Abstract

We developed an optical interferometric probe for measuring the geometrical thickness and refractive index of silicon wafers based on a Fizeau-type spectral-domain interferometer, as realized by adopting the optical fiber components of a circulator and a sheet-type beam splitter. The proposed method enables us to achieve a much simpler optical composition and higher immunity to air fluctuations owing to the use of fiber components and a common-path configuration as compared to a bulk-type optical configuration. A femtosecond pulse laser having a spectral bandwidth of 80 nm at a center wavelength of 1.55 µm and an optical spectrum analyzer having a wavelength uncertainty of 0.02 nm were used to acquire multiple interference signals in the frequency domain without a mechanical phase-shifting process. Among the many peaks in the Fourier-transformed signals of the measured interferograms, only three interference signals representing three different optical path differences were selected to extract both the geometrical thickness and group refractive index of a silicon wafer simultaneously. A single point on a double-sided polished silicon wafer was measured 90 times repetitively every two seconds. The geometrical thickness and group refractive index were found to be 476.89 µm and 3.6084, respectively. The measured thickness is in good agreement with that of a contact type method within the expanded uncertainty of contact-type instruments. Through an uncertainty evaluation of the proposed method, the expanded uncertainty of the geometrical thickness was estimated to be 0.12 µm (k = 2).

© 2014 Optical Society of America

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References

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2014 (1)

H.-J. Lee and K.-N. Joo, “Optical interferometric approach for measuring the geometrical dimension and refractive index profiles of a double-sided polished undoped Si wafer,” Meas. Sci. Technol. 25(7), 075202 (2014).
[Crossref]

2013 (1)

J. Park, J. Jin, J. W. Kim, and J.-A. Kim, “Measurement of thickness profile and refractive index variation of a silicon wafer using the optical comb of a femtosecond pulse laser,” Opt. Commun. 305(15), 170–174 (2013).
[Crossref]

2012 (3)

2010 (1)

2009 (1)

G. Nam, C.-S. Kang, H.-Y. So, and J. Choi, “An uncertainty evaluation for multiple measurements by GUM, III: using a correlation coefficient,” Accredit. Qual. Assur. 14(1), 43–47 (2009).
[Crossref]

2005 (1)

2003 (1)

1999 (1)

M. Kimura, Y. Saito, H. Daio, and K. Yakushiji, “A new method for the precise measurement of wafer roll off of silicon polished wafer,” Jpn. J. Appl. Phys. 38(1A), 38–39 (1999).
[Crossref]

1995 (1)

1991 (1)

Chen, L.

Choi, J.

G. Nam, C.-S. Kang, H.-Y. So, and J. Choi, “An uncertainty evaluation for multiple measurements by GUM, III: using a correlation coefficient,” Accredit. Qual. Assur. 14(1), 43–47 (2009).
[Crossref]

Coppola, G.

Daio, H.

M. Kimura, Y. Saito, H. Daio, and K. Yakushiji, “A new method for the precise measurement of wafer roll off of silicon polished wafer,” Jpn. J. Appl. Phys. 38(1A), 38–39 (1999).
[Crossref]

De Nicola, S.

Eom, T. B.

Ferraro, P.

Gillen, G. D.

Griesmann, U.

Guha, S.

Iodice, M.

Jin, J.

Joo, K.-N.

H.-J. Lee and K.-N. Joo, “Optical interferometric approach for measuring the geometrical dimension and refractive index profiles of a double-sided polished undoped Si wafer,” Meas. Sci. Technol. 25(7), 075202 (2014).
[Crossref]

Kang, C.-S.

Kim, J. W.

Kim, J.-A.

Kimura, M.

M. Kimura, Y. Saito, H. Daio, and K. Yakushiji, “A new method for the precise measurement of wafer roll off of silicon polished wafer,” Jpn. J. Appl. Phys. 38(1A), 38–39 (1999).
[Crossref]

Kumar, V. N.

Lee, H.-J.

H.-J. Lee and K.-N. Joo, “Optical interferometric approach for measuring the geometrical dimension and refractive index profiles of a double-sided polished undoped Si wafer,” Meas. Sci. Technol. 25(7), 075202 (2014).
[Crossref]

Lee, S.

Maeng, S.

Nam, G.

G. Nam, C.-S. Kang, H.-Y. So, and J. Choi, “An uncertainty evaluation for multiple measurements by GUM, III: using a correlation coefficient,” Accredit. Qual. Assur. 14(1), 43–47 (2009).
[Crossref]

O, B.

Park, J.

Rao, D. N.

Saito, Y.

M. Kimura, Y. Saito, H. Daio, and K. Yakushiji, “A new method for the precise measurement of wafer roll off of silicon polished wafer,” Jpn. J. Appl. Phys. 38(1A), 38–39 (1999).
[Crossref]

So, H.-Y.

G. Nam, C.-S. Kang, H.-Y. So, and J. Choi, “An uncertainty evaluation for multiple measurements by GUM, III: using a correlation coefficient,” Accredit. Qual. Assur. 14(1), 43–47 (2009).
[Crossref]

Suematsu, M.

Takeda, M.

Wang, Q.

Yakushiji, K.

M. Kimura, Y. Saito, H. Daio, and K. Yakushiji, “A new method for the precise measurement of wafer roll off of silicon polished wafer,” Jpn. J. Appl. Phys. 38(1A), 38–39 (1999).
[Crossref]

Accredit. Qual. Assur. (1)

G. Nam, C.-S. Kang, H.-Y. So, and J. Choi, “An uncertainty evaluation for multiple measurements by GUM, III: using a correlation coefficient,” Accredit. Qual. Assur. 14(1), 43–47 (2009).
[Crossref]

Appl. Opt. (3)

J. Opt. Soc. Am. B (1)

Jpn. J. Appl. Phys. (1)

M. Kimura, Y. Saito, H. Daio, and K. Yakushiji, “A new method for the precise measurement of wafer roll off of silicon polished wafer,” Jpn. J. Appl. Phys. 38(1A), 38–39 (1999).
[Crossref]

Meas. Sci. Technol. (1)

H.-J. Lee and K.-N. Joo, “Optical interferometric approach for measuring the geometrical dimension and refractive index profiles of a double-sided polished undoped Si wafer,” Meas. Sci. Technol. 25(7), 075202 (2014).
[Crossref]

Opt. Commun. (1)

J. Park, J. Jin, J. W. Kim, and J.-A. Kim, “Measurement of thickness profile and refractive index variation of a silicon wafer using the optical comb of a femtosecond pulse laser,” Opt. Commun. 305(15), 170–174 (2013).
[Crossref]

Opt. Express (4)

Other (1)

Guide to the expression of uncertainty in measurement, (International organization for standardization, 1993).

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Figures (3)

Fig. 1
Fig. 1 Optical layout of the Michelson’s type interferometer.
Fig. 2
Fig. 2 Optical layouts and images of the Fizeau-type interferometer used to measure the geometrical thickness and group refractive index of a silicon wafer (C: circulator, CL: collimating lens, BS: sheet-type beam splitter, M: mirror); (a) optical layout without a silicon wafer, (b) optical layout with a silicon wafer, (c) Top view image of the experimental setup, and (d) Image of the optical probe part.
Fig. 3
Fig. 3 Interference spectra and its Fourier transform: (a) interference spectrum obtained without a silicon wafer, (b) Fourier transformed data of the interference spectrum (a), (c) interference spectrum obtained with a silicon wafer, and (d) Fourier transformed data of the interference spectrum (c).

Tables (1)

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Table 1 Uncertainty Evaluation of T = 476.89 μm

Equations (4)

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I ( z ) = 1 2 I 0 [ 1 + cos ( 2 π c d f ) ] = 1 2 I 0 [ 1 + cos φ ( z ) ]
d = c 2 π | d φ ( f ) d f |
T = O P D 1 O P D 2 + O P D 3
N = O P D 3 / T

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