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: sjyou@kriss.re.kr.

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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