An analysis on transmission microwave frequency spectrum of cut-off probeD. W. Kim, S. J. You, B. K. Na, J. H. Kim, and H. Y. Chang Citation: Appl. Phys. Lett. 99, 131502 (2011); doi: 10.1063/1.3634022 View online: http://dx.doi.org/10.1063/1.3634022 View Table of Contents: http://apl.aip.org/resource/1/APPLAB/v99/i13 Published by the American Institute of Physics. Related ArticlesTechniques for the measurement of disruption halo currents in the National Spherical Torus Experiment Rev. Sci. Instrum. 82, 103502 (2011) Charge resolved electrostatic diagnostic of colliding copper laser plasma plumes Phys. Plasmas 18, 103104 (2011) Electron density measurement of inductively coupled plasmas by terahertz time-domain spectroscopy (THz-TDS) J. Appl. Phys. 110, 073303 (2011) A synchronized emissive probe for time-resolved plasma potential measurements of pulsed discharges Rev. Sci. Instrum. 82, 093505 (2011) Electrical time resolved metrology of dust particles growing in low pressure cold plasmas Phys. Plasmas 18, 093701 (2011) Additional information on Appl. Phys. Lett.Journal Homepage: http://apl.aip.org/ Journal Information: http://apl.aip.org/about/about_the_journal Top downloads: http://apl.aip.org/features/most_downloaded Information for Authors: http://apl.aip.org/authors
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An analysis on transmission microwave frequency spectrum of cut-off probe
D. W. Kim,1 S. J. You,2,a) B. K. Na,1 J. H. Kim,2 and H. Y. Chang1
1Department of Physics, Korea Advanced Institute of Science and Technology, Daejeon 305-701, Korea2Center for Vacuum Technology, Korea Research Institute of Standards and Science, Daejeon 305-306, Korea
(Received 30 June 2011; accepted 16 August 2011; published online 27 September 2011)
We investigated the formation mechanism of transmission microwave frequency (TMF) spectrum of
cut-off probe using a simple circuit model to elucidate the physics behind the TMF spectrum. The
result showed that the overall shape of the TMF spectrum of cut-off probe (N – shape spectrum) is
well reproduced with our proposed circuit model and can be understood as the combined result of
two different resonances caused by the elements between two probe tips (a sheath, a plasma, and a
vacuum which is filled by the plasma). Furthermore, based on this simple modeling, a more precise
method to find the plasma frequency by taking account with the e-n collision frequency and the
pressure limitation of the cut-off probe application is established. VC 2011 American Institute ofPhysics. [doi:10.1063/1.3634022]
A number of diagnostic methods which is available
even in complex plasma condition have been developed,
such as oscillation probe, absorption probe, impedance
probe, and cut-off probe.1–4 Among these diagnostic tools,
the cut-off probe using the physical phenomenon of cut-off
which is known to be reflected in the transmission micro-
wave frequency (TMF) spectrum is believed to be one of the
most promising diagnostic tool. The cut-off probe has many
advantages as following: The probe system is very simple
and robust. The calculation of electron density (ne) from the
measured plasma frequency (xpe) is not complicated
ðne ¼ x2pe�0me=e2Þ which is one of the simplest relation of
the plasma physics with less assumption.5 The theoretical
error bar is known to be small.6 In spite of these advantages
and wide applications of the probe, there is a little under-
standing about the TMF spectrum used in the determination
of the cut-off frequency. This TMF spectrum of the cut-off
probe corresponds to the IV-curve of Langmuir probe, dis-
closing the detail physics for the formation of the TMF spec-
trum is very important to optimize the cut-off probe.
In this letter, to elucidate the physics behind the TMF
spectrum of cut-off probe, we investigated the formation
mechanism for the TMF spectrum of cut-off probe using a
simple circuit model and an E/M wave simulation (CST
Microwave Studio). The results showed that the overall
shape of the TMF spectrum of cut-off probe (N – shape spec-trum) is well reproduced with the proposed circuit model
and can be understood as the combined result of two differ-
ent resonances caused by the elements between two probe
tips (a sheath, a plasma, and a vacuum which is filled by the
plasma). Furthermore, based on this simple modeling, a
more precise method to find the plasma frequency by taking
account with the e-n collision frequency and the pressure
limitation of the cut-off probe application were established.
In order to understand the physics on the TMF spectrum
of cut-off probe, two complementary simulation models
were used: One is a commercially available E/M wave simu-
lation which is direct numerical solver for the Maxwell equa-
tions for given boundary conditions.7–9 The other is a circuit
simulation using lumped circuit elements that we proposed.
The two simulations help our analysis for the cut-off probe
in a complementary way. The former simulation is a com-
plete solver of Maxwell equation in 3-dimensional space at
the given boundary conditions. This simulation is known to
be very accurate not only having a good agreement with
experiment but also having no frequency limitation for the
application. However, sometimes it is not suitable for the
speculation of the underlying physics because the simulation
includes lots of physical considerations and is too compli-
cated. The later simulation is very simple simulation which
cannot capture lots of physical considerations (e.g., wave
radiation, interference, diffraction, and cavity resonance) and
can apply in the limited range of frequency (low frequency),
but is good for the speculation of the underlying physics.
Kwon et al. reported that a sheath path between two
probe tips is insignificant to form the TMF spectrum.6,10
Therefore, we can model the cut-off probe as the interaction
between separated two cylindrical probe tips immersed in
the plasma medium.3,9,11
When we assume that the plasma is uniformly distrib-
uted in the presence of background gas that is driven by a
small amplitude of bulk plasma electric field of which wave-
length (k) is much larger than the plasma size (Ls), k� Ls,
most of the field associated with the system are confined to
the vicinity of the system.12 In this condition, elements near
cut-off antennas consume most of the power, thus the circuit
simulation to describe a localized plasma system around cut-
off antennas is possible. The plasma (bulk) can be treated as
an assemble of lumped elements having an admittance
Yp¼ ixC0þ 1/(ixLpþRp), where Lp is the inductance of the
bulk plasma ðx�2pe C�1
0 Þ, Rp is the resistance of the bulk
plasma (mmLp), and C0 is the vacuum capacitance (�0A=d for
the case of the slab geometry of bulk plasma).11 The sheath
connected to the bulk plasma in series can be also treated as
capacitor (Cs) in the simulation, because a conduction cur-
rent is negligible at high frequency.11 Therefore, the cut-off
probe can be modeled as shown in Figure 1. For more reality
in the calculation, we used two cylindrical capacitancea)Electronic mail: [email protected].
0003-6951/2011/99(13)/131502/3/$30.00 VC 2011 American Institute of Physics99, 131502-1
APPLIED PHYSICS LETTERS 99, 131502 (2011)
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models rather than the slab geometry model: one is a capaci-
tance model of two parallel transmission lines for the bulk
capacitor C0 ¼ p�0h=ln d�ðrþsÞrþs and the other capacitance
model of cylindrical coaxial line for the sheath capacitor
Cs ¼ 2p�0h=ln rþsr (where d is a gap distance between two
probe (antenna) tips, 2.16 mm, s is a fixed sheath width
(5�Debye length at ne¼ 2� 1010 cm�3 and Te¼ 2 eV) for
simplicity, 0.3719 mm, h is a length of the probe tip, 5 mm,
and r is radius of tip, 0.26 mm).13 The calculation of the
TMF spectrum of the circuit simulation was performed by
calculating the voltage measured on the network analyzer
ð ~Vd Þ of which input impedance is 50 X. The total impedance
of the cut-off probe system including the plasma and sheaths
is expressed as Ztot¼ 1/Ypþ 2/jxCs, and the TMF spectrum
of S21 is calculated as S21 ¼ 10log~Vd~Vr¼ 10log 50
50þZtotdB
� �
where ~Vd and ~Vr are voltages of detecting and radiating
antenna, respectively.
Figure 2 presents the results of the TMF spectrum calcu-
lated from the proposed circuit model, together with the
results from the E/M wave simulation which has been known
for good agreement with experimental result.7 As shown in
Figures 2(a) and 2(b), the circuit simulation can reproduce
not only the overall shape of characteristic TMF spectrum, N– shape spectrum having two extreme values around the cut-
off frequency, but also the evolution characteristics for cut-
off frequency point and its characteristics (width, depth)
with plasma parameters (electron density (Figure 2(a)) and
gas pressure (Figure 2(b))) except for the some of spike-like
peaks above the cut-off frequency (fr(xr/2p) � 1.27 GHz for
the cases considered in Figure 2(b)), which will comment on
later. It is interesting that although the circuit approximation
is not normally valid for the high frequency range above the
cut-off frequency, the overall shape of the TMF spectrum is well
reproduced in the circuit simulation over the frequency range.
By virtue of this circuit simulation, we can analyze the
extreme values (maximum and minimum values) of the S21
with familiar concepts of circuit. As shown in Figure 3, there
are two zero crossing points in phase spectrum (/) and these
two points coincide with these frequencies for two extreme
values in the TMF spectrum, respectively, these two extreme
values can be understood as resonances in circuit system.
Through the analysis of impedance for each elements at the
condition of resonances, it is readily shown that the cut-off
frequency point (the frequency point of minimum peak in the
TMF spectrum (S21)) is the frequency point of parallel reso-
nance mainly caused by inductor (Lp) of plasma and capacitor
(C0) of vacuum where plasma is therein. The frequency point
of maximum peak in the TMF spectrum (S21) is the series res-
onance in the circuit simulation mainly caused by inductor
(Lp) of the plasma and capacitor (Cs) of sheath. When the par-
allel resonance condition of the system (condition for cut-off)
is satisfied, the total impedance of the cut-off probe system
(Ztot in Figure 1) becomes maximum, so that most of voltage
applied from network analyzer ð ~Vr Þ is dropped between the
probe system (Ztot). This is the reason why there is minimum
value of the TMF spectrum (S21) at the cut-off frequency
point. On the contrary, when the series resonance condition
of the plasma (condition for peak of A (0.834 GHz) in
FIG. 1. (Color online) An equivalent circuit model of cut-off probe system.
FIG. 2. (Color online) Results of the E/M wave simulation and the circuit
model for TMF spectrum with various conditions: (a) different plasma den-
sity at p¼ 200 mTorr and Te¼ 2 eV, (b) different gas pressure at
ne¼ 2� 1010 cm�3 and Te¼ 2 eV.
FIG. 3. (Color online) Circuit simulation results of TMF and phase spec-
trum at the condition of ne¼ 2� 1010 cm�3, p¼ 200 mTorr, and Te¼ 2 eV.
131502-2 Kim et al. Appl. Phys. Lett. 99, 131502 (2011)
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Figure 3(a)) is satisfied, the total impedance of the cut-off
probe system (Ztot) including the sheath and plasma becomes
minimum, so that there is little voltage drop at the probe sys-
tem. This is the reason why there is maximum value of the
TMF spectrum (S21) at the frequency point A.
A interesting finding in our results is that the plasma fre-
quency xpe does not coincide with the resonance frequency
(cut-off frequency, xr) of minimum peak in the S21 as shown
in Figure 4. When the gas pressure is low and the condition
mm/xpe< 0.9 is satisfied, the xr is a good approximation of
xpe with error bar less than 10%. At the low pressure and
high density plasma where most of semiconductor process-
ing were performed and the condition mm/xpe< 0.1 is satis-
fied, especially, one can measure the electron density with
small error (< 0.52%) by choosing a frequency of minimum
peak in the S21 xr as a plasma frequency (xpe). However, the
gas pressure increases and approaching mm/xpe value to 1,
the discrepancy between xr and xpe becomes huge and the
xr is not a good approximation for xpe anymore. Therefore,
we can conclude that the exact plasma frequency value xpe
can be obtained from the TMF spectrum (S21) by using the
relation of Figure 4 taking account with the e-n collision fre-
quency, instead of simply choosing xr as xpe.
In addition to them, the theoretical limitation of the cut-
off probe for gas pressure can be formulated by using the con-
dition that the resonance peak disappears in the TMF spec-
trum (xr� 0) in Figure 4. The resonance associated with xr
disappears in Figure 4, when the mm/xpe is larger than 1.
Therefore, we can conclude that the cut-off probe is applicable
in the regime where the condition mm/xpe <� 1 is satisfied.
This result is well reflected in the result of both E/M wave and
circuit simulation as shown in Figure 2(b). The resonance
peak representing the cut-off point of which electron density
is 2� 1010 cm�3 disappears completely in Figure 2(b), when
the gas pressure is �3.5 Torr, because of mm/xpe� 7.95� 109/
7.96� 109� 1. Furthermore in the measurement of high pres-
sure discharge like an atmospheric discharge, only the high
density plasma of which plasma frequency is higher that the
e-n collision frequency is applicable for the cut-off probe
measurement, ne >� 1� 1015 cm�3 for atmospheric dis-
charge (P¼ 760 Torr and Te¼ 2 eV).4,7,14,15
Up to now, we have investigated the overall shape of the
TMF spectrum by considering the origin of the extreme val-
ues and analyzed the overall N – shape of the TMF spectrum.
However, there are still unrevealed spike-like peaks above
the cut-off frequency, which is known to normally appear in
a small plasma chamber condition.7,14 Because this wave
effect is beyond the scope of the circuit analysis in this letter,
the spike-like peaks in the TMF spectrum can not be repro-
duced by our circuit simulation. A further study for rigorous
analysis of these peaks will be presented in forthcoming
paper.
In conclusion, the equivalent simplified circuit model
and the E/M wave simulation model for cut-off probes reveal
the physics behind N – shape spectrum: The proposed circuit
model reproduces well the overall shape of TMF spectrum
of cut-off probe N – shape spectrum and reveals the origin as
the combined result of two different resonance caused by the
elements between two probe tips (a sheath, a plasma, and a
vacuum which is filled by the plasma). Furthermore, based
on the this simple modeling, a more precise method to find
the plasma frequency by taking account with the e-n
collision frequency and the pressure limitation of the cut-off
probe application is established.
This work was sponsored in part by the Korea Ministry
of Knowledge Economy (10034836, 10031812-2008-11) and
Korea Research Institute of Standards and Science (KRISS).
This research is supported by the Converging Research Cen-
ter Program through the Ministry of Education, Science and
Technology (2011K000766, 2011K000767).
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FIG. 4. Normalized resonance frequency of the TMF spectrum (S21) calcu-
lated from the circuit model against the normalized collision frequency.
131502-3 Kim et al. Appl. Phys. Lett. 99, 131502 (2011)
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