Abstract

Electromagnetic diffraction of a light wave by a single aperture of subwavelength width and subsequent propagation in a lossy medium are numerically investigated. This diffraction problem simulates exposure of a resist with an amplitude mask. It is found that there is the possibility of fabricating a λ/2 structure on a resist of λ/4 thickness, where λ is the wavelength of the exposing light in vacuum, by conventional contact or by proximity lithography. It is also found that an air gap between a mask and a resist of up to λ/2 does not have a significant effect on resolution. This approach permits easy and cost-effective fabrication of subwavelength structures and leads to wide availability of diffractive optical elements in the nonscalar domain.

© 2001 Optical Society of America

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  1. C. W. Haggans, R. K. Kostuk, “Polarization transformation properties of high spatial frequency surface-relief gratings and their applications,” in Micro-optics, H. P. Herzig, ed. (Taylor & Francis, London, 1997), Chap. 12.
  2. This view may be supported by, e.g., the following paper, which deals with the problem in a rather different way from ours: D. J. D. Carter, D. Gil, R. Menon, H. I. Smith, “Maskless nanolithgraphy with diffractive optics: zone-plate-array lithography (ZPAL),” in Diffractive Optics and Micro-Optics, Vol. 41 of 2000 OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000), pp. 105–107.
  3. A typical example is a Fresnel lens or a Fresnel zone plate, which has a coarse structure at the center and a much finer structure at the periphery.
  4. H. Schmid, H. Biebuyck, B. Michel, O. J. F. Martin, “Light-coupling masks for lensless, subwavelength optical lithography,” Appl. Phys. Lett. 72, 2379–2381 (1998).
    [CrossRef]
  5. H. Schmid, H. Biebuyck, B. Michel, O. J. F. Martin, N. Piller, “Light-coupling masks: an alternative, lensless approach to high resolution optical contact lithography,” J. Vac. Sci. Technol. B 16, 3422–3425 (1998).
    [CrossRef]
  6. O. J. F. Martin, N. B. Piller, H. Schmid, H. Biebuyck, B. Michel, “Energy flow in light-coupling masks for lensless optical lithography,” Opt. Express 3, 280–285 (1998), http://epubs.osa.org/opticsexpress .
    [CrossRef] [PubMed]
  7. O. J. F. Martin, C. Girard, A. Dereux, “Generalized field propagator for electromagnetic scattering and light confinement,” Phys. Rev. Lett. 74, 526–529 (1995).
    [CrossRef] [PubMed]
  8. R. J. Blaikie, M. M. Alkaisi, S. J. McNab, D. R. S. Cumming, R. Cheung, D. G. Hasko, “Nanolithography using optical contact exposure in the evanescent near field,” Microelectron. Eng. 46, 85–88 (1999).
    [CrossRef]
  9. M. M. Alkaisi, R. J. Blaikie, S. J. McNab, D. R. S. Cumming, “Sub-diffraction-limited patterning using evanescent near-field optical lithography,” Appl. Phys. Lett. 75, 3560–3562 (1999).
    [CrossRef]
  10. S. J. McNab, R. J. Blaikie, “Contrast in the evanescent near field of λ/20 period gratings for photolithography,” Appl. Opt. 39, 20–25 (2000).
    [CrossRef]
  11. J. G. Goodberlet, “Patterning 100 nm features using deep-ultraviolet contact photolithography,” Appl. Phys. Lett. 76, 667–669 (2000).
    [CrossRef]
  12. For example, see A. Taflove, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, Norwood, Mass., 1995).
  13. L. Novotny, D. W. Pohl, P. Regli, “Light propagation through nanometer-sized structures: the two-dimensional-aperture scanning near-field optical microscope,” J. Opt. Soc. Am. A 11, 1768–1779 (1994).
    [CrossRef]
  14. R. C. Weast, ed., CRC Handbook of Chemistry and Physics (CRC Press, Boca Raton, Fla., 1983).
  15. The value is obtained from the data for the S-1800 series in Micro Electronic Products Catalogue (Shipley Far East Ltd., Tokyo, in Japanese).
  16. E. Hecht, Optics (Addison-Wesley, Reading, Mass., 1998), p. 311.
  17. K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antennas Propag. AP-14, 302–307 (1966).
  18. J. B. Judkins, R. W. Ziolkowski, “Finite-difference time-domain modeling of nonperfectly conducting metallic thin-film grating,” J. Opt. Soc. Am. A 12, 1974–1982 (1995).
    [CrossRef]
  19. This expression is found also in Eq. (28) of R. J. Luebbers, D. Steich, K. Kunz, “FDTD calculation of scattering from frequency-dependent materials,” IEEE Trans. Antennas Propag. 41, 1249–1257 (1993).
    [CrossRef]
  20. In this paper the following values are used: (ω0, γ, ϵ∞, χs)=(3.897×1015 s-1, 1.171×1015 s-1, 3ϵ0,10) for chromium and (4.475×1015 s-1, 3.423×1015 s-1, 2.9ϵ0, 0.3) for resist.
  21. A. P. Zhao, A. Räisänen, S. R. Cvetkovic, “A fast and efficient FDTD algorithm for the analysis of planar microstrip discontinuities by using a simple source excitation scheme,” IEEE Microwave Guid. Wave Lett. 5, 341–343 (1995).
    [CrossRef]
  22. G. Mur, “Absorbing boundary conditions for the finite-difference approximation of the time-domain electromagnetic-field equations,” IEEE Trans. Electromagn. Compat. EMC-23, 377–382 (1981).
    [CrossRef]
  23. M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, UK, 1980), pp. 565–578.
  24. Ref. 16, Chap. 10, p. 49.
  25. E. Betzig, A. Harootunian, A. Lewis, M. Isaacson, “Near-field diffraction by a slit: implications for superresplution microscopy,” Appl. Opt. 25, 1890–1900 (1986).
    [CrossRef]
  26. J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1999), pp. 352–356.
  27. A thick resist is employed for Fig. 6, because the purpose here is to observe a typical intensity gradient, particularly in the xdirection, inside the resist. In fact, there is little difference between intensity profiles for thick (d=500 nm) and thin (d=100 nm) resist layers near the incident plane (x=0 nm).
  28. Strictly speaking, in particular when the intensity distribution contains abrupt changes in the x direction, the field extension for an unpolarized light source should be obtained by use of the sum of the intensities for TE and TM waves at each z position.
  29. D. C. Flanders, A. M. Hawryluk, H. I. Smith, “Spatial period division—a new technique for exposing submicrometer-linewidth periodic and quasiperiodic patterns,” J. Vac. Sci. Technol. 16, 1949–1952 (1979).
    [CrossRef]
  30. E. D. Palik, ed., Handbook of Optical Constants of Solids (Academic, Orlando, Fla., 1985).
  31. (ω0, γ, ϵ∞, χs)=(3.931×1015s-1, 1.643×1015 s-1, 3ϵ0, 1) in Fig. 10(b) and (6.363×1015 s-1, 1.915×1016s-1, 30ϵ0, 10) in Fig. 10(d).
  32. For example, such as explained in J. Hargreaves, “Liquid phase silylation of a bilayer resist system,” Microelectron. Eng. 45, 329–349 (1999).
    [CrossRef]

2000 (2)

S. J. McNab, R. J. Blaikie, “Contrast in the evanescent near field of λ/20 period gratings for photolithography,” Appl. Opt. 39, 20–25 (2000).
[CrossRef]

J. G. Goodberlet, “Patterning 100 nm features using deep-ultraviolet contact photolithography,” Appl. Phys. Lett. 76, 667–669 (2000).
[CrossRef]

1999 (3)

R. J. Blaikie, M. M. Alkaisi, S. J. McNab, D. R. S. Cumming, R. Cheung, D. G. Hasko, “Nanolithography using optical contact exposure in the evanescent near field,” Microelectron. Eng. 46, 85–88 (1999).
[CrossRef]

M. M. Alkaisi, R. J. Blaikie, S. J. McNab, D. R. S. Cumming, “Sub-diffraction-limited patterning using evanescent near-field optical lithography,” Appl. Phys. Lett. 75, 3560–3562 (1999).
[CrossRef]

For example, such as explained in J. Hargreaves, “Liquid phase silylation of a bilayer resist system,” Microelectron. Eng. 45, 329–349 (1999).
[CrossRef]

1998 (3)

H. Schmid, H. Biebuyck, B. Michel, O. J. F. Martin, “Light-coupling masks for lensless, subwavelength optical lithography,” Appl. Phys. Lett. 72, 2379–2381 (1998).
[CrossRef]

H. Schmid, H. Biebuyck, B. Michel, O. J. F. Martin, N. Piller, “Light-coupling masks: an alternative, lensless approach to high resolution optical contact lithography,” J. Vac. Sci. Technol. B 16, 3422–3425 (1998).
[CrossRef]

O. J. F. Martin, N. B. Piller, H. Schmid, H. Biebuyck, B. Michel, “Energy flow in light-coupling masks for lensless optical lithography,” Opt. Express 3, 280–285 (1998), http://epubs.osa.org/opticsexpress .
[CrossRef] [PubMed]

1995 (3)

O. J. F. Martin, C. Girard, A. Dereux, “Generalized field propagator for electromagnetic scattering and light confinement,” Phys. Rev. Lett. 74, 526–529 (1995).
[CrossRef] [PubMed]

J. B. Judkins, R. W. Ziolkowski, “Finite-difference time-domain modeling of nonperfectly conducting metallic thin-film grating,” J. Opt. Soc. Am. A 12, 1974–1982 (1995).
[CrossRef]

A. P. Zhao, A. Räisänen, S. R. Cvetkovic, “A fast and efficient FDTD algorithm for the analysis of planar microstrip discontinuities by using a simple source excitation scheme,” IEEE Microwave Guid. Wave Lett. 5, 341–343 (1995).
[CrossRef]

1994 (1)

1993 (1)

This expression is found also in Eq. (28) of R. J. Luebbers, D. Steich, K. Kunz, “FDTD calculation of scattering from frequency-dependent materials,” IEEE Trans. Antennas Propag. 41, 1249–1257 (1993).
[CrossRef]

1986 (1)

1981 (1)

G. Mur, “Absorbing boundary conditions for the finite-difference approximation of the time-domain electromagnetic-field equations,” IEEE Trans. Electromagn. Compat. EMC-23, 377–382 (1981).
[CrossRef]

1979 (1)

D. C. Flanders, A. M. Hawryluk, H. I. Smith, “Spatial period division—a new technique for exposing submicrometer-linewidth periodic and quasiperiodic patterns,” J. Vac. Sci. Technol. 16, 1949–1952 (1979).
[CrossRef]

1966 (1)

K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antennas Propag. AP-14, 302–307 (1966).

Alkaisi, M. M.

R. J. Blaikie, M. M. Alkaisi, S. J. McNab, D. R. S. Cumming, R. Cheung, D. G. Hasko, “Nanolithography using optical contact exposure in the evanescent near field,” Microelectron. Eng. 46, 85–88 (1999).
[CrossRef]

M. M. Alkaisi, R. J. Blaikie, S. J. McNab, D. R. S. Cumming, “Sub-diffraction-limited patterning using evanescent near-field optical lithography,” Appl. Phys. Lett. 75, 3560–3562 (1999).
[CrossRef]

Betzig, E.

Biebuyck, H.

O. J. F. Martin, N. B. Piller, H. Schmid, H. Biebuyck, B. Michel, “Energy flow in light-coupling masks for lensless optical lithography,” Opt. Express 3, 280–285 (1998), http://epubs.osa.org/opticsexpress .
[CrossRef] [PubMed]

H. Schmid, H. Biebuyck, B. Michel, O. J. F. Martin, “Light-coupling masks for lensless, subwavelength optical lithography,” Appl. Phys. Lett. 72, 2379–2381 (1998).
[CrossRef]

H. Schmid, H. Biebuyck, B. Michel, O. J. F. Martin, N. Piller, “Light-coupling masks: an alternative, lensless approach to high resolution optical contact lithography,” J. Vac. Sci. Technol. B 16, 3422–3425 (1998).
[CrossRef]

Blaikie, R. J.

S. J. McNab, R. J. Blaikie, “Contrast in the evanescent near field of λ/20 period gratings for photolithography,” Appl. Opt. 39, 20–25 (2000).
[CrossRef]

M. M. Alkaisi, R. J. Blaikie, S. J. McNab, D. R. S. Cumming, “Sub-diffraction-limited patterning using evanescent near-field optical lithography,” Appl. Phys. Lett. 75, 3560–3562 (1999).
[CrossRef]

R. J. Blaikie, M. M. Alkaisi, S. J. McNab, D. R. S. Cumming, R. Cheung, D. G. Hasko, “Nanolithography using optical contact exposure in the evanescent near field,” Microelectron. Eng. 46, 85–88 (1999).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, UK, 1980), pp. 565–578.

Carter, D. J. D.

This view may be supported by, e.g., the following paper, which deals with the problem in a rather different way from ours: D. J. D. Carter, D. Gil, R. Menon, H. I. Smith, “Maskless nanolithgraphy with diffractive optics: zone-plate-array lithography (ZPAL),” in Diffractive Optics and Micro-Optics, Vol. 41 of 2000 OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000), pp. 105–107.

Cheung, R.

R. J. Blaikie, M. M. Alkaisi, S. J. McNab, D. R. S. Cumming, R. Cheung, D. G. Hasko, “Nanolithography using optical contact exposure in the evanescent near field,” Microelectron. Eng. 46, 85–88 (1999).
[CrossRef]

Cumming, D. R. S.

R. J. Blaikie, M. M. Alkaisi, S. J. McNab, D. R. S. Cumming, R. Cheung, D. G. Hasko, “Nanolithography using optical contact exposure in the evanescent near field,” Microelectron. Eng. 46, 85–88 (1999).
[CrossRef]

M. M. Alkaisi, R. J. Blaikie, S. J. McNab, D. R. S. Cumming, “Sub-diffraction-limited patterning using evanescent near-field optical lithography,” Appl. Phys. Lett. 75, 3560–3562 (1999).
[CrossRef]

Cvetkovic, S. R.

A. P. Zhao, A. Räisänen, S. R. Cvetkovic, “A fast and efficient FDTD algorithm for the analysis of planar microstrip discontinuities by using a simple source excitation scheme,” IEEE Microwave Guid. Wave Lett. 5, 341–343 (1995).
[CrossRef]

Dereux, A.

O. J. F. Martin, C. Girard, A. Dereux, “Generalized field propagator for electromagnetic scattering and light confinement,” Phys. Rev. Lett. 74, 526–529 (1995).
[CrossRef] [PubMed]

Flanders, D. C.

D. C. Flanders, A. M. Hawryluk, H. I. Smith, “Spatial period division—a new technique for exposing submicrometer-linewidth periodic and quasiperiodic patterns,” J. Vac. Sci. Technol. 16, 1949–1952 (1979).
[CrossRef]

Gil, D.

This view may be supported by, e.g., the following paper, which deals with the problem in a rather different way from ours: D. J. D. Carter, D. Gil, R. Menon, H. I. Smith, “Maskless nanolithgraphy with diffractive optics: zone-plate-array lithography (ZPAL),” in Diffractive Optics and Micro-Optics, Vol. 41 of 2000 OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000), pp. 105–107.

Girard, C.

O. J. F. Martin, C. Girard, A. Dereux, “Generalized field propagator for electromagnetic scattering and light confinement,” Phys. Rev. Lett. 74, 526–529 (1995).
[CrossRef] [PubMed]

Goodberlet, J. G.

J. G. Goodberlet, “Patterning 100 nm features using deep-ultraviolet contact photolithography,” Appl. Phys. Lett. 76, 667–669 (2000).
[CrossRef]

Haggans, C. W.

C. W. Haggans, R. K. Kostuk, “Polarization transformation properties of high spatial frequency surface-relief gratings and their applications,” in Micro-optics, H. P. Herzig, ed. (Taylor & Francis, London, 1997), Chap. 12.

Hargreaves, J.

For example, such as explained in J. Hargreaves, “Liquid phase silylation of a bilayer resist system,” Microelectron. Eng. 45, 329–349 (1999).
[CrossRef]

Harootunian, A.

Hasko, D. G.

R. J. Blaikie, M. M. Alkaisi, S. J. McNab, D. R. S. Cumming, R. Cheung, D. G. Hasko, “Nanolithography using optical contact exposure in the evanescent near field,” Microelectron. Eng. 46, 85–88 (1999).
[CrossRef]

Hawryluk, A. M.

D. C. Flanders, A. M. Hawryluk, H. I. Smith, “Spatial period division—a new technique for exposing submicrometer-linewidth periodic and quasiperiodic patterns,” J. Vac. Sci. Technol. 16, 1949–1952 (1979).
[CrossRef]

Hecht, E.

E. Hecht, Optics (Addison-Wesley, Reading, Mass., 1998), p. 311.

Isaacson, M.

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1999), pp. 352–356.

Judkins, J. B.

Kostuk, R. K.

C. W. Haggans, R. K. Kostuk, “Polarization transformation properties of high spatial frequency surface-relief gratings and their applications,” in Micro-optics, H. P. Herzig, ed. (Taylor & Francis, London, 1997), Chap. 12.

Kunz, K.

This expression is found also in Eq. (28) of R. J. Luebbers, D. Steich, K. Kunz, “FDTD calculation of scattering from frequency-dependent materials,” IEEE Trans. Antennas Propag. 41, 1249–1257 (1993).
[CrossRef]

Lewis, A.

Luebbers, R. J.

This expression is found also in Eq. (28) of R. J. Luebbers, D. Steich, K. Kunz, “FDTD calculation of scattering from frequency-dependent materials,” IEEE Trans. Antennas Propag. 41, 1249–1257 (1993).
[CrossRef]

Martin, O. J. F.

H. Schmid, H. Biebuyck, B. Michel, O. J. F. Martin, “Light-coupling masks for lensless, subwavelength optical lithography,” Appl. Phys. Lett. 72, 2379–2381 (1998).
[CrossRef]

H. Schmid, H. Biebuyck, B. Michel, O. J. F. Martin, N. Piller, “Light-coupling masks: an alternative, lensless approach to high resolution optical contact lithography,” J. Vac. Sci. Technol. B 16, 3422–3425 (1998).
[CrossRef]

O. J. F. Martin, N. B. Piller, H. Schmid, H. Biebuyck, B. Michel, “Energy flow in light-coupling masks for lensless optical lithography,” Opt. Express 3, 280–285 (1998), http://epubs.osa.org/opticsexpress .
[CrossRef] [PubMed]

O. J. F. Martin, C. Girard, A. Dereux, “Generalized field propagator for electromagnetic scattering and light confinement,” Phys. Rev. Lett. 74, 526–529 (1995).
[CrossRef] [PubMed]

McNab, S. J.

S. J. McNab, R. J. Blaikie, “Contrast in the evanescent near field of λ/20 period gratings for photolithography,” Appl. Opt. 39, 20–25 (2000).
[CrossRef]

M. M. Alkaisi, R. J. Blaikie, S. J. McNab, D. R. S. Cumming, “Sub-diffraction-limited patterning using evanescent near-field optical lithography,” Appl. Phys. Lett. 75, 3560–3562 (1999).
[CrossRef]

R. J. Blaikie, M. M. Alkaisi, S. J. McNab, D. R. S. Cumming, R. Cheung, D. G. Hasko, “Nanolithography using optical contact exposure in the evanescent near field,” Microelectron. Eng. 46, 85–88 (1999).
[CrossRef]

Menon, R.

This view may be supported by, e.g., the following paper, which deals with the problem in a rather different way from ours: D. J. D. Carter, D. Gil, R. Menon, H. I. Smith, “Maskless nanolithgraphy with diffractive optics: zone-plate-array lithography (ZPAL),” in Diffractive Optics and Micro-Optics, Vol. 41 of 2000 OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000), pp. 105–107.

Michel, B.

H. Schmid, H. Biebuyck, B. Michel, O. J. F. Martin, “Light-coupling masks for lensless, subwavelength optical lithography,” Appl. Phys. Lett. 72, 2379–2381 (1998).
[CrossRef]

H. Schmid, H. Biebuyck, B. Michel, O. J. F. Martin, N. Piller, “Light-coupling masks: an alternative, lensless approach to high resolution optical contact lithography,” J. Vac. Sci. Technol. B 16, 3422–3425 (1998).
[CrossRef]

O. J. F. Martin, N. B. Piller, H. Schmid, H. Biebuyck, B. Michel, “Energy flow in light-coupling masks for lensless optical lithography,” Opt. Express 3, 280–285 (1998), http://epubs.osa.org/opticsexpress .
[CrossRef] [PubMed]

Mur, G.

G. Mur, “Absorbing boundary conditions for the finite-difference approximation of the time-domain electromagnetic-field equations,” IEEE Trans. Electromagn. Compat. EMC-23, 377–382 (1981).
[CrossRef]

Novotny, L.

Piller, N.

H. Schmid, H. Biebuyck, B. Michel, O. J. F. Martin, N. Piller, “Light-coupling masks: an alternative, lensless approach to high resolution optical contact lithography,” J. Vac. Sci. Technol. B 16, 3422–3425 (1998).
[CrossRef]

Piller, N. B.

Pohl, D. W.

Räisänen, A.

A. P. Zhao, A. Räisänen, S. R. Cvetkovic, “A fast and efficient FDTD algorithm for the analysis of planar microstrip discontinuities by using a simple source excitation scheme,” IEEE Microwave Guid. Wave Lett. 5, 341–343 (1995).
[CrossRef]

Regli, P.

Schmid, H.

O. J. F. Martin, N. B. Piller, H. Schmid, H. Biebuyck, B. Michel, “Energy flow in light-coupling masks for lensless optical lithography,” Opt. Express 3, 280–285 (1998), http://epubs.osa.org/opticsexpress .
[CrossRef] [PubMed]

H. Schmid, H. Biebuyck, B. Michel, O. J. F. Martin, N. Piller, “Light-coupling masks: an alternative, lensless approach to high resolution optical contact lithography,” J. Vac. Sci. Technol. B 16, 3422–3425 (1998).
[CrossRef]

H. Schmid, H. Biebuyck, B. Michel, O. J. F. Martin, “Light-coupling masks for lensless, subwavelength optical lithography,” Appl. Phys. Lett. 72, 2379–2381 (1998).
[CrossRef]

Smith, H. I.

D. C. Flanders, A. M. Hawryluk, H. I. Smith, “Spatial period division—a new technique for exposing submicrometer-linewidth periodic and quasiperiodic patterns,” J. Vac. Sci. Technol. 16, 1949–1952 (1979).
[CrossRef]

This view may be supported by, e.g., the following paper, which deals with the problem in a rather different way from ours: D. J. D. Carter, D. Gil, R. Menon, H. I. Smith, “Maskless nanolithgraphy with diffractive optics: zone-plate-array lithography (ZPAL),” in Diffractive Optics and Micro-Optics, Vol. 41 of 2000 OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000), pp. 105–107.

Steich, D.

This expression is found also in Eq. (28) of R. J. Luebbers, D. Steich, K. Kunz, “FDTD calculation of scattering from frequency-dependent materials,” IEEE Trans. Antennas Propag. 41, 1249–1257 (1993).
[CrossRef]

Taflove, A.

For example, see A. Taflove, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, Norwood, Mass., 1995).

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, UK, 1980), pp. 565–578.

Yee, K. S.

K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antennas Propag. AP-14, 302–307 (1966).

Zhao, A. P.

A. P. Zhao, A. Räisänen, S. R. Cvetkovic, “A fast and efficient FDTD algorithm for the analysis of planar microstrip discontinuities by using a simple source excitation scheme,” IEEE Microwave Guid. Wave Lett. 5, 341–343 (1995).
[CrossRef]

Ziolkowski, R. W.

Appl. Opt. (2)

Appl. Phys. Lett. (3)

J. G. Goodberlet, “Patterning 100 nm features using deep-ultraviolet contact photolithography,” Appl. Phys. Lett. 76, 667–669 (2000).
[CrossRef]

H. Schmid, H. Biebuyck, B. Michel, O. J. F. Martin, “Light-coupling masks for lensless, subwavelength optical lithography,” Appl. Phys. Lett. 72, 2379–2381 (1998).
[CrossRef]

M. M. Alkaisi, R. J. Blaikie, S. J. McNab, D. R. S. Cumming, “Sub-diffraction-limited patterning using evanescent near-field optical lithography,” Appl. Phys. Lett. 75, 3560–3562 (1999).
[CrossRef]

IEEE Microwave Guid. Wave Lett. (1)

A. P. Zhao, A. Räisänen, S. R. Cvetkovic, “A fast and efficient FDTD algorithm for the analysis of planar microstrip discontinuities by using a simple source excitation scheme,” IEEE Microwave Guid. Wave Lett. 5, 341–343 (1995).
[CrossRef]

IEEE Trans. Antennas Propag. (2)

This expression is found also in Eq. (28) of R. J. Luebbers, D. Steich, K. Kunz, “FDTD calculation of scattering from frequency-dependent materials,” IEEE Trans. Antennas Propag. 41, 1249–1257 (1993).
[CrossRef]

K. S. Yee, “Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media,” IEEE Trans. Antennas Propag. AP-14, 302–307 (1966).

IEEE Trans. Electromagn. Compat. (1)

G. Mur, “Absorbing boundary conditions for the finite-difference approximation of the time-domain electromagnetic-field equations,” IEEE Trans. Electromagn. Compat. EMC-23, 377–382 (1981).
[CrossRef]

J. Opt. Soc. Am. A (2)

J. Vac. Sci. Technol. (1)

D. C. Flanders, A. M. Hawryluk, H. I. Smith, “Spatial period division—a new technique for exposing submicrometer-linewidth periodic and quasiperiodic patterns,” J. Vac. Sci. Technol. 16, 1949–1952 (1979).
[CrossRef]

J. Vac. Sci. Technol. B (1)

H. Schmid, H. Biebuyck, B. Michel, O. J. F. Martin, N. Piller, “Light-coupling masks: an alternative, lensless approach to high resolution optical contact lithography,” J. Vac. Sci. Technol. B 16, 3422–3425 (1998).
[CrossRef]

Microelectron. Eng. (2)

R. J. Blaikie, M. M. Alkaisi, S. J. McNab, D. R. S. Cumming, R. Cheung, D. G. Hasko, “Nanolithography using optical contact exposure in the evanescent near field,” Microelectron. Eng. 46, 85–88 (1999).
[CrossRef]

For example, such as explained in J. Hargreaves, “Liquid phase silylation of a bilayer resist system,” Microelectron. Eng. 45, 329–349 (1999).
[CrossRef]

Opt. Express (1)

Phys. Rev. Lett. (1)

O. J. F. Martin, C. Girard, A. Dereux, “Generalized field propagator for electromagnetic scattering and light confinement,” Phys. Rev. Lett. 74, 526–529 (1995).
[CrossRef] [PubMed]

Other (15)

C. W. Haggans, R. K. Kostuk, “Polarization transformation properties of high spatial frequency surface-relief gratings and their applications,” in Micro-optics, H. P. Herzig, ed. (Taylor & Francis, London, 1997), Chap. 12.

This view may be supported by, e.g., the following paper, which deals with the problem in a rather different way from ours: D. J. D. Carter, D. Gil, R. Menon, H. I. Smith, “Maskless nanolithgraphy with diffractive optics: zone-plate-array lithography (ZPAL),” in Diffractive Optics and Micro-Optics, Vol. 41 of 2000 OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 2000), pp. 105–107.

A typical example is a Fresnel lens or a Fresnel zone plate, which has a coarse structure at the center and a much finer structure at the periphery.

R. C. Weast, ed., CRC Handbook of Chemistry and Physics (CRC Press, Boca Raton, Fla., 1983).

The value is obtained from the data for the S-1800 series in Micro Electronic Products Catalogue (Shipley Far East Ltd., Tokyo, in Japanese).

E. Hecht, Optics (Addison-Wesley, Reading, Mass., 1998), p. 311.

For example, see A. Taflove, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, Norwood, Mass., 1995).

E. D. Palik, ed., Handbook of Optical Constants of Solids (Academic, Orlando, Fla., 1985).

(ω0, γ, ϵ∞, χs)=(3.931×1015s-1, 1.643×1015 s-1, 3ϵ0, 1) in Fig. 10(b) and (6.363×1015 s-1, 1.915×1016s-1, 30ϵ0, 10) in Fig. 10(d).

In this paper the following values are used: (ω0, γ, ϵ∞, χs)=(3.897×1015 s-1, 1.171×1015 s-1, 3ϵ0,10) for chromium and (4.475×1015 s-1, 3.423×1015 s-1, 2.9ϵ0, 0.3) for resist.

M. Born, E. Wolf, Principles of Optics (Pergamon, Oxford, UK, 1980), pp. 565–578.

Ref. 16, Chap. 10, p. 49.

J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1999), pp. 352–356.

A thick resist is employed for Fig. 6, because the purpose here is to observe a typical intensity gradient, particularly in the xdirection, inside the resist. In fact, there is little difference between intensity profiles for thick (d=500 nm) and thin (d=100 nm) resist layers near the incident plane (x=0 nm).

Strictly speaking, in particular when the intensity distribution contains abrupt changes in the x direction, the field extension for an unpolarized light source should be obtained by use of the sum of the intensities for TE and TM waves at each z position.

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Figures (10)

Fig. 1
Fig. 1

Diffraction problems considered. Each layer lies along the x axis. The structure and fields are constant in the y direction.

Fig. 2
Fig. 2

Example of intensity distribution. a=200 nm, h=0 nm, d=500 nm for TM polarization. The intensity is normalized with the incident wave.

Fig. 3
Fig. 3

Intensity distribution for a=200 nm: (a) output to the air, TE wave; (b) output to the air, TM wave; (c) output to the d=500-nm resist coated on silica, TE wave; (d) output to the d=500-nm resist coated on silica, TM wave. The intensity is normalized with the incident wave. The gray scale in (a) also applies to (b), (c), and (d).

Fig. 4
Fig. 4

Directions of electromagnetic field components of a wave propagating along a boundary between a dielectric and a conductor. S is the Poynting vector. Black dots denote the direction of the y axis.

Fig. 5
Fig. 5

Intensity distribution inside the resist layer for a=200 nm and h=0 nm: (a) d=500 nm, TE wave; (b) d=500 nm, TM wave; (c) d=100 nm, TE wave; (d) d=100 nm, TM wave. The intensity is normalized with the incident wave. The gray scale in (a) also applies to (b), (c), and (d).

Fig. 6
Fig. 6

Three-dimensional representation of the intensity distribution: a=200 nm, h=0 nm, d=500 nm; (a) TE wave, (b) TM wave. The intensity is normalized with the incident wave.

Fig. 7
Fig. 7

Lateral field extension for contact lithography h=0 nm; 0.1, 0.2, and 0.4 correspond to intensity levels normalized with the incident wave. (a) d=100 nm, (b) d=50 nm.

Fig. 8
Fig. 8

Lateral field extension when a parallel air gap exists between a mask and a resist. a=200 nm, d=100 nm; 0.1, 0.2, and 0.4 correspond to intensity levels normalized with the incident wave.

Fig. 9
Fig. 9

Intensity distribution when a parallel air gap h=100 nm exists between a mask and the resist; a=200 nm, d=100 nm. (a) TE wave, (b) TM wave. The intensity is normalized with the incident wave. The gray scale in (a) also applies to (b).

Fig. 10
Fig. 10

Effects of optical properties of the substrate material on the intensity distribution: a=200 nm, h=0 nm, d=200 nm, TE wave. (a) nˆ=1.470, (b) nˆ=1.470-i0.387, (c) nˆ=5.570, (d) nˆ=5.570-i0.387. The top and bottom layers denote the substrate and the resist, respectively. The value in each layer is a complex refractive index of the medium. The intensity is normalized with the incident wave. The gray scale in (a) also applies to (b), (c), and (d).

Equations (3)

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ϵ˜=εϵ0+χsω02ω02-ω2+iγω,
ϵ˜=(n-iκ)2,
I(x, z)=n(x, z)|Ey(x, z; t)|2TE,n(x, z)|Ex(x, z; t)|2+|Ez(x, z; t)|2TM

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