Simultaneous measurement of emissivity and temperature of silicon wafers using a polarization technique

Measurement 43 (2010) 645–651

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Simultaneous measurement of emissivity and temperature of silicon wafers using a polarization technique Tohru Iuchi a,*, Atsushi Gogami b a b

Dept. of Mechanical Engineering, Toyo University, 2100 Kujirai, Kawagoe, Saitama 350-8585, Japan School of Engineering, Toyo University, 2100 Kujirai, Kawagoe, Saitama 350-8585, Japan

a r t i c l e

i n f o

Article history: Received 8 December 2009 Received in revised form 28 December 2009 Accepted 5 January 2010 Available online 11 January 2010 Keywords: Emissivity Temperature Polarization Uncertainty Silicon wafer

a b s t r a c t The emissivity of a silicon wafer under various conditions was theoretically and experimentally investigated. A quantitative relationship between the ratio of p-polarized to spolarized radiances, and the polarized emissivity was obtained, irrespective of the emissivity change of silicon wafers due to oxide film thickness under wide variations of impurity concentration. We propose a new radiation thermometry method that can measure both the temperature and the spectral polarized emissivity of a silicon wafer, and we estimate the uncertainty of these measurements. Currently, the expanded uncertainty of the temperature measurement is estimated to be 3.52 K (2k) and 3.80 (2k) for p-polarization and s-polarization, respectively, at temperatures above 900 K. Ó 2010 Elsevier Ltd. All rights reserved.

1. Introduction The inability to obtain an accurate and reproducible determination of silicon wafer temperature remains a major obstruction to reliable, high-quality processing. Radiometric temperature measurement is crucial to silicon manufacturing, because it is a non-contact, contaminantfree method [1–3]. The accuracy of this method is, however, limited by uncertainties in the emissivity of the silicon wafer and of the thin film layers deposited or grown on the wafer surface [4–6]. Therefore, an emissivity-compensated method is required to overcome the current difficulties in radiation thermometry [7–9]. In this paper, the emissivity of a silicon wafer under various conditions was simulated using a simple modeling of the spectral, directional, and polarization characteristics of thermal radiation. A relation between polarized radiance and emissivity was derived from the simulation. Successive experiments were carried out, resulting in a practical relationship between the ratio of p-polarized to s-polarized * Corresponding author. Tel.: +81 49 239 1326; fax: +81 49 233 9779. E-mail address: [email protected] (T. Iuchi). 0263-2241/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.measurement.2010.01.004

radiances and polarized emissivities. This relationship corresponded fairly well with the simulations. These findings represent a new radiation thermometry method, which can simultaneously measure both the temperature and the spectral polarized emissivity of a silicon wafer. In order to perform these experiments, a user-friendly hybrid surface temperature sensor developed by the authors was used for temperature calibration of the silicon wafers [10]. Finally, the uncertainty of the proposed radiometric temperature measurement method was determined. 2. Emissivity simulation Fig. 1 shows a model of a bare silicon wafer with an optically smooth surface on which an oxide layer (SiO2) with a thickness d was grown. n1, n2, and n3 are the refractive indices of air, the oxide film, and the wafer, respectively. Silicon wafers are opaque at a wavelength of k = 0.9 lm because of the Si band-gap energy of Eg = 1.12 eV. Therefore, radiance from the silicon wafer is limited to the media between the specimen surface and the oxide layer, as

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Let Ep,b(T) and Es,b(T) be p- and s-polarized blackbody radiance signals, respectively, at temperature T, as shown as:

Radiance

n Air n1 = 1.00

1

Oxide film : SiO2 n2 = 1.45

d

Substrate : Si n3= 3.65

2

Ep;b ðTÞ ¼ kp  Lk;b ðTÞ

ð10Þ

Es;b ðTÞ ¼ ks  Lk;b ðTÞ

ð11Þ

The polarized emissivity, ep(h1) or es(h1), at temperature T are defined from the following equation:

3

epðsÞ ðh1 Þ ¼ Fig. 1. Simulation model, composed of a silicon wafer and an oxide layer.

d¼

r212pðsÞ þ r 223pðsÞ þ 2r 12pðsÞ r 23pðsÞ cos d 1 þ r 212pðsÞ r 223pðsÞ þ 2r 12pðsÞ r 23pðsÞ cos d

2p  2n2  d  cos h2 ; k

;

ð1Þ

ð2Þ

r 12p ¼

n2 cos h1  n1 cos h2 ; n2 cos h1 þ n1 cos h2

ð3Þ

r 23p ¼

n3 cos h2  n2 cos h3 ; n3 cos h2 þ n2 cos h3

ð4Þ

r 12s ¼

n1 cos h1  n2 cos h2 ; n1 cos h1 þ n2 cos h2

ð5Þ

r 23s ¼

n2 cos h2  n3 cos h3 ; n2 cos h2 þ n3 cos h3

ð6Þ

n1 sin h1 ¼ n2 sin h2 ¼ n3 sin h3 ;

ð7Þ

where d is the phase delay of an electromagnetic wave inside the oxide film of thickness d. r12p(s) and r23p(s) are the amplitudes of the reflections of p- (or s-) polarized waves at the interface between the air and the oxide film, and the oxide film and the silicon wafer substrate, respectively. The p-polarized and s-polarized radiance signals Ep(T) and Es(T) in the direction h1, emitted by the silicon wafer at temperature T and measured by an optical sensor with a polarization filter are described, respectively, as:

Ep ðTÞ ¼ kp  ep ðh1 Þ  Lk;b ðTÞ; Es ðTÞ ¼ ks  es ðh1 Þ  Lk;b ðTÞ;

ð8Þ ð9Þ

where kp and ks are constant gain factors of an electric amplifier that converts the radiances detected by the optical sensor into the electrical output signals Ep(T) and Es(T), respectively. Lk,b(T) is the spectral blackbody radiance at temperature T and wavelength k.

Rps ¼

Ep ðTÞ ep ðh1 Þ  Ep;b ðTÞ ¼ : Es ðTÞ es ðh1 Þ  Es;b ðTÞ

ð13Þ

Fig. 2 shows simulated directional polarized emissivity

ep(s)(h1) of a bare silicon wafer (d = 0 nm) at k = 0.9 lm. Fig. 3 shows simulated relationships between the ratio of polarized radiances Rps and polarized emissivity ep(s)(h1) at h1 = 70° and k = 0.9 lm, with oxide film thickness d ranging between 0 (bare) and 950 nm. It is apparent from Fig. 3 that once Rps is determined from the measurement of Ep(T) and Es(T), the p-polarized emissivity ep(h1) or the s-polarized emissivity es(h1) of the silicon wafer can be uniquely obtained, irrespective of emissivity variations caused by changes in the oxide film thickness. This enables a new radiation thermometry method for silicon wafers, based upon a polarization technique. 3. Experiments Several experiments were performed to confirm the simulated results. Table 1 shows the measurement conditions, including details regarding the silicon wafers used in the experiments. The resistivity q and oxide layer thickness d of the specimens covered wide ranges from 0.01 to 2000 X cm and from 30 to 950 nm, respectively. Resistivity is closely related to the doped impurity concentration in a silicon wafer, and this relation is shown in Table 2 [14]. Fig. 4 shows an experimental system for the study of silicon wafer emissivity, including a polarized radiometer

1.0 p(s) ( 1)

epðsÞ ðh1 Þ ¼ 1 

ð12Þ

Let Rps be the ratio of p-polarized to s-polarized radiance signals, which can be expressed as,

Polarized emissivity,

shown in Fig. 1. Let n1, n2, and n3 be 1.0, 1.45, and 3.65 at k = 0.9 lm [11–12]. The extinction coefficients of both the oxide film and the silicon wafer are negligible at k = 0.9 lm near room temperature. The directional polarized emissivity ep(s)(h1) of the silicon wafer in a direction h1 can be derived from the following equations [9,13]:

EpðsÞ ðTÞ : EpðsÞ;b ðTÞ

p( 1)

0.8 0.6 0.4

s ( 1)

Simulated m

0.2 0.0

0

20

40 Angle,

60

80

1

Fig. 2. Simulated directional polarized emissivity of a bare silicon wafer (d = 0 nm) at k = 0.9 lm.

T. Iuchi, A. Gogami / Measurement 43 (2010) 645–651

Polarized emissivity,

p(s) (θ1)

1.0 0.8

Rps -

p

relation

Rps -

s

relation

0.6 0.4

Simulated θ1=70 , λ

0.2 0

1

1.5

2

2.5

Ratio of polarized radiances, Rps

3

Fig. 3. Simulated relationships between Rps and ep(s)(h1) at h1 = 70° and k = 0.9 lm.

Table 1 Measurement conditions for experiments. Specimen n-type silicon wafer, (100) plane Dimensions: 0.75 mm thick and 76.2 mm diameter (3 in.) Resistivity: q = 0.01, 1, and 2000 X cm Oxide film (SiO2) thickness: d = 30, 150, 350, 550, 750, and 950 nm Surface roughness: Ra = 0.03 lm (specular) Temperature T = 900–1000 K Wavelength k = 0.9 lm

Table 2 Relation between impurity concentration and resistivity of silicon wafers at room temperature. Resistivity (X cm)

Impurity concentration (cm3)

0.01 1

8  1019 6  1015

2000

3  1014

that measures directional polarized emissivity and a hybrid surface temperature sensor (see Fig. 5) that measures the surface temperature of a silicon wafer. The radiance emitted from an area 2 mm in diameter at the center of the specimen surface was divided into p- and s-polarized radiance by a polarizing beam-splitter cube (05FC 16 PB.7, Newport), transmitted through optical fibers, and finally detected by respective polarized radiometers (Si sensor, IR-FBWS-SP, Chino) sensitive at the wavelength of 0.9 lm [8]. The directional polarized emissivity, ep(s)(h1) in Eq. (12), which is the ratio of the specimen radiance to that of a blackbody at the same temperature, was continuously measured at angle h1, between 0° and 85° in accordance with the rotation of the supporting bar. A silicon wafer was placed on the heating furnace, and maintained at a high temperature between 900 and 1000 K by the temperature controller (KP1000, Chino). The surface temperature T of the silicon wafer was monitored by a hybrid surface temperature sensor, and the p- and s-polarized radiances Ep(T) and Es(T) were simultaneously measured

647

by polarized radiometers. The directional polarized emissivity ep(s)(h1) and the ratio Rps in Eqs. (12) and (13) were calculated using these signals, respectively. Fig. 5 shows a schematic diagram of the newly developed hybrid surface temperature sensor [10]. This sensor was based on the assumption that the temperature of the thin film was spatially uniform at any instant during the transient process [15]. The tip of the sensor includes a rectangular thin film of super alloy, Hastelloy (thickness: 30 lm, width: 5 mm, length: 17 mm) and a sapphire rod (diameter: 1.3 mm). Both ends of the thin metal film were supported by quartz plates, and its central portion, 5 mm in length, instantaneously contacted the surface of a silicon wafer. The thin film and the sapphire rod were closely spaced, with a gap of 1 mm. The radiant flux from the area (diameter: 2.2 mm) of the rear surface of the thin film was incident on the sapphire rod, and was transmitted through an optical fiber. The radiant flux was then detected as radiance signals by a compound sensor composed of Si and InGaAs detectors with sensitivities at 0.9 lm and 1.55 lm, respectively. When the emissivity of the rear surface of the film was known, the temperature of the film could be derived from the radiance signal. This enabled accurate determination of the surface temperature of the silicon wafer. The response time of the sensor was within 1 s, and the observable temperature range was 600–1000 K. We prepared many silicon wafers with different resistivities and oxide film thicknesses, as shown in Table 1, to study the reproducibility of the simulated emissivity results shown in Figs. 2 and 3. Fig. 6 shows the experimentally determined directional polarized emissivity ep(s)(h1) of a bare silicon wafer (d = 0 nm) with resistivity of q = 1 X cm at T = 1000 K and k = 0.9 lm. The simulated results are also shown in the figure, as dotted lines. Clearly, the experimental results correspond well to the simulations, except for angles above h1 = 85° because of technical limitations of the angle measurement. Fig. 7 shows simulated and experimental relationships between oxide film thickness d and polarized emissivity ep(s)(h1), for an experiment performed at a temperature of T = 1000 K, an angle of h1 = 30°, and a wavelength of k = 0.9 lm. Both p- and s-polarized emissivities in the simulated results were observed to change periodically with increasing film thickness. The experimental results, though there is limited experimental data available, showed behavior similar to the simulation. Fig. 8 shows another example of the measurement of the directional polarized emissivities of silicon wafers with different oxide film layers, d = 30 nm and 150 nm. Both the p- and s-polarized emissivities (ep(h1) and es(h1)) drastically changed with the oxide film thickness. These emissivity variations resulted in a high uncertainty in temperature measurement by conventional radiation thermometry. Fig. 9 shows the accumulated experimental results of directional polarized emissivities ep(s)(h1) of silicon wafers with different resistivities q from 0.01 to 2000 X cm, different temperatures T from 900 to 1000 K, but with the same oxide film thickness d of 30 nm. Both the p-polarized and s-polarized emissivities changed dramatically with the

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Hybrid-type surface temperature sensor

Compound sensor

Si & InGaAs Polarizer up and down Optical fiber n

1

Polarized radiometer Specimen 1=

Heater

0 ~ 85

Stepper motor Fig. 4. Experimental system for the measurement of polarized emissivity. The system was composed of a polarized radiometer and a hybrid surface temperature sensor.

Compound sensor

1.0

Si (λ = 0.9 μm)

Sapphire rod

Long pass filter

( φ1.3 mm)

InGaAs (λ = 1.55 μm)

Quartz plate 30 μm thick film

1 mm

45

Silicon wafer

5 mm

Polarized emissivity, ε

(θ ) p(s) 1

Fig. 5. Hybrid surface temperature sensor developed for the temperature calibration of silicon wafers.

1.0 0.8

εp

0.6 εs

0.4 0.2 0 0

d = 0 nm(bare) T = 1000 K ρ = 1 cm 30

Angle, θ 1

60

0.8 0.6 s

0.4

90

Fig. 6. Experimental and simulated results of directional polarized emissivities ep(s)(h1) of a bare silicon wafer (d = 0 nm).

angle h1, but the effects of resistivity q and temperature T on the emissivity were slight. Similar experiments were carried out for silicon wafers with different oxide films, from 30 to 950 nm thick. The directional polarized emissiv-

1 = 30 T = 1010 K

0.2 0

2.2 mm

Experimental Simulated

εp

p(s)

Optical fiber

Polarized emissivity,

Filter Half mirror

0

Experimental Simulated

200 400 600 Oxide film thickness d, nm

800

Fig. 7. Experimental and simulated relationships between oxide film thickness d and polarized emissivity ep(s)(h1 = 30°) of silicon wafers.

ity behaved as in Fig. 9 under the same oxide film thickness. Based on the above experimental results, we considered an emissivity-compensated radiation thermometry method. Fig. 10 shows experimental and simulated relationships between Rps, the ratio of the polarized radiance, and polarized emissivity ep(s)(h1) of silicon wafers at an angle h1 of 70°. Solid lines show simulated relations, and the circles and square points represent experimental data. These relations are valid over a wide range of resistivity from 0.01 to 2000 X cm, oxide film thicknesses from bare (d = 0 nm) to 950 nm, and temperatures from 900 to 1000 K. These results confirm that there is a one-to-one relationship between Rps and the p-polarized or s-polarized emissivities, despite wide variations of silicon wafer emissivity. Therefore, once the polarized radiance signals Ep (T) and Es (T) are measured and their ratio Rps is calculated, the p-polarized emissivity ep(h1) or the s-polarized emissivity es(h1) at angle h1 can be uniquely determined, resulting in an accurate temperature measurement. We obtained a lot of

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T. Iuchi, A. Gogami / Measurement 43 (2010) 645–651

1.0 Polarized emissivity, ε p(s) (θ1)

0.8

d = 150 nm

0.6

0.4

T = 1000 K ρ = 1 cm

0.2 0

(a) p-polarized 30

0

Angle, θ1

60

90

0.2

θ 1= 70

s-polarized

T = 900 ~ 1000 K ρ = 0.01 to 2000 cm d = 0 ~ 950 nm

0 0

0.5

1

1.5

2

2.5

3

3.5

Fig. 10. Experimental and simulated relationships between Rps and ep(s)(h1) of silicon wafers with wide range of resistivity and oxide film thickness at h1 = 70° and k = 0.9 lm.

0.8

d = 150 nm

0.6

specimen, and (b) the measurement principle utilizing the Rpsep(s)(h1) relation.

d = 30 nm

0.4

4.1. Hybrid surface temperature sensor

T = 1000 K ρ = 1 cm

0.2 0

(b) s-polarized 30

Angle, θ1

60

90

Fig. 8. Experimentally determined directional polarized emissivities ep(s)(h1) of a silicon wafers with different oxide film thicknesses (d = 30 and 150 nm).

1.0 Polarized emissivity, ε p(s) (θ1)

p-polarized

Ratio of polarized radiances, Rps

1.0

0

0.8 simulated

0.6

d = 30 nm

0.4

s-polarized emissivity, ε s (θ1)

p-polarized emissivity, ε p (θ1)

1.0

0.8

The uncertainty (a), of the hybrid surface temperature sensor was analyzed in detail [16]. Therefore, only the results were described here. The sources of uncertainty were fluctuations of the hybrid sensor, radiometer output repeatability, fluctuations of the silicon wafer surface at high temperature in air, emissivity variation of the pseudo-blackbody coating used to calibrate the hybrid surface temperature sensor, and fluctuations of the temperature distributions on the specimen surfaces. The combined uncertainty uh, due to the hybrid surface temperature sensor, was estimated to be 1.06 K.

p-polarized 4.2. Experimental relation realizing measurement principle

0.6 0.4

d = 30 nm, λ =0.9 µm T = 900 to 1000 K, ρ = 0.01, 1, 2000 cm

0.2

s-polarized

0 0

30

Angle, θ 1

60

90

Fig. 9. Experimentally determined directional polarized emissivity ep(s)(h1) of d = 30 nm silicon wafers with different resistivities (q and temperatures (T).

simulated and experimental Rpsep(s)(h1) relations by changing an angle h1. The angle h1 of 70° was a good choice, because the variation of the ratio Rps became large, resulting in a fine resolution.

4. Uncertainty of measurements The primary factors involved in the measurement uncertainty were (a) the hybrid surface temperature sensor used to monitor the surface temperature of the

The sources of uncertainty (b), the measurement principle (the Rpsep(s)(h1) relation), were mainly divided into two parts: (i) the polarized radiometer used to detect the p- and s-polarized radiances of silicon wafers, and (ii) deviation from the experimental relationship between the ratio of polarized radiances Rps and the polarized emissivity ep(s)(h1) (the Rpsep(s)(h1) relation). (i) The uncertainty of the polarized radiometer in Fig. 5 was composed of the output repeatability ur given by the manufacturer (Chino) and the temperature fluctuation ua in air. ur is specified as 0.70 K at 1000 K, and ua was measured to be 0.24 K at 1000 K. (ii) The uncertainty in the experimental relationship of the measurement principle was caused by deviations up, or us from the Rpsep(s )(h1) relation. The experimental relationships between Rps and ep(s)(h1) in Fig. 10 can be expressed as shown in Eqs. (14) and (15) for p- and s-polarizations, respectively, using the method of least squares, For p-polarization,

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ep ðh1 Þ ¼ 0:1019  Rps þ 0:6572;

ð14Þ

and for s-polarization,

es ðh1 Þ ¼ 0:0892  R3ps þ 0:6358  R2ps  1:6126  Rps þ 1:8281:

ð15Þ

The standard deviations Dep and Des of measured emissivities for p- and s-polarizations, were 0.016 and 0.010, respectively. The standard deviations up and us of converted temperatures originated from the emissivity deviations Dep and Des were calculated using the following equations [17],

upðsÞ ¼

1 DepðsÞ   T; n epðsÞ ðh1 Þ

5. Conclusions The emissivity behavior of silicon wafers was comprehensively investigated, using both simulation and experiment. Concluding remarks are as follows:

ð16Þ 1. Polarized emissivity of silicon wafers underwent large, cyclic changes with changing oxide film thickness, d.

c2 n¼ ; kT

ð17Þ

where c2 ð¼ 14388 lm  KÞ: Planck’s second constant. In calculating Eqs. (16) and (17), representative values of ep(h1) and es(h1) were taken as 0.85 and 0.45, respectively. up and us were calculated as 1.18 K and 1.39 K at T = 1000 K and k = 0.9 lm, respectively. 4.3. Other factors All measurement signals, including the polarized radiances of the radiometer and the hybrid surface temperature sensor, were transformed and processed by an A/D converter (Model NR-1000, Keyence) to obtain digital quantities at a resolution of 16 bits with a sampling rate of 100 ms. The uncertainties of the digitized signals were neglected, because the resolution was less than 0.1 K at reduced temperature. 4.4. Combined uncertainty The combined standard uncertainty uc of this method was calculated from Eq. (18), and the uncertainty budget for radiation thermometry based on the polarization technique is shown in Table 3,

uc ¼

The expanded uncertainty Uexpanded (k = 2) of the measurement principle was 3.52 K for p-polarization, and 3.80 K for s-polarization, respectively. The uncertainty of this radiation thermometry method will be greatly reduced, once improvements of the hybrid surface temperature sensor and the polarized radiometer are performed.

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u2h þ u2r þ u2a þ u2pðsÞ :

ð18Þ

Table 3 Uncertainty budget for the radiation thermometry method based on the polarization technique at T = 1000 K. Uncertainty source

ui/K

(a) Hybrid surface temperature sensor

uh = 1.06

(b) Measurement principle (i) Polarized radiometer output Temperature fluctuation in air (ii) Rpsep(s) relation Deviation of polarized emissivity

ur = 0.70 ua = 0.24 up = 1.18 us = 1.39

uc p-polarization s-polarization

1.76 1.90

Uexpanded (k = 2) p-polarization s-polarization

3.52 3.80

2. Experimentally observed polarized emissivities of silicon wafers having a wide range of resistivity q, from 0.01 to 2000 X cm, corresponded well with simulated emissivities at high temperatures over T = 900 K and a wavelength of k = 0.9 lm. This means that the resistivity relevant to doped impurity concentration did not affect the emissivity of silicon wafers over 900 K. 3. Emissivity-compensated radiation thermometry using the relationship between the ratio of polarized radiances (Rps) and polarized emissivity (ep(s)(h1)) is very promising. Currently, the expanded uncertainty (k = 2) of the method is estimated to be 3.52 K for p-polarization use, and 3.80 K for s-polarization use, for temperatures above 900 K, irrespective of large emissivity variations and wide changes of resistivity. 4. The hybrid surface temperature sensor was very useful for calibration of the surface temperature of silicon wafers, although further improvement is necessary. 5. In order to apply this method to a real semiconductor process, the intense background radiation noise from heating sources, such as lamp heaters, must be mitigated. This problem is under study. Acknowledgements The authors would like to express their thanks to K. Hiraka at Chino Corp. for his contributions to this study during his time as a graduate student at Toyo University. The present research was supported in part by the Ministry of Education, Science, Sports and Culture through a Grand-in-Aid for Scientific Research (C) (Project Number 20560403) and as a ‘‘High-Tech Research Center” Project for Private Universities through matching funds from the Ministry of Education, Sports, Science, and Technology, 2004–2008. References [1] B.E. Adams, The challenges of temperature measurement in the semiconductor industry, in: TEMPMEKO 7th International Symposium, Delft, 1999, pp. 1–10. [2] R.L. Anderson, Review of temperature measurements in the semiconductor industry, in: Proceedings of TEMPERATURE, vol. 6, New York, 1992, pp. 1117–1122.

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