Abstract

In spectrally resolved white-light interferometry (SRWLI), the white-light interferogram is decomposed into its monochromatic constituent. The phase of the monochromatic constituents can be determined using a phase-shifting technique over a range of wavelengths. These phase values have fringe order ambiguity. However, the variation of the phase with respect to the wavenumber is linear and its slope gives the absolute value of the optical-path difference. Since the path difference is related to the height of the test object at a point, a line profile can be determined without ambiguity. The slope value, though less precise helps us determine the fringe order. The fringe order combined with the monochromatic phase value gives the absolute profile, which has the precision of phase-shifting interferometry. The presence of noise in the phase may lead to the misidentification of fringe order, which in turn gives unnecessary jumps in the precise profile. The experimental details of measurement on standard samples with SRWLI are discussed in this paper.

© 2006 Optical Society of America

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  1. M. Davidson, K. Kaufman, I. Mazor, and F. Cohent, "An application of interference microscopy to integrated circuit inspection and metrology," in Integrated Circuit Metrology, Inspection, and Process Control, K. M. Monahan, ed., Proc. SPIE 775, 233-247 (1987).
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  4. T. Dresel, G. Häusler, and H. Venzke, "Three-dimensional sensing of rough surfaces by coherence radar," Appl. Opt. 31, 919-925 (1992).
    [CrossRef] [PubMed]
  5. P. J. Caber, "Interferometric profiler for rough surfaces," Appl. Opt. 32, 3438-3441 (1993).
    [CrossRef] [PubMed]
  6. P. Sandoz and G. Tribillon, "Profilometry by zero order interference fringe identification," J. Mod. Opt. 40, 1691-1700 (1993).
    [CrossRef]
  7. P. de Groot and L. Deck, "Surface profiling by analysis of white light interferograms in the spatial frequency domain," J. Mod. Opt. 42, 389-401 (1995).
    [CrossRef]
  8. K. G. Larkin, "Efficient nonlinear algorithm for envelope detection in white light interferometry," J. Opt. Soc. Am. A 13, 832-843 (1996).
    [CrossRef]
  9. P. Sandoz, "An algorithm for profilometry by white light phase shifting interferometry," J. Mod. Opt. 43, 1545-1554 (1996).
    [CrossRef]
  10. P. Sandoz, R. Devillers, and A. Plata, "Unambiguous profilometry by fringe-order identification in white-light phase-shifting interferometry," J. Mod. Opt. 44, 519-534 (1997).
    [CrossRef]
  11. A. Harasaki, J. Schmit, and J. C. Wyant, "Improved vertical-scanning interferometry," Appl. Opt. 39, 2107-2115 (2000).
    [CrossRef]
  12. A. Pfortner and J. Schwider, "Dispersion error in white-light Linnik interferometers and its implications for evaluation procedures," Appl. Opt. 40, 6223-6228 (2001).
    [CrossRef]
  13. P. de Groot, X. C. de Lega, J. Kramer, and M. Turzhitsky, "Determination of fringe order in white-light interference microscopy," Appl. Opt. 41, 4571-4578 (2002).
    [CrossRef] [PubMed]
  14. J. Schwider and L Zhou, "Dispersive interferometric profilometer," Opt. Lett. 19, 995-997 (1994).
    [CrossRef] [PubMed]
  15. P. Sandoz, G. Tribillon, and H. Perrin, "High resolution profilometry by using phase calculation algorithms for spectroscopic analysis of white light interferograms," J. Mod. Opt. 43, 701-708 (1996).
    [CrossRef]
  16. J. Calatroni, A. L. Guerrero, C. Sainz, and R. Escalona, "Spectrally-resolved white-light interferometry as a profilometry tool," Opt. Laser Technol. , 28, 485-489 (1996).
    [CrossRef]
  17. S. Suja Helen, M. P. Kothiyal, and R. S. Sirohi, "Analysis of spectrally resolved white light interferograms: use of a phase shifting technique," Opt. Eng. 40, 1329-1336 (2001).
    [CrossRef]
  18. S. K. Debnath and M. P. Kothiyal, "Optical profiler based on spectrally resolved white light interferometry," Opt. Eng. 44, 013606 (2005).
    [CrossRef]
  19. P. Hariharan, B. F. Oreb, and T. Eiju, "Digital phase-shifting interferometer: a simple error-compensating phase calculation algorithm," Appl. Opt. 26, 2504-2506 (1987).
    [CrossRef] [PubMed]
  20. A. Harasaki and J. C. Wyant, "Fringe modulation skewing effect in white light vertical scanning interferometry," Appl. Opt. 39, 2101-2106 (2000).
    [CrossRef]
  21. K. Creath, "Calibration of numerical aperture effects in interferometric microscope objectives," Appl. Opt. 28, 3333-3338 (1989).
    [CrossRef] [PubMed]
  22. A. Dubois, J. Selb, L. Vabre, and A. C. Boccara, "Phase measurements with wide-aperture interferometers," Appl. Opt. 39, 2326-2331 (2000).
    [CrossRef]

2005 (1)

S. K. Debnath and M. P. Kothiyal, "Optical profiler based on spectrally resolved white light interferometry," Opt. Eng. 44, 013606 (2005).
[CrossRef]

2002 (1)

2001 (2)

A. Pfortner and J. Schwider, "Dispersion error in white-light Linnik interferometers and its implications for evaluation procedures," Appl. Opt. 40, 6223-6228 (2001).
[CrossRef]

S. Suja Helen, M. P. Kothiyal, and R. S. Sirohi, "Analysis of spectrally resolved white light interferograms: use of a phase shifting technique," Opt. Eng. 40, 1329-1336 (2001).
[CrossRef]

2000 (3)

1997 (1)

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

1996 (4)

P. Sandoz, "An algorithm for profilometry by white light phase shifting interferometry," J. Mod. Opt. 43, 1545-1554 (1996).
[CrossRef]

P. Sandoz, G. Tribillon, and H. Perrin, "High resolution profilometry by using phase calculation algorithms for spectroscopic analysis of white light interferograms," J. Mod. Opt. 43, 701-708 (1996).
[CrossRef]

J. Calatroni, A. L. Guerrero, C. Sainz, and R. Escalona, "Spectrally-resolved white-light interferometry as a profilometry tool," Opt. Laser Technol. , 28, 485-489 (1996).
[CrossRef]

K. G. Larkin, "Efficient nonlinear algorithm for envelope detection in white light interferometry," J. Opt. Soc. Am. A 13, 832-843 (1996).
[CrossRef]

1995 (1)

P. de Groot and L. Deck, "Surface profiling by analysis of white light interferograms in the spatial frequency domain," J. Mod. Opt. 42, 389-401 (1995).
[CrossRef]

1994 (1)

1993 (2)

P. Sandoz and G. Tribillon, "Profilometry by zero order interference fringe identification," J. Mod. Opt. 40, 1691-1700 (1993).
[CrossRef]

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

1992 (1)

1990 (2)

1989 (1)

1987 (2)

M. Davidson, K. Kaufman, I. Mazor, and F. Cohent, "An application of interference microscopy to integrated circuit inspection and metrology," in Integrated Circuit Metrology, Inspection, and Process Control, K. M. Monahan, ed., Proc. SPIE 775, 233-247 (1987).

P. Hariharan, B. F. Oreb, and T. Eiju, "Digital phase-shifting interferometer: a simple error-compensating phase calculation algorithm," Appl. Opt. 26, 2504-2506 (1987).
[CrossRef] [PubMed]

Boccara, A. C.

Caber, P. J.

Calatroni, J.

J. Calatroni, A. L. Guerrero, C. Sainz, and R. Escalona, "Spectrally-resolved white-light interferometry as a profilometry tool," Opt. Laser Technol. , 28, 485-489 (1996).
[CrossRef]

Chim, S. C.

Cohent, F.

M. Davidson, K. Kaufman, I. Mazor, and F. Cohent, "An application of interference microscopy to integrated circuit inspection and metrology," in Integrated Circuit Metrology, Inspection, and Process Control, K. M. Monahan, ed., Proc. SPIE 775, 233-247 (1987).

Creath, K.

Davidson, M.

M. Davidson, K. Kaufman, I. Mazor, and F. Cohent, "An application of interference microscopy to integrated circuit inspection and metrology," in Integrated Circuit Metrology, Inspection, and Process Control, K. M. Monahan, ed., Proc. SPIE 775, 233-247 (1987).

de Groot, P.

P. de Groot, X. C. de Lega, J. Kramer, and M. Turzhitsky, "Determination of fringe order in white-light interference microscopy," Appl. Opt. 41, 4571-4578 (2002).
[CrossRef] [PubMed]

P. de Groot and L. Deck, "Surface profiling by analysis of white light interferograms in the spatial frequency domain," J. Mod. Opt. 42, 389-401 (1995).
[CrossRef]

de Lega, X. C.

Debnath, S. K.

S. K. Debnath and M. P. Kothiyal, "Optical profiler based on spectrally resolved white light interferometry," Opt. Eng. 44, 013606 (2005).
[CrossRef]

Deck, L.

P. de Groot and L. Deck, "Surface profiling by analysis of white light interferograms in the spatial frequency domain," J. Mod. Opt. 42, 389-401 (1995).
[CrossRef]

Devillers, R.

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

Dresel, T.

Dubois, A.

Eiju, T.

Escalona, R.

J. Calatroni, A. L. Guerrero, C. Sainz, and R. Escalona, "Spectrally-resolved white-light interferometry as a profilometry tool," Opt. Laser Technol. , 28, 485-489 (1996).
[CrossRef]

Guerrero, A. L.

J. Calatroni, A. L. Guerrero, C. Sainz, and R. Escalona, "Spectrally-resolved white-light interferometry as a profilometry tool," Opt. Laser Technol. , 28, 485-489 (1996).
[CrossRef]

Harasaki, A.

Hariharan, P.

Häusler, G.

Helen, S. Suja

S. Suja Helen, M. P. Kothiyal, and R. S. Sirohi, "Analysis of spectrally resolved white light interferograms: use of a phase shifting technique," Opt. Eng. 40, 1329-1336 (2001).
[CrossRef]

Kaufman, K.

M. Davidson, K. Kaufman, I. Mazor, and F. Cohent, "An application of interference microscopy to integrated circuit inspection and metrology," in Integrated Circuit Metrology, Inspection, and Process Control, K. M. Monahan, ed., Proc. SPIE 775, 233-247 (1987).

Kino, G. S.

Kothiyal, M. P.

S. K. Debnath and M. P. Kothiyal, "Optical profiler based on spectrally resolved white light interferometry," Opt. Eng. 44, 013606 (2005).
[CrossRef]

S. Suja Helen, M. P. Kothiyal, and R. S. Sirohi, "Analysis of spectrally resolved white light interferograms: use of a phase shifting technique," Opt. Eng. 40, 1329-1336 (2001).
[CrossRef]

Kramer, J.

Larkin, K. G.

Lee, B. S.

Mazor, I.

M. Davidson, K. Kaufman, I. Mazor, and F. Cohent, "An application of interference microscopy to integrated circuit inspection and metrology," in Integrated Circuit Metrology, Inspection, and Process Control, K. M. Monahan, ed., Proc. SPIE 775, 233-247 (1987).

Oreb, B. F.

Perrin, H.

P. Sandoz, G. Tribillon, and H. Perrin, "High resolution profilometry by using phase calculation algorithms for spectroscopic analysis of white light interferograms," J. Mod. Opt. 43, 701-708 (1996).
[CrossRef]

Pfortner, A.

Plata, A.

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

Sainz, C.

J. Calatroni, A. L. Guerrero, C. Sainz, and R. Escalona, "Spectrally-resolved white-light interferometry as a profilometry tool," Opt. Laser Technol. , 28, 485-489 (1996).
[CrossRef]

Sandoz, P.

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

P. Sandoz, "An algorithm for profilometry by white light phase shifting interferometry," J. Mod. Opt. 43, 1545-1554 (1996).
[CrossRef]

P. Sandoz, G. Tribillon, and H. Perrin, "High resolution profilometry by using phase calculation algorithms for spectroscopic analysis of white light interferograms," J. Mod. Opt. 43, 701-708 (1996).
[CrossRef]

P. Sandoz and G. Tribillon, "Profilometry by zero order interference fringe identification," J. Mod. Opt. 40, 1691-1700 (1993).
[CrossRef]

Schmit, J.

Schwider, J.

Selb, J.

Sirohi, R. S.

S. Suja Helen, M. P. Kothiyal, and R. S. Sirohi, "Analysis of spectrally resolved white light interferograms: use of a phase shifting technique," Opt. Eng. 40, 1329-1336 (2001).
[CrossRef]

Strand, T. C.

Tribillon, G.

P. Sandoz, G. Tribillon, and H. Perrin, "High resolution profilometry by using phase calculation algorithms for spectroscopic analysis of white light interferograms," J. Mod. Opt. 43, 701-708 (1996).
[CrossRef]

P. Sandoz and G. Tribillon, "Profilometry by zero order interference fringe identification," J. Mod. Opt. 40, 1691-1700 (1993).
[CrossRef]

Turzhitsky, M.

Vabre, L.

Venzke, H.

Wyant, J. C.

Zhou, L

Appl. Opt. (11)

K. Creath, "Calibration of numerical aperture effects in interferometric microscope objectives," Appl. Opt. 28, 3333-3338 (1989).
[CrossRef] [PubMed]

G. S. Kino and S. C. Chim, "Mirau correlation microscope," Appl. Opt. 29, 3775-3783 (1990).
[CrossRef] [PubMed]

B. S. Lee and T. C. Strand, "Profilometry with a coherence scanning microscope," Appl. Opt. 29, 3784-3788 (1990).
[CrossRef] [PubMed]

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

A. Dubois, J. Selb, L. Vabre, and A. C. Boccara, "Phase measurements with wide-aperture interferometers," Appl. Opt. 39, 2326-2331 (2000).
[CrossRef]

A. Harasaki and J. C. Wyant, "Fringe modulation skewing effect in white light vertical scanning interferometry," Appl. Opt. 39, 2101-2106 (2000).
[CrossRef]

A. Harasaki, J. Schmit, and J. C. Wyant, "Improved vertical-scanning interferometry," Appl. Opt. 39, 2107-2115 (2000).
[CrossRef]

T. Dresel, G. Häusler, and H. Venzke, "Three-dimensional sensing of rough surfaces by coherence radar," Appl. Opt. 31, 919-925 (1992).
[CrossRef] [PubMed]

A. Pfortner and J. Schwider, "Dispersion error in white-light Linnik interferometers and its implications for evaluation procedures," Appl. Opt. 40, 6223-6228 (2001).
[CrossRef]

P. de Groot, X. C. de Lega, J. Kramer, and M. Turzhitsky, "Determination of fringe order in white-light interference microscopy," Appl. Opt. 41, 4571-4578 (2002).
[CrossRef] [PubMed]

P. Hariharan, B. F. Oreb, and T. Eiju, "Digital phase-shifting interferometer: a simple error-compensating phase calculation algorithm," Appl. Opt. 26, 2504-2506 (1987).
[CrossRef] [PubMed]

J. Mod. Opt. (5)

P. Sandoz, "An algorithm for profilometry by white light phase shifting interferometry," J. Mod. Opt. 43, 1545-1554 (1996).
[CrossRef]

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

P. Sandoz and G. Tribillon, "Profilometry by zero order interference fringe identification," J. Mod. Opt. 40, 1691-1700 (1993).
[CrossRef]

P. de Groot and L. Deck, "Surface profiling by analysis of white light interferograms in the spatial frequency domain," J. Mod. Opt. 42, 389-401 (1995).
[CrossRef]

P. Sandoz, G. Tribillon, and H. Perrin, "High resolution profilometry by using phase calculation algorithms for spectroscopic analysis of white light interferograms," J. Mod. Opt. 43, 701-708 (1996).
[CrossRef]

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

Opt. Eng. (2)

S. Suja Helen, M. P. Kothiyal, and R. S. Sirohi, "Analysis of spectrally resolved white light interferograms: use of a phase shifting technique," Opt. Eng. 40, 1329-1336 (2001).
[CrossRef]

S. K. Debnath and M. P. Kothiyal, "Optical profiler based on spectrally resolved white light interferometry," Opt. Eng. 44, 013606 (2005).
[CrossRef]

Opt. Laser Technol. (1)

J. Calatroni, A. L. Guerrero, C. Sainz, and R. Escalona, "Spectrally-resolved white-light interferometry as a profilometry tool," Opt. Laser Technol. , 28, 485-489 (1996).
[CrossRef]

Opt. Lett. (1)

Other (1)

M. Davidson, K. Kaufman, I. Mazor, and F. Cohent, "An application of interference microscopy to integrated circuit inspection and metrology," in Integrated Circuit Metrology, Inspection, and Process Control, K. M. Monahan, ed., Proc. SPIE 775, 233-247 (1987).

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Figures (17)

Fig. 1
Fig. 1

Experimental setup for spectrally resolved white-light interferometry.

Fig. 2
Fig. 2

Spectral interferogram of a plane test surface inclined to the reference surface in the direction of the scan axis.

Fig. 3
Fig. 3

Average phase shift as a function of the wavenumber.

Fig. 4
Fig. 4

(a) Wrapped phase map of the plane surface shown in Fig. 2. (b) Scan of the unwrapped phase along the chromaticity axis from (a).

Fig. 5
Fig. 5

Slope profile of the plane surface whose spectral interferogram is shown in Fig. 2.

Fig. 6
Fig. 6

Phase profile of the plane surface whose interferogram is shown in Fig. 2 by using the phase data for λ = 580 nm .

Fig. 7
Fig. 7

Normalized spectral profile of the source.

Fig. 8
Fig. 8

(a) Spectral interferogram of the step sample A, (b) wrapped phase map of the interferogram in (a).

Fig. 9
Fig. 9

Slope profile of the step sample A.

Fig. 10
Fig. 10

Unwrapped phase scans at two pixels a and b on the vertical axis in the phase map shown in Fig. 8(b).

Fig. 11
Fig. 11

Phase profile of the step sample A obtained from the phase data λ = 580 nm .

Fig. 12
Fig. 12

Magnified view of a part of the phase profile (bottom left) shown in Fig. 11.

Fig. 13
Fig. 13

(a) Slope profile of the standard step sample B, (b) phase profile at λ = 580 nm of the standard step sample B.

Fig. 14
Fig. 14

Magnified view of a part of the phase profile (top right) shown in Fig. 13(b).

Fig. 15
Fig. 15

(a) Slope profile of the spherical surface, (b) phase profile at λ = 580 nm of the spherical surface in (a).

Fig. 16
Fig. 16

Line profile shown in Fig. 15(b) after removing sag.

Fig. 17
Fig. 17

Phase profile of the sample A, a. before and b. after removing jumps.

Tables (2)

Tables Icon

Table 1 Measurement of Step Height on an 89 nm VLSI Standard Sample

Tables Icon

Table 2 Measurement of Step Height on a 1.76 μm VLSI Standard Sample

Equations (13)

Equations on this page are rendered with MathJax. Learn more.

I ( z , σ ) = g ( σ ) { I r + I t + 2 ( I r I t ) 1 / 2 cos [ ϕ ( z , σ ) + ϕ 0 ] } ,
z = 1 4 π [ Δϕ ( z , σ ) Δ σ ] = S 4 π ,
ϕ ( σ ) = tan 1 [ 2 sin α ( σ ) ( I 2 - I 4 2 I 3 - I 5 - I 1 ) ] ,
α ( σ ) = arccos [ I 1 - I 5 2 ( I 2 - I 4 ) ] .
ψ = ϕ + 2 n π .
ψ = ϕ - 2 π int ( ϕ - 4 πσ z 2 π ) ,
z = ψ 4 π σ = 1 4 π σ [ ϕ 2 π int ( ϕ 4 πσ z 2 π ) ] ,
ϕ = + C = 4 πσ z + C ,
z = z + 1 4 π σ [ C - 2 π int ( C 2 π ) ] ,
z = z + Δ z ,
Δ z = 1 4 π σ ( C - 2 π M ) ,
M = int ( C 2 π ) .
| z ( i ) - z ( i ) - offset | λ / 4.

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