Abstract

We investigate the best method of characterizing high-divergence lasers, such as excimer lasers, to suppress fine-scale intensity nonuniformity that is due to coherence effects of lenslet homogenizers. We show by a detailed analysis of the lenslet homogenizer that, for highest accuracy, a direct measurement of the value of the autocorrelation function should be made at the separation p of the lenslet elements, identified as the critical spatial period. We show that the commonly used characterization of lasers by the 1/e 2 width of the angular divergence is not the most accurate test and may overstate or understate the effectiveness of a given laser.

© 2001 Optical Society of America

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References

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    [CrossRef]
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  6. K. N. Yokohama, N. S. Kawasaki, “Illumination optical apparatus and method having a wavefront splitter and an optical integrator,” U.S. patent5,815,249 (3September1998).
  7. S. Kawata, I. Hikima, Y. Ichihara, S. Watanabe, “Spatial coherence of KrF excimer lasers,” Appl. Opt. 31, 387–396 (1992).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  10. D. L. Wright, S. Guggenheimer, “Status of ISO/TC 172/SC9/WG1 on standardization of the measurement of beam widths, beam divergence, and propagation factor,” in Laser Energy Distribution Profiles: Measurement and Applications, J. M. Darchuk, ed., Proc. SPIE1834, 2–17 (1992).
    [CrossRef]
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  15. Z. Karny, S. Lavi, O. Kafri, “Direct determination of the number of transverse modes of a light beam,” Opt. Lett. 8, 409–411 (1983).
    [CrossRef] [PubMed]
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    [CrossRef]
  17. K. Lizuka, Engineering Optics (Springer-Verlag, New York, 1987), pp. 86–88.
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    [CrossRef] [PubMed]
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    [CrossRef]
  21. J. W. Goodman, Statistical Optics (Wiley, New York, 1985), p. 321.
  22. J. Gaskill, Linear Systems, Transforms, and Optics (Academic, New York, 1976), p. 139.
  23. E. L. O’Neill, Introduction to Statistical Optics (Addison-Wesley, Reading, Mass., 1963), pp. 99–100.
  24. Ref. 11, pp. 508–512.
  25. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), pp. 86–88.
  26. glad is a laser and physical optics computer modeling program and is a product of Applied Optics Research, 1087 Lewis River Road #217, Woodland, Wash. 98674.

1998 (1)

1997 (1)

B. A. See, “Measuring laser divergence,” Opt. Laser Technol. 29, 109–110 (1997).
[CrossRef]

1995 (1)

1993 (1)

A. E. Siegman, S. W. Townsend, “Output beam propagation and beam quality from a multimode stable-cavity laser,” IEEE J. Quantum Electron. 29, 1212–1217 (1993).
[CrossRef]

1992 (1)

1989 (2)

1986 (1)

1984 (1)

Z. B. Liu, J. P. Xie, K. Kuroda, I. Ogura, “Holographic double frequency grating shearing interferometer and its application to measurement of spatial coherence,” Seisan Kenkyu 36, 192–194 (1984).

1983 (2)

1973 (1)

Born, M.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, UK, 1980), pp. 265–268.

Buck, J.

Y. Lin, J. Buck, “Numerical modeling of the excimer beam,” in Metrology, Inspection, and Process Control for Microlithography XIII, B. Singh, ed., Proc. SPIE3677, 700–710 (1999).
[CrossRef]

Chen, Z.

Cordero-Davila, A.

Deng, X.

Gaskill, J.

J. Gaskill, Linear Systems, Transforms, and Optics (Academic, New York, 1976), p. 139.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), pp. 86–88.

J. W. Goodman, Statistical Optics (Wiley, New York, 1985), p. 321.

Guggenheimer, S.

D. L. Wright, S. Guggenheimer, “Status of ISO/TC 172/SC9/WG1 on standardization of the measurement of beam widths, beam divergence, and propagation factor,” in Laser Energy Distribution Profiles: Measurement and Applications, J. M. Darchuk, ed., Proc. SPIE1834, 2–17 (1992).
[CrossRef]

Han, C.-Y.

Hikima, I.

Ichihara, Y.

Ishi, Y.

Kafri, O.

Karny, Z.

Kawasaki, N. S.

K. N. Yokohama, N. S. Kawasaki, “Illumination optical apparatus and method having a wavefront splitter and an optical integrator,” U.S. patent5,815,249 (3September1998).

Kawata, S.

Kessler, T. J.

Kuroda, K.

Z. B. Liu, J. P. Xie, K. Kuroda, I. Ogura, “Holographic double frequency grating shearing interferometer and its application to measurement of spatial coherence,” Seisan Kenkyu 36, 192–194 (1984).

Lavi, S.

Lawrence, G. N.

Liang, X.

Lin, D.

C. Zhou, D. Lin, H. Yao, “Calculation and simulation of intensity distribution of uniform-illumination optical systems for submicron photolithography,” in Optical Microlithography X, G. E. Fuller, ed., Proc. SPIE3051, 652–657 (1997).
[CrossRef]

Lin, Y.

Y. Lin, T. J. Kessler, G. N. Lawrence, “Distributed phase plates for super-Gaussian focal-plane irradiance profiles,” Opt. Lett. 20, 764–766 (1995).
[CrossRef] [PubMed]

Y. Lin, J. Buck, “Numerical modeling of the excimer beam,” in Metrology, Inspection, and Process Control for Microlithography XIII, B. Singh, ed., Proc. SPIE3677, 700–710 (1999).
[CrossRef]

Liu, Z. B.

Z. B. Liu, J. P. Xie, K. Kuroda, I. Ogura, “Holographic double frequency grating shearing interferometer and its application to measurement of spatial coherence,” Seisan Kenkyu 36, 192–194 (1984).

Lizuka, K.

K. Lizuka, Engineering Optics (Springer-Verlag, New York, 1987), pp. 86–88.

Luna-Aguilar, E.

Ma, R.

Murata, K.

O’Neill, E. L.

E. L. O’Neill, Introduction to Statistical Optics (Addison-Wesley, Reading, Mass., 1963), pp. 99–100.

Ogura, I.

Z. B. Liu, J. P. Xie, K. Kuroda, I. Ogura, “Holographic double frequency grating shearing interferometer and its application to measurement of spatial coherence,” Seisan Kenkyu 36, 192–194 (1984).

Ozaki, Y.

Percino-Acarias, M. E.

Pilipesky, N. F.

B. Ya Zel’dovich, N. F. Pilipesky, V. V. Shkunov, Principles of Phase Conjugation (Springer-Verlag, New York, 1985), pp. 76–84.

See, B. A.

B. A. See, “Measuring laser divergence,” Opt. Laser Technol. 29, 109–110 (1997).
[CrossRef]

Shkunov, V. V.

B. Ya Zel’dovich, N. F. Pilipesky, V. V. Shkunov, Principles of Phase Conjugation (Springer-Verlag, New York, 1985), pp. 76–84.

Siegman, A. E.

A. E. Siegman, S. W. Townsend, “Output beam propagation and beam quality from a multimode stable-cavity laser,” IEEE J. Quantum Electron. 29, 1212–1217 (1993).
[CrossRef]

Takamoto, K.

Townsend, S. W.

A. E. Siegman, S. W. Townsend, “Output beam propagation and beam quality from a multimode stable-cavity laser,” IEEE J. Quantum Electron. 29, 1212–1217 (1993).
[CrossRef]

Valiev, K. A.

K. A. Valiev, L. V. Velikov, G. S. Volkov, D. Y. Zaroslov, “The optimization of excimer lasers radiation characteristics for projection lithography,” in Proceedings of the 1989 International Symposium on MicroProcess Conference, (Japan Society of Applied Physics, Tokyo, 1989), pp. 37–42.

Vazquez-Montiel, S.

Velikov, L. V.

K. A. Valiev, L. V. Velikov, G. S. Volkov, D. Y. Zaroslov, “The optimization of excimer lasers radiation characteristics for projection lithography,” in Proceedings of the 1989 International Symposium on MicroProcess Conference, (Japan Society of Applied Physics, Tokyo, 1989), pp. 37–42.

Volkov, G. S.

K. A. Valiev, L. V. Velikov, G. S. Volkov, D. Y. Zaroslov, “The optimization of excimer lasers radiation characteristics for projection lithography,” in Proceedings of the 1989 International Symposium on MicroProcess Conference, (Japan Society of Applied Physics, Tokyo, 1989), pp. 37–42.

Watanabe, S.

Wolf, E.

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, UK, 1980), pp. 265–268.

Wright, D. L.

D. L. Wright, S. Guggenheimer, “Status of ISO/TC 172/SC9/WG1 on standardization of the measurement of beam widths, beam divergence, and propagation factor,” in Laser Energy Distribution Profiles: Measurement and Applications, J. M. Darchuk, ed., Proc. SPIE1834, 2–17 (1992).
[CrossRef]

Wyant, J. C.

Xie, J. P.

Z. B. Liu, J. P. Xie, K. Kuroda, I. Ogura, “Holographic double frequency grating shearing interferometer and its application to measurement of spatial coherence,” Seisan Kenkyu 36, 192–194 (1984).

Ya Zel’dovich, B.

B. Ya Zel’dovich, N. F. Pilipesky, V. V. Shkunov, Principles of Phase Conjugation (Springer-Verlag, New York, 1985), pp. 76–84.

Yao, H.

C. Zhou, D. Lin, H. Yao, “Calculation and simulation of intensity distribution of uniform-illumination optical systems for submicron photolithography,” in Optical Microlithography X, G. E. Fuller, ed., Proc. SPIE3051, 652–657 (1997).
[CrossRef]

Yokohama, K. N.

K. N. Yokohama, N. S. Kawasaki, “Illumination optical apparatus and method having a wavefront splitter and an optical integrator,” U.S. patent5,815,249 (3September1998).

Yu, W.

Zarate-Vazquez, S.

Zaroslov, D. Y.

K. A. Valiev, L. V. Velikov, G. S. Volkov, D. Y. Zaroslov, “The optimization of excimer lasers radiation characteristics for projection lithography,” in Proceedings of the 1989 International Symposium on MicroProcess Conference, (Japan Society of Applied Physics, Tokyo, 1989), pp. 37–42.

Zhou, C.

C. Zhou, D. Lin, H. Yao, “Calculation and simulation of intensity distribution of uniform-illumination optical systems for submicron photolithography,” in Optical Microlithography X, G. E. Fuller, ed., Proc. SPIE3051, 652–657 (1997).
[CrossRef]

Appl. Opt. (6)

IEEE J. Quantum Electron. (1)

A. E. Siegman, S. W. Townsend, “Output beam propagation and beam quality from a multimode stable-cavity laser,” IEEE J. Quantum Electron. 29, 1212–1217 (1993).
[CrossRef]

J. Opt. Soc. Am. A (1)

Opt. Laser Technol. (1)

B. A. See, “Measuring laser divergence,” Opt. Laser Technol. 29, 109–110 (1997).
[CrossRef]

Opt. Lett. (2)

Seisan Kenkyu (1)

Z. B. Liu, J. P. Xie, K. Kuroda, I. Ogura, “Holographic double frequency grating shearing interferometer and its application to measurement of spatial coherence,” Seisan Kenkyu 36, 192–194 (1984).

Other (14)

K. A. Valiev, L. V. Velikov, G. S. Volkov, D. Y. Zaroslov, “The optimization of excimer lasers radiation characteristics for projection lithography,” in Proceedings of the 1989 International Symposium on MicroProcess Conference, (Japan Society of Applied Physics, Tokyo, 1989), pp. 37–42.

K. Lizuka, Engineering Optics (Springer-Verlag, New York, 1987), pp. 86–88.

B. Ya Zel’dovich, N. F. Pilipesky, V. V. Shkunov, Principles of Phase Conjugation (Springer-Verlag, New York, 1985), pp. 76–84.

Y. Lin, J. Buck, “Numerical modeling of the excimer beam,” in Metrology, Inspection, and Process Control for Microlithography XIII, B. Singh, ed., Proc. SPIE3677, 700–710 (1999).
[CrossRef]

J. W. Goodman, Statistical Optics (Wiley, New York, 1985), p. 321.

J. Gaskill, Linear Systems, Transforms, and Optics (Academic, New York, 1976), p. 139.

E. L. O’Neill, Introduction to Statistical Optics (Addison-Wesley, Reading, Mass., 1963), pp. 99–100.

Ref. 11, pp. 508–512.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), pp. 86–88.

glad is a laser and physical optics computer modeling program and is a product of Applied Optics Research, 1087 Lewis River Road #217, Woodland, Wash. 98674.

D. L. Wright, S. Guggenheimer, “Status of ISO/TC 172/SC9/WG1 on standardization of the measurement of beam widths, beam divergence, and propagation factor,” in Laser Energy Distribution Profiles: Measurement and Applications, J. M. Darchuk, ed., Proc. SPIE1834, 2–17 (1992).
[CrossRef]

M. Born, E. Wolf, Principles of Optics, 6th ed. (Pergamon, Oxford, UK, 1980), pp. 265–268.

K. N. Yokohama, N. S. Kawasaki, “Illumination optical apparatus and method having a wavefront splitter and an optical integrator,” U.S. patent5,815,249 (3September1998).

C. Zhou, D. Lin, H. Yao, “Calculation and simulation of intensity distribution of uniform-illumination optical systems for submicron photolithography,” in Optical Microlithography X, G. E. Fuller, ed., Proc. SPIE3051, 652–657 (1997).
[CrossRef]

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Figures (15)

Fig. 1
Fig. 1

Representative photolithographic system in a Kohler illumination configuration. An excimer laser is the source of illumination. It has an instantaneous speckle pattern but a smooth time-averaged envelope. A lenslet array (indicated by a 3 × 3 array) forms an array of point sources. The array of point sources is imaged by the condenser lens into the pupil of the relay lens. The degree of filling of the pupil of the relay lens is the σ value and determines the degree of partial coherence in the image of the mask formed at the photographic recording material on the extreme right. The envelope of the overlapped distribution is much flatter, although a fine microstructure is created.

Fig. 2
Fig. 2

Condenser subsystem. An excimer beam is incident on a lenslet array. All beams overlap at the rear focal plane of the large lens. This is the plane of the mask (target plane). The overlap of the beam produces a much flatter envelope. The beams from each lenslet are essentially collimated and have different angles when they overlap. A randomizing phase plate can be used for reduction of spatial coherence. Fine interference fringes are produced, with a period p′ of the order of hundreds of micrometers. These fine fringes must be suppressed down below a few percent so as to not be visible in the final exposure. We must have the spatial coherence width smaller than the lenslet element-to-element separation p—the characteristic period of the lenslet array—to suppress the coherent fringes.

Fig. 3
Fig. 3

Overlapping pupils from the lens array elements arrive at the target plane with angles corresponding to the angles of the chief rays. High-spatial-frequency fringes are produced, which are 100% modulated for the strictly coherent case. The period of the modulation at the target plane is p′ = λf/ p, where p is the separation between lenslet elements. In the strictly coherent case all elements interfere, and widely separated elements generate high-spatial-frequency modulation at the target plane. With reduced spatial coherence width, interference between second-order and higher-order neighbors is generally insignificant.

Fig. 4
Fig. 4

(a) Strictly coherent light produces strong coherent artifacts in the target plane at period p′ = λf/ p of the form sinc2. In this case a lenslet array of 8 × 8 elements is simulated. The same pattern exists cyclically across the plane of the mask. Four cycles of the pattern are shown. In this case the aperture covers 40 × 40 micrometers. The aperture must be filled uniformly and be aberration free to create this perfect pattern. For uniform filling of the 8 × 8 elements, the peak is 100 times the average intensity. (b) Fine structure at the target plane with an incident beam that has a Gaussian profile. The Gaussian beam rolls off to 1/e 2 at the edge of the lenslet array. The incident beam is aberration free. The plot is made to the same scale as (a). The peaks are 81 times the average value. Note that the ultrafine structure between the major peaks is reduced significantly by Gaussian apodization.

Fig. 5
Fig. 5

Randomizing phase plates reduce the spatial coherence and correspondingly reduce the modulation in the static pattern and reduce the modulation of the microstructure at the target plane (see Fig. 2 for an overview of the condenser system). A random arrangement of piston terms is shown in (a). The piston terms have the advantage that the point images created by the lenslets are completely unaffected. A slowly varying phase plate, as shown in (b), will have a similar performance. The randomizing plate can also be located behind the lens array, including locating it at or near the plane of lenslet focus points.

Fig. 6
Fig. 6

(a) Fine structure with a randomized phase plate included in the aperture. The incident beam has the same Gaussian envelope and normalization as Fig. 4(b). Note that there are still four identical cycles shown. The peak value is only six times the average value. The randomized phase plate reduced the coherent artifacts, for these conditions, by 13 times. (b) Same data as (a) except normalized to unit peak value to display the fine structure. Note that there are four identical cycles shown. The distribution is somewhat specklelike. Not only has the peak value been reduced by 13 times, but much of the fine-scale frequency p′ = λf/ p from Fig. 4(b) has been converted into ultrafine-scale features at harmonics of p′. These ultrafine-scale features are generally easier to smooth by the dynamic speckle effects, so this distribution is much more smoothable than the distribution of Fig. 4(b).

Fig. 7
Fig. 7

Incident Gaussian beam and randomized phase plate [the same conditions as Fig. 6(b)] with the addition of 24 waves of defocus measured at the edge of the lenslet array. The distribution is different in detail but the expected value of the peak is the same as if there were no defocus. The addition of low-order aberration to a fully randomized phase plate does not change the statistical properties of the fine-scale effects in the target plane.

Fig. 8
Fig. 8

Points A 1(x, y), A 2(x, y), and (A 3(x, y) at the same relative position in each lenslet element overlap at a common image point A′(x′, y′). The fringe visibility at point A′ at the mask can be computed when only the time-averaged mutual coherence of points A 1, A 2, and A 3 separated by distance p are considered.

Fig. 9
Fig. 9

Fine-scale modulation at a small local region about A′ at the target plane for a perfectly coherent, uniform intensity beam. See text for details.

Fig. 10
Fig. 10

Illumination of the lenslet array with a Gaussian envelope. See text for details.

Fig. 11
Fig. 11

Randomizing phase plate significantly reduces the correlation of all order of neighboring lenslet elements. See text for details.

Fig. 12
Fig. 12

Lenslet homogenizer illuminated by rapidly varying laser speckle with a smooth, rolled-off envelope. See text for details.

Fig. 13
Fig. 13

(a) Far field of two speckle distributions having the same 1/e 2 width with a Gaussian profile and with a flat profile. The flat (or nearly flat) power spectrum can be produced by an aperture at or near the far-field point in the laser. Two thousand speckle distributions were averaged to obtain the curves. (b) Two autocorrelation functions having the same 1/e 2 width in the far field [see (a)]. The Gaussian function has no sidelobe structure in its autocorrelation function. Speckle with a sinc autocorrelation function has large sidelobes in the wings (shown as |sinc|). A square far-field distribution can be created when internal apertures in the laser are imaged into the far field. If the period of the lenslet array is set at the distance indicated by point A, where the sinc function has a zero, the fringe visibility will be near zero so that nearest neighbor effects would be nearly completely suppressed. Similarly, interference effects from second-order and higher nearest neighbors would be suppressed as the zeros of the sinc function are evenly spaced. At operation point A, speckle with a sinc autocorrelation function would be much better than the Gaussian function. At operating point B the sinc function has a maximum, and the sinc curve is far higher than the Gaussian function. Because of differences in the shape of the autocorrelation function (including sidelobes), measurement of fringe visibility at the precise operating point yields the best accuracy.

Fig. 14
Fig. 14

Modulation of fine structure with speckle autocorrelation set to 14% at lenslet separation. This large fringe modulation at period p′ was selected to make the fringe structure more visible. The primary modulation arises from first nearest neighbor effects. Small artifacts at p′/2 are also visible because of second nearest neighbor interference. Time integration was taken over 10,000 integration times.

Fig. 15
Fig. 15

Effect of tilt of a nominally collimated beam at the input to a lens array. The chief rays through the lenslet elements are indicated. All chief rays focus to a point at the rear focal plane of the condenser lens. The case of zero tilt is indicated in the top figure. A tilt of the input by θ, as shown in the lower figure, causes the distribution to shift by x′ = fθ. For an ensemble of mutually incoherent tilts, the resulting distribution is the on-axis point response convolved with the angular distribution.

Equations (9)

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

RTΔx, Δy=0T Ad*x+Δx2, y+Δy2, tAdx-Δx2, y-Δy2, tdxdydt0T |Adx, y, t|2dxdydt,
RΔx, Δy=RsΔx, ΔyRdΔx, Δy.
Ax, y=C iN Aixi, yiexp-j 2πλfxix+yiy,
Ix, y=|Ax, y|2=|C|2iNjN Aixi, yiAj*xj, yj×expj 2πλfxj-xix+yj-yiy.
Aδx, y=nNmM Ax, yδxM+np, yM+mp,
Rsx, y=Aδx, yAδx, y,
Pdθx, θy= Rdx, yexpj 2πλxθx+yθydxdy,
Ix, yIx, y**Pfθx, fθy,
RΔx, Δy=RsΔx, ΔyRdΔx, Δy.

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