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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  1. The International Technology Roadmap for Semiconductors, 2011, Section “Starting Materials Technology Requirements,” Table FEP10, http://public.itrs.net .
  2. M. J. Jansen, H. Haitjema, and P. H. J. Schellekens, “A scanning wafer thickness and flatness interferometer,” Proc. SPIE5252, 334–345 (2004).
    [CrossRef]
  3. K. Freischlad, S. Tang, and J. Grenfell, “Interferometry for wafer dimensional metrology,” Proc. SPIE6672, 667202.1–6672021.4 (2007).
  4. K. Okada and J. Tsujiuchi, “Wavelength scanning interferometry for the measurement of both surface shapes and refractive index inhomogeneity,” Proc. SPIE1162, 395–401 (1989).
  5. 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]
  6. P. de Groot, “Measurement of transparent plates with wavelength-tuned phase-shifting interferometry,” Appl. Opt.39(16), 2658–2663 (2000).
    [CrossRef] [PubMed]
  7. L. L. Deck, “Multiple surface phase shifting interferometry,” Proc. SPIE4451, 424–431 (2001).
    [CrossRef]
  8. L. L. Deck, “Absolute distance measurements using FTPSI with a widely tunable IR laser,” Proc. SPIE4778, 218–226 (2002).
    [CrossRef]
  9. L. L. Deck, “Fourier-transform phase-shifting interferometry,” Appl. Opt.42(13), 2354–2365 (2003).
    [CrossRef] [PubMed]
  10. 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]
  11. 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. Express12(23), 5579–5594 (2004).
    [CrossRef] [PubMed]
  12. 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]
  13. 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]
  14. J. Jin, J. W. Kim, C.-S. Kang, J.-A. Kim, and T. B. Eom, “Thickness and refractive index measurements of a silicon wafer based on an optical comb,” Opt. Express18(17), 18339–18346 (2010).
    [CrossRef]
  15. R. E. Parks, L. Shao, A. Davies, and C. J. Evans, “Haidinger interferometer for silicon wafer TTV measurement,” Proc. SPIE4344, 496–505 (2001).
    [CrossRef]
  16. Q. Wang, U. Griesmann, and R. Polvani, “Interferometric thickness calibration of 300 mm silicon wafers,” Proc. SPIE6024, 602426.1–602426.5 (2005).
  17. 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]
  18. 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).
  19. F. Twyman and J. W. Perry, “Measuring small differences of refractive index,” Proc. Phys. Soc. Lond.34, 151 (1922).
    [CrossRef]
  20. 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]
  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).
    [CrossRef]
  22. F. E. Roberts and P. Langenbeck, “Homogeneity evaluation of very large disks,” Appl. Opt.8(11), 2311–2314 (1969).
    [CrossRef] [PubMed]
  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).
    [CrossRef] [PubMed]
  24. Y. Surrel, “Design of algorithms for phase measurements by the use of phase stepping,” Appl. Opt.35(1), 51–60 (1996).
    [CrossRef] [PubMed]
  25. Y. Surrel, “Fringe Analysis,” in P. K. Rastogi (Ed.), Photomechanics, Topics in Appl. Phys. 77, 52–102 (2000).
  26. 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).
  27. D. F. Edwards and E. Ochoa, “Infrared refractive index of silicon,” Appl. Opt.19(24), 4130–4131 (1980).
    [CrossRef] [PubMed]
  28. I. H. Malitson, “Interspecimen comparison of the refractive index of fused silica,” J. Opt. Soc. Am.55(10), 1205–1209 (1965).
    [CrossRef]
  29. 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]
  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. Actuators72(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. SPIE6672, 667202.1–6672021.4 (2007).

2005 (2)

Q. Wang, U. Griesmann, and R. Polvani, “Interferometric thickness calibration of 300 mm silicon wafers,” Proc. SPIE6024, 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. SPIE4778, 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. SPIE4344, 496–505 (2001).
[CrossRef]

L. L. Deck, “Multiple surface phase shifting interferometry,” Proc. SPIE4451, 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. Actuators72(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. SPIE1162, 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. SPIE4344, 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. SPIE4778, 218–226 (2002).
[CrossRef]

L. L. Deck, “Multiple surface phase shifting interferometry,” Proc. SPIE4451, 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. SPIE4344, 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. SPIE6672, 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. SPIE6672, 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. SPIE6024, 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. SPIE5252, 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. Express12(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. Actuators72(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. SPIE5252, 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. Actuators72(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. SPIE1162, 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. SPIE4344, 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. SPIE6024, 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. SPIE5252, 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. SPIE4344, 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. SPIE6672, 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. SPIE1162, 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. SPIE6024, 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. Actuators72(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. Actuators72(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. Actuators72(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. Actuators72(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)

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]

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]

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]

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

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

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]

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)

L. L. Deck, “Multiple surface phase shifting interferometry,” Proc. SPIE4451, 424–431 (2001).
[CrossRef]

L. L. Deck, “Absolute distance measurements using FTPSI with a widely tunable IR laser,” Proc. SPIE4778, 218–226 (2002).
[CrossRef]

R. E. Parks, L. Shao, A. Davies, and C. J. Evans, “Haidinger interferometer for silicon wafer TTV measurement,” Proc. SPIE4344, 496–505 (2001).
[CrossRef]

Q. Wang, U. Griesmann, and R. Polvani, “Interferometric thickness calibration of 300 mm silicon wafers,” Proc. SPIE6024, 602426.1–602426.5 (2005).

M. J. Jansen, H. Haitjema, and P. H. J. Schellekens, “A scanning wafer thickness and flatness interferometer,” Proc. SPIE5252, 334–345 (2004).
[CrossRef]

K. Freischlad, S. Tang, and J. Grenfell, “Interferometry for wafer dimensional metrology,” Proc. SPIE6672, 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. SPIE1162, 395–401 (1989).

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. Actuators72(1), 46–48 (1999).
[CrossRef]

Other (4)

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

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).

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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