Abstract

An interference fringe modulation skewing effect in white-light vertical scanning interferometry that can produce a batwings artifact in a step height measurement is described. The skewing occurs at a position on or close to the edge of a step in the sample under measurement when the step height is less than the coherence length of the light source used. A diffraction model is used to explain the effect.

© 2000 Optical Society of America

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References

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  1. N. Balsubramanian, “Optical system for surface topography measurement,” U.S. patent4,340,306 (20July1982).
  2. M. Davidson, K. Kaufman, I. Mazor, F. Cohen, “An application of interference microscope to integrated circuit inspection and metrology,” in Integrated Circuit Microscopy: Inspection and Process Control, K. M. Monahan, ed., Proc. SPIE775, 233–247 (1987).
  3. B. S. Lee, T. C. Strand, “Profilometry with a coherence scanning microscope,” Appl. Opt. 29, 3784–3788 (1990).
    [CrossRef] [PubMed]
  4. G. S. Kino, S. S. C. Chim, “Mirau correlation microscope,” Appl. Opt. 32, 3438–3783 (1990).
  5. D. K. Cohen, P. J. Caber, C. P. Brophy, “Rough surface profiler and method,” U.S. patent5,133,601 (28July1992).
  6. S. S. C. Chim, G. S. Kino, “Three-dimensional image realization in interference microscopy,” Appl. Opt. 31, 2550–2553 (1992).
    [CrossRef] [PubMed]
  7. P. J. Caber, “Interferometric profiler for rough surfaces,” Appl. Opt. 32, 3438–3441 (1993).
    [CrossRef] [PubMed]
  8. L. Deck, P. de Groot, “High-speed noncontact profiler based on scanning white-light interferometry,” Appl. Opt. 33, 7334–7338 (1994).
    [CrossRef] [PubMed]
  9. P. Hariharan, M. Roy, “White-light phase-stepping interferometry: measurement of the fractional interference order,” J. Mod. Opt. 42, 2357–2360 (1995).
    [CrossRef]
  10. K. G. Larkin, “Effective nonlinear algorithm for envelop detection in white light interferometry,” J. Opt. Soc. Am. A 13, 832–843 (1996).
    [CrossRef]
  11. J. C. Wyant, J. Schmit, “Computerized interferometric measurement of surface microstructure,” in Optical Inspection and Micromeasurements, C. Gorecki, ed., Proc. SPIE2782, 26–37 (1996).
    [CrossRef]
  12. P. Sandoz, “Wavelet transform as a processing tool in white-light interferometry,” Opt. Lett. 22, 1065–1067 (1997).
    [CrossRef] [PubMed]
  13. P. Sandoz, R. Devillers, A. Plata, “Unambiguous profilometry by fringe-order identification in white-light phase-shifting interferometry,” J. Mod. Opt. 44, 519–534 (1997).
    [CrossRef]
  14. R. J. Recknagel, G. Notni, “Analysis of white light interferograms using wavelet methods,” Opt. Commun. 148, 122–128 (1998).
    [CrossRef]
  15. M. Hart, D. G. Vass, M. L. Begbie, “Fast surface profiling by spectral analysis of white-light interferograms with Fourier transform spectroscopy,” Appl. Opt. 37, 1764–1769 (1998).
    [CrossRef]
  16. A. Harasaki, J. Schmit, J. C. Wyant, “Improved vertical- scanning interferometry,” Appl. Opt. 39, 2107–2115.
  17. Estimating the centroid of function m(i)[x, y] = {I(i)[x, y] - I(i - 1)[x, y]}2 gives the surface height h[x, y] at lateral position [x, y], where I(i)[x, y] is the intensity of vertical scanning position i in a correlogram for scanning steps of 90° and 270°. It can easily be shown that z¯=∑i imix, y∑i mix, y=h+Γ′4/λcos2π4/λh2πΓ0+Γ4/λsin2π4/λh for the symmetric coherence function, where Γ and Γ′ are the Fourier transform of the coherence function and its first derivative, respectively, and λ̅ is the mean wavelength of the white-light source. From knowledge of the coherence function we know that the second term is very small; thus the centroid of function m(i) is a good estimator of surface height h.
  18. A. Jendral, O. Bryngdahl, “Synthetic near-field holograms with localized information,” Opt. Lett. 20, 1204–1206 (1995).
    [CrossRef] [PubMed]

1998 (2)

1997 (2)

P. Sandoz, “Wavelet transform as a processing tool in white-light interferometry,” Opt. Lett. 22, 1065–1067 (1997).
[CrossRef] [PubMed]

P. Sandoz, R. Devillers, A. Plata, “Unambiguous profilometry by fringe-order identification in white-light phase-shifting interferometry,” J. Mod. Opt. 44, 519–534 (1997).
[CrossRef]

1996 (1)

1995 (2)

A. Jendral, O. Bryngdahl, “Synthetic near-field holograms with localized information,” Opt. Lett. 20, 1204–1206 (1995).
[CrossRef] [PubMed]

P. Hariharan, M. Roy, “White-light phase-stepping interferometry: measurement of the fractional interference order,” J. Mod. Opt. 42, 2357–2360 (1995).
[CrossRef]

1994 (1)

1993 (1)

1992 (1)

1990 (2)

Balsubramanian, N.

N. Balsubramanian, “Optical system for surface topography measurement,” U.S. patent4,340,306 (20July1982).

Begbie, M. L.

Brophy, C. P.

D. K. Cohen, P. J. Caber, C. P. Brophy, “Rough surface profiler and method,” U.S. patent5,133,601 (28July1992).

Bryngdahl, O.

Caber, P. J.

P. J. Caber, “Interferometric profiler for rough surfaces,” Appl. Opt. 32, 3438–3441 (1993).
[CrossRef] [PubMed]

D. K. Cohen, P. J. Caber, C. P. Brophy, “Rough surface profiler and method,” U.S. patent5,133,601 (28July1992).

Chim, S. S. C.

Cohen, D. K.

D. K. Cohen, P. J. Caber, C. P. Brophy, “Rough surface profiler and method,” U.S. patent5,133,601 (28July1992).

Cohen, F.

M. Davidson, K. Kaufman, I. Mazor, F. Cohen, “An application of interference microscope to integrated circuit inspection and metrology,” in Integrated Circuit Microscopy: Inspection and Process Control, K. M. Monahan, ed., Proc. SPIE775, 233–247 (1987).

Davidson, M.

M. Davidson, K. Kaufman, I. Mazor, F. Cohen, “An application of interference microscope to integrated circuit inspection and metrology,” in Integrated Circuit Microscopy: Inspection and Process Control, K. M. Monahan, ed., Proc. SPIE775, 233–247 (1987).

de Groot, P.

Deck, L.

Devillers, R.

P. Sandoz, R. Devillers, A. Plata, “Unambiguous profilometry by fringe-order identification in white-light phase-shifting interferometry,” J. Mod. Opt. 44, 519–534 (1997).
[CrossRef]

Harasaki, A.

Hariharan, P.

P. Hariharan, M. Roy, “White-light phase-stepping interferometry: measurement of the fractional interference order,” J. Mod. Opt. 42, 2357–2360 (1995).
[CrossRef]

Hart, M.

Jendral, A.

Kaufman, K.

M. Davidson, K. Kaufman, I. Mazor, F. Cohen, “An application of interference microscope to integrated circuit inspection and metrology,” in Integrated Circuit Microscopy: Inspection and Process Control, K. M. Monahan, ed., Proc. SPIE775, 233–247 (1987).

Kino, G. S.

Larkin, K. G.

Lee, B. S.

Mazor, I.

M. Davidson, K. Kaufman, I. Mazor, F. Cohen, “An application of interference microscope to integrated circuit inspection and metrology,” in Integrated Circuit Microscopy: Inspection and Process Control, K. M. Monahan, ed., Proc. SPIE775, 233–247 (1987).

Notni, G.

R. J. Recknagel, G. Notni, “Analysis of white light interferograms using wavelet methods,” Opt. Commun. 148, 122–128 (1998).
[CrossRef]

Plata, A.

P. Sandoz, R. Devillers, A. Plata, “Unambiguous profilometry by fringe-order identification in white-light phase-shifting interferometry,” J. Mod. Opt. 44, 519–534 (1997).
[CrossRef]

Recknagel, R. J.

R. J. Recknagel, G. Notni, “Analysis of white light interferograms using wavelet methods,” Opt. Commun. 148, 122–128 (1998).
[CrossRef]

Roy, M.

P. Hariharan, M. Roy, “White-light phase-stepping interferometry: measurement of the fractional interference order,” J. Mod. Opt. 42, 2357–2360 (1995).
[CrossRef]

Sandoz, P.

P. Sandoz, “Wavelet transform as a processing tool in white-light interferometry,” Opt. Lett. 22, 1065–1067 (1997).
[CrossRef] [PubMed]

P. Sandoz, R. Devillers, A. Plata, “Unambiguous profilometry by fringe-order identification in white-light phase-shifting interferometry,” J. Mod. Opt. 44, 519–534 (1997).
[CrossRef]

Schmit, J.

J. C. Wyant, J. Schmit, “Computerized interferometric measurement of surface microstructure,” in Optical Inspection and Micromeasurements, C. Gorecki, ed., Proc. SPIE2782, 26–37 (1996).
[CrossRef]

A. Harasaki, J. Schmit, J. C. Wyant, “Improved vertical- scanning interferometry,” Appl. Opt. 39, 2107–2115.

Strand, T. C.

Vass, D. G.

Wyant, J. C.

A. Harasaki, J. Schmit, J. C. Wyant, “Improved vertical- scanning interferometry,” Appl. Opt. 39, 2107–2115.

J. C. Wyant, J. Schmit, “Computerized interferometric measurement of surface microstructure,” in Optical Inspection and Micromeasurements, C. Gorecki, ed., Proc. SPIE2782, 26–37 (1996).
[CrossRef]

Appl. Opt. (7)

J. Mod. Opt. (2)

P. Sandoz, R. Devillers, A. Plata, “Unambiguous profilometry by fringe-order identification in white-light phase-shifting interferometry,” J. Mod. Opt. 44, 519–534 (1997).
[CrossRef]

P. Hariharan, M. Roy, “White-light phase-stepping interferometry: measurement of the fractional interference order,” J. Mod. Opt. 42, 2357–2360 (1995).
[CrossRef]

J. Opt. Soc. Am. A (1)

Opt. Commun. (1)

R. J. Recknagel, G. Notni, “Analysis of white light interferograms using wavelet methods,” Opt. Commun. 148, 122–128 (1998).
[CrossRef]

Opt. Lett. (2)

Other (5)

Estimating the centroid of function m(i)[x, y] = {I(i)[x, y] - I(i - 1)[x, y]}2 gives the surface height h[x, y] at lateral position [x, y], where I(i)[x, y] is the intensity of vertical scanning position i in a correlogram for scanning steps of 90° and 270°. It can easily be shown that z¯=∑i imix, y∑i mix, y=h+Γ′4/λcos2π4/λh2πΓ0+Γ4/λsin2π4/λh for the symmetric coherence function, where Γ and Γ′ are the Fourier transform of the coherence function and its first derivative, respectively, and λ̅ is the mean wavelength of the white-light source. From knowledge of the coherence function we know that the second term is very small; thus the centroid of function m(i) is a good estimator of surface height h.

J. C. Wyant, J. Schmit, “Computerized interferometric measurement of surface microstructure,” in Optical Inspection and Micromeasurements, C. Gorecki, ed., Proc. SPIE2782, 26–37 (1996).
[CrossRef]

D. K. Cohen, P. J. Caber, C. P. Brophy, “Rough surface profiler and method,” U.S. patent5,133,601 (28July1992).

N. Balsubramanian, “Optical system for surface topography measurement,” U.S. patent4,340,306 (20July1982).

M. Davidson, K. Kaufman, I. Mazor, F. Cohen, “An application of interference microscope to integrated circuit inspection and metrology,” in Integrated Circuit Microscopy: Inspection and Process Control, K. M. Monahan, ed., Proc. SPIE775, 233–247 (1987).

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Figures (9)

Fig. 1
Fig. 1

Profiles of (a) the 80-nm step-height standard, (b) the 460-nm step-height standard, (c) the 1.7 µm step-height standard measured with a Mirau interference microscope.

Fig. 2
Fig. 2

Profile of the 80-nm step-height standard measured by the phase-shifting technique.

Fig. 3
Fig. 3

Correlograms of the 80-nm height standard across the step discontinuity (a) far from the edge on the top side, (b) close to the edge on the top side, (c) close to the edge on the bottom side, (d) far from the edge on the bottom side.

Fig. 4
Fig. 4

Correlograms of the 460-nm height standard across the step discontinuity (a) far from the edge on the top side, (b) close to the edge on the top side, (c) close to the edge on the bottom side, (d) far from the edge on the bottom side.

Fig. 5
Fig. 5

Correlograms of the 1.7-µm height standard across the step discontinuity (a) far from the edge on the top side, (b) close to the edge on the top side, (c) close to the edge on the bottom side, (d) far from the edge on the bottom side.

Fig. 6
Fig. 6

Integrating energy of (a) the 80-nm step-height standard, (b) the 460-nm step-height standard, (c) the 1.7-µm step-height standard across the step discontinuity.

Fig. 7
Fig. 7

Schematic configuration of a Mirau interference microscope and a step-edge sample: PZT, piezoelectric.

Fig. 8
Fig. 8

Simulated correlograms of the 460-nm height standard (a) far from the step edge on the top side, (b) close to the step edge on the top side, (c) close to the step edge on the bottom side, (d) far from the step edge on the top side.

Fig. 9
Fig. 9

Calculated best focus frame of the 460-nm height standard: (a) the top portion close to the step edge and (b) the bottom portion close to the step edge.

Tables (1)

Tables Icon

Table 1 Influences of Measurement Parameters on Batwingsa

Equations (11)

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ux, y, z=-- ux0, y0, z=0×uphx-x0, y-y0, zdx0dy0,
uphx, y, z=-12πzexpikrr,
Uξ, ζ, z=Uξ, ζ, z=0×Uphξ, ζ, z,
Uphξ, ζ, z=exp-2πiz1λ2-ξ2+ζ21/2,
ux, y, z=-1/λ1/λ-1/λ1/λ Uξ, ζ, zexpi2πξx+ζydξdζ.
ux, z=-1/λ1/λ Uξ, zexpi2πξxdξ,
Uξ, z=Uξ, z=0exp-2πiz1λ2-ξ2.
Uξ, z, λ=Ulξ, z=0, λUphξ, zl, λ+Urξ, z=0, λUphξ, zr, λ×rectξN.A./λ.
ulx, zl, λ=al exp-i 2πλ zlrectx-L/4L/2,
urx, zr, λ=ar exp-i 2πλ zrrectx-3L/4L/2;
Ix, z=λ1λ2ux, z, λ+rectx-L/2L2dλ.

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