Rapid measurement of substrate temperatures by frequency-domain low-coherenceinterferometryTakayoshi Tsutsumi, Takayuki Ohta, Kenji Ishikawa, Keigo Takeda, Hiroki Kondo, Makoto Sekine, Masaru Hori,and Masafumi Ito Citation: Applied Physics Letters 103, 182102 (2013); doi: 10.1063/1.4827426 View online: http://dx.doi.org/10.1063/1.4827426 View Table of Contents: http://scitation.aip.org/content/aip/journal/apl/103/18?ver=pdfcov Published by the AIP Publishing Articles you may be interested in From amorphous to microcrystalline: Phase transition in rapid synthesis of hydrogenated silicon thin film in lowfrequency inductively coupled plasmas J. Appl. Phys. 108, 113520 (2010); 10.1063/1.3514006 Simultaneous measurement of substrate temperature and thin-film thickness on SiO 2 / Si wafer using optical-fiber-type low-coherence interferometry J. Appl. Phys. 105, 013110 (2009); 10.1063/1.3058592 Bulk and interface charge in low temperature silicon nitride for thin film transistors on plastic substrates J. Vac. Sci. Technol. A 22, 2256 (2004); 10.1116/1.1795822 Electronic and structural properties of doped amorphous and nanocrystalline silicon deposited at low substratetemperatures by radio-frequency plasma-enhanced chemical vapor deposition J. Vac. Sci. Technol. A 21, 1048 (2003); 10.1116/1.1586275 Pulse-modulated infrared-laser interferometric thermometry for non-contact silicon substrate temperaturemeasurement J. Vac. Sci. Technol. A 15, 2035 (1997); 10.1116/1.580676

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Rapid measurement of substrate temperatures by frequency-domainlow-coherence interferometry

Takayoshi Tsutsumi,1 Takayuki Ohta,2 Kenji Ishikawa,1 Keigo Takeda,1 Hiroki Kondo,1

Makoto Sekine,1 Masaru Hori,1 and Masafumi Ito2

1Department of Electrical Engineering and Computer Science, Graduate School of Engineering,Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464-8603, Japan2Department of Electrical and Electronic Engineering, Faculty of Science and Technology,Meijo University, 1-501 Shiogamaguchi, Tenpaku-ku, Nagoya 468-8502, Japan

(Received 4 September 2013; accepted 15 October 2013; published online 29 October 2013)

Rapid high-precision temperature monitoring systems for silicon wafers applicable even during

plasma processing have been developed using frequency-domain low-coherence interferometry

without a reference mirror. It was found to have a precision of 0.04 �C, a response time of 1 ms,

and a large tolerance to mechanical vibrations and fiber vending when monitoring the temperature

of commercial Si wafers. The performance is a substantial improvement over the previous

precision of 0.11 �C measured in a few seconds using a time-domain method. It is, therefore, a

powerful real-time technique to monitor rapidly varying wafer temperatures with high precision.VC 2013 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4827426]

Various processing technologies, such as plasma etching

and plasma enhanced chemical vapor deposition (PECVD),

have been used to fabricate semiconductor devices. In

plasma etching, both the etching profile and etching rate are

sensitive to the substrate temperature.1,2 The chemistry

depends upon the temperature of the chamber parts.3–7 To

achieve precise control, the wafer temperature must be accu-

rately measured and controlled.2 A variety of methods for

measuring the substrate temperature during plasma process-

ing have been proposed.8–11 However, thermocouples and

fluorescence thermometers involving contact sensors need

good thermal conductance and equilibrium between the wa-

fer and probe in order to measure the substrate temperature.

Particularly, at low pressures, insufficient contact between

the two often results in erroneous measurements.12

Consequently, noncontact methods can more accurately

measure the substrate temperature. Infrared radiation and

laser-interference thermometries are useful for select proc-

esses. However, there remain difficulties such as the limited

resolution and temperature range when monitoring silicon

wafers.13–16

In the previous studies, we developed a noncontact sub-

strate temperature measurement technique using a time-

domain low-coherence interferometer (TD-LCI).17–19 The

system solved issues of size, accuracy, and working tempera-

ture range. The time resolution was, however, limited to a

few seconds because the system used a mechanically

scanned mirror to obtain an interferogram for the substrate

temperature. Vibrational noise during a scan affected the op-

tical stability, leading to low temperature accuracy. Rapid

measurement times compared to typical vibrational periods

are required in order to build a robust system and to improve

the accuracy.

For this purpose, a temperature monitoring system using

a frequency-domain low-coherence interferometer (FD-LCI)

without a reference mirror has been developed. A conven-

tional FD-LCI having a reference mirror can potentially

measure substrate temperatures in a few milliseconds.20–22

The optical setup for a conventional FD-LCI is similar to that

for a TD-LCI. The only difference is that the reference mirror

is fixed in the case of the FD-LCI. When light from a low-

coherence source, such as a superluminescent diode (SLD),

irradiates a transparent substrate, interferograms are generated

in the time domain from interferences between the reflections

from the front and back surfaces of the substrate and the refer-

ence mirror. If the interference signal is collected using a

spectrometer with a fixed mirror, the spectrum of the signal,

known as a spectral interferogram, consists of direct current

(DC), cross-correlation, and auto-correlation terms.23 The

cross-correlation and auto-correlation terms represent the fre-

quency components of light reflected between the reference

mirror and the sample surfaces and between the front and

back surfaces of the sample, respectively. Since Fourier detec-

tion measures all of the light simultaneously, an inverse

Fourier transform of the spectral interferogram determines all

of the time-domain interferograms.21–24 The time interval

between interferograms, arising from the cross-correlation

terms, is used to derive the optical path length between the

front and back surfaces of the sample in the cross-correlation

type (CCT) of FD-LCI.

The FD-LCI proposed here for monitoring the tempera-

ture of Si substrates has no fixed reference mirror. In that

case, an interference signal is obtained from the light

reflected from the front and back surfaces of a plane-parallel

sample. The inverse Fourier transform (inverse-FFT) of the

spectral interferogram results in interferograms due to the

DC and auto-correlation terms. The FD-LCI without fixed

reference mirror is said to be of auto-correlation type (ACT).

The time interval between interferograms determines the op-

tical path length between the front and back surfaces of the

sample.

In the present study, high-precision rapid measurements

of Si substrate temperatures are demonstrated using ACT-FD-

LCI. The variation in the optical path length of a Si substrate

due to its temperature change depends on both the thermal

expansion and the temperature dependence of the refractive

0003-6951/2013/103(18)/182102/3/$30.00 VC 2013 AIP Publishing LLC103, 182102-1

APPLIED PHYSICS LETTERS 103, 182102 (2013)

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index. The substrate temperature can be estimated from the

optical path length of the substrate, if the length at room tem-

perature and its temperature dependence are known.18

Figure 1 is a schematic of the substrate temperature

monitoring system without a reference mirror, consisting of

a low-coherence light source, a spectrometer, a fiber coupler,

and optical fibers. The SLD is a light source with a central

wavelength of 1570 nm and a spectral bandwidth (full width

at half maximum) of 38 nm. Light from the SLD reflects

from the sample surfaces and interferes at the coupler. The

interference signal is measured by the spectrometer, having a

spectral resolution of 0.05 nm and a spectral range from

1520 to 1620 nm.

A 780-lm-thick Si wafer is placed in a blackbody fur-

nace to accurately control its temperature. The refractive

index n of Si is 3.48 at 20.1 �C.25 The optical path length is

z ¼ k02=4ndk; (1)

where k0 is the central wavelength and dk is the spectral re-

solution of the spectrometer. From Eq. (1), the optical thick-

ness is limited to 12.3 mm in vacuum, which corresponds to

3.54 mm in a Si wafer.

Figure 2 plots typical DC and auto-correlation peaks at

0 and 5593 lm, calculated from the inverse Fourier trans-

form of the spectral interferogram of the 780-lm-thick Si

substrate. The auto-correlation peak arises from interference

between light reflected from the front and back surfaces of

the wafer. Multiplying the refractive index of 3.48 by twice

the wafer thickness of 780 lm gives 5593 lm. This result

indicates that the thickness of a 3.54-mm-Si wafer can be

measured by an ACT-FD-LCI. Moreover, the minimum

measurable thickness of a layer depends on the coherence

length of the light source. If its spectrum is Gaussian, the co-

herence length is give by

lc ¼ 2ln2k02=pDk; (2)

where Dk is the full width at half maximum (FWHM). Using

this equation, the coherence length of the SLD is estimated

to be 28.6 lm, which corresponds to 8.22 lm in a Si wafer.

Wafer thicknesses ranging from 8.22 lm to 3.54 mm can

therefore be measured using this setup. Supercontinuum light

(SC) has a broader spectrum than SLDs, resulting in coher-

ence lengths of 3 to 7 lm.26 Thus, by using a SC, an

improvement in the minimum measurable thickness is

expected.

Figure 3 graphs the optical path length as a function of

the temperature of a Si wafer in the blackbody furnace. For

comparison, the wafer temperature was also measured using

a thermocouple in the furnace having a steady-state tempera-

ture. As the temperature increases, the optical path length

increases linearly. The standard deviation is found to be

8 nm at room temperature, corresponding to a temperature

error of 0.04 �C, which is a substantial improvement over the

resolution of 0.11 �C for a conventional TD-LCI.17 In addi-

tion, this method has the advantages that it suppresses elec-

trical shot and excess noise, and it is undisturbed by

mechanical vibrations because of the absence of a reference

mirror, in contrast to a TD-LCI which uses a moving

mirror.22,27–29 The signal-to-noise ratio of the interferogram

from the autocorrelation term increases from 19.4 to 39.1 dB

when the mirror is removed.

In either a TD-LCI or a CCT-FD-LCI using a dual-path

interferometer, compensation of the dispersion and polariza-

tion differences between the reference and sample light is

required. For an ACT-FD-LCI using a common-path inter-

ferometer, the polarization of the signal light was varied

using a polarization controller. The auto-correlation peak

shifts less than 11 nm, corresponding to a temperature error

of 0.04 �C. This result indicates that an ACT-FD-LCI has

reduced noise due to mechanical vibrations, fiber-induced

dispersion, and polarization mismatch. Consequently, an

FIG. 1. Fiber-optic Fourier-domain interferometer for temperature measure-

ments. Here, SLD is a superluminescent diode and L is a lens.

FIG. 2. Autocorrelation spectrum obtained from the inverse Fourier trans-

form of a spectral interferogram.

FIG. 3. Variation in the optical path length with temperature of a 780-lm-

thick Si wafer inside a blackbody furnace.

182102-2 Tsutsumi et al. Appl. Phys. Lett. 103, 182102 (2013)

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ACT-FD-LC is more stable and reliable than a conventional

TD-LCI or CCT-FD-LCI.30,31

The response speed of an ACT-FD-LCI is demonstrated

by temperature measurements of a Si wafer being rapidly

thermally annealed by halogen-lamp irradiation of its back

surface. For reference, a thermocouple is in contact with the

front surface of the wafer. Figure 4 plots the time evolution

of the temperature (at a resolution of 1 ms) measured using

both the ACT-FD-LCI and the thermocouple. The results

indicate that the ACT-FD-LCI measures the wafer tempera-

ture at a rate of 5.74 �C/s. In contrast, the thermocouple does

not correctly measure the wafer temperature, reporting an er-

roneous heating rate of 3.81 �C/s with a time delay exceeding

0.1 s. This failure arises from poor thermal contact between

the Si wafer and the thermocouple.

In conclusion, a high-precision rapid-response system for

measuring the temperature of silicon wafers has been devel-

oped and demonstrated using a FD-LCI employing auto-

correlation signals without a reference mirror, in contrast to a

conventional FD-LCI. The results exhibit a high precision of

0.04 �C with a response time as short as 1 ms when monitoring

the temperature of a commercial 780-lm-thick Si wafer.

Moreover, the system is less sensitive to mechanical vibra-

tions and to the details of the optical fiber manufacturing. This

temperature monitoring system is thus a powerful tool for

noncontact measurement of wafer temperatures during plasma

processing and other rapid thermal events.

This work was supported by the Knowledge Cluster

Initiative (The Second Stage) of the Ministry of Education

Culture, Sports, Science, and Technology of Japan

(MEXT).

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FIG. 4. Real-time monitoring of the temperature of a Si wafer upon 1 s of

irradiation by a halogen lamp. The data were collected using an autocorrela-

tion low-coherence interferometer (thin line) and a thermocouple (dots).

182102-3 Tsutsumi et al. Appl. Phys. Lett. 103, 182102 (2013)

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