Abstract

We describe a new mode of optical lithography called absorbance-modulation optical lithography (AMOL) in which a thin film of photochromic material is placed on top of a conventional photoresist and illuminated simultaneously by a focal spot of wavelength λ1 and a ring-shaped illumination of wavelength λ2. The λ1 radiation converts the photochromic material from an opaque to a transparent configuration, thereby enabling exposure of the photoresist, while the λ2 radiation reverses the transformation. As a result of these competing effects, the point-spread function that exposes the resist is strongly compressed, resulting in higher photolithographic resolution and information density. We show by modeling that the point-spread-function compression achieved via AMOL depends only on the absorbance distribution in the photostationary state. In this respect, absorbance modulation represents an optical nonlinearity that depends on the intensity ratio of λ1 and λ2 and not on the absolute intensity of either one alone. By inserting material parameters into the model, a lithographic resolution corresponding to λ113 is predicted.

© 2006 Optical Society of America

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References

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  1. Selected Papers on Resolution Enhancement Techniques in Optical Lithography, Vol. MS 178, F.M.Schellenberg, ed. (SPIE, 2004).
  2. A. P. Chu, K. K. Berggren, K. S. Johnson, and M. G. Prentiss, "A virtual slit for atom optics and nanolithography," Quantum Semiclassic. Opt. 8, 521-529 (1996).
    [CrossRef]
  3. L. Kastrup, H. Blom, C. Eggeling, and S. W. Hell, "Fluorescence fluctuation spectroscopy in subdiffraction focal volume," Phys. Rev. Lett. 94, 178104/1-5 (2005).
    [CrossRef]
  4. S. W. Hell, S. Jakobs, and L. Kastrup, "Imaging and writing at the nanoscale with focused visible light through saturable optical transitions," Appl. Phys. A 77, 859-860 (2003).
    [CrossRef]
  5. S. W. Hell, "Strategy for far-field optical imaging and writing without diffraction limit," Phys. Lett. A 326, 140-145 (2004).
    [CrossRef]
  6. B. F. Griffing and P. R. West, "Contrast enhanced photolithography," IEEE Electron Device Lett. 4, 14-16 (1983).
    [CrossRef]
  7. B. F. Griffing and P. R. West, "Contrast enhanced photoresists--processing and modeling," Polym. Eng. Sci. 23, 947-952 (1983).
    [CrossRef]
  8. J. C. Crano and R. J. Guglielmetti, Organic Photochromic and Thermochromic Compounds (Plenum, 1999).
  9. K. K. Berggren, A. Bard, J. L. Wilbur, J. D. Gillaspy, A. G. Helg, J. J. McClelland, S. L. Rolston, W. D. Phillip, M. Prentiss, and G. M. Whitesides, "Microlithography by using neutral metastable atoms and self-assembled monolayers," Science 269, 1255-1257 (1995).
    [CrossRef] [PubMed]
  10. M. D. Levenson, T. Ebihara, G. Dai, Y. Morikawa, N. Hayashi, and T. S. Meng, "Optical vortex masks for via levels," J. Microlithogr. Microfabr. Microsyst. 3, 293-304 (2004).
    [CrossRef]
  11. D. W. Prather and S. Shi, "Formulation and application of the finite-difference time-domain method for the analysis of axially symmetric diffractive optical elements," J. Opt. Soc. Am. A 16, 1131-1142 (1999).
    [CrossRef]
  12. V. V. Kotlyar, A. A. Almazov, S. N. Khonina, V. A. Soifer, H. Elfstrom, and J. Turunen, "Generation of phase singularity through diffracting a plane or Gaussian beam by a spiral phase plate," J. Opt. Soc. Am. A 22, 849-861 (2005).
    [CrossRef]
  13. S. N. Khonina, V. V. Kotlyar, M. V. Shinkaryev, V. A. Soifer, and G. V. Uspleniev, "The phase rotor filter," J. Mod. Opt. 39, 1147-1154 (1992).
    [CrossRef]
  14. M. Irie, "Diarylethenes for memories and switches," Chem. Rev. (Washington, D.C.) 100, 1685-1716 (2000).
  15. Y. Yokoyama, "Fulgides for memories and switches," Chem. Rev. (Washington, D.C.) 100, 1717-1739 (2000).
  16. R. Menon, A. Patel, E. E. Moon, and H. I. Smith, "An alpha prototype system for zone-plate-array lithography," J. Vac. Sci. Technol. B 22, 3032-3037 (2004).
    [CrossRef]
  17. D. Chao, A. Patel, T. Barwicz, H. I. Smith, and R. Menon, "Immersion zone-plate-array lithography," J. Vac. Sci. Technol. B 23, 2657-2661 (2005).
    [CrossRef]

2005

L. Kastrup, H. Blom, C. Eggeling, and S. W. Hell, "Fluorescence fluctuation spectroscopy in subdiffraction focal volume," Phys. Rev. Lett. 94, 178104/1-5 (2005).
[CrossRef]

D. Chao, A. Patel, T. Barwicz, H. I. Smith, and R. Menon, "Immersion zone-plate-array lithography," J. Vac. Sci. Technol. B 23, 2657-2661 (2005).
[CrossRef]

V. V. Kotlyar, A. A. Almazov, S. N. Khonina, V. A. Soifer, H. Elfstrom, and J. Turunen, "Generation of phase singularity through diffracting a plane or Gaussian beam by a spiral phase plate," J. Opt. Soc. Am. A 22, 849-861 (2005).
[CrossRef]

2004

R. Menon, A. Patel, E. E. Moon, and H. I. Smith, "An alpha prototype system for zone-plate-array lithography," J. Vac. Sci. Technol. B 22, 3032-3037 (2004).
[CrossRef]

M. D. Levenson, T. Ebihara, G. Dai, Y. Morikawa, N. Hayashi, and T. S. Meng, "Optical vortex masks for via levels," J. Microlithogr. Microfabr. Microsyst. 3, 293-304 (2004).
[CrossRef]

Selected Papers on Resolution Enhancement Techniques in Optical Lithography, Vol. MS 178, F.M.Schellenberg, ed. (SPIE, 2004).

S. W. Hell, "Strategy for far-field optical imaging and writing without diffraction limit," Phys. Lett. A 326, 140-145 (2004).
[CrossRef]

2003

S. W. Hell, S. Jakobs, and L. Kastrup, "Imaging and writing at the nanoscale with focused visible light through saturable optical transitions," Appl. Phys. A 77, 859-860 (2003).
[CrossRef]

2000

M. Irie, "Diarylethenes for memories and switches," Chem. Rev. (Washington, D.C.) 100, 1685-1716 (2000).

Y. Yokoyama, "Fulgides for memories and switches," Chem. Rev. (Washington, D.C.) 100, 1717-1739 (2000).

1999

1996

A. P. Chu, K. K. Berggren, K. S. Johnson, and M. G. Prentiss, "A virtual slit for atom optics and nanolithography," Quantum Semiclassic. Opt. 8, 521-529 (1996).
[CrossRef]

1995

K. K. Berggren, A. Bard, J. L. Wilbur, J. D. Gillaspy, A. G. Helg, J. J. McClelland, S. L. Rolston, W. D. Phillip, M. Prentiss, and G. M. Whitesides, "Microlithography by using neutral metastable atoms and self-assembled monolayers," Science 269, 1255-1257 (1995).
[CrossRef] [PubMed]

1992

S. N. Khonina, V. V. Kotlyar, M. V. Shinkaryev, V. A. Soifer, and G. V. Uspleniev, "The phase rotor filter," J. Mod. Opt. 39, 1147-1154 (1992).
[CrossRef]

1983

B. F. Griffing and P. R. West, "Contrast enhanced photolithography," IEEE Electron Device Lett. 4, 14-16 (1983).
[CrossRef]

B. F. Griffing and P. R. West, "Contrast enhanced photoresists--processing and modeling," Polym. Eng. Sci. 23, 947-952 (1983).
[CrossRef]

Almazov, A. A.

Bard, A.

K. K. Berggren, A. Bard, J. L. Wilbur, J. D. Gillaspy, A. G. Helg, J. J. McClelland, S. L. Rolston, W. D. Phillip, M. Prentiss, and G. M. Whitesides, "Microlithography by using neutral metastable atoms and self-assembled monolayers," Science 269, 1255-1257 (1995).
[CrossRef] [PubMed]

Barwicz, T.

D. Chao, A. Patel, T. Barwicz, H. I. Smith, and R. Menon, "Immersion zone-plate-array lithography," J. Vac. Sci. Technol. B 23, 2657-2661 (2005).
[CrossRef]

Berggren, K. K.

A. P. Chu, K. K. Berggren, K. S. Johnson, and M. G. Prentiss, "A virtual slit for atom optics and nanolithography," Quantum Semiclassic. Opt. 8, 521-529 (1996).
[CrossRef]

K. K. Berggren, A. Bard, J. L. Wilbur, J. D. Gillaspy, A. G. Helg, J. J. McClelland, S. L. Rolston, W. D. Phillip, M. Prentiss, and G. M. Whitesides, "Microlithography by using neutral metastable atoms and self-assembled monolayers," Science 269, 1255-1257 (1995).
[CrossRef] [PubMed]

Blom, H.

L. Kastrup, H. Blom, C. Eggeling, and S. W. Hell, "Fluorescence fluctuation spectroscopy in subdiffraction focal volume," Phys. Rev. Lett. 94, 178104/1-5 (2005).
[CrossRef]

Chao, D.

D. Chao, A. Patel, T. Barwicz, H. I. Smith, and R. Menon, "Immersion zone-plate-array lithography," J. Vac. Sci. Technol. B 23, 2657-2661 (2005).
[CrossRef]

Chu, A. P.

A. P. Chu, K. K. Berggren, K. S. Johnson, and M. G. Prentiss, "A virtual slit for atom optics and nanolithography," Quantum Semiclassic. Opt. 8, 521-529 (1996).
[CrossRef]

Crano, J. C.

J. C. Crano and R. J. Guglielmetti, Organic Photochromic and Thermochromic Compounds (Plenum, 1999).

Dai, G.

M. D. Levenson, T. Ebihara, G. Dai, Y. Morikawa, N. Hayashi, and T. S. Meng, "Optical vortex masks for via levels," J. Microlithogr. Microfabr. Microsyst. 3, 293-304 (2004).
[CrossRef]

Ebihara, T.

M. D. Levenson, T. Ebihara, G. Dai, Y. Morikawa, N. Hayashi, and T. S. Meng, "Optical vortex masks for via levels," J. Microlithogr. Microfabr. Microsyst. 3, 293-304 (2004).
[CrossRef]

Eggeling, C.

L. Kastrup, H. Blom, C. Eggeling, and S. W. Hell, "Fluorescence fluctuation spectroscopy in subdiffraction focal volume," Phys. Rev. Lett. 94, 178104/1-5 (2005).
[CrossRef]

Elfstrom, H.

Gillaspy, J. D.

K. K. Berggren, A. Bard, J. L. Wilbur, J. D. Gillaspy, A. G. Helg, J. J. McClelland, S. L. Rolston, W. D. Phillip, M. Prentiss, and G. M. Whitesides, "Microlithography by using neutral metastable atoms and self-assembled monolayers," Science 269, 1255-1257 (1995).
[CrossRef] [PubMed]

Griffing, B. F.

B. F. Griffing and P. R. West, "Contrast enhanced photolithography," IEEE Electron Device Lett. 4, 14-16 (1983).
[CrossRef]

B. F. Griffing and P. R. West, "Contrast enhanced photoresists--processing and modeling," Polym. Eng. Sci. 23, 947-952 (1983).
[CrossRef]

Guglielmetti, R. J.

J. C. Crano and R. J. Guglielmetti, Organic Photochromic and Thermochromic Compounds (Plenum, 1999).

Hayashi, N.

M. D. Levenson, T. Ebihara, G. Dai, Y. Morikawa, N. Hayashi, and T. S. Meng, "Optical vortex masks for via levels," J. Microlithogr. Microfabr. Microsyst. 3, 293-304 (2004).
[CrossRef]

Helg, A. G.

K. K. Berggren, A. Bard, J. L. Wilbur, J. D. Gillaspy, A. G. Helg, J. J. McClelland, S. L. Rolston, W. D. Phillip, M. Prentiss, and G. M. Whitesides, "Microlithography by using neutral metastable atoms and self-assembled monolayers," Science 269, 1255-1257 (1995).
[CrossRef] [PubMed]

Hell, S. W.

L. Kastrup, H. Blom, C. Eggeling, and S. W. Hell, "Fluorescence fluctuation spectroscopy in subdiffraction focal volume," Phys. Rev. Lett. 94, 178104/1-5 (2005).
[CrossRef]

S. W. Hell, "Strategy for far-field optical imaging and writing without diffraction limit," Phys. Lett. A 326, 140-145 (2004).
[CrossRef]

S. W. Hell, S. Jakobs, and L. Kastrup, "Imaging and writing at the nanoscale with focused visible light through saturable optical transitions," Appl. Phys. A 77, 859-860 (2003).
[CrossRef]

Irie, M.

M. Irie, "Diarylethenes for memories and switches," Chem. Rev. (Washington, D.C.) 100, 1685-1716 (2000).

Jakobs, S.

S. W. Hell, S. Jakobs, and L. Kastrup, "Imaging and writing at the nanoscale with focused visible light through saturable optical transitions," Appl. Phys. A 77, 859-860 (2003).
[CrossRef]

Johnson, K. S.

A. P. Chu, K. K. Berggren, K. S. Johnson, and M. G. Prentiss, "A virtual slit for atom optics and nanolithography," Quantum Semiclassic. Opt. 8, 521-529 (1996).
[CrossRef]

Kastrup, L.

L. Kastrup, H. Blom, C. Eggeling, and S. W. Hell, "Fluorescence fluctuation spectroscopy in subdiffraction focal volume," Phys. Rev. Lett. 94, 178104/1-5 (2005).
[CrossRef]

S. W. Hell, S. Jakobs, and L. Kastrup, "Imaging and writing at the nanoscale with focused visible light through saturable optical transitions," Appl. Phys. A 77, 859-860 (2003).
[CrossRef]

Khonina, S. N.

Kotlyar, V. V.

Levenson, M. D.

M. D. Levenson, T. Ebihara, G. Dai, Y. Morikawa, N. Hayashi, and T. S. Meng, "Optical vortex masks for via levels," J. Microlithogr. Microfabr. Microsyst. 3, 293-304 (2004).
[CrossRef]

McClelland, J. J.

K. K. Berggren, A. Bard, J. L. Wilbur, J. D. Gillaspy, A. G. Helg, J. J. McClelland, S. L. Rolston, W. D. Phillip, M. Prentiss, and G. M. Whitesides, "Microlithography by using neutral metastable atoms and self-assembled monolayers," Science 269, 1255-1257 (1995).
[CrossRef] [PubMed]

Meng, T. S.

M. D. Levenson, T. Ebihara, G. Dai, Y. Morikawa, N. Hayashi, and T. S. Meng, "Optical vortex masks for via levels," J. Microlithogr. Microfabr. Microsyst. 3, 293-304 (2004).
[CrossRef]

Menon, R.

D. Chao, A. Patel, T. Barwicz, H. I. Smith, and R. Menon, "Immersion zone-plate-array lithography," J. Vac. Sci. Technol. B 23, 2657-2661 (2005).
[CrossRef]

R. Menon, A. Patel, E. E. Moon, and H. I. Smith, "An alpha prototype system for zone-plate-array lithography," J. Vac. Sci. Technol. B 22, 3032-3037 (2004).
[CrossRef]

Moon, E. E.

R. Menon, A. Patel, E. E. Moon, and H. I. Smith, "An alpha prototype system for zone-plate-array lithography," J. Vac. Sci. Technol. B 22, 3032-3037 (2004).
[CrossRef]

Morikawa, Y.

M. D. Levenson, T. Ebihara, G. Dai, Y. Morikawa, N. Hayashi, and T. S. Meng, "Optical vortex masks for via levels," J. Microlithogr. Microfabr. Microsyst. 3, 293-304 (2004).
[CrossRef]

Patel, A.

D. Chao, A. Patel, T. Barwicz, H. I. Smith, and R. Menon, "Immersion zone-plate-array lithography," J. Vac. Sci. Technol. B 23, 2657-2661 (2005).
[CrossRef]

R. Menon, A. Patel, E. E. Moon, and H. I. Smith, "An alpha prototype system for zone-plate-array lithography," J. Vac. Sci. Technol. B 22, 3032-3037 (2004).
[CrossRef]

Phillip, W. D.

K. K. Berggren, A. Bard, J. L. Wilbur, J. D. Gillaspy, A. G. Helg, J. J. McClelland, S. L. Rolston, W. D. Phillip, M. Prentiss, and G. M. Whitesides, "Microlithography by using neutral metastable atoms and self-assembled monolayers," Science 269, 1255-1257 (1995).
[CrossRef] [PubMed]

Prather, D. W.

Prentiss, M.

K. K. Berggren, A. Bard, J. L. Wilbur, J. D. Gillaspy, A. G. Helg, J. J. McClelland, S. L. Rolston, W. D. Phillip, M. Prentiss, and G. M. Whitesides, "Microlithography by using neutral metastable atoms and self-assembled monolayers," Science 269, 1255-1257 (1995).
[CrossRef] [PubMed]

Prentiss, M. G.

A. P. Chu, K. K. Berggren, K. S. Johnson, and M. G. Prentiss, "A virtual slit for atom optics and nanolithography," Quantum Semiclassic. Opt. 8, 521-529 (1996).
[CrossRef]

Rolston, S. L.

K. K. Berggren, A. Bard, J. L. Wilbur, J. D. Gillaspy, A. G. Helg, J. J. McClelland, S. L. Rolston, W. D. Phillip, M. Prentiss, and G. M. Whitesides, "Microlithography by using neutral metastable atoms and self-assembled monolayers," Science 269, 1255-1257 (1995).
[CrossRef] [PubMed]

Shi, S.

Shinkaryev, M. V.

S. N. Khonina, V. V. Kotlyar, M. V. Shinkaryev, V. A. Soifer, and G. V. Uspleniev, "The phase rotor filter," J. Mod. Opt. 39, 1147-1154 (1992).
[CrossRef]

Smith, H. I.

D. Chao, A. Patel, T. Barwicz, H. I. Smith, and R. Menon, "Immersion zone-plate-array lithography," J. Vac. Sci. Technol. B 23, 2657-2661 (2005).
[CrossRef]

R. Menon, A. Patel, E. E. Moon, and H. I. Smith, "An alpha prototype system for zone-plate-array lithography," J. Vac. Sci. Technol. B 22, 3032-3037 (2004).
[CrossRef]

Soifer, V. A.

Turunen, J.

Uspleniev, G. V.

S. N. Khonina, V. V. Kotlyar, M. V. Shinkaryev, V. A. Soifer, and G. V. Uspleniev, "The phase rotor filter," J. Mod. Opt. 39, 1147-1154 (1992).
[CrossRef]

West, P. R.

B. F. Griffing and P. R. West, "Contrast enhanced photoresists--processing and modeling," Polym. Eng. Sci. 23, 947-952 (1983).
[CrossRef]

B. F. Griffing and P. R. West, "Contrast enhanced photolithography," IEEE Electron Device Lett. 4, 14-16 (1983).
[CrossRef]

Whitesides, G. M.

K. K. Berggren, A. Bard, J. L. Wilbur, J. D. Gillaspy, A. G. Helg, J. J. McClelland, S. L. Rolston, W. D. Phillip, M. Prentiss, and G. M. Whitesides, "Microlithography by using neutral metastable atoms and self-assembled monolayers," Science 269, 1255-1257 (1995).
[CrossRef] [PubMed]

Wilbur, J. L.

K. K. Berggren, A. Bard, J. L. Wilbur, J. D. Gillaspy, A. G. Helg, J. J. McClelland, S. L. Rolston, W. D. Phillip, M. Prentiss, and G. M. Whitesides, "Microlithography by using neutral metastable atoms and self-assembled monolayers," Science 269, 1255-1257 (1995).
[CrossRef] [PubMed]

Yokoyama, Y.

Y. Yokoyama, "Fulgides for memories and switches," Chem. Rev. (Washington, D.C.) 100, 1717-1739 (2000).

Appl. Phys. A

S. W. Hell, S. Jakobs, and L. Kastrup, "Imaging and writing at the nanoscale with focused visible light through saturable optical transitions," Appl. Phys. A 77, 859-860 (2003).
[CrossRef]

Chem. Rev. (Washington, D.C.)

M. Irie, "Diarylethenes for memories and switches," Chem. Rev. (Washington, D.C.) 100, 1685-1716 (2000).

Y. Yokoyama, "Fulgides for memories and switches," Chem. Rev. (Washington, D.C.) 100, 1717-1739 (2000).

IEEE Electron Device Lett.

B. F. Griffing and P. R. West, "Contrast enhanced photolithography," IEEE Electron Device Lett. 4, 14-16 (1983).
[CrossRef]

J. Microlithogr. Microfabr. Microsyst.

M. D. Levenson, T. Ebihara, G. Dai, Y. Morikawa, N. Hayashi, and T. S. Meng, "Optical vortex masks for via levels," J. Microlithogr. Microfabr. Microsyst. 3, 293-304 (2004).
[CrossRef]

J. Mod. Opt.

S. N. Khonina, V. V. Kotlyar, M. V. Shinkaryev, V. A. Soifer, and G. V. Uspleniev, "The phase rotor filter," J. Mod. Opt. 39, 1147-1154 (1992).
[CrossRef]

J. Opt. Soc. Am. A

J. Vac. Sci. Technol. B

R. Menon, A. Patel, E. E. Moon, and H. I. Smith, "An alpha prototype system for zone-plate-array lithography," J. Vac. Sci. Technol. B 22, 3032-3037 (2004).
[CrossRef]

D. Chao, A. Patel, T. Barwicz, H. I. Smith, and R. Menon, "Immersion zone-plate-array lithography," J. Vac. Sci. Technol. B 23, 2657-2661 (2005).
[CrossRef]

Phys. Lett. A

S. W. Hell, "Strategy for far-field optical imaging and writing without diffraction limit," Phys. Lett. A 326, 140-145 (2004).
[CrossRef]

Phys. Rev. Lett.

L. Kastrup, H. Blom, C. Eggeling, and S. W. Hell, "Fluorescence fluctuation spectroscopy in subdiffraction focal volume," Phys. Rev. Lett. 94, 178104/1-5 (2005).
[CrossRef]

Polym. Eng. Sci.

B. F. Griffing and P. R. West, "Contrast enhanced photoresists--processing and modeling," Polym. Eng. Sci. 23, 947-952 (1983).
[CrossRef]

Quantum Semiclassic. Opt.

A. P. Chu, K. K. Berggren, K. S. Johnson, and M. G. Prentiss, "A virtual slit for atom optics and nanolithography," Quantum Semiclassic. Opt. 8, 521-529 (1996).
[CrossRef]

Science

K. K. Berggren, A. Bard, J. L. Wilbur, J. D. Gillaspy, A. G. Helg, J. J. McClelland, S. L. Rolston, W. D. Phillip, M. Prentiss, and G. M. Whitesides, "Microlithography by using neutral metastable atoms and self-assembled monolayers," Science 269, 1255-1257 (1995).
[CrossRef] [PubMed]

Other

J. C. Crano and R. J. Guglielmetti, Organic Photochromic and Thermochromic Compounds (Plenum, 1999).

Selected Papers on Resolution Enhancement Techniques in Optical Lithography, Vol. MS 178, F.M.Schellenberg, ed. (SPIE, 2004).

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Figures (4)

Fig. 1
Fig. 1

Schematic of AMOL. The ring illumination at λ 2 creates a local subwavelength aperture for λ 1 , through which the underlying photoresist is exposed. After exposure, the RCEL recovers by exposure to λ 2 or thermally. The substrate is stepped, and the λ 1 , λ 2 exposure is repeated, effectively scanning the subwavelength aperture.

Fig. 2
Fig. 2

Absorbance modulation during exposure by a focused spot at λ 1 , together with a ring-shaped illumination at λ 2 . Illumination at λ 2 reverses the conversion from A to B, except at the center of the spot where the λ 2 intensity is 0. Thus, the nonlinearity introduced by the RCEL is significantly enhanced. The inset is a magnified view of the absorbance change from 0 to 0.2 ms , which clearly shows that points outside the center of the λ 1 spot reach a photostationary state much faster. The parameters used in the simulation are described in the text.

Fig. 3
Fig. 3

PSF compression via AMOL. During exposure by a focused spot at λ 1 , a ring-shaped spot at λ 2 also illuminates the same area as shown. Illumination at λ 2 suppresses the conversion from A to B except at the center of the spot, where its intensity is 0. Thus, the nonlinearity introduced by the RCEL is significantly enhanced.

Fig. 4
Fig. 4

Aerial image contrast of grating patterns as a function of the grating half-pitch with and without AMOL compression. The scanning-electron micrograph of 135 nm lines and spaces was patterned using an uncompressed PSF at λ 1 = 400 nm and NA = 0.85 .[17]

Equations (10)

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

D ( r , τ ) = I 01 ( r ) 0 τ 10 α 1 ( r , t ) d t ,
α 1 ( r , t ) = α 1 A + α 1 B = { ϵ 1 A [ A ( r , t ) ] + ϵ 1 B [ B ( r , t ) ] } l ,
f 1 ( r , t ) = I 01 ( r ) l [ 1 10 α 1 ( r , t ) ] ,
f 1 A ( r , t ) = I 01 ( r ) l ( 1 10 α 1 ( r , t ) ) α 1 A ( r , t ) α 1 ( r , t ) ,
= I 01 ( r ) l F 1 ( r , t ) α 1 A ( r , t ) ,
d [ A ( r , t ) ] d t = ϕ 1 A B I 01 ( r ) l F 1 ( r , t ) α 1 A ( r , t ) + ϕ 2 A B I 02 ( r ) l F 2 ( r , t ) α 2 A ( r , t ) k B A [ B ( r , t ) ] ϕ 1 B A I 01 ( r ) l F 1 ( r , t ) α 1 B ( r , t ) ϕ 2 B A I 02 ( r ) l F 2 ( r , t ) α 2 B ( r , t ) ,
[ A ] 0 = [ A ] + [ B ] ,
d [ A ( r , t ) ] d t = [ ( ϕ 1 A B ϵ 1 A + ϕ 1 B A ϵ 1 B ) I 01 ( r ) F 1 ( r , t ) + ( ϕ 2 A B ϵ 2 A + ϕ 2 B A ε 2 B ) I 02 ( r ) F 2 ( r , t ) + k B A ] [ A ( r , t ) ] [ k B A + ϕ 1 B A ϵ 1 B I 01 ( r ) F 1 ( r , t ) + ϕ 2 B A ϵ 2 B I 02 ( r ) F 2 ( r , t ) ] [ A ] 0 .
D ( r , τ ) I 01 ( r ) 0 τ 10 α 1 P S ( r ) d t = I 01 ( r ) τ ( 10 α 1 P S ( r ) ) ,
I 02 ( r ) J 0 ( a r ) H 1 ( a r ) J 1 ( a r ) H 0 ( a r ) r 2 ,

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