Abstract

This paper proposes a parametric analytical source model for overall representation of the physical distribution property of partially coherent illumination sources in lithographic tools. A set of smooth kernels is adopted to construct the analytical model for the multiple mainstream illumination sources. Corrected parametrical terms are subsequently presented for characterization of different physical distortions of and deviations from actual illumination sources. The corrected parametrical terms can be decomposed into Fourier series, which have special physical meanings of respectively indicating different distortion types, including shift of the center, tilt, and ellipticity, etc. We fully expected that the proposed analytical model will provide both simulation conditions and a theoretical basis for the resolution enhancement technique and related research fields.

© 2012 Optical Society of America

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References

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  1. F. M. Schellenberg, “A history of resolution enhancement technology,” Opt. Rev. 12, 83–89 (2005).
    [CrossRef]
  2. A. K. Wong, Optical Imaging in Projection Microlithography (SPIE, 2005), Chap. 4.
  3. B. J. Lin, Optical Lithography: Here is Why (SPIE, 2010), Chap. 3.
  4. E. Wolf, “New spectral representation of random sources and of the partially coherent fields that they generate,” Opt. Commun. 38, 3–6 (1981).
    [CrossRef]
  5. G. Perçin, A. Sezginer, and F. X. Zach, “Metrology for stepper illumination pupil profile,” J. Micro/nanolithogr. MEMS MOEMS 5, 023006 (2006).
  6. X. Ma and G. R. Arce, “PSM design for inverse lithography with partially coherent illumination,” Opt. Express 16, 20126–20141 (2008).
    [CrossRef]
  7. K. Yamazoe, “Fast fine-pixel aerial image calculation in partially coherent imaging by matrix representation of modified Hopkins equation,” Appl. Opt. 49, 3909–3915 (2010).
    [CrossRef]
  8. W. Liu, S. Y. Liu, T. T. Zhou, and L. J. Wang, “Aerial image based technique for measurement of lens aberrations up to 37th Zernike coefficient in lithographic tools under partial coherent illumination,” Opt. Express 17, 19278–19291 (2009).
    [CrossRef]
  9. C. Bodendorf, R. E. Schlief, and R. Ziebold, “Impact of measured pupil illumination fill distribution on lithography simulation and OPC models,” Proc. SPIE 5377, 1130–1145 (2004).
  10. J. Shin, C. Hwang, S. Lee, S. Woo, H. Cho, and J. Moon, “Understanding the impact of source displacement error on sub-90 nm patterns using a fresnel zone plate,” J. Vac. Sci. Technol. B 23, 2653–2656 (2005).
    [CrossRef]
  11. W. Liu, S. Y. Liu, T. L. Shi, and Z. R. Tang, “Generalized formulations for aerial image based lens aberration metrology in lithographic tools with arbitrarily shaped illumination sources,” Opt. Express 18, 20096–20104 (2010).
    [CrossRef]
  12. E. Barouch, S. L. Knodle, S. A. Orszag, and M. Yeung, “Illuminator optimization for projection printing,” Proc. SPIE 3679, 697–703 (1999).
  13. T. C. Barrett, “Impact of illumination pupil-fill spatial variation on simulated imaging performance,” Proc. SPIE 4000, 804–817 (2000).
  14. Y. Granik, “Source optimization for image fidelity and throughput,” J. Micro/nanolithogr. MEMS MOEMS 3, 509–522 (2004).
    [CrossRef]
  15. Y. Granik and K. Adam, “Analytical approximations of the source intensity distributions,” Proc. SPIE 5992, 599255 (2005).
  16. D. G. Flagello, B. Geh, R. Socha, P. Liu, Y. Cao, R. Stas, O. Natt, and J. Zimmermann, “Understanding illumination effects for control of optical proximity effects (OPE),” Proc. SPIE 6924, 69241U (2008).
  17. T. Matsuyama, N. Kita, and Y. Mizuno, “Pupilgram adjusting scheme using intelligent illuminator for ArF immersion exposure tool,” Proc. SPIE 7973, 79731H (2011).
  18. H. van der Laan, M. Dierichs, H. van Greevenbroek, E. McCoo, F. Stoffels, R. Pongers, and R. Willekers, “Aerial image measurement methods for fast aberration setup and illumination pupil verification,” Proc. SPIE 4346, 394–407 (2001).

2011 (1)

T. Matsuyama, N. Kita, and Y. Mizuno, “Pupilgram adjusting scheme using intelligent illuminator for ArF immersion exposure tool,” Proc. SPIE 7973, 79731H (2011).

2010 (2)

2009 (1)

2008 (2)

X. Ma and G. R. Arce, “PSM design for inverse lithography with partially coherent illumination,” Opt. Express 16, 20126–20141 (2008).
[CrossRef]

D. G. Flagello, B. Geh, R. Socha, P. Liu, Y. Cao, R. Stas, O. Natt, and J. Zimmermann, “Understanding illumination effects for control of optical proximity effects (OPE),” Proc. SPIE 6924, 69241U (2008).

2006 (1)

G. Perçin, A. Sezginer, and F. X. Zach, “Metrology for stepper illumination pupil profile,” J. Micro/nanolithogr. MEMS MOEMS 5, 023006 (2006).

2005 (3)

F. M. Schellenberg, “A history of resolution enhancement technology,” Opt. Rev. 12, 83–89 (2005).
[CrossRef]

Y. Granik and K. Adam, “Analytical approximations of the source intensity distributions,” Proc. SPIE 5992, 599255 (2005).

J. Shin, C. Hwang, S. Lee, S. Woo, H. Cho, and J. Moon, “Understanding the impact of source displacement error on sub-90 nm patterns using a fresnel zone plate,” J. Vac. Sci. Technol. B 23, 2653–2656 (2005).
[CrossRef]

2004 (2)

C. Bodendorf, R. E. Schlief, and R. Ziebold, “Impact of measured pupil illumination fill distribution on lithography simulation and OPC models,” Proc. SPIE 5377, 1130–1145 (2004).

Y. Granik, “Source optimization for image fidelity and throughput,” J. Micro/nanolithogr. MEMS MOEMS 3, 509–522 (2004).
[CrossRef]

2001 (1)

H. van der Laan, M. Dierichs, H. van Greevenbroek, E. McCoo, F. Stoffels, R. Pongers, and R. Willekers, “Aerial image measurement methods for fast aberration setup and illumination pupil verification,” Proc. SPIE 4346, 394–407 (2001).

2000 (1)

T. C. Barrett, “Impact of illumination pupil-fill spatial variation on simulated imaging performance,” Proc. SPIE 4000, 804–817 (2000).

1999 (1)

E. Barouch, S. L. Knodle, S. A. Orszag, and M. Yeung, “Illuminator optimization for projection printing,” Proc. SPIE 3679, 697–703 (1999).

1981 (1)

E. Wolf, “New spectral representation of random sources and of the partially coherent fields that they generate,” Opt. Commun. 38, 3–6 (1981).
[CrossRef]

Adam, K.

Y. Granik and K. Adam, “Analytical approximations of the source intensity distributions,” Proc. SPIE 5992, 599255 (2005).

Arce, G. R.

Barouch, E.

E. Barouch, S. L. Knodle, S. A. Orszag, and M. Yeung, “Illuminator optimization for projection printing,” Proc. SPIE 3679, 697–703 (1999).

Barrett, T. C.

T. C. Barrett, “Impact of illumination pupil-fill spatial variation on simulated imaging performance,” Proc. SPIE 4000, 804–817 (2000).

Bodendorf, C.

C. Bodendorf, R. E. Schlief, and R. Ziebold, “Impact of measured pupil illumination fill distribution on lithography simulation and OPC models,” Proc. SPIE 5377, 1130–1145 (2004).

Cao, Y.

D. G. Flagello, B. Geh, R. Socha, P. Liu, Y. Cao, R. Stas, O. Natt, and J. Zimmermann, “Understanding illumination effects for control of optical proximity effects (OPE),” Proc. SPIE 6924, 69241U (2008).

Cho, H.

J. Shin, C. Hwang, S. Lee, S. Woo, H. Cho, and J. Moon, “Understanding the impact of source displacement error on sub-90 nm patterns using a fresnel zone plate,” J. Vac. Sci. Technol. B 23, 2653–2656 (2005).
[CrossRef]

Dierichs, M.

H. van der Laan, M. Dierichs, H. van Greevenbroek, E. McCoo, F. Stoffels, R. Pongers, and R. Willekers, “Aerial image measurement methods for fast aberration setup and illumination pupil verification,” Proc. SPIE 4346, 394–407 (2001).

Flagello, D. G.

D. G. Flagello, B. Geh, R. Socha, P. Liu, Y. Cao, R. Stas, O. Natt, and J. Zimmermann, “Understanding illumination effects for control of optical proximity effects (OPE),” Proc. SPIE 6924, 69241U (2008).

Geh, B.

D. G. Flagello, B. Geh, R. Socha, P. Liu, Y. Cao, R. Stas, O. Natt, and J. Zimmermann, “Understanding illumination effects for control of optical proximity effects (OPE),” Proc. SPIE 6924, 69241U (2008).

Granik, Y.

Y. Granik and K. Adam, “Analytical approximations of the source intensity distributions,” Proc. SPIE 5992, 599255 (2005).

Y. Granik, “Source optimization for image fidelity and throughput,” J. Micro/nanolithogr. MEMS MOEMS 3, 509–522 (2004).
[CrossRef]

Hwang, C.

J. Shin, C. Hwang, S. Lee, S. Woo, H. Cho, and J. Moon, “Understanding the impact of source displacement error on sub-90 nm patterns using a fresnel zone plate,” J. Vac. Sci. Technol. B 23, 2653–2656 (2005).
[CrossRef]

Kita, N.

T. Matsuyama, N. Kita, and Y. Mizuno, “Pupilgram adjusting scheme using intelligent illuminator for ArF immersion exposure tool,” Proc. SPIE 7973, 79731H (2011).

Knodle, S. L.

E. Barouch, S. L. Knodle, S. A. Orszag, and M. Yeung, “Illuminator optimization for projection printing,” Proc. SPIE 3679, 697–703 (1999).

Lee, S.

J. Shin, C. Hwang, S. Lee, S. Woo, H. Cho, and J. Moon, “Understanding the impact of source displacement error on sub-90 nm patterns using a fresnel zone plate,” J. Vac. Sci. Technol. B 23, 2653–2656 (2005).
[CrossRef]

Lin, B. J.

B. J. Lin, Optical Lithography: Here is Why (SPIE, 2010), Chap. 3.

Liu, P.

D. G. Flagello, B. Geh, R. Socha, P. Liu, Y. Cao, R. Stas, O. Natt, and J. Zimmermann, “Understanding illumination effects for control of optical proximity effects (OPE),” Proc. SPIE 6924, 69241U (2008).

Liu, S. Y.

Liu, W.

Ma, X.

Matsuyama, T.

T. Matsuyama, N. Kita, and Y. Mizuno, “Pupilgram adjusting scheme using intelligent illuminator for ArF immersion exposure tool,” Proc. SPIE 7973, 79731H (2011).

McCoo, E.

H. van der Laan, M. Dierichs, H. van Greevenbroek, E. McCoo, F. Stoffels, R. Pongers, and R. Willekers, “Aerial image measurement methods for fast aberration setup and illumination pupil verification,” Proc. SPIE 4346, 394–407 (2001).

Mizuno, Y.

T. Matsuyama, N. Kita, and Y. Mizuno, “Pupilgram adjusting scheme using intelligent illuminator for ArF immersion exposure tool,” Proc. SPIE 7973, 79731H (2011).

Moon, J.

J. Shin, C. Hwang, S. Lee, S. Woo, H. Cho, and J. Moon, “Understanding the impact of source displacement error on sub-90 nm patterns using a fresnel zone plate,” J. Vac. Sci. Technol. B 23, 2653–2656 (2005).
[CrossRef]

Natt, O.

D. G. Flagello, B. Geh, R. Socha, P. Liu, Y. Cao, R. Stas, O. Natt, and J. Zimmermann, “Understanding illumination effects for control of optical proximity effects (OPE),” Proc. SPIE 6924, 69241U (2008).

Orszag, S. A.

E. Barouch, S. L. Knodle, S. A. Orszag, and M. Yeung, “Illuminator optimization for projection printing,” Proc. SPIE 3679, 697–703 (1999).

Perçin, G.

G. Perçin, A. Sezginer, and F. X. Zach, “Metrology for stepper illumination pupil profile,” J. Micro/nanolithogr. MEMS MOEMS 5, 023006 (2006).

Pongers, R.

H. van der Laan, M. Dierichs, H. van Greevenbroek, E. McCoo, F. Stoffels, R. Pongers, and R. Willekers, “Aerial image measurement methods for fast aberration setup and illumination pupil verification,” Proc. SPIE 4346, 394–407 (2001).

Schellenberg, F. M.

F. M. Schellenberg, “A history of resolution enhancement technology,” Opt. Rev. 12, 83–89 (2005).
[CrossRef]

Schlief, R. E.

C. Bodendorf, R. E. Schlief, and R. Ziebold, “Impact of measured pupil illumination fill distribution on lithography simulation and OPC models,” Proc. SPIE 5377, 1130–1145 (2004).

Sezginer, A.

G. Perçin, A. Sezginer, and F. X. Zach, “Metrology for stepper illumination pupil profile,” J. Micro/nanolithogr. MEMS MOEMS 5, 023006 (2006).

Shi, T. L.

Shin, J.

J. Shin, C. Hwang, S. Lee, S. Woo, H. Cho, and J. Moon, “Understanding the impact of source displacement error on sub-90 nm patterns using a fresnel zone plate,” J. Vac. Sci. Technol. B 23, 2653–2656 (2005).
[CrossRef]

Socha, R.

D. G. Flagello, B. Geh, R. Socha, P. Liu, Y. Cao, R. Stas, O. Natt, and J. Zimmermann, “Understanding illumination effects for control of optical proximity effects (OPE),” Proc. SPIE 6924, 69241U (2008).

Stas, R.

D. G. Flagello, B. Geh, R. Socha, P. Liu, Y. Cao, R. Stas, O. Natt, and J. Zimmermann, “Understanding illumination effects for control of optical proximity effects (OPE),” Proc. SPIE 6924, 69241U (2008).

Stoffels, F.

H. van der Laan, M. Dierichs, H. van Greevenbroek, E. McCoo, F. Stoffels, R. Pongers, and R. Willekers, “Aerial image measurement methods for fast aberration setup and illumination pupil verification,” Proc. SPIE 4346, 394–407 (2001).

Tang, Z. R.

van der Laan, H.

H. van der Laan, M. Dierichs, H. van Greevenbroek, E. McCoo, F. Stoffels, R. Pongers, and R. Willekers, “Aerial image measurement methods for fast aberration setup and illumination pupil verification,” Proc. SPIE 4346, 394–407 (2001).

van Greevenbroek, H.

H. van der Laan, M. Dierichs, H. van Greevenbroek, E. McCoo, F. Stoffels, R. Pongers, and R. Willekers, “Aerial image measurement methods for fast aberration setup and illumination pupil verification,” Proc. SPIE 4346, 394–407 (2001).

Wang, L. J.

Willekers, R.

H. van der Laan, M. Dierichs, H. van Greevenbroek, E. McCoo, F. Stoffels, R. Pongers, and R. Willekers, “Aerial image measurement methods for fast aberration setup and illumination pupil verification,” Proc. SPIE 4346, 394–407 (2001).

Wolf, E.

E. Wolf, “New spectral representation of random sources and of the partially coherent fields that they generate,” Opt. Commun. 38, 3–6 (1981).
[CrossRef]

Wong, A. K.

A. K. Wong, Optical Imaging in Projection Microlithography (SPIE, 2005), Chap. 4.

Woo, S.

J. Shin, C. Hwang, S. Lee, S. Woo, H. Cho, and J. Moon, “Understanding the impact of source displacement error on sub-90 nm patterns using a fresnel zone plate,” J. Vac. Sci. Technol. B 23, 2653–2656 (2005).
[CrossRef]

Yamazoe, K.

Yeung, M.

E. Barouch, S. L. Knodle, S. A. Orszag, and M. Yeung, “Illuminator optimization for projection printing,” Proc. SPIE 3679, 697–703 (1999).

Zach, F. X.

G. Perçin, A. Sezginer, and F. X. Zach, “Metrology for stepper illumination pupil profile,” J. Micro/nanolithogr. MEMS MOEMS 5, 023006 (2006).

Zhou, T. T.

Ziebold, R.

C. Bodendorf, R. E. Schlief, and R. Ziebold, “Impact of measured pupil illumination fill distribution on lithography simulation and OPC models,” Proc. SPIE 5377, 1130–1145 (2004).

Zimmermann, J.

D. G. Flagello, B. Geh, R. Socha, P. Liu, Y. Cao, R. Stas, O. Natt, and J. Zimmermann, “Understanding illumination effects for control of optical proximity effects (OPE),” Proc. SPIE 6924, 69241U (2008).

Appl. Opt. (1)

J. Micro/nanolithogr. MEMS MOEMS (2)

G. Perçin, A. Sezginer, and F. X. Zach, “Metrology for stepper illumination pupil profile,” J. Micro/nanolithogr. MEMS MOEMS 5, 023006 (2006).

Y. Granik, “Source optimization for image fidelity and throughput,” J. Micro/nanolithogr. MEMS MOEMS 3, 509–522 (2004).
[CrossRef]

J. Vac. Sci. Technol. B (1)

J. Shin, C. Hwang, S. Lee, S. Woo, H. Cho, and J. Moon, “Understanding the impact of source displacement error on sub-90 nm patterns using a fresnel zone plate,” J. Vac. Sci. Technol. B 23, 2653–2656 (2005).
[CrossRef]

Opt. Commun. (1)

E. Wolf, “New spectral representation of random sources and of the partially coherent fields that they generate,” Opt. Commun. 38, 3–6 (1981).
[CrossRef]

Opt. Express (3)

Opt. Rev. (1)

F. M. Schellenberg, “A history of resolution enhancement technology,” Opt. Rev. 12, 83–89 (2005).
[CrossRef]

Proc. SPIE (7)

E. Barouch, S. L. Knodle, S. A. Orszag, and M. Yeung, “Illuminator optimization for projection printing,” Proc. SPIE 3679, 697–703 (1999).

T. C. Barrett, “Impact of illumination pupil-fill spatial variation on simulated imaging performance,” Proc. SPIE 4000, 804–817 (2000).

Y. Granik and K. Adam, “Analytical approximations of the source intensity distributions,” Proc. SPIE 5992, 599255 (2005).

D. G. Flagello, B. Geh, R. Socha, P. Liu, Y. Cao, R. Stas, O. Natt, and J. Zimmermann, “Understanding illumination effects for control of optical proximity effects (OPE),” Proc. SPIE 6924, 69241U (2008).

T. Matsuyama, N. Kita, and Y. Mizuno, “Pupilgram adjusting scheme using intelligent illuminator for ArF immersion exposure tool,” Proc. SPIE 7973, 79731H (2011).

H. van der Laan, M. Dierichs, H. van Greevenbroek, E. McCoo, F. Stoffels, R. Pongers, and R. Willekers, “Aerial image measurement methods for fast aberration setup and illumination pupil verification,” Proc. SPIE 4346, 394–407 (2001).

C. Bodendorf, R. E. Schlief, and R. Ziebold, “Impact of measured pupil illumination fill distribution on lithography simulation and OPC models,” Proc. SPIE 5377, 1130–1145 (2004).

Other (2)

A. K. Wong, Optical Imaging in Projection Microlithography (SPIE, 2005), Chap. 4.

B. J. Lin, Optical Lithography: Here is Why (SPIE, 2010), Chap. 3.

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Figures (10)

Fig. 1.
Fig. 1.

Set of smooth kernels with g=0.3, p=0.5, t=1, and h=3.

Fig. 2.
Fig. 2.

Comparison of mainstream sources between radially symmetric intensity distributions and top-hat distributions, under the simulation conditions of circular source (σ=0.31), annular source (σo/σi=0.7/0.4), dipole source (σo/σi/θ0=0.7/0.4/22.5°), and quadrupole source (σo/σi/θ0=0.7/0.4/22.5°) using smooth parameters Po=Pi=Pθ=0.07.

Fig. 3.
Fig. 3.

Examples of the kernel-based parametric analytical model in characterizing the effects on different kind of power shifts of an annular source (σo/σi=0.85/0.6) under the smooth parameters Po=Pi=0.1: (a) power tilt in X-direction (aα1=0.2), (b) power tilt in Y-direction (bα1=0.2), (c) power HV ellipticity (aα2=0.2), and (d) power ST ellipticity (bα2=0.2).

Fig. 4.
Fig. 4.

Examples of the kernel-based parametric analytical model in characterizing the effects on different kind of geometric shifts of an annular source (σo/σi=0.85/0.6) under the smooth parameters Po=Pi=0.1: (a) pupil shifts in X/Y-directions (x0=0.15, and y0=0.15), (b) rings shifts in X/Y-directions (aβ1=0.07, aγ1=0.07, bβ1=0.07, and bγ1=0.07), (c) geometric HV ellipticity (aβ2=0.05, and aγ2=0.05), and (d) geometric ST ellipticity (bβ2=0.05, and bγ2=0.05).

Fig. 5.
Fig. 5.

Measured reference sources under different illumination settings: Measured Source 1 (σo/σi=0.95/0.6), Measured Source 2 (σo/σi=0.9/0.65), and Measured Source 3 (σo/σi=0.97/0.7).

Fig. 6.
Fig. 6.

Illustration of measured and fitted annular source: source intensity distribution is complete in the pupil plane.

Fig. 7.
Fig. 7.

Illustration of measured and fitted annular source: source intensity distribution is incomplete in the pupil plane.

Fig. 8.
Fig. 8.

Comparison of fitted results by using the proposed parametric source model and the traditional top-hat model for the Measured Source 3.

Fig. 9.
Fig. 9.

Comparison between measured and fitted annular sources under different illumination settings.

Fig. 10.
Fig. 10.

Similarity values of measured and fitted sources by using different fitting models, including the parametric source model, smooth source model, and the top-hat source model.

Equations (26)

Equations on this page are rendered with MathJax. Learn more.

Kg(x)=1πgStep(x)exp(x2g2).
Step(x)={1,x00,x<0,
Kg(x)=12+12erf(xg).
erf(x)=2π0xet2dt.
KP(x)=12+12xP2+x2,
Kt(x)=12+1πarctan(π2tx),
Kh(x)=12+12tanh(xh).
IC(r)=KP(σr),
IA(r)=KPo(σor)·KPi(rσi),
ID(r,θ)=IA(r)TD(θ),
IQ(r,θ)=IA(r)TQ(θ).
TD(θ)=KPθ(θ0|θ|)+KPθ(θ0|πθ|),
TQ(θ)=KPθ(θ0-|π4-θ|)+KPθ(θ0|3π4θ|)+KPθ(θ0|5π4θ|)+KPθ(θ0|7π4θ|).
IC*(x,y)=[1+α(θ*)]KP[σr*+γ(θ*)],
IA*(x,y)=[1+α(θ*)]·KPo[σor*+γ(θ*)]·KPi[r*σi+β(θ*)],
r*cos(θ*)=xx0,r*sin(θ*)=yy0.
α(θ*)=[aα1cos(θ*)+bα1sin(θ*)]+[aα2cos(2θ*)+bα2sin(2θ*)],
β(θ*)=[aβ1cos(θ*)+bβ1sin(θ*)]+[aβ2cos(2θ*)+bβ2sin(2θ*)],
γ(θ*)=[aγ1cos(θ*)+bγ1sin(θ*)]+[aγ2cos(2θ*)+bγ2sin(2θ*)].
ID*(r,θ)=IA*(r,θ)TD(θ),
IQ*(r,θ)=IA*(r,θ)TQ(θ),
JC(x,y)=IC*(x,y)/max[IC*(x,y)],
JA(x,y)=IA*(x,y)/max[IA*(x,y)],
JD(x,y)=ID*(x,y)/max[ID*(x,y)],
JQ(x,y)=IQ*(x,y)/max[IQ*(x,y)].
M(S1,S2)=1S2S11S2+S11=1-|S2S1|dxdy|S2+S1|dxdy.

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