Thin Solid Films 547 (2013) 280–284

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Thin Solid Films

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Plasma density measurement with ring-type cutoff probe

D.W. Kim a, S.J. You b, B.K. Na c, J.H. Kim b,⁎, Y.H. Shin b, H.Y. Chang c, W.Y. Oh a

a Department of Mechanical Engineering, Korea Advanced Institute of Science and Technology, Daejeon, 305-701, Republic of Koreab Center for Vacuum Technology, Korea Research Institute of Standards and Science, Daejeon, 305-306, Republic of Koreac Department of Physics, Korea Advanced Institute of Science and Technology, Daejeon, 305-701, Republic of Korea

⁎ Corresponding author.E-mail address: jhkim86@kriss.re.kr (J.H. Kim).

0040-6090/$ – see front matter © 2012 Elsevier B.V. Allhttp://dx.doi.org/10.1016/j.tsf.2012.11.049

a b s t r a c t

a r t i c l e i n f o

Available online 30 November 2012

Keywords:Plasma diagnosticsCutoff probeMicrowave probeProcessing monitoringPlasma density measurement

We proposed a cutoff probe with a ring-type detection tip enclosing a bar-type radiation tip. A comparativestudy between a proposed ring-type cutoff (RTC) probe and a conventional bar-type cutoff (BTC) probeshowed that the RTC probe solved the problem of the BTC probe, the large measurement uncertainty of theelectron density in a capacitively coupled plasma source. This improved characteristics of the RTC probemight have originated from the geometrical structure of the RTC probe concerning the monopole antennaeradiation. This proposed cutoff probe can be expected to expand the applicable diagnostic range and to en-hance the sensitivity of the cutoff probe.

© 2012 Elsevier B.V. All rights reserved.

1. Introduction

Recently, as the pattern sizes of semiconductor fabrication processeshas shrunk to below the 50 nm scale, numerous problems, such as load-ing, bowing, and notching effects, have been seriously reported. Toavoid these problems, a method of plasma process control based onthe diagnostics of plasma parameters has been proposed. Therefore,the precise measurement of plasma parameters becomes a very impor-tant issue in the plasma processes. In the plasma parameters, the elec-tron density is a fundamental plasma parameter informing the state ofthe plasma and estimating the process throughput. Because of this rea-son, a number of plasma diagnostics have been employed to measurethe electron density in the plasma.

The Langmuir probe is one of the oldest andmost reliable diagnosticmethods for electron density measurement. Research on the Langmuirprobe has been carried out over the past several decades [1], and theLangmuir probe has been used as a reference of measured electron den-sity in many papers [2,3]. However, the Langmuir probe shows inaccu-rate results when it is applied for reactive gas plasmas [4]. Instead ofusing this probe, diagnostic methods using microwaves, which canmeasure the electron density even with complex processing plasmaconditions, have been developed such as an impedance probe, a hairpinprobe, an absorption probe, and a cutoff probe [3,5–7] because the mi-crowave probes are relatively free from the effects of reactive gas andthe microwave frequency is insensitive to the thin layer deposition re-sult from reactive gas.

The cutoff probe is a promising microwave probe, and it is widelyused for measuring the electron density in the processing plasmas. It is

rights reserved.

not only a simple and robust method, but also a low-perturbationmeth-od. However, the conventional bar-type cutoff (BTC) probe has a prob-lem, the measurement uncertainty of the electron density in highpressure and RF noisy plasmas. To overcome this weakness, Kwon etal., used the resonance and 60 Hzperturbation effects on thephase spec-trum from the cutoff probe [8]. Recently, more precise measurement isenabled by analysis of the sheath effect on the determination of the plas-ma frequency [9]. However, back to the measurement basis of probehardware, improvement of the radiation and detection tips of the cutoffprobe through modification of them has not yet been performed.

In this paper, we propose a cutoff probe with a ring-type detectiontip enclosing a bar-type radiation tip. A comparative study between aproposed ring-type cutoff (RTC) probe and a conventional BTC probeshowed that the RTC probe solved the problem of the BTC probe, thelarge measurement uncertainty of the electron density in a capacitivelycoupled plasma (CCP) source. The electromagnetic (E/M) wave simula-tion was also performed to verify the improved characteristics of theRTC probe.

2. Experiments and simulation details

An experiment was conducted for comparative study between theconventional cutoff probe (BTC probe) and the improved cutoff probe(RTC probe). Fig. 1 shows the schematic structures of RTC and BTCprobes. The RTC probe has a ring-type detection tip enclosing abar-type radiation tip. The radius of the tip (r), the diameter of thering (2d), the height of the radiation tip (h), and the height of the detec-tion tip (b) are 0.26 mm, 4.32 mm, 10 mm, and 5 mm, respectively.Both the radiation anddetection tips are connected to a network analyz-er (HP 8753ET) though 50 Ω coaxial cables. Radiating waves on the ra-diation tip are fed from the network analyzer of ∼0.1 mW and aremeasured by the detection tip. The plasma frequency (fp), which is

Pump

13.56 MHz Matcher

Bar type cutoff probe Ring type cutoff probe

500 mm

50 mm

13.56 MHz Power

460 mm

Fig. 2. Comparative experiment setup between theRTC andBTCprobes in the CCP chamber.

281D.W. Kim et al. / Thin Solid Films 547 (2013) 280–284

directly related to the electron density, is determined by selecting thecutoff frequency (fc), fc∼ fp [10].

The electron density measurement was performed in a large areaCCP source generated by a 13.56 MHz RF power source (from 200 Wto 1000 W), as shown in Fig. 2. In the CCP source, an upper poweredelectrode 500 mm in diameter and a lower grounded electrode460 mm in diameter were separated by 50 mm. A base pressure was∼10−4Pa and discharge pressure was changed from 1.33 Pa to13.3 Pa in argon gas flow. The characteristics of the large area singleCCP source will be presented in a forthcoming paper. For a comparativestudy, the tips of RTC and BTC probes were positioned at the center ofthe discharge chamber, as shown in Fig. 2.

For the numerical analysis and comprehensive understanding ofradiation and detection property of waves, we used an E/Mwave sim-ulation. This is a direct numerical solver for the Maxwell equation atthe given boundary conditions (CST Microwave Studio). The E/Mwave simulation has been known to produce consistent results withexperiment [11,12]. The bulk plasma was treated as an immobile dis-persive dielectric material whose input parameters are a collision fre-quency (νm) and a plasma oscillation frequency (2πfp) related to theelectron density (ne) (Drude model [13]). The electron density andthe pressure (p) were 2×1010 cm−3 and 26.7 Pa, respectively, inthe E/M wave simulations. A sheath of the vacuum thin layer wasused as 0.3719 mm (5×Debye length) [12]. Fig. 3 shows the compo-nents of the E/M wave simulation model. A plasma, which is de-scribed by the Drude model, is contained by a grounded cubicchamber in which each side length (Lx, Ly, Lz) is 100 mm. Both two

(a)

Plasma

Sheathb

2d

h

Plasma

Sheath

s

2r

h

d

(b)

Fig. 1. Schematic structure of (a) the proposed RTC probe and (b) the conventional BTCprobe.

probe tips, which has holder lengths (Lh) of 50 mm, are located inthe center of the cubic chamber [14].

3. Results and discussion

For a comparative experiment of two different diagnostics, wemeasured the transmission microwave frequency (TMF) spectrum(S21) in a plasma at various discharge pressures and powers, andthe result is presented in Fig. 4. At first, Fig. 4 shows that the transmit-ted signal level of the RTC probe (see the red line) is ∼3 dB (∼2 timesin linear scale) higher than that of the BTC probe regardless of the ex-perimental conditions. As shown in Fig. 4(a), (b), and (c), at the lowpressure (1.33 Pa), the cutoff frequency peaks of the RTC and BTCprobes are sharp enough to determine the resonance frequency. Ifwe increase the gas pressure (6.67 Pa), as shown in Fig. 4(d), (e),and (f), the cutoff frequency peaks of the RTC and BTC probes canbe determined at the low power condition (200 W). However, theBTC probe shows a broadened cutoff frequency peak on the TMF spec-trum, reflecting the uncertainty increase for the electron density mea-surement (see the left–right arrow in Fig. 4(e) and (f)) at high power,

=

=

=

=

Fig. 3. Components of the E/M wave simulation model.

BTC probe RTC probe

500 W(b)

BTC probe RTC probe

1000 W(c)

BTC probe RTC probe

200 W(d)

BTC probe RTC probe

500 W(e)

Uncertainty BTC probe RTC probe

1000 W(f)

BTC probe RTC probe

500 W(h)

BTC probe RTC probe

1000 W(i)

BTC probe RTC probe

200 W(g)

0.0 0.5 1.0 1.5 2.0 2.5 3.0

-40

-30

-20

S21-

para

met

er (

dB)

Frequency (GHz)

BTC probe

RTC probe200 W(a)

Cutoff frequency peak0.0 0.5 1.0 1.5 2.0 2.5 3.0

Frequency (GHz)

0.0 0.5 1.0 1.5 2.0 2.5 3.0Frequency (GHz)

0.0 0.5 1.0 1.5 2.0 2.5 3.0Frequency (GHz)

0.0 0.5 1.0 1.5 2.0 2.5 3.0Frequency (GHz)

0.0 0.5 1.0 1.5 2.0 2.5 3.0Frequency (GHz)

0.0 0.5 1.0 1.5 2.0 2.5 3.0Frequency (GHz)

0.0 0.5 1.0 1.5 2.0 2.5 3.0Frequency (GHz)

0.0 0.5 1.0 1.5 2.0 2.5 3.0Frequency (GHz)

-40

-30

-20

S21-

para

met

er (

dB)

-40

-30

-20

S21-

para

met

er (

dB)

-40

-30

-20

S21-

para

met

er (

dB)

-40

-30

-20

S21-

para

met

er (

dB)

-40

-30

-20

S21-

para

met

er (

dB)

-40

-30

-20

S21-

para

met

er (

dB)

-40

-30

-20

S21-

para

met

er (

dB)

-40

-30

-20

S21-

para

met

er (

dB)

Fig. 4. TMF spectrum from the experiment at p=1.33 Pa of ((a), (b), and (c)), p=6.67 Pa of ((d), (e), and (f)), and p=13.3 Pa of ((g), (h), and (i)).

282 D.W. Kim et al. / Thin Solid Films 547 (2013) 280–284

200 400 600 800 1000

1010

Den

sity

(cm

-3)

Power (W)

RTC probe (1.33 Pa) RTC probe (6.67 Pa) RTC probe (13.3 Pa) BTC probe (1.33 Pa) BTC probe (6.67 Pa) BTC probe (13.3 Pa)

Fig. 5. Measured electron density with the measurement uncertainty calculated fromthe result of Fig. 4.

0 1 2 3 4 5-100

-80

-60

-40

-20

0

S21

(dB

)

Frequency (GHz)

BTC probe: Tips (10 mm,10 mm)RTC probe: Tips (10 mm, 18.57 mm)BTC probe: Tips (10 mm, 18.57 mm)

Cutoff frequency peak

(the radiation tip, the detection tip)

Fig. 6. TMF spectrum from the E/M wave simulation with different tip lengths of RTCand BTC probes at p=26.7 Pa and ne=2×1010 cm−3.

283D.W. Kim et al. / Thin Solid Films 547 (2013) 280–284

while the RTC probe shows a distinguishable cutoff frequency peak onthe TMF spectrum even at the high power condition. These results be-come more serious for the BTC probe, when the pressure increases(13.3 Pa, see Fig. 4(g), (h), and (i)). However, the cutoff frequencypeak of the RTC probe could be determined with a small measure-ment uncertainty compared with that of the BTC probe. This experi-mental result shows that there are less problems in the proposedRTC probe for the determination of the cutoff frequency comparedwith the conventional BTC probe.

Fig. 5 shows the electron density with measurement uncertainty(see the left–right arrow in Fig. 4) calculated from the result ofFig. 4. In this measurement, the uncertainty of each probe is definedas follows: in general, the whole shape of TMF spectra from cutoffprobe looks like N-shape, which is a repetition of positive, negative,and positive slopes, and a cutoff frequency peak is located betweenthe negative and positive slopes (see Fig. 4(a)). Because it was be-lieved that cutoff frequency was laid in the region between the lastfrequency of negative slope trend and the first frequency of the posi-tive slope trend, we selected the measurement uncertainty as a fre-quency regime of the left–right arrow in Fig. 4. Normally, the cutofffrequency peak of high Q-factor showed a narrow transition regionof the slope, meaning a small measurement uncertainty, but that oflow Q-factor did not show a narrow transition region of the slope,meaning a large measurement uncertainty. As mentioned before,the RTC probe shows a small measurement uncertainty comparedwith the BTC probe in a comprehensive range of experimental condi-tions. Together with the result of Fig. 4, this result shows that the pro-posed RTC probe is more precise diagnostics having better S/N ratioand smaller measurement uncertainty compared with the normalBTC probe.

To investigate the characteristics of the RTC probe, having better S/Nratio and lower measurement uncertainty theoretically, we performedtwo E/M wave simulations [11]. Fig. 6 shows the calculated TMF spec-trum of RTC and BTC probes in Fig. 1(a) and (b) (see the black and redlines in Fig. 6). The TMF spectrum of the RTC probe exhibits a highertransmitted signal level compared with that of the BTC probe, as in theresult of Fig. 4 (better S/N ratio). If we had used the detection probetip whose tip length was same as that of the RTC probe in the BTCprobe (see the black and green lines in Fig. 6), we could obtain a bettersignal level, as expected in previous paper [15]. However, as shown inFig. 6, the RTC probe spectrum exhibits higher Q-factor characteristicsnear the cutoff frequency compared with that of a BTC probe having asame length of detection tip. This result means that the physics behindthe improved RTC probe is not only the effect of the enlargement of

detection area (a tip length increase), but also the effect of the geomet-rical structure of the RTC probe.

To examine the geometrical structure effect of the RTC probe, we in-vestigated the spatial E-field profile at the cutoff frequency (1.27 GHz)for various cutoff probe systems, and the results are presented inFig. 7. As shown in Fig. 7, the RTCprobe clearly shows the resonant char-acteristics in the bulk plasma at the cutoff frequency. Normally the elec-tric field in the cutoff probe system is deposited in the sheath ratherthan the bulk plasma. However, when the cutoff phenomenon takesplace, a high electric field is evenly deposited in the bulk plasma, anda relatively low electric field is deposited in the sheath, as shown inFig. 7, because of a huge increase of the bulk plasma impedance at thecutoff frequency [14]. We can see this profile in the BTC probe systems,but it is somewhat obscure compared with that of the RTC probe sys-tem. This effective resonance characteristics of the RTCprobemay be re-sponsible for the high Q-factor of the cutoff frequency peak in the RTCprobe, as shown in Figs. 4 and 6. The physical reason for these effectiveresonance characteristics of the RTC probe is not understood clearly inthis state, but we believe that detection antennae of RTC probe receivesthe radiatingwave effectively by receiving radiated electricwaveswith-out disturbing the original monopole antennae radiation from the radi-ation probe tip. To reveal this physics behind, further research based onthe system modeling is needed.

4. Conclusion

In conclusion, we have proposed a cutoff probe with a ring-typedetection tip enclosing a bar-type radiation tip and verified improvedcharacteristics of the RTC probe by experiment and E/M wave simula-tion. Compared with the BTC probe, the advantage of the RTC probeare summarized as follows: 1) an increased signal level improvesthe S/N ratio and sensitivity, 2) the high Q-factor enables the plasmafrequency to be determined more precisely, and 3) the RTC probemaintains a good spatial resolution while increasing the signal leveland Q-factor due to the short length of the probe tips. This improvedcharacteristics of the RTC probe might have originated from the geo-metrical structure of the RTC probe concerning the monopole anten-nae radiation. This proposed cutoff probe can be expected to expandthe applicable diagnostic range and to enhance the sensitivity of thecutoff probe.

10 mm

13.57 mm(circumference)

5 mm

10 mm

18.57 mm10 mm

Fig. 7. Spatial E-field profile of RTC and BTC probes at the plasma frequency (1.27 GHz) from the E/M wave simulation at p=26.7 Pa and ne=2×1010 cm−3. The E-field value isnormalized with respect to maximum field in each plane.

284 D.W. Kim et al. / Thin Solid Films 547 (2013) 280–284

Acknowledgements

This research was supported by Korea Research Institute ofStandards and Science (KRISS) and the Converging Research Cen-ter Program through the Ministry of Education, Science andTechnology(2012K001234).

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