Abstract

We have demonstrated recently that, by using an ultrastable optical interferometer together with artificial neural networks (ANNs), track widths down to 60  nm can be measured with a 0.3 NA objective lens. We investigate the effective conditions for training ANNs. Experimental results will be used to show the characteristics of the training samples and the data format of the ANN inputs required to produce suitably trained ANNs. Results obtained with networks measuring double tracks, and classifying different structures, will be presented to illustrate the capability of the technique. We include a discussion on expansion of the application areas of the system, allowing it to be used as a general purpose instrument.

© 2007 Optical Society of America

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References

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    [CrossRef]
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2005 (1)

R. J. Smith, C. W. See, M. G. Somekh, A. Yacoot, and E. Choi, "Optical track width measurements below 100 nm using artificial neural networks," Meas. Sci. Technol. 16, 2397-2404 (2005).
[CrossRef]

1999 (1)

S. Haykin, Neural Networks—A Comprehensive Foundation, 2nd ed. (Prentice-Hall, 1999).

1998 (1)

1997 (1)

J. Nunn, W. Mirande, H. Jacobsen, and N. Talene, Challenges in the calibration of a photomask linewidth standard developed for the European Commission, VDE-VDI Conference Proceedings: Mask Technology for Integrated Circuits and Microcomponents, 53-68 (1997).
[PubMed]

1996 (2)

M. H. Hayes, Statistical Digital Signal Processing and Modeling (Wiley, 1996).

K. Gurney, An Introduction to Neural Networks (UCL Press, 1996).

1986 (1)

1985 (1)

1981 (1)

1974 (1)

R. W. Gerchberg, "Super-resolution through error energy reduction," Opt. Acta 21, 709-720 (1974).
[CrossRef]

1968 (1)

1967 (1)

1966 (2)

1964 (1)

1962 (1)

H. J. Landau and H. O. Pollak, "Prolate spheroidal wave functions, Fourier analysis, and uncertainty III: the dimension of the space of essentially time- and band-limited signals," Bell Syst. Tech. J. 41, 1295-1336 (1962).

1961 (3)

D. Slepian and H. O. Pollak, "Prolate spheroidal wave functions, Fourier analysis, and uncertainty I," Bell Syst. Tech. J. 40, 43-63 (1961).

H. J. Landau and H. O. Pollak, "Prolate spheroidal wave functions, Fourier analysis, and uncertainty II," Bell Syst. Tech. J. 40, 65-84 (1961).

H. Wolter, in Progress in Optics, E. Wolf, ed. (North-Holland, 1961), Vol. 1, Chap. 5.

1955 (1)

1927 (1)

E. T. Whittaker and G. N. Watson, A Course of Modern Analysis, 4th ed. (Cambridge University Press, 1927).

Barnes, C. W.

Choi, E.

R. J. Smith, C. W. See, M. G. Somekh, A. Yacoot, and E. Choi, "Optical track width measurements below 100 nm using artificial neural networks," Meas. Sci. Technol. 16, 2397-2404 (2005).
[CrossRef]

Clark, M.

Cox, I. J.

Gerchberg, R. W.

R. W. Gerchberg, "Super-resolution through error energy reduction," Opt. Acta 21, 709-720 (1974).
[CrossRef]

Goh, J. Y. L.

Gurney, K.

K. Gurney, An Introduction to Neural Networks (UCL Press, 1996).

Harris, J. L.

Harris, R. W.

Hayes, M. H.

M. H. Hayes, Statistical Digital Signal Processing and Modeling (Wiley, 1996).

Haykin, S.

S. Haykin, Neural Networks—A Comprehensive Foundation, 2nd ed. (Prentice-Hall, 1999).

Howard, S. J.

Jacobsen, H.

J. Nunn, W. Mirande, H. Jacobsen, and N. Talene, Challenges in the calibration of a photomask linewidth standard developed for the European Commission, VDE-VDI Conference Proceedings: Mask Technology for Integrated Circuits and Microcomponents, 53-68 (1997).
[PubMed]

Kawata, S.

Landau, H. J.

H. J. Landau and H. O. Pollak, "Prolate spheroidal wave functions, Fourier analysis, and uncertainty III: the dimension of the space of essentially time- and band-limited signals," Bell Syst. Tech. J. 41, 1295-1336 (1962).

H. J. Landau and H. O. Pollak, "Prolate spheroidal wave functions, Fourier analysis, and uncertainty II," Bell Syst. Tech. J. 40, 65-84 (1961).

Lukosz, W.

Minami, K.

Minami, S.

Mirande, W.

J. Nunn, W. Mirande, H. Jacobsen, and N. Talene, Challenges in the calibration of a photomask linewidth standard developed for the European Commission, VDE-VDI Conference Proceedings: Mask Technology for Integrated Circuits and Microcomponents, 53-68 (1997).
[PubMed]

Nunn, J.

J. Nunn, W. Mirande, H. Jacobsen, and N. Talene, Challenges in the calibration of a photomask linewidth standard developed for the European Commission, VDE-VDI Conference Proceedings: Mask Technology for Integrated Circuits and Microcomponents, 53-68 (1997).
[PubMed]

Pollak, H. O.

H. J. Landau and H. O. Pollak, "Prolate spheroidal wave functions, Fourier analysis, and uncertainty III: the dimension of the space of essentially time- and band-limited signals," Bell Syst. Tech. J. 41, 1295-1336 (1962).

H. J. Landau and H. O. Pollak, "Prolate spheroidal wave functions, Fourier analysis, and uncertainty II," Bell Syst. Tech. J. 40, 65-84 (1961).

D. Slepian and H. O. Pollak, "Prolate spheroidal wave functions, Fourier analysis, and uncertainty I," Bell Syst. Tech. J. 40, 43-63 (1961).

Rushforth, C. K.

Sawyer, N. B. E.

See, C. W.

R. J. Smith, C. W. See, M. G. Somekh, A. Yacoot, and E. Choi, "Optical track width measurements below 100 nm using artificial neural networks," Meas. Sci. Technol. 16, 2397-2404 (2005).
[CrossRef]

N. B. E. Sawyer, C. W. See, M. Clark, M. G. Somekh, and J. Y. L. Goh, "Ultrastable absolute-phase common-path optical profiler based on computer-generated holography," Appl. Opt. 37, 6716-6720 (1998).
[CrossRef]

Sheppard, C. J. R.

Slepian, D.

D. Slepian and H. O. Pollak, "Prolate spheroidal wave functions, Fourier analysis, and uncertainty I," Bell Syst. Tech. J. 40, 43-63 (1961).

Smith, R. J.

R. J. Smith, C. W. See, M. G. Somekh, A. Yacoot, and E. Choi, "Optical track width measurements below 100 nm using artificial neural networks," Meas. Sci. Technol. 16, 2397-2404 (2005).
[CrossRef]

Somekh, M. G.

R. J. Smith, C. W. See, M. G. Somekh, A. Yacoot, and E. Choi, "Optical track width measurements below 100 nm using artificial neural networks," Meas. Sci. Technol. 16, 2397-2404 (2005).
[CrossRef]

N. B. E. Sawyer, C. W. See, M. Clark, M. G. Somekh, and J. Y. L. Goh, "Ultrastable absolute-phase common-path optical profiler based on computer-generated holography," Appl. Opt. 37, 6716-6720 (1998).
[CrossRef]

Talene, N.

J. Nunn, W. Mirande, H. Jacobsen, and N. Talene, Challenges in the calibration of a photomask linewidth standard developed for the European Commission, VDE-VDI Conference Proceedings: Mask Technology for Integrated Circuits and Microcomponents, 53-68 (1997).
[PubMed]

Toraldo di Francia, G.

Watson, G. N.

E. T. Whittaker and G. N. Watson, A Course of Modern Analysis, 4th ed. (Cambridge University Press, 1927).

Whittaker, E. T.

E. T. Whittaker and G. N. Watson, A Course of Modern Analysis, 4th ed. (Cambridge University Press, 1927).

Wolter, H.

H. Wolter, in Progress in Optics, E. Wolf, ed. (North-Holland, 1961), Vol. 1, Chap. 5.

Yacoot, A.

R. J. Smith, C. W. See, M. G. Somekh, A. Yacoot, and E. Choi, "Optical track width measurements below 100 nm using artificial neural networks," Meas. Sci. Technol. 16, 2397-2404 (2005).
[CrossRef]

Appl. Opt. (2)

Bell Syst. Tech. J. (3)

D. Slepian and H. O. Pollak, "Prolate spheroidal wave functions, Fourier analysis, and uncertainty I," Bell Syst. Tech. J. 40, 43-63 (1961).

H. J. Landau and H. O. Pollak, "Prolate spheroidal wave functions, Fourier analysis, and uncertainty II," Bell Syst. Tech. J. 40, 65-84 (1961).

H. J. Landau and H. O. Pollak, "Prolate spheroidal wave functions, Fourier analysis, and uncertainty III: the dimension of the space of essentially time- and band-limited signals," Bell Syst. Tech. J. 41, 1295-1336 (1962).

J. Opt. Soc. Am. (7)

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

Meas. Sci. Technol. (1)

R. J. Smith, C. W. See, M. G. Somekh, A. Yacoot, and E. Choi, "Optical track width measurements below 100 nm using artificial neural networks," Meas. Sci. Technol. 16, 2397-2404 (2005).
[CrossRef]

Opt. Acta (1)

R. W. Gerchberg, "Super-resolution through error energy reduction," Opt. Acta 21, 709-720 (1974).
[CrossRef]

Other (7)

M. H. Hayes, Statistical Digital Signal Processing and Modeling (Wiley, 1996).

Although it can be shown readily that if a second profile is measured under a different experimental condition this will provide sufficient information to resolve the ambiguity.

H. Wolter, in Progress in Optics, E. Wolf, ed. (North-Holland, 1961), Vol. 1, Chap. 5.

E. T. Whittaker and G. N. Watson, A Course of Modern Analysis, 4th ed. (Cambridge University Press, 1927).

S. Haykin, Neural Networks—A Comprehensive Foundation, 2nd ed. (Prentice-Hall, 1999).

K. Gurney, An Introduction to Neural Networks (UCL Press, 1996).

J. Nunn, W. Mirande, H. Jacobsen, and N. Talene, Challenges in the calibration of a photomask linewidth standard developed for the European Commission, VDE-VDI Conference Proceedings: Mask Technology for Integrated Circuits and Microcomponents, 53-68 (1997).
[PubMed]

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Figures (10)

Fig. 1
Fig. 1

Training of ANN using samples of known dimensions and the back propagation algorithm.

Fig. 2
Fig. 2

Measurement repeatability: (a) BCR sample and (b) Si sample.

Fig. 3
Fig. 3

Measurement repeatability of double tracks. One ANN with two outputs: (a) track widths and (b) track separations.

Fig. 4
Fig. 4

Measurement repeatability with two tracks (100 and 240 nm) omitted from the training set.

Fig. 5
Fig. 5

Effects of the location of the omitted track on the measurement repeatability. “*”: error associated with the omitted track; “∘”: average error of the entire network; and “+”: the difference between the two.

Fig. 6
Fig. 6

Effects of number of omitted tracks on measurement repeatability.

Fig. 7
Fig. 7

Measurement of sample outside of the training range.

Fig. 8
Fig. 8

Effects of the locations of the input patterns to the ANN, (a) possible input points for the ANN; and (b) measurement repeatability using different combinations of input points.

Fig. 9
Fig. 9

Effects of incorrect target values: (a) measurement repeatability when a 5% error was imposed to one of the target value; and (b) the effects of the autocorrection routine on the measurement repeatability.

Fig. 10
Fig. 10

Classification of single and double tracks.

Tables (6)

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Table 1 Samples Used in the Experiments

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Table 2 Measurement Repeatability for the BCR and Si Samples

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Table 3 Measurement Repeatability for Double Tracks, Showing Percentages of Point Spread Function

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Table 4 Effects of the Locations of Missing Tracks on the ANNs. See Section 3.B.1

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Table 5 Measurement Repeatability (MER) (over 480 Runs) as Functions of the Number of Tracks (NTO) Omitted

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Table 6 Measurement Repeatability for Different Input Patterns to the ANN

Equations (2)

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v ( x ) = rect ( χ T ) u ( χ ) h ( x χ ) d χ + n ( x ) = T / 2 T / 2 u ( χ ) h ( x χ ) d χ + n ( x )
and   rect ( x ) = 1 for | x | 1 2 = 0   otherwise ,

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