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Applied Optics

Applied Optics


  • Vol. 42, Iss. 16 — Jun. 1, 2003
  • pp: 3259–3267

Resolution limit for two-dimensional crossed-grating patterns projected by a coherent beam

Yasuyuki Unno  »View Author Affiliations

Applied Optics, Vol. 42, Issue 16, pp. 3259-3267 (2003)

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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

OCIS Codes
(070.2580) Fourier optics and signal processing : Paraxial wave optics
(110.2960) Imaging systems : Image analysis
(110.3960) Imaging systems : Microlithography
(110.5220) Imaging systems : Photolithography
(350.5730) Other areas of optics : Resolution

Original Manuscript: February 3, 2003
Published: June 1, 2003

Yasuyuki Unno, "Resolution limit for two-dimensional crossed-grating patterns projected by a coherent beam," Appl. Opt. 42, 3259-3267 (2003)

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  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]

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