Abstract

The optical microscope measurement of small objects, 0.5 to 10 µm in diameter, is complicated by the apparent change in the dimension of the object with a change in the spatial coherence of the illumination. Coherent edgedetection methods have been developed for the measurement of line objects on integrated-circuit photo masks and wafers. A generalization is presented of the coherent threshold equation that permits the extension to any state of partial coherence of the illumination as well as extension to the measurement of nonplanar objects. In the latter case, a waveguide model is developed for imaging of lines patterned in thick layers and is compared with experimental data.

© 1982 Optical Society of America

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  1. W. T. Welford, in Optics in Metrology, P. Mollet, ed. (Pergamon, New York, 1960), p. 85.
  2. W. W. Bullis and D. Nyyssonen, in VLSI Electronics: Micro-structure Science, Vol. 3, N. G. Einspruch, ed. (Academic, New York, 1982), pp. 301–346.
  3. D. Nyyssonen, "Optical linewidth measurements on wafers," Proc. Soc. Photo-Opt. Instrum. Eng. 135, 115–119 (1978).
  4. D. Nyyssonen, "Calibration of optical systems for linewidth measurements on wafers," Proc. Soc. Photo-Opt. Instrum. Eng. 221, 119–126 (1980).
  5. L. C. Martin, The Theory of the Microscope (Blackie, London, 1966), Chaps. V and VIII.
  6. I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series and Products (Academic, New York, 1980), p. 7.
  7. E. C. Kintner, "Method for the calculation of partially coherent imagery," Appl. Opt. 17, 2747–2753 (1978).
  8. M. Born and E. Wolf, Principles of Optics, 5th ed. (Pergamon, Oxford, 1975), pp. 522–526.
  9. H. H. Hopkins, "Applications of coherence theory in microscopy and interferometry," J. Opt. Soc. Am. 47, 508–526 (1957).
  10. F. Zernike, "The concept of degree of coherence," Physica 5, 785–795 (1938).
  11. B. M. Wastrasiewicz, "Theoretical calculations of straight edges in partially coherent illumination," Proc. R. Soc. London Ser. A 293, 391–400 (1966).
  12. Ref. 8, p. 490.
  13. Ref. 8, p. 441.
  14. V. Coates, "Computerized optical system for precision linewidth measurements," in Proceedings of the Microelectronics Measurement Technology Seminar (Benwill, Boston, Mass., 1979), pp. 273–277.
  15. Ref. 8, p. 631.
  16. H. M. Smith, Principles of Holography (Wiley, New York, 1969), Chap. 4.
  17. R. S. Longhurst, Geometrical and Physical Optics, 2nd ed. (Wiley, New York, 1967), pp. 276–278.
  18. B. Richards and E. Wolf, "Electromagnetic diffraction in optical systems. II. Structure of the image field in an aplanatic system," Proc. R. Soc. London Ser. A 253, 358–379 (1959).
  19. C. B. Burckhardt, "Diffraction of a plane wave at a sinusoidally stratified dielectric grating," J. Opt. Soc. Am. 56, 1502–1509 (1966).
  20. F. G. Kaspar, "Diffraction by thick, periodically stratified gratings with complex dielectric constant," J. Opt. Soc. Am. 63, 37–45 (1973).
  21. F. G. Kaspar, "Computation of light transmitted by a thick grating, for application to contact printing," J. Opt. Soc. Am. 64, 1623–1630 (1974).
  22. F. L. McCrackin and J. P. Colson, "Computational techniques for the use of the exact Drude equations in reflection problems,"Nat. Bur. Stand. (U.S.) Monog. 256, 61–82 (1963).
  23. L. B. Felsen and N. Marcuvitz, Radiation and Scattering of Waves (Prentice-Hall, Englewood Cliffs, N.J., 1973), pp. 538–543.
  24. D. Nyyssonen, "High resolution microdensitometry of photographic emulsions," Ph.D. Thesis (University of Rochester, Rochester, N.Y., 1975).
  25. W. Streifer, D. R. Scifres and R. D. Burnham, "Analysis of grating-coupled radiation in GaAs:GaAlAs lasers and waveguides," IEEE J. Quantum Electron. QE-12, 422–428 (1976).
  26. W. Streifer, R. D. Burnham and D. R. Scifres, "Analysis of grating-coupled GaAs:GaAlAs lasers and waveguides—II: blazing effects," IEEE J. Quantum Electron. QE-12, 494–499 (1976).
  27. W. Lee and W. Streifer, "Radiation loss calculations for corrugateddielectric waveguides," J. Opt. Soc. Am. 68, 1701–1707 (1978).
  28. F. E. Scire and E. C. Teague, "Piezodriven 50-µm range stage with subnanometer resolution," Rev. Sci. Instrum. 49, 1735–1740 (1978).

1980 (1)

D. Nyyssonen, "Calibration of optical systems for linewidth measurements on wafers," Proc. Soc. Photo-Opt. Instrum. Eng. 221, 119–126 (1980).

1978 (4)

E. C. Kintner, "Method for the calculation of partially coherent imagery," Appl. Opt. 17, 2747–2753 (1978).

D. Nyyssonen, "Optical linewidth measurements on wafers," Proc. Soc. Photo-Opt. Instrum. Eng. 135, 115–119 (1978).

W. Lee and W. Streifer, "Radiation loss calculations for corrugateddielectric waveguides," J. Opt. Soc. Am. 68, 1701–1707 (1978).

F. E. Scire and E. C. Teague, "Piezodriven 50-µm range stage with subnanometer resolution," Rev. Sci. Instrum. 49, 1735–1740 (1978).

1976 (2)

W. Streifer, D. R. Scifres and R. D. Burnham, "Analysis of grating-coupled radiation in GaAs:GaAlAs lasers and waveguides," IEEE J. Quantum Electron. QE-12, 422–428 (1976).

W. Streifer, R. D. Burnham and D. R. Scifres, "Analysis of grating-coupled GaAs:GaAlAs lasers and waveguides—II: blazing effects," IEEE J. Quantum Electron. QE-12, 494–499 (1976).

1974 (1)

1973 (1)

1966 (2)

C. B. Burckhardt, "Diffraction of a plane wave at a sinusoidally stratified dielectric grating," J. Opt. Soc. Am. 56, 1502–1509 (1966).

B. M. Wastrasiewicz, "Theoretical calculations of straight edges in partially coherent illumination," Proc. R. Soc. London Ser. A 293, 391–400 (1966).

1963 (1)

F. L. McCrackin and J. P. Colson, "Computational techniques for the use of the exact Drude equations in reflection problems,"Nat. Bur. Stand. (U.S.) Monog. 256, 61–82 (1963).

1959 (1)

B. Richards and E. Wolf, "Electromagnetic diffraction in optical systems. II. Structure of the image field in an aplanatic system," Proc. R. Soc. London Ser. A 253, 358–379 (1959).

1957 (1)

1938 (1)

F. Zernike, "The concept of degree of coherence," Physica 5, 785–795 (1938).

Hopkins, H. H.

Martin, L. C.

L. C. Martin, The Theory of the Microscope (Blackie, London, 1966), Chaps. V and VIII.

Born, M.

M. Born and E. Wolf, Principles of Optics, 5th ed. (Pergamon, Oxford, 1975), pp. 522–526.

Bullis, W. W.

W. W. Bullis and D. Nyyssonen, in VLSI Electronics: Micro-structure Science, Vol. 3, N. G. Einspruch, ed. (Academic, New York, 1982), pp. 301–346.

Burckhardt, C. B.

Burnham, R. D.

W. Streifer, D. R. Scifres and R. D. Burnham, "Analysis of grating-coupled radiation in GaAs:GaAlAs lasers and waveguides," IEEE J. Quantum Electron. QE-12, 422–428 (1976).

W. Streifer, R. D. Burnham and D. R. Scifres, "Analysis of grating-coupled GaAs:GaAlAs lasers and waveguides—II: blazing effects," IEEE J. Quantum Electron. QE-12, 494–499 (1976).

Coates, V.

V. Coates, "Computerized optical system for precision linewidth measurements," in Proceedings of the Microelectronics Measurement Technology Seminar (Benwill, Boston, Mass., 1979), pp. 273–277.

Colson, J. P.

F. L. McCrackin and J. P. Colson, "Computational techniques for the use of the exact Drude equations in reflection problems,"Nat. Bur. Stand. (U.S.) Monog. 256, 61–82 (1963).

Felsen, L. B.

L. B. Felsen and N. Marcuvitz, Radiation and Scattering of Waves (Prentice-Hall, Englewood Cliffs, N.J., 1973), pp. 538–543.

Gradshteyn, I. S.

I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series and Products (Academic, New York, 1980), p. 7.

Kaspar, F. G.

Kintner, E. C.

Lee, W.

Longhurst, R. S.

R. S. Longhurst, Geometrical and Physical Optics, 2nd ed. (Wiley, New York, 1967), pp. 276–278.

Marcuvitz, N.

L. B. Felsen and N. Marcuvitz, Radiation and Scattering of Waves (Prentice-Hall, Englewood Cliffs, N.J., 1973), pp. 538–543.

McCrackin, F. L.

F. L. McCrackin and J. P. Colson, "Computational techniques for the use of the exact Drude equations in reflection problems,"Nat. Bur. Stand. (U.S.) Monog. 256, 61–82 (1963).

Nyyssonen, D.

D. Nyyssonen, "Calibration of optical systems for linewidth measurements on wafers," Proc. Soc. Photo-Opt. Instrum. Eng. 221, 119–126 (1980).

D. Nyyssonen, "Optical linewidth measurements on wafers," Proc. Soc. Photo-Opt. Instrum. Eng. 135, 115–119 (1978).

W. W. Bullis and D. Nyyssonen, in VLSI Electronics: Micro-structure Science, Vol. 3, N. G. Einspruch, ed. (Academic, New York, 1982), pp. 301–346.

D. Nyyssonen, "High resolution microdensitometry of photographic emulsions," Ph.D. Thesis (University of Rochester, Rochester, N.Y., 1975).

Richards, B.

B. Richards and E. Wolf, "Electromagnetic diffraction in optical systems. II. Structure of the image field in an aplanatic system," Proc. R. Soc. London Ser. A 253, 358–379 (1959).

Ryzhik, I. M.

I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series and Products (Academic, New York, 1980), p. 7.

Scifres, D. R.

W. Streifer, R. D. Burnham and D. R. Scifres, "Analysis of grating-coupled GaAs:GaAlAs lasers and waveguides—II: blazing effects," IEEE J. Quantum Electron. QE-12, 494–499 (1976).

W. Streifer, D. R. Scifres and R. D. Burnham, "Analysis of grating-coupled radiation in GaAs:GaAlAs lasers and waveguides," IEEE J. Quantum Electron. QE-12, 422–428 (1976).

Scire, F. E.

F. E. Scire and E. C. Teague, "Piezodriven 50-µm range stage with subnanometer resolution," Rev. Sci. Instrum. 49, 1735–1740 (1978).

Smith, H. M.

H. M. Smith, Principles of Holography (Wiley, New York, 1969), Chap. 4.

Streifer, W.

W. Lee and W. Streifer, "Radiation loss calculations for corrugateddielectric waveguides," J. Opt. Soc. Am. 68, 1701–1707 (1978).

W. Streifer, R. D. Burnham and D. R. Scifres, "Analysis of grating-coupled GaAs:GaAlAs lasers and waveguides—II: blazing effects," IEEE J. Quantum Electron. QE-12, 494–499 (1976).

W. Streifer, D. R. Scifres and R. D. Burnham, "Analysis of grating-coupled radiation in GaAs:GaAlAs lasers and waveguides," IEEE J. Quantum Electron. QE-12, 422–428 (1976).

Teague, E. C.

F. E. Scire and E. C. Teague, "Piezodriven 50-µm range stage with subnanometer resolution," Rev. Sci. Instrum. 49, 1735–1740 (1978).

Wastrasiewicz, B. M.

B. M. Wastrasiewicz, "Theoretical calculations of straight edges in partially coherent illumination," Proc. R. Soc. London Ser. A 293, 391–400 (1966).

Welford, W. T.

W. T. Welford, in Optics in Metrology, P. Mollet, ed. (Pergamon, New York, 1960), p. 85.

Wolf, E.

B. Richards and E. Wolf, "Electromagnetic diffraction in optical systems. II. Structure of the image field in an aplanatic system," Proc. R. Soc. London Ser. A 253, 358–379 (1959).

M. Born and E. Wolf, Principles of Optics, 5th ed. (Pergamon, Oxford, 1975), pp. 522–526.

Zernike, F.

F. Zernike, "The concept of degree of coherence," Physica 5, 785–795 (1938).

Appl. Opt. (1)

IEEE J. Quantum Electron. (2)

W. Streifer, D. R. Scifres and R. D. Burnham, "Analysis of grating-coupled radiation in GaAs:GaAlAs lasers and waveguides," IEEE J. Quantum Electron. QE-12, 422–428 (1976).

W. Streifer, R. D. Burnham and D. R. Scifres, "Analysis of grating-coupled GaAs:GaAlAs lasers and waveguides—II: blazing effects," IEEE J. Quantum Electron. QE-12, 494–499 (1976).

J. Opt. Soc. Am. (5)

Nat. Bur. Stand. U.S. Monog. (1)

F. L. McCrackin and J. P. Colson, "Computational techniques for the use of the exact Drude equations in reflection problems,"Nat. Bur. Stand. (U.S.) Monog. 256, 61–82 (1963).

Physica (1)

F. Zernike, "The concept of degree of coherence," Physica 5, 785–795 (1938).

Proc. R. Soc. London Ser. A (2)

B. M. Wastrasiewicz, "Theoretical calculations of straight edges in partially coherent illumination," Proc. R. Soc. London Ser. A 293, 391–400 (1966).

B. Richards and E. Wolf, "Electromagnetic diffraction in optical systems. II. Structure of the image field in an aplanatic system," Proc. R. Soc. London Ser. A 253, 358–379 (1959).

Proc. Soc. Photo-Opt. Instrum. Eng. (2)

D. Nyyssonen, "Optical linewidth measurements on wafers," Proc. Soc. Photo-Opt. Instrum. Eng. 135, 115–119 (1978).

D. Nyyssonen, "Calibration of optical systems for linewidth measurements on wafers," Proc. Soc. Photo-Opt. Instrum. Eng. 221, 119–126 (1980).

Rev. Sci. Instrum. (1)

F. E. Scire and E. C. Teague, "Piezodriven 50-µm range stage with subnanometer resolution," Rev. Sci. Instrum. 49, 1735–1740 (1978).

Other (13)

L. B. Felsen and N. Marcuvitz, Radiation and Scattering of Waves (Prentice-Hall, Englewood Cliffs, N.J., 1973), pp. 538–543.

D. Nyyssonen, "High resolution microdensitometry of photographic emulsions," Ph.D. Thesis (University of Rochester, Rochester, N.Y., 1975).

L. C. Martin, The Theory of the Microscope (Blackie, London, 1966), Chaps. V and VIII.

I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series and Products (Academic, New York, 1980), p. 7.

M. Born and E. Wolf, Principles of Optics, 5th ed. (Pergamon, Oxford, 1975), pp. 522–526.

W. T. Welford, in Optics in Metrology, P. Mollet, ed. (Pergamon, New York, 1960), p. 85.

W. W. Bullis and D. Nyyssonen, in VLSI Electronics: Micro-structure Science, Vol. 3, N. G. Einspruch, ed. (Academic, New York, 1982), pp. 301–346.

Ref. 8, p. 490.

Ref. 8, p. 441.

V. Coates, "Computerized optical system for precision linewidth measurements," in Proceedings of the Microelectronics Measurement Technology Seminar (Benwill, Boston, Mass., 1979), pp. 273–277.

Ref. 8, p. 631.

H. M. Smith, Principles of Holography (Wiley, New York, 1969), Chap. 4.

R. S. Longhurst, Geometrical and Physical Optics, 2nd ed. (Wiley, New York, 1967), pp. 276–278.

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