Abstract

The resolution limit for two-dimensional crossed-grating patterns created by projecting mask objects by using a coherent beam has been investigated. We consider first two conventional mask types, a binary-amplitude mask and a two-level phase-shifting mask, in analyzing relationships between a diffraction-beam configuration and an image-intensity distribution. Then we derive, as a mask that overcomes the resolution limit of the conventional ones, a four-level phase-shifting structure with which the minimum image period can be reduced to 2/2 times that of the two-level phase-shifting mask.

© 2003 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. H. J. Levinson, Principles of Lithography (SPIE Press, Bellingham, Wash., 2001).
  2. A. K.-K. Wong, Resolution Enhancement Techniques in Optical Lithography (SPIE Press, Bellingham, Wash., 2001).
    [CrossRef]
  3. 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]
  4. M. D. Levenson, D. S. Goodman, S. Lindsey, P. W. Bayer, H. A. E. Santini, “The phase-shifting mask II: Imaging simulations and submicrometer resist exposures,” IEEE Trans. Electron Devices ED-31, 753–763 (1984).
    [CrossRef]
  5. M. Shibuya, “Toka-shomei-you hi-toei-genban,” Japanese patent62-50811, No. 1441789 (in Japanese) (27October1987).
  6. T. Terasawa, N. Hasegawa, H. Fukuda, S. Katagiri, “Imaging characteristics of multi-phase-shifting and halftone phase-shifting masks,” Jpn. J. Appl. Phys. 30, 2991–2997 (1991).
    [CrossRef]
  7. Y. C. Pati, T. Kailath, “Phase-shifting masks for microlithography: automated design and mask requirements,” J. Opt. Soc. Am. A 11, 2438–2452 (1994).
    [CrossRef]
  8. M. D. Levenson, G. Dai, T. Ebihara, “The vortex mask: making 80-nm contacts with a twist!,” in 22nd Annual BACUS Symposium on Photomask Technology, B. J. Grenon, K. R. Kimmel, eds., Proc. SPIE4889, 1293–1303 (2002).
    [CrossRef]
  9. J. F. Nye, M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. London Ser. A 336, 165–190 (1974).
    [CrossRef]
  10. G. Molina-Terriza, J. Recolons, L. Torner, “The curious arithmetic of optical vortices,” Opt. Lett. 25, 1135–1137 (2000).
    [CrossRef]
  11. J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996).
  12. Ref. 11, Chap. 6.
  13. S. Nakao, A. Nakae, A. Yamaguchi, K. Tsujita, W. Wakamiya, “0.10-μm dense hole pattern formation by double exposure utilizing alternating a phase-shift mask using KrF excimer laser as exposure light,” Jpn. J. Appl. Phys. 38, 2686–2693 (1999).
    [CrossRef]

2000

1999

S. Nakao, A. Nakae, A. Yamaguchi, K. Tsujita, W. Wakamiya, “0.10-μm dense hole pattern formation by double exposure utilizing alternating a phase-shift mask using KrF excimer laser as exposure light,” Jpn. J. Appl. Phys. 38, 2686–2693 (1999).
[CrossRef]

1994

1991

T. Terasawa, N. Hasegawa, H. Fukuda, S. Katagiri, “Imaging characteristics of multi-phase-shifting and halftone phase-shifting masks,” Jpn. J. Appl. Phys. 30, 2991–2997 (1991).
[CrossRef]

1984

M. D. Levenson, D. S. Goodman, S. Lindsey, P. W. Bayer, H. A. E. Santini, “The phase-shifting mask II: Imaging simulations and submicrometer resist exposures,” IEEE Trans. Electron Devices ED-31, 753–763 (1984).
[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]

1974

J. F. Nye, M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. London Ser. A 336, 165–190 (1974).
[CrossRef]

Bayer, P. W.

M. D. Levenson, D. S. Goodman, S. Lindsey, P. W. Bayer, H. A. E. Santini, “The phase-shifting mask II: Imaging simulations and submicrometer resist exposures,” IEEE Trans. Electron Devices ED-31, 753–763 (1984).
[CrossRef]

Berry, M. V.

J. F. Nye, M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. London Ser. A 336, 165–190 (1974).
[CrossRef]

Dai, G.

M. D. Levenson, G. Dai, T. Ebihara, “The vortex mask: making 80-nm contacts with a twist!,” in 22nd Annual BACUS Symposium on Photomask Technology, B. J. Grenon, K. R. Kimmel, eds., Proc. SPIE4889, 1293–1303 (2002).
[CrossRef]

Ebihara, T.

M. D. Levenson, G. Dai, T. Ebihara, “The vortex mask: making 80-nm contacts with a twist!,” in 22nd Annual BACUS Symposium on Photomask Technology, B. J. Grenon, K. R. Kimmel, eds., Proc. SPIE4889, 1293–1303 (2002).
[CrossRef]

Fukuda, H.

T. Terasawa, N. Hasegawa, H. Fukuda, S. Katagiri, “Imaging characteristics of multi-phase-shifting and halftone phase-shifting masks,” Jpn. J. Appl. Phys. 30, 2991–2997 (1991).
[CrossRef]

Goodman, D. S.

M. D. Levenson, D. S. Goodman, S. Lindsey, P. W. Bayer, H. A. E. Santini, “The phase-shifting mask II: Imaging simulations and submicrometer resist exposures,” IEEE Trans. Electron Devices ED-31, 753–763 (1984).
[CrossRef]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996).

Hasegawa, N.

T. Terasawa, N. Hasegawa, H. Fukuda, S. Katagiri, “Imaging characteristics of multi-phase-shifting and halftone phase-shifting masks,” Jpn. J. Appl. Phys. 30, 2991–2997 (1991).
[CrossRef]

Kailath, T.

Katagiri, S.

T. Terasawa, N. Hasegawa, H. Fukuda, S. Katagiri, “Imaging characteristics of multi-phase-shifting and halftone phase-shifting masks,” Jpn. J. Appl. Phys. 30, 2991–2997 (1991).
[CrossRef]

Levenson, M. D.

M. D. Levenson, D. S. Goodman, S. Lindsey, P. W. Bayer, H. A. E. Santini, “The phase-shifting mask II: Imaging simulations and submicrometer resist exposures,” IEEE Trans. Electron Devices ED-31, 753–763 (1984).
[CrossRef]

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]

M. D. Levenson, G. Dai, T. Ebihara, “The vortex mask: making 80-nm contacts with a twist!,” in 22nd Annual BACUS Symposium on Photomask Technology, B. J. Grenon, K. R. Kimmel, eds., Proc. SPIE4889, 1293–1303 (2002).
[CrossRef]

Levinson, H. J.

H. J. Levinson, Principles of Lithography (SPIE Press, Bellingham, Wash., 2001).

Lindsey, S.

M. D. Levenson, D. S. Goodman, S. Lindsey, P. W. Bayer, H. A. E. Santini, “The phase-shifting mask II: Imaging simulations and submicrometer resist exposures,” IEEE Trans. Electron Devices ED-31, 753–763 (1984).
[CrossRef]

Molina-Terriza, G.

Nakae, A.

S. Nakao, A. Nakae, A. Yamaguchi, K. Tsujita, W. Wakamiya, “0.10-μm dense hole pattern formation by double exposure utilizing alternating a phase-shift mask using KrF excimer laser as exposure light,” Jpn. J. Appl. Phys. 38, 2686–2693 (1999).
[CrossRef]

Nakao, S.

S. Nakao, A. Nakae, A. Yamaguchi, K. Tsujita, W. Wakamiya, “0.10-μm dense hole pattern formation by double exposure utilizing alternating a phase-shift mask using KrF excimer laser as exposure light,” Jpn. J. Appl. Phys. 38, 2686–2693 (1999).
[CrossRef]

Nye, J. F.

J. F. Nye, M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. London Ser. A 336, 165–190 (1974).
[CrossRef]

Pati, Y. C.

Recolons, J.

Santini, H. A. E.

M. D. Levenson, D. S. Goodman, S. Lindsey, P. W. Bayer, H. A. E. Santini, “The phase-shifting mask II: Imaging simulations and submicrometer resist exposures,” IEEE Trans. Electron Devices ED-31, 753–763 (1984).
[CrossRef]

Shibuya, M.

M. Shibuya, “Toka-shomei-you hi-toei-genban,” Japanese patent62-50811, No. 1441789 (in Japanese) (27October1987).

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]

Terasawa, T.

T. Terasawa, N. Hasegawa, H. Fukuda, S. Katagiri, “Imaging characteristics of multi-phase-shifting and halftone phase-shifting masks,” Jpn. J. Appl. Phys. 30, 2991–2997 (1991).
[CrossRef]

Torner, L.

Tsujita, K.

S. Nakao, A. Nakae, A. Yamaguchi, K. Tsujita, W. Wakamiya, “0.10-μm dense hole pattern formation by double exposure utilizing alternating a phase-shift mask using KrF excimer laser as exposure light,” Jpn. J. Appl. Phys. 38, 2686–2693 (1999).
[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]

Wakamiya, W.

S. Nakao, A. Nakae, A. Yamaguchi, K. Tsujita, W. Wakamiya, “0.10-μm dense hole pattern formation by double exposure utilizing alternating a phase-shift mask using KrF excimer laser as exposure light,” Jpn. J. Appl. Phys. 38, 2686–2693 (1999).
[CrossRef]

Wong, A. K.-K.

A. K.-K. Wong, Resolution Enhancement Techniques in Optical Lithography (SPIE Press, Bellingham, Wash., 2001).
[CrossRef]

Yamaguchi, A.

S. Nakao, A. Nakae, A. Yamaguchi, K. Tsujita, W. Wakamiya, “0.10-μm dense hole pattern formation by double exposure utilizing alternating a phase-shift mask using KrF excimer laser as exposure light,” Jpn. J. Appl. Phys. 38, 2686–2693 (1999).
[CrossRef]

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]

M. D. Levenson, D. S. Goodman, S. Lindsey, P. W. Bayer, H. A. E. Santini, “The phase-shifting mask II: Imaging simulations and submicrometer resist exposures,” IEEE Trans. Electron Devices ED-31, 753–763 (1984).
[CrossRef]

J. Opt. Soc. Am. A

Jpn. J. Appl. Phys.

S. Nakao, A. Nakae, A. Yamaguchi, K. Tsujita, W. Wakamiya, “0.10-μm dense hole pattern formation by double exposure utilizing alternating a phase-shift mask using KrF excimer laser as exposure light,” Jpn. J. Appl. Phys. 38, 2686–2693 (1999).
[CrossRef]

T. Terasawa, N. Hasegawa, H. Fukuda, S. Katagiri, “Imaging characteristics of multi-phase-shifting and halftone phase-shifting masks,” Jpn. J. Appl. Phys. 30, 2991–2997 (1991).
[CrossRef]

Opt. Lett.

Proc. R. Soc. London Ser. A

J. F. Nye, M. V. Berry, “Dislocations in wave trains,” Proc. R. Soc. London Ser. A 336, 165–190 (1974).
[CrossRef]

Other

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996).

Ref. 11, Chap. 6.

M. D. Levenson, G. Dai, T. Ebihara, “The vortex mask: making 80-nm contacts with a twist!,” in 22nd Annual BACUS Symposium on Photomask Technology, B. J. Grenon, K. R. Kimmel, eds., Proc. SPIE4889, 1293–1303 (2002).
[CrossRef]

M. Shibuya, “Toka-shomei-you hi-toei-genban,” Japanese patent62-50811, No. 1441789 (in Japanese) (27October1987).

H. J. Levinson, Principles of Lithography (SPIE Press, Bellingham, Wash., 2001).

A. K.-K. Wong, Resolution Enhancement Techniques in Optical Lithography (SPIE Press, Bellingham, Wash., 2001).
[CrossRef]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (14)

Fig. 1
Fig. 1

Relationship between an optical image and resist pattern profile after development, assuming the use of negative-type photoresist. Modulation period d in the optical image corresponds to the feature size of d′ (=d/2) of the photoresist when the image transformation is ideal.

Fig. 2
Fig. 2

Image formation with one-dimensional mask patterns. (a) The object is called a binary-amplitude mask. (b) The object is called a two-level phase-shifting mask in which the negative amplitude yields the phase difference π. To produce an image with the same modulation period, the mask pattern period of (b) becomes twice as large as that of (a).

Fig. 3
Fig. 3

Conventional masks used to create two-dimensional crossed-grating patterns: (a) binary amplitude and (b) two-level phase shifting. The hatched regions are opaque, and the phase of the light transmitting regions in (b) is changed so that each nearest neighbor has a pair of 0 and π.

Fig. 4
Fig. 4

Modeling of an optical system used for the analyses. Mask pattern g(x, y) on the object plane is vertically illuminated by a coherent beam, yielding an amplitude distribution G(f x , f y ) on the pupil plane. An intensity distribution I(x, y) is created on the image plane through a projection lens with NA = sin θ.

Fig. 5
Fig. 5

Mask-pattern composition in a unit cell given by -dxd and -dyd, where the optical properties are characterized by the opening size of a x × a y and phase function ϕ(x, y). The structure is assumed to be periodic in both the x and the y directions.

Fig. 6
Fig. 6

Points of nonzero amplitudes on the pupil plane produced by the binary-amplitude mask on condition that the pattern size is close to the resolution limit. When d < 1, only point (f x , f y ) = (0, 0) remains in the range of f x 2 + f y 2 ≤ 1.

Fig. 7
Fig. 7

Image-intensity distribution produced by the binary-amplitude mask assumed on the object plane. The image period is restricted by d ≥ 1 in this case.

Fig. 8
Fig. 8

Points of nonzero amplitudes on the pupil plane produced by the two-level phase-shifting mask on condition that the pattern size be close to the resolution limit. When d < 2/2, no points remain in the range of f x 2 + f y 2 ≤ 1.

Fig. 9
Fig. 9

Image-intensity distribution produced by the two-level phase-shifting mask assumed on the object plane. The image period is restricted by d2/2 in this case.

Fig. 10
Fig. 10

Amplitude distribution on the pupil plane that is necessary to realize the smallest image period for two-dimensional crossed-grating patterns. The sign of the amplitude is reversed between the two points on the f x and f y axes, so that the image intensity becomes zero at (x, y) = (0, 0) on the image plane.

Fig. 11
Fig. 11

Intensity distribution on the image plane created by assuming the distribution of Fig. 10 on the pupil plane. The minimum image period in this case can reach as low as d = 1/2, which is smaller than the limit of Fig. 9.

Fig. 12
Fig. 12

Step functions ν(u) and w(u) used to describe the mask-pattern structure for creating the image distribution in Fig. 11. It is assumed that the functions in the range of -dud are repeated to infinity on the u axis.

Fig. 13
Fig. 13

Complex amplitude transmittance on the mask pattern to produce the image in Fig. 11. The phase difference in the mask openings is actually realized by controlling the thickness of the mask substrate made of dielectric materials.

Fig. 14
Fig. 14

Comparison of image qualities on the line of y = d/2 produced by the binary-amplitude mask, the two-level phase-shifting mask, and the four-level phase-shifting mask at each resolution limit, i.e., d = 1, 2/2, and 1/2, respectively.

Equations (37)

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

Gfx, fy=± gx, yexp-i2πfxx+fyydxdy,
Ix, y=P Gfx, fyexp-i2πfxx+fyydfxdfy2,
fx2+fy21,
GPfx, fyGfx, fyfx2+fy210otherwise
Ix, y=± GPfx, fyexp-i2πfxx+fyydfxdfy2
gx, y=m=- δx-2mdn=- δy-2nd  j=01rect2x+2j-1d2ax ×k=01rect2y+2k-1d2ayexpiϕx, y
rect(u)=1|u|1/20otherwise.
Gfx, fy=Δfx, fyΦfx, fy,
Δfx, fy=±m=- δx-2mdn=- δy-2ndexp-i2πfxx+fyydxdy =14d2m=- δfx-m2dn=- δfy-n2d,
Φfx, fy=±j=01rect2x+2j-1d2ax ×k=01rect2y+2k-1d2ayexpiϕx, y×exp-i2πfxx+fyydxdy =j=01k=01XY expiϕx, y×exp-i2πfxx+fyydxdy.
X:j-12d-ax2xj-12d+ax2, Y:k-12d-ay2yk-12d+ay2,
Φfx, fy=4axaysincfxaxsincfyay×cosπfxdcosπfyd
sinc(u)sinπuπu.
Gfx, fy=axayd2m=- δfx-m2dn=- δfy-n2d×sincfxaxsincfyaycosπfxdcosπfyd,
GPfx, fy=14 δfxδfy-12πδfx+1dδfy +δfx-1dδfy+δfxδfy+1d+δfxδfy-1d,
Ix, y=116-12πcos2πxd+cos2πyd +1π2cos2πxd+cos2πyd2
ϕx, y=0xy<0πxy>0
Φfx, fy=4axay sincfxaxsincfyay ×sinπfxdsinπfyd,
Gfx, fy=axayd2m=- δfx-m2dn=- δfy-n2d ×sincfxaxsincfyaysinπfxdsinπfyd
GPfx, fy=2π2δfx+12dδfy+12d-δfx +12dδfy-12d-δfx-12dδfy+12d+δfx-12dδfy-12d,
Ix, y=16π41-cos2πxd1-cos2πyd
GPfx, fy=Qδfx+12dδfy-Qδfx-12dδfy +Rδfxδfy+12d-Rδfxδfy-12d,
Ix, y=I1x+I2y+I3x, y
I1x=2|Q|21-cos2πxd, I2y=2|R|21-cos2πyd, I3x, y=4QR*+RQ*sinπxdsinπyd,
|Q|2=|R|20, QR*+RQ*=0,
Ix, y=2|Q|22-cos2πxd-cos2πyd,
r=q, β=α+n-1/2π,
GPfx, fy=iqδfx+12dδfy-iqδfx-12dδfy +qδfxδfy+12d-qδfxδfy-12d
gx, y=± Gfx, fyexpi2πfxx+fyydfxdfy.
gPx, y=2qsinπxd-i sinπyd,
gPx, y=22νPxwPy-iwPxνPy
νPu42q sinπu/d, wPu1/2.
νu=4πn=11nsinnπ2sinnπ4sinnπud, wu=12+4πn=11ncosnπ2sinnπ4cosnπud,
gx, y=22νxwy-iwxνy,
gx, y=expi7π/4d/4x3d/4d/4y3d/4expi5π/4-3d/4x-d/4d/4y3d/4expi3π/4-3d/4x-d/4-3d/4y-d/4expiπ/4d/4x3d/4-3d/4y-d/40otherwise
Ix, y=12π22-cos2πxd-cos2πyd
Ix, y=12π21-cos2πxd +12π21-cos2πyd

Metrics