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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 18 — Aug. 27, 2012
  • pp: 20078–20089

Modified Roberts-Langenbeck test for measuring thickness and refractive index variation of silicon wafers

Jungjae Park, Lingfeng Chen, Quandou Wang, and Ulf Griesmann  »View Author Affiliations

Optics Express, Vol. 20, Issue 18, pp. 20078-20089 (2012)

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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

OCIS Codes
(120.0120) Instrumentation, measurement, and metrology : Instrumentation, measurement, and metrology
(120.3180) Instrumentation, measurement, and metrology : Interferometry
(120.4630) Instrumentation, measurement, and metrology : Optical inspection
(140.3070) Lasers and laser optics : Infrared and far-infrared lasers
(160.6000) Materials : Semiconductor materials

ToC Category:
Instrumentation, Measurement, and Metrology

Original Manuscript: May 22, 2012
Revised Manuscript: July 18, 2012
Manuscript Accepted: July 20, 2012
Published: August 17, 2012

Jungjae Park, Lingfeng Chen, Quandou Wang, and Ulf Griesmann, "Modified Roberts-Langenbeck test for measuring thickness and refractive index variation of silicon wafers," Opt. Express 20, 20078-20089 (2012)

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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).

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