IOP PUBLISHING
JOURNAL OF PHYSICS D: APPLIED PHYSICS
J. Phys. D: Appl. Phys. 43 (2010) 043001 (21pp)
doi:10.1088/0022-3727/43/4/043001
TOPICAL REVIEW
Plasma-chemical reactions: low pressure
acetylene plasmas
J Benedikt
Faculty for Physics and Astronomy, Research Group Reactive Plasmas, Ruhr-Universität Bochum,
Universitätsstr. 150, 44780 Bochum, Germany
Received 29 September 2009, in final form 9 November 2009
Published 12 January 2010
Online at stacks.iop.org/JPhysD/43/043001
Abstract
Reactive plasmas are a well-known tool for material synthesis and surface modification. They
offer a unique combination of non-equilibrium electron and ion driven plasma chemistry,
energetic ions accelerated in the plasma sheath at the plasma–surface interface, high fluxes of
reactive species towards surfaces and a friendly environment for thermolabile objects.
Additionally, small negatively charged clusters can be generated, because they are confined in
the positive plasma potential. Plasmas in hydrocarbon gases, and especially in acetylene, are a
good example for the discussion of different plasma-chemical processes. These plasmas are
involved in a plethora of possible applications ranging from fuel conversion to formation of
single wall carbon nanotubes. This paper provides a concise overview of plasma-chemical
reactions (PCRs) in low pressure reactive plasmas and discusses possible experimental and
theoretical methods for the investigation of their plasma chemistry. An up-to-date summary of
the knowledge about low pressure acetylene plasmas is given and two particular examples are
discussed in detail: (a) Ar/C2 H2 expanding thermal plasmas with electron temperatures below
0.3 eV and with a plasma chemistry initiated by charge transfer reactions and (b) radio
frequency C2 H2 plasmas, in which the energetic electrons mainly control PCRs.
(Some figures in this article are in colour only in the electronic version)
and may serve as nucleation centres for the formation of
nanoparticles. Plasmas are relatively safe and environmentally
friendly, the material content is usually very low reducing
hazards for operating personnel and limiting the production
of harmful products. The high kinetic energy of electrons
makes plasmas nonselective with a high fragmentation degree,
which makes it sometimes difficult to predict the results
of plasma-chemical processes. On the other hand, the
preferential vibrational excitation of molecular species can
selectively promote otherwise endothermic reaction channels.
The application of these plasmas is usually confined to highadded-value products, because vacuum reactors with complex
substrate handling systems and with expensive pumps are
necessary for their operation.
There is an extensive scientific and industrial interest in
hydrocarbon chemistry since it plays an important role in many
applications such as combustion [1, 2], deposition of diamond
and diamond-like carbon (DLC) films [3, 4], generation of
1. Introduction
Low temperature plasmas are a fascinating medium in which
electrons, ions and reactive neutral species can coexist
under non-equilibrium, but steady conditions. The electrons
with high average energy of several electronvolts control
ionization, dissociation and excitation of molecules and
atoms and substitute and extend the role of temperature,
which is otherwise the driving force in chemical vapour
deposition (CVD) processes. Heavy particles can stay at
moderate temperatures slightly above room temperature (room
temperature to a few thousands of kelvins). Additionally,
charged species can be manipulated by electromagnetic fields
allowing for an additional control of a plasma-chemical
process. Positive ions are accelerated towards surfaces
surrounding plasma and resulting ion bombardment can
promote deposition or etching processes. Negative ions are,
in contrast, trapped within the positive plasma potential well
0022-3727/10/043001+21$30.00
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© 2010 IOP Publishing Ltd
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J. Phys. D: Appl. Phys. 43 (2010) 043001
Topical Review
carbon nanotubes, nanowalls and other nanostructures [5, 6]
or tritium retention in future fusion devices [7]. Moreover,
hydrocarbon chemistry is also involved in the formation of
(proto-)planets in the interstellar space [8], or it determines
the composition of the hydrocarbon rich atmosphere of
Saturn’s moon Titan [9]. However, despite this interest,
the hydrocarbon chemistry and carbon-based film growth
mechanisms are still not well understood. The primary reason
is the ability of carbon to form double and triple bonds
leading to a large family of radicals, molecules and ions
coexisting together in the gas phase. Almost any combination
of hydrogen and carbon atoms can exist in the form of several
isomers, which can be excited in metastable states, they can
be resonantly stabilized with delocalized electrons or they can
make very stable organic compounds. The densities of these
species have to be measured, spatially and temporally resolved
in the best case, to be able to understand the plasma chemistry
involved. This is putting high demands on the diagnostic tools
and requires combined experimental and theoretical modelling
efforts.
Acetylene (C2 H2 ) has many properties that make it an
interesting precursor gas. It is a linear molecule with low
hydrogen content (only 1 : 1 ratio between H and C) and a
strong triple bond between the two carbon atoms (bond energy
9.97 eV), which is usually conserved in, for example, electron
impact collisions. For example, the appearance potential of
20.85 ± 0.05 eV of CH+ fragment ion in dissociative electron
impact ionization (EII) of the C2 H2 molecule is much higher
than appearance potential of the C2 H+2 parent ion (11.40 eV)
[10]. C2 H2 is unstable in its pure form and can explosively
decompose in an exothermic reaction when compressed above
200 kPa. It is therefore supplied being dissolved in acetone in
bottles filled with a porous medium. The pyrolysis of C2 H2
starts already at 400 ◦ C with C4 H4 and C6 H6 molecules as
main products [11, 12]. Soot is formed very quickly at higher
temperatures in the so-called HACA mechanism (hydrogen
abstraction C2 H2 addition to aromatic compounds) [13].
C2 H2 is involved in plasma technology both as product and
as precursor gas. It can be generated in atmospheric pressure
thermal arc plasmas in natural gas with applied power in
the megawatt range and production rate of 25 000 tons year−1
[14]. As a precursor gas, it is used in a low pressure plasma
deposition of carbon nanotubes [15], or in deposition of
hard DLC layers [16]. These layers are used for example
in tribological applications or as protective coatings. The
presence of C2 H2 in atmospheric pressure processes such as
combustion or pyrolyses or in low pressure plasmas leads very
often to soot or dust particle generation [13]. The particles
generated in low pressure plasma can be used to study for
example instabilities induced by particle presence [17, 18]
or they can serve as IR-spectra analog for carbonaceous
interstellar dust [19].
The aim of this paper is to give the reader (i) an overview
of plasma-chemical reactions (PCRs) in low pressure plasmas
with the discussion of their importance for C2 H2 discharges
and with the references to the available literature data with
cross sections and reaction rates, (ii) to show examples of
possible experimental and theoretical methods used for the
investigation of the plasma chemistry in low pressure plasmas
and (iii) to discuss up-to-date knowledge about the plasma
chemistry in low pressure C2 H2 plasmas.
2. Plasma and PCRs
Low temperature plasma is an ionized gas with free electrons
and free positive and negative ions showing collective
behaviour [20]. In its bulk, it exhibits quasi-neutral behaviour
with the same number of positive ions and negative ions and
electrons. At its boundaries, a so-called sheath is formed
with a positive space charge. The formation of sheaths is
a consequence of the higher mobility of electrons, which
can leave the plasma more easily than ions. Plasma is
usually formed by applying constant or alternating electric
or electromagnetic fields to a low pressure gas mixture.
Plasma properties (electron and ion densities, electron
energy distribution function (EEDF), plasma composition,
gas temperature, etc) result from the equilibrium between
power dissipation in heating of electrons, generation of
plasma species in electron collisions and the losses due to
recombination in the gas phase or at the wall. The regions
of plasma generation and losses can spatially overlap but they
can also be remote as in the case of expanding thermal plasma
(ETP) discussed below.
The non-equilibrium character of low pressure plasmas
is caused by the fact that the electron mass is at least several
thousand times smaller than the mass of other ‘heavy’ particles.
Mainly electrons are heated by electromagnetic fields, which,
combined with very small energy transfer to heavy particles in
elastic collisions (2mel /Mhp ), leads to electron temperature
much higher than the ion or neutral particle temperature.
Plasma chemistry offers many advantages compared with
neutral gas chemistry in CVD processes. Energetic electrons
are responsible for excitation, dissociation and ionization
of the gas promoting production of highly reactive species.
Additionally, effective vibrational excitation of molecules
in collisions with electrons combined with slow vibration–
translation relaxation often results in larger population
of higher vibrational levels compared with a Boltzmann
distribution defined by the overall gas temperature [14].
This vibrational excitation promotes otherwise endothermic
reactions. Moreover, the collision rates of ions with neutral
particles are enhanced by polarization forces. Since electrons
initiate the plasma chemistry, the gas temperature can stay low
and allows the treatment of temperature-sensitive materials.
Additionally, various surface processes can be triggered by
energetic ion bombardment. The main disadvantages of
plasma are their complexity and low selectivity.
2.1. Elementary PCRs
The reaction probability of two particles A and B with a relative
velocity vrel = |vA − vB | in a single collision is described by
the vrel dependent collision cross section σAB (vrel ). A collision
of two hard spheres with radii r1 and r2 can serve as an example
here. The collision cross section is given by σhs = π(r1 + r2 )2
and a collision occurs, if the trajectory of one sphere passes
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J. Phys. D: Appl. Phys. 43 (2010) 043001
Topical Review
the other sphere at an impact parameter smaller than rhs =
r1 + r2 . Geometric (kinetic) cross section between 10−16 and
10−15 cm2 is obtained for typical atomic radii. The particular
cross section can, however, exceeds this geometric one by
several orders of magnitude due to interaction force between
reacting species (e.g. mutual cation–anion recombination) or
it can be much smaller, if the chemical reaction is for example
endothermic exhibiting a large activation barrier.
Reaction probability, interaction frequency, mean free
path, reaction rate and rate coefficient can be calculated with
the help of this cross section, if the densities of both species
nA and nB and their velocity distribution functions fA (vA ) and
fB (vB ) are known. Reaction probability of one particle A with
velocity vA with particles B on a path with length dx is
Pcoll (dx) = nB dx [σAB (vrel )fB (vB )]dvB = nB σAB dx, (1)
carry away the excess energy. Ionization of molecules can also
result in dissociative ionization (DI): a molecular ion is formed
at first in its repulsive non-bonding state, which dissociates
quickly in one ionized and one or several neutral fragments.
The threshold energy of DI is usually higher than that of direct
ionization because at least one chemical bond has to be broken.
Direct and DI cross sections can be measured with high
accuracy in crossed electron molecule beam experiments [21].
They are available for most stable hydrocarbon molecules
(CH4 , C2 H2 , C2 H4 , C2 H6 , C3 H6 , C3 H8 ) [22, 23] and for
some molecular fragments (CDx , x = 1–4) [24, 25]. EII
cross sections have very similar slopes in the near-threshold
energy region for most of the above-mentioned hydrocarbon
molecules and have typical maximum values of few 10−16 cm2 .
The total ionization cross section scales approximately with the
size of the hydrocarbon molecules in the electron energy range
above 20 eV, following empirical additivity rules [26].
EII can also involve electronically excited atoms or
molecules in the so-called stepwise ionization processes. They
occur usually at high pressures and high electron densities
and they can be neglected in low pressure plasmas considered
here [14].
its interaction frequency with particles B is
νAB = vA nB σAB ,
(2)
and its mean free path between these reactions/collisions is
λA = (nB σAB )−1 .
(3)
Electron impact dissociation, electronic excitation and
dissociative excitation. The collision of a free electron with
a valence electron can, next to ionization, lead also to the
electronic excitation of the target particle (in collisions with
both atoms and molecules) or its dissociation or dissociative
excitation (in collisions with molecules or their fragments).
These are again non-resonant processes, in which the incoming
electron can carry away the excess energy, and their cross
sections have similar energy dependence as ionization cross
sections with corresponding threshold energy. In the case
of dissociation, the valence electron is excited to an antibonding molecular orbital in a Franck–Condon step followed
by the dissociation of the excited molecule. The newly formed
fragments may carry substantial energy in this case [14, 20].
The extended discussion of cross sections and branching ratios
for collisions of electrons with hydrocarbon species with one
to three carbon atoms can be found in the works of Janev and
Reiter [27, 28]. It should be noted here that this work has been
motivated by a fusion research and the fitting curves provided
there do not reproduce very well the cross sections in the nearthreshold region (for example, the EII cross section for C2 H2 is
zero below 15.4 eV in their fit, whereas the ionization threshold
is already at 11.4 eV!). The use of correct value in nearthreshold energy region is very important in the simulation
of low pressure discharges and the measured values should be
preferentially used.
Integrating over both distribution functions, a reaction rate RAB
and a rate coefficient kAB (sometimes also called reaction rate
constant) can be determined:
RAB = nA nB
[vrel σAB (vrel )fA (vA )fB (vB )] dvA dvB
= nA nB vrel σAB (vrel ),
kAB = vrel σAB (vrel ),
(4)
(5)
It should be noted that the internal energy (vibrational,
electronic) can result in different cross sections and it should
be checked whether excited species have to be considered
separately to ground state species.
A discussion of cross sections of elementary PCRs will
be given in the following with highlighted issues relevant to
C2 H2 plasmas. The extended treatment of this topic can be
found elsewhere [14, 20].
2.1.1. Reactions involving electrons.
Electron impact ionization. Ionization is the most important
reaction for sustaining plasmas, since it is the primary source of
ions and electrons in the plasma volume. EII can be described
as a collision of a free incoming electron with a valence
electron of a target particle in which sufficient energy, larger
than ionization energy, is transferred to the valence electron.
The dependence of the cross section on the energy of the
incoming electron can be described qualitatively very well by
the Thomson formula derived from a classical treatment of this
collision. The cross section is zero below a threshold energy,
which is the ionization energy of the valence electron of a
given species, and rises linearly just above this energy. The
cross section reaches then its maximum at energies around
50 to 100 eV followed by a slow decrease at higher energies.
EII is a non-resonant process in which the free electrons can
Vibrational excitation by electron impact and dissociative
electron attachment (DEA). The vibrational excitation of
polyatomic species in collisions with electrons is an effective
and important process in plasma chemistry. The excitation
proceeds through the formation of short-lived negative ion
resonance (NIR), in which the incoming electron is captured
into a low-lying unoccupied molecular orbital (LUMO) having
typically anti-bonding character. The geometry of the NIR
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J. Phys. D: Appl. Phys. 43 (2010) 043001
Topical Review
complex (interatomic distances and bond angles) starts to
rearrange in response to the new electronic structure and the
resulting repulsive force when the NIR is formed. When the
electron leaves the NIR by autodetachment after some time
(typically 10−15 to 10−11 s), the atomic nuclei are at much
larger distances than in the equilibrium situation and the neutral
particle is now in a vibrationally excited state. When the
lifetime of the NIR is long enough for the nuclei to reach large
distances, dissociative attachment resulting in the formation
of a stable negative ion fragment of the original particle can
occur [29, 30]. The whole process is resonant, because the
incoming electron is captured and its kinetic energy has to
match the energy for the transition to the LUMO. Typical
cross sections are in the range of gas-kinetic cross sections
for vibrational excitation and ∼10−20 cm2 range for DEA.
Vibrational excitation is responsible for the major
part of energy exchange between electrons and molecules.
Additionally, a slow vibrational–translational (VT) relaxation
in gases such as N2 , CO, H2 or CO2 can result in
significant overpopulation of higher vibrational levels. The VT
relaxation is faster in gases with polyatomic molecules [14]
but nevertheless the measured vibrational temperature is
very often still higher than the rotational temperature. For
example, rotational and vibrational temperatures of CH
radicals measured in Ar/C2 H2 ETP have been Trot = 1190 K
and Tvib = 2940 K [31]. The cross sections of electron
collisions can be determined in beam experiments or in socalled swarm measurements [32]. The data are available for
the hydrocarbon gases CH4 , C2 H2 , C2 H4 , C2 H6 , C3 H6 and
C3 H8 [32, 33].
The cross sections for DEA have been recently measured
with high accuracy for C2 H2 and C4 H2 [34] and data are also
available for other hydrocarbon molecules [35].
energy of an ion–electron complex cannot be re-distributed
among several reaction products. Radiative electron–ion
recombination is slow, since it requires a photon to be emitted
in the short time span of ion–electron interaction. Three body
electron–ion recombination, in which the excess energy is
removed in collisions with other electrons, is negligible at
electron densities typical for low pressure plasmas.
2.1.2. Reactions involving ions.
Ion–ion recombination in binary collisions. Ion–ion recombination is the most important ion loss in electronegative gases
at pressures lower than 1000 Pa. Three body ion–ion recombination is important at higher pressures and can be neglected in
our case. The collision cross section of binary ion–ion recombination exceeds the gas-kinetic cross section by several orders
of magnitude due to the long range Coulomb attractive force.
The cross section is only weakly dependent on the nature of
the ion [42] and can by approximated by formula derived by
Hickman [43].
Ion–neutral reactions. Ion–neutral reactions are typically
10 times faster than reactions of neutral particles due to
the attractive polarization potential of the induced dipole
moment of the neutral particle. Since the polarization
potential scales with distance as r −3 the incoming ion can
be captured when the impact parameter is smaller than socalled Langevin radius [14, 20]. The resulting Langevin
cross section is inversely proportional to the velocity and,
therefore, the rate coefficients for ion–neutral reactions are
temperature (velocity) independent (cf equation (5)). The
rate coefficients can be measured, for example, in drift
tube experiments, in flowing afterglow devices, in the ion
source of mass spectrometers, in ion cyclotron resonance
mass spectrometer or in beam experiments [44]. Reactions
of positive hydrocarbon ions have been well studied by
many authors [45–48] and the rate coefficients for these
reactions can be found for example in the UMIST database
for astrochemistry 2006 [49].
There is much less information regarding the reactions of
negative hydrocarbon ions. Their generation and detection
are more challenging and only few studies report their
measurements in hydrocarbon plasmas. Negative ions are
formed in DEA reactions and in the following ion–neutral
reactions. These ions serve as nucleation centres for dust
particle growth in low pressure plasmas [50–52] and the
understanding of their chemistry is therefore important for
understanding of dust particle generation. However, there is
only the C− anion listed in the UMIST database without any
rate coefficients for C2n H− negative ions typically observed in
C2 H2 plasmas. The C2 H2 plasma simulation studies [53, 54]
adopt usually the rate coefficients reported for SiH−
n ions
with SiH4 and SiHm radicals [55]. This is only a crude
approximation and there is an urgent need for the experimental
data for reactions of these anions.
The reaction of negative ion with a neutral particle can lead
to loss of electron, a so-called associative detachment (AD).
AD reactions are one of important loss channels of negative
Dissociative electron recombination. Dissociative recombination (DR) of an electron with a positive molecular ion is a
very fast process due to strong Coulomb interaction between
colliding particles. This reaction has no activation barrier
and the cross section is inversely proportional to the electron velocity. It is the main loss reaction of molecular ions
in low pressure plasmas in electropositive gases. The conservation of momentum and energy requires the formation of
two or more dissociation products, which can accommodate
the excess energy in the form of kinetic energy. The distribution of different molecular fragments among the products
(so-called branching ratio) depends on the electron energy and
the internal excitation of the colliding ion.
The rate coefficient for DR and the distribution of
dissociation products can be determined in ion storage ring
experiments [36]. Ions in their electronic ground state are
usually measured. These measurements have been done
for CH+ [37], C2 H+ , C2 H+3 , C2 H+4 [38], C2 H+2 [39], C3 H+n
(n = 1–8) [40] and C4 H+n (n = 1–9) [41] ions. However,
as will be shown later, when the molecular ion is in an excited
state the relative abundances of the dissociation products can
change.
In contrast to molecular ions, the recombination of atomic
ions with electrons is much slower, because the internal
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J. Phys. D: Appl. Phys. 43 (2010) 043001
Topical Review
−
ions. The AD of C−
n and Cn H anions with atomic H have
been reported in the literature with rates close to Langevin
limit [56]. It was shown that addition of atomic hydrogen to
C2 H2 plasma prevents dust particle generation, most probably
due to effective reduction of negative ion densities in these AD
reactions [57].
Dominant reactions are those between neutral species with
high density and radicals. The reaction rate is high due to the
high density of the stable molecules and large rate coefficients
close to the gas-kinetic collision limit, due to the localized free
electron on the radical. Radical–radical reactions may have
similar rate coefficients; however, radical densities are much
lower compared with stable molecules.
The two-to-one (or three body) association reactions are
often included in low pressure plasma chemistry models.
However, these reactions should be considered with care, since
they are not elementary reactions and their rate coefficients
depend strongly on pressure. These reactions are important at
higher pressures (combustion, pyrolysis) and proceed through
the formation of an activated complex with excess energy,
which is stabilized in a collision with a third body:
Charge transfer (CT) reactions. An electron is transferred
between a neutral particle and a positive or negative ion
in a CT reaction. It can proceed as a resonant process if
the electronic levels has the same energy, otherwise it is
referred to as being non-resonant [14]. As in the previous
case, they are driven by polarization forces and the cross
section exceeds the gas-kinetic one. CT reactions can result
in a dissociation of the newly formed ion. These reactions
are the most important ionization processes of hydrocarbon
molecules in remote plasmas, where for example C2 H2 is
admixed into a decaying plasma afterglow of noble gas plasma
with cold electrons. A prominent example is an Ar/C2 H2
ETP, where the electron temperature is below 0.3 eV and any
direct ionization of acetylene/precursor molecules by electron
impact is negligible. Reaction rate coefficients and branching
ratios of CT reactions between Ar+ ion with simple aliphatic
hydrocarbons at thermal energy have been measured by Tsuji
et al in flowing afterglow apparatus [58].
k1 (T )
A + B AB∗ ,
k−1 (T )
kM (T )
AB∗ + M −→ AB + M.
k1 (T )
k−1 (T )
(6)
with k1 (T ) and k−1 (T ) being the temperature dependent
forward and reverse reaction constants. The temperature
dependent rate coefficient is usually given as
k(T ) = AT n exp(−B/kB T )
(9)
The overall production rate of AB can be derived from the
rate equations at equilibrium situation (dnAB∗ /dt = 0) with
constant density of the activated complex:
dnAB∗
(10)
= nA nB k1 − nAB∗ k−1 − nAB∗ nM kM = 0,
dt
dnAB
k1 n M k M
= nAB∗ nM kM = nA nB
= nA nB kov . (11)
dt
k−1 + nM kM
At high densities of the third collision partner (nM kM k−1 ),
the overall rate coefficient kov is independent of this density
(so-called high pressure limit) and is just equal to the forward
reaction constant k1 , which can be very large. However, kov
is proportional to nM at low density of M with the slope equal
to k1 kM /k−1 . The corresponding reaction is then negligible
or of minor importance under low pressure conditions. Only
the association reaction of H with C4 H2 leading to the iC4 H3
radical (H2 C=C. –C≡CH) is predicted to have a significant
rate coefficient (∼3 × 10−12 cm3 s−1 ) at the pressure of 4 Pa
and gas temperature of 400 K [63]. Association reactions
can, however, play an important role at intermediate pressures
(few hundreds to few thousands of Pascal). Table 1 lists
the rate coefficient (at 400 K if not specified otherwise) of
most common hydrocarbon radicals in C2 H2 plasmas. Only
elementary reactions (two-to-two) are reported here except
the case of the above mentioned association reaction between
C4 H2 and H. It is clearly visible in table 1 that big differences
between reactivities of hydrocarbon radicals exist. Radicals
with a low number of H atoms (C, CH and C2 H) are much
more reactive than radicals with a high number of H atoms.
This is one reason for the difference between plasmas from
C2 H2 compared with plasmas from other simple hydrocarbon
molecules. Radicals with a low number of H atoms (mainly
C2 H) are preferentially formed in C2 H2 plasmas resulting in
extremely fast polymerization rates.
2.1.3. Reactions of neutral species. Mutual gas phase
reactions between neutral species are a source of new products
in the plasma chemistry. Most probable are second order
reactions of the type:
A+B C+D
(8)
(7)
in cm3 s−1 units. The measurements of rate coefficients,
especially for highly exothermic reactions of unsaturated
hydrocarbon radicals such as C2 H with low-lying electronic
states, are inherently complex and they have to be measured
under clearly specified physical and chemical conditions [59].
This complexity results in discrepancies among available
experimental results. Directly measured rate coefficients from
recent experiments should be preferred. Several databases with
rate coefficients exist online, for example NIST database [60]
or GAPHYOR database for atoms, molecules, gases and
plasmas [61].
Additional care has to be taken, when excited species are
involved, because their reactions can be accelerated compared
with reactions of ground state particles. For example, the
rate coefficients for reactions of ground and first electronically
excited states of C2 radicals with C2 H2 are significantly
different [62]. These excited species should be treated
separately from the ground state species in plasma chemistry
models.
2.1.4. Surface reactions. The surfaces confining plasma
play an important role in plasma chemistry. They represent
a geometrical boundary to the plasma and serve as source
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J. Phys. D: Appl. Phys. 43 (2010) 043001
Topical Review
Table 1. Reactions between hydrocarbon radicals and stable molecules at Tgas = 400 K.
Species
H
C
H2
C2 H 2
C 2 H4
C 4 H2
C 4 H4
CH2
a
H
CH4
CH
1.8 E−17g
CH3 +H2
1 E−17a
1.73 E−18c
C2 H3 +H2
∼E−12o
iC4 H3
∼3 E−12a
1.5 E−10e
CH+H
<5 E−15a,h
Products
2.6 E−10j
C3 /C3 H+H2 /H
2.1 E−10l
Products
?
1–5 E−11
H2 +C
6 E−12f
CH2 +H
1.7–7.6 E−11a
Products
3 E−10k
Products
2.6 E−10m
Products
?
?
?
CH3
a
9.5 E−11
CH+H2
<5 Ee-15a
Products
<1 E−16a
Products
<1.4 E−14a
Products
<1 E−14a
Products
9.75 E−14a
Products
?
C2 H
b
5.6 E−19
H2 +CH2
1.8 E−18b
CH4 + H
<1 E−18a
Products
<1 E−16a
Products
<1 E−16a
Products
?
<1 E−15a
Products
C 2 H3
c
<1 E−20
C2 +H2
1.38 E−12d
C2 H2 +H
4.41 E−12i
C2 H2 + CH3
1.3 E−10d
C 4 H2 + H
1.13 E−10n
C4 H4 +H
>1 E−10p
Products
6.6 E−11q
Products
5 E−11d
C2 H2 +H2
<1 E−17c,d
C2 H4 +H
7.2 E−17c
C2 H4 +CH3
6.1 E−15a
C4 H4 + H
2.2 E−13d
Products
?
?
a
NIST database [60], b Baulch et al [70], c Tsang et al [64], d Laufehr and Fahr [59], e Lin et al [68] at 300 K, f Becker
et al [74], g Sutherland et al [65], h at 300 K, i Ceursters et al [69], j Guadagnini et al [66], k Thiesemann et al [75],
l
Bergeat et al [67] at 298 K, m Thiesemann et al [76], n Vakhtin et al [73], o Klippenstein et al [63] for pressure of 4 Pa
and T ∼ 400 K—the only association reaction in this table with relatively high reaction constant, p Landera et al [71],
q
Tanzawa et al [72].
and sink for the phase particles. Surface reactions can also
significantly influence the composition of the gas mixture, in
which the plasma is ignited. The surface chemistry depends
on the surface properties (material, structure, dangling bond
density etc) and the energy and type of incoming particles.
Electrons are either captured directly at the surface of dielectric
materials or they are transported away by conductors. On
the other hand, the surface is a source of electrons as
well. Secondary electrons are emitted with probability γs
(secondary electron emission coefficient) upon impact of ions,
of metastables or of high energy photons. These secondary
electrons play an important role in igniting and sustaining the
discharge. Ions are neutralized upon impact with the surface.
Upon approaching the surface, they are accelerated by the
sheath voltage gaining a substantial amount of kinetic energy.
The resulting energetic ion bombardment leads to structural
changes in the surface material (bond breakage, displacement,
implantation) and to sputtering in the form of atoms and
small molecular fragments. The sputtering can be physical
or chemical. Physical sputtering occurs, if the momentum
transfer in the collision cascade leads to an energy transfer
to a surface atom exceeding its surface binding energy. In
chemical sputtering, in contrast, a volatile product is formed
in the material by a synergistic ion–neutral reaction, diffuses
to the surface and desorbs (cf figure 1). The volatile product
can be either formed in reactions of neighbouring displaced
atoms (for example a H2 formation by recombination of two
displaced H atoms [77]) or in a reaction of an incident neutral
particle at the defect site generated in a collision cascade at the
surface and in the subsurface region [78]. This ion–radial or
ion–neutral synergism is very often observed [79, 80, 81] and
is exploited in anisotropic etching or in ion-assisted thin film
growth [77].
Neutral particles (usually with low kinetic energy) can,
depending on their reactivity, be reflected back to the gas phase
with reflection probability r, they can react at the surface to
form volatile products with a recombination probability γ or
they can form chemical bond with the surface (film growth)
Figure 1. Scheme of interaction of energetic ions with the surface.
(Colour online.)
with a probability s, cf figure 2. Both latter events leads to
the loss of the particle from the gas phase and are described
by the overall surface reaction probability β = s + γ = 1 − r.
The loss of the reactive neutrals at the surface is very important
at low pressure plasmas where diffusion is fast and collision
frequency in the gas phase is small. The surface reaction
probability can depend sensitively on surface conditions such
as density of reactive sites and it can vary upon different plasma
conditions. Synergistic effects often occur, where the flux of
6
J. Phys. D: Appl. Phys. 43 (2010) 043001
Topical Review
the following) and they are mainly lost in the gas phase. It is
usually enough to only know the densities of main reaction
partners (e.g. neutral species with high densities such as
precursor gas and stable products) and the rate coefficients
to be able to estimate this lifetime. For example, the lifetime
of the C2 H radical in a discharge with 1 Pa partial pressure
of C2 H2 (nC2 H2 ∼ 2.4 × 1014 cm−3 ) is about τC2 H ∼ 32 µs
(the rate coefficient of 1.3 × 10−10 cm3 s−1 from table 1 has
been used and only reactions with C2 H2 have been considered).
This lifetime can now be compared with the loss time due to
diffusion to the reactor wall and reactions there given by
τdiff =
one species to the surface enhances the reactivity of some other
particle there. The well studied example is the surface reaction
probability of CH3 radicals at hydrogenated amorphous carbon
(a-C:H) surface, which can be enhanced from less than 10−4
to 10−2 , if the surface density of dangling bonds is enhanced
by the flux of atomic hydrogen [82]. On the other hand, the
very reactive radicals such as C2 H will stick with very high
probability even at a hydrogen-passivated surface.
2eff = 20 +
4D (1 − β/2) volume
v
β
surface area
(14)
with 0 the ‘geometrical’ diffusion length depending on
reactor geometry, v the particle kinetic velocity and β the
surface reaction probability discussed previously. We can
again estimate the diffusion loss time for the C2 H radical
(β ∼ 1) in 1 Pa of C2 H2 gas between two parallel plates
(for simplicity with infinite area) at a separation of 6 cm
(volume/surface area = 3 cm). With a diffusion coefficient of
C2 H
∼ 195 µs.
5×104 cm2 s−1 we obtain a diffusion loss time τdiff
This is 6 times longer than the lifetime due to gas phase
reactions calculated previously. The C2 H radical is, therefore,
mainly lost in gas phase reactions under these conditions. In
general, the main loss channel of a given species will depend
on the densities of other reactants, the rate coefficients, the
absolute pressure and the chamber geometry (both determining
the diffusion speed) and the surface reactivity.
To make this discussion complete, the residence time
should be mentioned as well. It is the upper limit for a
lifetime of any neutral species in the reactor and is given by
the ratio of the reactor volume to the actual pumping speed:
τres = Vreactor /Spump . The residence time is typically hundreds
of milliseconds to several minutes long.
The times τr , τdiff and τres are of course only rough
estimates not considering any spatial distributions in densities
and gradients in, e.g., gas temperature or the size of the
active plasma volume compared with the reactor volume. A
sophisticated modelling is necessary for a better treatment of
these issues.
2.2. Kinetics of PCRs
As already given in equations (1)–(5), the reaction rate depends
on the densities of reacting particles and the corresponding
rate coefficient, which is calculated by averaging the cross
section over the velocity distribution function of both colliding
particles. The density and energy distribution functions result
in reverse from the energy transfer and generation and loss
processes in elementary reactions in the gas phase and at the
surface. In addition, the densities depend on the transport
due to convection or diffusion and on acceleration of charged
particles by electromagnetic fields. Especially important is the
knowledge of EEDF, which is very often non-Maxwellian due
to many inelastic collisions with heavy particles and a relatively
low rate of thermalization collisions with other electrons in
low pressure weakly ionized plasma. Since Langmuir probe
measurements are difficult in depositing and electronegative
plasmas the EEDF is usually calculated with the help of a
Boltzman solver discussed later.
Any detailed discussion of the kinetics of PCRs is beyond
the scope of this paper and the reader is referred to the literature
[14, 20]. However, it is useful to know how to estimate typical
time scales (lifetimes of particles) observed in PCRs. Single
particles undergo chemical reactions with a frequency given
by equation (2). The inverted value of the sum of frequencies
of all gas phase reactions is an average lifetime τr of a single
particle before it is lost in gas phase reactions.
1
.
i n i ki
(13)
where eff is an effective diffusion length and D a diffusion
coefficient. The effective diffusion length can be expressed
with the help of an empirical formula [83]:
Figure 2. Scheme of interaction of neutral reactive species with the
surface. (Colour online.)
τr = 2eff
,
D
3. Study of PCRs
In a given plasma-chemical process, one wants usually to know
the densities and fluxes of reactive species, which play the
dominant role in the e.g. deposition or etching process. It is
possible to measure some of them directly, with experimental
difficulty increasing with increasing reactivity and decreasing
density of these species. Additionally, the overall production
or loss rates of these species can be determined, when
(12)
For very reactive radicals such as C or C2 H, this lifetime is
shorter than typical diffusion time to the wall (discussed in
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J. Phys. D: Appl. Phys. 43 (2010) 043001
Topical Review
parameter scans are done or when time resolved measurements
at abrupt changes in experimental conditions are followed (e.g.
at plasma ignition or shut down). One wants also to know
reaction mechanisms leading to the generation of these species.
Additional information and modelling of plasma is needed
in this case: electron density and EEDF, the level of internal
(ro-vibrational and electronic) excitation of species and the rate
coefficients or collision cross sections of occurring reactions.
Moreover, temporal and spatial variations of these parameters
can also play key role in the process. Any proposed reaction
mechanism can then be fitted with the help of these data and a
model of PCRs to the measured species densities to verify or
falsify it. One should keep in mind that it is impossible to be
certain that a proposed mechanism is correct. A mechanism
may be correct, if it is consistent with the observed data and if
no experimental evidence demonstrates that it is incorrect.
these species, because they take part in chemical reactions and
they are also dissociated in collisions with electrons. However,
their measurements do not always lead to detailed information
about the actual reaction mechanisms. Usually, many reaction
pathways can lead to their production and they themselves do
not contribute to e.g. deposition or etching of material.
Much more information about the plasma chemistry is
obtained when the densities of reactive radicals and ions
are measured. Their measurement is much more complex,
since these species have low densities with large gradients
towards the wall being caused by their high surface reactivity.
Advanced diagnostic techniques with high sensitivity such as
laser absorption spectroscopy (AS), laser induced fluorescence
spectroscopy or mass spectrometry have to be used. The
selection of a suitable diagnostic tool depends on the species
to be detected, the location where it should be measured
(volume versus wall) and the geometrical constraints at a
given plasma reactor. A combination of several diagnostics
is usually necessary. Laser based diagnostics are suitable for
the detection of transient reactive species. They are usually
very sensitive and they can measure line-integrated densities
(absorption techniques) or spatially resolved densities (e.g.
laser induced fluorescence). However, they are limited to
species with an optical transition within the spectral range
of the used laser system and with known constants of the
optical transition. This is especially limiting in the case of
hydrocarbon plasmas with their rich family of Cx Hy reactive
and stable species. From this point of view mass spectrometry
is a very suitable diagnostic to study hydrocarbon gas plasmas
and it will be discussed in detail here. Additionally, a short
summary of other diagnostic techniques used for quantitative
measurements in low pressure hydrocarbon plasmas will be
provided as well.
3.1. Experimental techniques for study of PCRs
3.1.1. Determination of plasma parameters. The electron
density and EEDF are two of the most important plasma
parameters to know since they are needed for the determination
of rates of electron impact driven reactions. The most
straightforward measurement of these parameters with
Langmuir probe (LP) is unfortunately not possible due to
the formation of insulating layer on the probe tip and other
methods has to be used. Microwave interferometry has
been used instead to measure electron densities in CH4 and
C2 H2 containing plasmas [57, 84, 85]. Alternatively, a plasma
absorption probe [86, 87] can be used and it has been applied to
measure electron density in Ar/C2 H2 plasma containing dust
particles [88]. The EEDF in reactive depositing plasmas is
usually estimated by solving the Boltzmann equation in the
two-term approximation [54, 89, 90]. Optionally, GordilloVázquez et al [91] have used optical emission spectroscopy
(OES) to determine electron mean electron temperature
in low pressure RF Ar/H2 /C2 H2 and Ar/H2 /CH4 plasmas.
Measurement of emission or absorption spectra also provides
information about internal excitation of plasma species
(their ro-vibrational excitation characterized by rotational and
vibrational temperature) [31, 84]. The rotational temperature
can usually be used to estimate gas temperature, an important
parameter when reactions with strong temperature dependence
occur.
Mass spectrometry. Mass spectrometry is capable of
measuring charged species according to their mass/charge
ratio. These species can originate directly from the plasma
or a neutral species can be ionized in the ionizer of the mass
spectrometer (MS). It does not have limitations inherent to
optical techniques, such as the dependence on existence of
suitable optical transitions of the species of interest and it also
measures ground state species directly. Once installed on the
plasma reactor, MS can provide data for most of the species
entering the MS, very important feature especially in the case
of hydrocarbon plasmas.
The principle of MS measurements is as follows: ions may
originate directly from the plasma or they are generated in a
so-called ionizer. Typically, a beam of electrons generated
by a hot filament is accelerated to a selected energy with a
narrow energy spread (Eelect ∼ 0.5 eV). This beam ionizes
neutral species present in the ionizer in the EII process. The
ions are extracted and focused into a quadrupole mass filter
formed by four parallel rods held at combination of alternating
and constant voltages. Only ions with selected mass-to-charge
ratio have stable trajectories on the axis of the mass filter and
are allowed to pass through it into the detector (e.g. secondary
electron multiplier). The ionizer is replaced by ion focusing
optics when ions originating directly from the plasma are
3.1.2. Measurement of plasma composition. The knowledge
of absolute densities of species involved in PCRs is always
very important information, since it allows, together with
the knowledge of energy distribution functions and reaction
cross sections, us to determine reaction rates quantitatively.
The densities of precursor gases and stable neutral plasma
chemistry products are usually the easiest to measure. They
have, due to their negligible reactivity at the surface, much
higher densities compared with transient reactive species,
which does not require high sensitivity diagnostics. They
have homogeneous density distributions over the whole reactor
volume, so they can be measured outside the active plasma
region or in the exhaust line. It is important to know densities of
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J. Phys. D: Appl. Phys. 43 (2010) 043001
Topical Review
measured. The ion energy distribution function can also
be determined, when a Bessel box or a sector field energy
filter is placed in front of the quadrupole mass filter. Mass
spectrometers have to be placed in a low pressure environment
(<10−5 mbar) for its proper operation.
In the case of neutral particle detection, the MS signal Si
of species i is proportional to its density in the ionizer [92–
94]. The unknown density of a given species i in the ionizer
can be determined, when another species j of known density
is measured under the same conditions and with the same MS
settings. The unknown density ni is then
ni,ionizer =
nj,ionizer
σj (E)
· F (mi , mj ) ·
· Si ,
Sj
σi (E)
(15)
where σi (E) and σj (E) are the ionization cross sections of
species i and j at electron energy E.
The function F (mi , mj ) expresses the mass dependent
transmission function of the MS and it can be calibrated by
measuring gases with known densities [94].
The measurement of neutral compounds in the plasma
reactor is achieved by connecting the MS pumping stage with
the plasma chamber through a small sampling orifice in such a
way that the ionizer is in direct line-of-sight with this orifice.
Stable and reactive species can reach the ionizer without being
lost in the collision with the wall and can be therefore detected.
The background density due to the pressure in the MS pumping
stage has to be separated from the density due to directly
sampled species arriving into the ionizer without any collision.
It is very useful to use multiple stage differential pumping
housing connected by aligned orifices leading to the formation
of a molecular beam (cf figure 3). The background signal
has still to be separated from the beam signal with the help
of a mechanical beam chopper allowing to measure the signal
intensity due to background only [92, 95]. Ideally, the chopper
should be placed in the last pumping stage housing the MS.
Its movement between blocking and open position should not
change the background density. If it is placed in one of the
preceding stages, the MB does not enter the last pumping stage
when blocked and the background density decreases. In this
case, the calibration procedure delivers proper results only if
the chopping frequency is much faster than the residence time
of the species in the MS pumping stage [95].
The density of the species in the molecular beam is
linearly proportional to the density at the sampling orifice (with
only geometry dependent constants) when the gas extraction
through the sampling orifice is effusive:
ni,MB (x) =
1 rs 2
ni,plasma ,
4 x
Figure 3. Scheme of the formation and measurement of the
molecular beam in double differential pumping stage. (Colour
online.)
molecule, which is typically several electron volts larger.
Therefore, the radical can be detected by lowering the electron
energy below the threshold for DI of the parent molecule.
When the measurements are performed with varying electron
energy at fixed mass, both the IP of the radical as well
as the appearance potential of the ions from DI of stable
atoms or molecules can be determined and used for species
identification.
TIMS has been successfully applied for radical density
measurements, for example, in SiH4 /CH4 /H2 glow discharge
plasmas [96], Cl2 plasmas used for Si etching [97], O2 and N2
plasmas [98, 99] and hot filament diamond CVD [100]. TIMS
can also be used for identifying and measuring the density of
excited species in a plasma. Agarwal et al reported TIMS
measurement of absolute densities of electronically excited
N2 in an inductively coupled N2 plasma [99]. Alternative
ionization schemes may also be used. For example, Fujii
used Li+ -ion-attachment mass spectrometry to study a C2 H2
microwave plasma [101]. However, the above-mentioned
calibration method cannot be used in this case.
Neutral species can also be measured with higher electron
energy, typically 70 eV, using the fact that EI ionization cross
section has its maximum there. Direct ionization is, however,
accompanied by DI in this case and a so-called cracking
pattern is obtained for each molecular species with signals at
the masses of the parent ion and of the fragment ions. The
final mass spectrum of a measured gas mixture is a linear
combination of cracking patterns of all constituents of the
mixture. The concentrations of these constituents can be
obtained by fitting the measured spectrum with calibration
cracking patterns [102, 103]. The acquisition of an overview
spectrum of all masses takes several tens of seconds. A better
time resolution of ∼100 ms can be achieved when a step-scan
procedure is employed [104, 105].
Mass spectrometry can be used to measure positive and
negative ions originating directly from the plasma. Since no
ionization is necessary and there are no ions in the background
(16)
where rs is the radius of the sampling orifice and x the
distance between sampling orifice and the ionizer. Under these
conditions, the densities of species i and j at the sampling
orifice can replace the ionizer densities in equation (15).
Threshold ionization mass spectrometry (TIMS) is used
for the measurement of transient reactive species. The TIMS
technique utilizes the difference of the EII threshold of a given
radical and the electron impact DI threshold of the parent
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Topical Review
gas in the MS, single stage differential pumping is sufficient.
There are, however, differences compared with measurements
of neutral species. First, ion fluxes through the sampling orifice
are measured and not ion densities. These fluxes are larger
for lighter ions due to their higher velocity at the same ion
density and ion energy. Positive ions are usually accelerated
in the sheath in front of the reactor wall gaining up to few
tens of electronvolts kinetic energy and the ion optics of the
MS may introduce chromatic aberation errors if the ion energy
distribution function is not monoenergetic [106]. Additionally,
negative ions are trapped in the plasma potential well and their
extraction is only possible when the plasma is operated in a
pulsed mode. If the pulsing frequency is faster than the rates
of diffusion losses of neutral species, the plasma composition is
only slightly altered. Deschenaux et al have measured negative
ions mass spectra (together with positive and neutral species)
in CH4 , C2 H2 and C2 H4 [107].
There are of course limitations connected with mass
spectrometry. It is not as sensitive as for example laser
based techniques, it does not provide information about
(ro-)vibrational excitation of the measured species and the
measures is always only at the surface. The quantitative
measurements are also very sensitive to systematic errors and
a very careful design and calibration of the whole measuring
system has to be performed.
molecules [116]. Two-photon absorption LIF (TALIF) can be
used to access species with optical transitions absorbing in the
VUV region such as H, O or N [117, 118].
OES is often used for its simplicity of application as an
indirect indication of plasma composition. However, it has
to be stressed that it exhibits several drawbacks. First, not
all species are emitting light in the 200–900 nm wavelength
range usually used for the OES measurements. In the case
of hydrocarbon plasmas, the H, CH and C2 emission lines
are usually detected. This often leads to the erroneous
conclusion that these species play a dominant role in the
plasma chemistry, underestimating the role of polyatomic
radicals whose emission lines are not located in this wavelength
region. Additionally, the emission intensity is proportional
to the density of the excited state and not to that of the
ground state and it provides, therefore, more information about
production rates of these excited state rather than about the
density of corresponding ground states. OES should be used
with care for estimation of plasma composition and species
densities.
3.1.3.
Time dependent measurements. Time resolved
measurements of transient changes of species densities after
abrupt change in experimental conditions can provide very
valuable information about kinetics of PCRs and they can
be used, together with time scale analysis with the help
of equations (12) and (13), to estimate gas phase reaction
constants or surface reaction probabilities. Time resolved mass
spectrometry measurements have been used for example for
testing polymerization reactions in C2 H2 plasmas (cf the next
section) or for determining surface reaction probabilities of
C2 H5 and CH3 radicals [119].
Temporal changes can of course be also followed by laser
based diagnostics. For example, CRD spectroscopy has been
used to probe quick transient changes in Si and SiH3 densities
induced by a short modulation of plasma density by applying
an additional bias voltage to the substrate. Combining these
measurements with total partial pressure variation, the rate
coefficient of Si atoms with SiH4 in the gas phase and reaction
probability of SiH3 radical at the surface could be determined
in an Ar/SiH4 ETP [120, 121].
Other commonly used diagnostics. The densities of stable
and reactive species can be measured by many diagnostics
besides MS [108]. Here some commonly used methods
to study low pressure hydrocarbon plasmas are listed and
commented.
AS measures the line integrated densities of absorbing
species. Tunable diode laser AS in the infrared region has
been used to measure concentrations of CH4 , C2 H2 and C2 H6
molecules and CH3 radical in CH4 containing low pressure
plasmas [84, 109, 110]. The sensitivity of AS can be enhanced
by several orders of magnitude when so-called cavity ring
down spectroscopy (CRDS) is applied [111, 112]. In CRDS, a
laser pulse is injected into a high-finesse optical cavity formed
by two highly reflecting mirrors and is stored there for up to
several microseconds. The pulse is monitored by measuring
the exponential decay of light intensity transmitted through
one of these mirrors. The advantage of CRDS is its long
effective absorption path due to multi-passing. This path is
several hundreds or thousands times longer than a single pass,
increasing hence correspondingly the sensitivity. Additionally,
an absorption rate (temporal evolution of light intensity) is
measured instead of an absolute absorption. This makes CRDS
insensitive to variation of a laser pulse intensity. Measurements
of H(n = 2) [113], C(1 S0 ) [114], CH [31, 113] or C2 [113], in
hydrocarbon plasmas have been reported. Berden et al have
provided a summary of the literature (published before 2001)
reporting CRD measurements of a variety of species [112].
Spatially resolved measurements (not line integrated) can
be performed by means of laser induced fluorescence (LIF).
The species are first excited by a short laser pulse followed
by the measurement of the emission of the excited state. LIF
have been used to measure CH, C2 and C3 radicals [115] or H2
3.2. Modelling of plasma chemistry
Modelling of plasmas including PCRs is essential in
understanding plasma based processes, since the level of
complexity of plasmas is too large and not all plasma
parameters can be measured. However, because not all
necessary input data needed for modelling are known, the
modelling results should always be validated by experimental
measurements.
Two approaches will be discussed in the following. First,
a simple zero- or quasi-one-dimensional kinetic models based
on rate equations will be presented. Second, the modelling
of a complete plasma based on fluid and hybrid models
including PCRs will be briefly summarized with references
to the literature for further reading.
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Topical Review
distributions of densities and other plasma parameters and
they cannot self-consistently treat electrons and ions and their
coupling to electromagnetic fields. To resolve this and to allow
for example the determination of spatially resolved fluxes of
reactive particles towards the surface or formation and densities
of positive and negative ions, more advanced one- or twodimensional fluid or hybrid models have to be used.
3.2.1. Zero-dimensional kinetic models. These models are
based on a set of linear differential equations (rate equations)
for the densities of plasma species, which are derived from
continuity equations for gas phase species:
∂ni ∂ni
+ D i ∇ 2 ni ,
(17)
+ ∇(ni vd ) = ∂t
∂t col
where ni is the density of ith particle, vd is the drift velocity
of the species and right-hand side describes the changes due
to collisions and diffusion with diffusion coefficient Di . If
we assume perfectly mixed reactor conditions (no density
gradients) and zero drift velocity, we can write
∂ni
ni
Fi
ni
=±
−
nk nl kkl (T ) +
−
,
∂t
V
τres
τdiff
k,l
3.2.2. Fluid and hybrid models. Fluid models use particle,
momentum and energy density balance equations derived from
velocity moments of the Boltzmann equation. They are
coupled to Poisson’s equation for electric field and electric
potential making the calculation self-consistent. Typically, the
particle density balance is considered for all plasma species,
the momentum conservation equation is replaced by a drift–
diffusion approximation and the energy density balance is
incorporated only for electrons [53, 54]. It is important to
determine the EEDF properly since it can deviate strongly
from a Maxwellian distribution. It can be calculated for a given
reduced electric field and gas mixture by solving the Boltzmann
equation in the two-term approximation [131]. For pressures
below few tens of pascals, the electron mean free path is too
long and the EEDF is no longer defined by the local electric
field there, where this field is strong, e.g. in sheaths. A kinetic
equation for electron motion has to be solved for an accurate
calculation of the EEDF. Particle-in-cell Monte Carlo collision
(PIC-MCC) methods can be used to solve this equation and can
be combined with a fluid model in a hybrid model [132, 133].
A one-dimensional approximation is suitable for systems,
where one dimension plays a dominant role, for example
the position in between electrodes in a parallel plate reactor
with an electrode spacing much smaller than their diameter.
More complicated geometries or processes, where also the
radial distributions are important, require modelling in two
dimensions to reach good agreement with the experimental
data. For example, Mankelevich et al [134] have reported a
model of sub-atmospheric pressure Ar/CH4 /H2 MW plasmas
used for diamond film deposition. The results of their model
have been validated by absolute density measurements of
radicals (H(n = 2), CH, C2 ) and stable plasma chemistry
products (C2 H2 , CH4 ). Other 2D fluid model of Ar/H2 /C2 H2
reactive plasma has been presented by Ostrikov et al [135]. It
should be noted that computational demands limits the number
of species and reactions implemented in 2D models. For
example, no negative ions, larger hydrocarbon molecules and
polymerization reactions have been included in this latter work
limiting the validity of the results. The overview of possible
modelling approaches to PCRs has been given recently by
Bogaerts et al [136].
(18)
where Fi is the particle flux into the reactor with volume V ,
τdiff is the reactor diffusion time as described in equation (13)
and τres is the residence time. The assumption of no density
gradients is not valid for reactive radical species and their
resulting densities are only averaged densities. These rate
equations have been used for example to check the possible
production mechanism of C2n H2 molecules in RF C2 H2
plasma [122]. Doyle and coworkers have used a kinetic model
to simulate radical and stable species densities in CH4 and
C2 H2 low pressure RF plasmas [123, 124] with reasonable
agreement between measured and modelled densities.
Zero-dimensional models can be made quasi-onedimensional for the case of e.g. ETPs, in which a precursor
gas is injected into an expanding plasma beam and the
plasma chemistry evolves along the beam z-axis (plug-down
geometry). All species then move with the same drift velocity
vd (z). When homogeneous densities across the beam diameter
A(z) are assumed, the rate equation can be rewritten as [125]
1 ∂[A(z)ni (z)vd (z)]
=±
nk nl kkl (T ),
A(z)
∂z
k,l
(19)
where the beam area A(z) is z-dependent due to the diffusion
of the species in the radial direction. The electron temperature
is only around 0.3 eV so the electrons are involved only in DR
reactions described easily by single rate coefficients. All other
reactions with high threshold energies can be neglected. A very
good agreement between measured and modelled densities
of hydrocarbon radicals has been achieved in an Ar/C2 H2
ETP [126]. The same plasma and also a similar dc-arc jet
reactor with CH4 /H2 /Ar feedstock gas mixture have been
modelled by Mankelevich et al with very good agreement
between measurements and model results [127].
Many other authors have used kinetic models to study
PCRs in gas mixtures with hydrocarbon gases. Morrison
et al [128] studied low pressure electron cyclotron resonance
plasma in CH4 used for deposition of a-C:H films. GordilloVázquez et al [89, 90, 129, 130] have studied RF and MW
discharges in CH4 /H2 and C2 H2 /H2 gas mixtures with a careful
consideration of the parameter range, for which a periodaveraged EEDF can be used.
These models, however, cannot consider all the
complexity of plasmas and PCRs. They neglect spatial
4. Low pressure acetylene plasmas
Plasma chemistry and the role of different PCRs in low
pressure C2 H2 plasmas will be discussed in the following.
Two examples will be considered: (1) the Ar/C2 H2 ETP with
electron temperature below 1 eV and the plasma chemistry
initiated by CT reactions and (2) capacitively coupled RF
plasmas in C2 H2 with electron impact driven plasma chemistry.
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(a)
Topical Review
Cascaded arc:
Ar (~100 sccs)
C2 H2+,∗ + e → products,
Ar
(b)
where the star at the acetylene ion indicates possible internal
excitation. The rate coefficients for reactions (20) and (21) are
kCT = 4.2 ± 1.4 × 10−10 cm3 s−1 and kDR ∼ 1 × 10−7 cm3 s−1 ,
respectively [58, 140]. The plasma chemistry following this
primary dissociation step is controlled by the ratio of the
injected C2 H2 flow to the ion and electron flow from the
cascaded arc:
(C2 H2 )
.
(22)
F =
(Ar + , e− )
Movable
housing
cathode
(3x)
25 - 55 cm
C2H2
injection
ETP
copper
plates
The precursor gas is efficiently depleted and plasma
chemistry is dominated by CT and DR reactions at low
admixtures of a precursor gas (F < 1). On the other hand,
when the flux of precursor gas is higher (F 1), ions and
electrons are depleted and neutral particle reactions dominate.
The ETP source is, under these conditions, an intense
source of reactive neutral particles. The deposition of SiO2 ,
hydrogenated amorphous or crystalline silicon, amorphous
silicon nitride or a-C:H films have been realized at very high
deposition rates with this type of discharge [141–145].
By admixing C2 H2 gas into the plasma a fast deposition
of a-C:H films with deposition rate up to 70 nm s−1 can be
achieved. Deposited films can be classified as medium hard
with hardness up to 17 GPa and a density of 1.7–2.1 g cm−3
[146, 147]. In contrast to the widely used low pressure PECVD
a-C:H deposition methods, where application of energetic ion
bombardment during the growth is necessary to maintain good
mechanical properties of the film [3], the ETP is capable of
depositing good quality a-C:H films even without energetic
ion bombardment of the film surface. The good film quality
is, however, only achieved under F > 1 conditions.
The understanding and proposed mechanisms of the
plasma chemistry and the a-C:H film growth in ETP strongly
depended on the available experimental data. The way this
understanding has evolved over one decade of experiments
nicely illustrates, how important it is to have as complete as
possible information about gas composition, rate coefficients
and surface reactivities. A short overview is given here:
from MS measurements of C2 H2 depletion, Langmuir probe
measurements and film properties it was established that
the Ar/C2 H2 ETP chemistry is dominated by CT and DR
reactions [148, 149]. The C2 H radical has been suggested as
the most probable product and a probable growth precursor. A
simple model based on the interaction of C2 H and H with the
surface could explain qualitatively the observed trends [150].
CRDS measurements of C, CH and C2 radicals led to the
conclusion that the contribution of these species to the growth
of hard a-C:H films is negligible [31, 114, 151]. A MS was
also used to monitor C4 H2 and C6 H2 molecules, formed in
C2 H driven polymerization reactions under F > 1 conditions.
Based on these results and regarding the high reactivity of the
C2 H radical in the gas phase the C2 H has been excluded as
growth precursor [152]. It was speculated about condensation
of C4 H2 at the plasma-activated surface in an effort to explain
the film growth. Finally, the threshold ionization MBMS and a
simple plug-down plasma chemistry model have been applied
to resolve this issue.
Shutter
nozzle
(anode)
low pressure
chamber
T1
T2
Chopper
T
3
QMS
Ionizer
Figure 4. Schematic drawing of the cascaded arc plasma source (a)
and ETP setup with implemented mass spectrometer in the substrate
holder (b).
4.1. Expanding thermal plasma
ETP is a thermal plasma generated at high pressure, which
expands into the low pressure reaction chamber. It can be used
in deposition or etching applications. It was first introduced
by Mäcker [137] and figure 4(a) shows the version used
at the Eindhoven University of Technology. A dc thermal
arc plasma is generated at sub-atmospheric pressure inside a
4 mm diameter channel with a length of several centimetres.
The channel is formed by several insulated and water-cooled
copper plates. Argon gas flow up to 200 sccs (standard cubic
centimetres per second, 1 sccs = 2.69×1019 particles s−1 ) can
be applied. The generated plasma is thermal with electron and
gas temperatures of about 1 eV [138]. The ionization degree
depends on the arc power and argon flow and varies from 5%
to 25%.
This thermal argon plasma expands into the low pressure
vessel. The expansion is supersonic until a stationary shock,
located approximately 5 cm downstream from the nozzle, after
which it is subsonic. Te drops in the expansion to less than
0.3 eV [139]. The pressure difference between the cascaded
arc and the vessel makes the arc operation independent of the
conditions in the expansion vessel, an ideal characteristic for
parameter studies.
Precursor gas is admixed to the expanding plasma through
an injection ring surrounding the plasma. Since Te is very
low, electron impact dissociation, excitation, ionization and
also electron attachment, all with high energy thresholds, can
be neglected. Plasma chemistry is then initiated by primary
CT reactions between precursor gas molecules and argon
ions followed by DR reactions of molecular ions with cold
electrons. For C2 H2 as precursor gas one obtains
Ar + + C2 H2 → Ar + C2 H2+,∗ ,
(21)
(20)
12
J. Phys. D: Appl. Phys. 43 (2010) 043001
Topical Review
A MBMS setup has been developed with the sampling
orifice at the substrate level to measure the plasma composition
at that position [95, 126], cf figure 4(b). 21 different
transient reactive hydrocarbon species and molecules have
been detected: CHy (y = 0–4), C2 Hy (y = 0,1,2), C3 Hy (y =
0,1,2), C3 Hy (y = 0,1,2), C4 Hy (y = 0,1,2),C5 Hy (y =
0,1,4,6) and C6 Hy (y = 2,6) [95]. Their absolute densities
have been determined as a function of C2 H2 flow, cascaded
arc current and distance from the cascaded arc [94, 95, 126].
The plasma chemistry in ETP can be represented to a
good approximation by a plug-down geometry in which the
(forward) plasma chemistry evolves along the expansion axis,
starting at the injection ring, where C2 H2 is admixed to the
argon ETP, and is terminated after the transport time (∼1 ms)
at the substrate holder, where reactive species contribute to
film growth. Only species with low surface reactivity (e.g.
CH2 ) or stable molecules get into the plasma background. The
effect of background processes resulting from a recirculation
of these stable products or from surface reactions is negligible.
A numerical quasi one-dimensional plasma chemistry model
based on particle conservation equations for the species
number density along the expansion axis has been developed
with only chemical reactions and CT and DR reactions being
considered. The model provides the species averaged number
densities across the beam at given distances from the injection
ring assuming (to the first approximation) that the directed
velocity is constant (1000 m s−1 ) along the subsonic part of
the expansion. The argon ion and electron fluence, the ETP
beam radius at the injection ring and some unknown reaction
constants are used as fitting parameters to optimize the model
output [126].
As already mentioned, the plasma chemistry is initiated by
CT and DR reactions (20) and (21). The DR reaction of ground
state C2 H+2 ion has been studied in ion storage ring experiments
and has five exit channels with the following yields:
+,gr
C2 H2
+ e → C2 H + H
→ C2 + H + H
→ 2CH
→ CH2 + C
→ C2 + H2
50%,
30%,
13%,
5%,
2%.
Figure 5. Densities of C, CH, CH2 , C2 and C2 radicals in Ar/C2 H2
ETP as a function of C2 H2 flow. Data taken from [126]. (Colour
online.)
yields of DR of ground state C2 H+2 ions are used in the
plasma chemistry simulation model, the relative magnitudes
of simulated densities of primary products do not correspond
to the measured ones. The measured CH density is much
too low and the C and CH2 densities are too high [126]. A
reasonable agreement between the simulated and experimental
data is obtained when modified yields are used for different
branches (23)–(27) of the DR reaction:
C2 H2+,ETP + e → C2 H + H
→ C2 + H + H
→ 2CH
→ CH2 + C
→ C 2 + H2
26%,
41%,
7%,
26%,
0%.
(28)
(29)
(30)
(31)
(32)
This is the most probably caused by the presence of internally
excited C2 H2+,∗ ion. It can be formed from the ground
state C2 H2 in the CT reaction with argon ion due to the
difference between ionization energy of C2 H2 (11.4 eV) and
argon (15.76 eV). This energy difference is large enough to
form, e.g., vinylidene H2 C=C+ ion, an isomer of C2 H+2 . The
DR of the H2 C=C+ ion with an electron will preferably yield the
CH2 + C channel and it will suppress the CH + CH and C2 H + H
channels, explaining hence the experimental observations.
Similar dependence on internal excitation of C2 H+2 ion has also
been observed for ion–molecule reactions [47].
Figure 6 shows the densities of C3 , C3 H, C4 and C4 H
radicals together with C2 H radical for comparison. These
radicals show second order behaviour since they are formed
in the reactions of primary radicals with C2 H2 . They are not
detected under F < 1 conditions, appear when F ∼ 1 and
are most abundant at C2 H2 rich conditions with F > 1. C4
and C4 H are formed in reactions of C2 and C2 H with C2 H2
and their densities drops again at very high C2 H2 flows since
both radicals further react with C2 H2 . This is not the case for
C3 and C3 H (and also C5 and C5 H not shown here). They are
formed dominantly in reactions of C atoms with C2 H2 . The
beam experiment of Cartechini et al with ground state C and
C2 H2 indicated that both C3 and C3 H are produced with similar
rates [153]. However, the much higher C3 density suggests
(23)
(24)
(25)
(26)
(27)
All possible carbon containing products of reaction (21)
have been detected and are shown in figure 5. The C2 H and
CH2 radicals are predominantly produced in the primary CT
and DR reactions and they therefore show first order behaviour.
They have maximum densities under F ∼ 1 conditions and
react away due to reactions with C2 H2 under F > 1 conditions
and due to secondary CT and DR reactions under F < 1
conditions. The density profile of C, CH and C2 radicals
is different from that of C2 H and CH2 due to secondary CT
and DR reactions of primary products with another argon ion
and electron pair. These reactions are also sources of C, CH
and C2 and their densities have therefore maxima under ionand electron-rich conditions (F < 1). All radicals shown in
figure 5 react very fast with acetylene and their densities are
very low under F 1 conditions.
With the knowledge of absolute radical densities we
can inspect the primary DR reaction (21). When measured
13
J. Phys. D: Appl. Phys. 43 (2010) 043001
Topical Review
Figure 6. Densities of C2 H, C3 , C3 H, C4 and C4 H radicals in
Ar/C2 H2 ETP as a function of C2 H2 flow. Data taken from [126].
(Colour online.)
Figure 7. Schematic representation of the plasma chemistry in
Ar/C2 H2 ETP. (Colour online.)
4.2. RF Plasmas
that conditions in ETP plasmas (gas temperature ∼1600 K and
possible internal excitation of reactants) favour C3 over C3 H as
reaction product. The C3 and C3 H densities reach maximum
values, which are independent of C2 H2 flow under F > 1
conditions. This is caused by the very low rate coefficient
with C2 H2 . The reaction coefficient of C3 radical with C2 H2
was measured up to the temperature of 610 K [154] and it
was found to be in the order of 10−14 cm3 s−1 . The reaction
coefficient of C3 H is expected to be similar. The reaction rates
are so slow because both radicals are resonantly stabilized; the
unpaired electrons are delocalized as a result of the existence
of two or more closely spaced resonant electronic structures.
Two isomeric forms, cyclic and linear, are possible for both C3
and C3 H, but it was not possible to distinguish which one has
been detected. The molecular dynamic studies indicates that
the cyclic form is more reactive at the surface [155].
The C3 radical has the highest density among the detected
radicals and since it has a very high sticking probability of
0.1–1 [156, 157] it is also the dominant contributor to the film
growth under F > 1 conditions. Additionally, it was shown
that the film refractive index (∼density) scales linearly with the
C3 density [126]. The film growth from C3 and other detected
radicals could also be successfully simulated in molecular
dynamics studies [155, 158].
The fact that C3 is an important growth precursor was quite
surprising and it is a result of several beforehand unknown or
unseen factors combined together: first, the primary CT and
DR reactions produce much more C than expected when only
ground state C2 H+2 ions are considered, second, the reaction
of C with C2 H2 favours the production of C3 radical under
ETP plasma conditions, third, the C3 radical does not react
with C2 H2 and other hydrocarbon molecules because it is
resonantly stabilized and fourth, the low energy electrons are
not able to dissociate C3 radicals, which would be otherwise the
case in e.g. low pressure plasmas treated in the next section.
The ETP is in this sense more selective than plasmas with
energetic electrons. The reaction pathways in Ar/C2 H2 ETP
are summarized in figure 7.
Low pressure non-equilibrium C2 H2 plasmas with energetic
electrons, generated typically by alternating voltages at RF
or MW frequencies, are used for deposition of DLC films or
for generation of hydrocarbon nanoparticles. Their plasma
chemistry is more complex compared with ETP. Electron
impact dissociation is responsible for the highly unselective
fragmentation of polyatomic species. Electron attachment
results in the formation of negative ions and EII is a source
of many positive ions. Additional cation–anion neutralization
reactions, ion–neutral reactions and reactions of neutral
hydrocarbon species increase further this complexity. All this
makes it difficult to resolve the chemistry pathways leading to
e.g. thin film deposition or cluster growth.
On the other hand, these plasmas are more common
than ETPs. They have been studied by many authors and
many experimental data and several simulations are available.
A short and in no way comprehensive overview of these
results will be given here with a summary of the up-to-date
understanding of the PCRs in this kind of plasma.
4.2.1.
Experimental results.
The vast majority of
plasma chemistry studies has been performed by MS
measurements of positive ions and neutral products
[101, 104, 105, 107, 123, 159–163]. Figure 8(a) shows the
neutral species mass spectrum measured with 70 eV electron
energy in an Ar/He/C2 H2 RF plasma [105]. Partial pressures of
measured species have been determined by decomposition of
the MS spectra with the help of Bayesian statistics [102, 103]
and are shown in figure 8(b). Figures 9 and 10 show
measurements of Deschenaux et al [107] of mass spectra of
positive ions and additionally also negative ions in an RF
capacitively coupled plasmas in C2 H2 used for dust particle
growth. The total pressure of p = 10 Pa, a C2 H2 gas flow of
C2 H2 = 8 sccm and an output RF power of P = 40 W have
been used. The negative mass spectrum has been measured
with the discharge pulsed at 500 Hz to allow the negative ions to
leave the positive plasma potential. Deschenaux et al have also
measured a mass spectrum of neutral species [164], which is
14
partial pressure [Pa]
-1
ion counts [s ]
J. Phys. D: Appl. Phys. 43 (2010) 043001
10
7
10
6
10
5
10
4
10
3
10
2
10
4 (He)
2
26
Topical Review
(a)
40 (Ar)
50
13
acetone
74
58
98
0
10
-1
10
-2
10
-3
10
-4
C2H2
H2, He, Ar and acetone
C4H2
CH4
C2H4
C3H4,6
C4H4 C6H2
C5H4 C H C8H2
6 4
C6H6
0
20
40
(b)
not shown
60
80
C8H6
100
126
120
128
140
152
160
Figure 10. Measured negative ion mass spectrum in low pressure
RF C2 H2 plasma. Reproduced with permission from [107]
copyright 1999 IOP Publishing.
m/z
Figure 8. The mass spectrum of neutral species measured with
70 eV electron energy in Ar/He/C2 H2 in plasma 1 s after plasma
ignition (a) and partial pressures of hydrocarbon molecules as
obtained from Bayes analysis (b). Adopted with permission
from [105] copyright 2008 American Chemical Society. (Colour
online.)
C2 H2 plasmas at 0.1–0.7 Torr pressure range in purified C2 H2
without and with the addition of He, Ar and Xe gases. Only
H2 and C4 H2 were observed as neutral products and ionic
species were dominated by C4 H+2 , C4 H+3 and C2 H+2 ions.
Additionally, a very fast formation of a visible precipitates
and a significant pressure drop has been observed for high
pressures and powers; however, no statement has been made
about a possible deposition mechanism. The addition of noble
gases has not significantly changed the plasma chemistry. No
significant exchange of potential energy between acetylene
and rare gas ions or metastables has been observed. Rare
gas ions have been detected only at low levels (<5%) and
only at pressures <0.3 Torr. Similar observations have been
made by other authors as well [159]. Positive ions have been
sampled at two positions: through the powered electrode and
at the grounded wall. The ions measured at the powered
electrode have been mainly formed in collisions of neutrals
with energetic electrons. The positive ion spectrum at the
grounded wall contained mainly products of ion–molecule
condensation reactions of the type:
C2 H2 + C2n H2 −→ (C2n+2 H4+ )∗ −→ C2n+2 H4+ ,
−→ C2n+2 H3+ + H,
−→ C2n+2 H2+ + H2
Figure 9. Measured positive ion mass spectrum in low pressure RF
C2 H2 plasma. Reproduced with permission from [107] copyright
1999 IOP Publishing.
(33)
(34)
(35)
in which C2 H2 is the main reaction partner. As expected,
the relative abundances of these ions were pressure dependent
and shifted from dominant presence of C2 H+2 at low pressure
to larger ions at higher pressures. It was confirmed by
measurements of Fujii [101] of a MW discharge at ∼200–
6700 Pa pressure range with C6 H+2 being the ion with highest
signal intensity and with decreasing relative presence of
C2 H+2 and C4 H+2 at higher pressures. It was shown that the
branching of reaction (35) depends also on internal excitation
of molecular ions [47, 48]. The rate coefficients for these
reactions are typically between 10−10 and 10−9 cm3 s−1 in the
case of acyclic ions. The cyclic ions are less reactive with
C2 H2 [48]. The plasma chemistry models can reproduce very
well the MS measurements of positive ions [53, 54] because
very similar to spectrum shown in figure 8(a). All spectra show
a typical feature of C2 H2 plasmas: species with an even number
of carbon atoms are dominant plasma chemistry products. This
behaviour is not observed in plasmas with other hydrocarbon
gases such as CH4 or C2 H4 . Although, species with an odd
number of C atoms are also detected in C2 H2 plasmas, their
densities stay always at very low levels and they originate, as
will be shown later, partially from impurities in commonly used
industry grade acetylene (acetone, C2 H4 ) and from surface
reactions.
Positive ions. The measurement of positive ions with MS
is straightforward and was reported by many authors in the
literature. Vasile and Smolinsky [160] have characterized
15
J. Phys. D: Appl. Phys. 43 (2010) 043001
Topical Review
reliable rate coefficients are available and reaction pathways
leading to positive ion formation are well understood.
The decrease in C2 H2 partial pressure visible in figure 11(a)
shows that it is very effectively consumed in PCRs. This strong
decrease is typical for low pressure C2 H2 discharges and noble
gas is usually added to the mixture to keep the pressure at set
value.
Figure 11(b) shows the presence of C2 H4 even before
plasma ignition indicating that C2 H4 is an impurity in the
source gas. Additionally, also acetone was detected in the
industry grade C2 H2 gas used in this study. The concentrations
of C2 H4 and acetone were around 1% and their influence on the
plasma chemistry could be tested by using acetone-free C2 H2
gas and by adding a known amount of C2 H4 (up to 8%) into the
gas mixture. The presence of acetone in the discharge has no
big influence: it leads to the formation of stable CO molecules
and a slight increase in CH4 and H2 signals [104, 105]. The
effect of C2 H4 addition is more complex. Its presence does
not affect the formation of polyacetylenes; however, the MS
signals of Cn H4 (n = 3–6) species increase linearly with
C2 H4 addition [165]. For example, the C4 H4 molecule is
produced in reaction of C2 H4 with C2 H with a rate coefficient
of k = (1.13 ± 0.14) × 10−10 cm3 s−1 [73]. C2 H4 serves most
probably as a precursor for the formation of Cn H4 molecules.
But C2 H4 is not just an external impurity. It was argued
that C2 H4 is also generated directly in the plasma [165],
especially at times longer than 2.5 s after plasma ignition under
conditions, in which the relative concentration of molecular
hydrogen and also CH4 is high (cf figure 11(c). It is well
known that atomic hydrogen leads to erosion of hydrocarbon
films [166, 167] and it is therefore plausible that some species
are generated at the surface of the hydrocarbon film as etch
products under hydrogen rich conditions. To check this
hypothesis a gas composition of Ar/H2 plasma generated in an
inductively coupled plasma reactor with a thick hydrocarbon
film on the wall has been measured by means of residual gas
analyzer (RGA). The plasma conditions were Ar gas flow
5 sccm, H2 gas flow 0.5 sccm, total gas pressure 3 Pa and
applied power 200 W. The hydrocarbon film was generated
in Ar/C2 H2 gas mixture under similar conditions and the RGA
was a small MS device (Prisma QMS 200) connected to the
reactor through 400 µm orifice. Figure 12 shows the partial
pressures of H2 , CH4 and C2 H4 as a function of time after
plasma ignition, first in a pure Ar plasma and then after turning
on 0.5 sccm of H2 flow into the reactor. It is clearly visible
that CH4 and C2 H4 are generated when H2 is present in the
reactor, however, only when the plasma is switched on. C2 H6
molecules have been detected as well, but with densities at
least ten times lower than those of CH4 and C2 H4 . This
experiment clearly shows that CH4 and C2 H4 are produced in
surface reactions of hydrogen at the plasma-activated surface
of a hydrocarbon film (and most probably also dust particles,
if present). It is consistent with the observation that H2 , CH4
and C2 H4 are released from the hydrocarbon layers in the
thermal desorption experiments [168] even at temperatures as
low as 400 K. The fluxes of ions, excited species and hydrogen
atoms may accelerate significantly this release. Additionally,
it was already shown previously that C8 H6 (most probably
phenylacetylene) is also formed in surface reactions [104].
Neutral species. The generation of neutral plasma chemistry
products is dominated by reactions of C2 H radicals. C2 H
is formed in electron impact dissociation of C2 H2 with a
threshold energy of 7.5 eV [28]:
C2 H2 + e− (Eel 7.5 eV) −→ C2 H + H + e− .
(36)
Breaking the triple bond of C2 H2 in electron impact
dissociation of ground state acetylene is less probable due to a
high threshold of ∼10 eV. The C2 H radical reacts very quickly
with almost all hydrocarbon molecules. Its carbon–carbon
bond is conserved and products with even number of carbon
atoms are mainly formed (cf table 1).
The dominant neutral plasma chemistry products are
H–(C=C)n –H polyacetylene molecules, which are formed in
polymerization reactions involving C2 H radicals:
C2n H2 + C2 H → C2n+2 H2 + H.
(37)
Rate coefficients for the C2 H addition to C2 H2 and C4 H2
are 1.3 × 10−10 cm3 s−1 and >10−10 cm3 s−1 , respectively
(cf table 1).
Doyle [123] has measured absolute densities of C4 H2 ,
C6 H2 and additionally also H2 in RF C2 H2 plasmas at 4 Pa,
which was used to deposit hard DLC films. The conversion
rates of product species and the growth of thin film have
been estimated in a chemistry model based on steady-state
rate equations. Experimentally measured yields of C4 H2 ,
C6 H2 , and film growth could be reproduced very well. It
was discussed that C2 H radicals are not the dominant growth
precursor. C4 H3 and C6 H3 were proposed instead with small
contribution of C2 H and C2 H3 . However, the author admits
that his model is not much sensitive to the exact chemistry
involved. No comment on possible formation of dust particles
has been made.
Consoli et al [104, 105, 165] have studied the temporal
evolution of absolute densities of neutral plasma chemistry
products in an RF CCP from Ar/He/C2 H2 via molecular beam
mass spectrometry. The applied power was rather high, 80 W,
and the plasma composition changed quickly after plasma
ignition. The measurement was, therefore, performed in a
step-scan procedure yielding a time resolution of 100 ms.
Polyacetylenes up to C10 H2 were detected together with nine
other stable hydrocarbon molecules. Radical measurements
were not possible because of the large distance between
sampling orifice and plasma. Figure 8 shows the measured
mass spectrum at 1 s after plasma ignition and corresponding
decomposed partial pressures of detected compounds. The
overview of the evolution of partial pressures for the most
important species in the first 4.5 s after plasma ignition is
shown in figure 11. Time resolved measurements clearly
confirmed that the polymerization sequence (37) is a source
for polyacetylenes. Two seconds after plasma ignition, the
densities start scaling with the C2 H2 signal (cf the same slopes
at density evolutions in figure 11(a). An equilibrium between
production and losses inside the plasma volume is reached.
16
J. Phys. D: Appl. Phys. 43 (2010) 043001
Topical Review
vinylidene anion H2 C=C− , HC≡CH− is unstable with respect
to autodetachment). It is interesting to note that C6 H− was the
first negative ion detected in the interstellar medium [169]. The
reaction pathway leading to the formation of C6 H− in C2 H2
plasmas is not resolved at the moment. No experimental data
are available for DEA to C6 H2 , however, it is expected, based
on the photoelectron spectroscopy measurements and simple
correlation diagram [170], that it has three resonances: one
below 0 eV (not accessible), one around 3.6 eV and one around
7.3 eV [171]. The shape resonance around 3.6 eV has a high
energy with a large autodetachment width and it will unlikely
play a role in DEA [171]. Therefore, it is expected that the
rate of DEA to C6 H2 will be smaller than to C4 H2 and cannot
explain the observed high C6 H− signal. We have proposed
that branched and internally excited C6 H2 particles, formed
in reactions of C2 H with central carbon atoms of C4 H2 , could
have large cross sections for DEA and could serve as precursors
for C6 H− anions [54]. However, the reaction of C2 H with the
central C atoms in C4 H2 will probably have a higher activation
barrier and much lower reaction probability, as it is the case for
reactions with H [63]. This reaction pathway will, therefore,
have most probably only a marginal contribution to C6 H−
formation. More plausible seems the ion–neutral reaction
between C4 H− and C2 H2 . The rate coefficient is not known,
but it should be higher than 10−12 cm3 s−1 value used in C2 H2
plasma chemistry models [53, 54]. This value was estimated
based on the analogy to SiH3− +SiH4 reaction in silane plasmas.
The low rate coefficient of SiH3− + SiH4 reaction corresponds
to the low reactivity of the SiH3 radicals with SiH4 . Since
C2 H (and probably also C4 H) is much more reactive towards
C2 H2 it is very probable that also the C2n H− anion reaction
with C2 H2 can reach values close to the ∼10−10 –10−9 cm3 s−1
rate coefficient of hydrocarbon cations. C4 H− is probably
formed both in DEA to C4 H2 (which is more effective than
DEA to C2 H2 due to a 20 times larger cross section, even
if the resonance is located at higher energy of 5.25 eV [54])
and in ion–molecule reactions. The reaction pathway leading
to H2 C=C− detected at mass 26 is not known. Nucleation
of dust particles proceeds most probably through sequential
anion-C2 H2 reactions.
partial pressure [Pa]
1
10
(a)
0
10
-1
10
-2
10
-3
10
-4
10
-1 (b)
10
-2
10
-3
10
-4
10
-5
10
-1
10
-2
10
-3
10
-4
10
-5
10
C2H 2
C4H 2
C6H 2
C8H 2
C2H 4
C4H 4
C6H 4
(c)
C H4
H2
C6H 6
(relative only)
no plasma
0.4s
1.0s
1.5s
2.0s
2.5s
3.0s
3.5s
4.0s
4.5s
species
0.007
plasma off
H2 partial pressure [Pa]
0.20
plasma on
0.006
0.005
H2 gas
0.15
H2
flow on
C2H4
0.10
0.003
plasma on
0.002
0.05
0.00
-200
0.004
C H4
0.001
0.000
0
200
400
600
CH4 and C2H4 partial pressure [Pa]
Figure 11. The density evolution of hydrocarbon species detected in
low pressure Ar/He/C2 H2 plasma. Adopted with permission
from [105] copyright 2008 American Chemical Society. (Colour
online.)
800
Time after plasma ignition [s]
Figure 12. The measured densities of CH4 and C2 H4 species in
Ar/H2 plasma in reactor with a-C:H film covered wall. Plasma
switched on at 0 s, H2 flow switched on at 190 s. (Colour online.)
Negative ions. C2 H2 plasmas are well known for their
ability to form very quickly dust particles. This fact is
a result of an effective generation of negative ions, which
serve as nucleation centres for dust particles [52]. Negative
ion formation in C2 H2 plasmas is favoured due to lowlying NIRs at 2.95 eV (σ2.95 eV ∼ 3.7×10−20 cm2 ) for
C2 H2 and at 5.25 eV (σ5.25 eV ∼ 7.3 × 10−19 cm2 ) for
diacetylene [34], which overlap effectively with the EEDF.
Other frequently used hydrocarbon molecules have resonances
located at higher energies, CH4 and C2 H4 at around 10 eV
or C2 H6 at 9 eV, resulting in a very small overlap with the
EEDF and very low production rates of negative ions. It
was shown experimentally [107] that the negative ion mass
spectra measured in CH4 and C2 H4 discharges exhibit much
lower signal intensities compared with the mass spectrum in
figure 10. Moreover, it was demonstrated that dust particle
production in CH4 plasma proceeds first through generation
of C2 H2 [57]. The anion with the highest signal intensity
in figure 10 is C6 H− followed by more than 10 times
−
smaller signals of C4 H− , C8 H−
2 and C2 H2 (most probably a
4.2.2. Summary of PCRs in C2 H2 plasmas with energetic
electrons.
PCRs in low pressure C2 H2 plasma are
schematically summarized in figure 13. The main compounds
are polyacetylenes, positive ions with an even number of
carbon atoms and two or more hydrogens and negative ions
also with even number of carbon atoms and with one or
two hydrogens. Neutral species with four or more hydrogen
atoms and with both even or odd number of carbon atoms
are much less abundant. The following PCRs have been
recognized. (i) polyacetylenes (C2n H2 ) are generated in C2 H
driven polymerization starting with C2 H2 . C2 H2 has usually
the highest density and the densities of larger polyacetylenes
decrease with their length. The C2 H radical is generated
in electron impact dissociation of C2 H2 . (ii) Positive ions
are generated in EII of polyacetylenes and in the C2 H2
driven polymerization in ion–C2 H2 reactions. Their relative
abundances are determined by the C2 H2 partial pressure.
17
J. Phys. D: Appl. Phys. 43 (2010) 043001
Topical Review
5. Conclusions
The PCRs in low pressure non-equilibrium plasmas and the
experimental and theoretical methods for their investigation
have been briefly summarized with emphasis on processes
taking place in low pressure C2 H2 discharges. A plethora of
reaction mechanism is involved that together with the complex
hydrocarbon chemistry make these plasmas very complex and
difficult to investigate. It was shown that as much as possible
information has to be gathered in order to understand the PCRs.
The knowledge of plasma composition, the fingerprint of PCRs
and the seed for the theoretical plasma models, is essential and
the most important knowledge.
Two examples of low pressure C2 H2 plasmas have been
discussed in detail. First, it was shown that a remote
Ar/C2 H2 ETP with low electron temperature of 0.3 eV is a
very effective radical source with plug-down plasma chemistry
and with relatively high selectivity compared with plasmas
with energetic electrons. The plasma chemistry is initiated
by CT and DR reactions. This type of plasma can generate
large numbers of resonantly stabilized radicals unreactive in
the gas phase, which have, however, large sticking probability
and contribute dominantly to the film growth. Second,
an RF capacitively coupled plasma with a typical electron
temperature of several electronvolts has been introduced as a
commonly used low pressure plasma, which contains energetic
electrons. Electron collisions with polyacetylenes and C2 H
and C2 H2 driven polymerization of neutral and ionic species
play a dominant role. Parallel to these volume reactions,
surface reactions of most probably hydrogen atoms and
energetic ions with grown a-C:H films and dust particles are
source of additional hydrogen rich species.
Figure 13. The reaction pathways in low pressure C2 H2 plasmas.
(Colour online.)
(iii) Negative ions are generated in DEA to polyacetylenes
followed by C2 H2 induced polymerization in anion-C2 H2
reactions. The DEA to C4 H2 is most probably more effective
than to C2 H2 due to larger cross section and is, therefore, the
most important initialization reaction of this polymerization
chain. The most abundant negative ion is C6 H− . Experimental
data (rate coefficients and DEA cross sections) necessary
to explain this observation in detail are unfortunately not
available. This negative ion polymerization route leads to
dust particle formation. (iv) Atomic hydrogen is a byproduct
in most of the gas phase reactions. This hydrogen leads in
combination with ion fluxes to the surface to erosion and
chemical sputtering of the a-C:H film formed on the reactor
walls (and probably also to erosion and chemical sputtering
of the dust particles if present). The main products of the
surface reactions are H2 , CH4 and C2 H4 . These species can
polymerize further into Cx H4 species in reactions with C2 H.
(v) The growth of a-C:H films is probably due to deposition
of radicals with high sticking coefficient but at the same time
low or only moderate reactivity in the gas phase. Possible
candidates are resonantly stabilized iC4 H3 formed in reaction
of H atom with C4 H2 or C2 H3 . The C2 H radical can also
contribute to the film growth, however, its importance for
growth depends on the partial pressure of C2 H2 , since it is very
quickly lost in gas phase reactions. No direct measurements of
radical fluxes towards the surface and corresponding growth
rates are available at the moment.
Acknowledgments
The author would like to thank Achim von Keudell and Richard
van de Sanden for their support in the past and current work
presented in this review, Michael Allan and Olivier May for
the fruitful discussion about dissociative attachment reactions.
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