameters. The source term in eq. (14) is
calculated analogously to the thermal power input in eq. (7) but with the
microscopic contribution of process 18 in table 1 for every electron in each
time step. The contribution of gas phase losses of metastables (through
processes 39 in table 1) is not considered in the metastable density balance
calculation. The validity of this simplification is supported by the collision
statistical analysis, showing that the average probability of associative
detachment is $<1$% of the probability of metastable excitation for all
conditions.

To obtain proper pressure, temperature, and gas composition dependent
diffusion coefficients we utilize the predictions of the Chapman-Enskog theory
[77, 78], resulting in the general form

$D\approx D_{0}\frac{p_{0}}{p}\left(\frac{T}{T_{0}}\right)^{3/2},$ (15)

where $D_{0}$ is the gas composition dependent diffusion coefficient at a
reference pressure $p_{0}=1$ Pa and reference temperature $T_{0}=300$ K. The
values of $D_{0}$ for O2 molecules in pure O2 and Ne gases are estimated as
$D_{0}^{\rm O_{2}}=2.07~{}{\rm m}^{2}/{\rm s}$ and $D_{0}^{\rm Ne}=3.29~{}{\rm
m}^{2}/{\rm s}$. Values for arbitrary mixing ratios are calculated by linear
interpolation between these two extremes.

The dominant loss process of ${\rm O_{2}(a^{1}\Delta_{g})}$ metastables is the
de-excitation at the electrodes, which is incorporated in the boundary
conditions. Similarly to the gas heating calculation, due to the low pressure
condition, where the collision mean free path is comparable to the
characteristic size of the system, the boundary condition is of the third
kind, relating the boundary value with its gradient as

$\frac{n_{\rm m}(x=0/L)}{\kappa}=\left|\frac{\partial n_{\rm m}}{\partial
x}\right|_{x=0/L},$ (16)

with $\kappa=l(2-\alpha)/(\sqrt{3}\alpha)$, where $l$ is the collision mean
free path of O2 molecules, and $\alpha=8\cdot 10^{-4}$ is the surface
destruction (de-excitation or quenching) probability. The mean free path is
calculated from the diffusion coefficient using the formula derived from the
kinetic theory of gases [79]

$l=\frac{4}{\sqrt{3\pi}}\left(\frac{m}{3k_{\rm B}T}\right)^{1/2}D.$ (17)

With all terms evaluated eq. (14) is solved using the Thomas tridiagonal
algorithm, the metastable density values at the boundaries $n_{\rm m}(x=0/L)$
are adjusted, and the solution is iterated until the boundary conditions (16)
are met.

###  3.5 Electron power absorption

The characteristics of the electron power absorption have been investigated
using the Boltzmann term method. This method, which provides spatio-temporally
resolved information about the electric field and the power absorbed by the
electrons, has been thoroughly described in earlier works [80, 50, 56].
Therefore, here only a short overview is given. The Boltzmann term analysis is
based on the electron momentum balance equation, which can be rearranged for
the electric field, which then can be divided into various terms, given by
$E_{\rm tot}=E_{\rm in}+E_{\nabla p}+E_{\rm Ohm}$ [56], where

$\displaystyle E_{\rm in}$ $\displaystyle=-\frac{m_{\rm e}}{n_{\rm
e}e}\left[\frac{\partial}{\partial t}(n_{\rm e}u_{\rm
e})+\frac{\partial}{\partial x}(n_{\rm e}u_{\rm e}^{2})\right],$
$\displaystyle E_{\nabla p}$ $\displaystyle=-\frac{1}{n_{\rm
e}e}\frac{\partial}{\partial x}p_{\parallel},$ $\displaystyle E_{\rm Ohm}$
$\displaystyle=-\frac{\Pi_{\rm c}}{n_{\rm e}e}.$ (18)

Here $m_{\rm e}$ and $e$ are the electron mass and charge, respectively,
$n_{\rm e}$ is the electron density, $u_{\rm e}$ is the mean velocity,
$\Pi_{\rm c}$ is the electron momentum loss and $p_{\parallel}$ denotes the
diagonal element of the pressure tensor. Each of these electric field terms
corresponds to a distinct physical mechanism: $E_{\rm in}$ is the electric
field term originating from inertial effects; $E_{\rm Ohm}$, the Ohmic
electric field, is a consequence of electrons colliding with the particles of
the background gas, and $E_{\nabla p}$ is due to pressure effects. This
electric field term can be split into two additional terms, according to
$E_{\nabla p}=E_{\nabla n}+E_{\nabla T}$, where

$\displaystyle E_{\nabla n}$ $\displaystyle=-\frac{T_{\parallel}}{n_{\rm
e}e}\frac{\partial n_{\rm e}}{\partial x},$ $\displaystyle E_{\nabla T}$
$\displaystyle=-\frac{1}{e}\frac{\partial T_{\parallel}}{\partial x},$ (19)

where $T_{\parallel}=p_{\parallel}/n_{\rm e}$ is the parallel electron
temperature. $E_{\nabla n}$ is, in regions where quasineutrality holds,
identical to the “classical ambipolar” electric field [81] and $E_{\nabla T}$
originates from the spatial gradient of the electron temperature. From the
electric field terms the corresponding power absorption terms can be easily
calculated by multiplying each of these terms with the spatio-temporally
resolved electron conduction current density, $j_{\rm c}$.

###  3.6 Simulation parameters

Table 2 lists the most important physical and numerical parameters of the
simulations grouped according to the gas pressure. The physical parameters
were chosen to cover a low to intermediate pressure regime and a wide mixing
range. The numerical parameters were chosen to ensure the fulfillment of the
usual stability and accuracy requirements imposed on the explicit
electrostatic PIC/MCC scheme. For a recent detailed discussion on these
criteria and the effect of different numerical parameters on the simulation
results see e.g. [82].

Table 2: Physical and numerical parameters of the discharges studied.

Physical parameters: |  |  |  |  |  |
---|---|---|---|---|---|---
gas pressure | $p$ | 15 Pa | 31 Pa | 62 Pa | 125 Pa | 250 Pa | 500 Pa
O2 concentration range | [%] | 50–90 | 10–90 | 10–90 | 10–90 | 10–90 | 10–70
electrode separation | $L$ | 2.5 cm
environment temperature | $T_{\infty}$ | 295 K
peak-to-peak voltage | $V_{\rm pp}$ | 350 V
frequency | $f$ | 10 MHz ($T_{\rm RF}=1/f=100$ ns)
Numerical parameters: |  |  |  |  |  |
cell size | $\Delta x$ | $L/511$
nominal electrode area | $A$ | 1 cm2
time step size | $\Delta t$ | $T_{\rm RF}/6000$ | $T_{\rm RF}/6000$ | $T_{\rm RF}/8000$ | $T_{\rm RF}/12000$ | $T_{\rm RF}/20000$ | $T_{\rm RF}/30000$
electron & Ne+ ion weight factor | $W_{\rm e}$ | 1 500 | 2 500 | 4 000 | 4 000 | 8 000 | 10 000
O${}_{2}^{+}$ & O- ion weight factor | $W_{\rm O}$ | 60 000 | 50 000 | 40 000 | 40 000 | 64 000 | 50 000
O${}_{2}^{\rm f}$ molecule weight factor | $W_{\rm O_{2}^{f}}$ | 120 000 | 75 000 | 40 000 | 12 000 | 8 000 | 50 000
Nef atom weight factor | $W_{\rm Ne^{f}}$ | 60 000 | 20 000 | 12 000 | 4 000 | 8 000 | 10 000

Further parameters specific to surface processes, heat conductivity, and
metastable molecule diffusion are introduced in the previous sections.

##  4 Results and discussion

###  4.1 Experimental results

Figure 6: Spatio-temporal plots of the electron impact excitation rate from
the ground state into the Ne $\rm{3p_{0}}$ state measured by PROES [a.u.] in
Ne-O2 CCPs at different neutral gas pressures: 15 Pa (first row), 31 Pa
(second row), 62 Pa (third row), 125 Pa (fourth row), 250 Pa (fifth row) and
500 Pa (sixth row), for different neon/oxygen concentration of the background
gas mixture: 10% Ne–90% O2 (first column), 30% Ne–70% O2 (second column), 50%
Ne–50% O2 (third column), 70% Ne–30% O2 (fourth column), 90% Ne–10% O2 (fifth
column). The powered electrode is located at $x/L=0$, while the grounded
electrode is at $x/L=1$. The labels I.-VI. in panels (b1) and (b5) indicate
the different excitation features explained in the text. Discharge conditions:
$L=2.5$ cm, $f=10$ MHz, $V_{\rm{pp}}=350$ V.

Figure 6 shows the spatio-temporal distribution of the electron impact
excitation rate from the ground state into the Ne $\rm{3p_{0}}$ state measured
by PROES at six different pressures: 15 Pa (first row), 31 Pa (second row), 62
Pa (third row), 125 Pa (fourth row), 250 Pa (fifth row) and 500 Pa (sixth
row). At a given pressure (panels in a given row), results obtained for
different neon/oxygen concentration of the background gas mixture (with
decreasing O2 concentration in panels from left to right) are shown: 10%
Ne–90% O2 (first column), 30% Ne–70% O2 (second column), 50% Ne–50% O2 (third
column), 70% Ne–30% O2 (fourth column), 90% Ne–10% O2 (fifth column). All
panels of figure 6 cover one RF period on the horizontal axes, and the
vertical axes show the distance from the powered electrode.

At the lowest pressure of 15 Pa (first row), excitation at both the expanding
and the collapsing sheath edges can be observed, as well as in the bulk
region. The strongest excitation is found at the bulk side of the collapsing
sheath edge at both electrodes. At this pressure, measurements have been
performed for O2 concentrations between 50% and 90% in the background gas
mixture. For all cases, the spatio-temporal distribution of the excitation
rate exhibits similar patterns (panels (a1)–(c1)), independently of the Ne/O2
mixing ratio, suggesting hybrid $\alpha$-DA discharge operation mode (with
dominant electron power absorption and excitation due to the DA-mode). The
main excitation patterns observed at this pressure are labeled in panel (b1):
I. indicates the excitation peak at the expanding sheath edge ($\alpha$-peak),
II. denotes the excitation in the central bulk region (drift feature), and
III. signals the excitation at the collapsing sheath edge (ambipolar peak).

At 31 Pa (second row), for O2 concentrations decreasing from 90% to 30%
(panels (a2)-(d2)), strong excitation at the expanding sheath edge
($\alpha$-peak, I.) and significant excitation in the bulk region (drift
feature, II.) with a weak excitation peak at the collapsing sheath edge
(ambipolar peak, III.) are found, suggesting a hybrid $\alpha$-DA discharge
operation mode (with dominant $\alpha$-mode). By decreasing the O2
concentration at this pressure, the $\alpha$-peak (I.) at the expanding sheath
edge is enhanced. At the lowest O2 concentration of 10%, the ambipolar peak
(III.) at the collapsing sheath edge vanishes and the excitation plot suggests
discharge operation in pure $\alpha$-mode (see panel (e2)).

At 62 Pa (third row), the excitation is concentrated at the expanding sheath
edges, a strong $\alpha$-peak (I.) is exhibited, suggesting a dominant
$\alpha$-mode for all Ne-O2 mixtures. Weak excitation in the bulk region
(drift feature, II.) is visible only in the case of the highest O2
concentration (see panel (a3)).

At 125 Pa (fourth row), similarly to the results obtained at 62 Pa, strong
$\alpha$ excitation peaks (I.) at the expanding sheath edges can be observed
for all Ne-O2 mixtures. At this pressure, excitation in the bulk region (drift
feature, II.) is also present, for O2 concentrations above 50% (see panels
(a4)-(c4)). By increasing the O2 concentration in the mixture, the excitation
in the bulk gets more and more pronounced.

At 250 Pa (fifth row), the excitation at the expanding sheath edges
($\alpha$-peak, I.) is present for all Ne-O2 mixtures. Up to 50% O2
concentration this is the dominant excitation pattern (see panels (c5)-(e5)).
Starting from 50% O2 concentration, the excitation in the bulk region is
enhanced with the increasing O2 content of the mixture (see panels (a5)-(c5)),
and two distinct excitation peaks develop in the bulk. For 10% Ne–90% O2
(panel (a5)) and 30% Ne–70% O2 (panel (b5)), the strongest excitation can be
observed in these patterns, labeled as IV. and V. in panel (b5), in the bulk
region. At the highest O2 concentration, the excitation is dominated by these
new features (panel (a5)), which are different from the excitation patterns
characteristic of the DA-mode. At 250 Pa pressure, at high O2 concentrations,
at both electrodes, there are two distinct excitation peaks (I. and V.) close
to each other at the bulk side of the expanding sheath edge and one excitation
peak (IV.) at the collapsing sheath edge. Under these conditions, the spatio-
temporal distribution of the electron impact excitation rate to the Ne
$\rm{3p_{0}}$ state indicates the presence of the $\alpha$-mode in combination
with some electron power absorption dynamics resulting in the formation of the
two bulk excitation patterns (IV. and V.), the origin of which will be
clarified later. For high O2 concentrations, weak excitation at the phase of
maximum sheath expansion at both electrodes can be also observed (see panels
(a5) and (b5)), which suggests the presence of the $\gamma$-mode. The
corresponding excitation pattern is labeled as VI. in panel (b5).

At the highest pressure of 500 Pa (sixth row), measurements have been carried
out for up to 70% O2 concentration. At the lowest O2 concentration of 10%, a
single excitation peak is seen at both electrodes at the expanding sheath edge
($\alpha$-peak, I.), indicating discharge operation in pure $\alpha$-mode
(panel (e6)). Excitation in the bulk and development of two additional
excitation peaks (IV. and V.) is visible starting from 30% O2 concentration
(see panels (b6)-(d6)). Compared to the 250 Pa case, at this high pressure,
the development of patterns IV. and V. starts at a lower O2 concentration (30%
vs. 50% at 250 Pa). These two excitation patterns are intensified as the O2
concentration is increased, clearly dominating the excitation at 70% and 50%
O2 concentrations (panels (b6) and (d6)), while only weak excitation in the
close vicinity of the expanding sheath edge ($\alpha$-peak, I.) can be
observed in these cases.

The observed mode transitions as a function of the pressure and O2 admixture
are related to changes of the electronegativity of the discharge, which will
be discussed in detail later based on the simulation results.

In summary, at the lowest pressure, weak $\alpha$-peak, strong ambipolar peak,
and weak drift features are found in the excitation rate. With increasing
pressure, the $\alpha$-peak and the drift feature are enhanced, while the
ambipolar peak is reduced. At intermediate pressures, the $\alpha$-peak is the
dominant excitation pattern in all mixtures. Further increase of the pressure
leads to the formation of two distinct excitation peaks at the edges of the
bulk region, which dominate the excitation at high O2 concentrations. At the
highest pressure, these excitation peaks are enhanced and the development of
these features is found also in mixtures with lower O2 concentration.

###  4.2 Simulation results

In order to reveal the physics behind the formation of the different
excitation patterns observed experimentally by PROES in the wide pressure
range and gas mixing range presented above, especially those found at high
pressures and high O2 concentrations in the bulk region, PIC/MCC simulations
have been performed. The PIC/MCC simulations covered the whole parameter
regime studied by PROES, i.e. pressures between 15 Pa and 500 Pa, and Ne/O2
concentrations between 10% and 90%, at 10 MHz and 350 V peak-to-peak voltage.

Figure 7: Time averaged particle density distributions obtained for different
pressures and neon/oxygen concentrations of the background gas mixture: (a) 15
Pa, 30% Ne–70% O2, (b) 31 Pa, 30% Ne–70% O2, (c) 500 Pa, 30% Ne–70% O2, and
(d) 500 Pa, 90% Ne–10% O2. Discharge conditions: $L=2.5$ cm, $f=10$ MHz,
$V_{\rm{pp}}=350$ V. Figure 8: (a) Time averaged ratio of the negative ion
(O-) density and electron density (local electronegativity, $\beta(x)$) for
different pressures and neon/oxygen concentrations of the background gas
mixture (for the same discharge conditions as those in figure 7). (b) Global
electronegativity of the discharge, $\beta$ as a function of pressure for
different neon/oxygen concentrations of the background gas mixture. Discharge
conditions: $L=2.5$ cm, $f=10$ MHz, $V_{\rm{pp}}=350$ V. Figure 9: Time
averaged $\rm{O_{2}(a^{1}\Delta_{g})}$ singlet delta oxygen metastable
molecule concentration obtained for 30% Ne–70% O2 gas mixture at different
pressures. Discharge conditions: $L=2.5$ cm, $f=10$ MHz, $V_{\rm{pp}}=350$ V.

Figure 7 shows PIC/MCC simulation results on the time averaged density
distributions of charged particles and fast neutrals traced in the simulations
for exemplary cases from the wide parameter regime. Panels of figure 7 show
results obtained for different neutral gas pressures and different neon/oxygen
concentration of the background gas mixture: (a) 15 Pa, 30% Ne–70% O2, (b) 31
Pa, 30% Ne–70% O2, (c) 500 Pa, 30% Ne–70% O2, and (d) 500 Pa, 90% Ne–10% O2.
(Note that the PROES results corresponding to these cases are shown in panels
(b1), (b2), (b6), and (e6) of figure 6, respectively.) At 15 Pa, 30% Ne–70% O2
mixture (panel (a)), the time averaged electron density exhibits local maxima
at the edges of the narrow bulk region, and it is significantly lower than the
density of negative O- ions in the bulk. The electronegativity is very high in
the discharge center, the ratio of the negative ion density and electron
density is about 100 (figure 8(a)). The global electronegativity (the ratio of
the density of negative ions and electrons averaged over the electrode gap) is
about 30 under these conditions (see figure 8(b)). The density of Ne+ ions is
about three orders of magnitude lower than the density of O${}_{2}^{+}$ ions
in the discharge center and the density of fast neutral species is high over
the whole discharge gap. In this gas mixture, local maxima in the time
averaged electron density distribution at the edges of the bulk region and the
high negative ion density in the bulk are found also at a higher pressure of
31 Pa (panel (b)). However, at 31 Pa the electron density is enhanced in the
discharge center compared to the 15 Pa case, while the density of Ne+ ions, as
well as the density of fast neutrals, decreases in the bulk. The
electronegativity is maximum in the discharge center (figure 8(a)), the global
electronegativity of the discharge is about 25 (figure 8(b)). By increasing
the pressure to 500 Pa for the 30% Ne–70% O2 mixture (panel (c)), the time
averaged electron density exhibits its maximum in the discharge center and
local minima at the bulk edges. The density of Ne+ ions as well as the density
of fast neutrals drops in the bulk. The bulk region is wide at this high
pressure. The O- density profile has a local minimum in the discharge center
and local maxima near the edges of the bulk region. Consequently, the
electronegativity has a local minimum in the center and local maxima at the
bulk-sheath boundary (figure 8(a)). In the discharge center, the density of
negative ions is about one order of magnitude higher than the electron
density. The global electronegativity is about 8 under these conditions
(figure 8(b)). By decreasing the O2 concentration in the mixture to 10% at
this high pressure (figure 7(d)), the density of electrons increases, while
the O- density remains high in the bulk region. The O- density is about four
times higher than the electron density in the discharge center. The global
electronegativity has a low value of about 2 under these conditions, i.e. the
discharge remains electronegative also in case of the lowest O2 concentration
of 10% in the mixture. As it can be seen in figure 8(b), the global
electronegativity decreases with increasing the pressure in all mixtures. For
O2 concentrations above 30% the electronegativity does not depend on the Ne/O2
concentration ratio in the background gas mixture.

The simulation results show that the self-consistently calculated density of
singlet delta oxygen metastable molecules increases with the pressure.
However, the $\rm{O_{2}(a^{1}\Delta_{g})}$ density remains low in all cases,
below 3% of the density of background O2 molecules. Figure 9 shows the time
averaged density distribution of $\rm{O_{2}(a^{1}\Delta_{g})}$ molecules in
the gap as a function of pressure for 30% Ne–70% O2 gas mixture. At low
pressures, the metastable density profiles are flat, while at high pressures,
profiles with peak metastable density in the center of the discharge are
obtained. This is due to the pressure dependence of the diffusion coefficient
(see eq. 14, at high pressure the diffusion slows down).

Figure 10: (a) Wall temperature, $T_{\rm wall}$ as a function of pressure for
different Ne-O2 concentrations of the background gas mixture. (b) Spatial
distribution of the gas temperature with respect to the wall temperature
(solid lines; left vertical axis), and spatial distribution of the thermal
power input density, $P(x)$ (dashed lines; right vertical axis) for three
different pressure values in case of 30% Ne–70% O2 gas mixture. Discharge
conditions: $L=2.5$ cm, $f=10$ MHz, $V_{\rm{pp}}=350$ V.

The change of the wall temperature as a function of pressure for various Ne/O2
concentrations of the background gas mixture is shown in figure 10(a). The
wall temperature, $T_{\rm wall}$, increases significantly compared to the
initial wall temperature (which was set to 300 K in the simulations) with
increasing the pressure. At a given pressure, $T_{\rm wall}$ decreases with
decreasing the O2 content in the gas mixture. This is due to the different
efficiency of the power absorption of Ne and O2 at identical discharge
conditions. In panel (b) of figure 10 the spatial distribution of the gas
temperature with respect to the wall temperature (left vertical axis) and the
power input field (right vertical axis) are shown at three different pressures
for the 30% Ne–70% O2 case. The temperature profiles show the maximum gas
temperature in the discharge center at all pressures, which is only slightly
higher than the temperature of the electrodes. Compared to the wall
temperature, an increase by only about 1.5 K in the discharge center is found
at the highest pressure. The simulations revealed that at the low electrical
power levels of the present setup, being only a few Watts, the increased
temperature of the gas is mainly due to the increased temperature of the
electrodes, and the gas temperature does not significantly change within the
gap.

Figure 11: Spatio-temporal plots of the electron-impact excitation rate [a.u.]
from the ground state into the Ne $\rm{3p_{0}}$ state obtained from PIC/MCC
simulations of in Ne-O2 CCPs at different neutral gas pressures: 15 Pa (first
row), 31 Pa (second row), 62 Pa (third row), 125 Pa (fourth row), 250 Pa
(fifth row) and 500 Pa (sixth row), for different neon/oxygen concentration of
the background gas mixture: 10% Ne–90% O2 (first column), 30% Ne–70% O2
(second column), 50% Ne–50% O2 (third column), 70% Ne–30% O2 (fourth column),
90% Ne–10% O2 (fifth column). The powered electrode is located at $x/L=0$,
while the grounded electrode is at $x/L=1$. Discharge conditions: $L=2.5$ cm,
$f=10$ MHz, $V_{\rm{pp}}=350$ V.

Figure 11 shows the spatio-temporal distribution of the electron impact
excitation rate from the ground state into the Ne $\rm{3p_{0}}$ state obtained
from PIC/MCC simulations for discharge conditions identical to those presented
in Figure 6. Similarly to Figure 6, panels in a given row show the results
obtained for a given pressure, for different Ne–O2 mixtures, for decreasing O2
concentration in panels from left to right. At the lowest pressure of 15 Pa
(first row), the spatio-temporal distribution of the electron impact
excitation rate measured by PROES is well reproduced by the simulations for
all mixtures, the excitation patterns I.–III. observed by PROES at this
pressure can be identified in the simulation results as well. At 31 Pa (second
row), in agreement with the PROES results, the strongest excitation is found
at the expanding sheath edges (pattern I.) in all mixtures. At 62 Pa and 125
Pa (third and fourth rows), the simulation results are in good agreement with
the PROES results in all cases. At 250 Pa (fifth row), the formation of the
two distinct excitation patterns at the edges of the bulk region (IV. and V.)
observed in the PROES results are also captured in the simulations, as well as
the presence of the additional excitation pattern (VI.) at the phase of
maximum sheath expansion at both electrodes. At the highest pressure of 500 Pa
(sixth row), the main excitation patterns revealed by PROES are reproduced by
the simulations (including their relative intensity).

In the following, the simulation results are analysed in detail in four
representative cases: (i) 15 Pa, 30% Ne–70% O2, (ii) 31 Pa, 30% Ne–70% O2,
(iii) 500 Pa, 30% Ne–70% O2, and (iv) 500 Pa, 90% Ne–10% O2. For these cases,
the spatio-temporal plots of the electron-impact excitation rate from the
ground state into the Ne $\rm{3p_{0}}$ state are shown in panels (b1), (b2),
(b6), and (e6) of figure 6 (PROES) and figure 11 (PIC/MCC simulation),
respectively. Under these conditions, the main excitation patterns identified
above (labeled I.-VI. in figure 6) are exhibited. The time averaged particle
density distributions and the electronegativity obtained for these four cases
were presented in figure 7 and figure 8(a), respectively, and discussed above.

Figure 12: Spatio-temporal plot of the electron-impact excitation rate,
$S_{\rm exc}$ (a), the electron density, $n_{\rm e}$ (b), temporal snapshots
of the electron density (solid color curves) as well as the temporally
averaged negative ion (O-) density (dashed black curve) divided by a factor of
50 (c), spatio-temporal plot of the Ohmic power absorption, $P_{\rm Ohm}$ (d),
of the ambipolar power absorption, $P_{\nabla n}$ (d) as well as temporal
snapshots of the Ohmic and the ambipolar electric field, $E_{\rm Ohm}$ and
$E_{\nabla n}$, respectively (f) for 15 Pa and 30% Ne–70% O2 gas mixture. The
color of the curves in panel (c) denote the respective time instance in panel
(b). The vertical dashed black lines in panels (d,e) indicate the time
instance at which panel (f) is plotted. The horizontal dashed magenta lines
indicate the edges of the masked regions in panel (f). The powered electrode
is located at $x/L=0$, while the grounded electrode is at $x/L=1$. Discharge
conditions: $L=2.5$ cm, $f=10$ MHz, $V_{\rm{pp}}=350$ V.

Figure 12 shows PIC/MCC simulation results for various discharge
characteristics obtained for 30% Ne–70% O2 gas mixture at 15 Pa. The spatio-
temporal distribution of the electron-impact excitation rate from the ground
state into the Ne ${\rm 3p_{0}}$ state, $S_{\rm exc}$ is shown in panel (a)
(not normalized, otherwise same as panel (b1) of figure 11), while that of the
electron density, $n_{\rm e}$ is shown in panel (b). In panel (b), four time
instances within the RF period are marked with vertical dashed lines in
different colours. The electron densities in the discharge gap corresponding
to these time instances, i.e. temporal snapshots of the electron density are
shown in panel (c), where the color of the solid curves denote the respective
time instance in panel (b). At all selected time instances, sharp electron
density peaks can be seen at the edges of the bulk region (one peak at the
powered/grounded electrode side at $t/T_{\rm RF}$ values of 0 and 0.5; peaks
at both sides at $t/T_{\rm RF}$ values of 0.25 and 0.75), while the electron
density is low in the discharge center. In panel (c) the temporally averaged
negative ion (O-) density divided by a factor of 50 is also included (dashed
black line) to illustrate that the density of O- ions is much higher than the
electron density in the bulk region. As it can be seen in figure 7(a), the
time averaged O- density is about two orders of magnitude higher than the time
averaged electron density in the discharge center. As a consequence of this,
the ratio of the O- ion and electron density, i.e. the electronegativity is
high (about 100) in the discharge center (figure 8(a)). Under these conditions
the ratio of negative ions and electrons averaged over the electrode gap, i.e.
the global electronegativity is also high (about 30, see figure 8(b)). The
spatio-temporal plots of the Ohmic power absorption, $P_{\rm Ohm}$, and the
ambipolar power absorption, $P_{\nabla n}$, are shown in panels (d) and (e),
respectively. Due to the high electronegativity in the discharge center, the
conductivity of the plasma is low in the bulk region. Consequently, the Ohmic
power absorption, $P_{\rm Ohm}$, peaks in the discharge center at the times of
maximum RF current within the RF period, as it can be seen in panel (d). The
ambipolar power absorption, $P_{\nabla n}$, peaks at the edges of the bulk
region at the time of sheath collapse at both electrodes (see panel (e)) due
to the local maximum of the electron density and the corresponding large
gradients in the electron density (panels (b) and (c)). Under these
conditions, the ambipolar power absorption is the dominant power absorption
mechanism. Panel (f) shows temporal snapshots of the Ohmic and ambipolar
electric field, $E_{\rm Ohm}$ and $E_{\nabla p}$, respectively, at a selected
time instance indicated by black vertical dashed lines in panels (d) and (e).
At this time, the Ohmic electric field has a negative sign in the bulk, while
the ambipolar electric field changes the sign three times. The sum of these
two terms results in a strong electric field at the grounded electrode side of
the bulk (at the instantaneous collapsing sheath side) and a weak, almost zero
electric field at the powered electrode side of the bulk (at the instantaneous
expanding sheath side). Electrons accelerated by these electric fields induce
strong excitation (III.) at the collapsing sheath edge and weaker excitation
(II.) in the discharge center (see panel (a)). Weak excitation at the
expanding sheath edge (I.) can be also observed. These are excitation patterns
characteristic of a hybrid $\alpha$-DA discharge operation mode with dominant
DA-mode, specific to electronegative discharges (panel (a)).

Figure 13: Various discharge characteristics – same as those presented in
figure 12 – obtained for 31 Pa and 30% Ne–70% O2 gas mixture. Discharge
conditions: $L=2.5$ cm, $f=10$ MHz, $V_{\rm{pp}}=350$ V.

Discharge characteristics obtained from the simulations performed for the same
gas mixture as in case of Figure 12, i.e. 30% Ne–70% O2, but at a higher
pressure of 31 Pa, are shown in Figure 13. In this case, the spatio-temporal
distribution of the excitation rate is dominated by the $\alpha$-peaks (I.) in
combination with drift features (II.) in the bulk and ambipolar peaks (III.)
at the collapsing sheath edges. Similarly to the 15 Pa case, the electron
density profiles plotted at different time instances show strong peaks at the
edges of the bulk region (panel (c)). The electron density is low in the bulk
(panels (b) and (c)), however it is enhanced in the discharge center compared
to the 15 Pa case. Similarly to the 15 Pa case, the electronegativity is
maximum in the discharge center (figure 8(a)) and the global electronegativity
has a high value of about 25 (figure 8(b)). The Ohmic power absorption peaks
in the discharge center (panel (d)) and its magnitude is similar to that
obtained at 15 Pa. The ambipolar power absorption peaks at the edges of the
bulk region (panel (e)) and its magnitude is significantly reduced compared to
the 15 Pa case. The superposition of the Ohmic electric field and the
ambipolar electric field at the selected time instance (panel (f)) results in
a strong electric field at the powered electrode side of the bulk (at the
instantaneous expanding sheath side) as well as at the grounded electrode side
of the bulk (at the instantaneous collapsing sheath side). The electrons
accelerated by these electric fields induce the strong excitation peak (I.) at
the expanding sheath edge and the weaker excitation peak (III.) at the
collapsing sheath edge. The nonzero electric field in the discharge center
leads to excitation in the central bulk region (feature II.) These are
excitation patterns characteristic of a hybrid $\alpha$-DA discharge operation
mode with dominant $\alpha$-mode (panel (a)).

Figure 14:  Various discharge characteristics – same as those presented in
figure 12 – obtained for 500 Pa and 30% Ne–70% O2 gas mixture. Discharge
conditions: $L=2.5$ cm, $f=10$ MHz, $V_{\rm{pp}}=350$ V.

The discharge characteristics obtained at a very high pressure of 500 Pa in
30% Ne–70% O2 gas mixture are shown in figure 14. Under these conditions a
weak $\alpha$-peak (I.) and two additional excitation peaks (IV. and V.) in
about the same time interval are found in both halves of the RF period, as
well as weak excitation patterns (VI.) in the sheaths (panel (a)). The
electron density distributions at different time instances show a local
minimum close to the bulk edges, at about the position of maximum sheath
expansion at both electrodes and maximum in the center of the discharge
(panels (b) and (c)). The time averaged density of negative ions has a local
minimum in the center and local maxima at the borders of the sheath region
(note that the time averaged O- density is divided by 50 in panel (c)). The
reason for this is the increasing locality of the charged particle transport
as a function of pressure. During sheath expansion, energetic electrons are
created at the expanding sheath edge, which induce a local formation of O-
ions via high-energy threshold dissociative attachment (reaction 20 in table
1). At low pressures, these processes are not localized at the sheath edge. As
a consequence of these characteristics, the electronegativity has a local
maximum at about the positions of local minima in the electron density (figure
8(a)), which leads to the development of drift electric fields in these
regions. These are enhanced by the bulk electric field induced by the high
collisionality of the plasma at this high pressure. Therefore, both the
collisionality due to the high pressure and the electronegativity of the
discharge contribute to the ohmic power absorption term. As a result of the
superposition of these two effects, the Ohmic power absorption peaks at the
edges of the bulk (panel (d)), in the same regions where the excitation
patterns IV. and V. are found. Compared to the Ohmic power absorption, the
ambipolar power absorption (panel (e)) is less significant under these
conditions. This can be seen also in panel (f) which shows the Ohmic and
ambipolar electric fields at the selected time instance: the ambipolar
electric field is weak compared to the Ohmic field. The Ohmic field plotted at
the time instance indicated in panel (d) shows local maxima at the bulk edges
which are responsible for the excitation peaks IV. and V. at the bulk edges.

Figure 15:  Various discharge characteristics – same as those presented in
figure 12 – obtained for 500 Pa and 90% Ne–10% O2 gas mixture. Discharge
conditions: $L=2.5$ cm, $f=10$ MHz, $V_{\rm{pp}}=350$ V. Figure 16: Spatio-
temporal plots of the oxygen ionization rate [a.u.] obtained from PIC/MCC
simulations of Ne-O2 CCPs at different neutral gas pressures: 15 Pa (first
row), 31 Pa (second row), 62 Pa (third row), 125 Pa (fourth row), 250 Pa
(fifth row) and 500 Pa (sixth row), for different neon/oxygen concentration of
the background gas mixture: 10% Ne–90% O2 (first column), 30% Ne–70% O2
(second column), 50% Ne–50% O2 (third column), 70% Ne–30% O2 (fourth column),
90% Ne–10% O2 (fifth column). The powered electrode is located at $x/L=0$,
while the grounded electrode is at $x/L=1$. Discharge conditions: $L=2.5$ cm,
$f=10$ MHz, $V_{\rm{pp}}=350$ V.

The simulation results obtained at the highest pressure of 500 Pa by
increasing the Ne concentration to 90%, i.e. for the 90% Ne–10% O2 gas
mixture, are shown in figure 15. Under these conditions strong excitation is
found only at the expanding sheath edges (pattern I.) at both electrodes
(panel (a)). The electron density profiles for the different time instances
show only small local minima at the edges of the bulk region (panel (c)). The
time averaged O- density has a local minimum in the center and local maxima at
the borders of the sheath region. The discharge remains electronegative (the
global electronegativity is about 2, see figure 8(b)). The spatio-temporal
distribution of the Ohmic power absorption (panel (d)) shows peaks at the
edges of the bulk, but these are less pronounced compared to the case of high
O2 concentration at the same pressure. The ambipolar power absorption (panel
(e)) is mainly concentrated at the expanding sheath edges and has about the
same magnitude as the Ohmic power absorption. At this low O2 concentration of
10% in the mixture, there are no local maxima in the Ohmic electric field at
the bulk edges at the selected time instance, and the ambipolar electric field
exhibits only slight modulation in the gap (panel (f)). Under these
conditions, the discharge operates in $\alpha$-mode.

In summary, based on the PIC/MCC simulation results, the mechanisms behind the
development of the various excitation features revealed by the PROES
measurements in Ne-O2 CCPs in the wide pressure range for different gas mixing
ratios have been successfully revealed.

Finally, figure 16 shows the spatio-temporal distribution of the electron
impact ionization rate of oxygen obtained from PIC/MCC simulations for
different pressures and different Ne-O2 mixtures (for the same conditions as
those covered in case of the PROES results presented in figure 6 and the
excitation rates in figure 11). The ionization patterns seen in panels of
figure 16 reflect the excitation patterns of figure 11. This means that the
PROES measurement results in mixtures of Ne and O2 under the conditions
studied probe both the excitation and the ionization dynamics in the
discharge. Under these conditions, the PROES measurements provide correct
information on the discharge operation mode.

##  5 Conclusions

We have performed Phase Resolved Optical Emission Spectroscopy (PROES)
measurements combined with 1d3v Particle-in-Cell/Monte Carlo Collisions
(PIC/MCC) simulations in low-pressure capacitively coupled neon-oxygen gas
mixture plasmas. This study covered a wide pressure range and a wide mixing
range of Ne and O2 gases for a geometrically symmetric plasma reactor with a
gap length of 2.5 cm, operated at a driving frequency of 10 MHz and a peak-to-
peak voltage of 350 V. The pressure of the gas mixture was varied between 15
Pa and 500 Pa, while the neon/oxygen concentration was changed between 10% and
90%.

For all discharge conditions, the spatio-temporal distribution of the
electron-impact excitation rate from the Ne ground state into the Ne
$\rm{3p_{0}}$ state was recorded by PROES. The measured electron-impact
excitation rate from the Ne ground state into the Ne $\rm{3p_{0}}$ state was
compared to the PIC/MCC simulation results on the Ne excitation rate,
resulting in a good qualitative agreement in the whole parameter regime. At
the lowest pressure, a weak $\alpha$-peak at the expanding sheath edge, strong
ambipolar peak, and weak drift feature in the bulk region were found in the
excitation rates. With increasing pressure, the $\alpha$-peak and the drift
feature were found to be enhanced, while the ambipolar peak was reduced. At
intermediate pressures, the $\alpha$-peak was found to be the dominant
excitation pattern in all mixtures. Further increase of the pressure resulted
in the formation of two distinct excitation peaks at the edges of the bulk
region, which dominated the excitation at high O2 concentrations.

Based on the emission/excitation patterns, multiple discharge operation
regimes were identified. It was found that the localized bright emission
features at the bulk boundaries at high pressures and high O2 concentrations
are caused by local maxima in the electronegativity. The relative
contributions of the ambipolar and the Ohmic electron power absorption were
found to vary strongly with the discharge parameters: the Ohmic power
absorption was enhanced by both the high collisionality at high pressures and
the high electronegativity at low pressures. In the wide parameter regime
covered in this study, the PROES measurements were found to accurately probe
the ionization dynamics in the discharge, i.e. the discharge operation mode.

The simulation revealed that the temperature of the electrodes increases
significantly compared to the initial wall temperature with increasing the gas
pressure. It was found that the power deposition within the gas causes only a
slight increase of the gas temperature above the temperature of the
electrodes, which was, however, found to be significant due to the heating of
the electrodes by the particles from the plasma. This finding points out the
importance of the thermal balance of the electrode construction in determining
the electrode and gas temperatures under operating conditions at moderate
electrical power levels.

This work was supported by the Hungarian National Research, Development and
Innovation Office via grants K-134462 and FK-128924, by the German Research
Foundation (DFG) within the frame of the collaborative research centre SFB-TR
87 (project C1), SFB-CRC 1316 (project A4), by the project, “Electron heating
in capacitive RF plasmas based on moments of the Boltzmann equation: from
fundamental understanding to knowledge based process control” (No. 428942393),
and by the ÚNKP-21-1 New National Excellence Program of the Ministry for
Innovation and Technology from the source of the National Research,
Development and Innovation Fund.

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