Abstract

The influence of polarization on the image formation of one-dimensional periodic patterns in a projection optical lithography system has been investigated. Assuming a linear polarizer at the lens pupil, I derived a simple expression representing the image intensity as the summation over spatial-frequency harmonics as well as three orthogonal polarizations. I calculated the coefficient for each image component as a function of the pattern frequency by independently varying the degree of partial coherence such that the image qualities of the two extreme polarization cases could be thoroughly compared.

© 1998 Optical Society of America

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References

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  1. P. Rai-Choudhury, ed., Microlithography, Vol. 1 of Handbook of Microlithography, Micromachining, and Microfabrication (SPIE Press, Bellingham, Wash., 1997).
  2. M. D. Levenson, N. S. Viswanathan, R. A. Simpson, “Improving resolution in photolithography with a phase-shifting mask,” IEEE Trans. Electron. Devices ED-29, 1828–1836 (1982).
    [CrossRef]
  3. A. Suzuki, M. Noguchi, “Sub-half micron exposure system with optimized illumination,” IEICE Trans. Electron. E76-C, 13–18 (1993).
  4. H. Fukuda, T. Terasawa, S. Okazaki, “Spatial filtering for depth of focus enhancement in optical lithography,” J. Vac. Sci. Technol. B 9, 3113–3116 (1991).
    [CrossRef]
  5. Y. Unno, “Polarization effect of illumination light,” in Optical/Laser Microlithography VI, J. D. Cuthbert, ed., Proc. SPIE1927, 879–891 (1993).
    [CrossRef]
  6. S. Asai, I. Hanyu, M. Takikawa, “Resolution limit for optical lithography using polarized light illumination,” Jpn. J. Appl. Phys. Part 1 32, 5863–5866 (1993).
    [CrossRef]
  7. M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1980), Chap. 10.
  8. R. E. Swing, J. R. Glay, “Ambiguity of the transfer function with partially coherent illumination,” J. Opt. Soc. Am. 57, 1180–1189 (1967).
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  9. R. J. Becherer, G. B. Parrent, “Nonlinearity in optical imaging systems,” J. Opt. Soc. Am. 57, 1479–1486 (1967).
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  10. M. S. Yeung, “Modeling high numerical aperture optical lithography,” in Optical/Laser Microlithography, B. J. Lin, ed., Proc. SPIE922, 149–164 (1988).
  11. K. Matsumoto, T. Tsuruta, “Issues and method of designing lenses for optical lithography,” Opt. Eng. 31, 2657–2664 (1992).
    [CrossRef]
  12. D. G. Flagello, T. Milster, A. E. Rosenbluth, “Theory of high-NA imaging in homogeneous thin films,” J. Opt. Soc. Am. A 13, 53–64 (1996).
    [CrossRef]
  13. C. A. Mack, “Photoresist process optimization,” in KTI Microelectronics Seminar Interface ’87 (KTI Chemicals, Sunnyvale, Calif.1987), pp. 153–167.
  14. F. A. Jenkins, H. E. White, Fundamentals of Optics (McGraw-Hill, New York, 1965), Chap. 9.
  15. B. Richards, 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).
    [CrossRef]
  16. T. Tsuruta, Oyo Kogaku (Baifu-kan, Tokyo, 1990), Chap. 2 (in Japanese).
  17. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).
  18. J. J. Stamnes, Waves in Focal Regions (Hilger, Bristol, UK, 1986), Chap. 16.
  19. E. C. Kintner, “Method for the calculation of partially coherent imagery,” Appl. Opt. 17, 2747–2753 (1978).
    [CrossRef] [PubMed]

1996

1993

A. Suzuki, M. Noguchi, “Sub-half micron exposure system with optimized illumination,” IEICE Trans. Electron. E76-C, 13–18 (1993).

S. Asai, I. Hanyu, M. Takikawa, “Resolution limit for optical lithography using polarized light illumination,” Jpn. J. Appl. Phys. Part 1 32, 5863–5866 (1993).
[CrossRef]

1992

K. Matsumoto, T. Tsuruta, “Issues and method of designing lenses for optical lithography,” Opt. Eng. 31, 2657–2664 (1992).
[CrossRef]

1991

H. Fukuda, T. Terasawa, S. Okazaki, “Spatial filtering for depth of focus enhancement in optical lithography,” J. Vac. Sci. Technol. B 9, 3113–3116 (1991).
[CrossRef]

1982

M. D. Levenson, N. S. Viswanathan, R. A. Simpson, “Improving resolution in photolithography with a phase-shifting mask,” IEEE Trans. Electron. Devices ED-29, 1828–1836 (1982).
[CrossRef]

1978

1967

1959

B. Richards, 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).
[CrossRef]

Asai, S.

S. Asai, I. Hanyu, M. Takikawa, “Resolution limit for optical lithography using polarized light illumination,” Jpn. J. Appl. Phys. Part 1 32, 5863–5866 (1993).
[CrossRef]

Becherer, R. J.

Born, M.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1980), Chap. 10.

Flagello, D. G.

Fukuda, H.

H. Fukuda, T. Terasawa, S. Okazaki, “Spatial filtering for depth of focus enhancement in optical lithography,” J. Vac. Sci. Technol. B 9, 3113–3116 (1991).
[CrossRef]

Glay, J. R.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

Hanyu, I.

S. Asai, I. Hanyu, M. Takikawa, “Resolution limit for optical lithography using polarized light illumination,” Jpn. J. Appl. Phys. Part 1 32, 5863–5866 (1993).
[CrossRef]

Jenkins, F. A.

F. A. Jenkins, H. E. White, Fundamentals of Optics (McGraw-Hill, New York, 1965), Chap. 9.

Kintner, E. C.

Levenson, M. D.

M. D. Levenson, N. S. Viswanathan, R. A. Simpson, “Improving resolution in photolithography with a phase-shifting mask,” IEEE Trans. Electron. Devices ED-29, 1828–1836 (1982).
[CrossRef]

Mack, C. A.

C. A. Mack, “Photoresist process optimization,” in KTI Microelectronics Seminar Interface ’87 (KTI Chemicals, Sunnyvale, Calif.1987), pp. 153–167.

Matsumoto, K.

K. Matsumoto, T. Tsuruta, “Issues and method of designing lenses for optical lithography,” Opt. Eng. 31, 2657–2664 (1992).
[CrossRef]

Milster, T.

Noguchi, M.

A. Suzuki, M. Noguchi, “Sub-half micron exposure system with optimized illumination,” IEICE Trans. Electron. E76-C, 13–18 (1993).

Okazaki, S.

H. Fukuda, T. Terasawa, S. Okazaki, “Spatial filtering for depth of focus enhancement in optical lithography,” J. Vac. Sci. Technol. B 9, 3113–3116 (1991).
[CrossRef]

Parrent, G. B.

Richards, B.

B. Richards, 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).
[CrossRef]

Rosenbluth, A. E.

Simpson, R. A.

M. D. Levenson, N. S. Viswanathan, R. A. Simpson, “Improving resolution in photolithography with a phase-shifting mask,” IEEE Trans. Electron. Devices ED-29, 1828–1836 (1982).
[CrossRef]

Stamnes, J. J.

J. J. Stamnes, Waves in Focal Regions (Hilger, Bristol, UK, 1986), Chap. 16.

Suzuki, A.

A. Suzuki, M. Noguchi, “Sub-half micron exposure system with optimized illumination,” IEICE Trans. Electron. E76-C, 13–18 (1993).

Swing, R. E.

Takikawa, M.

S. Asai, I. Hanyu, M. Takikawa, “Resolution limit for optical lithography using polarized light illumination,” Jpn. J. Appl. Phys. Part 1 32, 5863–5866 (1993).
[CrossRef]

Terasawa, T.

H. Fukuda, T. Terasawa, S. Okazaki, “Spatial filtering for depth of focus enhancement in optical lithography,” J. Vac. Sci. Technol. B 9, 3113–3116 (1991).
[CrossRef]

Tsuruta, T.

K. Matsumoto, T. Tsuruta, “Issues and method of designing lenses for optical lithography,” Opt. Eng. 31, 2657–2664 (1992).
[CrossRef]

T. Tsuruta, Oyo Kogaku (Baifu-kan, Tokyo, 1990), Chap. 2 (in Japanese).

Unno, Y.

Y. Unno, “Polarization effect of illumination light,” in Optical/Laser Microlithography VI, J. D. Cuthbert, ed., Proc. SPIE1927, 879–891 (1993).
[CrossRef]

Viswanathan, N. S.

M. D. Levenson, N. S. Viswanathan, R. A. Simpson, “Improving resolution in photolithography with a phase-shifting mask,” IEEE Trans. Electron. Devices ED-29, 1828–1836 (1982).
[CrossRef]

White, H. E.

F. A. Jenkins, H. E. White, Fundamentals of Optics (McGraw-Hill, New York, 1965), Chap. 9.

Wolf, E.

B. Richards, 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).
[CrossRef]

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1980), Chap. 10.

Yeung, M. S.

M. S. Yeung, “Modeling high numerical aperture optical lithography,” in Optical/Laser Microlithography, B. J. Lin, ed., Proc. SPIE922, 149–164 (1988).

Appl. Opt.

IEEE Trans. Electron. Devices

M. D. Levenson, N. S. Viswanathan, R. A. Simpson, “Improving resolution in photolithography with a phase-shifting mask,” IEEE Trans. Electron. Devices ED-29, 1828–1836 (1982).
[CrossRef]

IEICE Trans. Electron.

A. Suzuki, M. Noguchi, “Sub-half micron exposure system with optimized illumination,” IEICE Trans. Electron. E76-C, 13–18 (1993).

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

J. Vac. Sci. Technol. B

H. Fukuda, T. Terasawa, S. Okazaki, “Spatial filtering for depth of focus enhancement in optical lithography,” J. Vac. Sci. Technol. B 9, 3113–3116 (1991).
[CrossRef]

Jpn. J. Appl. Phys. Part 1

S. Asai, I. Hanyu, M. Takikawa, “Resolution limit for optical lithography using polarized light illumination,” Jpn. J. Appl. Phys. Part 1 32, 5863–5866 (1993).
[CrossRef]

Opt. Eng.

K. Matsumoto, T. Tsuruta, “Issues and method of designing lenses for optical lithography,” Opt. Eng. 31, 2657–2664 (1992).
[CrossRef]

Proc. R. Soc. London Ser. A

B. Richards, 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).
[CrossRef]

Other

T. Tsuruta, Oyo Kogaku (Baifu-kan, Tokyo, 1990), Chap. 2 (in Japanese).

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

J. J. Stamnes, Waves in Focal Regions (Hilger, Bristol, UK, 1986), Chap. 16.

M. S. Yeung, “Modeling high numerical aperture optical lithography,” in Optical/Laser Microlithography, B. J. Lin, ed., Proc. SPIE922, 149–164 (1988).

P. Rai-Choudhury, ed., Microlithography, Vol. 1 of Handbook of Microlithography, Micromachining, and Microfabrication (SPIE Press, Bellingham, Wash., 1997).

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, New York, 1980), Chap. 10.

C. A. Mack, “Photoresist process optimization,” in KTI Microelectronics Seminar Interface ’87 (KTI Chemicals, Sunnyvale, Calif.1987), pp. 153–167.

F. A. Jenkins, H. E. White, Fundamentals of Optics (McGraw-Hill, New York, 1965), Chap. 9.

Y. Unno, “Polarization effect of illumination light,” in Optical/Laser Microlithography VI, J. D. Cuthbert, ed., Proc. SPIE1927, 879–891 (1993).
[CrossRef]

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Figures (9)

Fig. 1
Fig. 1

Schematic of a projection lithography system. The angles θ s , θ o , and θ i are used to define the numerical apertures of the condenser lens (NA s ), the projection lens on the object side (NA o ), and the projection lens on the image side (NA), respectively.

Fig. 2
Fig. 2

Definitions of illumination and diffraction beams. The polarization vector is specified for the beam after it has passed through the polarizer.

Fig. 3
Fig. 3

Application of the conservation law for the amount of energy that the same ray has to convey in the object and in the image spaces.

Fig. 4
Fig. 4

Diffraction beams from an equal line–space pattern in object space. An incident beam with the unit amplitude propagating in the direction of (s x , s y ) is assumed.

Fig. 5
Fig. 5

Integral calculation of ∬ H(h x , h y )U(h x - f, h y )dh x dh y , which is represented by the hatched region.

Fig. 6
Fig. 6

Image decomposition in terms of the spatial-frequency harmonics: [i] the constant background, [ii] the fundamental harmonic image, and [iii] the second-higher harmonic image.

Fig. 7
Fig. 7

Calculation results of ξ(0, f) and ξ(f, -f) (ξ = x, y, z) for the two polarization cases (left, ω = 0°; right, ω = 90°). A projection system with NA = 0.6 and m = 0.2 is assumed.

Fig. 8
Fig. 8

Contour plots of the Lsp on the (f/NA) - (σ) coordinates (left, ω = 0°; right, ω = 90°). The values are normalized by k × NA.

Fig. 9
Fig. 9

Ratio of the Lsp values for ω = 0° and ω = 90°.

Equations (28)

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a · u × ê z = b · u × ê z .
b x u x ,   u y = u x 2 1 - u x 2 - u y 2 1 / 2 +   u y 2 cos   ω - u x u y 1 - 1 - u x 2 - u y 2 1 / 2 sin   ω u x 2 + u y 2 , b y u x ,   u y = - u x u y 1 - 1 - u x 2 - u y 2 1 / 2 cos   ω + u x 2 + u y 2 1 - u x 2 - u y 2 1 / 2 sin   ω u x 2 + u y 2 , b z u x ,   u y = - u x cos   ω - u y sin   ω .
1 / 2 μ t x ,   t y 2 cos   α d Ω A d A = ν u x ,   u y 2 cos   β d Ω B d B ,
d A / d B = 1 / m 2
d Ω A / d Ω B = sin   α d α / sin   β d β = m 2 cos   β / cos   α
ν u x ,   u y = ν - t x / m , - t y / m = μ t x ,   t y / 2
f / NA > 1 + σ / 3 ,
ν h x + f ,   h y = 2 / 2 π     - 1 st   order , ν h x ,   h y = 2 / 4     0 th   order , ν h x - f ,   h y = 2 / 2 π     + 1 st   order ,
U u x ,   u y = 1 0 u x 2 + u y 2 NA otherwise
Φ ˆ u x ,   u y = Φ u x ,   u y + Δ 1 - u x 2 - u y 2 1 / 2 .
E x ,   y ,   0 = 2 4 ξ = x , y , z   E ξ x ,   y ,   0 ê ξ ,
E ξ x ,   y ,   0 = U h x ,   h y b ξ h x ,   h y exp ik Φ ˆ h x ,   h y + h x x + h y y + 2 / π U h x - f ,   h y × b ξ h x - f ,   h y exp ik Φ ˆ h x - f ,   h y + h x - f x + h y y + 2 / π × U h x + f ,   h y b ξ h x + f ,   h y exp ik × Φ ˆ h x + f ,   h y + h x + f x + h y y ,
P ξ u x ,   u y U u x ,   u y b ξ u x ,   u y exp ik Φ ˆ u x ,   u y ,
E ξ = P ξ h x ,   h y exp ik h x x + h y y + 2 / π × P ξ h x - f ,   h y exp ik h x - f x + h y y + 2 / π P ξ h x + f ,   h y exp ik h x + f x + h y y ,
E ξ E ξ * = | P ξ h x ,   h y | 2 + 4 / π 2 | P ξ h x - f ,   h y | 2 + | P ξ h x + f ,   h y | 2 + 2 / π P ξ h x ,   h y × P ξ * h x - f ,   h y exp ikfx + P ξ h x ,   h y × P ξ * h x + f ,   h y exp - ikfx + P ξ h x - f ,   h y P ξ * h x ,   h y exp - ikfx + P ξ h x + f ,   h y P ξ * h x ,   h y exp ikfx + 4 / π 2 × P ξ h x - f ,   h y P ξ * h x + f ,   h y exp - i 2 kfx + P ξ h x + f ,   h y P ξ * h x - f ,   h y exp i 2 kfx ,
H h x ,   h y = 1 0 h x 2 + h y 2 σ NA otherwise ,
I x = ξ = x , y , z     H h x ,   h y E ξ E ξ * d h x d h y ,
T ξ f 1 ,   f 2     H h x ,   h y P ξ h x - f 1 ,   h y × P ξ * h x - f 2 ,   h y d h x d h y ,
I x = ξ = x , y , z T ξ 0 ,   0 + 4 / π 2 T ξ f ,   f + T ξ - f ,   - f + 2 / π T ξ 0 ,   f exp ikfx + T ξ 0 ,   - f × exp - ikfx + T ξ f ,   0 exp - ikfx + T ξ - f ,   0 exp ikfx + 4 / π 2 T ξ f ,   - f × exp - i 2 kfx + T ξ - f ,   f exp i 2 kfx .
T ξ f ,   f = T ξ - f ,   - f , T ξ 0 ,   f = T ξ 0 ,   - f = T ξ * f ,   0 = T ξ * - f ,   0 , T ξ f ,   - f = T ξ - f ,   f .
I x = ξ = x , y , z T ξ 0 ,   0 + 8 / π 2 T ξ f ,   f + 8 / π Re   T ξ 0 ,   f cos kfx + 8 / π 2 T ξ f ,   - f cos 2 kfx ,
ξ = x , y , z   T ξ 0 ,   0 =   H h x ,   h y d h x d h y = π σ 2 NA 2 ,
ξ = x , y , z   T ξ f ,   f = π σ 2 NA 2 σ 2 NA 2 γ 1 + NA 2 γ 2   - f   NA   sin   γ 2 0 0 f 1 - σ NA 1 - σ NA f   1 + σ NA f 1 + σ NA .
I x = I 0 f 1 + ξ = x , y , z Re   T ˆ ξ 0 ,   f cos kfx + T ˆ ξ f ,   - f cos 2 kfx ,
Lsp d   ln   I x d x = | d I x / d x | I x ,     x = n ± 1 / 4 m d ,
Lsp = kf   ξ = x , y , z Re   T ˆ ξ 0 ,   f / 1 - ξ = x , y , z   T ˆ ξ f ,   - f ,
Lsp ω = 0 ° Lsp ω = 90 ° T ˆ x 0 0 ,   f + T ˆ z 0 0 ,   f T ˆ y 90 0 ,   f + T ˆ z 90 0 ,   f × 1 - T ˆ y 90 f ,   - f - T ˆ z 90 f ,   - f 1 - T ˆ x 0 f ,   - f - T ˆ z 0 f ,   - f
Lsp ω = 0 ° Lsp ω = 90 ° = T ˆ x 0 0 ,   f + T ˆ z 0 0 ,   f T ˆ y 90 0 ,   f + T ˆ z 90 0 ,   f ,

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