Abstract

Optical designers are encouraged to adopt aspheric and free-form surfaces into an increasing number of design spaces because of their improved performance. However, residual tooling marks from advanced aspheric fabrication techniques are difficult to remove. These marks, typically in the mid-spatial frequency (MSF) regime, give rise to structured image artifacts. Using a theory developed in previous publications, this paper applies the fundamentals of MSF modeling to demonstrate how MSF errors are evaluated and toleranced in an optical system. Examples of as-built components with MSF errors are analyzed using commercial optical design software.

© 2010 Optical Society of America

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2010 (1)

2007 (3)

J. J. Kumler and J. B. Caldwell, “Measuring surface slope error on precision aspheres,” Proc. SPIE 6671, 66710U (2007).
[CrossRef]

R. B. Jenkin, S. Triantaphillidou, and M. A. Richardson, “Effective pictorial information capacity as an image quality metric,” Proc. SPIE 6494, 64940O (2007).
[CrossRef]

K. Lenhardt, “Optics for digital photography,” Proc. SPIE 6834, 68340W (2007).
[CrossRef]

2005 (3)

S. H. Lee, M. Chandhok, J. Roberts, and B. J. Rice, “Characterization of flare on Intel’s EUV MET,” Proc. SPIE 5751, 293–300 (2005).
[CrossRef]

S. H. Lee, Y. Shroff, and M. Chandhok, “Flare and lens aberration requirements for EUV lithographic tools,” Proc. SPIE 5751, 707–714 (2005).
[CrossRef]

C. Beder, “Aspheres for high speed cine lenses,” Proc. SPIE 5962, 59620V (2005).
[CrossRef]

2004 (5)

G. Erdei, G. Szarvas, and E. Lorincz, “Tolerancing surface accuracy of aspheric lenses used for imaging purposes,” Proc. SPIE 5249, 718–728 (2004).
[CrossRef]

M. Chandhok, S. H. Lee, C. Krautschik, B. J. Rice, E. Panning, M. Goldstein, and M. Shell, “Determination of the flare specification and methods to meet the CD control requirements for the 32nm node using EUVL,” Proc. SPIE 5374, 86–95(2004).
[CrossRef]

M. Chandhok, S. H. Lee, C. G. Krautschik, G. Zhang, B. J. Rice, M. Goldstein, E. Panning, R. Bristol, A. R. Stivers, and M. Shell, “Comparison of techniques to measure the point spread function due to scatter and flare in EUV lithography systems,” Proc. SPIE 5374, 854–860 (2004).
[CrossRef]

S. P. Renwick, “Flare and its effects on imaging,” Proc. SPIE 5377, 442–450 (2004).
[CrossRef]

M. Shibuya, H. Ezaki, T. Fukui, N. Watanabe, and A. Nishikata, “Random aberration and local flare,” Proc. SPIE 5377, 1910–1920 (2004).
[CrossRef]

2003 (3)

C. A. Mack, “Measuring and modeling flare in optical lithography,” Proc. SPIE 5040, 151–161 (2003).
[CrossRef]

S. P. Renwick, S. D. Slonaker, and T. Ogata, “Size-dependent flare and its effect on imaging,” Proc. SPIE 5040, 24–32(2003).
[CrossRef]

D. Williams and P. D. Burns, “Low-frequency MTF estimation for digital imaging devices using slanted-edge analysis,” Proc. SPIE 5294, 93–101 (2003).
[CrossRef]

2002 (2)

B. M. La Fontaine, M. V. Dusa, A. Acheta, C. Chen, A. Bourov, H. J. Levinson, L. C. Litt, M. Mulder, R. Seltman, and J. van Praagh, “Flare and its impact on low-k1 KrF and ArF lithography,” Proc. SPIE 4691, 44–56 (2002).
[CrossRef]

L. C. Litt, A. Bourov, B. M. La Fontaine, and E. M. Apelgren, “Evaluation and characterization of flare in ArF lithography,” Proc. SPIE 4691, 1442–1452 (2002).
[CrossRef]

2000 (1)

1997 (1)

J. Park, H. Kang, J. Moon, and M. Lee, “Measuring flare and its effect on process latitude,” Proc. SPIE 3051, 708–713(1997).
[CrossRef]

1995 (1)

D. M. Aikens, C. R. Wolfe, and J. K. Lawson, “Use of power spectral density (PSD) functions in specifying optics for the National Ignition Facility,” Proc. SPIE 2576, 281–292 (1995).
[CrossRef]

1979 (1)

R. J. Noll, “Effect of mid and high spatial frequencies on optical performance,” Opt. Eng. 18, 137–142 (1979).

1975 (2)

1974 (1)

1972 (1)

1968 (1)

1953 (1)

Acheta, A.

B. M. La Fontaine, M. V. Dusa, A. Acheta, C. Chen, A. Bourov, H. J. Levinson, L. C. Litt, M. Mulder, R. Seltman, and J. van Praagh, “Flare and its impact on low-k1 KrF and ArF lithography,” Proc. SPIE 4691, 44–56 (2002).
[CrossRef]

Aikens, D. M.

D. M. Aikens, C. R. Wolfe, and J. K. Lawson, “Use of power spectral density (PSD) functions in specifying optics for the National Ignition Facility,” Proc. SPIE 2576, 281–292 (1995).
[CrossRef]

Apelgren, E. M.

L. C. Litt, A. Bourov, B. M. La Fontaine, and E. M. Apelgren, “Evaluation and characterization of flare in ArF lithography,” Proc. SPIE 4691, 1442–1452 (2002).
[CrossRef]

Beder, C.

C. Beder, “Aspheres for high speed cine lenses,” Proc. SPIE 5962, 59620V (2005).
[CrossRef]

Bourov, A.

B. M. La Fontaine, M. V. Dusa, A. Acheta, C. Chen, A. Bourov, H. J. Levinson, L. C. Litt, M. Mulder, R. Seltman, and J. van Praagh, “Flare and its impact on low-k1 KrF and ArF lithography,” Proc. SPIE 4691, 44–56 (2002).
[CrossRef]

L. C. Litt, A. Bourov, B. M. La Fontaine, and E. M. Apelgren, “Evaluation and characterization of flare in ArF lithography,” Proc. SPIE 4691, 1442–1452 (2002).
[CrossRef]

Bristol, R.

M. Chandhok, S. H. Lee, C. G. Krautschik, G. Zhang, B. J. Rice, M. Goldstein, E. Panning, R. Bristol, A. R. Stivers, and M. Shell, “Comparison of techniques to measure the point spread function due to scatter and flare in EUV lithography systems,” Proc. SPIE 5374, 854–860 (2004).
[CrossRef]

Burns, P. D.

D. Williams and P. D. Burns, “Low-frequency MTF estimation for digital imaging devices using slanted-edge analysis,” Proc. SPIE 5294, 93–101 (2003).
[CrossRef]

Caldwell, J. B.

J. J. Kumler and J. B. Caldwell, “Measuring surface slope error on precision aspheres,” Proc. SPIE 6671, 66710U (2007).
[CrossRef]

Chandhok, M.

S. H. Lee, M. Chandhok, J. Roberts, and B. J. Rice, “Characterization of flare on Intel’s EUV MET,” Proc. SPIE 5751, 293–300 (2005).
[CrossRef]

S. H. Lee, Y. Shroff, and M. Chandhok, “Flare and lens aberration requirements for EUV lithographic tools,” Proc. SPIE 5751, 707–714 (2005).
[CrossRef]

M. Chandhok, S. H. Lee, C. G. Krautschik, G. Zhang, B. J. Rice, M. Goldstein, E. Panning, R. Bristol, A. R. Stivers, and M. Shell, “Comparison of techniques to measure the point spread function due to scatter and flare in EUV lithography systems,” Proc. SPIE 5374, 854–860 (2004).
[CrossRef]

M. Chandhok, S. H. Lee, C. Krautschik, B. J. Rice, E. Panning, M. Goldstein, and M. Shell, “Determination of the flare specification and methods to meet the CD control requirements for the 32nm node using EUVL,” Proc. SPIE 5374, 86–95(2004).
[CrossRef]

Chen, C.

B. M. La Fontaine, M. V. Dusa, A. Acheta, C. Chen, A. Bourov, H. J. Levinson, L. C. Litt, M. Mulder, R. Seltman, and J. van Praagh, “Flare and its impact on low-k1 KrF and ArF lithography,” Proc. SPIE 4691, 44–56 (2002).
[CrossRef]

Church, E. L.

Dallas, W.

Dallas, W. J.

Dusa, M. V.

B. M. La Fontaine, M. V. Dusa, A. Acheta, C. Chen, A. Bourov, H. J. Levinson, L. C. Litt, M. Mulder, R. Seltman, and J. van Praagh, “Flare and its impact on low-k1 KrF and ArF lithography,” Proc. SPIE 4691, 44–56 (2002).
[CrossRef]

Erdei, G.

G. Erdei, G. Szarvas, and E. Lorincz, “Tolerancing surface accuracy of aspheric lenses used for imaging purposes,” Proc. SPIE 5249, 718–728 (2004).
[CrossRef]

Ezaki, H.

M. Shibuya, H. Ezaki, T. Fukui, N. Watanabe, and A. Nishikata, “Random aberration and local flare,” Proc. SPIE 5377, 1910–1920 (2004).
[CrossRef]

Fukui, T.

M. Shibuya, H. Ezaki, T. Fukui, N. Watanabe, and A. Nishikata, “Random aberration and local flare,” Proc. SPIE 5377, 1910–1920 (2004).
[CrossRef]

Goldstein, M.

M. Chandhok, S. H. Lee, C. Krautschik, B. J. Rice, E. Panning, M. Goldstein, and M. Shell, “Determination of the flare specification and methods to meet the CD control requirements for the 32nm node using EUVL,” Proc. SPIE 5374, 86–95(2004).
[CrossRef]

M. Chandhok, S. H. Lee, C. G. Krautschik, G. Zhang, B. J. Rice, M. Goldstein, E. Panning, R. Bristol, A. R. Stivers, and M. Shell, “Comparison of techniques to measure the point spread function due to scatter and flare in EUV lithography systems,” Proc. SPIE 5374, 854–860 (2004).
[CrossRef]

Harvey, J. E.

J. E. Harvey, “Light scattering characteristics of optical surfaces,” Ph.D. dissertation (publication no. AAT 7707332) (University of Arizona, 1976).

Jenkin, R. B.

R. B. Jenkin, S. Triantaphillidou, and M. A. Richardson, “Effective pictorial information capacity as an image quality metric,” Proc. SPIE 6494, 64940O (2007).
[CrossRef]

Kang, H.

J. Park, H. Kang, J. Moon, and M. Lee, “Measuring flare and its effect on process latitude,” Proc. SPIE 3051, 708–713(1997).
[CrossRef]

Krautschik, C.

M. Chandhok, S. H. Lee, C. Krautschik, B. J. Rice, E. Panning, M. Goldstein, and M. Shell, “Determination of the flare specification and methods to meet the CD control requirements for the 32nm node using EUVL,” Proc. SPIE 5374, 86–95(2004).
[CrossRef]

Krautschik, C. G.

M. Chandhok, S. H. Lee, C. G. Krautschik, G. Zhang, B. J. Rice, M. Goldstein, E. Panning, R. Bristol, A. R. Stivers, and M. Shell, “Comparison of techniques to measure the point spread function due to scatter and flare in EUV lithography systems,” Proc. SPIE 5374, 854–860 (2004).
[CrossRef]

Kumler, J. J.

J. J. Kumler and J. B. Caldwell, “Measuring surface slope error on precision aspheres,” Proc. SPIE 6671, 66710U (2007).
[CrossRef]

Kuwabara, G.

La Fontaine, B. M.

B. M. La Fontaine, M. V. Dusa, A. Acheta, C. Chen, A. Bourov, H. J. Levinson, L. C. Litt, M. Mulder, R. Seltman, and J. van Praagh, “Flare and its impact on low-k1 KrF and ArF lithography,” Proc. SPIE 4691, 44–56 (2002).
[CrossRef]

L. C. Litt, A. Bourov, B. M. La Fontaine, and E. M. Apelgren, “Evaluation and characterization of flare in ArF lithography,” Proc. SPIE 4691, 1442–1452 (2002).
[CrossRef]

Lawson, J. K.

D. M. Aikens, C. R. Wolfe, and J. K. Lawson, “Use of power spectral density (PSD) functions in specifying optics for the National Ignition Facility,” Proc. SPIE 2576, 281–292 (1995).
[CrossRef]

Lee, M.

J. Park, H. Kang, J. Moon, and M. Lee, “Measuring flare and its effect on process latitude,” Proc. SPIE 3051, 708–713(1997).
[CrossRef]

Lee, S. H.

S. H. Lee, Y. Shroff, and M. Chandhok, “Flare and lens aberration requirements for EUV lithographic tools,” Proc. SPIE 5751, 707–714 (2005).
[CrossRef]

S. H. Lee, M. Chandhok, J. Roberts, and B. J. Rice, “Characterization of flare on Intel’s EUV MET,” Proc. SPIE 5751, 293–300 (2005).
[CrossRef]

M. Chandhok, S. H. Lee, C. Krautschik, B. J. Rice, E. Panning, M. Goldstein, and M. Shell, “Determination of the flare specification and methods to meet the CD control requirements for the 32nm node using EUVL,” Proc. SPIE 5374, 86–95(2004).
[CrossRef]

M. Chandhok, S. H. Lee, C. G. Krautschik, G. Zhang, B. J. Rice, M. Goldstein, E. Panning, R. Bristol, A. R. Stivers, and M. Shell, “Comparison of techniques to measure the point spread function due to scatter and flare in EUV lithography systems,” Proc. SPIE 5374, 854–860 (2004).
[CrossRef]

Lenhardt, K.

K. Lenhardt, “Optics for digital photography,” Proc. SPIE 6834, 68340W (2007).
[CrossRef]

Levinson, H. J.

B. M. La Fontaine, M. V. Dusa, A. Acheta, C. Chen, A. Bourov, H. J. Levinson, L. C. Litt, M. Mulder, R. Seltman, and J. van Praagh, “Flare and its impact on low-k1 KrF and ArF lithography,” Proc. SPIE 4691, 44–56 (2002).
[CrossRef]

Litt, L. C.

B. M. La Fontaine, M. V. Dusa, A. Acheta, C. Chen, A. Bourov, H. J. Levinson, L. C. Litt, M. Mulder, R. Seltman, and J. van Praagh, “Flare and its impact on low-k1 KrF and ArF lithography,” Proc. SPIE 4691, 44–56 (2002).
[CrossRef]

L. C. Litt, A. Bourov, B. M. La Fontaine, and E. M. Apelgren, “Evaluation and characterization of flare in ArF lithography,” Proc. SPIE 4691, 1442–1452 (2002).
[CrossRef]

Lorincz, E.

G. Erdei, G. Szarvas, and E. Lorincz, “Tolerancing surface accuracy of aspheric lenses used for imaging purposes,” Proc. SPIE 5249, 718–728 (2004).
[CrossRef]

Mack, C. A.

C. A. Mack, “Measuring and modeling flare in optical lithography,” Proc. SPIE 5040, 151–161 (2003).
[CrossRef]

Matsuda, S.

Milster, T. D.

Moon, J.

J. Park, H. Kang, J. Moon, and M. Lee, “Measuring flare and its effect on process latitude,” Proc. SPIE 3051, 708–713(1997).
[CrossRef]

Mulder, M.

B. M. La Fontaine, M. V. Dusa, A. Acheta, C. Chen, A. Bourov, H. J. Levinson, L. C. Litt, M. Mulder, R. Seltman, and J. van Praagh, “Flare and its impact on low-k1 KrF and ArF lithography,” Proc. SPIE 4691, 44–56 (2002).
[CrossRef]

Nishikata, A.

M. Shibuya, H. Ezaki, T. Fukui, N. Watanabe, and A. Nishikata, “Random aberration and local flare,” Proc. SPIE 5377, 1910–1920 (2004).
[CrossRef]

Nitoh, T.

Noll, R. J.

R. J. Noll, “Effect of mid and high spatial frequencies on optical performance,” Opt. Eng. 18, 137–142 (1979).

Ogata, T.

S. P. Renwick, S. D. Slonaker, and T. Ogata, “Size-dependent flare and its effect on imaging,” Proc. SPIE 5040, 24–32(2003).
[CrossRef]

Panning, E.

M. Chandhok, S. H. Lee, C. Krautschik, B. J. Rice, E. Panning, M. Goldstein, and M. Shell, “Determination of the flare specification and methods to meet the CD control requirements for the 32nm node using EUVL,” Proc. SPIE 5374, 86–95(2004).
[CrossRef]

M. Chandhok, S. H. Lee, C. G. Krautschik, G. Zhang, B. J. Rice, M. Goldstein, E. Panning, R. Bristol, A. R. Stivers, and M. Shell, “Comparison of techniques to measure the point spread function due to scatter and flare in EUV lithography systems,” Proc. SPIE 5374, 854–860 (2004).
[CrossRef]

Park, J.

J. Park, H. Kang, J. Moon, and M. Lee, “Measuring flare and its effect on process latitude,” Proc. SPIE 3051, 708–713(1997).
[CrossRef]

Renwick, S. P.

S. P. Renwick, “Flare and its effects on imaging,” Proc. SPIE 5377, 442–450 (2004).
[CrossRef]

S. P. Renwick, S. D. Slonaker, and T. Ogata, “Size-dependent flare and its effect on imaging,” Proc. SPIE 5040, 24–32(2003).
[CrossRef]

Rice, B. J.

S. H. Lee, M. Chandhok, J. Roberts, and B. J. Rice, “Characterization of flare on Intel’s EUV MET,” Proc. SPIE 5751, 293–300 (2005).
[CrossRef]

M. Chandhok, S. H. Lee, C. Krautschik, B. J. Rice, E. Panning, M. Goldstein, and M. Shell, “Determination of the flare specification and methods to meet the CD control requirements for the 32nm node using EUVL,” Proc. SPIE 5374, 86–95(2004).
[CrossRef]

M. Chandhok, S. H. Lee, C. G. Krautschik, G. Zhang, B. J. Rice, M. Goldstein, E. Panning, R. Bristol, A. R. Stivers, and M. Shell, “Comparison of techniques to measure the point spread function due to scatter and flare in EUV lithography systems,” Proc. SPIE 5374, 854–860 (2004).
[CrossRef]

Richardson, M. A.

R. B. Jenkin, S. Triantaphillidou, and M. A. Richardson, “Effective pictorial information capacity as an image quality metric,” Proc. SPIE 6494, 64940O (2007).
[CrossRef]

Rimmer, M.

M. Rimmer, “A tolerancing procedure based on modulation transfer function (MTF),” in G.E.Wiese, ed., Selected Papers on Optical Tolerancing (SPIE Press, 1978), pp. 66–70

Roberts, J.

S. H. Lee, M. Chandhok, J. Roberts, and B. J. Rice, “Characterization of flare on Intel’s EUV MET,” Proc. SPIE 5751, 293–300 (2005).
[CrossRef]

Rosenbruch, K.

Rosenhauer, K.

Saito, T. T.

Seltman, R.

B. M. La Fontaine, M. V. Dusa, A. Acheta, C. Chen, A. Bourov, H. J. Levinson, L. C. Litt, M. Mulder, R. Seltman, and J. van Praagh, “Flare and its impact on low-k1 KrF and ArF lithography,” Proc. SPIE 4691, 44–56 (2002).
[CrossRef]

Shell, M.

M. Chandhok, S. H. Lee, C. G. Krautschik, G. Zhang, B. J. Rice, M. Goldstein, E. Panning, R. Bristol, A. R. Stivers, and M. Shell, “Comparison of techniques to measure the point spread function due to scatter and flare in EUV lithography systems,” Proc. SPIE 5374, 854–860 (2004).
[CrossRef]

M. Chandhok, S. H. Lee, C. Krautschik, B. J. Rice, E. Panning, M. Goldstein, and M. Shell, “Determination of the flare specification and methods to meet the CD control requirements for the 32nm node using EUVL,” Proc. SPIE 5374, 86–95(2004).
[CrossRef]

Shibuya, M.

M. Shibuya, H. Ezaki, T. Fukui, N. Watanabe, and A. Nishikata, “Random aberration and local flare,” Proc. SPIE 5377, 1910–1920 (2004).
[CrossRef]

Shroff, Y.

S. H. Lee, Y. Shroff, and M. Chandhok, “Flare and lens aberration requirements for EUV lithographic tools,” Proc. SPIE 5751, 707–714 (2005).
[CrossRef]

Simmons, L. B.

Slonaker, S. D.

S. P. Renwick, S. D. Slonaker, and T. Ogata, “Size-dependent flare and its effect on imaging,” Proc. SPIE 5040, 24–32(2003).
[CrossRef]

Stivers, A. R.

M. Chandhok, S. H. Lee, C. G. Krautschik, G. Zhang, B. J. Rice, M. Goldstein, E. Panning, R. Bristol, A. R. Stivers, and M. Shell, “Comparison of techniques to measure the point spread function due to scatter and flare in EUV lithography systems,” Proc. SPIE 5374, 854–860 (2004).
[CrossRef]

Stone, B. D.

Stover, J. C.

Szarvas, G.

G. Erdei, G. Szarvas, and E. Lorincz, “Tolerancing surface accuracy of aspheric lenses used for imaging purposes,” Proc. SPIE 5249, 718–728 (2004).
[CrossRef]

Tamkin, J. M.

Triantaphillidou, S.

R. B. Jenkin, S. Triantaphillidou, and M. A. Richardson, “Effective pictorial information capacity as an image quality metric,” Proc. SPIE 6494, 64940O (2007).
[CrossRef]

van Praagh, J.

B. M. La Fontaine, M. V. Dusa, A. Acheta, C. Chen, A. Bourov, H. J. Levinson, L. C. Litt, M. Mulder, R. Seltman, and J. van Praagh, “Flare and its impact on low-k1 KrF and ArF lithography,” Proc. SPIE 4691, 44–56 (2002).
[CrossRef]

Watanabe, N.

M. Shibuya, H. Ezaki, T. Fukui, N. Watanabe, and A. Nishikata, “Random aberration and local flare,” Proc. SPIE 5377, 1910–1920 (2004).
[CrossRef]

Williams, D.

D. Williams and P. D. Burns, “Low-frequency MTF estimation for digital imaging devices using slanted-edge analysis,” Proc. SPIE 5294, 93–101 (2003).
[CrossRef]

Wolfe, C. R.

D. M. Aikens, C. R. Wolfe, and J. K. Lawson, “Use of power spectral density (PSD) functions in specifying optics for the National Ignition Facility,” Proc. SPIE 2576, 281–292 (1995).
[CrossRef]

Youngworth, R. N.

Zavada, J. M.

Zhang, G.

M. Chandhok, S. H. Lee, C. G. Krautschik, G. Zhang, B. J. Rice, M. Goldstein, E. Panning, R. Bristol, A. R. Stivers, and M. Shell, “Comparison of techniques to measure the point spread function due to scatter and flare in EUV lithography systems,” Proc. SPIE 5374, 854–860 (2004).
[CrossRef]

Appl. Opt. (8)

J. Opt. Soc. Am. (1)

Opt. Eng. (1)

R. J. Noll, “Effect of mid and high spatial frequencies on optical performance,” Opt. Eng. 18, 137–142 (1979).

Proc. SPIE (18)

D. Williams and P. D. Burns, “Low-frequency MTF estimation for digital imaging devices using slanted-edge analysis,” Proc. SPIE 5294, 93–101 (2003).
[CrossRef]

R. B. Jenkin, S. Triantaphillidou, and M. A. Richardson, “Effective pictorial information capacity as an image quality metric,” Proc. SPIE 6494, 64940O (2007).
[CrossRef]

K. Lenhardt, “Optics for digital photography,” Proc. SPIE 6834, 68340W (2007).
[CrossRef]

C. Beder, “Aspheres for high speed cine lenses,” Proc. SPIE 5962, 59620V (2005).
[CrossRef]

J. J. Kumler and J. B. Caldwell, “Measuring surface slope error on precision aspheres,” Proc. SPIE 6671, 66710U (2007).
[CrossRef]

D. M. Aikens, C. R. Wolfe, and J. K. Lawson, “Use of power spectral density (PSD) functions in specifying optics for the National Ignition Facility,” Proc. SPIE 2576, 281–292 (1995).
[CrossRef]

G. Erdei, G. Szarvas, and E. Lorincz, “Tolerancing surface accuracy of aspheric lenses used for imaging purposes,” Proc. SPIE 5249, 718–728 (2004).
[CrossRef]

J. Park, H. Kang, J. Moon, and M. Lee, “Measuring flare and its effect on process latitude,” Proc. SPIE 3051, 708–713(1997).
[CrossRef]

B. M. La Fontaine, M. V. Dusa, A. Acheta, C. Chen, A. Bourov, H. J. Levinson, L. C. Litt, M. Mulder, R. Seltman, and J. van Praagh, “Flare and its impact on low-k1 KrF and ArF lithography,” Proc. SPIE 4691, 44–56 (2002).
[CrossRef]

L. C. Litt, A. Bourov, B. M. La Fontaine, and E. M. Apelgren, “Evaluation and characterization of flare in ArF lithography,” Proc. SPIE 4691, 1442–1452 (2002).
[CrossRef]

C. A. Mack, “Measuring and modeling flare in optical lithography,” Proc. SPIE 5040, 151–161 (2003).
[CrossRef]

S. P. Renwick, S. D. Slonaker, and T. Ogata, “Size-dependent flare and its effect on imaging,” Proc. SPIE 5040, 24–32(2003).
[CrossRef]

M. Chandhok, S. H. Lee, C. Krautschik, B. J. Rice, E. Panning, M. Goldstein, and M. Shell, “Determination of the flare specification and methods to meet the CD control requirements for the 32nm node using EUVL,” Proc. SPIE 5374, 86–95(2004).
[CrossRef]

M. Chandhok, S. H. Lee, C. G. Krautschik, G. Zhang, B. J. Rice, M. Goldstein, E. Panning, R. Bristol, A. R. Stivers, and M. Shell, “Comparison of techniques to measure the point spread function due to scatter and flare in EUV lithography systems,” Proc. SPIE 5374, 854–860 (2004).
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S. P. Renwick, “Flare and its effects on imaging,” Proc. SPIE 5377, 442–450 (2004).
[CrossRef]

M. Shibuya, H. Ezaki, T. Fukui, N. Watanabe, and A. Nishikata, “Random aberration and local flare,” Proc. SPIE 5377, 1910–1920 (2004).
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S. H. Lee, Y. Shroff, and M. Chandhok, “Flare and lens aberration requirements for EUV lithographic tools,” Proc. SPIE 5751, 707–714 (2005).
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Figures (21)

Fig. 1
Fig. 1

Example of beam footprints (from Ref. [2]). Surfaces far from the stop have ray bundles from each field point that are smaller than the diameter of the part.

Fig. 2
Fig. 2

(a) Relationship between grating equation and diffracted beam location at image plane for a single lens. (b) Reimaging the first-order beam from a front lens surface containing a MSF gratinglike error for a three-lens system (see text for details).

Fig. 3
Fig. 3

Point spread function of MSF error with one and two spatial frequencies. Surface error of 0.2 waves for each frequency component: (a) 25 cycles per aperture and (b) 25 and 23 cycles per aperture.

Fig. 4
Fig. 4

Effects of multiple cross terms. Six sinusoids: 50, 47.5, 45, 42.5, 30, and 38 cycles across pupil: (a) phase error across pupil, (b) PSF with zero error, (c) PSF with 0.025 waves for each component, RMS error = 0.077 waves, and (d) difference between (c) and (b) showing cross-term peaks roughly half the first-order peak amplitudes.

Fig. 5
Fig. 5

First-order layout of diffracted light into the coordinate system of aperture stop.

Fig. 6
Fig. 6

Image of diffraction orders before and after truncation by the aperture stop for a square aperture and sinusoidal surface error: (a) unapertured far field and (b) 1 mm pupil, propagated 60 mm and truncated by 1 mm pupil then transformed to the far field.

Fig. 7
Fig. 7

Field-dependent structure errors from parent and resulting PSF. For an optical element far from the stop, the beam footprint is substantially smaller than the part, sampling different portions of the element across the field.

Fig. 8
Fig. 8

Modulation transfer function for perfect lens with 24 cycles per aperture MSF phase error, 0.098 waves PV error ( 0.15 μm surface PV height). Top trace shows contrast normalized by diffraction-limited MTF curve.

Fig. 9
Fig. 9

Comparison of MSF error and defocus for equivalent RMS errors. (a) 0.11 mm of defocus creates wavefront error of 0.066 RMS, creating a drop of 20% in MTF. (b) On-axis and off-axis MTF for a rotational sinusoid on test lens of Fig. 1 ( f / 10 ) with 0.22 waves PV surface height (0.065 waves RMS). On-axis pupil is rotationally symmetric, while off-axis pupil is gratinglike. The MTF drop is approximately 30%.

Fig. 10
Fig. 10

Loss in MTF and RMS wavefront error versus surface PV phase for a single radial sinusoidal MSF component. Figure 1 optical system ( 50 mm EFL at f / 10 ). Surface S2 with 0.5 mm period. Eight cycles per aperture diameter presents a rotational pattern on axis and a gratinglike pattern at 20 ° off axis.

Fig. 11
Fig. 11

Cooke triplet used in image simulations with sinusoidal phase surfaces on S1 and S4.

Fig. 12
Fig. 12

Image simulation using a f / 20 Cooke triplet: column 1, image files; column 2, horizontal trace across center. (a) Object, (b) image with no errors, (c) single surface grating, 0.097 waves RMS, and (d) 0.2 wave PV sinusoid on S1 and stop surface S4.

Fig. 13
Fig. 13

Surface profiler trace locations. At each radius, nine points are used ( 0 ° taken twice) to interpolate the surface around a circumference. This is repeated at each radial point to construct the surface simulation. The height scale is mm × 10 4 .

Fig. 14
Fig. 14

Example of an as-built surface: (a) surface profiles at four azimuth angles, (b) radii after removal of base curvature, (c) 3D reconstruction, and (d) height map of surface reconstruction.

Fig. 15
Fig. 15

All-plastic camera lens with diamond-turned surfaces: (a) as-designed MTF, (b) layout, and (c) height profiles of skins added to S2 and S8. (S2, 1.0 μm PV height scale, 4.7 mm diameter; and S8, 1.8 μm PV height scale, 3.0 mm diameter.)

Fig. 16
Fig. 16

Nominal performance of the system in Fig. 13: left column, wavefront error; center, PSF; right, image simulation of one-eighth of the full-field target; top row, on-axis; center, 50% full field; and bottom, 70% full field.

Fig. 17
Fig. 17

Performance of system in Fig. 13 with as-built MSF errors on S2: left column, wavefront error; center, PSF; and right, image simulation of one-eighth of the full-field target. Top row, on-axis; center, 50% full field; and bottom, 70% full field.

Fig. 18
Fig. 18

Performance of system in Fig. 13 with as-built MSF errors on S8: left column, wavefront error; center, PSF; and right, image simulation of one-eighth of the full-field target. Top row, on-axis; center, 50% full field; and bottom, 70% full field.

Fig. 19
Fig. 19

Performance of system in Fig. 13 with as-built MSF errors on S 2 + S 8 : left column, wavefront error; center, PSF; and right, image simulation of one-eighth of the full-field target. Top row, on-axis; center, 50% full field; and bottom, 70% full field.

Fig. 20
Fig. 20

MTF and PSF trace of Fig. 13. Three field positions (center, 50%, and 70% full field) are plotted along with the diffraction-limited MTF. Because this system is not diffraction limited, the normalized 70% field profile is normalized to the nominal MTF in Fig. 13. (a) Error on S2, (b) error on S8, and (c) error on S2 and S8.

Fig. 21
Fig. 21

Analytical MTF drop versus PV surface phase height for a single sinusoidal phase error across the pupil.

Tables (1)

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Table 1 Beam Footprint and Min/Max Spatial Frequency for Each Surface of Test Lens

Equations (12)

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s d = D 2.44 p .
s 3 = z i 1 θ M 2 M 3 ,
M 2 = z i 2 z o 2 , M 3 = z i 3 z o 3 ,
h ( x s ) = 1 2 β o + 1 2 = 1 β A cos ( 2 π ξ o x s ) + 1 2 = 1 β B sin ( 2 π ξ o x s ) ,
D = 1 ξ o .
U s ( x s ) = rect ( x s D ) = 1 exp [ i φ cos ( 2 π ξ o x s + γ ) ] = rect ( x s D ) U s 1 ( x s ) U s 2 ( x s ) ,
γ = arctan ( β B β A ) and φ = ( 2 π λ ) 2 ( n 1 ) 2 [ ( β A 2 ) 2 + ( β B 2 ) 2 ] .
U s ( x s ) = m = c m , exp [ i ( 2 π m ξ o x s + γ ) ] ,
c m , = exp ( i γ ) i m J m ( φ ) ,
U i ( x i ) = A o { m = i m J m ( φ ) sinc [ ( ξ m ξ o ) D ] exp ( i γ ) * m = i m J m ( φ + 1 ) sinc { [ ξ m ( + 1 ) ξ o ] D } exp ( i γ + 1 ) * } | ξ = x i λ z i ,
MTF ( ξ ) = | tri ( ξ λ z i D ) { m = J m 2 ( φ β ) cos ( 2 π λ z i m ξ ξ o ) } | ξ = x i λ z i ,
MTF min ( φ β ) = | { m = N N J m 2 ( φ β ) cos ( 2 π λ z i m ξ o 2 λ z i ξ o ) } | ,

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