C4F8 dissociation in an inductively coupled plasma
M. T. Radtke,a) J. W. Coburn, and David B. Graves
Department of Chemical Engineering, University of California, Berkeley, California
共Received 11 July 2002; accepted 21 April 2003; published 13 June 2003兲
A study of the dissociation of a small concentration of cyclic-C4F8 (c-C4F8) in a predominately
argon, low pressure inductively coupled plasma is reported. Measurements of electron density,
plasma potential, and electron energy distribution function 共EEDF兲 were made at several pressures
and over a range of dilute Ar/C4F8 plasmas using a Langmuir probe. The c-C4F8 concentration in
the plasma was estimated using appearance potential mass spectrometry and ion mass spectrometry.
Optical emission spectroscopy was used to estimate the gas temperature and total neutral number
density. Volume-averaged total dissociation rate coefficients for c-C4F8 ionization and total
dissociation into neutrals were calculated using reported cross sections and the measured EEDFs.
Rate coefficients inferred by both methods were in agreement within experimental uncertainties and
approximations of the model, indicating that the dissociation cross sections are accurate. © 2003
American Vacuum Society. 关DOI: 10.1116/1.1582456兴
I. INTRODUCTION
Plasma chemical processes are widely used for a variety
of etching, deposition, cleaning, and other surface modification purposes in semiconductor device manufacturing. Models of these plasmas offer many potential benefits to experimentalists and industrial users of plasma processes.
However, development of convincing models of plasmas
with realistically complex chemistries has proven difficult.
Many attempts to model the complex chemistry occurring in
these plasmas have been made over many years, but it is
clear that one of the major stumbling blocks is the lack of an
adequate experimental database. Most of the experimental
work conducted has been done in commercial plasma tools,
with neither in in situ detection of the neutral and ionic species present, nor the other key plasma characteristics such as
plasma density, plasma potential, or the electron energy distribution function.
However, even studies that attempt to develop a fundamental understanding of the chemically active plasma have
struggled. A major difficulty has been that typically only a
few chemical species have been measured, or that quantitative measurements have been difficult or impossible. At a
minimum, it is generally necessary to measure all of the
major neutral and ionic species present, as well as the plasma
properties such as electron and ion densities, plasma potential, and the electron energy distribution function 共EEDF兲.
The key is in conducting systematic experimental studies,
coupled with modeling. The present work is a small step in
the direction of developing a coordinated modelingexperimental program to systematically develop reliable
models of chemically active plasmas.
The strategy we have followed in the work reported here
is to measure key plasma properties in dilute c-C4F8 in argon
mixtures. Plasma properties were measured over a range of
dilute c-C4F8 inlet concentrations and gas pressures. Plasma
a兲
Author to whom correspondence should be addressed; electronic mail:
[email protected]
1038
J. Vac. Sci. Technol. A 21„4…, JulÕAug 2003
properties were also measured in a pure argon plasma to
characterize plasma property changes with c-C4F8 addition.
In the present article, we report the dissociation characteristics of c-C4F8.
Cyclic-C4F8 is now commonly used for plasma etching of
dielectric thin films, especially silicon dioxide and silicon
nitride. The gas is known to dissociate readily, and will often
contribute to the formation of polymer-like surface layers
that assist in increasing etch selectivity. Recently, Morgan1
has proposed a form for the total electron-impact cross section for dissociation of c-C4F8 into neutrals based on swarm
data. Sugai and Toyoda2 have reported values for the cross
sections for the electron-impact dissociation of c-C4F8 to
CFx radicals 共CF, CF2, and CF3) and fluorocarbon positive
⫹
⫹
⫹
⫹
ions (CF⫹ CF⫹
2 , CF3 , C2F3 , C2F4 , and CF3F5 ). Toyoda
3
4,5
et al. and Jiao et al. have measured partial and total
ionization cross sections for c-C4F8 using mass spectrometry. Bibby and Carter,6 Kurepa,7 and Beran and Kevan8
have also made measurements of the total ionization cross
section. Christophorou and Olthoth9 have recently recommended a total dissociative ionization cross section based on
the available experimental measurements.
The cross sections for dissociative ionization and dissociation into neutrals are the focus of this article. By measuring the electron density and the electron energy distribution,
the total dissociation rate coefficient can be estimated if the
cross sections are known. Using the proposed cross sections,
we computed the total dissociation rate coefficient at four
pressures 共1, 3, 5, and 10 mTorr兲 and at approximately the
same, relatively low rf power 共⬃30– 40 W deposited兲. Low
powers were used to insure only partial c-C4F8 dissociation.
The EEDFs varied significantly over these four pressures,
allowing the EEDFs to be integrated over different parts of
the cross sections, resulting in a range of total dissociation
rate coefficients.
The result of the article is a comparison of the total dissociation rate coefficients inferred from integrating the measured EEDFs over the proposed cross sections to the value
0734-2101Õ2003Õ21„4…Õ1038Õ10Õ$19.00
©2003 American Vacuum Society
1038
1039
Radtke, Coburn, and Graves: C4F8 dissociation in an inductively coupled plasma
1039
FIG. 1. Experimental setup.
obtained from the model c-C4F8 mass balance under the four
sets of conditions. Given the uncertainties in the various
measurements and the simplified model, the two approaches
gave values essentially in agreement with each other. We
conclude that the proposed cross sections are in agreement
with our measurements.
Of course, the results reported here are only a small part
of the overall problem alluded to above. The experimental
conditions were chosen to minimize complexities like
changes in the EEDF or plasma density from changes in gas
phase composition resulting from plasma chemistry. A focus
on total dissociation cross section obviates the need for
branching ratios, and a parent gas like c-C4F8 is unlikely to
reform at walls, eliminating another major source of model
uncertainty. Nevertheless, using small concentrations of molecular gases in well-characterized rare gas discharges can be
exploited in other ways. Limited but successful studies such
as this help develop confidence in our ability to measure and
predict key plasma physical and chemical properties, and
therefore lay the foundation for more ambitious future work.
A. Ion mass spectrometry
Positive ions are sampled through a 325 ␮m diameter
aperture in the chamber wall. Three Einzel lenses are used to
focus the positive ions, and a UT9 300-C quadrupole mass
spectrometer 共QMS兲 is used for ion detection. The QMS is
oriented in the direction of ion travel and the ionizer is
turned off, giving a direct measure of the ion flux from the
plasma. The mass spectrometer is differentially pumped and
has a base pressure below 10⫺7 Torr. Under these conditions,
the mean free path for ion collisions is much larger than the
chamber dimensions, so it can be assumed that the ions from
the plasma reach the detector of the mass spectrometer without suffering any gas phase collisions, resulting in an accurate measure of the ion flux composition through the aperture. Integration of areas under each peak is used to calculate
the ion signals. Correction factors for the mass dependence
on detection and transmission efficiency are given by the
manufacturer. Transmission and detection efficiencies depend on the plasma potential, so the corrected QMS measurement gives only relative ion flux; absolute fluxes can be
calculated with the Langmuir probe or ion flux probe measurements.
II. EXPERIMENT
The experimental reaction chamber used for this work is
shown in Fig. 1. The plasma is operated in a cylindrical
chamber with a height of 10 cm and a diameter of 20 cm.
The plasma is powered inductively by a 5-turn coil and operated at 13.56 MHz rf power through an alumina dielectric
window. A Faraday shield is used to minimize capacitive
coupling to the plasma and a Tesla coil is used to ignite the
plasma. Ion and neutral mass spectrometers, the Langmuir
probe, and the microbalance are all located in the same axial
plane, 7.6 cm below the alumina dielectric.
JVST A - Vacuum, Surfaces, and Films
B. Neutral mass spectrometry
Measurement of neutral species is done with a Hiden
Analytical PIC300 QMS; MASSOFT™ software is used to interface the QMS with a personal computer. Neutrals are
sampled through a 900 ␮m diameter aperture diametrically
opposite the ion collection aperture. The QMS is mounted in
the cross-beam mode to minimize the effects of ions, metastables, and photons from the plasma. The ionizer for the
mass spectrometer is located line-of-sight to the plasma
sample aperture. Neutral flow between the aperture and the
1040
Radtke, Coburn, and Graves: C4F8 dissociation in an inductively coupled plasma
ionizer is in the molecular flow regime, so neutral species
reach the ionizer without suffering any gas phase collisions.
Background gas in the QMS chamber can make a significant
contribution to the QMS signal for both stable and radical
species.10 Three stages of differential pumping are used to
minimize the background signal, and a slotted wheel rotary
beam chopper in the third differential pumping stage is used
for beam modulation to subtract the background signal.10
Appearance potential mass spectrometry 共APMS兲 is used
to measure radical and stable molecule densities in the
plasma. APMS detection exploits the difference between the
direct and dissociative ionization threshold, where the appearance signal below the dissociative ionization threshold is
used for radical density measurements. Absolute number
densities of radicals are calibrated using the argon signal
with the plasma off as a calibration. Densities calculated
from dissociative ion fragments of parent species 共such as
c-C4F8) are calibrated from dissociation fragments of the
parent species with the plasma off. Corrections of the mass
dependence on detection and transmission efficiency are
given by the manufacturer. Details on the mass spectrometer
measurements can be found in Ref. 11.
C. Langmuir probe
The Langmuir probe is located in the same axial plane as
the mass spectrometer apertures; the radial position can be
adjusted. The Langmuir probe tip consists of a cylindrical
platinum wire, with a diameter of 125 ␮m and a length of 6
mm. The Faraday shield in the system minimizes capacitive
coupling between the coil and the plasma, so rf distortion of
the Langmuir probe signal should be minimized. Three parallel LC filters tuned to 13.56 MHz and its harmonics are
used to minimize any remaining rf distortion. A copper plug
inside the alumina Langmuir probe holder provides 60 pF of
capacitance between the probe and the plasma; this is much
larger than the capacitance between probe and ground, further reducing the rf distortion. Further details of the experimental Langmuir probe setup can be found in Ref. 12.
The Langmuir probe is used to generate I p ⫺V p probe
traces. The second derivative of the probe traces in the electron retardation range gives the electron energy probability
function 共EEPF兲, and the dc part of the plasma potential is
taken as the zero crossing of the second derivative of the
probe trace.13 The EEDF, electron density, average electron
energy, and electron temperature are derived from the EEPF.
The energy difference between the peak and zero crossing of
the EEPF remained at approximately 1 eV under all plasma
conditions, indicating that the Langmuir probe measurements
were reliable.14
Deposition on the probe tip and the chamber walls can
distort EEPF measurements. The probe tip is kept red-hot
before and during the Langmuir probe scans in order to keep
it clean while maintaining a constant work function. Using
small c-C4F8 concentrations help minimize wall deposition.
Langmuir probe scans in argon plasmas in a clean chamber
at the experimental conditions were completed and showed
J. Vac. Sci. Technol. A, Vol. 21, No. 4, JulÕAug 2003
1040
that the Langmuir probe scans did appear to be free from
distortions caused by wall deposits under the experimental
conditions.
D. Ion flux probe
A wall-mounted ion flux probe was used to measure positive ion fluxes to the wall. The probe is biased negatively and
measures total positive ion current. The probe is a stainless
steel disk at the chamber wall in the same axial plane as the
Langmuir probe, with a diameter of 1.11 cm and an area of
0.97 cm2.
E. Optical emission
Optical emission spectroscopy 共OES兲 is used for specie
detection and neutral gas temperature measurements. In
OES, radical and neutral species are excited to resonant energy states via electron impact excitation, releasing photons
in the UV-visible range after decay to lower energy states.
Separate spectrometers were used for specie identification
and rotational and vibration temperature measurements.
Temperature measurements were taken using a McPherson model 207 Czerny-Turner monochromater with 1800
mm⫺1 holographic grating, a 0.67 m focal length, and an
effective spectral range of 260– 870 nm. The maximum resolution is 0.011 nm full width at half maximum 共FWHM兲. A
Hamamatsu model R943-02 photomultiplier tube was used
as the detector and a Keithley model 485 picoammeter was
used to measure the photomultiplier tube current. Optical
emission is detected through a port in the same plane as the
other diagnostics 共see Fig. 1兲. Temperature measurements are
made by adding a small amount of nitrogen to the plasma
and measuring the N2 second positive emission system; a
simulation is used to approximate rotational and vibrational
temperatures.15 Translational and rotational energy modes
are assumed to exchange energy efficiently, so the rotational
and translational temperatures were assumed to be in
equilibrium.16
A PC2000-UV-VIS-ISA spectrometer is also used with
this system and can simultaneously measure a complete
spectrum with an effective range of 200 and 850 nm. The
PC2000 spectrometer is supported with Ocean Optics OOIBase32™. The resolution ranges from 0.3 to 10.0 nm
FWHM, and the grating is 600 mm⫺1. Spectra taken at each
experimental condition were used to test the variation of the
OES spectra with c-C4F8 concentration.
III. MODEL
The model consists of a mass balance on c-C4F8 in a
predominantly argon plasma. The cross sections were tested
by independently calculating the total dissociation rate coefficient using two methods: a mass balance on c-C4F8 and by
integrating the dissociation cross sections over measured EEPFs. Runs were completed at 1, 3, 5, and 10 mTorr. At each
of these pressures, diagnostic measurements were made at 0,
0.47,0.94, 1.42, 1.90, and 2.39 inlet % c-C4F8. Measurements were not completed at 0.47% C4F8 at 1 mTorr because
1041
Radtke, Coburn, and Graves: C4F8 dissociation in an inductively coupled plasma
TABLE I. Temperature of neutrals in plasma at plasma wall 共using mass
spectrometer兲 and a line-of-sight average temperature measurement using
optical emission.
Pressure
共mTorr兲
Power
共W兲
T 共K兲
at wall
⫹/⫺20 °C
T rot 共K兲
optical emission
⫹/⫺30 °C
1
3
5
10
36.9
44.1
35.8
24.69
303
303
297
306
430
440
440
450
1041
flow is conductance limited under the experimental conditions 共cf. Fig. 1兲, so the outlet c-C4F8 flow rate was calculated with the measured densities and the ratio of conductances, which are inversely proportional to the square root of
molecular weight 关Eq. 共3兲兴.18
F CoutF
4 8
out
F Ar
⫽
n C4F8C C4F8
n ArC Ar
⫽
n C4F8
n Ar
冉 冊
M Ar
M C4 F 8
1/2
.
共3兲
B. EEPF
of mass flow controller limitations. A relatively low rf power
was used to keep the electron density low. This has the advantage that the c-C4F8 is not completely dissociated, and
the gas heating that accompanies higher plasma densities can
be avoided.
It was assumed in this analysis that all the c-C4F8 dissociation comes from electron impact. We ignored the possible
effects of argon metastables in dissociating c-C4F8, based in
part on measurements and analyses reported elsewhere, and
in part on an analysis described in Appendix A.17 Another
potential loss mechanism for c-C4F8 is formation of C4F⫺
8,
followed by dissociative recombination. However, estimates
suggest this is also an unimportant dissociation pathway, and
was therefore neglected ni the analysis 共see Appendix B兲.
A. c-C4F8 mass balance
A global c-C4F8 species mass balance used to calculate
the c-C4F8 total dissociation rate coefficients (k diss,C4F8) is
shown in the following equation:
F in,C4F8⫺F out,C4F8⫽k diss,C4F8n C4F8n e V,
共1兲
where F is the flow rate in s⫺1, k diss is the dissociation rate
coefficient in cm3/s, n i is the species density in cm⫺3, and V
is the plasma volume in cm3. We considered it unlikely that
wall or gas phase recombination would result in c-C4F8 reformation. As a result, c-C4F8 is assumed to enter the chamber only by flow. Although wall deposition is substantial
when the plasma is on, dissociation fragments are assumed
to be responsible for deposition, not c-C4F8, so deposition
does not appear in the c-C4F8 mass balance.
As mentioned previously, the neutral gas density and pressure were measured at the aperture near the chamber wall.
Despite using low pressure and low power to minimize gradients in the plasma, neutral gas temperature and density
gradients still exist. In order to approximate the gradients,
optical emission spectroscopy was used to measure line of
sight average rotational temperature 共see Table I兲. The neutral gas temperature can be estimated at the chamber wall,11
so an average plasma c-C4F8 density was calculated by scaling the c-C4F8 wall density with temperature,
n C4F8 ,avg⫽n C4F8 ,wall
冉
冊
T avg共 rot兲
.
T wall
共2兲
Using the average c-C4F8 density, the outlet c-C4F8 flow rate
was calibrated with the known argon flow rate. The outlet
JVST A - Vacuum, Surfaces, and Films
Spatially resolved rate coefficients for dissociative ionization and dissociation into neutrals were calculated by integration of the c-C4F8 cross sections 共␴兲 over the measured
EEPFs 关 f (␧,r,z) 兴 .
k diss,C4F8共 r,z 兲 ⫽
1
n e 共 r,z 兲
冑 冕
2e
me
⬁
0
␴ C4F8共 ␧ 兲 f 共 ␧,r,z 兲 ␧d␧.
共4兲
The total dissociation rate coefficient was then calculated as
the sum of the rate coefficients for dissociative ionization
and dissociation into neutrals, and compared with the rate
coefficients calculated from the mass balance to test the cross
section.
total
neutrals
ions
k diss,C
F ⫽k diss,C F ⫹k diss,C
4 8
4 8
4 F8
.
共5兲
Spatial variations in the EEDF and electron density were
approximated based on the nonlocal electron kinetics.19 A
two-dimensional plasma potential map was approximated using the Langmuir probe potential measurements, equipment
symmetry, and a normalized plasma potential map from a
fluid plasma model.20 The plasma potential profile was used
with the measured EEPF to calculated volume-averaged dissociation rate coefficients for each condition. Some smoothing and extrapolation of the EEPF tail was done to improve
the accuracy of the rate coefficient integration in Eq. 共4兲. In
order to check that this did not introduce artifacts into the
EEPF, extra probe measurements were made at each experimental pressure and higher input powers, where the noise in
the tail region of the EEPF is lower, to help determine the
shape of the tail. 共Recall that the original measurements were
made at lower power to minimize dissociation and the creation of plasma gradients.兲 In any case, the smoothed and
extrapolated region of the EEPF’s contribution to the total
dissociation ranged from 11.2% at 1 mTorr to 18.8% at 10
mTorr.
IV. RESULTS
A. c-C4F8 measurements
Since the C 4 F ⫹
8 parent ion is unstable, it could not be
used as a measure of the c-C4F8 density. Therefore, the C2F⫹
4
and C3F⫹
5 dissociative ionization fragments were used to determine the c-C4F8 density. Obviously, a possible artifact is
direct ionization from the radicals C2F4 and C 3 F 5 . Evidence
suggests that this is not significant. First, the ion mass spectrometer shows that both these ions are present in significant
1042
Radtke, Coburn, and Graves: C4F8 dissociation in an inductively coupled plasma
FIG. 2. Ion densities in plasma for 2% inlet C4F8 /Ar plasma at 10 mTorr and
⫹
25.6 W deposited power. C2F⫹
4 and C3F5 are primarily from C4F8 dissociation and were used to calculate the C4F8 density.
quantities in the plasma, and are therefore good candidates
for potential dissociative ionization ions 共cf. Fig. 2兲. In addition, Hayashi et al. reported these ions as coming predominantly from dissociative ionization of c-C4F8 and being the
predominant dissociative ionization products.21 Measurements in the appearance potential mass spectrometer also
support this conclusion. C3F⫹
5 signal scans at 10 mTorr for
pure c-C4F8 with no plasma and for the Ar/c-C4F8 at the run
condition are shown in Fig. 3. The threshold and shape of the
C3F⫹
5 signal is the same with the plasma on and off, indicating that all the C3F⫹
5 signal is from dissociative ionization of
c-C4F8. The c-C4F8 density in the plasma was calculated
with Eq. 共6兲, where S is the slope of the signal after the
background is subtracted off. This was repeated for all experimental conditions.
FIG. 3. Mass spectrometer scans at m/e⫽131 (C3F⫹
5 ) in C4F8 with plasma
off and in C4F8 mixture with the plasma on. The shape of the signals is the
same, indicating that all of the C3F⫹
5 signal is from dissociative ionization of
C4F8.
J. Vac. Sci. Technol. A, Vol. 21, No. 4, JulÕAug 2003
1042
FIG. 4. Mass spectrometer scans at m/e⫽100 (C2F⫹
4 ) in C4F8 with plasma
off and in C4F8 mixture with the plasma on. The threshold is slightly lower
when the plasma is on, indicating that there is probably a little C2F4 present.
n Con F
4 8
n CoffF
4 8
on
⫽
SC
⫹
4F8→C3F5
.
off
⫹
F
→C
F
4 8
3 5
SC
共6兲
The same procedure was used to calculate the C4F8 from the
⫹
C2F⫹
4 ion. Scans of the C2F4 signal with the plasma on and
off are shown in Fig. 4. The small signal below the apparent
dissociative ionization threshold at about 14 eV is most
likely from direct ionization of C2F4 or possibly from dissociative ionization of some larger radical. Ideally, the slope of
the signal from direct ionization should be subtracted off in
calculating the C4F8 density, as shown in Eq. 共7兲. However,
given the relatively small signal-to-noise ratio, we elected to
neglect this and simply assumed the signal was due exclusively to the parent C4F8, using the following expression:
⫹
FIG. 5. C4F8 density independently calculated the C2F⫹
4 and C3F5 ions are in
agreement. An average density value was used.
1043
Radtke, Coburn, and Graves: C4F8 dissociation in an inductively coupled plasma
FIG. 6. Electron energy probability functions 共EEPFs兲 at 10 mTorr. EEPF is
suppressed with increasing C4F8 addition.
n Con F
on
SC
⫹
4F8→C2F4
1043
FIG. 8. EEPFs at 3 mTorr. EEPF does not change significantly with C4F8
addition.
on
⫺S C
⫹
2F4→C2F4
An important element of the strategy of the article is to be
able to measure the EEPF under all conditions so that the
dissociation cross sections can be tested. A key question is to
what extent the molecular gas and its dissociation fragments
affect the electron characteristics. Electron energy probability functions were measured with a Langmuir probe for each
experimental condition. Langmuir probe scans were completed in pure argon at the same plasma conditions as the
plasma mixture 共e.g., deposited power, pressure, and input
flow rates兲, in order to check the reliability of the Langmuir
probe scans in the depositing environment. EEPF scans are
shown at each pressure and inlet composition in Figs. 6 –9,
and show that the EEPF is independent of inlet c-C4F8 flow
at 1, 3, and 5 mTorr, but is suppressed with increasing
c-C4F8 concentration at 10 mTorr. The reduction in the magnitude but not the shape of the EEPF suggests that the electron density is reduced but the electron energy distribution is
unchanged. A possible explanation for the electron density
suppression at 10 mTorr is the addition of more energy loss
channels with higher concentrations of the molecular gas. As
FIG. 7. EEPFs at 5 mTorr. EEPF does not change significantly with C4F8
addition.
FIG. 9. EEPFs at 1 mTorr. EEPF does not change significantly with C4F8
addition.
4 8
n CoffF
4 8
⫽
off
⫹
4F8→C2F4
SC
.
共7兲
c-C4F8 densities calculated using both the C3F⫹
5 and the
ion
and
assuming
dissociative
ionization
are
in generC2F⫹
4
ally good agreement as illustrated in Fig. 5. In most cases,
⫹
the C3F⫹
5 signal was too small to be useful, so the C2F4
signal was used exclusively as a measure of the c-C4F8 density.
B. EEPF measurements
JVST A - Vacuum, Surfaces, and Films
1044
Radtke, Coburn, and Graves: C4F8 dissociation in an inductively coupled plasma
FIG. 10. Electron density vs inlet % C4F8 for each pressure. Electron density
is suppressed at 10 mTorr.
a further test, the EEPF data were processed to generate electron densities, plasma potentials, and average electron energies (T e ). Figures 10–12 demonstrate that, except for electron density at 10 mTorr, these quantities also do not show a
variation with composition. These experimental conditions
result in a range of EEPFs with which to test the cross sections and mass balance model.
Ion wall current was measured with a planar ion flux
probe. This measurement was used to independently estimate
the central plasma positive ion density, using the approximate ion Bohm velocity at the sheath edge. Comparison of
the values for positive ion density estimated from the ion
wall probe in Fig. 13 with the peak electron density measurements in Fig. 10 offer support for our conclusion that the
plasma remains electropositive with at most, a relatively
small contribution from negative ions at the highest pressure
of 10 mTorr.
C. Dissociation rate coefficients
The proposed cross sections for dissociative ionization
and dissociation into neutrals are plotted with the smoothed
FIG. 11. Plasma potential vs inlet % C4F8 for each pressure.
J. Vac. Sci. Technol. A, Vol. 21, No. 4, JulÕAug 2003
1044
FIG. 12. Average electron energy vs inlet % C4F8 for each pressure. 共Electron temperature is 2/3 the average energy for a Maxwellian EEDF.兲
EEPFs at each pressure in Fig. 14. Over this pressure range,
the EEPFs are sufficiently different to allow different parts of
the cross section to be tested. Rate coefficients for dissociative ionization and dissociation into neutrals were calculated
by integrating the respective cross sections over the EEPFs;
the total dissociation rate coefficient (k diss,tot) is a sum of the
two.
The rate coefficients for c-C4F8 total dissociation rate coefficients calculated from the EEPF and from the mass balance are shown for each pressure in Figs. 15共a兲–15共d兲. Also
shown are the contribution to the rate coefficient as calculated from the EEPF from dissociative ionization and dissociation into neutral for each pressure. The error bars are the
95% uncertainty limits based on multiple measurements.
These are the spatially averaged rate coefficients. The rate
coefficients calculated from the EEPF and from the mass
balance are nearly independent with c-C4F8 inlet fraction.
This is the best evidence that dissociation comes almost exclusively from electron impact collisions, and that therefore
metastables and negative ions do not play an important role
in c-C4F8 dissociation. The total dissociation rate coeffi-
FIG. 13. Ion density calculated from ion flux probe measurements is similar
to Langmuir probe measurements.
1045
Radtke, Coburn, and Graves: C4F8 dissociation in an inductively coupled plasma
FIG. 14. Electron energy probability functions 共EEPFs兲 and cross sections
共␴兲 for dissociative ionization and dissociation into neutrals 共Refs. 1 and 4兲.
cients calculated from the mass balance and from the EEPF
are in reasonably good agreement at 3, 5, and 10 mTorr, but
agreement was not as good at 1 mTorr.
1045
cients calculated by the two methods indicates that the proposed cross sections were accurate within model and experimental uncertainties. The analysis rests on the assumption
that only electron impact of c-C4F8 is responsible for dissociation. The major uncertainties in the analysis are the possible confounding role of metastable argon in dissociation
and the possibility that negative ions are present. However,
experimental results showed that the rate coefficients for dissociation did not change significantly with varying inlet
c-C4F8 composition in the plasma. It is expected that the
effects of metastables and negative ions would be a function
of the inlet c-C4F8 concentration, especially at low concentration. The independence of the results with inlet flow of
c-C4F8 implies that the metastable argon and negative ion
concentrations in the plasma, although not directly measured,
were unlikely to be significant under the conditions used in
the present study. Dissociative ionization is predicted to become increasingly more important at lower pressures, ranging from ⬃5% of the total dissociation at 10 mTorr to ⬃35%
at 1 mTorr.
ACKNOWLEDGMENTS
V. SUMMARY AND CONCLUSIONS
A proposed cross section for c-C4F8 total dissociation was
tested in dilute c-C4F8 /Ar plasma. A Langmuir probe was
used to make EEDF measurements and the total dissociation
rate coefficient was calculated by integrating the total dissociation cross section over the measured EEPFs. The total
dissociation cross section included contributions from dissociative ionization and dissociation into neutral fragments.
The total dissociation rate coefficient was independently calculated using a reactor mass balance and measured c-C4F8
density. Measurements were conducted over a range of dilute
c-C4F8 inlet compositions 共⬍2.4 mol %兲 and at pressures of
1, 3, 5, and 10 mTorr. Comparison between the rate coeffi-
FIG. 15. c-C4F8 total dissociation rate coefficients were calculated from the
mass balance. Rate coefficients for dissociative ionization and dissociation
into neutrals were calculated with the respective cross sections and measured EEPFs; the total dissociation rate coefficient is the sum of the two rate
coefficients.
JVST A - Vacuum, Surfaces, and Films
The authors would like to thank Dr. David Frasier for
useful discussions. This work was made possible, in part, by
support from was NSF/SRC Engineering Center for Environmentally Benign Semiconductor Manufacturing.
APPENDIX A: ROLE OF AR METASTABLES
It was assumed in this analysis that electron impact is the
dominant c-C4F8 dissociation pathway,
e⫹C4F8→dissociation products.
共A1兲
However, this neglects dissociation by argon metastable species,
ArM ⫹C4F8→dissociation products.
共A2兲
Metastables are known to play an important role in plasma
chemistry under some conditions, but have been found to
play a smaller role for high density inductive discharges.22–24
Small amounts of a molecular gas have been shown to drastically reduce metastable densities for low density capacitive
plasmas.25 Argon metastable density in the plasmas we study
here should be a function of C4F8 concentration since the
molecular species will quench the metastable states. However, it may be the case that even though the metastable
density changes with molecular species density, the electron
population and all other kinetic processes in the plasma are
essentially unaffected. If argon metastables were playing an
important role in dissociation, the inferred molecular dissociation rate coefficient from the mass balance should be a
function of c-C4F8 concentration and therefore inlet flow
rate. However, Fig. 15 shows that the dissociation rate coefficients do not change with inlet c-C4F8 concentration, implying that the metastables do not play an important role in
dissociation.
To help support this conclusion, estimates of the argon
metastable density in the plasma and of the rate of molecular
1046
Radtke, Coburn, and Graves: C4F8 dissociation in an inductively coupled plasma
1046
TABLE II. Summary of argon metastable (ArM ) kinetics.
e
k Ar
tot
k Ar
Q
k Ar
Q
k Cx Fy
e⫹Ar→e⫹ArM
e⫹ArM →e⫹Ar*
ArM ⫹Ar→Ar⫹Ar*
e⫹ArM ⫹Cx Fy →Ar⫹Cv Fw •••
ArM →Ar共walls兲
k rec
excitation
electron quenching
argon quenching
fluorocarbon dissociative
quenching
diffusion: D mAr/⌳ 2o 关Ar兴
Ref.
Ref.
Ref.
Ref.
26
27
28
29
Ref. 28
dissociation via metastable channels also indicate that metastables do not play an important role under these experimental conditions. An estimate of argon metastable density can
be made from the following expression: rate coefficients in
Eq. 共A3兲 are defined in Table II.
M
→
n Ar
e
n e n Ar
k Ar
Q
Q
rec
k tot
e n e ⫹k Ar⫹ 兺 k C x F y n C x F y ⫹k
.
共A3兲
The value for C4F8 dissociative metastable quenching has not
been measured to our knowledge, so the highest measured
metastable quenching rate coefficient in the literature (10⫺9
cm⫺3) was used to put an upper bound on the quenching
rate. A comparison of the rates of molecular dissociation
from each channel at 1 and 10 mTorr is made in Table III,
and it can be seen that the rate of metastable quenching by
C4F8 is at least a factor of 3 to 4 lower than the value of
dissociation from electron impact. The percentage of the
quenching that results in dissociation has not been reported
for C4F8, but this represents an upper bound on the dissociation.
Another way to infer the presence and effects of metastables is through optical emission. If metastable species
were present in significant quantities, then changes in metastable species density should affect the emission spectrum,
especially for certain transitions that are known to involve
metastables. An optical emission spectrum 共200– 800 nm兲
was taken for each experimental condition. All detected
peaks were identified as argon transitions. The rate of argon
excitation is given by
R exc⫽k exc,Arn Arn e V,
共A4兲
where k exc,Ar is the excitation rate coefficient (cm3/s) 共a
function of the EEPF兲, and n Ar and n e are the argon and
electron densities 共cm⫺3), respectively. The excitation rate
coefficient should be independent of C4F8 density if metastables are not affecting electron kinetics. Experimentally,
the absolute optical emission rate was observed to change
when electron and argon densities change as a result of C4F8
concentration changes. However, by normalizing the OES
signal intensity with electron and argon number density, the
effective excitation rate coefficient can be inferred,
TABLE III. Comparison of rates.
1 mTorr
10 mTorr
n M (cm⫺3)
r quench(ArM ) s⫺1
r diss共elec兲 s⫺1
3.7⫻1010
4.6⫻1010
1.0⫻1016
1.7⫻1017
4.8⫻1016
4.0⫻1017
J. Vac. Sci. Technol. A, Vol. 21, No. 4, JulÕAug 2003
FIG. 16. Corrected OES signal for a 811.15 nm peak and total OES signal do
not change with fluorocarbon addition. 共Corrected signal ⫽ OES signal
关 n e 共0% FC兲/n e ] 关 n Ar共0% FC兲/n Ar].)
k exc,Ar⬀OES signal
冉
n e 共 0% FC兲
ne
冊冉
冊
n Ar共 0% FC兲
. 共A5兲
n Ar
Figure 16 is a plot of emission intensity from the transition
resulting in emission at 811.5 nm and the total integrated
emission intensity as a function of inlet C4F8 flow rate. These
normalized emission intensities can be seen to be essentially
independent of C4F8 inlet flow. In summary, the mass
balance-inferred effective dissociation rate, the normalized
optical emission intensity, the measured EEPF, and the
model estimates of the argon metastable dissociation rate
compared to electron impact dissociation all suggest that argon metastables are unimportant in C4F8 dissociation under
the conditions of the experiments reported here.
Appendix B: Role of negative ions
Negative ions can also conceivably play an important role
in C4F8 dissociation. Low energy electrons are known to
readily attach to C4F8 to form an excited C4F⫺
8 followed by
either autodetachment to reform C4F8 or dissociation into a
negative ion and a radical, as summarized in the following
equations:
electron attachment:
autodetachment:
e⫹C4F8→C4F⫺
8,
C4F⫺
8 →C4F8*⫹e,
dissociative attachment:
⫹F⫺, . . . .
共B1兲
共B2兲
⫺
C4F⫺
8 →C3F5⫹CF3 , C4F7
共B3兲
Literature values for total and dissociative electron attachment cross sections and measured EEPFs were used to calculate the attachment rate coefficients by integration of the
cross sections over the EEPFs.14 Table IV is a comparison of
the dissociative attachment rate coefficient to the total dissociation rate coefficient, indicating that neglecting dissociative
attachment is justified.
Recombination between positive ions and C4F⫺
8 is another
potential loss mechanism for C4F8. Literature values for the
1047
Radtke, Coburn, and Graves: C4F8 dissociation in an inductively coupled plasma
5
TABLE IV. Electron impact dissociation rate.
K diss,tot(⫻108 cm3/s)
k att(⫻108 cm3/s)
k att,diss(⫻108 cm3/s)
1.06
0.46
0.37
0.32
0.013
0.015
1 mTorr
10mTorr
⫺5
lifetime of C4F⫺
and 5⫻10⫺4 s; therefore
8 are between 10
the rate coefficient for spontaneous autodetachment (k det) is
between 105 and 2⫻103 s⫺1. If the rate of attachment and
autodetachment were nearly equal, the ratio of the negative
ion to the parent molecule density can be written as
C4F⫺
8
C4F8
⬇
k attachn e
.
k det
共B4兲
Under the conditions of the experiment, the ratio of C4F⫺
8 to
C4F8 was calculated to be between 0.000 62 and 0.032. Using
the ion–ion neutralization rate constant for chlorine (5
⫻10⫺8 cm3/s), 30 the upper bound for the total ion-ion neutralization rate was approximated at 1012 s⫺1. This is much
lower than the total electron impact dissociation rate (4.8
⫻1016⫻1017 s⫺1), indicating that positive ion/C4F⫺
8 recombination is not important compared to electron impact dissociation.
1
L. Morgan, Kinema Research and Software, L.L.C.
H. Sugai and H. Toyoda, J. Vac. Sci. Technol. A 10, 1193 共1992兲.
3
H. Toyoda, M. Ito, and H. Sugai, Jpn. J. Appl. Phys., Part 1 36, 3770
共1997兲.
4
C. Q. Jiao, A. Garscadden, and P. D. Haaland, in Gaseous Dielectrics
VIII, edited by L. G. Christophorou and J. K. Olthoth 共Kluwer Academic/
Plenum, New York, 1998兲, p. 57.
2
JVST A - Vacuum, Surfaces, and Films
1047
C. Q. Jiao, A. Garscadden, and P. D. Haaland, Chem. Phys. Lett. 297, 121
共1998兲.
6
M. M. Bibby and G. Carter, Trans. Faraday Soc. 59, 2455 共1963兲.
7
M. V. Kurepa, Third Cz. Conference on Electronics and Vacuum Physics
Transactions, 1965 共unpublished兲, p. 107.
8
J. A. Beran and L. Kevan, J. Phys. Chem. 73, 3866 共1969兲.
9
L. G. Christophorou and J. K. Olthoth, J. Phys. Chem. Ref. Data 30, 449
共2001兲.
10
H. Singh, J. W. Coburn, and D. B. Graves, J. Vac. Sci. Technol. A 17,
2447 共1999兲.
11
H. Singh, J. W. Coburn, and D. B. Graves, J. Vac. Sci. Technol. A 18, 299
共2000兲.
12
H. Singh, J. W. Coburn, and D. B. Graves, J. Appl. Phys. 87, 4098 共2000兲.
13
M. J. Druyvesteyn, Z. Phys. 64, 781 共1930兲.
14
V. A. Godyak and V. I. Kolobov, Phys. Rev. Lett. 81, 3157 共1992兲.
15
E. Tonnis and D. B. Graves, J. Vac. Sci. Technol. A 20, 1787 共2002兲.
16
J. L. Cooper and J. C. Whitehead, J. Chem. Soc., Faraday Trans. 89, 1287
共1993兲.
17
M. Kiehlbauch and D. B. Graves, J. Appl. Phys. 91, 3539 共2002兲.
18
M. Ohring, The Material Science of Thin Films 共Academic, San Diego,
1992兲, pp. 57– 60.
19
I. B. Bernstein and T. Holstein, Phys. Rev. 94, 1475 共1954兲.
20
M. Kiehlbauch, U. C. Berkeley, 2000.
21
H. Hayashi et al., J. Vac. Sci. Technol. A 17, 2557 共1999兲.
22
D. Leonhardt et al., J. Appl. Phys. 83, 2971 共1998兲.
23
K. Hioki et al., J. Vac. Sci. Technol. A 18, 864 共2000兲.
24
F. Tochikubo et al., Jpn. J. Appl. Phys., Part 1 33, 4271 共1994兲.
25
T. Kimura and K. Ohe, Plasma Sources Sci. Technol. 8, 553 共1999兲.
26
A. A. Mityureva and V. V. Smirnov, J. Phys. B 27, 1869 共1994兲.
27
R. S. Schappe, M. B. Schulman, L. W. Anderson, and C. C. Lin, Phys.
Rev. A 50, 444 共1994兲.
28
J. H. Kolts and D. W. Setzer, J. Chem. Phys. 68, 4848 共1978兲.
29
J. E. Valazco, J. H. Kolts, and D. W. Setser, J. Chem. Phys. 69, 4357
共1978兲.
30
G. L. Rogoff, J. M. Kramer, and R. B. Piejak, IEEE Trans. Plasma Sci.
14, 103 共1986兲.