Abstract

Diffraction from a periodic structure is sensitive to small changes in the shape of that structure. It is possible to exploit this behavior of the scatter data for accurate, precise, rapid, nondestructive, and in situ measurements of grating structures. We present the use of rigorous coupled-wave theory to generate diffraction profiles to train a partial least-squares (PLS) multivariate calibration routine. The resulting PLS calibration model was applied to experimental diffraction data from gratings in etched bulk silicon to predict etch depths. A single-detector scanning scatterometer was used to measure the scatter from 32-μm-pitch structures illuminated with a He–Ne laser beam. The scatterometer measured the diffraction patterns from grating structures at 14 die locations on each of a set of five wafers. The theoretically based PLS estimator was then used to predict etch depths from scatterometry data obtained from the 70 different grating structures. The etch depth predictions were in excellent agreement with those obtained with a scanning force microscope (i.e., 0.9-μm-deep structures were predicted with an average error of 0.007 μm). This is a significant step toward the solution of the parametric inverse grating diffraction problem: that of quantitative prediction of structure dimensions from the measurement of scatter data.

© 1994 Optical Society of America

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  4. R. D. Larrabee, M. T. Postek, “Precision, accuracy, uncertainty and traceability and their application to submicrometer dimensional metrology,” Solid-State Electron. 36, 673–684 (1993).
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    [CrossRef]
  7. K. P. Bishop, S. M. Gaspar, L. M. Milner, S. Sohail, H. Naqvi, J. R. McNeil, “Grating line shape characterization using scatterometry,” in International Conference on the Application and Theory of Periodic Structures, J. M. Lerner, W. R. McKinney, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1545, 64–73 (1991).
    [CrossRef]
  8. S. S. H. Naqvi, J. R. McNeil, R. H. Krukar, K. P. Bishop, “Scatterometry and the simulation of diffraction-based metrology,” Microlith. World 2(3), 5–16 (1993).
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    [CrossRef]
  10. L. M. Milner, K. P. Bishop, S. S. H. Naqvi, J. R. McNeil, “Stepper focus characterization using diffraction from latent images,”J. Vac. Sci. Technol. B 11, 1258–1266 (1993).
    [CrossRef]
  11. S. S. H. Naqvi, S. M. Gaspar, K. C. Hickman, J. R. McNeil, “Linewidth measurement of gratings on photomasks: a simple technique,” Appl. Opt. 31, 1377–1384 (1992).
    [CrossRef] [PubMed]
  12. R. Krukar, A. Kornblit, L. Clark, J. Kruskal, D. Lambert, E. A. Reitman, R. A. Gottscho, “Reactive ion etching and depth characterization using statistical and neural network analysis of light scattering data,” J. Appl. Phys. 74, 3698–3706 (1993).
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    [CrossRef]
  22. I. C. Botten, M. S. Creig, R. C. McPhedran, “Highly conducting lamellar diffraction gratings,” Opt. Acta 28, 1103–1106 (1981).
    [CrossRef]
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    [CrossRef]
  24. E. V. Thomas, D. M. Haaland, “Comparison of multivariate calibration methods for quantitative spectral analysis,” Anal. Chem. 62, 1091–1099 (1990).
    [CrossRef]
  25. D. M. Haaland, “Multivariate calibration methods applied to the quantitative analysis of infrared spectra,” in Computer-Enhanced Analytical Spectroscopy, P. C. Jurf, ed. (Plenum, New York, 1992), Vol. 3, pp. 1–30.
  26. D. M. Haaland, E. V. Thomas, “Partial least squares methods for spectral analysis. I. Relation to other quantitative calibration methods and the extraction of qualitative information,” Anal. Chem. 60, 1193–1202 (1988).
    [CrossRef]
  27. D. M. Haaland, “Multivariate calibration methods applied to quantitative FT-IR analysis,” in Practical Fourier Transform Infrared Spectroscopy, J. R. Ferraro, K. Krishnan, eds. (Academic, San Diego, Calif., 1990), pp. 395–468.
  28. R. E. Aries, D. P. Lidiard, R. A. Spragg, “Principal component analysis,” Chem. Ber. 27, 821–824 (1991).
  29. G. Wahba, “Practical approximate solutions to linear operator equations when the data are noisy,” SIAM J. Numer. Anal. 14, 651–667 (1977).
    [CrossRef]
  30. D. M. Haaland, “Quantitative infrared analysis of borophosphosilicate films using multivariate statistical methods,” Anal. Chem. 60, 1208–1217 (1988).
    [CrossRef]
  31. B. Wangmaneerat, T. M. Niemczyk, D. M. Haaland, “Determination of temperature and composition of phosphosilicate glass thin films from infrared emission spectral data,” Appl. Spectrosc. 46, 1447–1453 (1992).
    [CrossRef]
  32. J. E. Franke, L. Zhang, T. M. Niemczyk, D. M. Haaland, J. H. Linn, “Quantitative analysis of IR reflection spectra from phosphosilicate glass films,”J. Electrochem. Soc. 140, 1425–1429 (1993).
    [CrossRef]
  33. D. M. Haaland, R. G. Easterling, “Improved sensitivity of infrared spectroscopy by the application of least squares methods,” Appl. Spectrosc. 34, 539–548 (1980).
    [CrossRef]

1993

R. D. Larrabee, M. T. Postek, “Precision, accuracy, uncertainty and traceability and their application to submicrometer dimensional metrology,” Solid-State Electron. 36, 673–684 (1993).
[CrossRef]

S. S. H. Naqvi, J. R. McNeil, R. H. Krukar, K. P. Bishop, “Scatterometry and the simulation of diffraction-based metrology,” Microlith. World 2(3), 5–16 (1993).

L. M. Milner, K. P. Bishop, S. S. H. Naqvi, J. R. McNeil, “Stepper focus characterization using diffraction from latent images,”J. Vac. Sci. Technol. B 11, 1258–1266 (1993).
[CrossRef]

J. E. Franke, L. Zhang, T. M. Niemczyk, D. M. Haaland, J. H. Linn, “Quantitative analysis of IR reflection spectra from phosphosilicate glass films,”J. Electrochem. Soc. 140, 1425–1429 (1993).
[CrossRef]

L. Li, C. W. Haggans, “Convergence of the coupled-wave approach for lamellar diffraction gratings,” J. Opt. Soc. Am. A 10, 1184–1189 (1993).
[CrossRef]

R. Krukar, A. Kornblit, L. Clark, J. Kruskal, D. Lambert, E. A. Reitman, R. A. Gottscho, “Reactive ion etching and depth characterization using statistical and neural network analysis of light scattering data,” J. Appl. Phys. 74, 3698–3706 (1993).
[CrossRef]

1992

B. Wangmaneerat, T. M. Niemczyk, D. M. Haaland, “Determination of temperature and composition of phosphosilicate glass thin films from infrared emission spectral data,” Appl. Spectrosc. 46, 1447–1453 (1992).
[CrossRef]

S. S. H. Naqvi, S. M. Gaspar, K. C. Hickman, J. R. McNeil, “Linewidth measurement of gratings on photomasks: a simple technique,” Appl. Opt. 31, 1377–1384 (1992).
[CrossRef] [PubMed]

K. C. Hickman, S. M. Gaspar, S. S. H. Naqvi, K. P. Bishop, J. R. McNeil, G. D. Tipton, D. L. Draper, B. R. Stallard, “Use of diffraction from latent images to improve lithography control,”J. Vac. Sci. Technol. B 10, 2259–2266 (1992).
[CrossRef]

S. S. H. Naqvi, S. M. Gaspar, K. C. Hickman, K. P. Bishop, L. M. Milner, R. H. Krukar, G. A. Petersen, “Scatterometry applied to microelectronic processing,” Microlith. World 1(6), 16–22 (1992).

S. D. Brown, R. S. Bear, T. B. Blank, “Chemometrics,” Anal. Chem. 64, 22R–49R (1992).
[CrossRef]

1991

R. E. Aries, D. P. Lidiard, R. A. Spragg, “Principal component analysis,” Chem. Ber. 27, 821–824 (1991).

1990

E. V. Thomas, D. M. Haaland, “Comparison of multivariate calibration methods for quantitative spectral analysis,” Anal. Chem. 62, 1091–1099 (1990).
[CrossRef]

1988

D. M. Haaland, E. V. Thomas, “Partial least squares methods for spectral analysis. I. Relation to other quantitative calibration methods and the extraction of qualitative information,” Anal. Chem. 60, 1193–1202 (1988).
[CrossRef]

D. M. Haaland, “Quantitative infrared analysis of borophosphosilicate films using multivariate statistical methods,” Anal. Chem. 60, 1208–1217 (1988).
[CrossRef]

1987

K. R. Beebe, B. R. Kowalski, “An introduction to multivariate calibration and analysis,” Anal. Chem. 59, 1007A–1017A (1987).

M. Postek, D. Joy, “Submicrometer microelectronics dimensional metrology: scanning electron microscopy,”J. Res. Nat. Bur. Stand. 92, 205–228 (1987).
[CrossRef]

1985

T. K. Gaylord, M. G. Moharram, “Analysis and applications of optical diffraction by gratings,” Proc. IEEE 73, 894–937 (1985).
[CrossRef]

1984

H. A. Martens, T. Naes, “Multivariate calibration. I. Concepts and distinctions,” Trends Anal. Chem. 3, 204–210 (1984).
[CrossRef]

T. Naes, H. A. Martens, “Multivariate calibration. II. Chemometric methods,” Trends Anal. Chem. 3, 266–271 (1984).
[CrossRef]

1981

I. C. Botten, M. S. Creig, R. C. McPhedran, “Highly conducting lamellar diffraction gratings,” Opt. Acta 28, 1103–1106 (1981).
[CrossRef]

1980

1978

M. G. Buehler, S. D. Grant, W. R. Thurber, “Bridge and van der Pauw sheet resistors for characterizing the line width of conducting layers,”J. Electrochem. Soc. 125, 650–654 (1978).
[CrossRef]

1977

G. Wahba, “Practical approximate solutions to linear operator equations when the data are noisy,” SIAM J. Numer. Anal. 14, 651–667 (1977).
[CrossRef]

Aries, R. E.

R. E. Aries, D. P. Lidiard, R. A. Spragg, “Principal component analysis,” Chem. Ber. 27, 821–824 (1991).

Bear, R. S.

S. D. Brown, R. S. Bear, T. B. Blank, “Chemometrics,” Anal. Chem. 64, 22R–49R (1992).
[CrossRef]

Beebe, K. R.

K. R. Beebe, B. R. Kowalski, “An introduction to multivariate calibration and analysis,” Anal. Chem. 59, 1007A–1017A (1987).

Bishop, K. P.

L. M. Milner, K. P. Bishop, S. S. H. Naqvi, J. R. McNeil, “Stepper focus characterization using diffraction from latent images,”J. Vac. Sci. Technol. B 11, 1258–1266 (1993).
[CrossRef]

S. S. H. Naqvi, J. R. McNeil, R. H. Krukar, K. P. Bishop, “Scatterometry and the simulation of diffraction-based metrology,” Microlith. World 2(3), 5–16 (1993).

K. C. Hickman, S. M. Gaspar, S. S. H. Naqvi, K. P. Bishop, J. R. McNeil, G. D. Tipton, D. L. Draper, B. R. Stallard, “Use of diffraction from latent images to improve lithography control,”J. Vac. Sci. Technol. B 10, 2259–2266 (1992).
[CrossRef]

S. S. H. Naqvi, S. M. Gaspar, K. C. Hickman, K. P. Bishop, L. M. Milner, R. H. Krukar, G. A. Petersen, “Scatterometry applied to microelectronic processing,” Microlith. World 1(6), 16–22 (1992).

K. P. Bishop, S. M. Gaspar, L. M. Milner, S. Sohail, H. Naqvi, J. R. McNeil, “Grating line shape characterization using scatterometry,” in International Conference on the Application and Theory of Periodic Structures, J. M. Lerner, W. R. McKinney, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1545, 64–73 (1991).
[CrossRef]

Blank, T. B.

S. D. Brown, R. S. Bear, T. B. Blank, “Chemometrics,” Anal. Chem. 64, 22R–49R (1992).
[CrossRef]

Botten, I. C.

I. C. Botten, M. S. Creig, R. C. McPhedran, “Highly conducting lamellar diffraction gratings,” Opt. Acta 28, 1103–1106 (1981).
[CrossRef]

Breidne, M.

A. Roger, M. Breidne, “Grating profile reconstruction by an inverse scattering method,” Opt. Commun. 35, 299–302 (1980).
[CrossRef]

Brown, S. D.

S. D. Brown, R. S. Bear, T. B. Blank, “Chemometrics,” Anal. Chem. 64, 22R–49R (1992).
[CrossRef]

Buehler, M. G.

M. G. Buehler, S. D. Grant, W. R. Thurber, “Bridge and van der Pauw sheet resistors for characterizing the line width of conducting layers,”J. Electrochem. Soc. 125, 650–654 (1978).
[CrossRef]

Clark, L.

R. Krukar, A. Kornblit, L. Clark, J. Kruskal, D. Lambert, E. A. Reitman, R. A. Gottscho, “Reactive ion etching and depth characterization using statistical and neural network analysis of light scattering data,” J. Appl. Phys. 74, 3698–3706 (1993).
[CrossRef]

Creig, M. S.

I. C. Botten, M. S. Creig, R. C. McPhedran, “Highly conducting lamellar diffraction gratings,” Opt. Acta 28, 1103–1106 (1981).
[CrossRef]

Draper, D. L.

K. C. Hickman, S. M. Gaspar, S. S. H. Naqvi, K. P. Bishop, J. R. McNeil, G. D. Tipton, D. L. Draper, B. R. Stallard, “Use of diffraction from latent images to improve lithography control,”J. Vac. Sci. Technol. B 10, 2259–2266 (1992).
[CrossRef]

Easterling, R. G.

Franke, J. E.

J. E. Franke, L. Zhang, T. M. Niemczyk, D. M. Haaland, J. H. Linn, “Quantitative analysis of IR reflection spectra from phosphosilicate glass films,”J. Electrochem. Soc. 140, 1425–1429 (1993).
[CrossRef]

Gaspar, S. M.

S. S. H. Naqvi, S. M. Gaspar, K. C. Hickman, J. R. McNeil, “Linewidth measurement of gratings on photomasks: a simple technique,” Appl. Opt. 31, 1377–1384 (1992).
[CrossRef] [PubMed]

S. S. H. Naqvi, S. M. Gaspar, K. C. Hickman, K. P. Bishop, L. M. Milner, R. H. Krukar, G. A. Petersen, “Scatterometry applied to microelectronic processing,” Microlith. World 1(6), 16–22 (1992).

K. C. Hickman, S. M. Gaspar, S. S. H. Naqvi, K. P. Bishop, J. R. McNeil, G. D. Tipton, D. L. Draper, B. R. Stallard, “Use of diffraction from latent images to improve lithography control,”J. Vac. Sci. Technol. B 10, 2259–2266 (1992).
[CrossRef]

K. P. Bishop, S. M. Gaspar, L. M. Milner, S. Sohail, H. Naqvi, J. R. McNeil, “Grating line shape characterization using scatterometry,” in International Conference on the Application and Theory of Periodic Structures, J. M. Lerner, W. R. McKinney, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1545, 64–73 (1991).
[CrossRef]

Gaylord, T. K.

T. K. Gaylord, M. G. Moharram, “Analysis and applications of optical diffraction by gratings,” Proc. IEEE 73, 894–937 (1985).
[CrossRef]

Gottscho, R. A.

R. Krukar, A. Kornblit, L. Clark, J. Kruskal, D. Lambert, E. A. Reitman, R. A. Gottscho, “Reactive ion etching and depth characterization using statistical and neural network analysis of light scattering data,” J. Appl. Phys. 74, 3698–3706 (1993).
[CrossRef]

Grant, S. D.

M. G. Buehler, S. D. Grant, W. R. Thurber, “Bridge and van der Pauw sheet resistors for characterizing the line width of conducting layers,”J. Electrochem. Soc. 125, 650–654 (1978).
[CrossRef]

Haaland, D. M.

J. E. Franke, L. Zhang, T. M. Niemczyk, D. M. Haaland, J. H. Linn, “Quantitative analysis of IR reflection spectra from phosphosilicate glass films,”J. Electrochem. Soc. 140, 1425–1429 (1993).
[CrossRef]

B. Wangmaneerat, T. M. Niemczyk, D. M. Haaland, “Determination of temperature and composition of phosphosilicate glass thin films from infrared emission spectral data,” Appl. Spectrosc. 46, 1447–1453 (1992).
[CrossRef]

E. V. Thomas, D. M. Haaland, “Comparison of multivariate calibration methods for quantitative spectral analysis,” Anal. Chem. 62, 1091–1099 (1990).
[CrossRef]

D. M. Haaland, E. V. Thomas, “Partial least squares methods for spectral analysis. I. Relation to other quantitative calibration methods and the extraction of qualitative information,” Anal. Chem. 60, 1193–1202 (1988).
[CrossRef]

D. M. Haaland, “Quantitative infrared analysis of borophosphosilicate films using multivariate statistical methods,” Anal. Chem. 60, 1208–1217 (1988).
[CrossRef]

D. M. Haaland, R. G. Easterling, “Improved sensitivity of infrared spectroscopy by the application of least squares methods,” Appl. Spectrosc. 34, 539–548 (1980).
[CrossRef]

D. M. Haaland, “Multivariate calibration methods applied to quantitative FT-IR analysis,” in Practical Fourier Transform Infrared Spectroscopy, J. R. Ferraro, K. Krishnan, eds. (Academic, San Diego, Calif., 1990), pp. 395–468.

D. M. Haaland, “Multivariate calibration methods applied to the quantitative analysis of infrared spectra,” in Computer-Enhanced Analytical Spectroscopy, P. C. Jurf, ed. (Plenum, New York, 1992), Vol. 3, pp. 1–30.

Haggans, C. W.

Hatab, Z. R.

S. S. H. Naqvi, J. R. McNeil, R. H. Krukar, Z. R. Hatab, “Grating parameter estimation using scatterometry,” in Miniature and Micro-Optics and Micromechanics, N. C. Gallagher, C. Roychoudhuri, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1992, 171–180 (1993).
[CrossRef]

Hickman, K. C.

S. S. H. Naqvi, S. M. Gaspar, K. C. Hickman, J. R. McNeil, “Linewidth measurement of gratings on photomasks: a simple technique,” Appl. Opt. 31, 1377–1384 (1992).
[CrossRef] [PubMed]

K. C. Hickman, S. M. Gaspar, S. S. H. Naqvi, K. P. Bishop, J. R. McNeil, G. D. Tipton, D. L. Draper, B. R. Stallard, “Use of diffraction from latent images to improve lithography control,”J. Vac. Sci. Technol. B 10, 2259–2266 (1992).
[CrossRef]

S. S. H. Naqvi, S. M. Gaspar, K. C. Hickman, K. P. Bishop, L. M. Milner, R. H. Krukar, G. A. Petersen, “Scatterometry applied to microelectronic processing,” Microlith. World 1(6), 16–22 (1992).

Joy, D.

M. Postek, D. Joy, “Submicrometer microelectronics dimensional metrology: scanning electron microscopy,”J. Res. Nat. Bur. Stand. 92, 205–228 (1987).
[CrossRef]

Kornblit, A.

R. Krukar, A. Kornblit, L. Clark, J. Kruskal, D. Lambert, E. A. Reitman, R. A. Gottscho, “Reactive ion etching and depth characterization using statistical and neural network analysis of light scattering data,” J. Appl. Phys. 74, 3698–3706 (1993).
[CrossRef]

Kowalski, B. R.

K. R. Beebe, B. R. Kowalski, “An introduction to multivariate calibration and analysis,” Anal. Chem. 59, 1007A–1017A (1987).

Krukar, R.

R. Krukar, A. Kornblit, L. Clark, J. Kruskal, D. Lambert, E. A. Reitman, R. A. Gottscho, “Reactive ion etching and depth characterization using statistical and neural network analysis of light scattering data,” J. Appl. Phys. 74, 3698–3706 (1993).
[CrossRef]

R. Krukar, “A methodology for the use of diffracted scatter analysis to measure the critical dimension of periodic structures,” Ph.D. dissertation (University of New Mexico, Albuquerque, N.M., 1993).

Krukar, R. H.

S. S. H. Naqvi, J. R. McNeil, R. H. Krukar, K. P. Bishop, “Scatterometry and the simulation of diffraction-based metrology,” Microlith. World 2(3), 5–16 (1993).

S. S. H. Naqvi, S. M. Gaspar, K. C. Hickman, K. P. Bishop, L. M. Milner, R. H. Krukar, G. A. Petersen, “Scatterometry applied to microelectronic processing,” Microlith. World 1(6), 16–22 (1992).

S. S. H. Naqvi, J. R. McNeil, R. H. Krukar, Z. R. Hatab, “Grating parameter estimation using scatterometry,” in Miniature and Micro-Optics and Micromechanics, N. C. Gallagher, C. Roychoudhuri, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1992, 171–180 (1993).
[CrossRef]

Kruskal, J.

R. Krukar, A. Kornblit, L. Clark, J. Kruskal, D. Lambert, E. A. Reitman, R. A. Gottscho, “Reactive ion etching and depth characterization using statistical and neural network analysis of light scattering data,” J. Appl. Phys. 74, 3698–3706 (1993).
[CrossRef]

Lambert, D.

R. Krukar, A. Kornblit, L. Clark, J. Kruskal, D. Lambert, E. A. Reitman, R. A. Gottscho, “Reactive ion etching and depth characterization using statistical and neural network analysis of light scattering data,” J. Appl. Phys. 74, 3698–3706 (1993).
[CrossRef]

Larrabee, R. D.

R. D. Larrabee, M. T. Postek, “Precision, accuracy, uncertainty and traceability and their application to submicrometer dimensional metrology,” Solid-State Electron. 36, 673–684 (1993).
[CrossRef]

Li, L.

Lidiard, D. P.

R. E. Aries, D. P. Lidiard, R. A. Spragg, “Principal component analysis,” Chem. Ber. 27, 821–824 (1991).

Linn, J. H.

J. E. Franke, L. Zhang, T. M. Niemczyk, D. M. Haaland, J. H. Linn, “Quantitative analysis of IR reflection spectra from phosphosilicate glass films,”J. Electrochem. Soc. 140, 1425–1429 (1993).
[CrossRef]

Martens, H. A.

T. Naes, H. A. Martens, “Multivariate calibration. II. Chemometric methods,” Trends Anal. Chem. 3, 266–271 (1984).
[CrossRef]

H. A. Martens, T. Naes, “Multivariate calibration. I. Concepts and distinctions,” Trends Anal. Chem. 3, 204–210 (1984).
[CrossRef]

Maystre, D.

McNeil, J. R.

S. S. H. Naqvi, J. R. McNeil, R. H. Krukar, K. P. Bishop, “Scatterometry and the simulation of diffraction-based metrology,” Microlith. World 2(3), 5–16 (1993).

L. M. Milner, K. P. Bishop, S. S. H. Naqvi, J. R. McNeil, “Stepper focus characterization using diffraction from latent images,”J. Vac. Sci. Technol. B 11, 1258–1266 (1993).
[CrossRef]

S. S. H. Naqvi, S. M. Gaspar, K. C. Hickman, J. R. McNeil, “Linewidth measurement of gratings on photomasks: a simple technique,” Appl. Opt. 31, 1377–1384 (1992).
[CrossRef] [PubMed]

K. C. Hickman, S. M. Gaspar, S. S. H. Naqvi, K. P. Bishop, J. R. McNeil, G. D. Tipton, D. L. Draper, B. R. Stallard, “Use of diffraction from latent images to improve lithography control,”J. Vac. Sci. Technol. B 10, 2259–2266 (1992).
[CrossRef]

K. P. Bishop, S. M. Gaspar, L. M. Milner, S. Sohail, H. Naqvi, J. R. McNeil, “Grating line shape characterization using scatterometry,” in International Conference on the Application and Theory of Periodic Structures, J. M. Lerner, W. R. McKinney, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1545, 64–73 (1991).
[CrossRef]

S. S. H. Naqvi, J. R. McNeil, R. H. Krukar, Z. R. Hatab, “Grating parameter estimation using scatterometry,” in Miniature and Micro-Optics and Micromechanics, N. C. Gallagher, C. Roychoudhuri, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1992, 171–180 (1993).
[CrossRef]

McPhedran, R. C.

I. C. Botten, M. S. Creig, R. C. McPhedran, “Highly conducting lamellar diffraction gratings,” Opt. Acta 28, 1103–1106 (1981).
[CrossRef]

Milner, L. M.

L. M. Milner, K. P. Bishop, S. S. H. Naqvi, J. R. McNeil, “Stepper focus characterization using diffraction from latent images,”J. Vac. Sci. Technol. B 11, 1258–1266 (1993).
[CrossRef]

S. S. H. Naqvi, S. M. Gaspar, K. C. Hickman, K. P. Bishop, L. M. Milner, R. H. Krukar, G. A. Petersen, “Scatterometry applied to microelectronic processing,” Microlith. World 1(6), 16–22 (1992).

K. P. Bishop, S. M. Gaspar, L. M. Milner, S. Sohail, H. Naqvi, J. R. McNeil, “Grating line shape characterization using scatterometry,” in International Conference on the Application and Theory of Periodic Structures, J. M. Lerner, W. R. McKinney, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1545, 64–73 (1991).
[CrossRef]

Moharram, M. G.

T. K. Gaylord, M. G. Moharram, “Analysis and applications of optical diffraction by gratings,” Proc. IEEE 73, 894–937 (1985).
[CrossRef]

Monahan, K. M.

M. R. Rodgers, K. M. Monahan, “Using the atomic force microscope to measure submicron dimension of integrated circuit devices and processes,” in Integrated Circuit Metrology, Inspection, and Process Control V, W. H. Arnold, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1464, 358–366 (1991).
[CrossRef]

Naes, T.

H. A. Martens, T. Naes, “Multivariate calibration. I. Concepts and distinctions,” Trends Anal. Chem. 3, 204–210 (1984).
[CrossRef]

T. Naes, H. A. Martens, “Multivariate calibration. II. Chemometric methods,” Trends Anal. Chem. 3, 266–271 (1984).
[CrossRef]

Naqvi, H.

K. P. Bishop, S. M. Gaspar, L. M. Milner, S. Sohail, H. Naqvi, J. R. McNeil, “Grating line shape characterization using scatterometry,” in International Conference on the Application and Theory of Periodic Structures, J. M. Lerner, W. R. McKinney, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1545, 64–73 (1991).
[CrossRef]

Naqvi, S. S. H.

L. M. Milner, K. P. Bishop, S. S. H. Naqvi, J. R. McNeil, “Stepper focus characterization using diffraction from latent images,”J. Vac. Sci. Technol. B 11, 1258–1266 (1993).
[CrossRef]

S. S. H. Naqvi, J. R. McNeil, R. H. Krukar, K. P. Bishop, “Scatterometry and the simulation of diffraction-based metrology,” Microlith. World 2(3), 5–16 (1993).

S. S. H. Naqvi, S. M. Gaspar, K. C. Hickman, J. R. McNeil, “Linewidth measurement of gratings on photomasks: a simple technique,” Appl. Opt. 31, 1377–1384 (1992).
[CrossRef] [PubMed]

S. S. H. Naqvi, S. M. Gaspar, K. C. Hickman, K. P. Bishop, L. M. Milner, R. H. Krukar, G. A. Petersen, “Scatterometry applied to microelectronic processing,” Microlith. World 1(6), 16–22 (1992).

K. C. Hickman, S. M. Gaspar, S. S. H. Naqvi, K. P. Bishop, J. R. McNeil, G. D. Tipton, D. L. Draper, B. R. Stallard, “Use of diffraction from latent images to improve lithography control,”J. Vac. Sci. Technol. B 10, 2259–2266 (1992).
[CrossRef]

S. S. H. Naqvi, J. R. McNeil, R. H. Krukar, Z. R. Hatab, “Grating parameter estimation using scatterometry,” in Miniature and Micro-Optics and Micromechanics, N. C. Gallagher, C. Roychoudhuri, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1992, 171–180 (1993).
[CrossRef]

Niemczyk, T. M.

J. E. Franke, L. Zhang, T. M. Niemczyk, D. M. Haaland, J. H. Linn, “Quantitative analysis of IR reflection spectra from phosphosilicate glass films,”J. Electrochem. Soc. 140, 1425–1429 (1993).
[CrossRef]

B. Wangmaneerat, T. M. Niemczyk, D. M. Haaland, “Determination of temperature and composition of phosphosilicate glass thin films from infrared emission spectral data,” Appl. Spectrosc. 46, 1447–1453 (1992).
[CrossRef]

Petersen, G. A.

S. S. H. Naqvi, S. M. Gaspar, K. C. Hickman, K. P. Bishop, L. M. Milner, R. H. Krukar, G. A. Petersen, “Scatterometry applied to microelectronic processing,” Microlith. World 1(6), 16–22 (1992).

Postek, M.

M. Postek, D. Joy, “Submicrometer microelectronics dimensional metrology: scanning electron microscopy,”J. Res. Nat. Bur. Stand. 92, 205–228 (1987).
[CrossRef]

Postek, M. T.

R. D. Larrabee, M. T. Postek, “Precision, accuracy, uncertainty and traceability and their application to submicrometer dimensional metrology,” Solid-State Electron. 36, 673–684 (1993).
[CrossRef]

Reitman, E. A.

R. Krukar, A. Kornblit, L. Clark, J. Kruskal, D. Lambert, E. A. Reitman, R. A. Gottscho, “Reactive ion etching and depth characterization using statistical and neural network analysis of light scattering data,” J. Appl. Phys. 74, 3698–3706 (1993).
[CrossRef]

Rodgers, M. R.

M. R. Rodgers, K. M. Monahan, “Using the atomic force microscope to measure submicron dimension of integrated circuit devices and processes,” in Integrated Circuit Metrology, Inspection, and Process Control V, W. H. Arnold, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1464, 358–366 (1991).
[CrossRef]

Roger, A.

A. Roger, M. Breidne, “Grating profile reconstruction by an inverse scattering method,” Opt. Commun. 35, 299–302 (1980).
[CrossRef]

A. Roger, D. Maystre, “Inverse scattering method in electromagnetic optics: application to diffraction gratings,”J. Opt. Soc. Am. 70, 1483–1495 (1980).
[CrossRef]

Sohail, S.

K. P. Bishop, S. M. Gaspar, L. M. Milner, S. Sohail, H. Naqvi, J. R. McNeil, “Grating line shape characterization using scatterometry,” in International Conference on the Application and Theory of Periodic Structures, J. M. Lerner, W. R. McKinney, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1545, 64–73 (1991).
[CrossRef]

Spragg, R. A.

R. E. Aries, D. P. Lidiard, R. A. Spragg, “Principal component analysis,” Chem. Ber. 27, 821–824 (1991).

Stallard, B. R.

K. C. Hickman, S. M. Gaspar, S. S. H. Naqvi, K. P. Bishop, J. R. McNeil, G. D. Tipton, D. L. Draper, B. R. Stallard, “Use of diffraction from latent images to improve lithography control,”J. Vac. Sci. Technol. B 10, 2259–2266 (1992).
[CrossRef]

Thomas, E. V.

E. V. Thomas, D. M. Haaland, “Comparison of multivariate calibration methods for quantitative spectral analysis,” Anal. Chem. 62, 1091–1099 (1990).
[CrossRef]

D. M. Haaland, E. V. Thomas, “Partial least squares methods for spectral analysis. I. Relation to other quantitative calibration methods and the extraction of qualitative information,” Anal. Chem. 60, 1193–1202 (1988).
[CrossRef]

Thurber, W. R.

M. G. Buehler, S. D. Grant, W. R. Thurber, “Bridge and van der Pauw sheet resistors for characterizing the line width of conducting layers,”J. Electrochem. Soc. 125, 650–654 (1978).
[CrossRef]

Tipton, G. D.

K. C. Hickman, S. M. Gaspar, S. S. H. Naqvi, K. P. Bishop, J. R. McNeil, G. D. Tipton, D. L. Draper, B. R. Stallard, “Use of diffraction from latent images to improve lithography control,”J. Vac. Sci. Technol. B 10, 2259–2266 (1992).
[CrossRef]

Wahba, G.

G. Wahba, “Practical approximate solutions to linear operator equations when the data are noisy,” SIAM J. Numer. Anal. 14, 651–667 (1977).
[CrossRef]

Wangmaneerat, B.

Zhang, L.

J. E. Franke, L. Zhang, T. M. Niemczyk, D. M. Haaland, J. H. Linn, “Quantitative analysis of IR reflection spectra from phosphosilicate glass films,”J. Electrochem. Soc. 140, 1425–1429 (1993).
[CrossRef]

Anal. Chem.

S. D. Brown, R. S. Bear, T. B. Blank, “Chemometrics,” Anal. Chem. 64, 22R–49R (1992).
[CrossRef]

K. R. Beebe, B. R. Kowalski, “An introduction to multivariate calibration and analysis,” Anal. Chem. 59, 1007A–1017A (1987).

E. V. Thomas, D. M. Haaland, “Comparison of multivariate calibration methods for quantitative spectral analysis,” Anal. Chem. 62, 1091–1099 (1990).
[CrossRef]

D. M. Haaland, E. V. Thomas, “Partial least squares methods for spectral analysis. I. Relation to other quantitative calibration methods and the extraction of qualitative information,” Anal. Chem. 60, 1193–1202 (1988).
[CrossRef]

D. M. Haaland, “Quantitative infrared analysis of borophosphosilicate films using multivariate statistical methods,” Anal. Chem. 60, 1208–1217 (1988).
[CrossRef]

Appl. Opt.

Appl. Spectrosc.

Chem. Ber.

R. E. Aries, D. P. Lidiard, R. A. Spragg, “Principal component analysis,” Chem. Ber. 27, 821–824 (1991).

J. Appl. Phys.

R. Krukar, A. Kornblit, L. Clark, J. Kruskal, D. Lambert, E. A. Reitman, R. A. Gottscho, “Reactive ion etching and depth characterization using statistical and neural network analysis of light scattering data,” J. Appl. Phys. 74, 3698–3706 (1993).
[CrossRef]

J. Electrochem. Soc.

J. E. Franke, L. Zhang, T. M. Niemczyk, D. M. Haaland, J. H. Linn, “Quantitative analysis of IR reflection spectra from phosphosilicate glass films,”J. Electrochem. Soc. 140, 1425–1429 (1993).
[CrossRef]

M. G. Buehler, S. D. Grant, W. R. Thurber, “Bridge and van der Pauw sheet resistors for characterizing the line width of conducting layers,”J. Electrochem. Soc. 125, 650–654 (1978).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

J. Res. Nat. Bur. Stand.

M. Postek, D. Joy, “Submicrometer microelectronics dimensional metrology: scanning electron microscopy,”J. Res. Nat. Bur. Stand. 92, 205–228 (1987).
[CrossRef]

J. Vac. Sci. Technol. B

K. C. Hickman, S. M. Gaspar, S. S. H. Naqvi, K. P. Bishop, J. R. McNeil, G. D. Tipton, D. L. Draper, B. R. Stallard, “Use of diffraction from latent images to improve lithography control,”J. Vac. Sci. Technol. B 10, 2259–2266 (1992).
[CrossRef]

L. M. Milner, K. P. Bishop, S. S. H. Naqvi, J. R. McNeil, “Stepper focus characterization using diffraction from latent images,”J. Vac. Sci. Technol. B 11, 1258–1266 (1993).
[CrossRef]

Microlith. World

S. S. H. Naqvi, S. M. Gaspar, K. C. Hickman, K. P. Bishop, L. M. Milner, R. H. Krukar, G. A. Petersen, “Scatterometry applied to microelectronic processing,” Microlith. World 1(6), 16–22 (1992).

S. S. H. Naqvi, J. R. McNeil, R. H. Krukar, K. P. Bishop, “Scatterometry and the simulation of diffraction-based metrology,” Microlith. World 2(3), 5–16 (1993).

Opt. Acta

I. C. Botten, M. S. Creig, R. C. McPhedran, “Highly conducting lamellar diffraction gratings,” Opt. Acta 28, 1103–1106 (1981).
[CrossRef]

Opt. Commun.

A. Roger, M. Breidne, “Grating profile reconstruction by an inverse scattering method,” Opt. Commun. 35, 299–302 (1980).
[CrossRef]

Proc. IEEE

T. K. Gaylord, M. G. Moharram, “Analysis and applications of optical diffraction by gratings,” Proc. IEEE 73, 894–937 (1985).
[CrossRef]

SIAM J. Numer. Anal.

G. Wahba, “Practical approximate solutions to linear operator equations when the data are noisy,” SIAM J. Numer. Anal. 14, 651–667 (1977).
[CrossRef]

Solid-State Electron.

R. D. Larrabee, M. T. Postek, “Precision, accuracy, uncertainty and traceability and their application to submicrometer dimensional metrology,” Solid-State Electron. 36, 673–684 (1993).
[CrossRef]

Trends Anal. Chem.

H. A. Martens, T. Naes, “Multivariate calibration. I. Concepts and distinctions,” Trends Anal. Chem. 3, 204–210 (1984).
[CrossRef]

T. Naes, H. A. Martens, “Multivariate calibration. II. Chemometric methods,” Trends Anal. Chem. 3, 266–271 (1984).
[CrossRef]

Other

S. S. H. Naqvi, J. R. McNeil, R. H. Krukar, Z. R. Hatab, “Grating parameter estimation using scatterometry,” in Miniature and Micro-Optics and Micromechanics, N. C. Gallagher, C. Roychoudhuri, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1992, 171–180 (1993).
[CrossRef]

K. P. Bishop, S. M. Gaspar, L. M. Milner, S. Sohail, H. Naqvi, J. R. McNeil, “Grating line shape characterization using scatterometry,” in International Conference on the Application and Theory of Periodic Structures, J. M. Lerner, W. R. McKinney, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1545, 64–73 (1991).
[CrossRef]

M. R. Rodgers, K. M. Monahan, “Using the atomic force microscope to measure submicron dimension of integrated circuit devices and processes,” in Integrated Circuit Metrology, Inspection, and Process Control V, W. H. Arnold, ed., Proc. Soc. Photo-Opt. Instrum. Eng.1464, 358–366 (1991).
[CrossRef]

R. Krukar, “A methodology for the use of diffracted scatter analysis to measure the critical dimension of periodic structures,” Ph.D. dissertation (University of New Mexico, Albuquerque, N.M., 1993).

R. Petit, ed., Electromagnetic Theory of Gratings (Springer-Verlag, Berlin, 1980).
[CrossRef]

D. M. Haaland, “Multivariate calibration methods applied to quantitative FT-IR analysis,” in Practical Fourier Transform Infrared Spectroscopy, J. R. Ferraro, K. Krishnan, eds. (Academic, San Diego, Calif., 1990), pp. 395–468.

D. M. Haaland, “Multivariate calibration methods applied to the quantitative analysis of infrared spectra,” in Computer-Enhanced Analytical Spectroscopy, P. C. Jurf, ed. (Plenum, New York, 1992), Vol. 3, pp. 1–30.

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Figures (7)

Fig. 1
Fig. 1

Rectangular-shaped large-period etched silicon grating.

Fig. 2
Fig. 2

Angle-scanning scatterometer. θi is the angle of incidence, and θs is the angle at which the scattered light is detected.

Fig. 3
Fig. 3

Angle-resolved scatter measurement of a 32-μm-pitch diffraction grating illuminated with a normally incident laser beam.

Fig. 4
Fig. 4

Comparison of theoretical and experimental diffraction data.

Fig. 5
Fig. 5

Effect of grating-height change on theoretical diffraction intensity data. A beam from a He–Ne laser is assumed to be normally incident upon the etched silicon (n = 3.87, k = 0.007) grating.

Fig. 6
Fig. 6

Effect of incident-field wavelength on calibration characteristics.

Fig. 7
Fig. 7

Calibration results for the narrow-range prediction case.

Tables (2)

Tables Icon

Table 1 Comparison of Predicted and AFM-Measured Etch Depth for the Broad-Range Calibration Case

Tables Icon

Table 2 Comparison of Predicted and AFM-Measured Etch Depth for the Narrow-Range Calibration Case

Equations (5)

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

sin θ i + sin θ n = n ( λ / d ) ,
A = TB + E ,
d = Tv + e d ,
A = A - t 1 b 1 T ,
SEP = [ 1 m i = 1 m ( e i ) 2 ] 1 / 2 ,

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