Abstract

We describe a method to simultaneously measure thickness variation and refractive index homogeneity of 300 mm diameter silicon wafers using a wavelength-shifting Fizeau interferometer operating at 1550 nm. Only three measurements are required, corresponding to three different cavity configurations. A customized phase shifting algorithm is used to suppress several high order harmonics and minimize intensity sampling errors. The new method was tested with both silicon and fused silica wafers and measurement results proved to be highly repeatable. The reliability of the method was further verified by comparing the measured thickness variation of a 150 mm diameter wafer to a measurement of the wafer flatness after bonding the wafer to an optical flat.

© 2012 OSA

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    [CrossRef] [PubMed]
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  8. L. L. Deck, “Absolute distance measurements using FTPSI with a widely tunable IR laser,” Proc. SPIE 4778, 218–226 (2002).
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    [CrossRef] [PubMed]
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  21. P. F. Forman, “A Note on possible errors due to thickness variations in testing nominally parallel plates,” Appl. Opt. 3(5), 646–647 (1964).
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  22. F. E. Roberts and P. Langenbeck, “Homogeneity evaluation of very large disks,” Appl. Opt. 8(11), 2311–2314 (1969).
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  23. J. Schwider, R. Burow, K.-E. Elssner, R. Spolaczyk, and J. Grzanna, “Homogeneity testing by phase sampling interferometry,” Appl. Opt. 24(18), 3059–3061 (1985).
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    [CrossRef] [PubMed]
  30. U. Gösele and Q.-Y. Tong, “Semiconductor wafer bonding,” Annu. Rev. Mater. Sci. 28(1), 215–241 (1998).
    [CrossRef]
  31. V. Greco, F. Marchesini, and G. Molesini, “Optical contact and van der Waals interactions: the role of the surface topography in determining the bonding strength of thick glass plates,” J. Opt. A, Pure Appl. Opt. 3(1), 85–88 (2001).
    [CrossRef]
  32. Z.-X. Xiao, G.-Y. Wu, Z.-H. Li, G.-B. Zhang, Y.-L. Hao, and Y.-Y. Wang, “Silicon-glass wafer bonding with silicon hydrophilic fusion bonding technology,” Sens. Actuators 72(1), 46–48 (1999).
    [CrossRef]
  33. H. Moriceau, F. Rieutord, F. Fournel, Y. Le Tice, L. Di Cioccio, C. Morales, A. M. Charvet, and C. Deguet, “Overview of recent direct wafer bonding advances and applications,” Adv. Nat. Sci.: Nanosci. Nanotechnol. 1(043004), 1–11 (2010).

2010 (3)

2007 (2)

J. Burke, K. Hibino, R. Hanayama, and B. F. Oreb, “Simultaneous measurement of several near-parallel surfaces with wavelength-shifting interferometry and a tunable phase-shifting method,” Opt. Lasers Eng. 45(2), 326–341 (2007).
[CrossRef]

K. Freischlad, S. Tang, and J. Grenfell, “Interferometry for wafer dimensional metrology,” Proc. SPIE 6672, 667202.1–6672021.4 (2007).

2005 (2)

Q. Wang, U. Griesmann, and R. Polvani, “Interferometric thickness calibration of 300 mm silicon wafers,” Proc. SPIE 6024, 602426.1–602426.5 (2005).

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]

2004 (3)

2003 (2)

T. L. Schmitz, A. Davies, C. J. Evans, and R. E. Parks, “Silicon wafer thickness variation measurements using the National Institute of Standards and Technology infrared interferometer,” Opt. Eng. 42(8), 2281–2290 (2003).
[CrossRef]

L. L. Deck, “Fourier-transform phase-shifting interferometry,” Appl. Opt. 42(13), 2354–2365 (2003).
[CrossRef] [PubMed]

2002 (1)

L. L. Deck, “Absolute distance measurements using FTPSI with a widely tunable IR laser,” Proc. SPIE 4778, 218–226 (2002).
[CrossRef]

2001 (3)

R. E. Parks, L. Shao, A. Davies, and C. J. Evans, “Haidinger interferometer for silicon wafer TTV measurement,” Proc. SPIE 4344, 496–505 (2001).
[CrossRef]

L. L. Deck, “Multiple surface phase shifting interferometry,” Proc. SPIE 4451, 424–431 (2001).
[CrossRef]

V. Greco, F. Marchesini, and G. Molesini, “Optical contact and van der Waals interactions: the role of the surface topography in determining the bonding strength of thick glass plates,” J. Opt. A, Pure Appl. Opt. 3(1), 85–88 (2001).
[CrossRef]

2000 (1)

1999 (1)

Z.-X. Xiao, G.-Y. Wu, Z.-H. Li, G.-B. Zhang, Y.-L. Hao, and Y.-Y. Wang, “Silicon-glass wafer bonding with silicon hydrophilic fusion bonding technology,” Sens. Actuators 72(1), 46–48 (1999).
[CrossRef]

1998 (1)

U. Gösele and Q.-Y. Tong, “Semiconductor wafer bonding,” Annu. Rev. Mater. Sci. 28(1), 215–241 (1998).
[CrossRef]

1996 (1)

1990 (1)

1989 (1)

K. Okada and J. Tsujiuchi, “Wavelength scanning interferometry for the measurement of both surface shapes and refractive index inhomogeneity,” Proc. SPIE 1162, 395–401 (1989).

1985 (1)

1980 (1)

1969 (1)

1965 (1)

1964 (1)

1963 (1)

1922 (1)

F. Twyman and J. W. Perry, “Measuring small differences of refractive index,” Proc. Phys. Soc. Lond. 34, 151 (1922).
[CrossRef]

Benck, E. C.

Burke, J.

Burow, R.

Charvet, A. M.

H. Moriceau, F. Rieutord, F. Fournel, Y. Le Tice, L. Di Cioccio, C. Morales, A. M. Charvet, and C. Deguet, “Overview of recent direct wafer bonding advances and applications,” Adv. Nat. Sci.: Nanosci. Nanotechnol. 1(043004), 1–11 (2010).

Chu, J.

Davies, A.

T. L. Schmitz, A. Davies, C. J. Evans, and R. E. Parks, “Silicon wafer thickness variation measurements using the National Institute of Standards and Technology infrared interferometer,” Opt. Eng. 42(8), 2281–2290 (2003).
[CrossRef]

R. E. Parks, L. Shao, A. Davies, and C. J. Evans, “Haidinger interferometer for silicon wafer TTV measurement,” Proc. SPIE 4344, 496–505 (2001).
[CrossRef]

de Groot, P.

Deck, L. L.

L. L. Deck, “Fourier-transform phase-shifting interferometry,” Appl. Opt. 42(13), 2354–2365 (2003).
[CrossRef] [PubMed]

L. L. Deck, “Absolute distance measurements using FTPSI with a widely tunable IR laser,” Proc. SPIE 4778, 218–226 (2002).
[CrossRef]

L. L. Deck, “Multiple surface phase shifting interferometry,” Proc. SPIE 4451, 424–431 (2001).
[CrossRef]

Deguet, C.

H. Moriceau, F. Rieutord, F. Fournel, Y. Le Tice, L. Di Cioccio, C. Morales, A. M. Charvet, and C. Deguet, “Overview of recent direct wafer bonding advances and applications,” Adv. Nat. Sci.: Nanosci. Nanotechnol. 1(043004), 1–11 (2010).

Di Cioccio, L.

H. Moriceau, F. Rieutord, F. Fournel, Y. Le Tice, L. Di Cioccio, C. Morales, A. M. Charvet, and C. Deguet, “Overview of recent direct wafer bonding advances and applications,” Adv. Nat. Sci.: Nanosci. Nanotechnol. 1(043004), 1–11 (2010).

Edwards, D. F.

Elssner, K.-E.

Eom, T. B.

Evans, C. J.

T. L. Schmitz, A. Davies, C. J. Evans, and R. E. Parks, “Silicon wafer thickness variation measurements using the National Institute of Standards and Technology infrared interferometer,” Opt. Eng. 42(8), 2281–2290 (2003).
[CrossRef]

R. E. Parks, L. Shao, A. Davies, and C. J. Evans, “Haidinger interferometer for silicon wafer TTV measurement,” Proc. SPIE 4344, 496–505 (2001).
[CrossRef]

Fairman, P. S.

Forman, P. F.

Fournel, F.

H. Moriceau, F. Rieutord, F. Fournel, Y. Le Tice, L. Di Cioccio, C. Morales, A. M. Charvet, and C. Deguet, “Overview of recent direct wafer bonding advances and applications,” Adv. Nat. Sci.: Nanosci. Nanotechnol. 1(043004), 1–11 (2010).

Freischlad, K.

K. Freischlad, S. Tang, and J. Grenfell, “Interferometry for wafer dimensional metrology,” Proc. SPIE 6672, 667202.1–6672021.4 (2007).

Gillen, G. D.

Gösele, U.

U. Gösele and Q.-Y. Tong, “Semiconductor wafer bonding,” Annu. Rev. Mater. Sci. 28(1), 215–241 (1998).
[CrossRef]

Greco, V.

V. Greco, F. Marchesini, and G. Molesini, “Optical contact and van der Waals interactions: the role of the surface topography in determining the bonding strength of thick glass plates,” J. Opt. A, Pure Appl. Opt. 3(1), 85–88 (2001).
[CrossRef]

Grenfell, J.

K. Freischlad, S. Tang, and J. Grenfell, “Interferometry for wafer dimensional metrology,” Proc. SPIE 6672, 667202.1–6672021.4 (2007).

Griesmann, U.

J. Chu, U. Griesmann, Q. Wang, J. A. Soons, and E. C. Benck, “Deformation-free form error measurement of thin, plane-parallel optics floated on a heavy liquid,” Appl. Opt. 49(10), 1849–1858 (2010).
[CrossRef] [PubMed]

Q. Wang, U. Griesmann, and R. Polvani, “Interferometric thickness calibration of 300 mm silicon wafers,” Proc. SPIE 6024, 602426.1–602426.5 (2005).

Grzanna, J.

Guha, S.

Haitjema, H.

M. J. Jansen, H. Haitjema, and P. H. J. Schellekens, “A scanning wafer thickness and flatness interferometer,” Proc. SPIE 5252, 334–345 (2004).
[CrossRef]

Hanayama, R.

J. Burke, K. Hibino, R. Hanayama, and B. F. Oreb, “Simultaneous measurement of several near-parallel surfaces with wavelength-shifting interferometry and a tunable phase-shifting method,” Opt. Lasers Eng. 45(2), 326–341 (2007).
[CrossRef]

K. Hibino, R. Hanayama, J. Burke, and B. F. Oreb, “Tunable phase-extraction formulae for simultaneous shape measurement of multiple surfaces with wavelength-shifting interferometry,” Opt. Express 12(23), 5579–5594 (2004).
[CrossRef] [PubMed]

Hao, Y.-L.

Z.-X. Xiao, G.-Y. Wu, Z.-H. Li, G.-B. Zhang, Y.-L. Hao, and Y.-Y. Wang, “Silicon-glass wafer bonding with silicon hydrophilic fusion bonding technology,” Sens. Actuators 72(1), 46–48 (1999).
[CrossRef]

Hibino, K.

Jansen, M. J.

M. J. Jansen, H. Haitjema, and P. H. J. Schellekens, “A scanning wafer thickness and flatness interferometer,” Proc. SPIE 5252, 334–345 (2004).
[CrossRef]

Jin, J.

Kang, C.-S.

Kim, J. W.

Kim, J.-A.

Langenbeck, P.

Le Tice, Y.

H. Moriceau, F. Rieutord, F. Fournel, Y. Le Tice, L. Di Cioccio, C. Morales, A. M. Charvet, and C. Deguet, “Overview of recent direct wafer bonding advances and applications,” Adv. Nat. Sci.: Nanosci. Nanotechnol. 1(043004), 1–11 (2010).

Li, Z.-H.

Z.-X. Xiao, G.-Y. Wu, Z.-H. Li, G.-B. Zhang, Y.-L. Hao, and Y.-Y. Wang, “Silicon-glass wafer bonding with silicon hydrophilic fusion bonding technology,” Sens. Actuators 72(1), 46–48 (1999).
[CrossRef]

Malitson, I. H.

Marchesini, F.

V. Greco, F. Marchesini, and G. Molesini, “Optical contact and van der Waals interactions: the role of the surface topography in determining the bonding strength of thick glass plates,” J. Opt. A, Pure Appl. Opt. 3(1), 85–88 (2001).
[CrossRef]

Molesini, G.

V. Greco, F. Marchesini, and G. Molesini, “Optical contact and van der Waals interactions: the role of the surface topography in determining the bonding strength of thick glass plates,” J. Opt. A, Pure Appl. Opt. 3(1), 85–88 (2001).
[CrossRef]

Morales, C.

H. Moriceau, F. Rieutord, F. Fournel, Y. Le Tice, L. Di Cioccio, C. Morales, A. M. Charvet, and C. Deguet, “Overview of recent direct wafer bonding advances and applications,” Adv. Nat. Sci.: Nanosci. Nanotechnol. 1(043004), 1–11 (2010).

Moriceau, H.

H. Moriceau, F. Rieutord, F. Fournel, Y. Le Tice, L. Di Cioccio, C. Morales, A. M. Charvet, and C. Deguet, “Overview of recent direct wafer bonding advances and applications,” Adv. Nat. Sci.: Nanosci. Nanotechnol. 1(043004), 1–11 (2010).

Murty, M. V. R. K.

Ochoa, E.

Okada, K.

K. Okada, H. Sakuta, T. Ose, and J. Tsujiuchi, “Separate measurements of surface shapes and refractive index inhomogeneity of an optical element using tunable-source phase shifting interferometry,” Appl. Opt. 29(22), 3280–3285 (1990).
[CrossRef] [PubMed]

K. Okada and J. Tsujiuchi, “Wavelength scanning interferometry for the measurement of both surface shapes and refractive index inhomogeneity,” Proc. SPIE 1162, 395–401 (1989).

Oreb, B. F.

Ose, T.

Parks, R. E.

T. L. Schmitz, A. Davies, C. J. Evans, and R. E. Parks, “Silicon wafer thickness variation measurements using the National Institute of Standards and Technology infrared interferometer,” Opt. Eng. 42(8), 2281–2290 (2003).
[CrossRef]

R. E. Parks, L. Shao, A. Davies, and C. J. Evans, “Haidinger interferometer for silicon wafer TTV measurement,” Proc. SPIE 4344, 496–505 (2001).
[CrossRef]

Perry, J. W.

F. Twyman and J. W. Perry, “Measuring small differences of refractive index,” Proc. Phys. Soc. Lond. 34, 151 (1922).
[CrossRef]

Polvani, R.

Q. Wang, U. Griesmann, and R. Polvani, “Interferometric thickness calibration of 300 mm silicon wafers,” Proc. SPIE 6024, 602426.1–602426.5 (2005).

Rieutord, F.

H. Moriceau, F. Rieutord, F. Fournel, Y. Le Tice, L. Di Cioccio, C. Morales, A. M. Charvet, and C. Deguet, “Overview of recent direct wafer bonding advances and applications,” Adv. Nat. Sci.: Nanosci. Nanotechnol. 1(043004), 1–11 (2010).

Roberts, F. E.

Sakuta, H.

Schellekens, P. H. J.

M. J. Jansen, H. Haitjema, and P. H. J. Schellekens, “A scanning wafer thickness and flatness interferometer,” Proc. SPIE 5252, 334–345 (2004).
[CrossRef]

Schmitz, T. L.

T. L. Schmitz, A. Davies, C. J. Evans, and R. E. Parks, “Silicon wafer thickness variation measurements using the National Institute of Standards and Technology infrared interferometer,” Opt. Eng. 42(8), 2281–2290 (2003).
[CrossRef]

Schwider, J.

Shao, L.

R. E. Parks, L. Shao, A. Davies, and C. J. Evans, “Haidinger interferometer for silicon wafer TTV measurement,” Proc. SPIE 4344, 496–505 (2001).
[CrossRef]

Soons, J. A.

Spolaczyk, R.

Surrel, Y.

Tang, S.

K. Freischlad, S. Tang, and J. Grenfell, “Interferometry for wafer dimensional metrology,” Proc. SPIE 6672, 667202.1–6672021.4 (2007).

Tong, Q.-Y.

U. Gösele and Q.-Y. Tong, “Semiconductor wafer bonding,” Annu. Rev. Mater. Sci. 28(1), 215–241 (1998).
[CrossRef]

Tsujiuchi, J.

K. Okada, H. Sakuta, T. Ose, and J. Tsujiuchi, “Separate measurements of surface shapes and refractive index inhomogeneity of an optical element using tunable-source phase shifting interferometry,” Appl. Opt. 29(22), 3280–3285 (1990).
[CrossRef] [PubMed]

K. Okada and J. Tsujiuchi, “Wavelength scanning interferometry for the measurement of both surface shapes and refractive index inhomogeneity,” Proc. SPIE 1162, 395–401 (1989).

Twyman, F.

F. Twyman and J. W. Perry, “Measuring small differences of refractive index,” Proc. Phys. Soc. Lond. 34, 151 (1922).
[CrossRef]

Wang, Q.

J. Chu, U. Griesmann, Q. Wang, J. A. Soons, and E. C. Benck, “Deformation-free form error measurement of thin, plane-parallel optics floated on a heavy liquid,” Appl. Opt. 49(10), 1849–1858 (2010).
[CrossRef] [PubMed]

Q. Wang, U. Griesmann, and R. Polvani, “Interferometric thickness calibration of 300 mm silicon wafers,” Proc. SPIE 6024, 602426.1–602426.5 (2005).

Wang, Y.-Y.

Z.-X. Xiao, G.-Y. Wu, Z.-H. Li, G.-B. Zhang, Y.-L. Hao, and Y.-Y. Wang, “Silicon-glass wafer bonding with silicon hydrophilic fusion bonding technology,” Sens. Actuators 72(1), 46–48 (1999).
[CrossRef]

Wu, G.-Y.

Z.-X. Xiao, G.-Y. Wu, Z.-H. Li, G.-B. Zhang, Y.-L. Hao, and Y.-Y. Wang, “Silicon-glass wafer bonding with silicon hydrophilic fusion bonding technology,” Sens. Actuators 72(1), 46–48 (1999).
[CrossRef]

Xiao, Z.-X.

Z.-X. Xiao, G.-Y. Wu, Z.-H. Li, G.-B. Zhang, Y.-L. Hao, and Y.-Y. Wang, “Silicon-glass wafer bonding with silicon hydrophilic fusion bonding technology,” Sens. Actuators 72(1), 46–48 (1999).
[CrossRef]

Zhang, G.-B.

Z.-X. Xiao, G.-Y. Wu, Z.-H. Li, G.-B. Zhang, Y.-L. Hao, and Y.-Y. Wang, “Silicon-glass wafer bonding with silicon hydrophilic fusion bonding technology,” Sens. Actuators 72(1), 46–48 (1999).
[CrossRef]

Adv. Nat. Sci.: Nanosci. Nanotechnol. (1)

H. Moriceau, F. Rieutord, F. Fournel, Y. Le Tice, L. Di Cioccio, C. Morales, A. M. Charvet, and C. Deguet, “Overview of recent direct wafer bonding advances and applications,” Adv. Nat. Sci.: Nanosci. Nanotechnol. 1(043004), 1–11 (2010).

Annu. Rev. Mater. Sci. (1)

U. Gösele and Q.-Y. Tong, “Semiconductor wafer bonding,” Annu. Rev. Mater. Sci. 28(1), 215–241 (1998).
[CrossRef]

Appl. Opt. (12)

F. E. Roberts and P. Langenbeck, “Homogeneity evaluation of very large disks,” Appl. Opt. 8(11), 2311–2314 (1969).
[CrossRef] [PubMed]

J. Schwider, R. Burow, K.-E. Elssner, R. Spolaczyk, and J. Grzanna, “Homogeneity testing by phase sampling interferometry,” Appl. Opt. 24(18), 3059–3061 (1985).
[CrossRef] [PubMed]

K. Okada, H. Sakuta, T. Ose, and J. Tsujiuchi, “Separate measurements of surface shapes and refractive index inhomogeneity of an optical element using tunable-source phase shifting interferometry,” Appl. Opt. 29(22), 3280–3285 (1990).
[CrossRef] [PubMed]

Y. Surrel, “Design of algorithms for phase measurements by the use of phase stepping,” Appl. Opt. 35(1), 51–60 (1996).
[CrossRef] [PubMed]

P. de Groot, “Measurement of transparent plates with wavelength-tuned phase-shifting interferometry,” Appl. Opt. 39(16), 2658–2663 (2000).
[CrossRef] [PubMed]

L. L. Deck, “Fourier-transform phase-shifting interferometry,” Appl. Opt. 42(13), 2354–2365 (2003).
[CrossRef] [PubMed]

K. Hibino, B. F. Oreb, P. S. Fairman, and J. Burke, “Simultaneous measurement of surface shape and variation in optical thickness of a transparent parallel plate in wavelength-scanning Fizeau interferometer,” Appl. Opt. 43(6), 1241–1249 (2004).
[CrossRef] [PubMed]

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]

M. V. R. K. Murty, “A Note on the testing of homogeneity of large-aperture parallel plates of glass,” Appl. Opt. 2(12), 1337–1339 (1963).
[CrossRef]

P. F. Forman, “A Note on possible errors due to thickness variations in testing nominally parallel plates,” Appl. Opt. 3(5), 646–647 (1964).
[CrossRef]

D. F. Edwards and E. Ochoa, “Infrared refractive index of silicon,” Appl. Opt. 19(24), 4130–4131 (1980).
[CrossRef] [PubMed]

J. Chu, U. Griesmann, Q. Wang, J. A. Soons, and E. C. Benck, “Deformation-free form error measurement of thin, plane-parallel optics floated on a heavy liquid,” Appl. Opt. 49(10), 1849–1858 (2010).
[CrossRef] [PubMed]

J. Opt. A, Pure Appl. Opt. (1)

V. Greco, F. Marchesini, and G. Molesini, “Optical contact and van der Waals interactions: the role of the surface topography in determining the bonding strength of thick glass plates,” J. Opt. A, Pure Appl. Opt. 3(1), 85–88 (2001).
[CrossRef]

J. Opt. Soc. Am. (1)

Opt. Eng. (1)

T. L. Schmitz, A. Davies, C. J. Evans, and R. E. Parks, “Silicon wafer thickness variation measurements using the National Institute of Standards and Technology infrared interferometer,” Opt. Eng. 42(8), 2281–2290 (2003).
[CrossRef]

Opt. Express (2)

Opt. Lasers Eng. (1)

J. Burke, K. Hibino, R. Hanayama, and B. F. Oreb, “Simultaneous measurement of several near-parallel surfaces with wavelength-shifting interferometry and a tunable phase-shifting method,” Opt. Lasers Eng. 45(2), 326–341 (2007).
[CrossRef]

Proc. Phys. Soc. Lond. (1)

F. Twyman and J. W. Perry, “Measuring small differences of refractive index,” Proc. Phys. Soc. Lond. 34, 151 (1922).
[CrossRef]

Proc. SPIE (7)

M. J. Jansen, H. Haitjema, and P. H. J. Schellekens, “A scanning wafer thickness and flatness interferometer,” Proc. SPIE 5252, 334–345 (2004).
[CrossRef]

K. Freischlad, S. Tang, and J. Grenfell, “Interferometry for wafer dimensional metrology,” Proc. SPIE 6672, 667202.1–6672021.4 (2007).

K. Okada and J. Tsujiuchi, “Wavelength scanning interferometry for the measurement of both surface shapes and refractive index inhomogeneity,” Proc. SPIE 1162, 395–401 (1989).

L. L. Deck, “Multiple surface phase shifting interferometry,” Proc. SPIE 4451, 424–431 (2001).
[CrossRef]

L. L. Deck, “Absolute distance measurements using FTPSI with a widely tunable IR laser,” Proc. SPIE 4778, 218–226 (2002).
[CrossRef]

R. E. Parks, L. Shao, A. Davies, and C. J. Evans, “Haidinger interferometer for silicon wafer TTV measurement,” Proc. SPIE 4344, 496–505 (2001).
[CrossRef]

Q. Wang, U. Griesmann, and R. Polvani, “Interferometric thickness calibration of 300 mm silicon wafers,” Proc. SPIE 6024, 602426.1–602426.5 (2005).

Sens. Actuators (1)

Z.-X. Xiao, G.-Y. Wu, Z.-H. Li, G.-B. Zhang, Y.-L. Hao, and Y.-Y. Wang, “Silicon-glass wafer bonding with silicon hydrophilic fusion bonding technology,” Sens. Actuators 72(1), 46–48 (1999).
[CrossRef]

Other (4)

Y. Surrel, “Fringe Analysis,” in P. K. Rastogi (Ed.), Photomechanics, Topics in Appl. Phys. 77, 52–102 (2000).

U. Griesmann, “A toolbox for designing and analyzing phase-shifting interferometry algorithms with characteristic polynomials,” in Optical Fabrication and Testing, OSA Technical Digest (CD), Optical Society of America, paper OMA2 (2010).

The International Technology Roadmap for Semiconductors, 2011, Section “Starting Materials Technology Requirements,” Table FEP10, http://public.itrs.net .

U. Griesmann, Q. Wang, M. Tricard, P. Dumas, and C. Hall, “Manufacture and metrology of 300 mm silicon wafers with ultra-low thickness variation,” in Proceedings of AIP Conference931, 105–110 (2007).

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Figures (9)

Fig. 1
Fig. 1

Schematic representation of the original Roberts-Langenbeck test: (a) front surface measurement with both surfaces coated, (b) back surface measurement after removal of the front surface coating, (c) transmission measurement after removal of coatings. A fourth measurement of the empty cavity is also required.

Fig. 2
Fig. 2

Schematic representation of the three measurements: (a) wafer cavity (measurement 1), (b) wafer transmission (measurement 2), (c) empty cavity (measurement 3).

Fig. 3
Fig. 3

Experimental setup for 300 mm wafer metrology based on the NIST IR3 interferometer.

Fig. 4
Fig. 4

Phase shifted intensity sampled at a single pixel of a silicon wafer cavity (a) wavelength scanning result with high sampling resolution, (b) sampled intensity data at 13 equally spaced wavelengths.

Fig. 5
Fig. 5

Three OPD measurement results of a 300 mm glass wafer ((a)-(c)) and silicon wafer ((d)-(f)): (a) W1, (b) W2, (c) W3, (d) W1, (e) W2, (f) W3.

Fig. 6
Fig. 6

Measurement results for thickness variation and refractive index variation of a glass wafer ((a)-(c)) and a silicon wafer ((d)-(f)): (a) thickness variation, (b) refractive index variation, (c) mid cross-section profile in (a) and (b), (d) thickness variation, (e) refractive index variation, (f) mid cross-section profile in (d) and (e). The best-fit constant gradient has been removed from all results.

Fig. 7
Fig. 7

Thickness variation comparison between two cases with and without refractive index variation: (a) glass wafer, (b) silicon wafer.

Fig. 8
Fig. 8

Wafer status before (a) and after (b) optical contact to a Zerodur flat.

Fig. 9
Fig. 9

Thickness variation results of a 150 mm silicon wafer: (a) modified Roberts-Langenbeck method, (b) bonded wafer, (c) comparison between the two results for a mid cross-section profile.

Tables (1)

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Table 1 Uncertainty Budget

Equations (6)

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W 1 ( x,y )=2Δ( n( x,y )t( x,y ) ) W 2 ( x,y )=2Δ{ ( 1n( x,y ) )t( x,y ) }+2( z 3 ( x,y )+ z 4 ( x,y ) ) =2Δt( x,y )2Δ( n( x,y )t( x,y ) )+2( z 3 ( x,y )+ z 4 ( x,y ) ) W 3 ( x,y )=2{ z 3 ( x,y )+ z 4 ( x,y ) }
t( x,y )= t 0 +Δt( x,y ) = t 0 + z 1 ( x,y )+ z 2 ( x,y ) n( x,y )= n 0 +Δn( x,y )
Δt= 1 2 [ W 1 +( W 2 W 3 ) ] Δn= 1 2 t 0 [ ( 1 n 0 ) W 1 n 0 ( W 2 W 3 ) ]
t 0 = ( Δφ ) λ 0 2 4π( Δλ ) n 0 = 4π ( 1550.47× 10 9 ) 2 4π×0.89× 10 9 ×3.4871 774.59μm
u( Δt )= 1 2 u 2 ( W 1 )+ u 2 ( W 2 )+ u 2 ( W 3 )
u( Δn )= ( ( Δn ) n 0 ) 2 u 2 ( n 0 )+ ( ( Δn ) t 0 ) 2 u 2 ( t 0 )+ k=1 3 ( Δn W k ) 2 u 2 ( W k )

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