Abstract

We discuss a ray and a van Cittert–Zernike characterization of spatial coherence in condensers for projection systems. We present a rule of thumb with which to estimate the modulus of the coherence function at a given point of the illuminated object and a ray-tracing methodology with which to determine this modulus. For uniform illumination of the pupil we relate the modulus of the coherence function and the pupil-filling factor. We suggest that the rms of the angular ray spread at a given object point is an appropriate metric with which to characterize local coherence properties.

© 2001 Optical Society of America

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References

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  1. Y. Borodovsky, “Partial coherence variations linked to line-width changes,” Solid State Technol. 38, 42 (1995).
  2. J. P. Kirk, C. J. Progler, “Pupil illumination in situ measurement of partial coherence,” in Optical Microlithography, L. Van de Hove, ed., Proc. SPIE3334, 281–288 (1998).
  3. I. M. Grodnensky, E. Morita, K. Suwa, S. Hirukawa, “Characterization of spatial coherence uniformity in exposure tools,” in Optical Microlithography, L. Van de Hove, ed., Proc. SPIE3334, 289–296 (1998).
  4. M. Ceglio, A. M. Hawryluk, G. E. Sommargren, “Front-end design issues in soft-x-ray projection lithography,” Appl. Opt. 32, 7050–7056 (1993).
    [CrossRef] [PubMed]
  5. G. E. Sommargren, L. G. Seppala, “Condenser optics, partial coherence, and imaging for soft-x-ray projection lithography,” Appl. Opt. 32, 6938–6944 (1993).
    [CrossRef] [PubMed]
  6. W. C. Sweatt, “Condenser for illuminating a ring field,” U.S. patent5,361,292 (1November1994).
  7. H. H. Hopkins, “The concept of partial coherence in optics,” Proc. R. Soc. London Ser. A 208, 263–277 (1951).
    [CrossRef]
  8. M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1959), Chap. 10, Sec. 4.2.
  9. D. S. Goodman, A. E. Rosenbluth, “Condenser aberrations in Kohler illumination,” in Optical/Laser Microlithography, B. J. Lin, ed., Proc. SPIE922, 108–126 (1988).
    [CrossRef]

1995 (1)

Y. Borodovsky, “Partial coherence variations linked to line-width changes,” Solid State Technol. 38, 42 (1995).

1993 (2)

1951 (1)

H. H. Hopkins, “The concept of partial coherence in optics,” Proc. R. Soc. London Ser. A 208, 263–277 (1951).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1959), Chap. 10, Sec. 4.2.

Borodovsky, Y.

Y. Borodovsky, “Partial coherence variations linked to line-width changes,” Solid State Technol. 38, 42 (1995).

Ceglio, M.

Goodman, D. S.

D. S. Goodman, A. E. Rosenbluth, “Condenser aberrations in Kohler illumination,” in Optical/Laser Microlithography, B. J. Lin, ed., Proc. SPIE922, 108–126 (1988).
[CrossRef]

Grodnensky, I. M.

I. M. Grodnensky, E. Morita, K. Suwa, S. Hirukawa, “Characterization of spatial coherence uniformity in exposure tools,” in Optical Microlithography, L. Van de Hove, ed., Proc. SPIE3334, 289–296 (1998).

Hawryluk, A. M.

Hirukawa, S.

I. M. Grodnensky, E. Morita, K. Suwa, S. Hirukawa, “Characterization of spatial coherence uniformity in exposure tools,” in Optical Microlithography, L. Van de Hove, ed., Proc. SPIE3334, 289–296 (1998).

Hopkins, H. H.

H. H. Hopkins, “The concept of partial coherence in optics,” Proc. R. Soc. London Ser. A 208, 263–277 (1951).
[CrossRef]

Kirk, J. P.

J. P. Kirk, C. J. Progler, “Pupil illumination in situ measurement of partial coherence,” in Optical Microlithography, L. Van de Hove, ed., Proc. SPIE3334, 281–288 (1998).

Morita, E.

I. M. Grodnensky, E. Morita, K. Suwa, S. Hirukawa, “Characterization of spatial coherence uniformity in exposure tools,” in Optical Microlithography, L. Van de Hove, ed., Proc. SPIE3334, 289–296 (1998).

Progler, C. J.

J. P. Kirk, C. J. Progler, “Pupil illumination in situ measurement of partial coherence,” in Optical Microlithography, L. Van de Hove, ed., Proc. SPIE3334, 281–288 (1998).

Rosenbluth, A. E.

D. S. Goodman, A. E. Rosenbluth, “Condenser aberrations in Kohler illumination,” in Optical/Laser Microlithography, B. J. Lin, ed., Proc. SPIE922, 108–126 (1988).
[CrossRef]

Seppala, L. G.

Sommargren, G. E.

Suwa, K.

I. M. Grodnensky, E. Morita, K. Suwa, S. Hirukawa, “Characterization of spatial coherence uniformity in exposure tools,” in Optical Microlithography, L. Van de Hove, ed., Proc. SPIE3334, 289–296 (1998).

Sweatt, W. C.

W. C. Sweatt, “Condenser for illuminating a ring field,” U.S. patent5,361,292 (1November1994).

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1959), Chap. 10, Sec. 4.2.

Appl. Opt. (2)

Proc. R. Soc. London Ser. A (1)

H. H. Hopkins, “The concept of partial coherence in optics,” Proc. R. Soc. London Ser. A 208, 263–277 (1951).
[CrossRef]

Solid State Technol. (1)

Y. Borodovsky, “Partial coherence variations linked to line-width changes,” Solid State Technol. 38, 42 (1995).

Other (5)

J. P. Kirk, C. J. Progler, “Pupil illumination in situ measurement of partial coherence,” in Optical Microlithography, L. Van de Hove, ed., Proc. SPIE3334, 281–288 (1998).

I. M. Grodnensky, E. Morita, K. Suwa, S. Hirukawa, “Characterization of spatial coherence uniformity in exposure tools,” in Optical Microlithography, L. Van de Hove, ed., Proc. SPIE3334, 289–296 (1998).

W. C. Sweatt, “Condenser for illuminating a ring field,” U.S. patent5,361,292 (1November1994).

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1959), Chap. 10, Sec. 4.2.

D. S. Goodman, A. E. Rosenbluth, “Condenser aberrations in Kohler illumination,” in Optical/Laser Microlithography, B. J. Lin, ed., Proc. SPIE922, 108–126 (1988).
[CrossRef]

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Figures (6)

Fig. 1
Fig. 1

Optical layout showing an incoherent source, a condenser working in Kohler illumination, the mask plane, two points P1 and P2, and the optical field from a point in the source arriving at the two points in the mask plane.

Fig. 2
Fig. 2

Diagram of ray-tracing methodology for evaluating the pupil-filling factor of a point at the mask. A mirror image of the condenser optics is created within the ray-tracing software.

Fig. 3
Fig. 3

Cylindrical lens as an astigmatic condenser. At the sagittal focus a line illumination is formed that coincides with the mask to be illuminated. At the medial focus an almost circular illumination is produced.

Fig. 4
Fig. 4

The illumination at a mask located at the astigmatic lens’s sagittal focus is a narrow line, represented here by the rectangle. The letters represents points where coherence is evaluated.

Fig. 5
Fig. 5

Pupil fill that is due to points A–D in the mask, as shown by spot diagrams.

Fig. 6
Fig. 6

Fourier transform of the pupil-fill geometries of Fig. 5. Frame E corresponds to the Fourier transform of the ideal circular pupil fill.

Tables (1)

Tables Icon

Table 1 Pupil-Filling Factors for Points along the Line Illumination at the Mask

Equations (24)

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γ12=1I1I2u1u2*dσ,
u1=A1 exp-2π/λiW1σx,σy,x1,y1, u2=A2 exp-2π/λiW2σx,σy,x2,y2
I1=A1dσ,  I2= |A2|dσ.
γ12=1I1I2 A1 exp-2π/λiW1σx,σy,x1,y1A2* exp2π/λiW2σx,σy,x2,y2dσxdσy
=1I1I2 A1A2* exp-2π/λiΔWσx,σy,P1,P2×dσxdσy,
ΔWσx,σy,P1,P2=W1-W2
γ12A1A2*I1I21+ikΔW-12 k2ΔW2dσxdσy,
|γ12|2A1A2*A1*A2I1I21+ikΔW-12 k2ΔW2dσ×1-ikΔW-12 k2ΔW2dσ
1-k2ΔW2dσdσ+k2ΔWdσ2dσ2=1-k2σΔW2,
|γ12|1-k2σΔW21/2
W1=W000+W200σ2+W111σxx1+σyy1+W020ρ12,
W2=W000+W200σ2+W111σxx2+σyy2+W020ρ22,
ΔW=W111σxx1-x2+W111σyy1-y2+W020ρ12-ρ22,
σΔW2=x1-x22αx2+y1-y22αy2,
|γ12|1-k2Δx2αx2+Δy2αy21/2
|γ12|1-k22Δx2αx2+Δy2αy2.
αx,y=σNA2,
|γ12|1-σ2NA2k2r28,
σ8 1-|γ12|NA2k2r21/2
d=0.1558λσNA.
R=0.61λNA,
dR4σ.
σx,y=2αx,yNA,
σ=σx=σy.

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