Uncertainty of a hybrid surface temperature sensor for silicon wafers
and comparison with an embedded thermocouple
Tohru Iuchi
1,a͒
and Atsushi Gogami
2,b͒
1
Department of Mechanical Engineering, Toyo University, 2100 Kujirai, Kawagoe, Saitama 350-8585, Japan
2
Toyo University, 2100 Kujirai, Kawagoe, Saitama 350-8585, Japan
͑Received 14 April 2009; accepted 23 November 2009; published online 31 December 2009͒
We have developed a user-friendly hybrid surface temperature sensor. The uncertainties of
temperature readings associated with this sensor and a thermocouple embedded in a silicon wafer
are compared. The expanded uncertainties ͑k =2͒ of the hybrid temperature sensor and the
embedded thermocouple are 2.11 and 2.37 K, respectively, in the temperature range between 600
and 1000 K. In the present paper, the uncertainty evaluation and the sources of uncertainty are
described. © 2009 American Institute of Physics. ͓doi:10.1063/1.3274676͔
In order to develop in situ radiation thermometry for a
silicon wafer, it is important to calibrate the surface tempera-
ture and consider the emissivity change in the silicon wafer
under test conditions. Unfortunately, conventional methods
of temperature measurement using a thermocouple are labo-
rious because the welding of the thermocouple to the surface
of the silicon wafer is difficult.
1–3
In order to overcome this
problem, we developed a hybrid surface temperature sensor
that is easy to manipulate under test conditions. This sensor
is comprised of a metal film that contacts a specimen and a
radiometer that measures the radiance of the rear surface of
the thin film. If the emissivity of the rear surface is known,
the temperature of the thin film can be derived from the
radiance signal. Then, the surface temperature of the speci-
men can be accurately determined.
4,5
The first version of the hybrid surface sensor required a
response time of several tens of seconds, and the measure-
ment was limited to the temperature range from 900 to 1000
K.
4
Then, an improved version of this sensor having a rapid
response of within 1 s was developed.
5
The uncertainty in the
improved sensor was estimated to be 0.5 K as the evaluation
was restricted only to the fluctuation of temperature readings
of the hybrid surface sensor.
The present paper describes the overall uncertainty
evaluation of a further improved hybrid sensor for use in the
temperature range from 600 to 1000 K. We compared the
uncertainties of the hybrid temperature sensor and an embed-
ded thermocouple.
Figure 1 shows a schematic diagram of the measurement
system, including the hybrid surface temperature sensor, the
monitoring radiometer, and the heating furnace. The furnace
temperature is measured and controlled by a type K sheathed
thermocouple inside the furnace.
The transient temperature T of the film of the hybrid
surface sensor can be obtained as follows:
T − T
0
T
f
− T
0
=1−exp
ͩ
−
t
ͪ
, ͑1͒
where T
0
is the initial temperature of the film when the film
contacts the specimen surface at time t=0, T
f
is the final
temperature reading the film approaches, and
is the thermal
time constant of the system.
5
There is always a difference,
⌬T
h
͑=T
s
−T
f
͒, between the surface temperature T
s
of the ob-
ject and T
f
. Under the constant contact pressure ͑40 kPa͒ of
the film on the object, ⌬T
h
is treated as the known systematic
error with uncertainty u
h
. The effect of the conductive heat
loss induced by the contact is included in ⌬T
h
and u
h
. Thus,
the surface temperature T
s
of the silicon wafer is obtained as
follows:
T
s
= T
f
+ ⌬T
h
+ u
h
. ͑2͒
Figure 2 shows the configuration of a type K thermo-
couple ͑diameter: 0.2 mm͒ embedded in a silicon wafer,
where ͑a͒ shows the location of the embedded thermocouple,
and ͑b͒ is a side view of the thermocouple inside the silicon
wafer. The temperature difference, ⌬T
e
͑=T
s
−T
e
͒, between
the surface temperature T
s
, and the temperature reading T
e
of
the embedded thermocouple is caused by the heat transfer
loss of the thermocouple lead wires. Here, ⌬T
e
is taken as a
known systematic error with an uncertainty u
e
. Then, T
s
is
derived as follows:
T
s
= T
e
+ ⌬T
e
+ u
e
. ͑3͒
The uncertainties of the measurements are based on Ref.
6. Heat-resistant blackbody coating was painted onto the sili-
con wafer.
4,5
The reading by the monitoring radiometer ͑IR-
FBWS-SP, CHINO͒ is assumed to be the true surface tem-
perature T
s
, with a combined standard uncertainty u
M
that is
caused in part by the uncertainty of the effective emissivity
of the blackbody coating. We assume that fluctuates within
Ϯ⌬, which results in temperature fluctuation u
, which is
given as follows:
u
= Ϯ
1
n
·
⌬
· T, ͑4͒
a͒
Electronic mail: iuchi@toyonet.toyo.ac.jp. Tel.: ϩ81-49-239-1326. FAX:
ϩ81-49-233-9779.
b͒
Electronic mail: gn0070013@toyonet.toyo.ac.jp.
REVIEW OF SCIENTIFIC INSTRUMENTS 80, 126109 ͑2009͒
0034-6748/2009/80͑12͒/126109/3/$25.00 © 2009 American Institute of Physics80, 126109-1