Quantum cascade laser investigations of CH4 and C2H2 interconversion in hydrocarbon/H2 gas mixtures during microwave plasma enhanced chemical vapor deposition of diamond

Abstract

CH 4 and C2H2 molecules (and their interconversion) in hydrocarbon/rare gas/H2 gas mixtures in a microwave reactor used for plasma enhanced diamond chemical vapor deposition (CVD) have been investigated by line-of-sight infrared absorption spectroscopy in the wavenumber range of 1276.5−1273.1 cm−1 using a quantum cascade laser spectrometer. Parameters explored include process conditions [pressure, input power, source hydrocarbon, rare gas (Ar or Ne), input gas mixing ratio], height (z) above the substrate, and time (t) after addition of hydrocarbon to a pre-existing Ar/H2 plasma. The line integrated absorptions so obtained have been converted to species number densities by reference to the companion two-dimensional (r,z) modeling of the CVD reactor described in Mankelevich et al. [J. Appl. Phys. 104, 113304 (2008)]. The gas temperature distribution within the reactor ensures that the measured absorptions are dominated by CH4 and C2H2 molecules in the cool periphery of the reactor. Nonetheless, the measurements prove to be of enormous value in testing, tensioning, and confirming the model predictions. Under standard process conditions, the study confirms that all hydrocarbon source gases investigated (methane, acetylene, ethane, propyne, propane, and butane) are converted into a mixture dominated by CH4 and C2H2. The interconversion between these two species is highly dependent on the local gas temperature and the H atom number density, and thus on position within the reactor. CH4→C2H2 conversion occurs most efficiently in an annular shell around the central plasma (characterized by 1400<Tgas<2200 K), while the reverse transformation C2H2→CH4 is favored in the more distant regions where Tgas<1400 K. Analysis of the multistep interconversion mechanism reveals substantial net consumption of H atoms accompanying the CH4→C2H2 conversion, whereas the reverse C2H2→CH4 process only requires H atoms to drive the reactions; H atoms are not consumed by the overall conversion.

Full text

Quantum cascade laser investigations of CH4and C2H2interconversion
in hydrocarbon/H2gas mixtures during microwave plasma
enhanced chemical vapor deposition of diamond
Jie Ma,1Andrew Cheesman,1Michael N. R. Ashfold,1,a兲Kenneth G. Hay,2
Stephen Wright,2Nigel Langford,2Geoffrey Duxbury,2and Yuri A. Mankelevich3
1School of Chemistry, University of Bristol, Bristol BS8 1TS, United Kingdom
2Department of Physics, University of Strathclyde, John Anderson Building, 107 Rottenrow,
Glasgow G4 0NG, United Kingdom
3Skobel’tsyn Institute of Nuclear Physics, Moscow State University, Leninskie Gory, Moscow 119991, Russia
共Received 31 July 2008; accepted 19 June 2009; published online 5 August 2009兲
CH4and C2H2molecules 共and their interconversion兲in hydrocarbon/rare gas/H2gas mixtures in
a microwave reactor used for plasma enhanced diamond chemical vapor deposition 共CVD兲have
been investigated by line-of-sight infrared absorption spectroscopy in the wavenumber range of
1276.5−1273.1 cm−1 using a quantum cascade laser spectrometer. Parameters explored include
process conditions 关pressure, input power, source hydrocarbon, rare gas 共Ar or Ne兲, input gas mixing
ratio兴, height 共z兲above the substrate, and time 共t兲after addition of hydrocarbon to a pre-existing
Ar/H2plasma. The line integrated absorptions so obtained have been converted to species number
densities by reference to the companion two-dimensional 共r,z兲modeling of the CVD reactor
described in Mankelevich et al. 关J. Appl. Phys. 104, 113304 共2008兲兴. The gas temperature
distribution within the reactor ensures that the measured absorptions are dominated by CH4and
C2H2molecules in the cool periphery of the reactor. Nonetheless, the measurements prove to be of
enormous value in testing, tensioning, and confirming the model predictions. Under standard
process conditions, the study confirms that all hydrocarbon source gases investigated 共methane,
acetylene, ethane, propyne, propane, and butane兲are converted into a mixture dominated by CH4
and C2H2. The interconversion between these two species is highly dependent on the local gas
temperature and the H atom number density, and thus on position within the reactor. CH4
→C2H2conversion occurs most efficiently in an annular shell around the central plasma
共characterized by 1400⬍Tgas⬍2200 K兲, while the reverse transformation C2H2→CH4is favored
in the more distant regions where Tgas ⬍1400 K. Analysis of the multistep interconversion
mechanism reveals substantial net consumption of H atoms accompanying the CH4→C2H2
conversion, whereas the reverse C2H2→CH4process only requires H atoms to drive the reactions;
H atoms are not consumed by the overall conversion. © 2009 American Institute of Physics.
关DOI: 10.1063/1.3176971兴
I. INTRODUCTION
Microwave 共MW兲plasma activation of dilute hydrocar-
bon in hydrogen gas mixtures finds widespread use as a route
to growing high quality diamond films by chemical vapor
deposition 共CVD兲methods.1–4As discussed previously,5the
H2molecules dissociate following excitation within the
plasma ball, and the resulting H atoms diffuse throughout the
reactor volume. The lack of efficient H atom loss processes
in these gas mixtures ensures that H atom densities in the
cooler periphery of the reactor are far in excess of those
expected on the basis of local thermodynamic equilibrium. H
atoms fulfill a number of important roles in the CVD
process—both in the gas phase and at the gas-surface inter-
face. The studies described here focus on aspects of the
former, where H atoms drive radical formation via the so-
called “H-shifting” abstraction reactions 共1兲and 共2兲and, in
the cooler regions, third-body stabilized H addition reactions
共3兲and 共4兲that culminate in the interconversion between
C1共CHy兲and C2共C2Hx兲species,1,6
CHy+HCHy−1 +H
2,y=4−1, 共1兲
C2Hx+HC2Hx−1 +H
2,x=6−1, 共2兲
C1Hy+H共+M兲C1Hy+1共+M兲,yⱖ0, 共3兲
C2Hx+H共+M兲C2Hx+1共+M兲,xⱖ0. 共4兲
Interconversions between CHyand C2Hxspecies occur on
timescales that are much shorter than the transit time for
feedstock gas through most CVD reactors, leading to the
expectation that the distribution of CHy,C
2Hx, etc., species
present in an activated hydrocarbon/H2gas mixture should
be rather insensitive to the choice of hydrocarbon feedstock
gas. Such a view is supported by early studies7demonstrat-
ing growth of diamond films with similar morphologies and
at similar rates from a range of different hydrocarbon source
a兲Author to whom correspondence should be addressed. Tel.: 共117兲-
9288312/3. FAX: 共117兲-9250612. Electronic mail:
mike.ashfold@bris.ac.uk.
JOURNAL OF APPLIED PHYSICS 106, 033305 共2009兲
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gases 共at a constant input carbon mole fraction兲, and by Fou-
rier transform infrared absorption8and molecular beam mass
spectrometry9,10 measurements of the densities of various of
the more abundant stable species 共e.g., CH4,C
2H2, and
C2H4兲in MW activated CH4/H2and C2H2/H2gas mixtures.
Both of these gas phase diagnostic experiments had some
limitations, however. The former gave no spatial informa-
tion, while the latter only returned relative 共rather than abso-
lute兲concentrations.
There is a continuing need for new and improved, quan-
titative, nonintrusive, in situ probes of the gas phase chem-
istry and composition, both to refine our understanding of the
diamond CVD process and for improved process control ap-
plications. Celii et al.11,12 demonstrated the potential appli-
cability of infrared tunable diode laser absorption spectros-
copy methods for detecting CH3radicals, and C2H2and
C2H4molecules, in HF activated CH4/H2gas mixtures in the
late 1980s, but the subsequent take-up of such methods has
been slow. In part, this is because such methods provide
line-of-sight absorbances, which can only be turned into ab-
solute column 共or number兲densities given detailed knowl-
edge of the 共generally very inhomogeneous兲distribution of
species concentrations and temperatures along the viewing
column. Measurements of this kind are thus of limited quan-
titative value in the absence of companion high level reactor
modeling. Such detailed studies are now starting to appear,
however—notably measurements of CH3radicals, as well as
the stable species C2H2,CH
4, and C2H6, in MW activated
CH4/H2mixtures in a quartz bell jar reactor used for dia-
mond CVD.13–15
We recently demonstrated16 the use of a quantum cas-
cade 共QC兲laser17–19 for probing CH4and C2H2molecules,
and their interconversion, ina2kWMWreactor operating
with both CH4/Ar/H2and C2H2/Ar/H2feedstock gas mix-
tures, as a function of process conditions 共e.g., input hydro-
carbon mole fraction, total gas pressure, and applied MW
power兲. We also exploited the rapid output frequency sweep
共“chirp”兲rate of pulsed QC lasers to gain insights into the
time evolution of the CH4/C2H2ratio when either is intro-
duced into, or removed from, a pre-existing Ar/H2plasma.
Here we present higher sensitivity single pass QC laser ab-
sorption measurements of CH4and C2H2molecules, and
their interconversion, in this MW reactor, as functions of the
above process conditions, the H2/Ar mixing ratio, and verti-
cal distance 共z兲above the substrate surface for a wider vari-
ety of feedstock hydrocarbon source gases 共not only methane
and acetylene but also n-propane, n-butane, ethene, and pro-
pyne兲. These data serve to demonstrate the efficiency with
which all precursor hydrocarbons are processed to 共locally
equilibrated兲mixtures dominated by CH4and C2H2under
typical CVD conditions. As noted previously,14–16 gas tem-
perature and number density considerations dictate that the
bulk of the monitored CH4and C2H2molecules are localized
in the cooler periphery of the reactor, remote from the
plasma ball. Complementary, spatially resolved, column den-
sity measurements of radical species 关C2共a兲and CH共X兲兴 and
of electronically excited H共n=2兲atoms—obtained by cavity
ring down spectroscopy—are described elsewhere.20 These
transient species are concentrated in the plasma ball itself.
Both data sets serve to tension and validate the detailed two-
dimensional 共2D兲modeling of the gas phase chemistry pre-
vailing in this high pressure MW CVD reactor.5
II. EXPERIMENTAL
Details of the custom-designed MW reactor 共2 kW, 2.45
GHz Muegge power supply and generator兲and of the QC
laser spectrometer 共Cascade Technologies Ltd., operating
with a 7.85
␮
m laser兲have been presented previously.16
Here we detail improvements implemented since the initial
study. One enhancement involved changes to the reactor
viewing apertures. The 4 mm diameter apertures that defined
the previous viewing column have been replaced by two
25 mm共vert.兲⫻5.5 mm共horiz.兲slot apertures, which allow
operation of the reactor in two configurations as illustrated in
Fig. 1. In configuration I, each slot is sealed by thin rectan-
gular polished CVD diamond windows 共Element Six Ltd.兲
mounted on wedged flanges to reduce etalon effects, thereby
maintaining the same 共l=19 cm兲column length as before.
Alternative, matched flanges are used in configuration II.
Each of these flanges is fabricated with a tongue that projects
into the slot aperture and supports three 5.8 mm diameter,
wedged 共2°兲, thin 共300
␮
m兲diamond windows 共the centers
of which are, respectively, 1, 11, and 21 mm above the sub-
strate surface兲. Countersinking the windows reduces the col-
umn length to l=14 cm, thereby reducing the 共dominant兲
contribution to absorption from cold gas at the ends of the
viewing column. The second improvement allows for spatial
profiling. The complete optical assembly 共laser, beam steer-
ing optics, and detector兲is now mounted on a rigid platform
that can be translated vertically, with better than 1 mm pre-
cision, relative to the fixed MW reactor—thereby enabling
spatially resolved, line-of-sight column density measure-
ments with configuration I as a function of z, the vertical
distance above the top surface of the 30 mm diameter Mo
substrate. zvalues were read from a rigidly mounted vernier
scale, and z=0 determined by finding the platform setting at
which the substrate first impeded transmission of the probe
laser beam. The third improvement involves the detectivity
of the QC laser spectrometer. The liquid nitrogen cooled
mercury cadmium telluride 共MCT兲detector with external
transimpedence amplifier used previously to monitor the
FIG. 1. Schematic diagram of the CVD reactor illustrating the position of
the substrate, plasma ball, and the windows for optical probing using con-
figurations I and II.
033305-2 Ma et al. J. Appl. Phys. 106, 033305 共2009兲
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transmitted IR intensity was replaced by a new photovoltaic
MCT detector with a two stage Peltier cooler and a built-in
amplifier 共Vigo兲. This has a built-in immersion lens 共en-
abling improved radiation collection兲and a wider bandwidth
共that removes most of the overshoot of the pulsed laser sig-
nal兲. As illustrated below, this detector returns spectra with
substantially better signal to noise ratios, allowing observa-
tion of many weak spectral features not recognized in the
original study.
The source gases used, along with suppliers and stated
purities, were as follows: CH4共BOC, 99.5%兲,C
2H2共BOC,
98.5%兲, ethene 共Argo, 99.7%兲,n-propane 共Argo, 99%兲,
n-butane 共Argo, 99.4%兲, propyne 共Argo, 96%兲,H
2共BOC,
99.995%兲, and Ar and Ne 共BOC, 99.995%兲. The hydrocar-
bon, H2, and Ar共Ne兲gas flows were metered through three
separate mass flow controllers 共MFCs兲共mks兲, calibrated for
CH4,H
2, and Ar; flow rates of the neon and the various
nonmethane hydrocarbons were derived using the manufac-
turer correction factors 共where available兲and, in the case of
C2H2, verified independently by IR absorption spectroscopy
共see Tables Iand II兲.
III. RESULTS AND DISCUSSION
A. Preamble
To aid the subsequent discussion, absorption spectra of
room temperature samples of CH4and C2H2recorded over
the wavenumber range of 1276.5−1273.1 cm−1 using reac-
tor configuration I are shown in Figs. 2and 3. The pressures
in each case have been chosen deliberately so that the stron-
gest features are saturated, thereby allowing weaker features
to be seen more clearly. Lines evident in Fig. 2are attribut-
able to rovibrational transitions of the 40
1fundamental bands
of 12CH4and 13CH4共and associated hot bands originating
from both the 21and 41levels of 12CH4兲,21 as detailed by the
assignment combs in the figure and the listing in Table I. The
most intense features in the case of C2H2共Fig. 3兲are P
branch transitions within the 40
150
1combination band of the
12C2H2isotopomer.21 Hot band absorptions are again identi-
fiable, originating from levels carrying one and two quanta
of excitation in
␯
4and/or
␯
5共the trans- and cis-bending
modes, respectively兲22—as detailed in Table II. Several weak
features remain unassigned in Fig. 3; these are most likely
attributable to H12C13CH.
Measurements of room temperature gas mixtures pro-
vide a means of testing the absolute calibration of the MFCs.
Plot 共b兲in Fig. 2shows the CH4number densities obtained
by plotting the integrated absorbances 共in cm−1兲of the
4F23 –5F12 line measured for various
a%CH4/7%Ar/balance H2mixtures, scaled by the appropri-
ate S共298 K兲value 关3.67⫻10−20 cm−1/共molecule cm−2兲
共Ref. 21兲兴 and then divided by ᐉ=19 cm, against those cal-
culated from the set flow rates and pressure 共assuming ideal
gas behavior兲. The gradient of this straight-line correlation is
TABLE I. Wavenumbers, assignments, and S共T兲line strength factors 共Ref. 21兲of CH4transitions observed in
the wavenumber range of 1276.5− 1273.1 cm−1.
Wavenumber
共cm−1兲
Line intensity
关10−24 cm−1共mol cm−2兲−1兴
E⬙
共cm−1兲
Vibrational
transition
Rotational
transition
C
isotope298 K 450 K 3000 K
1276.331 05 123 639 8.21 1433.9722 41
23F25–4F13 12
1276.262 06 23.5 55.7 0.192 949.888 40
113F14–13F21 13
1275.945 66 564 2180 17 1250.836 40
115F24−15F11 12
1275.947 76 564 2180 17 1250.837 40
115F15–15F21 12
共Sum兲共1128兲共4360兲共34兲
1275.779 28 671 400 0.139 104.778 40
13A21–4A11 13
1275.621 60 1.51 11.0 0.248 1639.651 21
140
14F29−4F15 12
1275.386 78 24 400 15 900 6.35 157.137 40
14E2–5E112
1275.326 54 401 240 0.083 104.780 40
13F22–4F11 13
1275.041 68 36 700 23 900 9.53 157.139 40
14F23–5F12 12
1274.984 82 269 159 0.0552 104.781 40
13E2–4E113
1274.786 13 86.6 62.3 0.0295 219.937 40
16F11–6F22 12
1274.213 93 79.3 413 5.28 1432.524 40
13E3–4E212
1274.016 90 398 238 0.0823 104.785 40
13F13–4F21 13
1273.881 63 34.7 174 2.09 1409.376 41
23E2–4E112
1273.875 25 1.66 60.4 19.7 2623.659 40
122A23−22A11 12
1273.864 56 1.00 36.3 11.8 2623.677 40
122F28−22F12 12
1273.858 75 0.669 24.3 7.90 2623.687 40
122E5−22E212
共Sum兲共3.329兲共121兲共39.4兲
1273.840 15 11.1 119 5.12 1878.424 41
210A13–10A22 12
1273.782 40 13.6 171 9.56 1975.015 40
119E4−19E112
1273.782 49 20.4 257 14.4 1975.013 40
119F17–19F22 12
1273.782 57 34.0 428 23.9 1975.008 40
119A13–19A21 12
共Sum兲共68.0兲共856兲共47.86兲
1273.469 77 52.2 261 3.13 1409.007 41
23F14–4F22 12
1273.418 31 120 626 7.99 1432.181 41
23F15–4F23 12
033305-3 Ma et al. J. Appl. Phys. 106, 033305 共2009兲
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reassuringly close to 1, validating the ideal gas assumption
and the MFC and pressure gauge calibrations. The C2H2feed
gas used in these experiments was metered with the same
MFC 共i.e., calibrated for CH4兲. Plot 共b兲in Fig. 3compares
the corresponding measured 关via the P共23 ,e兲line of 12C2H2
and assuming S共298 K兲= 2.24⫻10−20 cm−1/
共molecule cm−2兲共Ref. 21兲兴 and calculated 共using the ideal
gas law兲C2H2number densities. The calculated column den-
sities in this plot again assume that the various
b%C2H2/7%Ar/balance H2mixtures behave ideally and, in
addition, that the MFC calibration factor is the same for CH4
and C2H2. The gradient of the resulting plot 共⬃0.95兲reflects
共i兲the purity 共or otherwise兲of the C2H2source gas and 共ii兲
the reduced conductance 共of the CH4MFC兲for C2H2.
One other aspect of these spectra and line assignments
merits comment. Although narrow, the probed wavenumber
range allows both CH4and C2H2to be monitored in a spread
of energy levels. In the case of CH4, for example, this range
allows sampling of v=0 molecules with both low 共e.g., J
=4兲and high 共e.g., J=19兲rotational quantum numbers and
of molecules in levels with v2=1 and v4=1 共low Jin each
case兲. The relative populations of these levels, and thus the
associated transition line strengths S共T兲, are temperature de-
pendent. Under CVD conditions, the gas temperatures along
TABLE II. Wavenumbers, assignments, and ground state term values of
C2H2transitions observed in the wavenumber range of 1276.5
−1273.1 cm−1 共Refs. 21 and 22兲.
Wavenumber
共cm−1兲a,b
E⬙a
共cm−1兲
Vibrational
transition
Spin
weighting
Rotational
transitionb
1276.336 63 1262 41
250
1共⌸u−⌸g兲1P共23, f兲
1276.258 06 1708 40
152
3共⌺u−⌺g兲1P共14, e兲
1276.140 79 1775 41
251
2共⌺g−⌺u兲1P共19, f兲
1275.958 59 1177 40
151
2共⌸g−⌸u兲3P共19, e兲
1275.716 61 1743 40
152
3共⌬u−⌬g兲1P共15, f兲
1275.614 95 1881 42
350
1共⌬u−⌬g兲1P共23, f兲
1275.580 94 1881 42
350
1共⌬u−⌬g兲3P共23, e兲
1275.566 59 1743 40
152
3共⌬u−⌬g兲3P共15, e兲
1275.512 22 649 40
150
1共⌺u
+−⌺g
+兲3P共23, e兲
1275.423 25 1792 41
251
2共⌬g−⌬u兲3P共19, e兲
1275.374 66 1262 41
250
1共⌸u−⌸g兲3P共23, e兲
1275.288 62 1792 41
251
2共⌬g−⌬u兲1P共19, f兲
1274.647 40 1822 41
251
2共⌺g−⌺u兲3P共20, f兲
1274.479 50 1177 40
151
2共⌸g−⌸u兲1P共19, f兲
1274.362 03 1167 40
150
1共⌬u
e−⌺g
+e兲3P共31, e兲c
1274.156 39 1318 41
250
1共⌸u−⌸g兲3P共24, f兲
1273.974 56 1732 40
152
3共⌺u−⌺g兲3P共15, e兲
1273.857 01 1822 41
251
2共⌺g−⌺u兲3P共20, f兲
1273.819 72 1225 40
151
2共⌸g−⌸u兲1P共20, f兲
1273.516 79 1781 40
152
3共⌬u−⌬g兲3P共16, f兲
1273.452 72 1995 42
350
1共⌺u
+−⌺g
+兲3P共25, e兲
1273.366 60 1937 42
350
1共⌬u−⌬g兲3P共24, f兲
1273.319 71 1781 40
152
3共⌬u−⌬g兲1P共16, e兲
1273.261 95 706 40
150
1共⌺u
+−⌺g
+兲1P共24, e兲
1273.103 87 1319 41
250
1共⌸u−⌸g兲1P共24, e兲
aApproximated using values of rotation constants and band origins in Ref.
22.
beand findicate the l-doubling components of the ⌸and ⌬vibrational
states.
cTransition is due to rotational l-resonance between ⌬u
eand ⌺u
+esublevels of
the same Jvalue, see Ref. 25.
FIG. 2. 共a兲Single pass transmission spectra of a room temperature sample
of CH4in the wavenumber range of 1276.5− 1273.1 cm−1.共b兲shows the
CH4number density obtained by plotting the integrated absorbances 共in
cm−1兲of the 40
14F23–5F12 line measured for various
a%CH4/7%Ar/balance H2mixture, scaled by the appropriate S共298 K兲
value and then divided by ᐉ=19 cm, against those calculated from the set
flow rates and pressure 共assuming ideal gas behavior兲.
FIG. 3. 共a兲Single pass transmission spectra of a room temperature sample
of C2H2in the wavenumber range of 1276.5−1273.1 cm−1.共b兲shows the
C2H2number density obtained by plotting the integrated absorbances 共in
cm−1兲of the 40
150
1P共23, e兲line measured for various
b%C2H2/7%Ar/balance H2mixture, scaled by the appropriate S共298 K兲
value and then divided by ᐉ=19 cm, against those calculated from the set
flow rates and pressure 共assuming ideal gas behavior兲.
033305-4 Ma et al. J. Appl. Phys. 106, 033305 共2009兲
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the probed column span the range from room temperature to
⬃3000 K.5,20 As Table Ishows, our relative sensitivity to
CH4共v=0,J=19兲molecules rises ⬎10-fold and subsequently
declines over this temperature range, while our sensitivity to
CH4共v=0,J=4兲molecules drops by ⬃5⫻103. Even modest
temperature changes can cause significant changes in Sfac-
tor, as exemplified by the case of the 41
2P共4兲transition on
increasing Tfrom 300 to 450 K. The Tdependence in the
case of C2H2is less dramatic, since all of the levels moni-
tored involve broadly similar Jvalues 共J⬃20兲. However, as
Table II illustrates, the probed wavelength range allows
access to C2H2molecules with v=0 共E⬙⬃650 cm−1兲,
v4/5=1 共E⬙⬃1150–1300 cm−1兲, and v4/5=2 共E⬙
⬃1700–2000 cm−1兲. The temperature dependence of the vi-
brational partition function will ensure greatest relative sen-
sitivity to the most vibrationally excited C2H2molecules at
higher T. The HITRAN database21 currently lists S共T兲factors
for C2H2共v=0兲molecules only, but S共T兲factors for other
transitions of interest 共with v⬎0兲can be estimated as shown
in the Appendix.
B. Spatially resolved CH4and C2H2absorption and
number density profiles
Figure 4compares and contrasts absorption spectra re-
corded in the narrower wavenumber range of 1276.2
−1274.0 cm−1 with both reactor configurations, at z
=11 mm, using x%CH4/7%Ar/balance H2关Fig. 4共a兲兴and
y%C2H2/7%Ar/balance H2关Fig. 4共b兲兴gas mixtures at a to-
tal flow rate of F=565 SCCM 共SCCM denotes standard cu-
bic centimeter per minute at STP兲, pressure p= 150 Torr,
and applied MW power P= 1.5 kW, as functions of the car-
bon flow rate. For ease of display, the two spectra for each
carbon flow recorded with the different experimental con-
figurations have been offset vertically by 0.05 absorbance
units, and the pairs of spectra recorded with different carbon
flow rates have each been offset vertically by larger amounts.
The configuration I measurements are comparable to those
reported previously16 and have thus been repeated at fewer
carbon flow rates. The line at 1275.042 cm−1 is due solely to
CH4共v=0兲molecules, whereas both CH4共v=0兲and
C2H2共v4=1兲molecules can contribute to the blended line at
⬃1275.38 cm−1. The peaks at 1275.512 and 1274.156 cm−1
are both entirely due to C2H2molecules—in their v= 0 and
v4=1 levels, respectively. The more detailed analysis of the
respective parent room temperature absorption spectra re-
ported in Tables Iand II shows the remaining line, at
⬃1275.95 cm−1, to be a blended feature, involving contribu-
tions from both C2H2共v5=1兲and CH4共v=0,J=15兲
molecules—rather than being wholly associated with
C2H2共v5=1兲molecules as presumed previously.16 Figures
4共c兲and 4共d兲show the line integrated absorbances 共LIAs兲
derived for the various unblended peaks, for both reactor
configurations, plotted as functions of “carbon” flow rate
FIG. 4. Absorption spectra of activated 共a兲x%CH4/7%Ar/H2and 共b兲y%C2H2/7%Ar/H2gas mixtures using three different carbon flow rates, recorded over
the wavenumber range of 1276.5− 1274.0 cm−1.KeyCH
4and C2H2features are labeled; detailed assignments of these transitions are given in Tables Iand
II. The upper/lower spectrum in each pair was recorded using configuration I/II. For display purposes, the upper of the two spectra measured at each carbon
flow rate has been raised vertically by 0.05 absorbance units, and each pair of spectra in each panel has been offset vertically by larger amounts. The total flow
rate 共F=565 SCCM兲, pressure 共p=150 Torr兲, and applied MW power 共P= 1.5 kW兲were the same for each of the spectra. 共c兲and 共d兲show the LIAs for the
CH440
14F23–5F12 共䊏兲,C
2H240
150
1P共23, e兲共쎲兲, and C2H241
250
1P共24, f兲共䉱兲lines of interest, and their variation with carbon flow rate.
033305-5 Ma et al. J. Appl. Phys. 106, 033305 共2009兲
Downloaded 06 Aug 2009 to 137.222.40.127. Redistribution subject to AIP license or copyright; see http://jap.aip.org/jap/copyright.jsp

共where CH4and C2H2flow rates of xand ySCCM equate to
carbon flow rates of, respectively, xand 2ySCCM兲.
Several points emerge from these data. The same peaks
are apparent in all spectra recorded at a given carbon flow
rate, irrespective of the identity of the input hydrocarbon,
again emphasizing the efficient methane ↔acetylene inter-
conversion. The absorption measured at low 共5 SCCM兲car-
bon flow rate is largely attributable to CH4, but C2H2absorp-
tion features become increasingly evident at higher carbon
flow rates. The previous suggestion16 of a population inver-
sion between the v5=1 and v=0 levels of C2H2at low car-
bon flow rates is incorrect. The ⬃1275.95 cm−1 feature mea-
sured at low carbon input fractions is actually attributable to
rotationally “hot” CH4molecules. None of the data reported
here contradicts the assumption that the rotational and vibra-
tional state populations of these stable hydrocarbon species
are in local thermodynamic equilibrium. The nonobservation
of the 共cold兲13CH4feature at 1275.7793 cm−1 in spectra
recorded at low carbon flow rate serves to reinforce the very
different S共T兲dependences of this line and of neighboring
共hot兲CH4feature at ⬃1275.95 cm−1—detailed in Table I.
Source gas dependent differences also become more evident
in the spectra recorded at higher carbon flow rates. The spec-
trum recorded with 40 SCCM CH4is dominated by the CH4
feature, whereas the largest peak in the spectrum recorded
with 20 SCCM C2H2is due to C2H2. These trends can be
seen more clearly in the LIA plots 关Figs. 4共c兲and 4共d兲兴and
will be discussed in more detail in Sec. III D.
Figures 4共c兲and 4共d兲also highlight the differences in
LIAs measured using configurations I and II. Reducing the
length of the viewing column from l=19 to l= 14 cm results
in varying reductions in all LIAs 关by ⬃66%in the case of
CH4and by, respectively, ⬃50%and ⬃33%in the case of
C2H2共v=0兲and C2H2共v4=1兲molecules兴, reflecting their dif-
fering spatial distributions but also reinforcing the model
predictions5that most of the CH4and C2H2number density
is concentrated in the cooler regions near the wall of the
reactor. Spectra taken at the lowest 共5 SCCM兲carbon flow
rates show no discernible C2H2共v=0兲absorption. Thus it is
valid to attribute all of the absorption at 1275.95 cm−1 in
such spectra to the CH440
1Q15F21 and F11 transitions. Their
combined intensity, relative to that of the CH440
1P5F12 line
at 1275.04 cm−1, provides a route for estimating the gas
temperature 共Tgas兲in the columns bounded by the water
cooled reactor wall that distinguish configurations I and II.
Specifically, we calculate the difference in the LIAs 共⌬LIA兲
measured for each line under identical process conditions
and compare this ratio with the 共temperature dependent兲ratio
of the respective S共T兲line strength factors. The latter ratio
varies rapidly with Tand matches ⌬LIA when
T⬃330 K—a sensible value for the average gas temperature
in this region. Knowing Tgas and the difference in path
lengths ⌬l=5 cm, we can use the measured ⌬LIA values
and the appropriate S共T=330 K兲line strength factor to esti-
mate the average CH4number density in this region. The
value so derived, NCH4 ⬃4.4⫻1016 cm−3, matches well 共to
within 20%兲with the ideal gas estimate at this Tgas, given the
assumption that CH4is the only hydrocarbon present under
these dilute carbon conditions. Equivalent calculations at
higher carbon flow rates, and at all three zpositions 共1, 10.5,
and 20.5 mm兲, return CH4and C2H2number density esti-
mates that agree well 共to within factors of ⬃1.3 for CH4and
⬃2 for C2H2兲with the corresponding r= 6 cm values re-
ported in Ref. 5.
Figure 5shows absorption spectra of activated 共a兲
CH4/Ar/H2and 共b兲C2H2/Ar/H2gas mixtures recorded in
the narrow wavenumber range of 1274.1−1273.0 cm−1,
which contains an isolated line associated with C2H2,v=0,
J=24 molecules and a blended clump of lines around
1273.8 cm−1. The absence of the 1273.262 cm−1 feature in
spectra recorded at the lowest carbon flow rate accords with
the conclusion 共from Fig. 4兲that any features evident in such
spectra are likely attributable to CH4. Thus the very weak
absorption evident at ⬃1273.78 cm−1 in the F共CH4兲
=5 SCCM spectrum in Fig. 5共a兲is most plausibly assigned
to a cluster of blended lines associated with CH4共v=0兲mol-
ecules in a highly excited 共J=19兲rotational level. Additional
features are apparent at slightly higher wavenumber in spec-
tra recorded at higher carbon flow rates. Inspection of Tables
Iand II reveal several potential contributors to this clump.
FIG. 5. Absorption spectra of activated 共a兲x%CH4/7%Ar/H2and 共b兲y%C2H2/7%Ar/H2gas mixtures using three different carbon flow rates, recorded over
the wavenumber range 1274.1− 1273.0 cm−1 using configuration II at z= 21 mm. Selected CH4and C2H2features are indicated; detailed assignments of these
transitions are given in Tables Iand II. For display purposes, the various spectra have been offset vertically. The total flow rate 共F=565 SCCM兲, pressure
共p=150 Torr兲, and applied MW power 共P=1.5 kW兲were the same for each of the spectra.
033305-6 Ma et al. J. Appl. Phys. 106, 033305 共2009兲
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Two hot band absorptions associated with CH4共v4=1兲mol-
ecules lie in this range, with associated S共T兲factors that are
comparable to that of the 40
1P19 line once T⬃450 K, but
the clear showing of the 1273.262 cm−1 feature indicates
that we need to consider possible contributions from C2H2
also—specifically the two P共20兲transitions at
1273.857 cm−1 共originating from the 4151level兲and at
1273.820 cm−1 共from the v5=1 level兲. These two transitions
have respective nuclear spin weightings of 3 and 1. At room
temperature, the effect of the population difference far out-
weighs the different nuclear spin statistics, and the lower
wavenumber line is dominant 共see Fig. 3兲. Under base oper-
ating conditions, however, the two lines appear with similar
LIAs—reflecting the convergence in relative populations of
the two levels as Tincreases. As in Fig. 4, the C2H2features
are seen to grow in relative importance at higher carbon flow
rates and, at a given carbon flow rate, to be consistently
greater when using C2H2as the source gas.
Figure 6shows the calculated5rdependence of the total
number densities of CH4,C
2H2,C
2H4, and C2H6and of Tgas
for the standard process condition 共25 SCCM CH4,40
SCCM Ar, 500 SCCM H2,p= 150 Torr, P= 1.5 kW兲at z
=0.5 mm 关Fig. 6共a兲兴and z=10.5 mm 关Fig. 6共b兲兴. These
clearly illustrate the way in which Tgas effects and gas phase
chemistry combine to concentrate the stable hydrocarbon
species in the cool regions at the periphery of the reactor.
Even with the recessed windows, therefore, the measured
LIAs will be dominated by gas at the ends of the probed
column and any detailed comparison between experiment
and model calculation requires that we give due consider-
ation to the differences between the model and experimental
geometries. Specifically, the probed column in configuration
II extends to r=7 cm, and it is therefore necessary to ex-
trapolate the model outputs for a further 1 cm. The recessed
window mount is in good thermal contact with the reactor
wall so, for the purpose of this exercise, we choose to retain
the model predictions out to the largest calculated rvalue
and assume that thereafter Tdeclines linearly to 300 K at r
=7 cm. We also assume that the mole fraction 共X兲of each
species remains constant in the 1 cm extension region, but
note that the model outputs actually show the mole fractions
of all stable hydrocarbon species increasing by factors of
1.5–2 over the range of 5.5⬍r⬍6 cm, presumably as a re-
sult of thermodiffusion effects. This allows estimation of
nCH4,nC2H2,Tgas, the relevant S共T兲factors, and thus the re-
spective contributions to the total column absorption from
each cell usinga1mmgrid spacing in the region of 6 ⬍r
⬍7 cm. Summing all contributions 共modeled and extrapo-
lated兲from the range of −7 ⬍r⬍7 cm yields a calculated
LIA for direct comparison with experimental measurements
at the various process conditions.
The 2D model takes account of the changes in plasma
parameters and conditions 关e.g., Tgas, the electron tempera-
ture 共Te兲, and concentration 共ne兲, the power density and the
plasma chemistry兴induced by varying reactor parameters
such as p,P, and the mole fractions of CH4and Ar in the
process gas mixture. Detailed descriptions of this model pro-
cedure, which uses the plasma size as an external parameter,
are presented in accompanying publications.5,20,23 By way of
example, the maximal values of neand Teare predicted to
increase by ⬃30%and ⬃5%, respectively, upon introducing
just 5 SCCM of CH4共i.e., 0.88% CH4兲into an Ar/H2plasma
operating under what, otherwise, would constitute base
conditions.5,23 Increasing the CH4flow rate further, up to the
base value F共CH4兲=25 SCCM 共i.e., 4.4% CH4兲leads to less
pronounced changes in ne共a further ⬃5%increase兲and Te关a
⬃3%decline relative to that at F共CH4兲=5 SCCM兴. The 2D
model returns the following typical values for the plasma
parameters in the plasma core: Te⬃1.25–1.45 eV, Tgas
⬃2800–2950 K, power densities of 20 – 40 W cm−3, re-
duced electric fields E/N⬃25–30 Td, and ne⬃3
⫻1011 cm−3.5,20,23 The effects of heavy 共⬎90%兲dilution of
FIG. 6. Plots showing the rdependent CH4,C
2H2,C
2H4, and C2H6number
densities and Tgas values calculated for the standard process conditions
关F共CH4兲=25 SCCM, F共Ar兲=40 SCCM, F共H2兲=500 SCCM, p
=150 Torr, P= 1.5 kW兴at 共a兲z= 0.5 mm and 共b兲z= 10.5 mm. Panel 共c兲
shows a decomposition of the calculated rdependent C2H2total number
density shown in 共b兲into number densities in the following quantum states:
v=0, J=23; and individual ᐉ-doublets of v5=1, J=20; v4=1, J=24; and
v4=1+v5=1, J=20. Vertical dashed lines indicate the centers of gravity of
the various state-specific number density distributions.
033305-7 Ma et al. J. Appl. Phys. 106, 033305 共2009兲
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the process gas mixture by various noble gases 共He, Ne, Ar,
Kr兲on both the plasma parameters and on nanocrystalline
diamond deposition processes have also been investigated24
experimentally and theoretically using the present 2D model
for both Ar/H/C and He/H/C mixtures.
Table III compares the LIAs derived from such analyses
of the 2D model outputs for the standard operating condi-
tions 共at three different zvalues兲and for three alternative p,
P, and F共CH4兲conditions, with the corresponding values
determined from measurements on the 1275.042 cm−1 line
of CH4共v=0兲and the 1275.512 cm−1 line of C2H2共v=0兲.
The model calculations reproduce the experimentally mea-
sured CH4LIAs rather well, under all process conditions, but
consistently underestimate the corresponding experimental
LIA value for C2H2. Most of the C2H2and, particularly, the
CH4absorption is from gas at the periphery of the reactor.5
The S共T兲line strength factor for the P共23兲line used when
monitoring C2H2共v=0兲molecules falls with deceasing T共for
T⬍450 K兲, and we are unable to conceive of a physically
plausible alternative Tgas共r兲dependence at large rthat would
allow the calculated XC2H2 value to give a significantly larger
absorbance. This leads us to suspect that the model calcula-
tion underestimates XC2H2 in the cooler region of the viewing
column. We can envisage two factors that may contribute to
this underestimation. First, the predicted LIAs would be
greater if XC2H2 共and XCH4兲increased through the region 6
⬍r⬍7 cm, rather than remain constant 共as currently as-
sumed兲. Thermodiffusion considerations would favor the
former scenario, but we see no robust way of predicting the
necessary X共r⬎6cm兲dependences. Second, the present cal-
culations return C2H4and C2H6number densities of
⬃1016 cm−3 at large r共see Fig. 6兲. It is quite possible that
aspects of the gas phase chemical mechanism at large ror,
more probably, the assumed gas-surface chemistry occurring
at the reactor walls 共that determines the interconversion be-
tween the various hydrocarbon species at low Tgas and thus
the local C2H2number density兲needs further refinement.
Given local thermodynamic equilibrium, the partition
functions calculated in the Appendix allow estimation of the
fraction of nC2H2 in any given v,Jlevel at a given T. Figure
6共c兲shows the relevant decomposition for probed levels
highlighted in Figs. 4and 5, namely, the v=0, J= 23 level
共E⬙=649 cm−1兲and for individual ᐉ-doublets of the v5=1,
J=20 共E⬙=1225 cm−1兲,v4=1, J=24 共E⬙= 1318 cm−1兲, and
v4=1+v5=1, J=20 共E⬙=1822 cm−1兲levels—plotted as a
function of r. As expected, the centers of gravity of the pre-
dicted state-specific number density distributions show a pro-
gressive shift to smaller rwith increasing E⬙共r
¯
⬃6.5, 5.9,
5.8, and 5.7 cm, respectively兲but the effect is quite
modest—emphasizing, once again, the localization of num-
ber density in the cooler periphery of the reactor. The last
two columns in Table III compare LIAs for the unblended
C2H241
250
1P共24, f兲feature at 1274.156 cm−1 measured un-
der a range of process conditions with those calculated using
the predicted state-specific number density distributions and
the appropriate S共T兲factors derived as outlined in the Ap-
pendix. Again, the experiment returns values that are consis-
tently two or more times greater than the model calculations,
with the greatest discrepancy at small z.
Figure 7shows the LIAs for the CH440
14F23 –5F12,
C2H240
150
1P共23,e兲and C2H241
250
1P共24, f兲transitions for 共a兲
25 SCCM CH4/40 SCCM Ar/500 SCCM H2and 共b兲12.5
SCCM C2H2/40 SCCM Ar/512.5 SCCM H2gas mixtures
operating at standard conditions of total pressure and input
power. The LIA of each of the monitored species is seen to
decline with increasing zand, in each case, the hydrocarbon
source gas shows relatively more strongly. Reference to Fig.
7and to Table III suggests that the 2D model is rather suc-
cessful in capturing the zdependence of the 共absolute兲CH4
and 共relative兲C2H2densities at large r.
C. Variation in CH4and C2H2LIAs with process
conditions
The upper two panels in Fig. 8show the ways in which
the LIAs for the same three probe transitions measured at z
=11 mm vary with input MW power under otherwise stan-
dard conditions; all three decline with increasing P, irrespec-
tive of whether the hydrocarbon source is provided by 共a兲
F共CH4兲=25 SCCM or 共b兲F共C2H2兲= 12.5 SCCM. The
lower two panels show corresponding measurements illus-
trating the effect of varying the total process gas pressure p
while otherwise retaining standard process conditions of 共c兲
CH4/Ar/H2and 共d兲C2H2/Ar/H2mixing ratio, flow rate,
and input MW power. The LIA of the source gas 共CH4兲is
always greatest in the former case, and the measured LIAs
all increase roughly linearly with increasing p. In the case of
the C2H2/Ar/H2input gas mixture, however, the LIAs of the
C2H2共v=0兲and C2H2共v4=1兲transitions both increase near
linearly with p, while that for CH4rises much less steeply.
TABLE III. Comparison of measured 共exp兲and predicted 共mod兲LIAs for the CH440
1P5F12,C
2H240
150
1P共23, e兲, and C2H241
250
1P共24, f兲transitions as a
function of process conditions.
Process conditions CH440
1P5F12 C2H240
150
1P共23, e兲C2H241
250
1P共24, f兲
F共CH4兲
共SCCM兲
p
共Tor r兲
P
共kW兲
d
共mm兲
LIAexp
共cm−1兲
LIAmod
共cm−1兲
LIAexp
共cm−1兲
LIAmod
共cm−1兲
LIAexp
共cm−1兲
LIAmod
共cm−1兲
25 150 1.50 1 0.0104 0.0088 0.0066 0.0024 0.000 96 0.000 27
25 150 1.50 11 0.0070 0.0076 0.0036 0.0020 0.000 48 0.000 21
25 150 1.50 21 0.0065 0.0085 0.0034 0.0019 0.000 34 0.000 21
5 150 1.50 11 0.0034 0.0030 0 0.0002 0 0.000 02
25 150 1.25 11 0.0081 0.0085 0.0040 0.0022 0.000 46 0.000 23
25 75 1.50 11 0.0026 0.0035 0.0026 0.0010 0.000 32 0.000 11
033305-8 Ma et al. J. Appl. Phys. 106, 033305 共2009兲
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Reference to Table III shows, again, that the 2D model cal-
culations for the standard CH4/Ar/H2gas mixture captures
the observed Pand pdependences of the CH4LIAs quanti-
tatively and the relative variation in the C2H2LIAs.
The interpretation of these apparently simple trends re-
quires consideration of several contributory factors. We start
by considering the Pvariations and the case of a CH4/Ar /H2
gas mixture. The 2D model calculations for P= 1.25 and 1.5
kW show that increasing Presults in a slightly hotter, larger
plasma region, some increase in Tgas at large rand a higher H
atom density 共nH兲throughout the reactor. The increase in Tgas
leads to a steeper temperature 共and thus total number den-
sity兲gradient at large r, which has the effect of concentrating
more of the number density in the coolest periphery of the
reactor and thus reducing the effective length of the column
that contains most of the cold hydrocarbon gas. The LIA of
all stable hydrocarbons thus declines with increasing P.
Scrutiny of Fig. 8共a兲shows that the decline in the C2H2LIA
is less steep than that for CH4. Two factors contribute to this
trend. First, higher Presults in higher nHand thus a greater
processing efficiency of the input CH4共which is the source
of the C2H2under these conditions兲. Second, the S共T兲depen-
dence of the 40
150
1P共23,e兲transition used to monitor
C2H2共v=0兲molecules increases with Tin the range of 300
⬍T⬍450 K, so any increase in Tgas at large ras a result of
FIG. 7. Plots showing the zdependences of the LIAs for the CH440
14F23–5F12 共䊏兲,C
2H240
150
1P共23, e兲共쎲兲and C2H241
250
1P共24, f兲共䉱兲transitions measured
for 共a兲F共CH4兲=25 SCCM, F共Ar兲= 40 SCCM, F共H2兲= 500 SCCM, and 共b兲F共C2H2兲= 12.5 SCCM, F共Ar兲=40 SCCM, F共H2兲= 512.5 SCCM gas mixtures
operating at standard conditions of total pressure and input power.
FIG. 8. Illustration of the Pand pdependences of the LIAs for the CH440
14F23–5F12 共䊏兲,C
2H240
150
1P共23, e兲共쎲兲, and C2H241
250
1P共24, f兲共䉱兲transitions
measured at z=11 mm for 25 SCCM CH4/40 SCCM Ar /500 SCCM H2关共a兲and 共c兲兴 and 12.5 SCCM C2H2/40 SCCM Ar /512.5 SCCM H2关共b兲and
共d兲兴 gas mixtures operating at standard conditions of total pressure 关共a兲and 共b兲兴 and input power 关共c兲and 共d兲兴. The open symbols in 共a兲and 共c兲show the
corresponding LIAs for the CH440
14F23–5F12 and C2H240
150
1P共23, e兲transitions returned by the 2D model calculations.
033305-9 Ma et al. J. Appl. Phys. 106, 033305 共2009兲
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increasing Pwill have a positive effect on the measured LIA.
The data for the C2H2/Ar/H2gas mixture 关Fig. 8共b兲兴display
slightly different trends. In this case, the LIA of the source
gas 共C2H2兲shows the steeper decline with increasing P. This
can be understood if the main effect of increasing Pis to
increase Tgas and nHand thus the extent of gas processing 共by
which the CH4is produced兲.
We now consider the observed variations in LIAs with p.
The 2D model calculations for the standard CH4/Ar/H2gas
mixture show that doubling pfrom 75 Torr to 共the standard兲
150 Torr results in an approximately fourfold increase in nH
at the center of the plasma ball 共equivalent to an approxi-
mately twofold increase in the H atom mole fraction兲, but a
⬃50-fold drop in nH共from ⬃3⫻1010 to ⬃6⫻108cm−3兲at
r=6 cm. The same calculations show little change in Tgas at
r=6 cm as a result of this increase in p. The reduction in nH
at large ris mainly attributable to the p−1 dependence of the
diffusion coefficients and thus the H atom diffusional trans-
fer rate from the source region 共the plasma ball兲, but will be
exacerbated by the increased opportunity for reactive loss
through reaction with hydrocarbon species at higher p. This
latter point may be significant in explaining the pdepen-
dence of the LIAs measured with the C2H2/Ar/H2gas mix-
ture. In this case, the LIA of the source hydrocarbon 共in both
its v=0 and v4= 1 levels兲increases roughly linearly with p,
as expected, but that for CH4grows more slowly at higher p.
All of the CH4in this mixture is formed by reactions involv-
ing H atoms, principally in regions of moderate Tgas. The
reduction in nHat large rat high pwill lead to a reduction in
C2H2→CH4conversion probability in the peripheral regions
共where most of the monitored CH4is located兲, thus account-
ing for the observed negative curvature in the CH4LIA at the
highest pstudied.
Similar considerations can account for the observed
variations in the LIAs for the same three probe transitions
when varying the Ar/H2共or Ne/H2兲ratio in
CH4/Ar共Ne兲/H2and C2H2/Ar共Ne兲/H2gas mixtures. Fig-
ures 9共a兲and 9共b兲show sample absorption spectra measured
at z=11 mm for CH4/Ne/H2and C2H2/Ne/H2gas mix-
tures. The carbon and total flow rates were the same in all
cases 共25 and 565 SCCM, respectively兲, as were p共150 Torr兲
and P共1.5 kW兲, with the only variable being the Ne/H2
ratio. Figures 9共c兲and 9共d兲show how the LIAs for the three
unblended lines of interest vary with Ne flow rate. Equiva-
lent measurements involving CH4/Ar/H2and C2H2/Ar/H2
gas mixtures return virtually identical LIA versus F共Ar兲
plots. The most striking feature of these plots is the very
different behavior of the C2H2and CH4LIAs; the former are
relatively insensitive to the Ne/H2ratio 共or actually increase
in the case that CH4is the source gas兲, whereas the CH4LIA
falls more than fivefold over the investigated range of Ne
flow rates—with the result that the strongest absorption at
high F共Ne兲is due to C2H2共v=0兲molecules. Indeed, in the
case of the C2H2/Ne/H2gas mixture, vibrationally hot
C2H2共v5=1兲molecules contribute ⬃50%of the LIA of the
blended feature at ⬃1275.3 cm−1, with the result that it ac-
tually appears more intense than the neighboring CH4共v=0兲
feature at 1275.04 cm−1. This should be contrasted with the
FIG. 9. Absorption spectra of activated 共a兲25 SCCM CH4/xSCCM Ne/共540−x兲SCCM H2and 共b兲12.5 SCCM CH4/xSCCM Ne /共552.5
−x兲SCCM H2gas mixtures using three different Ne flow rates, recorded at z=11 mm over the wavenumber range of 1276.2 − 1274.0 cm−1. Three unblended
CH4and C2H2features are labeled; detailed assignments of these transitions are given in Tables Iand II. The total p共150 Torr兲and P共1.5 kW兲were the same
for each of the spectra. 共c兲and 共d兲show the LIAs for the three unblended lines of interest and their variation with Ne flow rate.
033305-10 Ma et al. J. Appl. Phys. 106, 033305 共2009兲
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spectrum obtained with the 2.5 SCCM C2H2/40
SCCM Ar/522.5 SCCM H2gas mixture 关Fig. 4共b兲兴, which
is dominated by CH4absorptions and the higher frequency of
these two lines is just 2/3 as intense as the 1275.04 cm−1
feature 关consistent with the respective lower state degenera-
cies 共see Table I兲兴. The rationale for the present observations
is similar to that used to explain the observed pdependent
variations in LIA. Substituting H2with rare gas 共Ne or Ar兲
reduces the thermal conductivity of the gas, resulting in an
increase in Tgas in the plasma region. This facilitates CH4
→C2H2conversion in the hotter regions and explains the
increase in C2H2LIA with increasing F共Ne兲in Fig. 9共c兲.
Increased Tgas in the plasma region will encourage H2disso-
ciation 共and thus an increase in nH兲, but such increases will
be countered by the reduction in F共H2兲. As in the case of
increasing p, therefore, we can anticipate that increasing
F共Ne兲will result in a progressive decrease in nHat larger r
and thus a reduced probability for CH4formation via reac-
tion 共3兲in the cooler regions of the reactor—consistent with
the observed decline in CH4LIA.
D. Use of other hydrocarbon feedstock gases
Four other hydrocarbon source gases 共ethane, propyne,
n-propane, and n-butane兲were investigated in addition to
CH4and C2H2; all were found to show broadly similar be-
havior. The scan range of the QC laser spans part of the 90
2
absorption band of propyne, as illustrated by the spectrum of
a 5 Torr room temperature sample of propyne shown in Fig.
10. This absorption is also clearly evident in spectra of
8.3 SCCM propyne/40 SCCM Ar/516.7 SCCM H2gas
samples at room temperature and p= 150 Torr, but com-
pletely disappears once the plasma is ignited—to be replaced
by the familiar absorption lines of CH4and C2H2. Figures
11共a兲–11共d兲show LIAs for the standard probe transitions for
CH4共v=0兲and C2H2共v=0兲measured with these four alter-
native hydrocarbons under otherwise standard conditions at
z=11 mm plotted as a function of carbon flow rate F共C兲.
The quoted flow rates rely on use of the manufacturer cor-
rection factors 共where available兲and may not be as reliable
as those quoted previously for CH4and C2H2. Nonetheless, a
number of common trends are readily apparent—that are
very reminiscent of those observed when using C2H2as the
source gas 关Fig. 4共d兲兴. In all cases, the dominant LIA at low
carbon flow rate is associated with CH4, but this LIA stops
increasing once F共C兲⬃15 SCCM. The LIAs of the transi-
tions used to monitor C2H2in its v= 0 and v4= 1 levels both
increase with F共C兲. Notwithstanding the caveat regarding the
accuracies of the quoted carbon flow rates, there is a notable
and consistent difference at high F共C兲between the upper
plots 共involving unsaturated hydrocarbon source gases兲and
the lower plots 共involving alkanes兲; in the former cases, the
C2H2LIA has actually grown to exceed the CH4LIA. This
may well be a real effect, since the choice of hydrocarbon
affects the overall C/H ratio. In the case of a
40 SCCM CH4/40 SCCM Ar/485 SCCM H2flow, for
example, the overall C/H ratio in the input gas mixture is
40/1130= 0.0354. Use of C3H8or C4H10 at the same carbon
flow rate 关i.e., 10 SCCM in the case of C4H10, with F共H2兲
raised to 515 SCCM to conserve the same Ftotal兴gives the
same input C/H ratio. For the unsaturated hydrocarbons,
however, the input C/H ratio will necessarily be higher. For
example, the equivalent calculation for F共propyne兲
=13.33 SCCM 关and F共H2兲= 511.67 SCCM兴yields an input
C/H ratio of 0.0372. Figures 11共e兲and 11共f兲show, respec-
tively, the LIAs for the probed CH4共v=0兲and C2H2共v=0兲
probe transitions for these four source gases plotted on a
common C/H ratio scale. The detailed explanation of such
trends is again guided by the 2D modeling results, but is
reserved pending description of the time evolution of the
LIAs of interest following introduction of both CH4and
C2H2into a pre-existing Ar/H2plasma.
E. Time dependence of the LIAs following addition of
CH4„C2H2…to a pre-existing Ar/H2plasma
The fast spectral acquisition rate achievable with the
chirped QC laser allows study of the way in which the vari-
ous LIAs approach their asymptotic values following intro-
duction of a hydrocarbon flow to a pre-existing Ar/H2
plasma. Figure 12 shows illustrative spectra recorded at dif-
ferent times after the addition of 共a兲F共CH4兲=25 SCCM and
共b兲F共C2H2兲=12.5 SCCM to an Ar/H2plasma operating
with F共Ar兲=40 SCCM, F共H2兲appropriate to ensure that the
asymptotic Ftotal =565 SCCM, p=150 Torr, and P
=1.5 kW. As noted previously,16 the unblended 共and the
blended兲CH4共v=0兲features appear at earliest time, even
when using C2H2as the source gas. As shown in Figs. 12共c兲
and 12共d兲, the C2H2共v=0兲and C2H2共v4=1兲absorption fea-
tures appear later 共as do features associated with the v5=1
level of C2H2兲and take longer to attain their asymptotic LIA
values. Such data provide a further—in this case, time-
dependent—illustration of the effect of varying the C/H ra-
tio. Qualitatively at least, the data display all of the same
trends as noted previously. At low C/H ratio 共early time in
these experiments兲the main hydrocarbon detected is CH4,
but C2H2LIAs grow in relative intensity at later time 共higher
C/H ratio兲.
FIG. 10. Part of the 90
2absorption band of a 5 Torr room temperature sample
of propyne.
033305-11 Ma et al. J. Appl. Phys. 106, 033305 共2009兲
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F. Mechanism of CH4^C2H2interconversion and its
spatial dependence
Figure 13 displays 共production-loss兲rates of H atoms,
CH4,C
2H2, and C2H4plotted as a function of zat r= 0 re-
turned by the 2D model calculations for standard process
conditions: i.e., 25 SCCM CH4, 40 SCCM Ar , 500
SCCM H2,p= 150 Torr, P= 1.5 kW. The zdependence of
these calculated 共production-loss兲rate profiles are relatively
unaffected by reducing F共CH4兲to 5 SCCM or pto 75 Torr,
although both such changes reduce the respective magni-
tudes of the rates. To a reasonable approximation, these pro-
files are radially symmetric in the r,zspace above the sub-
strate. As noted in Ref. 5inspection of such figures
encourages discussion of the reactor volume in terms of three
concentric volumes: A, the plasma region 共that is located
directly above the substrate, contains the highest Tgas and is
characterized by large H atom production rates兲;B, an annu-
lar shell characterized by 1400⬍Tgas⬍2200 K, efficient
conversion of CH4共and C2H4兲into C2H2and the consump-
tion of H atoms required for this conversion; and C, the
cooler outer region 共Tgas ⬍1400 K兲characterized by net
conversion of C2H2into CH4共and C2H4兲and low H atom
consumption rates. Tables IV and Vsummarize the more
important reaction sequences 共i.e., those involving elemen-
tary steps with calculated rates⬎1017 cm−3 s−1兲that drive
these transformations in the centers of region B共z=3.5 cm,
where Tgas ⬃1900 K兲and region C共z= 4.8 cm, where Tgas
⬃1100 K兲. Several of the elementary steps in the CH4
→C2H2conversion scheme shown in Table IV consume H
atoms—consistent with the substantial calculated H atom
loss rate in region B共⬃4⫻1016 cm−3 s−1兲. The calculated H
atom 共production-loss兲rate in region C, in contrast, is
small—consistent with the reduced mechanism listed in
Table V. H atoms are needed to drive C2H2→CH4conver-
sion in region C, but they are not 共substantially兲consumed
by this conversion.
Such 2D model outputs provide a rationale for all of the
trends observed experimentally. Under standard process con-
ditions, CH4or C2H2feedstock gas is converted into a mix-
ture containing both of these hydrocarbons 共Fig. 4兲. The full
2D modeling predicts the presence of other stable hydrocar-
bons also 共C2H4,C
2H6, etc.兲at lower mole fraction, but the
tuning range of the available QC laser precludes the possi-
bility of observing these species. Thermodiffusion drives the
stable hydrocarbon species toward regions of lower Tgas but
chemical processing is occurring in parallel—driving net
CH4↔C2H2interconversion forward in region Band back-
ward in region C. The gas composition in the outermost parts
of the reactor may be further complicated by wall reactions
and the effects of local stagnation volumes, which are prob-
FIG. 11. LIAs for the standard probe transitions of CH4共v=0兲and C2H2共v=0兲measured at z=11 mm in four different hydrocarbon /Ar/H2gas mixtures at
p=150 Torr and P= 1.5 kW, as a function of carbon flow rate: 共a兲ethane, 共b兲propyne, 共c兲n-propane, and 共d兲n-butane. F共Ar兲and Ftotal were maintained
constant at, respectively, 40 and 565 SCCM throughout, and F共H2兲adjusted to compensate as F共hydrocarbon兲was varied. The CH4共v=0兲and C2H2共v=0兲LIA
data for these four molecules are plotted on a common C/H ratio scale in panels 共e兲and 共f兲, respectively.
033305-12 Ma et al. J. Appl. Phys. 106, 033305 共2009兲
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ably not treated well in the model calculations. The gas com-
position in this region may be further complicated by trans-
port of 共unprocessed兲source gas—the LIAs shown in Figs.
4共c兲and 4共d兲clearly indicate a relative excess of the respec-
tive source gas at higher carbon flow rates. The number den-
sity profiles 共dictated by Tgas兲and S共T兲line strength factors
mean that the present QC laser measurements studies 共and
any other line-of-sight IR studies of stable hydrocarbon spe-
cies in such reactors兲are necessarily heavily biased toward
material in region C—the cold periphery of the reactor 共re-
call Fig. 6兲. Even when using recessed windows 共configura-
tion II兲, therefore, gas in the hot plasma region 共A兲makes no
direct contribution to the measured LIAs. As Fig. 11 shows,
all of the alternative hydrocarbon source gases investigated
are processed, efficiently, to similar CH4/C2H2mixtures.
The time dependent studies 共Fig. 12兲provide a particu-
larly clear illustration of the role of region C.Att=0, this
region contains just Ar, H2, and H atoms. Upon adding CH4
共or any other hydrocarbon兲through inlets sited at the top of
the reactor, the shortest diffusion path is directly
downwards—i.e., transport localized in the outer region 共C兲.
As Table Vshows, CH4is the most stable hydrocarbon in
this region. Hence the dominance of the CH4features at
early t—irrespective of the choice of input hydrocarbon. The
input carbon must traverse a longer path in order for C2H2to
build up in the viewing column within region C—from the
gas inlets, through C, into B关where the requisite CH4
→C2H2occurs 共Table IV兲兴, and then radially outward again
into the cooler part of the viewing column. This longer dif-
fusional path is reflected by the longer observed buildup time
for the C2H2LIA 共Fig. 12兲. The efficiency of C2H2→CH4
processing in region Cdepends on the local C/H ratio. In the
time dependent studies, this ratio increases with tuntil reach-
ing the asymptotic value appropriate to the chosen process
conditions.
Finally we revisit the results of the steady state experi-
ments in the context of the above discussion. At low carbon
flow rates 关F共C兲=5 SCCM兴, the C/H ratio in region Cis
sufficiently low that all hydrocarbon species in this region
are processed to CH4—consistent with the dominance of
CH4features in the absorption spectra measured under these
conditions 共Figs. 4and 11兲. Increasing F共C兲leads to a pro-
gressive increase in the C/H ratio in region Cand in the
FIG. 12. Absorption spectra recorded at z= 11 mm at different times tafter addition of 共a兲F共CH4兲= 25 SCCM and 共b兲F共C2H2兲= 12.5 SCCM to an Ar /H2
plasma operating with F共Ar兲=40 SCCM, F共H2兲appropriate to ensure that the asymptotic Ftotal = 565 SCCM, p= 150 Torr and P= 1.5 kW. Plots 共c兲and 共d兲
show the growth of the LIAs for the standard CH4共v=0兲,C
2H2共v=0兲, and C2H2共v4=1兲probe transitions as a function of time after switching on the
hydrocarbon MFC 共which defines t=0兲.
FIG. 13. Calculated 共production-loss兲rates of H atoms, CH4,C
2H2, and
C2H4共and Tgas兲plotted as functions of zat r=0 for standard process con-
ditions: i.e., F共CH4兲=25 SCCM, F共Ar兲=40 SCCM, F共H2兲=500 SCCM,
p=150 Torr, P= 1.5 kW.
033305-13 Ma et al. J. Appl. Phys. 106, 033305 共2009兲
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C2H2/CH4ratio in region B. Diffusive transport ensures that
the steady state C2H2density in region Cthus increases
also—to levels that are easily detectable in the single pass
line-of-sight IR absorption spectrum. As already discussed
共Sec. III C兲, increasing p共at constant input mixing ratio兲or
substituting part of F共H2兲with Ar 共or Ne兲has the effect of
reducing nHin region C, thereby reducing the probability of
C2H2→CH4conversion in this region and increasing the
relative showing of C2H2共as compared with CH4兲in the
line-of-sight IR absorption spectrum.
IV. CONCLUSION
The QCL measurements reported here serve to highlight
many of the strengths and the limitations of applying line-of-
sight absorption methods to stable gas phase species in a
reactor containing very large temperature 共and number den-
sity兲gradients. The principle limitation is that the measured
absorptions are associated with molecules in the cool periph-
ery of the reactor 共C兲; the present measurements provide no
direct measure of molecules in the central plasma region 共A兲
from whence diamond growth occurs. Notwithstanding, they
are hugely informative with regards to gas processing within
the reactor, and to testing, tensioning and refining the com-
panion 2D model calculations. The present studies show that
any chosen hydrocarbon source gas will be converted into a
mixture dominated by CH4and C2H2, and that the continu-
ing interconversion between these two species depends sen-
sitively on both Tgas and nH, and thus on process conditions
共pressure, input power, input gas mixing ratios, etc.兲and lo-
cation within the reactor. CH4→C2H2conversion occurs
most efficiently in regions characterized by 1400⬍Tgas
⬍2200 K, which correlate with an annular shell 共region B兲
around the central plasma 共region A兲, whereas the reverse
transformation C2H2→CH4is favored in the outermost re-
gion 共C兲where Tgas ⬍1400 K.
ACKNOWLEDGMENTS
The Bristol group is grateful to EPSRC for the award of
a portfolio grant 共LASER兲, to Element Six Ltd for financial
support and the long term loan of the MW reactor, to the
University of Bristol and the Overseas Research Scholarship
共ORS兲scheme for a postgraduate scholarship 共J.M.兲, and to
colleagues J. J. Henney, K. N. Rosser and Dr. C. M. Western
and Dr. J. A. Smith for their many contributions to the work
described here. The Strathclyde group is grateful to EPSRC
for funding the initial part of their QC laser spectrometer
development program and for a research studentship 共to
K.G.H.兲, to NERC for funding subsequent QC laser spec-
trometer development, and to the Leverhulme Trust for the
award of an Emeritus Fellowship 共to G.D.兲. Y.A.M. is
pleased to acknowledge support from RF Government for
Key Science Schools Grant No. 133.2008.2. The collabora-
tion between Bristol and Moscow is supported by a Royal
Society Joint Project Grant.
TABLE IV. Simplified CH4→C2H2conversion mechanism highlighting key elementary reactions with rates
⬎1017 cm−3 s−1 under standard process conditions at z=3.5 cm 共i.e., region B兲, where Tgas ⬃1900 K.
Reaction
Reaction rate
/共cm−3 s−1兲
Net conversion; net rate
/共cm−3 s−1兲
1CH
4+H→CH3+H27.28⫻1019 CH4→CH3; 2.5⫻1017
2CH
3+H2→CH4+H 7.14⫻1019
3CH
3+H共+M兲↔CH4共+M兲1.20⫻1018
4CH
3+H→1CH2+H25.24⫻1018 CH3→1/3CH2; 1.6⫻1017
51CH2+H2→CH3+H 5.11⫻1018
63CH2+H2→CH3+H 2.97⫻1017
7CH
3+H→3CH2+H23.27⫻1017
81CH2共+M兲→3CH2共+M兲1.89⫻1018 1CH2→3CH2; 1.3 ⫻1017
93CH2共+M兲→1CH2共+M兲1.76⫻1018
10 3CH2+CH4→C2H4+H21.35⫻1017 CHx+CHy→C2H4; 1.35⫻1017
11 C2H4+H→C2H3+H21.53⫻1018 C2H4→C2H3; 2.1 ⫻1017
12 C2H3+H2→C2H4+H 1.32 ⫻1018
13 C2H3+H→C2H2+H22.36⫻1017 C2H3→C2H2; 2.1⫻1017
14 C2H3共+M兲→C2H2+H共+M兲7.14⫻1017
15 C2H2+H共+M兲→C2H3共+M兲7.40⫻1017
TABLE V. Simplified C2H2→CH4conversion mechanism highlighting key
elementary reactions with rates ⬎1017 cm−3 s−1 under standard process con-
ditions at z=4.8 cm 共i.e., region C兲, where Tgas ⬃1100 K.
Reaction
Reaction rate
/共cm−3 s−1兲
Net conversion; net rate
/共cm−3 s−1兲
1C
2H2+H共+M兲→C2H3共+M兲2.32⫻1017 C2H2→C2H3; 2.1⫻1017
2C
2H3+H2→C2H4+H 2.78⫻1017 C2H3→C2H4; 2.1⫻1017
3C
2H4+H共+M兲→C2H5共+M兲1.54⫻1017 C2H4→C2H5; 1.3⫻1017
4C
2H5+H→CH3+CH31.42⫻1017 C2H5→2CH3;1.4⫻1017
5CH
3+H2→CH4+H 1.00⫻1018 CH3→CH4; 2.1⫻1017
6CH
4+H→CH3+H27.93⫻1017
033305-14 Ma et al. J. Appl. Phys. 106, 033305 共2009兲
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APPENDIX
The estimation of S共T兲line strengths for transitions from
vibrationally excited levels of C2H2involves calculation of
the internal 共vibration and rotation兲partition function in the
rigid rotor, harmonic oscillator limit using analytical formu-
las as outlined by Herzberg.26 Such an approach is justified
in the present context given the small size of the rotational
constant 共B=1.1766 cm−1兲relative to the Tgas values of in-
terest. In this limit, the fraction of the total population in any
given level mwith energy Emis given by
nm
N=gmexp共−Em/kT兲
Qint
,共A1兲
where gmincorporates the rotational 共2J+1兲and nuclear spin
共3 or 1, for ortho- and para-levels, respectively兲degenera-
cies. Qint is the internal 共rotation, vibration兲partition func-
tion, given by
Qint =共kT/
␴
hcB兲
兿i关1 − exp共−
␻
ihc/kT兲兴di,共A2兲
where
␻
iis the wavenumber of fundamental vibration iwith
degeneracy di, the product in the denominator runs over the
five fundamental modes of vibration, and
␴
is the symmetry
factor 共2 in the case of C2H2兲.
Figure 14 shows the calculated Tdependence of n/N
关Eq. 共A1兲兴for the following levels of C2H2:v=0, J=23
共which shows much the strongest absorption in this spectral
region兲;v5=1, J=20 共E⬙=1225 cm−1兲;v4=1, J=24 共E⬙
=1319 cm−1兲; and v4=1+v5=1, J=20 共E⬙=1822 cm−1兲.As
noted earlier 共Sec. III B兲, the two J= 20 levels have different
nuclear spin statistical weights. Also shown 共right hand axis兲
is the S共T兲curve for the 40
150
1P共23兲transition.21 The two
vertical axes have been scaled to highlight the 共expected兲
reasonable match between the respective Tdependences,
thereby demonstrating that the above approach offers a sen-
sible route to predicting S共T兲factors and thus to determining
the scaling factor 共proportional to the Einstein B-coefficient兲
from the best-fit straight line between nand Sover the com-
plete range of T. All of the C2H2transitions of interest in-
volve ⌬v4=⌬v5=1 changes in vibrational quantum number.
We therefore assume that all have the same 共or similar兲Ein-
stein B-coefficients. The right hand axis in Fig. 14 thus pro-
vides estimates of the S共T兲factors for the transitions of in-
terest involving levels with v⬎0. We estimate that the
cumulative error in this procedure is ⬃5%, which is well
within the error associated with LIA measurements involving
these weak lines.
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FIG. 14. Plot showing the calculated Tdependence of n/N关Eq. 共A1兲兴for
selected C2H2levels of interest: v=0, J=23 共E⬙= 649 cm−1,䊏兲;v5=1, J
=19 共E⬙=1177 cm−1,䉭兲;v5=1, J=20 共E⬙=1225 cm−1,〫兲;v4=1, J=24
共E⬙=1319 cm−1,䊊兲; and v4=1+v5=1, J=20 共E⬙=1822 cm−1,䉮兲. Also
shown 共solid curve and right hand scale兲is the S共T兲line strength factor for
the 40
150
1P共23兲transition from HITRAN 共Ref. 21兲. The two vertical axes
have been scaled to highlight the analogous Tdependences and to establish
the best-fit scaling factor linking nand S. The inset shows the various n/N
values at high Ton an expanded 共25 times兲vertical scale.
033305-15 Ma et al. J. Appl. Phys. 106, 033305 共2009兲
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