Optical and Langmuir probe diagnostics of an Argon plasma
in an RF reactive magnetron sputtering system
Shinsuke Mori1, Houssam Fakhouri2, Jerome Pulpytel2, Farzaneh Arefi-Khonsari2
1. Department of Chemical Engineering, Tokyo Institute of Technology, 152-8552 Tokyo, Japan
2. LGPPTS, Université Pierre et Marie Curie, ENSCP, 75231 Paris, France
Abstract: Plasma diagnostics of an argon RF magnetron reactive sputtering
system, used for the deposition of titanium oxide or titanium oxide doped with
nitrogen were performed using optical emission spectroscopy and Langmuir
probe systems. In the optical method, we have used a modified corona model to
estimate the electron temperature, which has been recently developed by Boffard
et al. [1] The influence of electron energy distribution function (EEDF) on the
estimation of electron temperature by the modified corona model is addressed.
Electron temperature estimated by the optical method assuming MaxwellianEEDF is much lower than that measured by the Langmuir probe system in the
experimental conditions tested. However, when non-Maxwellian EEDF
calculated by Boltzmann solver including electron-electron collisions was
applied to the modified corona model, the discrepancy between the optical
method and the Langmuir probe system was improved and the estimated electron
temperatures are almost identical with those of the Langmuir probe systems.
Keywords: Reactive Magnetron Sputtering, Langmuir Probe, Optical Emission
Spectroscopy, Corona Model, Argon plasma
1. Introduction
2. Experimental
Optical emission spectroscopy (OES) has been
most widely employed as a non-intrusive diagnostic
tool to characterize plasma alternative to Langmuir
probe system. In order to determine the electron
temperature by the OES method, one usually applies
the so-called line-ratio technique. The determination
of electron temperature in low-temperature plasma
by the OES method, however, is still unreliable and
needs to be developed. In this study, we have used a
modified corona model to estimate the electron
temperature, which has been recently developed by
Boffard et al. and adopted to an argon ICP system
showing good agreement with Langmuir probe
results [1]. This method was applied to a magnetron
discharge system in this study which allowed to
examine the agreement between the OES and
Langmuir probe results under a variety of plasma
conditions.
We used the SPT120-H model which is a Sputter
Deposition System (PLASMIONIQUE), comprised
of a MAGNION-02 magnetron sputtering gun, with
an appropriate pumping system. The RF power
generator delivered a maximum power of 300 W at a
frequency of 13.56 MHz. A metallic Ti target (50
mm diameter) having a purity of 99.95%, was
sputtered in a reactive gas atmosphere containing Ar,
O2 and N2. Different nitrogen to oxygen ratios were
used. The initial base pressure was between 3 to
7x10-6 Torr, while the total working pressure was
between 3 to 20 mTorr. The Langmuir probe system
is an RF compensated Smartprobe from Scientific
Systems. A detailed description of the Langmuir
probe system is explained elsewhere [2]. The target
to Langmuir probe distance was about 10 mm. The
radial position of the probe tip is 15 mm away from
the center of the target.
3. Langmuir probe results
Figures 1 and 2 show the experimental results of
the Langmuir probe measurements. Electron density
increases and electron temperature decreases with an
increase in a pressure, monotonously. When the N2
is added into the feed gas, electron temperature
decreases at higher pressures, although the influence
of O2 mixture on the electron temperature is
negligible. On the other hand, the influence of O2
mixture on the electron density is more significant as
compared with N2 admixtures. In general, the
poisoning effect on the sputtering target is more p
prominent in the case of O2 admixtures and the
electron energy loss due to the inelastic collisions is
more significant in the case of N2 admixtures
because
Electron density (1010 cm-3)
5
4. OES model
In order to estimate the electron temperature by
the OES data, we utilized modified corona model
developed by Boffard et al [1]. Here, we explain the
model briefly. In the simplest corona model, only
two processes are considered: the electron-impact
excitation from the ground-state species and the
spontaneous radiations from the excited species.
Then, the rate balance equation and emission
intensity Iij become as follows:
ne n0 k0 i = ni Σj Aij
4
(1)
Æ
Iij = hvij Aij ni = hvij Γij ne [n0 k0 i]
Æ
3
2
● : Pure-Ar: 20sccm
△ : O2/Ar = 2sccm/20sccm
▽ : N2/Ar = 2sccm/20sccm
1
0
0
5
10
15
20
Pressure (mTorr)
Figure 1. Electron number density measured by Langmuir
probe at a radial position of R = 15mm in a 200 W Ar plasma.
5
Electron temperature (eV)
because of the resonant vibrational excitations [3].
Therefore, it would be reasonable to consider that
the reduction in the electron density and electron
temperature may be mostly related to the poisoning
effect and the inelastic collisions, respectively.
4
2
● : Pure-Ar: 20sccm
△ : O2/Ar = 2sccm/20sccm
▽ : N2/Ar = 2sccm/20sccm
5
10
15
Æ
(1) If the apparent excitation cross sections are used
instead of direct excitation cross sections, the
radiative cascade from the higher-lying levels
can be considered.
(3) Electron impact excitations from the long-lived
lower levels have to be considered.
0
0
where ne is electron density, n0 is the number density
of the atoms in the ground level, ni is the number
density of atoms in the level-i, hvij is the energy gap
between levels i and j, k0 i is the electron impact rate
constants out of the ground level-0, Aij is the
Einstein coefficient for the i Æ j transition, Γij (= Aij
/ Σj Aij ) is the branching fraction. The corona model
can be more generalized after the proper
modifications [1]:
(2) In order to consider the radiation trapping due to
the reabsorption of line radiation by the lower
level, the effective branching fraction Γijeff (= Rij
Γij , where Rij is a reabsorption factor) should be
utilized instead of Γij.
3
1
(2)
20
Pressure (mTorr)
Figure 2. Electron temperature measured by Langmuir probe
at a radial position of R = 15mm in a 200 W Ar plasma.
After having considered the modifications listed
above (1-3), eq. (2) can be generalized as follows:
Iij = hvij Γijeff ne [Σl nl kl
app
i ]
Æ
(3)
Æ
=
I pq / v pq
∑ nk
∑ nk
Γijeff
l
eff
Γpq
l
app
l l →i
app
l l→ p
(4)
Two lines in Ar(3p54p Æ 3p54s) transition array (2px
Æ 1sy in paschen’s notation) are chosen for the line
intensity ratio and Γijeff can be simplified as unity for
these two lines [4]: 750.39 nm (2p1 Æ 1s2) and
811.53 nm (2p9 Æ 1s5). In this study, the model
assumes that the 2p1 and 2p9 levels were populated
by electron-impact excitation from the ground state
and from the 1s3 and 1s5 metastable levels.
The density of the Ar(3p54s) levels (1s3 and 1s5
levels) were estimated considering the reabsorption
of 3p54p to 3p54s emissions by the Ar(3p54s) levels
using the least square method developed in the paper
reported by Schulze et al. [5] When the common
upper level is chosen, the line intensity ratio is
simplified and determined by the escape factors γ.
I ij / vij
I ik / vik
=
Γijeff
Γikeff
=
γ ij Aij
γ ik Aik
11.83 eV
11.72 eV
11.62 eV
11.55 eV
0
5
10
15
20
Pressure (mTorr)
Figure 4. Number densities of Ar(3p54s) levels in a 200 W
Ar plasma derived from the OES branching fraction
method of Schulze et al. [5]. Key: 1s2 level (▽), 1s3 level
(X), 1s4 level (▲), 1s5 level (●).
100
10-1
3.0 eV
4.0 eV
5.0 eV
-2
10
10-3
2.0 eV
10-4
10-5
2p1(J=0)
2p2(J=1)
10-6
2p3(J=2)
2p4(J=1)
0
5
10
15
20
25
30
Electron energy (eV)
811.53 nm
852.14 nm
794.82 nm
840.82 nm
738.40 nm
706.72 nm
826.45 nm
727.29 nm
696.54 nm
2p9(J=3)
750.39 nm
109
(5)
Because the escape factor is a function of the lower
level density, we can estimate the latter by
comparing the experimental line intensity ratio with
the calculated one using eq (5). Schulze et al.
estimated the density of the lower levels, Ar(3p54s),
using 5 intensity ratios with the least square method.
Figure 3 shows the Ar lines utilized in this study.
13.48 eV
13.33 eV
13.30 eV
13.28 eV
13.08 eV
1010
EEDF (eV-3/2)
I ij / vij
Our calculation results are shown in Figure 4 and
seem to be reasonable as compared with other
experimental measurements [4,5]: the number
density of Ar(3p54s) levels are around 109 to 1010
1/cm3 and the density of 1s5 metastable is much
higher than that of 1s3 level and the densities of 1s2
and 1s4 are almost identical.
Number density (1/cm3)
where nl is the number density of atoms in the initial
level-l, kl iapp is the apparent electron impact rate
constants out of the initial level-l. Then the line
intensity ratio becomes as follows:
1s2(J=1)
1s3(J=0)
1s4(J=1)
1s5(J=2)
Figure 3. Partial energy level diagram for Ar(3p54pÆ 3p54s).
Line intensity ratios of 696.54nm: 826.45nm, 727.29nm:
826.45nm, 706.72nm: 840.82nm, 738.40nm: 840.82nm, and
794.82nm: 852.14nm are used for the estimation of Ar(3p54s)
levels and 750.39 nm: 811.53 nm is used for the corona model.
Figure 5. EEDF used in the calculation of rate constants for
the electron impact excitation of Ar.
Key: Maxwellian-EEDF ( … ), EEDF calculated including
electron-electron collisions (―), EEDF calculated excluding
electron-electron collisions (- - -).
Finally, we calculated the line intensity ratio
using eq. (4) and from the best fit with the
experimental line intensity ratio, the electron
temperature has been determined. In order to
evaluate the influence of electron energy distribution
function (EEDF) on the estimation of electron
temperature by the corona model, we utilized three
different EEDFs for the calculation of rate constants
kl iapp in eq. (4): Maxwellian-EEDF, EEDFcalculated by the Boltzmann solver (Bolsig+ [6,7])
excluding the electron-electron collisions, and
EEDF-calculated including the electron-electron
collisions. As shown in the Figure 5, when the
electron-electron collisions are considered in the
calculation of EEDF, the high energy electrons are
increased and the shape of EEDF becomes similar to
the Maxwellian-EEDF.
Æ
5. Comparison of Langmuir probe
results and those of OES method
Electron temperatures estimated by the modified
corona model are shown in Figure 6. For the
comparison, Langmuir probe results are also plotted
in this figure. Electron temperature estimated by the
modified corona model assuming Maxwellian-EEDF
is much lower than that measured by the Langmuir
probe system in the experimental conditions tested.
On the other hand, the modified corona model using
the non-Maxwellian EEDF calculated by the
Boltzmann
solver
without
electron-electron
collisions gives higher electron temperatures.
However, when non-Maxwellian EEDF calculated
by Boltzmann solver including electron-electron
collisions was applied to the modified corona model,
the estimated electron temperatures are almost
identical with those of the Langmuir probe systems.
6. Conclusions
Plasma diagnostics of an argon RF magnetron
reactive sputtering system, used for the deposition of
titanium oxide or titanium oxide doped with nitrogen
were performed using optical emission spectroscopy
and Langmuir probe systems. Electron temperatures
are 2.2-4.5 eV and electron densities are 1.6-4.5 x
1010 cm-3 by the Lanmuir probe measurements.
Electron temperature estimated by the optical
method assuming Maxwellian-EEDF is much lower
than that measured by the Langmuir probe system in
the experimental conditions tested. On the other
hand, the modified corona model using the nonMaxwellian EEDF calculated by the Boltzmann
solver without electron-electron collisions gives
higher electron temperatures. However, when nonMaxwellian EEDF calculated by Boltzmann solver
including electron-electron collisions was applied to
the modified corona model, the estimated electron
temperatures are almost identical with those of the
Langmuir probe systems.
5
Electron temperature (eV)
References
4
[1] J. B. Boffard et al, Plasma Sources Sci. Technol.
19, 065001 (2010).
3
[2] J. Pulpytel, F. Arefi-Khonsari and W. Morscheidt,
J. Phys. D: Appl. Phys. 38, 1390-1395 (2005).
2
[3] J. Pulpytel, W. Morscheidt and F. Arefi-Khonsari,
J. Appl. Phys. 101, 073308 (2007).
● : Langmuir probe (R = 15 mm)
△ : OES (calculated-EEDF w/o e-e collisions)
▽ : OES (calculated-EEDF with e-e collisions)
× : OES (Maxwellian-EEDF)
1
0
0
5
10
15
20
Pressure (mTorr)
Figure 6. Comparison of electron temperatures estimated
by different methods in a 200 W Ar plasma.
[4] J. B. Boffard et al, Plasma Sources Sci. Technol.
18, 035017 (2009).
[5] M. Schulze et al, J. Phys. D: Appl. Phys. 41,
065206 (2008).
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