Abstract

We have proposed a modified method to improve the measurement uncertainty of the geometrical thickness and refractive index of a silicon wafer. Because measurement resolution based on Fourier domain analysis depends on the spectral bandwidth of a light source directly, a femtosecond pulse laser having the broad spectral bandwidth of about 100 nm was adopted as a new light source. A phase detection algorithm in Fourier domain was also modified to minimize the effect related to environmental disturbance. Since the wide spectral bandwidth may cause a dispersion effect in the optical parts of the proposed interferometer, it was considered carefully through numerical simulations. In conclusion, the measurement uncertainty of geometrical thickness was estimated to be 48 nm for a double-polished silicon wafer having the geometrical thickness of 320.7 μm, which was an improvement of about 20 times that obtained by the previous method.

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References

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  1. Y. Zhang, P. Parikh, P. Golubtsov, B. Stephenson, M. Bonsaver, J. Lee, and M. Hoffman, "Wafer shape measurement and its influence on chemical mechanical planarization," in Proceedings of the First International Symposium on Chemical Mechanical Planarization, I. Ali and S. Raghavan, eds. (The Electrochemical Society, Pennington, New Jersey, 1997), pp. 91-96.
  2. 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(Part 1, No. 1A), 38–39 (1999).
    [CrossRef]
  3. G. Coppola, P. Ferraro, M. Iodice, and S. De Nicola, “Method for measuring the refractive index and the thickness of transparent plates with a lateral-shear, wavelength-scanning interferometer,” Appl. Opt. 42(19), 3882–3887 (2003).
    [CrossRef] [PubMed]
  4. P. Maddaloni, G. Coppola, P. De Natale, S. De Nicola, P. Ferraro, M. Gioffre, and M. Iodice, “Thickness measurement of thin transparent plates with a broad-band wavelength scanning interferometer,” IEEE Photon. Technol. Lett. 16(5), 1349–1351 (2004).
    [CrossRef]
  5. G. D. Gillen and S. Guha, “Use of Michelson and Fabry-Perot interferometry for independent determination of the refractive index and physical thickness of wafers,” Appl. Opt. 44(3), 344–347 (2005).
    [CrossRef] [PubMed]
  6. J. Jin, J. W. Kim, C.-S. Kang, J.-A. Kim, and T. B. Eom, “Thickness and refractive index measurement of a silicon wafer based on an optical comb,” Opt. Express 18(17), 18339–18346 (2010).
    [CrossRef] [PubMed]
  7. 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]
  8. D. F. Edwards and E. Ochoa, “Infrared refractive index of silicon,” Appl. Opt. 19(24), 4130–4131 (1980).
    [CrossRef] [PubMed]

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)

2004 (1)

P. Maddaloni, G. Coppola, P. De Natale, S. De Nicola, P. Ferraro, M. Gioffre, and M. Iodice, “Thickness measurement of thin transparent plates with a broad-band wavelength scanning interferometer,” IEEE Photon. Technol. Lett. 16(5), 1349–1351 (2004).
[CrossRef]

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(Part 1, No. 1A), 38–39 (1999).
[CrossRef]

1980 (1)

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.

P. Maddaloni, G. Coppola, P. De Natale, S. De Nicola, P. Ferraro, M. Gioffre, and M. Iodice, “Thickness measurement of thin transparent plates with a broad-band wavelength scanning interferometer,” IEEE Photon. Technol. Lett. 16(5), 1349–1351 (2004).
[CrossRef]

G. Coppola, P. Ferraro, M. Iodice, and S. De Nicola, “Method for measuring the refractive index and the thickness of transparent plates with a lateral-shear, wavelength-scanning interferometer,” Appl. Opt. 42(19), 3882–3887 (2003).
[CrossRef] [PubMed]

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(Part 1, No. 1A), 38–39 (1999).
[CrossRef]

De Natale, P.

P. Maddaloni, G. Coppola, P. De Natale, S. De Nicola, P. Ferraro, M. Gioffre, and M. Iodice, “Thickness measurement of thin transparent plates with a broad-band wavelength scanning interferometer,” IEEE Photon. Technol. Lett. 16(5), 1349–1351 (2004).
[CrossRef]

De Nicola, S.

P. Maddaloni, G. Coppola, P. De Natale, S. De Nicola, P. Ferraro, M. Gioffre, and M. Iodice, “Thickness measurement of thin transparent plates with a broad-band wavelength scanning interferometer,” IEEE Photon. Technol. Lett. 16(5), 1349–1351 (2004).
[CrossRef]

G. Coppola, P. Ferraro, M. Iodice, and S. De Nicola, “Method for measuring the refractive index and the thickness of transparent plates with a lateral-shear, wavelength-scanning interferometer,” Appl. Opt. 42(19), 3882–3887 (2003).
[CrossRef] [PubMed]

Edwards, D. F.

Eom, T. B.

Ferraro, P.

P. Maddaloni, G. Coppola, P. De Natale, S. De Nicola, P. Ferraro, M. Gioffre, and M. Iodice, “Thickness measurement of thin transparent plates with a broad-band wavelength scanning interferometer,” IEEE Photon. Technol. Lett. 16(5), 1349–1351 (2004).
[CrossRef]

G. Coppola, P. Ferraro, M. Iodice, and S. De Nicola, “Method for measuring the refractive index and the thickness of transparent plates with a lateral-shear, wavelength-scanning interferometer,” Appl. Opt. 42(19), 3882–3887 (2003).
[CrossRef] [PubMed]

Gillen, G. D.

Gioffre, M.

P. Maddaloni, G. Coppola, P. De Natale, S. De Nicola, P. Ferraro, M. Gioffre, and M. Iodice, “Thickness measurement of thin transparent plates with a broad-band wavelength scanning interferometer,” IEEE Photon. Technol. Lett. 16(5), 1349–1351 (2004).
[CrossRef]

Guha, S.

Iodice, M.

P. Maddaloni, G. Coppola, P. De Natale, S. De Nicola, P. Ferraro, M. Gioffre, and M. Iodice, “Thickness measurement of thin transparent plates with a broad-band wavelength scanning interferometer,” IEEE Photon. Technol. Lett. 16(5), 1349–1351 (2004).
[CrossRef]

G. Coppola, P. Ferraro, M. Iodice, and S. De Nicola, “Method for measuring the refractive index and the thickness of transparent plates with a lateral-shear, wavelength-scanning interferometer,” Appl. Opt. 42(19), 3882–3887 (2003).
[CrossRef] [PubMed]

Jin, J.

Kang, C.-S.

J. Jin, J. W. Kim, C.-S. Kang, J.-A. Kim, and T. B. Eom, “Thickness and refractive index measurement of a silicon wafer based on an optical comb,” Opt. Express 18(17), 18339–18346 (2010).
[CrossRef] [PubMed]

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]

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(Part 1, No. 1A), 38–39 (1999).
[CrossRef]

Maddaloni, P.

P. Maddaloni, G. Coppola, P. De Natale, S. De Nicola, P. Ferraro, M. Gioffre, and M. Iodice, “Thickness measurement of thin transparent plates with a broad-band wavelength scanning interferometer,” IEEE Photon. Technol. Lett. 16(5), 1349–1351 (2004).
[CrossRef]

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]

Ochoa, E.

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(Part 1, No. 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]

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(Part 1, No. 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)

IEEE Photon. Technol. Lett. (1)

P. Maddaloni, G. Coppola, P. De Natale, S. De Nicola, P. Ferraro, M. Gioffre, and M. Iodice, “Thickness measurement of thin transparent plates with a broad-band wavelength scanning interferometer,” IEEE Photon. Technol. Lett. 16(5), 1349–1351 (2004).
[CrossRef]

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(Part 1, No. 1A), 38–39 (1999).
[CrossRef]

Opt. Express (1)

Other (1)

Y. Zhang, P. Parikh, P. Golubtsov, B. Stephenson, M. Bonsaver, J. Lee, and M. Hoffman, "Wafer shape measurement and its influence on chemical mechanical planarization," in Proceedings of the First International Symposium on Chemical Mechanical Planarization, I. Ali and S. Raghavan, eds. (The Electrochemical Society, Pennington, New Jersey, 1997), pp. 91-96.

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Figures (5)

Fig. 1
Fig. 1

Optical layout of the proposed measurement system of geometrical thickness and refractive index of a silicon wafer using a femtosecond pulse laser having a spectral bandwidth of over 100 nm.

Fig. 2
Fig. 2

(a) Full spectrum envelope of the femtosecond pulse laser, (b) the optical comb of the femtosecond pulse laser having mode spacing of 50 GHz (~0.4 nm) after the Febry-Perot filter.

Fig. 3
Fig. 3

Fourier transformed results of two interference spectra, (a) Ray 1 and (b) Ray 2.

Fig. 4
Fig. 4

Phase versus wave vector graph for three optical path differences, L1, L2, and L3.

Fig. 5
Fig. 5

Simulation results about peak shift caused by dispersion effect: (a) peak shift of L2, (b) peak shift of L3.

Tables (2)

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Table 1 Measurement results of a silicon wafer

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Table 2 Uncertainty budget

Equations (8)

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I( f,L )= I 0 (f){ 1+cos( 2πf L c ) }= I 0 (f){ 1+cosφ( f,L ) }
Δt= 1 NΔf
φ( f,L )=Im{ ln( I ( f,L ) ) }
L= c 2π dφ df = dφ dk
T= L 2 ( L 3 L 1 )
N= L 2 T
u( T )= i=1 3 ( T L i ) 2 u 2 ( L i )+2 i=1 2 j=i+1 3 ( T L i )( T L j )u( L i , L j )
u( L i , L j )=r( L i , L j )u( L i )u( L j )

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