Abstract

A three-beam scanning optical interferometric microscopic technique applied to roughness characterization of optical flats is described. The technique is based on the heterodinization of three coherent optical beams. One of the beams, the probe beam, is focused on the surface under test. A second beam is obtained after being reflected by a reference surface. Finally, the last beam consists of one of the first orders of diffraction that emerges of a Bragg-cell. The three beams are coherently added at the sensitive surface of a photodetector that integrates the overall intensity of the beams. We show analytically that, the electrical signal at the output of the photodetector, is a time-varying signal whose amplitude is proportional to the surface local vertical height. We characterize experimentally the frequency response of the system by measuring the profile of three different gratings. We show measurements of the roughness of an optical flat processed by means of the frequency response of the system.

© 2007 Optical Society of America

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  1. M. Davidson, K. Kaufman, I. Mazor, and F. Cohen, "An application of interference microscopy to integrated circuit inspection and metrology," Proc. SPIE 775, 233-247 (1987).
  2. P. J. Caber, "Interferometric profiler for rough surfaces," Appl. Opt. 32, 3438-3441 (1993).
    [CrossRef] [PubMed]
  3. J. M. Bennettm and J. H. Dancy, "Stylus profiling instrument for measuring statistical properties of smooth optical surfaces," Appl. Opt. 20,1785 (1981).
    [CrossRef]
  4. J. F. Song and T. V. Vorburger, "Stylus profiling at high resolution and low force," App. Opt. 30, 42-50 (1991).
    [CrossRef]
  5. J. Jahanmir and J. C. Wyant, "Comparison of surface roughness measured with an optical profiler and a scanning probe microscope," Proc. SPIE 1720, 111-118 (1992).
    [CrossRef]
  6. J. M. Bennett, M. M. Tehrani, J. Jahanmir, J. C. Podlesny, and T. L. Balter, "Topographic measurements of supersmooth dielectric films made with a mechanical profiler and a scanning force microscope," Appl. Opt. 34, 209-212 (1995).
    [CrossRef] [PubMed]
  7. B. Singh, "Application of atomic force microscopy to lithography characterization and control," Proc. SPIE 3677, 2-9 (1999).
    [CrossRef]
  8. D. Walker, H. Yang, and S. Kim, "Novel hybrid stylus for nanometric profilometry for large optical surfaces," Opt. Express 11, 1793-1798 (2003).
    [CrossRef] [PubMed]
  9. G. W. Johnson, D. C. Leiner, D. T. Moore, "Phase-locked Interferometry," Proc. SPIE 126, 152-160 (1977).
  10. K. Creath and J. C. Wyant, "Absolute measurement of surface roughness," Appl. Opt. 29, 3823-3827 (1990).
    [CrossRef] [PubMed]
  11. K. Phan, J. Nistler, and B. Singh, "Metrology issues associated with submicron linewidths," Proc. SPIE 1464, 424-437 (1991).
    [CrossRef]
  12. K. Creath, "Submicron linewidth measurement using an interferometric optical profiler," Proc. SPIE 1464, 474-483 (1991).
    [CrossRef]
  13. B. Wang, S. Marchese-Ragona, and T. C. Bristow, "Roughness characterization of ultrasmooth surfaces using common-path interferometry," Proc. SPIE 3619, 121-127, (1999).
    [CrossRef]
  14. S.-H. Lu, C.-I. Chiueh, and C.-C. Lee, "Differential wavelength-scanning heterodyne interferometer for measuring large step height," Appl. Opt. 41, 5866-5871 (2002).
    [CrossRef] [PubMed]
  15. H. J. Tiziani, "Optical methods for precision measurements," Opt. Quantum Electron. 21, 253-282 (1989).
    [CrossRef]
  16. J. Murakowski, M. Cywiak, B. Rosner, and D. van der Weide, "Far field optical imaging with subwavelength resolution," Opt. Comm. 185, 295-303 (2000).
    [CrossRef]
  17. E. Marx, I. Malik, Y. E. Strausser, T. Bristow, M. Poduje, and J. Stover, "Power spectral densities: a multiple technique study of different Si wafer surfaces," J. Vac. Sci. Technol. 20, 31-41 (2002).
    [CrossRef]
  18. P. Lorenzo Juárez, M. Cywiak, B. Barrientos, and J. M. Flores Moreno, "Three Gaussian beam heterodyne interferometer for surface profiling," Opt. Commun. 268, 209-214 (2006).
    [CrossRef]
  19. P. de Groot, X. Colonna de Lega, "Signal modeling for low-coherence geight-scanning interference microscopy," Appl. Opt. 43, 4821-4831 (2004).
    [CrossRef] [PubMed]
  20. A. Harasaki, J. Schmit, and J. C. Wyant, "Improved vertical-scanning interferometry," Appl. Opt. 39, 2107-2115 (2000).
    [CrossRef]
  21. A. Kuhle, B.-G. Rosen, and J. Garnaes, "Comparison of roughness measurement with atomic force microscopy and interference microscopy," Proc. SPIE 5188, 154-161 (2003).
    [CrossRef]

2006 (1)

P. Lorenzo Juárez, M. Cywiak, B. Barrientos, and J. M. Flores Moreno, "Three Gaussian beam heterodyne interferometer for surface profiling," Opt. Commun. 268, 209-214 (2006).
[CrossRef]

2004 (1)

2003 (2)

D. Walker, H. Yang, and S. Kim, "Novel hybrid stylus for nanometric profilometry for large optical surfaces," Opt. Express 11, 1793-1798 (2003).
[CrossRef] [PubMed]

A. Kuhle, B.-G. Rosen, and J. Garnaes, "Comparison of roughness measurement with atomic force microscopy and interference microscopy," Proc. SPIE 5188, 154-161 (2003).
[CrossRef]

2002 (2)

E. Marx, I. Malik, Y. E. Strausser, T. Bristow, M. Poduje, and J. Stover, "Power spectral densities: a multiple technique study of different Si wafer surfaces," J. Vac. Sci. Technol. 20, 31-41 (2002).
[CrossRef]

S.-H. Lu, C.-I. Chiueh, and C.-C. Lee, "Differential wavelength-scanning heterodyne interferometer for measuring large step height," Appl. Opt. 41, 5866-5871 (2002).
[CrossRef] [PubMed]

2000 (2)

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

J. Murakowski, M. Cywiak, B. Rosner, and D. van der Weide, "Far field optical imaging with subwavelength resolution," Opt. Comm. 185, 295-303 (2000).
[CrossRef]

1999 (2)

B. Singh, "Application of atomic force microscopy to lithography characterization and control," Proc. SPIE 3677, 2-9 (1999).
[CrossRef]

B. Wang, S. Marchese-Ragona, and T. C. Bristow, "Roughness characterization of ultrasmooth surfaces using common-path interferometry," Proc. SPIE 3619, 121-127, (1999).
[CrossRef]

1995 (1)

1993 (1)

1992 (1)

J. Jahanmir and J. C. Wyant, "Comparison of surface roughness measured with an optical profiler and a scanning probe microscope," Proc. SPIE 1720, 111-118 (1992).
[CrossRef]

1991 (3)

K. Phan, J. Nistler, and B. Singh, "Metrology issues associated with submicron linewidths," Proc. SPIE 1464, 424-437 (1991).
[CrossRef]

K. Creath, "Submicron linewidth measurement using an interferometric optical profiler," Proc. SPIE 1464, 474-483 (1991).
[CrossRef]

J. F. Song and T. V. Vorburger, "Stylus profiling at high resolution and low force," App. Opt. 30, 42-50 (1991).
[CrossRef]

1990 (1)

1989 (1)

H. J. Tiziani, "Optical methods for precision measurements," Opt. Quantum Electron. 21, 253-282 (1989).
[CrossRef]

1987 (1)

M. Davidson, K. Kaufman, I. Mazor, and F. Cohen, "An application of interference microscopy to integrated circuit inspection and metrology," Proc. SPIE 775, 233-247 (1987).

1981 (1)

1977 (1)

G. W. Johnson, D. C. Leiner, D. T. Moore, "Phase-locked Interferometry," Proc. SPIE 126, 152-160 (1977).

Balter, T. L.

Barrientos, B.

P. Lorenzo Juárez, M. Cywiak, B. Barrientos, and J. M. Flores Moreno, "Three Gaussian beam heterodyne interferometer for surface profiling," Opt. Commun. 268, 209-214 (2006).
[CrossRef]

Bennett, J. M.

Bennettm, J. M.

Bristow, T.

E. Marx, I. Malik, Y. E. Strausser, T. Bristow, M. Poduje, and J. Stover, "Power spectral densities: a multiple technique study of different Si wafer surfaces," J. Vac. Sci. Technol. 20, 31-41 (2002).
[CrossRef]

Bristow, T. C.

B. Wang, S. Marchese-Ragona, and T. C. Bristow, "Roughness characterization of ultrasmooth surfaces using common-path interferometry," Proc. SPIE 3619, 121-127, (1999).
[CrossRef]

Caber, P. J.

Chiueh, C.-I.

Cohen, F.

M. Davidson, K. Kaufman, I. Mazor, and F. Cohen, "An application of interference microscopy to integrated circuit inspection and metrology," Proc. SPIE 775, 233-247 (1987).

Colonna de Lega, X.

Creath, K.

K. Creath, "Submicron linewidth measurement using an interferometric optical profiler," Proc. SPIE 1464, 474-483 (1991).
[CrossRef]

K. Creath and J. C. Wyant, "Absolute measurement of surface roughness," Appl. Opt. 29, 3823-3827 (1990).
[CrossRef] [PubMed]

Cywiak, M.

P. Lorenzo Juárez, M. Cywiak, B. Barrientos, and J. M. Flores Moreno, "Three Gaussian beam heterodyne interferometer for surface profiling," Opt. Commun. 268, 209-214 (2006).
[CrossRef]

J. Murakowski, M. Cywiak, B. Rosner, and D. van der Weide, "Far field optical imaging with subwavelength resolution," Opt. Comm. 185, 295-303 (2000).
[CrossRef]

Dancy, J. H.

Davidson, M.

M. Davidson, K. Kaufman, I. Mazor, and F. Cohen, "An application of interference microscopy to integrated circuit inspection and metrology," Proc. SPIE 775, 233-247 (1987).

de Groot, P.

Flores Moreno, J. M.

P. Lorenzo Juárez, M. Cywiak, B. Barrientos, and J. M. Flores Moreno, "Three Gaussian beam heterodyne interferometer for surface profiling," Opt. Commun. 268, 209-214 (2006).
[CrossRef]

Garnaes, J.

A. Kuhle, B.-G. Rosen, and J. Garnaes, "Comparison of roughness measurement with atomic force microscopy and interference microscopy," Proc. SPIE 5188, 154-161 (2003).
[CrossRef]

Harasaki, A.

Jahanmir, J.

Johnson, G. W.

G. W. Johnson, D. C. Leiner, D. T. Moore, "Phase-locked Interferometry," Proc. SPIE 126, 152-160 (1977).

Kaufman, K.

M. Davidson, K. Kaufman, I. Mazor, and F. Cohen, "An application of interference microscopy to integrated circuit inspection and metrology," Proc. SPIE 775, 233-247 (1987).

Kim, S.

Kuhle, A.

A. Kuhle, B.-G. Rosen, and J. Garnaes, "Comparison of roughness measurement with atomic force microscopy and interference microscopy," Proc. SPIE 5188, 154-161 (2003).
[CrossRef]

Lee, C.-C.

Leiner, D. C.

G. W. Johnson, D. C. Leiner, D. T. Moore, "Phase-locked Interferometry," Proc. SPIE 126, 152-160 (1977).

Lorenzo Juárez, P.

P. Lorenzo Juárez, M. Cywiak, B. Barrientos, and J. M. Flores Moreno, "Three Gaussian beam heterodyne interferometer for surface profiling," Opt. Commun. 268, 209-214 (2006).
[CrossRef]

Lu, S.-H.

Malik, I.

E. Marx, I. Malik, Y. E. Strausser, T. Bristow, M. Poduje, and J. Stover, "Power spectral densities: a multiple technique study of different Si wafer surfaces," J. Vac. Sci. Technol. 20, 31-41 (2002).
[CrossRef]

Marchese-Ragona, S.

B. Wang, S. Marchese-Ragona, and T. C. Bristow, "Roughness characterization of ultrasmooth surfaces using common-path interferometry," Proc. SPIE 3619, 121-127, (1999).
[CrossRef]

Marx, E.

E. Marx, I. Malik, Y. E. Strausser, T. Bristow, M. Poduje, and J. Stover, "Power spectral densities: a multiple technique study of different Si wafer surfaces," J. Vac. Sci. Technol. 20, 31-41 (2002).
[CrossRef]

Mazor, I.

M. Davidson, K. Kaufman, I. Mazor, and F. Cohen, "An application of interference microscopy to integrated circuit inspection and metrology," Proc. SPIE 775, 233-247 (1987).

Moore, D. T.

G. W. Johnson, D. C. Leiner, D. T. Moore, "Phase-locked Interferometry," Proc. SPIE 126, 152-160 (1977).

Murakowski, J.

J. Murakowski, M. Cywiak, B. Rosner, and D. van der Weide, "Far field optical imaging with subwavelength resolution," Opt. Comm. 185, 295-303 (2000).
[CrossRef]

Nistler, J.

K. Phan, J. Nistler, and B. Singh, "Metrology issues associated with submicron linewidths," Proc. SPIE 1464, 424-437 (1991).
[CrossRef]

Phan, K.

K. Phan, J. Nistler, and B. Singh, "Metrology issues associated with submicron linewidths," Proc. SPIE 1464, 424-437 (1991).
[CrossRef]

Podlesny, J. C.

Poduje, M.

E. Marx, I. Malik, Y. E. Strausser, T. Bristow, M. Poduje, and J. Stover, "Power spectral densities: a multiple technique study of different Si wafer surfaces," J. Vac. Sci. Technol. 20, 31-41 (2002).
[CrossRef]

Rosen, B.-G.

A. Kuhle, B.-G. Rosen, and J. Garnaes, "Comparison of roughness measurement with atomic force microscopy and interference microscopy," Proc. SPIE 5188, 154-161 (2003).
[CrossRef]

Rosner, B.

J. Murakowski, M. Cywiak, B. Rosner, and D. van der Weide, "Far field optical imaging with subwavelength resolution," Opt. Comm. 185, 295-303 (2000).
[CrossRef]

Schmit, J.

Singh, B.

B. Singh, "Application of atomic force microscopy to lithography characterization and control," Proc. SPIE 3677, 2-9 (1999).
[CrossRef]

K. Phan, J. Nistler, and B. Singh, "Metrology issues associated with submicron linewidths," Proc. SPIE 1464, 424-437 (1991).
[CrossRef]

Song, J. F.

J. F. Song and T. V. Vorburger, "Stylus profiling at high resolution and low force," App. Opt. 30, 42-50 (1991).
[CrossRef]

Stover, J.

E. Marx, I. Malik, Y. E. Strausser, T. Bristow, M. Poduje, and J. Stover, "Power spectral densities: a multiple technique study of different Si wafer surfaces," J. Vac. Sci. Technol. 20, 31-41 (2002).
[CrossRef]

Strausser, Y. E.

E. Marx, I. Malik, Y. E. Strausser, T. Bristow, M. Poduje, and J. Stover, "Power spectral densities: a multiple technique study of different Si wafer surfaces," J. Vac. Sci. Technol. 20, 31-41 (2002).
[CrossRef]

Tehrani, M. M.

Tiziani, H. J.

H. J. Tiziani, "Optical methods for precision measurements," Opt. Quantum Electron. 21, 253-282 (1989).
[CrossRef]

van der Weide, D.

J. Murakowski, M. Cywiak, B. Rosner, and D. van der Weide, "Far field optical imaging with subwavelength resolution," Opt. Comm. 185, 295-303 (2000).
[CrossRef]

Vorburger, T. V.

J. F. Song and T. V. Vorburger, "Stylus profiling at high resolution and low force," App. Opt. 30, 42-50 (1991).
[CrossRef]

Walker, D.

Wang, B.

B. Wang, S. Marchese-Ragona, and T. C. Bristow, "Roughness characterization of ultrasmooth surfaces using common-path interferometry," Proc. SPIE 3619, 121-127, (1999).
[CrossRef]

Wyant, J. C.

Yang, H.

App. Opt. (1)

J. F. Song and T. V. Vorburger, "Stylus profiling at high resolution and low force," App. Opt. 30, 42-50 (1991).
[CrossRef]

Appl. Opt. (7)

J. Vac. Sci. Technol. (1)

E. Marx, I. Malik, Y. E. Strausser, T. Bristow, M. Poduje, and J. Stover, "Power spectral densities: a multiple technique study of different Si wafer surfaces," J. Vac. Sci. Technol. 20, 31-41 (2002).
[CrossRef]

Opt. Comm. (1)

J. Murakowski, M. Cywiak, B. Rosner, and D. van der Weide, "Far field optical imaging with subwavelength resolution," Opt. Comm. 185, 295-303 (2000).
[CrossRef]

Opt. Commun. (1)

P. Lorenzo Juárez, M. Cywiak, B. Barrientos, and J. M. Flores Moreno, "Three Gaussian beam heterodyne interferometer for surface profiling," Opt. Commun. 268, 209-214 (2006).
[CrossRef]

Opt. Express (1)

Opt. Quantum Electron. (1)

H. J. Tiziani, "Optical methods for precision measurements," Opt. Quantum Electron. 21, 253-282 (1989).
[CrossRef]

Proc. SPIE (8)

M. Davidson, K. Kaufman, I. Mazor, and F. Cohen, "An application of interference microscopy to integrated circuit inspection and metrology," Proc. SPIE 775, 233-247 (1987).

K. Phan, J. Nistler, and B. Singh, "Metrology issues associated with submicron linewidths," Proc. SPIE 1464, 424-437 (1991).
[CrossRef]

K. Creath, "Submicron linewidth measurement using an interferometric optical profiler," Proc. SPIE 1464, 474-483 (1991).
[CrossRef]

B. Wang, S. Marchese-Ragona, and T. C. Bristow, "Roughness characterization of ultrasmooth surfaces using common-path interferometry," Proc. SPIE 3619, 121-127, (1999).
[CrossRef]

G. W. Johnson, D. C. Leiner, D. T. Moore, "Phase-locked Interferometry," Proc. SPIE 126, 152-160 (1977).

B. Singh, "Application of atomic force microscopy to lithography characterization and control," Proc. SPIE 3677, 2-9 (1999).
[CrossRef]

J. Jahanmir and J. C. Wyant, "Comparison of surface roughness measured with an optical profiler and a scanning probe microscope," Proc. SPIE 1720, 111-118 (1992).
[CrossRef]

A. Kuhle, B.-G. Rosen, and J. Garnaes, "Comparison of roughness measurement with atomic force microscopy and interference microscopy," Proc. SPIE 5188, 154-161 (2003).
[CrossRef]

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Figures (7)

Fig. 1.
Fig. 1.

Experimental set up. M and BS stand for a mirror and a beam splitter respectively. Phase-shifter 1 introduces a phase shift of value ϕP in the probe beam with respect to the reference beam. Phase shifter 2 introduces a phase shift of value ϕM in the modulating beam with respect to the reference beam. The attenuators are introduced to make equal the three intensities at the plane of detection.

Fig. 2. (a)
Fig. 2. (a)

Line-profile obtained with an atomic force microscope.

Fig. 2. (b)
Fig. 2. (b)

Normalized line-profile obtained with the proposed technique.

Fig. 3.
Fig. 3.

Plot of the normalized frequency response of the system and the corresponding noise distribution.

Fig. 4.
Fig. 4.

Inverse frequency response (limited in frequency) of the system.

Fig. 5.
Fig. 5.

Normalized output signal obtained from a line scan of an optical flat obtained by the system.

Fig. 6.
Fig. 6.

Profile calculated by using the inverse frequency response of the system for the optical flat.

Equations (11)

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

Ψ R = I 0 exp ( ikz R ) exp ( l t ) ,
Ψ p = I 0 exp ( ikz p + φ p ) exp ( l t ) exp [ i 4 π λ h ( x ) ] ,
Ψ M = I 0 exp ( ikz M + φ M ) exp [ i ( ω l + ω s ) t ] .
Ψ T = Ψ R + Ψ P + Ψ M .
Ψ T = I 0 exp ( i ω l t ) I 0 exp ( i ω l t ) exp [ i 4 π λ h ( x ) ] . + i I 0 exp [ i ( ω l + ω s ) t ]
I = I 0 + 4 I 0 sin 2 [ 2 π λ h ( x ) ] 4 I 0 sin [ 2 π λ h ( x ) ] cos [ 2 π λ h ( x ) ω s t ] .
V = ρ A d I
= ρ A d { I 0 + 4 I 1 sin 2 [ 2 π λ h ( x ) ] 4 I 0 sin [ 2 π λ h ( x ) ] cos [ 2 π λ h ( x ) ω s t ] } ,
V ( x 0 ) = 4 P 0 sin [ 2 π λ h ( x 0 ) ] ,
G u v = exp [ π 2 r 0 2 2 ( u 2 + v 2 ) ] ,
S N = E { f 2 ( t ) } E { n 2 ( t ) } = + S f ( ω ) + S n ( ω ) ,

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