Abstract

With the development of microelectronics, the demand for silicon wafers is greatly increased for various purposes, especially the use of thin wafers for smart cards, cellular phones and stacked packages. In this paper, we describe an innovative scheme of combining wavelength scanning interferometry (4 nm tuning range centered at 1550 nm) with spectroscopic reflectometry that enables us to measure the thickness profile of thin wafers below 100 μm with high thickness resolution. The performance of this method is compared with that of an existing technique and verified by measuring several thin wafers.

© 2010 OSA

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References

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  1. M. J. Jansen, H. Haitjema, and P. H. J. Schellekens, “A scanning wafer thickness and flatness interferometer,” Proc. SPIE 5856, 334–345 (2004).
    [CrossRef]
  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]
  3. L. L. Deck, “Multiple surface phase shifting interferometry,” Proc. SPIE 4451, 424–431 (2001).
    [CrossRef]
  4. Y.-S. Ghim and S.-W. Kim, “Fast, precise, tomographic measurements of thin films,” Appl. Phys. Lett. 91(9), 091903 (2007).
    [CrossRef]
  5. Y.-S. Ghim and S.-W. Kim, “Spectrally resolved white-light interferometry for 3D inspection of a thin-film layer structure,” Appl. Opt. 48(4), 799–803 (2009).
    [CrossRef] [PubMed]
  6. L. L. Deck, “Absolute distance measurements using FTPSI with a widely tunable IR laser,” Proc. SPIE 4778, 218–226 (2002).
    [CrossRef]
  7. L. L. Deck, C. V. Peski, and R. Eandi, “Measurements of hard pellicles for 157 nm lithography using Fourier transform phase-shifting interferometry,” Proc. SPIE 5130, 555–559 (2003).
    [CrossRef]
  8. A. Suratkar, Y.-S. Ghim, and A. Davies, “Uncertainty analysis on the absolute thickness of a cavity using a commercial wavelength scanning interferometer,” Proc. SPIE 7063, 70630R (2008).
    [CrossRef]
  9. This is the Zygo VeriFire MSTTM ( http://www.zygo.com/?/met/interferometers/verifire/mst ).
  10. C. M. Herzinger, B. Johs, W. A. McGahan, J. A. Woollam, and W. Paulson, “Ellipsometric determination of optical constants for silicon and thermally grown silicon dioxide via a multi-sample, multi-wavelength, multi-angle investigation,” J. Appl. Phys. 83(6), 3323–3336 (1998).
    [CrossRef]
  11. H. G. Tompkins, and W. A. McGahan, Spectroscopic Ellipsometry and Reflectometry: A User’s Guide (John Wiley & Sons. Inc, 1999).
  12. A. Suratkar, Absolute distance (thickness) metrology using wavelength scanning interferometry (UNC Chralotte, 2009).
  13. The Levenberg-Marquardt function is available as LEASTSQ in the MATLAB software.
  14. L. L. Deck, “Fourier-transform phase-shifting interferometry,” Appl. Opt. 42(13), 2354–2365 (2003).
    [CrossRef] [PubMed]

2009

2008

A. Suratkar, Y.-S. Ghim, and A. Davies, “Uncertainty analysis on the absolute thickness of a cavity using a commercial wavelength scanning interferometer,” Proc. SPIE 7063, 70630R (2008).
[CrossRef]

2007

Y.-S. Ghim and S.-W. Kim, “Fast, precise, tomographic measurements of thin films,” Appl. Phys. Lett. 91(9), 091903 (2007).
[CrossRef]

2004

M. J. Jansen, H. Haitjema, and P. H. J. Schellekens, “A scanning wafer thickness and flatness interferometer,” Proc. SPIE 5856, 334–345 (2004).
[CrossRef]

2003

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, C. V. Peski, and R. Eandi, “Measurements of hard pellicles for 157 nm lithography using Fourier transform phase-shifting interferometry,” Proc. SPIE 5130, 555–559 (2003).
[CrossRef]

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

2002

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

2001

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

1998

C. M. Herzinger, B. Johs, W. A. McGahan, J. A. Woollam, and W. Paulson, “Ellipsometric determination of optical constants for silicon and thermally grown silicon dioxide via a multi-sample, multi-wavelength, multi-angle investigation,” J. Appl. Phys. 83(6), 3323–3336 (1998).
[CrossRef]

Davies, A.

A. Suratkar, Y.-S. Ghim, and A. Davies, “Uncertainty analysis on the absolute thickness of a cavity using a commercial wavelength scanning interferometer,” Proc. SPIE 7063, 70630R (2008).
[CrossRef]

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]

Deck, L. L.

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

L. L. Deck, C. V. Peski, and R. Eandi, “Measurements of hard pellicles for 157 nm lithography using Fourier transform phase-shifting interferometry,” Proc. SPIE 5130, 555–559 (2003).
[CrossRef]

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]

Eandi, R.

L. L. Deck, C. V. Peski, and R. Eandi, “Measurements of hard pellicles for 157 nm lithography using Fourier transform phase-shifting interferometry,” Proc. SPIE 5130, 555–559 (2003).
[CrossRef]

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]

Ghim, Y.-S.

Y.-S. Ghim and S.-W. Kim, “Spectrally resolved white-light interferometry for 3D inspection of a thin-film layer structure,” Appl. Opt. 48(4), 799–803 (2009).
[CrossRef] [PubMed]

A. Suratkar, Y.-S. Ghim, and A. Davies, “Uncertainty analysis on the absolute thickness of a cavity using a commercial wavelength scanning interferometer,” Proc. SPIE 7063, 70630R (2008).
[CrossRef]

Y.-S. Ghim and S.-W. Kim, “Fast, precise, tomographic measurements of thin films,” Appl. Phys. Lett. 91(9), 091903 (2007).
[CrossRef]

Haitjema, H.

M. J. Jansen, H. Haitjema, and P. H. J. Schellekens, “A scanning wafer thickness and flatness interferometer,” Proc. SPIE 5856, 334–345 (2004).
[CrossRef]

Herzinger, C. M.

C. M. Herzinger, B. Johs, W. A. McGahan, J. A. Woollam, and W. Paulson, “Ellipsometric determination of optical constants for silicon and thermally grown silicon dioxide via a multi-sample, multi-wavelength, multi-angle investigation,” J. Appl. Phys. 83(6), 3323–3336 (1998).
[CrossRef]

Jansen, M. J.

M. J. Jansen, H. Haitjema, and P. H. J. Schellekens, “A scanning wafer thickness and flatness interferometer,” Proc. SPIE 5856, 334–345 (2004).
[CrossRef]

Johs, B.

C. M. Herzinger, B. Johs, W. A. McGahan, J. A. Woollam, and W. Paulson, “Ellipsometric determination of optical constants for silicon and thermally grown silicon dioxide via a multi-sample, multi-wavelength, multi-angle investigation,” J. Appl. Phys. 83(6), 3323–3336 (1998).
[CrossRef]

Kim, S.-W.

McGahan, W. A.

C. M. Herzinger, B. Johs, W. A. McGahan, J. A. Woollam, and W. Paulson, “Ellipsometric determination of optical constants for silicon and thermally grown silicon dioxide via a multi-sample, multi-wavelength, multi-angle investigation,” J. Appl. Phys. 83(6), 3323–3336 (1998).
[CrossRef]

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]

Paulson, W.

C. M. Herzinger, B. Johs, W. A. McGahan, J. A. Woollam, and W. Paulson, “Ellipsometric determination of optical constants for silicon and thermally grown silicon dioxide via a multi-sample, multi-wavelength, multi-angle investigation,” J. Appl. Phys. 83(6), 3323–3336 (1998).
[CrossRef]

Peski, C. V.

L. L. Deck, C. V. Peski, and R. Eandi, “Measurements of hard pellicles for 157 nm lithography using Fourier transform phase-shifting interferometry,” Proc. SPIE 5130, 555–559 (2003).
[CrossRef]

Schellekens, P. H. J.

M. J. Jansen, H. Haitjema, and P. H. J. Schellekens, “A scanning wafer thickness and flatness interferometer,” Proc. SPIE 5856, 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]

Suratkar, A.

A. Suratkar, Y.-S. Ghim, and A. Davies, “Uncertainty analysis on the absolute thickness of a cavity using a commercial wavelength scanning interferometer,” Proc. SPIE 7063, 70630R (2008).
[CrossRef]

Woollam, J. A.

C. M. Herzinger, B. Johs, W. A. McGahan, J. A. Woollam, and W. Paulson, “Ellipsometric determination of optical constants for silicon and thermally grown silicon dioxide via a multi-sample, multi-wavelength, multi-angle investigation,” J. Appl. Phys. 83(6), 3323–3336 (1998).
[CrossRef]

Appl. Opt.

Appl. Phys. Lett.

Y.-S. Ghim and S.-W. Kim, “Fast, precise, tomographic measurements of thin films,” Appl. Phys. Lett. 91(9), 091903 (2007).
[CrossRef]

J. Appl. Phys.

C. M. Herzinger, B. Johs, W. A. McGahan, J. A. Woollam, and W. Paulson, “Ellipsometric determination of optical constants for silicon and thermally grown silicon dioxide via a multi-sample, multi-wavelength, multi-angle investigation,” J. Appl. Phys. 83(6), 3323–3336 (1998).
[CrossRef]

Opt. Eng.

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]

Proc. SPIE

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

M. J. Jansen, H. Haitjema, and P. H. J. Schellekens, “A scanning wafer thickness and flatness interferometer,” Proc. SPIE 5856, 334–345 (2004).
[CrossRef]

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

L. L. Deck, C. V. Peski, and R. Eandi, “Measurements of hard pellicles for 157 nm lithography using Fourier transform phase-shifting interferometry,” Proc. SPIE 5130, 555–559 (2003).
[CrossRef]

A. Suratkar, Y.-S. Ghim, and A. Davies, “Uncertainty analysis on the absolute thickness of a cavity using a commercial wavelength scanning interferometer,” Proc. SPIE 7063, 70630R (2008).
[CrossRef]

Other

This is the Zygo VeriFire MSTTM ( http://www.zygo.com/?/met/interferometers/verifire/mst ).

H. G. Tompkins, and W. A. McGahan, Spectroscopic Ellipsometry and Reflectometry: A User’s Guide (John Wiley & Sons. Inc, 1999).

A. Suratkar, Absolute distance (thickness) metrology using wavelength scanning interferometry (UNC Chralotte, 2009).

The Levenberg-Marquardt function is available as LEASTSQ in the MATLAB software.

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Figures (6)

Fig. 1
Fig. 1

(a) A schematic diagram of wavelength scanning interferometer for measuring of characteristics of a wafer; BS: beam splitter, CL: collimating lens, IL: imaging lens, CCD: charge coupled device, (b) single-side polished wafer as a reference, and (c) double-side polished wafer as a specimen.

Fig. 2
Fig. 2

Plot of real and simulation data using the optimization technique: (a) merit function ζ(d) and its lower envelope vs. thickness value with a 4 nm tuning range (real data), (b) the lower envelope of merit function ζ(d) vs. thickness value according to the tuning range; black: 4 nm tuning range, red: 30 nm tuning range, blue: 100 nm tuning range (simulation).

Fig. 3
Fig. 3

Simulation results for a 4 nm tuning range in the merit function: (a) the true thickness profile (black) and estimated thickness profile (red) and (b) the true thickness profile (black) and unwrapped thickness profile (red).

Fig. 4
Fig. 4

Comparisons of measurement results: (a) an interferogram of a wafer with ~200 μm thickness viewed in monochromatic light, (b) the relative thickness map of (a) measured with the MST using the Fourier method, (c) the absolute thickness map of (a) measured with the proposed method and (d) the difference between our measurement and the MST Fourier measurement, after removing the average absolute thickness from our measurement (1 pixel = 110 μm).

Fig. 5
Fig. 5

Simulation results: (a) the interferogram and structure of the virtual wafer with ~200 μm thickness, (b) the error map of the virtual wafer measured with Fourier technique, (c) the error map of the virtual wafer measured with our proposed technique, (d) the simulated PV of the error maps of the virtual wafer using the two methods as the tuning range of source is increased.

Fig. 6
Fig. 6

An exemplary measurement result: (a) an interferogram of specimen with ~60 μm thickness viewed in monochromatic light and (b) 3-D thickness map profile, 1 pixel=100 μm.

Tables (1)

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Table 1 Uncertainty Estimates

Equations (2)

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T ( d ; k ) sam = | r [ 1 exp ( j2 k n d ) ] 1 r 2 exp ( j2 k n d ) | 2
ζ ( d ) = i = 1 N | T i ( d ; k i ) sam E i ( k i ) sam | m

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