PS451 Final Year Project Literature Survey:
The Processes and Applications of Spectroscopy:
Characterizing Plasma Emissions
Daniel Hurley
Student ID: 12377626
Class: PHA4
Supervisor: Dr. Bert Ellingboe
2015
Abstract
This literature survey focuses on the science of spectroscopy and
how it is applied to plasmas. Spectroscopy is used to determine the
characteristics of plasmas, such as, the electron temperature and den-
sities. If enough information is gathered from a plasma, the emit-
ting species can be identified. Plasma is the most abundant state of
matter in the universe, from the Aurora Borealis to the ionized hy-
drogen clouds in space. There are several types of plasmas and some
require their own diagnostic method. By investigating the emissions
from plasmas, collisional radiative models can be used to determine
these characteristics. In this literature survey, I will mention several
experiments that contributed to the growing number of methods to
analyse plasmas, and the assumptions these methods used. I explain
the basic instrumentation and set up of a typical spectroscopic exper-
iment. There have been a number of advances in plasma spectroscopy
and technology, and plasma spectroscopy has industry applications in
areas such as medicine, food analysis and many other disciplines.
1
Contents
1 Introduction 3
2 Plasma Spectroscopy 4
2.1 The Basic Science Behind Spectroscopy . . . . . . . . . . . . . . . . 4
2.2 Plasma . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.3 Instruments and Set-up . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.4 Identifying Species . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
3 Low Temperature Plasma Emissions 11
3.1 Population, Electron Density and Temperature . . . . . . . . . . . . 11
3.2 Measuring Line Width and Profile . . . . . . . . . . . . . . . . . . . 14
3.3 Collisional-Radiative Models . . . . . . . . . . . . . . . . . . . . . . 16
3.4 Assumptions in CR Models and Theory . . . . . . . . . . . . . . . . 17
4 Applications and Advances in Plasma Research 19
5 Conclusions 21
6 Appendices and Acknowledgements 22
2
1 Introduction
Newton started the science of spectroscopy when he studied the colours of the
rainbow, in the 1600s. Newton saw the relationship between wavelength and spec-
tral lines. Since then, spectroscopy has become a fundamental branch of science
that describes the interactions between matter and electromagnetic radiation. The
spectrometry work over the last few hundred years contributed to the formation
of what is known today as quantum mechanics. Atomic Spectroscopy is still stud-
ied today because it is useful when trying to acquire the energy level structure of
complicated atoms.[1] Spectroscopy has a wide range of applications in the world,
and in space, today. Spectroscopy is used to study the electromagnetic radiation
that comes from stars and other bodies in the solar system and beyond. Using
spectrometry techniques, the type of radiative energy, the type of material, and
the type of interaction between the energy and the material can be identified e.g.
emission and absorption lines. Plasmas were originally studied because they were
a source of radiation. They have been studied for the spectrochemical analysis
and atomic structure of the plasmas. Plasma spectroscopy studies the dynamic
characteristics of a plasmas radiation i.e. the atoms and ions releasing radiation.[2]
Plasma can be characterized with the help of collisional radiative models. These
models are used to identify characteristics of plasmas such as electron density and
temperature. But, the correct conditions for practical spectrometry must be cho-
sen. The data gathered can be affected by processes such as line broadening and
temperature. Depending on what region of the electromagnetic spectrum is being
studied, limitations arise.[3]
3
2 Plasma Spectroscopy
2.1 The Basic Science Behind Spectroscopy
Spectroscopy is the study of the interactions between matter and electromagnetic
radiation. By observing the emission, absorption or scattering of electromagnetic
waves by matter, the physical processes behind these interactions are be identified.
This provides insight into the properties of atoms and particles. [4][5] A simple
spectroscopy set-up would consist of a sample, a source of light, a monochromator
and a detector. The light beam from the light source passes through the sample.
The light passed through the sample is split by the monochromator. The light
from the monochromator is detected by the detector. The intensity of the light
vs the frequency of the light is recorded. The three focus areas of spectroscopy
are emission, absorption and Raman scattering. Emission spectroscopy focuses on
the transitions from high energy levels to low energy levels. Absorption focuses
on transitions from low energy levels to higher energy levels. Raman spectroscopy
focuses on the scattering of light due to vibrations. The difference between emis-
sion and absorption is illustrated in Figure 1.[5] The relationship between energy
Figure 1: Emission and Absorption Spectroscopy[6]
4
and frequency of a charged atomic oscillator is described by the Planck-Einstein
relation:
E = hv =hc
λ= hc
−v (1)
Where E is the energy, h is Planck’s constant, λ is the wavelength,−v is the
wave number, and v is frequency. This relationship can be used to determine
the energy transition between levels by observing the wavelength of the emitted
photon in emission spectroscopy. In absorption spectroscopy, the wavelength of
the light before and after entering a sample can be compared, and the change in
energy for that photon can be quantized.[2]
Ei = hvi and Ej = hvj (2)
The allowed transitions between energy levels can be mapped for a chemical
species. In hydrogen, each energy level is defined by:
En = −E0
n2(3)
Where En the electron energy at level n is, E0 is 13.6 eV for hydrogen, and
n is energy level. The allowed transitions between these levels are defined by the
hydrogen spectral series i.e. Lyman, Balmer, Paschen etc. The amount of energy
required to transition between one energy level to another is defined by:
∆E = E0(1
m2− 1
n2) (4)
Where m is the lower energy level and n is the higher energy level. By observing
the energy of the emitted photon, the spectral lines observed can be classified. [5]
The transitions between energy levels are illustrated in Figure 2. This shows the
spectral line series for Lyman, Balmer and Paschen.
5
Figure 2: Spectral Line Series
The Maxwell-Boltzmann distribution describes the probability of what speed
a particle has. This depends on the temperature and mass of the particle.
Nj
Ni
= exp(−∆E
kT) (5)
Where Nj is the higher state population, Ni is the lower state population, k is the
Boltzmann Constant, T is the temperature, and E is the energy.[5]
6
2.2 Plasma
Plasma is the fourth state of matter i.e. ionized gas. Plasma can be partially
or completely ionized. Plasma is an electrically neutral medium of positive and
negative particles. These particles are unbound. Charges create electrical currents
and magnetic fields. These charges are affected by one another’s fields.[7]
There are three main components that define plasma:
• The particle density n (Particles/cm)• The temperature T (eV)• The magnetic field B (T)
There are many types of plasma. Three general examples of the types of
Plasmas found on and off earth are listed below. [4]
Non-fusion terrestrial plasmas:
• Neon Signs, Fluorescent Lamps, Arcs• Typical Density of about 1014 - 1022 m−3 and Temperature of a few eV• Very common plasmas on earth• Inexpensive production
Fusion terrestrial plasmas:
• Fully ionized Hydrogen and Deuterium• Typical Density of about 1020 m−3 and temperatures in multiples of 104 eV• Very expensive to produce• Quite rare on earth
Space plasmas:
• Density varies from 106 - 1020 m−3 depending on location• Temperatures of up to 100 eV• Fully ionized (usually)
Three important sources of photons are from bremsstrahlung, radiative recom-
bination and bound-bound transitions. [8] Partially ionized gas is of particular
interest for my final year project. Low temperature plasmas typically have cold
ions and neutrals, and hot electrons. Each species is characterized by its own
temperature.
7
2.3 Instruments and Set-up
In plasma spectrometry, typically, Czerny-Turner monochromators are used to
split incoming electromagnetic radiation into separate components. The Czerny-
Turner configuration can be seen Figure 3. The choice of grating and focal length
for these monochromators are important because they determine the resolution
that can be worked with. The blaze angle of a grating determines the sensitivity
of the grating. A CCD detector is at the exit of the monochromator. These are
able to record specific wavelength ranges.[3] The basic process of a spectroscopic
experiment using plasma: Electromagnetic light is emitted from the plasma. The
light enters the entrance slit of a monochromator. The light is split by the diffrac-
tion grating in the monochromator. The desired component of light exits through
the exit slit and is detected by a CCD camera. The species is then identified using
various spectroscopic techniques.
Figure 3: Czerny-Turner Spectrometer Configuration[9]
There are limitations in plasma spectroscopy. So, choosing the correct condi-
tions to work in is important. The temperature and the region of the EM spectrum
can have an effect on the results of a spectroscopic experiment. The 200 nm to
1000 nm range encapsulates the visible spectrum, along with part of the UV and IR
8
Figure 4: Spectra for H2 and D2 indicating P, Q and R branches[10]
spectra. Working outside of the 200 nm to 1000 nm range will cause issues to arise
as mentioned in [3]. When working in a range less than 200 nm, quartz glass and
Oxygen cause issues. Quarts glass becomes less transparent, and Oxygen absorbs
light. This means a vacuum path must be set up to prevent Oxygen absorbing the
light. When working in a range above 1000 nm, noise becomes an issue. Thermal
background noise must be compensated for using detection equipment. This raises
experimental costs. Emission and absorption spectroscopy require different meth-
ods. Emission spectroscopy is considered a straight-forward process and ideal for
learning the properties of plasmas. Absorptions spectroscopy on the other hand,
is more difficult to conduct. The hydrogen and deuterium spectra for this region
can be seen in Figure 4.[3]
2.4 Identifying Species
Spectroscopy is very important for identifying the species within a plasma. This
can be achieved by analysing the emission intensity. Particles emit radiation.
9
The a product of the rate that the upper state is populated, and the electron
collisions, and what fraction of the upper state decays through the pathway, gives
the emission intensity. Once the atomic data for the transitions and the electron
temperature is known, the relative intensities for all the emission lines can be
calculated. For excited atomic hydrogen, the population is coupled to H and H+
particles with their own densities. This relationship is given as:
nH(p) = nHneRH(p) + nH+neRH+(p) (6)
Where RH(p) and RH+(p) are the population coefficients which are calculated
using a collisional radiative model. Line identification can be difficult as the
higher order lines may be near the line that is to be identified. This is why it
highly important to use filters. These filters block out the unwanted lines that may
interfere with the line being analysed. Choosing a filter to work with depends on
the region of the EM spectrum being analysed. Filters can be expensive depending
on which region or how close the lines are together. The position of the line is
the identifier in spectroscopy. Using the position, the lines can be identified using
databases (IAEA and NIST are recommended[8]) that contain accurate values for
these lines and can therefore be cross-referenced with the data obtained.[3]
Figure 5: Gas temperature obtained from the fit of the computer simulation to
the measurement of a vibrational band of N2 [3]
10
3 Low Temperature Plasma Emissions
3.1 Population, Electron Density and Temperature
In low temperature plasmas, Telectron � Tion ≥ Tneutral with Te = 8eV and typ-
ically have a small percentage of ionization. Nearly all the molecules are in the
vibrational ground state and deviations from the 2000 Kelvin distribution do not
change the upper Fulcher state population.
dnupperdt
= (nlower)(ne)
∫ ∞0
σ(v)F (v)dv (7)
Where σ(v) is the velocity dependent cross section and F (v) is the EEDF. Elec-
trons have sufficient energy to cause energy state transitions in the gas. This
depends on the electron temperature and the change in energy for that transition,
and the cross section. The cross section for the l→p excitation is given by:
σl,p = 2/(XUl,p)[1+sl,pexp(−rl,pUl,p)]×[Al,p[lnUl,p+1/(2Ul,p)]+(Bl,p−Al,pln2/x)(1−1/Ul,p)]πa20
(8)
Where Ul,p is the electron energy, X is the energy difference of the levels, Al,p and
Bl,p are the parameters of the Born approximation, and a0 is the Bohr radius.
These parameters are adjustable for different scenarios. Different excitation chan-
nels happen at different rates. To understand plasma reactions, the vibrational
excitation of molecular hydrogen in the ground state is of particular interest. Vi-
brations are associated with the stretching and bending of molecules. Identifying
the species becomes easier when the vibrational level is known. The vibrational
population in ground state hydrogen molecules is an important component for the
formation of negative ions in plasma. In an experiment to determine the vibra-
tional population in the hydrogen ground state, Fantz says “Vibrationally exited
molecules lead to the formation of negative ions and to an increase in ionization and
dissociation rate coefficients”. It was also found that there is no collisional swap-
ping in the higher states.[10] The vibrational population is given by the Boltzmann
distribution. See equation 5. Raman scattering techniques were used to measure
the vibrational population of radio frequency plasma in an experiment by V. A.
Shakhatov.[11] A typical population density for low temperature plasma would be
ne ≈ 1017m−3. The typical electron temperature for plasma would be Te ≈ 5eV .
11
By using different diagnostic gases, the electron density and electron temperature
can be determined from the line ratios from emission lines and the electron den-
sity. Using collisional radiative models, ratios of effective emission rate coefficients
can be identified. Emission rate coefficients are dependent on electron density and
electron temperature. In low temperature plasma, the electron temperature is
highly important for analysing these line emissions. Figure 6 shows the ratio of
emission coefficients for the helium line at 728 nm to Argon at 750 nm.[3]
The calculation of the negative ion population density can be simplified to this
equation:
nH− =Hy
neC1(
Hα
Hβ
1
C2
− 1). (9)
This can be used to monitor the negative ion densities.
The processes of plasmas can be seen in the excitation pathways of hydrogen.
There are four pathways for molecular hydrogen.
Firstly, the direct ionization from electron impact is given by:
H2(X1Σ+
g ) + e→ H+2 (X2Σ+
g ) + e+ e (10)
The second excitation pathway starts from the ground state and produces an
exited molecule:
H2(X1Σ+
g ) + e→ H∗2 + e (11)
H∗2 + e→→ H∗∗2 + e
H∗∗2 + e→ H+2 (X2Σ+
g ) + e+ e
Third is the dissociative ionization from an unstable molecular hydrogen ion
is given by:
H2(X1Σ+
g ) + e→ H(1s) +H+ + e+ e (12)
Forth is the ionization from excited hydrogen atoms from dissociative excita-
tion of molecular hydrogen is given by:
H2(X1Σ+
g ) + e→ H(1s) +H∗ + e (13)
H∗ + e→→ H∗∗ + e
H∗∗ + e→ H+ + e+ e
12
If the atomic data is known for a transition, and the electron temperature is
known, then it is possible to calculate the relative intensities of the emission lines
of the plasma. [12] [13]
Figure 6: Ratio of emission rate coefficients forHe728Ar750
[3]
13
3.2 Measuring Line Width and Profile
The spectral lines detected from plasmas can be broadened; this means the lines
may have shifted positions, and are not as sharp as they could be. A common
example of this is Doppler broadening. Doppler broadening occurs in the visible
to UV region. Atoms travelling towards the detector will have different transition
frequencies from those at rest. In terms of wavelength, width of the spectral line
at the half height of the profile, called the Full-Width Half-Maximum (FWHM),
is expressed as:
2∆λ 21
= 2√
ln 2λ0
( 2kTiMic2
) 12
(14)
Where λ0 is the central wavelength, Ti is the ion temperature, λ 21
is the Doppler
half width in terms of wavelength, c is the speed of light, and k is the Boltzmann
constant.[2] The line width and FWHM can be seen in Figure 7. A common
type of broadening that occurs is The Doppler Effect. This causes a shift in the
central wavelength. Other types of broadening can occur due to quasi-static and
temporal changes in the atomic states of the ions that are emitting energy. Line
width is a regular concern in experimental plasma research. The profile shape of
spectral lines depends on the density of charged particles. Stark Line broadening
complicated the interpretation of an experiment to investigate the relationship
between plasma and liquids in an experiment by P. Bruggeman.[14] The Spectral
line intensity is given by:
Iij = Nj · Aij · Eij (15)
Where Iij is line intensity, Nj is the upper state density, Aij is Einstein Coefficient,
Eij is the photon energy.[8]
14
Figure 7: Line Width[15]
15
3.3 Collisional-Radiative Models
Photons carry information about plasmas. Using theoretical plasma spectroscopy
techniques, the thermodynamic properties of plasma and the behaviour of plasma
can be modelled. Different models are required for different plasmas. For collisional-
radiative plasmas, the population distribution is determined using rate equations,
taking into account the collisional and radiative processes. Other effects such
as radiation transport and density effects must be included in a model.[16] The
master equations for the construction of a Collisional-Radiative Model are: [17]
dn+
dt=dnedt
= −ne(ΣiRi + neΣiQi)n+ + neΣiSei ni (16)
dnidt
= neΣi 6=jnjKeji−nine(Sei +Σj 6=iK
eij)+n+n
2eQ
ei−niΣj<iAij+Σj>iAijnj+n+neRi
(17)
Collisional-Radiative Models are coded versions of the radiating properties of
ions and atoms within plasmas, constructed using the above master equations 16
and 17. They show the relationship between the ground state population and the
particle density.[18] “Collisional-radiative models describe the intermediate state
which exists before full thermal equilibrium is reached, but where the electron den-
sity is sufficiently high for electron collisions to compete with radiation in altering
the occupancy of excited atomic and ionic states”.[19] Collisional Radiative mod-
els were made for atomic hydrogen in high velocity plasma flow in an experiment
by S. Sun and H. Wang. They investigated the kinetic processes of a hydrogen
plasma arc-jet thruster. They discovered that a collisional radiative model worked
for different regions of the arc-jet. They concluded that the population densi-
ties of the excited states of hydrogen followed the Boltzmann distribution. In
the lower states, however, the population density deviated from the Boltzmann
distribution.[20]
16
3.4 Assumptions in CR Models and Theory
Plasma spectrometry experiments cannot be conducted without the use of certain
assumptions. The Maxwell distribution is used to describe the electron impact
process in low temperature plasmas, even though it is not entirely justified. For
the rate coefficient, there is a steep dependence on electron temperature at low
temperatures and the quality of the cross section. An experimental error of a
factor of 2 must be applied in the case of low temperature plasma diagnostics as
seen in figure 6.[3]
The rate coefficient is described by: [3]
Xexc(Te) =
∫ ∞Ethr
σ(E)(2
me
)12
√Ef(E)dE (18)
In an experiment, by U. Fantz, and B. Heger, to show the spectroscopic di-
agnostics of the vibrational populations of the electron ground state of H2, as-
sumptions were used for the diagnostics method. The Franck-Condon principle
for electron impact excitation was assumed to be valid. [10] The Franck-Condon
principle states that “the intensity of a vibronic transition is proportional to the
square of the overlap integral between the vibrational wave functions of the two
states that are involved in the transition”. This means that one energy level may
not be able to get to certain excited states as the probability of finding the popu-
lation at the same location in the next state is very low. Using this assumption,
it was possible to characterize the population using the vibrational temperature.
These assumptions were justified by the use of a collisional radiative model, which
qualitatively tested it’s validity. The Franck-Condon assumption allows for the
identification of H+ particles if there is an ion temperature higher than the gas
temperature and lower than the Franck-Condon energy. [21]
According to H. K. Chung, assumptions must be made when creating colli-
sional radiative models. For example, “the ionization potential depression model
of Stewart and Pyatt is used to suppress bound states due to continuum lower-
ing”. In coronal plasmas, at low density, the excited state population density is
so low that they are assumed to be populated from the ground state by collisional
excitation and depopulation by spontaneous emission. So, in this case, the excited
population is proportional to the stark broadening. [16]
17
In the experiment previously mentioned by S. Sun and H. Wang, it was assumed
that the plasma they investigated was electrically neutral, optically thin, and
that the energy distribution was Maxwellian. It was also assumed that electron
to atom collision frequencies dominates the kinetics, so ions to atom collisions
were neglected. This allowed the calculation of the cross-sections for super-elastic
collisions and three-body recombinations using the detailed balance principle. In
order to analyse the results, it was assumed that the initial distribution of the
excited states followed the Boltzmann distribution.[20]
18
4 Applications and Advances in Plasma Research
Innovations have been made in the medical applications of plasmas. Plasmas can
be used in anticancer therapy that does not have an affect on the areas near the
tissue of interest. This method is based on the dielectric barrier discharge principle.
This device is made of two planar electrodes separated by a gap. However, the
human body can act as one of these electrodes, meaning non thermal atmospheric
plasma may be used as in anticancer therapy. This has been successfully tested on
mice with a resulting 60 percent increase in lifespan due to tumour size reduction.
The experiment did not exceed 5 days however. Considering the difference in size
between mice and humans, longer duration and exposure to plasma therapy may
be required, which has not extensively been investigated in terms of safety in this
experiment.[22]
Plasmas are used to produce negative ion sources. A new, non-invasive, method
to diagnose plasmas and determine the negative ion densities was created by U.
Fantz and D Wunderlich. Using optical emission spectroscopy, this method anal-
yses the Balmer line ratio of Hα and Hβ and discovered that there was a linear
correlation between the line ratio and the negative ion density of the source. This
method was applied to Radio Frequency plasmas in the IPP. Although, there were
uncertainties, due to the use of a collisional radiative model, in this experiment
resulting a 20 percent error bar. The reliability of a collisional-radiative model
depends on the input data quality. This uncertainty is due to the assumption that
the error in the negative ion density is less than 40 percent. [23]
Plasma research is a continually growing field of research. A popular topic at
the moment is in relation to plasmas in contact with liquids. In an experimental
evaluation of this interaction, it was discovered that the emission spectrum is de-
termined mainly by the production processes and kinetics of the emitting species,
after investigating a 600 Nano second pulsed discharge in Oxygen bubbles using
temporal optical emission spectroscopy.[14]
Plasma spectroscopy is also used to identify metals in wine and arsenic in foods.
Wine is a complex organic compound, making it difficult to analyse. Spectroscopy
can be applied to separate the components, making them easier to identify. The
spectroscopy techniques used are preferable to any other as they are not prone to
19
interference from organic compounds. This is because there is a high temperature
involved in the atomization steps. Spectroscopy is a fast and highly accurate
technique for determining the imperfections in wines.[24]
Plasma spectroscopy is regularly used in astronomy to study the constituents
of stellar and interstellar material. Plasma is the most abundant state of matter in
the universe, making it an area of high interest for spectroscopy. The constituents
of space plasmas can be derived from lines observed by telescopes, such as the
XMM-Newton. Advances have been made in plasma diagnostics of coronae using
spectroscopy. Obtaining the temperature and densities of plasmas in the past
relied upon the use of atomic databases, which contain information based on the
plasma structure, such as line emissivity. The XMM-Newton telescope is equipped
with gratings that provide higher resolution than previous missions. Gratings on
the newer telescopes can resolve in the Angstrom range, making it possible to
obtain larger amounts of information from just a few lines. Now, it is possible to
determine the temperature and densities of stellar plasmas just by observing the
lines. The new technology reduces the need for global models.[25] Ionized hydrogen
clouds can be examined using plasma spectrometry. By examining the emissions
of a cloud, the components of that plasma can be identified and analysed. Using
collisional radiative models, as discussed in an earlier section, can help to the
identify the stellar and interstellar material that makes up any star or cloud.[26]
20
5 Conclusions
Spectroscopy is an exciting field of scientific research. Ever since Newton observed
the rainbow, new techniques and methods have been discovered on how to analyse
the spectra of plasmas. Spectroscopy is a vital science to industry and plasma
spectroscopy is a key branch in this industry. Space science benefits greatly from
the discoveries made in optical emission spectroscopy. Now it is easier to gather
information about stellar and interstellar plasmas due to advances in technology
i.e. high resolution gratings and collisional-radiative models and anticancer ther-
apy. As the mysteries of plasmas are uncovered, they will undoubtedly benefit our
knowledge of atomic structures and interactions. With spectroscopy, the charac-
teristics of plasmas such as the electron density and electron temperatures can
be identified. Collisional-radiative models can be used to compare the behaviours
of plasmas. Choosing the appropriate parameters, such as temperature and the
region of the spectrum, to work with is important for spectroscopic experiments.
Plasma spectroscopy is a relatively new field of research, so numerous discoveries
can be expected in the near future. The information I have gathered for this sur-
vey will aid me in my final year project as it has provided a basis for my knowledge
of plasmas and spectroscopy.
21
6 Appendices and Acknowledgements
References
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22
[9] Stackexchange.com, “Czerny-Turner Configuration Illustration,” 2015.
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cf9e94355b577cf8626445ce8d59dc3d
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and A. Gicquel, “Measurement of vibrational, gas, and rotational
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[13] K. Sawada, K. Eriguchi, and T. Fujimoto, “Hydrogen-atom spectroscopy
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s1&Agg=doi
[14] P. Bruggeman, T. Verreycken, M. A. Gonzalez, J. L. Walsh, M. G. Kong,
C. Leys, and D. C. Schram, “Optical emission spectroscopy as a diagnostic
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