22nd International Symposium on Plasma Chemistry
July 5-10, 2015; Antwerp, Belgium
Measurement of the electron-impact excitation rate coefficients from argon 1s
states to 3p states
Z.-W. Cheng1, X.-M. Zhu2, N. Sadeghi3, F.-X. Liu1 and Y.-K. Pu1
1
2
Department of Engineering Physics, Tsinghua University, 1000084 Beijing, P.R. China
Institute for Plasma and Atomic Physics, Ruhr-University Bochum, 44780 Bochum, Germany
3
LIPhy, Université Grenoble Alpes & CNRS, UMR 5588, 38041 Grenoble, France
Abstract: The rate coefficients for the electron-impact excitation from argon 1s to 3p
states are determined in the electron temperature (T e ) range of 0.8 to 1.2 eV, in the
afterglow of a capacitive argon discharge by using the temporal behavior of different state
densities. The measured parameters include the densities of the 3p states (by optical
emission), the densities of the four argon 1s states (by diode laser absorption) and T e (by a
Langmuir probe and a line-ratio technique). Among the 24 rate coefficients obtained in this
work, the results for excitation from the two resonance states (1s 2 and 1s 4 ) are reported
here for the first time. As for the excitation from the two metastable states (1s 3 and 1s 5 ),
the measured rate coefficients are compared with the available values from the distorted
wave method and the electron beam experiment.
Keywords: electron-impact rate coefficient, argon 1s states, 3p states, afterglow
1. Introduction
An accurate set of collisional cross sections and rate
coefficients of the main kinetic process in plasma
discharges are essential for their modelling, simulation
and diagnostics. In particular for a low temperature argoncontaining plasma, some population models for argon 3p
states combined with the measured optical emission from
these states are proposed to determine the electron
temperature (T e ) [1], the electron density (n e ) [2] and the
metastable density (n m ) [3]. In these models, the electronimpact excitation from argon 1s states is an important
production process for 3p states due to the small energy
gap and the large rate coefficients compared with the
direct excitation from the ground state [4, 5].
In this work, the rate coefficients for the transitions
1s 3 →3p 1-4 , 1s 5 →3p 1-8, 10 , 1s 2 →3p 1-4 and 1s 4 →3p 1-5, 7, 8
(relative to that of 1s 5 →3p 9 ) are determined with a
population model for Ar(3p) in the afterglow of an rf
pulsed capacitive discharge, provided the following
parameters are measured: the 3p state density, the 1s state
density and T e . This technique is very similar to that used
in our previous work [6, 7], where the rate coefficients for
the electron-impact excitation from argon 1s states to 2p
states were obtained.
2. Experimental setup
The present work utilizes the same apparatus as that in
[6], thus only a brief description of the experimental setup is given here. The capacitive discharge is formed
between two aluminum electrodes (diameters of 377 mm
and 322 mm, respectively) with a gap distance of 50 mm.
The discharges are produced by rf power at 13.56 MHz
and 60 MHz, respectively. The rf power is pulsed with a
duty cycle of 15% and a repetition frequency of 3 kHz.
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The gas pressure is monitored by a capacitance diaphragm
gauge (MKS Baratron 622A).
The main production processes for Ar(3p) in a low
pressure argon-containing discharge is the excitation from
ground and 1s state. Performing the experiment in the
afterglow allows us to neglect the ground excitation.
When attempting to determine the metastable excitation
rate coefficients in the afterglow, one needs to reduce the
contribution to the emission intensity from the resonance
excitation as much as possible. In addition, the separate
contribution from each metastable state needs to be
determined. To reduce the contribution from the
resonance excitation, the argon ground state density and
power of the discharge should be as low as possible. On
the other hand, in order to separate out the contribution
from the two metastable states, two discharges with
different value of n 1s3 /n 1s5 are conducted. The discharge
with higher value of n 1s3 /n 1s5 can be realized by mixing
Kr, which has a much stronger quenching effect on 1s 5
than 1s 3 . Therefore, an Ar (20 mTorr) discharge with a
peak power of 15 W (13.56 MHz) and an Ar (20 mTorr) /
Kr (10 mTorr) mixture discharge with a peak power of 60
W (13.56 MHz) are used to measure the metastable
excitation rate coefficients.
When attempting to determine the resonance excitation
rate coefficients from the measured parameters in the
afterglow, one needs to arrange the discharge parameters
so that the values of n 1s2 /n 1s5 and n 1s4 /n 1s5 are as high as
possible. For this purpose, a high argon ground state
density can be used to increase the density of the two
resonance states through radiation trapping. On the other
hand, the density of the metastable states can be reduced
by the quenching effect of O 2 . Therefore, an Ar (60
mTorr) / O 2 (1 mTorr) mixture discharge with a peak
1
power of 60 W (60 MHz) is used for the determination of
the resonance excitation rate coefficients.
A diode laser system used to measure the time-resolved
density of the four 1s state [7]. The monochromator
system described in [6] is used to measure the timeresolved emission intensity of the 3p states from 0 to 40
µs after the rf power is turned off. A single Langmuir
probe SPL2000 (Plasmart, Inc.) is applied to obtain the
temporally resolved electron temperature in the afterglow.
3. Method
Similar as the case of 2p state discussed in [7], the
following assumptions can be made in the afterglow of a
low pressure argon-containing discharge:
• In the afterglow, 3p state can be considered quasistationary due to that the characteristic decay time of
3p state is much longer than their lifetime;
• The contribution from the ground state excitation is
negligible due to the low T e (≤ 1 eV).
Therefore, the rate equation for a 3p state is
5
∑n n
e 1s j
j =2
Q1s j →3 pi = A3 pi n3 pi , i = 1 − 10 .
(1)
Qxleff→−3repi ≡ Qxleff→3 pi / Q1s5 →3 p9，xl =
1s, m , r , (7)
as a number representative of the rate coefficient for the
xl → 3p i excitation, relative to that for 1s 5 →3p 9 .
Figure 1 shows Q1effs →−3rep and Q1effs →−3rep obtained from
6
4
equation (3) with the measured parameters (emission line
ratios and T e ) in the pure Ar and Ar/Kr mixing
discharges.
Even
though
Q1effs →−3repi represents
the
contribution from all four 1s states, the excitation from
the two metastable states is dominant due to the low
resonance state density [6]. This is also confirmed by the
eff − re
eff − re
obtained Q1s →3 p4 and Q1s →3 p6 , which is nearly a constant
with T e (as well as time in the afterglow). In fact, if the
resonance excitation is important, Q1effs →−3rep and Q1effs →−3rep will
4
6
decrease fast with time due to the fast decay of n 1s2 /n 1s5
and n 1s4 /n 1s5 in the afterglow. Under this condition, the
term represents the resonance state excitation in equation
(4) can be neglected, so equation (4) becomes
n1s Q1s3 →3 pi Q1s5 →3 pi
.
(8)
+
Q1effs→−3repi =
Qmeff→−3repi ≡ 3
n1s5 Q1s5 →3 p9 Q1s5 →3 p9
Here n3p is the density of 3p i state, n e is the electron
i
density,
n1s j is the density of 1s j state, A3 p is the sum of
i
the Einstein coefficient for the spontaneous transition
from 3p i states to all lower levels, including 1s, 2s and 3d
groups. Q1s →3 p is the apparent rate coefficient of the
j
i
electron-impact excitation from 1s j to 3p i state.
Combined with the measured line ratio, it obtains:
5
n1s j Q1s j →3 pi
∑n
j =2
1s5
Q1s5 →3 p9
=
A3 pi A3 p9 →1s5 I 3 pi →1s j
.
(2)
A3 p9 A3 pi →1s j I 3 p9 →1s5
Here 3p 9 is selected to be a “reference state”.
Equation (2) can be rewritten as
Q1effs→3 pi A3 pi A3 p9 →1s5 I 3 pi →1s j .
=
Q1s5 →3 p9 A3 p9 A3 pi →1s j I 3 p9 →1s5
(3)
Here Q1effs→3 p is defined as the effective rate coefficient of
i
the excitation taking account of the contribution from all
four 1s states
5
Q1effs→3 pi ≡ ∑
n1s j
j = 2 n1s5
Q1s j →3 pi ≡ Qreff→3 pi + Qmeff→3 pi .
(4)
Here Qmeff→3 p is defined as the effective rate coefficient of
i
the metastable excitation, which represents the
contribution from both 1s 3 and 1s 5
Qmeff→3 p i ≡ n1s3 / n1s5 ⋅ Q1s3 →3 pi + Q1s5 →3 pi ,
eff
r →3 pi
and Q
(5)
is that represents the contribution from both
1s 2 and 1s 4
(6)
Qreff→3 pi ≡ n1s2 / n1s5 ⋅ Q1s2 →3 pi + n1s4 / n1s5 ⋅ Q1s4 →3 pi .
Since line ratios are used to obtain the relative values of
the rate coefficients (equation (2)), so we define
2
Fig. 1. The relative effective rate coefficients of the 1s
excitation: (a) 3p 4 , (b) 3p 6 . Under the discharge
condition: Ar (20 mTorr), 15 W peak power (red circles)
and Ar (20 mTorr) + Kr (10 mTorr), 60 W peak power
(black squares).
This is the equation to be used to obtain the rate
coefficients for the metastable excitation. Notice that the
right hand side of the equation contains the contribution
of excitation from both 1s 3 and 1s 5 . In these two
discharges, the value of n 1s3 /n 1s5 is about 0.15 (pure Ar
discharge) and 0.25 (Ar/Kr discharge), respectively [6].
As shown in figure 1(a), Qmeff→−3rep increases from about
4
0.15 (pure Ar discharge) to about 0.23 (Ar/Kr discharge)
due to the increase of n 1s3 /n 1s5 . So the contribution from
1s 3 to 3p 4 is important in these two discharges and the
rate coefficients from 1s 3 and 1s 5 can be obtained
simultaneously by solving equation (8) with these two
different values of n 1s3 /n 1s5 . In figure 1(b), however, it
can be seen that Qmeff→−3rep in these two discharges have
6
almost the same value. It indicates that, for 3p 6 , the
contribution from 1s 3 is much smaller than that from 1s 5
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and can be neglected. As a consequence, Q1effs →− re3 p cannot be
3
6
obtained due to its small contribution (< 5%).
On the other hand, as discussed in section 2, an Ar / O 2
mixture discharge is used to obtain the resonance
excitation rate coefficients. Due to the O 2 quenching
effect on the metastable states and radiation trapping,
during the first 20 µs in the afterglow, the values of
n 1s4 /n 1s5 and n 1s2 /n 1s5 can be as large as 0.40 and 0.16,
respectively [7]. Under this condition, for the 3p states
with large resonance excitation rate coefficients, the
contribution from the resonance excitation is comparable
to that from the metastables. With the obtained metastable
excitation rate coefficients and the measured 1s state
density, the rate coefficients for the resonance excitation
can be obtained from equations (3) and (4),
Qreff→−3 repi ≡
=
n1s2 Q1s2 →3 pi
n1s5 Q1s5 →3 p9
+
A3 pi A3 p9 →1s5 I 3 pi →1s j
A3 p9 A3 pi →1s j I 3 p9 →1s5
n1s4 Q1s4 →3 pi
.
n1s5 Q1s5 →3 p9
(9)
3
slower than n 1s2 /n 1s5 , but faster than n 1s4 /n 1s5 . It indicates
that for 3p 3 , the two terms in equation (9) are comparable
to each other. In this case, by assuming Q1s →3 p / Q1s →3 p
2
− Q=
，i 1=
− 10, j 2 − 5
Figure 2 shows the relative rate coefficients Q1effs→−3rep ,
3,7
eff − re
Qmeff→−3rep3,7 and Qr→3 p3,7 obtained by equations (3), (8) and (9),
respectively. The decrease in Q
7
controlled by both n 1s2 /n 1s5 and n 1s4 /n 1s5 . Fortunately, the
values of decay rate of n 1s2 /n 1s5 and n 1s4 /n 1s5 are very
different from each other. This allows us to conclude that
the second term in equation (6) is dominant since both
Qreff→−3pre7 and n 1s4 /n 1s5 have similar decay rate. For this
reason, the current experimental technique cannot be used
to obtain the rate coefficient for the transition 1s 2 →3p 7
due to its small contribution (< 5%) in the afterglow.
However, figure 2(b) shows that Qreff→−3 rep decreases
3
5
9
and Q1s →3 p / Q1s →3 p as two unknown constants, the
4
3
5
9
eff − re
m →3 p i
eff − re
1s →3 p3,7
the excitation from the four 1s states have almost the
same T e dependence, which is caused by the close values
of the threshold energy for the excitation from each 1s to
3p states [5]. Therefore, the time variation in Qreff→−3pre is
(black circles) with
time is mainly due to the rapid decrease of Qreff→−3 rep (blue
3,7
stars), since Qmeff→−3rep (red squares) remains more or less a
3,7
constant in the afterglow.
values of Q1s →3 p / Q1s →3 p and Q1s →3 p / Q1s →3 p can be
obtained by fitting equation (9) with the measured values
of n 1s2 /n 1s5 , n 1s4 /n 1s5 and Qreff→−2 rep .
2
3
5
9
4
3
5
9
3
4. Results And Discussion
The rate coefficients (relative to that of 1s 5 →3p 9 ) for
the transitions from the four 1s states to 3p 1 , 3p 2 , 3p 3 and
3p 4 states are shown in figures 3-6. Meanwhile, the rate
coefficients for the excitation from 1s 3 and 1s 5 obtained
from the cross sections measured by the electron beam
experiment [5] and those calculated by the distorted wave
method [8] are also shown in figures 3-6, for comparison
purposes.
Fig. 2. The relative effective rate coefficients of the 1s
excitation (black circles), the metastable excitation (red
squares) and the resonance excitation (blue stars) to 3p
states: (a) 3p7, (b) 3p3.
Under the condition:
Ar (20 mTorr) +O 2 (1 mTorr), 60 W peak power.
Figure 2(a) shows that Qreff→−3 rep decreases with almost the
7
same rate as n 1s4 /n 1s5 , which indicates that, for 3p 7 , the
first term in equation (9) is much smaller than the second
term and can be neglected. In fact, equation (9) indicates
that Qreff→−3 rep is a function of four quantities: n 1s2 /n 1s5 ,
Fig. 3.
The rate coefficients (relative to that of
1s5 → 3p9) from the four 1s states to 3p1.
7
n 1s4 /n 1s5 , Q1s →3 p / Q1s →3 p and Q1s →3 p / Q1s →3 p . Among
2
7
5
9
4
7
5
9
them,
the
Q1s4 →3 p7 / Q1s5 →3 p9
and
Q1s2 →3 p7 / Q1s5 →3 p9
can be considered as a constant with
values
of
time. This is due to the fact that the rate coefficients for
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As shown in figures 3-6, the rate coefficients (relative
to Q 1s5-3p9 ) for 16 excitation processes are presented. We
can put these rate coefficients into three categories: (1)
eight rate coefficients are reported for the first time (such
as 1s 2 → 3p 2 in figure 4(d)); (2) five of them were
previously reported with both measured values (electron
3
beam [5]) and calculated ones (distorted wave method
[8]), such as 1s 5 → 3p 2 in figure 4(a); (3) the last three
were previously reported with the calculated data only.
Fig. 4.
The rate coefficients (relative to that of
1s5 → 3p9) from the four 1s states to 3p2.
For the five rate coefficients in category (2), four of
them obtained in this work agree fairly well with those
measured in the electron beam experiment [5]. They
include the transitions 1s 5 → 3p 1 , 3p 2 (figures 3(a), 4(a))
and 1s 3 → 3p 2 , 3p 4 (figures 4(c) and 6(c)). For the
transition 1s 3 → 3p 1 (figures 3(c)), our rate coefficient is
larger than that measured in the electron beam experiment
by a factor of 4.
For the rate coefficients in category (3) (1s 5 → 3p 3 , 3p 4
and 1s 3 → 3p 3 in figures 5(a), 5(c) and 6(a),
respectively), our measured rate coefficients are always
larger than the calculated ones [8]. For the transition 1s 5
→3p 4 (figures 6(a)), the difference is as large as one
order of magnitude.
5. Conclusions
The electron-impact excitation rate coefficients from
the argon 1s to 3p states are measured in the afterglow of
an rf pulsed capacitive discharge, in the T e range of 0.8 to
1.2 eV. Three discharges with different distribution of 1s
state densities are conducted to obtain 24 rate coefficients.
Thirteen of them are those for the metastable state
excitation. These rate coefficients are compared with
those measured in the electron beam experiment and
calculated by the distorted wave method. For the
resonance excitation, the eleven rate coefficients obtained
in this work are reported for the first time.
6. Acknowledgements
The authors are grateful to Dr John Boffard and
Dr Tsanko Vaskov Tsankov for their helpful discussion.
The work is supported in part by the National Natural
Science Foundation of China under Grant No. 10935006
and the Advanced Micro-Fabrication Equipment Inc.
Fig. 5. The rate coefficients (relative to that of 1s 5 →
3p 9 ) from the four 1s states to 3p 3 .
7. References
[1] J.B. Boffard, R.O. Jung, C.C. Lin, L.E. Aneskavich
and A.E. Wendt. J. Phys. D: Appl. Phys., 45,
045201 (2012)
[2] X.M. Zhu and Y.-K. Pu. J. Phys. D: Appl. Phys.,
40, 2533-2538 (2007)
[3] N. Fox-Lyon, A.J. Knoll, J. Franek, V. Demidov,
V. Godyak, M. Koepke and G.S. Oehrlein. J. Phys.
D: Appl. Phys., 46, 485202 (2013)
[4] T. Weber, J.B. Boffard and C.C. Lin. Phys. Rev.
A, 68, 032719 (2003)
[5] R.O. Jung, J.B. Boffard, L.W. Anderson and
C.C. Lin. Phys. Rev. A, 75, 052707 (2007)
[6] Z.W. Cheng, X.M. Zhu, F.X. Liu and Y.-K. Pu.
J. Phys D: Appl Phys., 47, 275203 (2014)
[7] Z.W. Cheng, X.M. Zhu, F.X. Liu and Y.-K. Pu.
Plasma Sources Sci. Technol., accepted (2015)
[8] L. Sharma, R. Srivastava and A.D. Stauffer. Phys.
Rev. A, 76, 024701 (2007)
Fig. 6. The rate coefficients (relative to that of 1s 5 →
3p 9 ) from the four 1s states to 3p 4 .
4
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