Abstract

In optical lithography, it is a serious problem that aberrations in projection lenses reduce the imaging quality. Therefore techniques to measure the aberrations are required that will predict the adverse effects of aberrations on lithographic imagery and reduce them. We present a measurement method that uses a fine grating and its imaging condition to quantify coma, astigmatism, and spherical aberration. With this method, these aberrations can be described with simple expressions from the measured results. Application of this method revealed the coma of Zernike polynomials for our krypton fluoride (KrF) excimer-laser scanner.

© 1999 Optical Society of America

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References

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  1. T. Brunner, “Impact of lens aberrations on optical lithography,” IBM J. Res. Dev. 41, 57–67 (1997).
    [CrossRef]
  2. M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1980), pp. 203–232, 459–490.
  3. D. Malacara, Optical Shop Testing (Wiley, New York, 1978).
  4. R. P. Grosso, R. Crane, “Precise optical evaluation using phase measuring interferometric techniques,” in Interferometry, G. Hopkins, ed., Proc. SPIE192, 65–74 (1979).
    [CrossRef]
  5. D. G. Flagello, B. Geh, “Lithography lens testing: analysis of measured aerial images, interferometric data and photoresist measurements,” in Optical Microlithography IX, G. E. Fuller, ed., Proc. SPIE2726, 788–798 (1996).
    [CrossRef]
  6. J. P. Kirk, “Astigmatism and field curvature from pin-bars,” in Optical/Laser Microlithography IV, V. Pol, ed., Proc. SPIE1463, 282–291 (1991).
    [CrossRef]
  7. J. P. Kirk, “Measurement of astigmatism in microlithography lenses,” in Optical Microlithography XI, L. V. den Hove, ed., Proc. SPIE3334, 848–854 (1998).
    [CrossRef]
  8. T. Farrell, R. Nunes, D. Samuels, A. Thomas, R. Ferguson, A. Molless, A. Wong, W. Conley, D. Wheeler, S. Credendino, M. Naeem, P. Hoh, Z. Lu, “Challenge of 1-Gb DRAM development when using optical lithography,” in Optical Microlithography X, G. E. Fuller, ed., Proc. SPIE3051, 333–341 (1997).
    [CrossRef]
  9. T. Saito, H. Watanabe, Y. Okuda, “Effect of variable sigma aperture on lens distortion and its pattern size dependence,” in Metrology, Inspection, and Process Control for Microlithography X, S. K. Jones, ed., Proc. SPIE2725, 414–423 (1996).
    [CrossRef]
  10. T. Saito, H. Watanabe, Y. Okuda, “Overlay error of fine patterns by lens aberration using modified illumination,” in Optical Microlithography X, G. E. Fuller, ed., Proc. SPIE3051, 686–696 (1997).
    [CrossRef]
  11. T. Sato, H. Nomura, “Coma aberration measurement by relative shift of displacement with pattern dependence,” Jpn. J. Appl. Phys. 37, 3553–3557 (1998).
    [CrossRef]
  12. H. Nomura, T. Sato, “Overlay error due to lens coma and asymmetric illumination dependence on pattern feature,” in Metrology, Inspection, and Process Control for Microlithography XII, L. V. den Hove, ed., Proc. SPIE3332, 199–210 (1998).
    [CrossRef]
  13. R. R. Shannon, J. C. Wyant, Applied Optics and Optical Engineering (Academic, San Diego, Calif., 1992), Vol. XI.

1998 (1)

T. Sato, H. Nomura, “Coma aberration measurement by relative shift of displacement with pattern dependence,” Jpn. J. Appl. Phys. 37, 3553–3557 (1998).
[CrossRef]

1997 (1)

T. Brunner, “Impact of lens aberrations on optical lithography,” IBM J. Res. Dev. 41, 57–67 (1997).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1980), pp. 203–232, 459–490.

Brunner, T.

T. Brunner, “Impact of lens aberrations on optical lithography,” IBM J. Res. Dev. 41, 57–67 (1997).
[CrossRef]

Conley, W.

T. Farrell, R. Nunes, D. Samuels, A. Thomas, R. Ferguson, A. Molless, A. Wong, W. Conley, D. Wheeler, S. Credendino, M. Naeem, P. Hoh, Z. Lu, “Challenge of 1-Gb DRAM development when using optical lithography,” in Optical Microlithography X, G. E. Fuller, ed., Proc. SPIE3051, 333–341 (1997).
[CrossRef]

Crane, R.

R. P. Grosso, R. Crane, “Precise optical evaluation using phase measuring interferometric techniques,” in Interferometry, G. Hopkins, ed., Proc. SPIE192, 65–74 (1979).
[CrossRef]

Credendino, S.

T. Farrell, R. Nunes, D. Samuels, A. Thomas, R. Ferguson, A. Molless, A. Wong, W. Conley, D. Wheeler, S. Credendino, M. Naeem, P. Hoh, Z. Lu, “Challenge of 1-Gb DRAM development when using optical lithography,” in Optical Microlithography X, G. E. Fuller, ed., Proc. SPIE3051, 333–341 (1997).
[CrossRef]

Farrell, T.

T. Farrell, R. Nunes, D. Samuels, A. Thomas, R. Ferguson, A. Molless, A. Wong, W. Conley, D. Wheeler, S. Credendino, M. Naeem, P. Hoh, Z. Lu, “Challenge of 1-Gb DRAM development when using optical lithography,” in Optical Microlithography X, G. E. Fuller, ed., Proc. SPIE3051, 333–341 (1997).
[CrossRef]

Ferguson, R.

T. Farrell, R. Nunes, D. Samuels, A. Thomas, R. Ferguson, A. Molless, A. Wong, W. Conley, D. Wheeler, S. Credendino, M. Naeem, P. Hoh, Z. Lu, “Challenge of 1-Gb DRAM development when using optical lithography,” in Optical Microlithography X, G. E. Fuller, ed., Proc. SPIE3051, 333–341 (1997).
[CrossRef]

Flagello, D. G.

D. G. Flagello, B. Geh, “Lithography lens testing: analysis of measured aerial images, interferometric data and photoresist measurements,” in Optical Microlithography IX, G. E. Fuller, ed., Proc. SPIE2726, 788–798 (1996).
[CrossRef]

Geh, B.

D. G. Flagello, B. Geh, “Lithography lens testing: analysis of measured aerial images, interferometric data and photoresist measurements,” in Optical Microlithography IX, G. E. Fuller, ed., Proc. SPIE2726, 788–798 (1996).
[CrossRef]

Grosso, R. P.

R. P. Grosso, R. Crane, “Precise optical evaluation using phase measuring interferometric techniques,” in Interferometry, G. Hopkins, ed., Proc. SPIE192, 65–74 (1979).
[CrossRef]

Hoh, P.

T. Farrell, R. Nunes, D. Samuels, A. Thomas, R. Ferguson, A. Molless, A. Wong, W. Conley, D. Wheeler, S. Credendino, M. Naeem, P. Hoh, Z. Lu, “Challenge of 1-Gb DRAM development when using optical lithography,” in Optical Microlithography X, G. E. Fuller, ed., Proc. SPIE3051, 333–341 (1997).
[CrossRef]

Kirk, J. P.

J. P. Kirk, “Astigmatism and field curvature from pin-bars,” in Optical/Laser Microlithography IV, V. Pol, ed., Proc. SPIE1463, 282–291 (1991).
[CrossRef]

J. P. Kirk, “Measurement of astigmatism in microlithography lenses,” in Optical Microlithography XI, L. V. den Hove, ed., Proc. SPIE3334, 848–854 (1998).
[CrossRef]

Lu, Z.

T. Farrell, R. Nunes, D. Samuels, A. Thomas, R. Ferguson, A. Molless, A. Wong, W. Conley, D. Wheeler, S. Credendino, M. Naeem, P. Hoh, Z. Lu, “Challenge of 1-Gb DRAM development when using optical lithography,” in Optical Microlithography X, G. E. Fuller, ed., Proc. SPIE3051, 333–341 (1997).
[CrossRef]

Malacara, D.

D. Malacara, Optical Shop Testing (Wiley, New York, 1978).

Molless, A.

T. Farrell, R. Nunes, D. Samuels, A. Thomas, R. Ferguson, A. Molless, A. Wong, W. Conley, D. Wheeler, S. Credendino, M. Naeem, P. Hoh, Z. Lu, “Challenge of 1-Gb DRAM development when using optical lithography,” in Optical Microlithography X, G. E. Fuller, ed., Proc. SPIE3051, 333–341 (1997).
[CrossRef]

Naeem, M.

T. Farrell, R. Nunes, D. Samuels, A. Thomas, R. Ferguson, A. Molless, A. Wong, W. Conley, D. Wheeler, S. Credendino, M. Naeem, P. Hoh, Z. Lu, “Challenge of 1-Gb DRAM development when using optical lithography,” in Optical Microlithography X, G. E. Fuller, ed., Proc. SPIE3051, 333–341 (1997).
[CrossRef]

Nomura, H.

T. Sato, H. Nomura, “Coma aberration measurement by relative shift of displacement with pattern dependence,” Jpn. J. Appl. Phys. 37, 3553–3557 (1998).
[CrossRef]

H. Nomura, T. Sato, “Overlay error due to lens coma and asymmetric illumination dependence on pattern feature,” in Metrology, Inspection, and Process Control for Microlithography XII, L. V. den Hove, ed., Proc. SPIE3332, 199–210 (1998).
[CrossRef]

Nunes, R.

T. Farrell, R. Nunes, D. Samuels, A. Thomas, R. Ferguson, A. Molless, A. Wong, W. Conley, D. Wheeler, S. Credendino, M. Naeem, P. Hoh, Z. Lu, “Challenge of 1-Gb DRAM development when using optical lithography,” in Optical Microlithography X, G. E. Fuller, ed., Proc. SPIE3051, 333–341 (1997).
[CrossRef]

Okuda, Y.

T. Saito, H. Watanabe, Y. Okuda, “Overlay error of fine patterns by lens aberration using modified illumination,” in Optical Microlithography X, G. E. Fuller, ed., Proc. SPIE3051, 686–696 (1997).
[CrossRef]

T. Saito, H. Watanabe, Y. Okuda, “Effect of variable sigma aperture on lens distortion and its pattern size dependence,” in Metrology, Inspection, and Process Control for Microlithography X, S. K. Jones, ed., Proc. SPIE2725, 414–423 (1996).
[CrossRef]

Saito, T.

T. Saito, H. Watanabe, Y. Okuda, “Overlay error of fine patterns by lens aberration using modified illumination,” in Optical Microlithography X, G. E. Fuller, ed., Proc. SPIE3051, 686–696 (1997).
[CrossRef]

T. Saito, H. Watanabe, Y. Okuda, “Effect of variable sigma aperture on lens distortion and its pattern size dependence,” in Metrology, Inspection, and Process Control for Microlithography X, S. K. Jones, ed., Proc. SPIE2725, 414–423 (1996).
[CrossRef]

Samuels, D.

T. Farrell, R. Nunes, D. Samuels, A. Thomas, R. Ferguson, A. Molless, A. Wong, W. Conley, D. Wheeler, S. Credendino, M. Naeem, P. Hoh, Z. Lu, “Challenge of 1-Gb DRAM development when using optical lithography,” in Optical Microlithography X, G. E. Fuller, ed., Proc. SPIE3051, 333–341 (1997).
[CrossRef]

Sato, T.

T. Sato, H. Nomura, “Coma aberration measurement by relative shift of displacement with pattern dependence,” Jpn. J. Appl. Phys. 37, 3553–3557 (1998).
[CrossRef]

H. Nomura, T. Sato, “Overlay error due to lens coma and asymmetric illumination dependence on pattern feature,” in Metrology, Inspection, and Process Control for Microlithography XII, L. V. den Hove, ed., Proc. SPIE3332, 199–210 (1998).
[CrossRef]

Shannon, R. R.

R. R. Shannon, J. C. Wyant, Applied Optics and Optical Engineering (Academic, San Diego, Calif., 1992), Vol. XI.

Thomas, A.

T. Farrell, R. Nunes, D. Samuels, A. Thomas, R. Ferguson, A. Molless, A. Wong, W. Conley, D. Wheeler, S. Credendino, M. Naeem, P. Hoh, Z. Lu, “Challenge of 1-Gb DRAM development when using optical lithography,” in Optical Microlithography X, G. E. Fuller, ed., Proc. SPIE3051, 333–341 (1997).
[CrossRef]

Watanabe, H.

T. Saito, H. Watanabe, Y. Okuda, “Effect of variable sigma aperture on lens distortion and its pattern size dependence,” in Metrology, Inspection, and Process Control for Microlithography X, S. K. Jones, ed., Proc. SPIE2725, 414–423 (1996).
[CrossRef]

T. Saito, H. Watanabe, Y. Okuda, “Overlay error of fine patterns by lens aberration using modified illumination,” in Optical Microlithography X, G. E. Fuller, ed., Proc. SPIE3051, 686–696 (1997).
[CrossRef]

Wheeler, D.

T. Farrell, R. Nunes, D. Samuels, A. Thomas, R. Ferguson, A. Molless, A. Wong, W. Conley, D. Wheeler, S. Credendino, M. Naeem, P. Hoh, Z. Lu, “Challenge of 1-Gb DRAM development when using optical lithography,” in Optical Microlithography X, G. E. Fuller, ed., Proc. SPIE3051, 333–341 (1997).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1980), pp. 203–232, 459–490.

Wong, A.

T. Farrell, R. Nunes, D. Samuels, A. Thomas, R. Ferguson, A. Molless, A. Wong, W. Conley, D. Wheeler, S. Credendino, M. Naeem, P. Hoh, Z. Lu, “Challenge of 1-Gb DRAM development when using optical lithography,” in Optical Microlithography X, G. E. Fuller, ed., Proc. SPIE3051, 333–341 (1997).
[CrossRef]

Wyant, J. C.

R. R. Shannon, J. C. Wyant, Applied Optics and Optical Engineering (Academic, San Diego, Calif., 1992), Vol. XI.

IBM J. Res. Dev. (1)

T. Brunner, “Impact of lens aberrations on optical lithography,” IBM J. Res. Dev. 41, 57–67 (1997).
[CrossRef]

Jpn. J. Appl. Phys. (1)

T. Sato, H. Nomura, “Coma aberration measurement by relative shift of displacement with pattern dependence,” Jpn. J. Appl. Phys. 37, 3553–3557 (1998).
[CrossRef]

Other (11)

H. Nomura, T. Sato, “Overlay error due to lens coma and asymmetric illumination dependence on pattern feature,” in Metrology, Inspection, and Process Control for Microlithography XII, L. V. den Hove, ed., Proc. SPIE3332, 199–210 (1998).
[CrossRef]

R. R. Shannon, J. C. Wyant, Applied Optics and Optical Engineering (Academic, San Diego, Calif., 1992), Vol. XI.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, 1980), pp. 203–232, 459–490.

D. Malacara, Optical Shop Testing (Wiley, New York, 1978).

R. P. Grosso, R. Crane, “Precise optical evaluation using phase measuring interferometric techniques,” in Interferometry, G. Hopkins, ed., Proc. SPIE192, 65–74 (1979).
[CrossRef]

D. G. Flagello, B. Geh, “Lithography lens testing: analysis of measured aerial images, interferometric data and photoresist measurements,” in Optical Microlithography IX, G. E. Fuller, ed., Proc. SPIE2726, 788–798 (1996).
[CrossRef]

J. P. Kirk, “Astigmatism and field curvature from pin-bars,” in Optical/Laser Microlithography IV, V. Pol, ed., Proc. SPIE1463, 282–291 (1991).
[CrossRef]

J. P. Kirk, “Measurement of astigmatism in microlithography lenses,” in Optical Microlithography XI, L. V. den Hove, ed., Proc. SPIE3334, 848–854 (1998).
[CrossRef]

T. Farrell, R. Nunes, D. Samuels, A. Thomas, R. Ferguson, A. Molless, A. Wong, W. Conley, D. Wheeler, S. Credendino, M. Naeem, P. Hoh, Z. Lu, “Challenge of 1-Gb DRAM development when using optical lithography,” in Optical Microlithography X, G. E. Fuller, ed., Proc. SPIE3051, 333–341 (1997).
[CrossRef]

T. Saito, H. Watanabe, Y. Okuda, “Effect of variable sigma aperture on lens distortion and its pattern size dependence,” in Metrology, Inspection, and Process Control for Microlithography X, S. K. Jones, ed., Proc. SPIE2725, 414–423 (1996).
[CrossRef]

T. Saito, H. Watanabe, Y. Okuda, “Overlay error of fine patterns by lens aberration using modified illumination,” in Optical Microlithography X, G. E. Fuller, ed., Proc. SPIE3051, 686–696 (1997).
[CrossRef]

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Figures (12)

Fig. 1
Fig. 1

Schematic diagram of a simple reduction projector.

Fig. 2
Fig. 2

Imaging of a grating pattern under reduced σ illumination.

Fig. 3
Fig. 3

Diffracted beams at the exit pupil: (a) P is too small, (b) three diffracted beams are in the projection NA, (c) P is too large, σ is not sufficiently small, or both.

Fig. 4
Fig. 4

Relationship between illumination coherence σ and pupil radius ρ at the center of the ±1st diffraction orders. Thick solid line, P = λ/NA(1 - σ). Longer-dashed line, P = 3λ/NA(1 + σ). Shorter-dashed line, P = 3λ/NA(1 + σ). Three-beam interference is achieved at the regions of Conditions I and II. Condition I is for L = S patterns; Condition II is for LS patterns.

Fig. 5
Fig. 5

Relationship between a wave-front aberration at best focus and a defocus term. Thick solid curves, wave-front aberration; Dotted lines, a defocusing terms. Thin solid lines, straight lines between W-1) and W+1).

Fig. 6
Fig. 6

Wave-front function of primary coma Z 6.

Fig. 7
Fig. 7

Wave-front function of primary astigmatism Z 4.

Fig. 8
Fig. 8

Wave-front function of primary spherical aberration Z 8.

Fig. 9
Fig. 9

Mark patterns for measuring coma with a grating pattern. The A mark is composed of a several-micrometer open-square pattern and a submicrometer grating pattern. The B mark is composed of two open-square patterns to overlay the outer pattern of the A mark and a part of the grating pattern of the A mark. The measurement mark is fabricated by double exposure of the A and B marks.

Fig. 10
Fig. 10

Double-exposure method for measuring mark fabrication.

Fig. 11
Fig. 11

Size and focal dependence of relative pattern shifts for a grating. Arrows show the relative pattern shift of fine grating patterns from 2.0-µm isolated lines. Rectangles show the static exposure fields of 25 mm × 8 mm.

Fig. 12
Fig. 12

Coma map in the static exposure field of 25 mm × 8 mm.

Tables (2)

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Table 1 Zernike Polynomial up to 16 Terms

Tables Icon

Table 2 Experimental Conditions

Equations (17)

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Condition IλNA1-σP3λNA1+σ  L=S, Condition IIλNA1-σP2λNA1+σ  LS,
Wρ=1-1-ρ2δFδF2 ρ2=2Z3ρ2,
ρ=λP1NA.
Wevenρ=1-1-ρ2δFρ22 δF,
Woddρ=δxPλNA=ρδx,
Wρ, θ=Z63ρ2-2ρ cos θ+Z73ρ2-2ρ sin θ,
WXρ=Z63ρ2-2ρ,  WYρ=Z73ρ2-2ρ.
WXρ=Z63ρ3,  WYρ=Z73ρ3.
WXρ±1=±δxPλNA,  WYρ±1=±δyPλNA,
Z6P23NA2λ2 δx,  Z7P23NA2λ2 δy.
Wρ, θ=Z4ρ2 cos 2θ,
Z414 δF0°/90°.
Z51/4δF±45°.
Wρ=Z86ρ4-6ρ2+1,
Wρ=6Z8ρ4.
Wρi=ρi22δFi+C=6Z8ρi4, Wρj=ρj22δFj+C=6Z8ρj4,
Z8112δFi-jρi2-ρj2.

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