Abstract

A nanolithography technique based on the interference of surface plasmons (SPs) is proposed and demonstrated to modulate the localized exposure energy. The SP waves participating in interference are excited by two distinct structures, namely, the grating and the nanotaper. Constructive or destructive interference, which ultimately causes an enhanced or reduced modulation to the localized energy, can be obtained merely by adjusting the distance of the grating and the taper. Detailedly speaking, the localized energy can be modulated consecutively with a constant periodicity, and the modulation range of energy is extremely wide, for instance, the maximum energy is nearly 3 orders of magnitude larger than the minimum by our FDTD simulation results. Moreover, since the localized electric field at the taper tip, which leads to the exposure of the photoresist, is extremely sensitive to interference, it suggests a potential way to produce patterns with different depths and critical widths in one chip via beforehand programming and reasonably controlling the corresponding interference of SPs.

© 2008 Optical Society of America

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  1. M. Rothschild, T. M. Bloomstein, J. E. Curtin, D. K. Downs, T. H. Fedynyshyn, D. E. Hardy, R. R. Kunz, V. Liberman, J. H. C. Sedlacek, R. S. Uttaro, A. K. Bates, and C. V. Peski, "157 nm: deepest deep-ultraviolet yet," J. Vac. Sci. Technol. B 17, 3262-3266 (1999).
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    [CrossRef]
  3. J. P. Silverman, "Challenges and progress in x-ray lithography," J. Vac. Sci. Technol. B 16, 3137-3141 (1998).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  7. M. Switkes and M. Rothschild, "Immersion lithography at 157 nm," J. Vac. Sci. Technol. B 19, 2353-2356 (2001).
    [CrossRef]
  8. J. G. Goodberlet and H. Kavak, "Patterning sub-50 nm features with near-field embedded-amplitude masks," Appl. Phys. Lett. 81, 1315-1317 (2002).
    [CrossRef]
  9. M. M.  Alkaisi, R. J.  Blaikie, S. J.  McNab, R.  Cheung, and D. R. S.  Cumming, "Sub-diffraction-limited patterning using evanescent near-field optical lithography," Appl. Phys. Lett.  75, 3560-3562 (1999).
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    [CrossRef]
  12. X. Luo and T. Ishihara, "Subwavelength photolithography based on surface-plasmon polariton resonance," Opt. Express. 12, 3055-3065 (2004).
    [CrossRef] [PubMed]
  13. W. Srituravanich, N. Fang, C. Sun, Q. Luo, and X. Zhang, "Plasmonic nanolithography," Nano Lett. 4, 1085-1088 (2004).
    [CrossRef]
  14. Z. W. Liu, Q. H. Wei, and X. Zhang, "Surface plasmon interference nanolithography," Nano Lett. 5, 957-961 (2005).
    [CrossRef] [PubMed]
  15. A. V. Zayats and I. I. Smolyaninov, "Near-field photonic: surface plasmon polaritons and locallized surface plasmons," J. Opt. A: Pure Appl. Opt. 5, S16-S50 (2003).
    [CrossRef]
  16. Q1. V.  Zayats, I. I.  Smolyaninov, and A. A.  Maradudin, "Nano-optics of surface plasmon polaritons," Phys. Rep.  408, 131-314 (2005).
    [CrossRef]
  17. X. Wei, X. Luo, X. Dong and C. Du, "Localized surface plasmon nanolithography with ultrahigh resolution," Opt. Express. 15, 14177-14183 (2007).
    [CrossRef] [PubMed]
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  19. A. Bouhelier, J. Renger, M. R. Beversluis, and L. Novotny, "Plasmon-coupled tip-enhanced near-field optical microscopy", J. Microsc. 210, 220-224 (2003).
    [CrossRef] [PubMed]
  20. M. I. Stockman, S. V. Faleev, and D. J. Bergman, "Localization versus delocalization of surface plasmons in nanosystems: Can one state have both characteristics?," Phys. Rev. Lett. 87, 167401-167404 (2001).
    [CrossRef] [PubMed]
  21. P. B. Johnson and R. W. Christy, "Optical constants of the noble metals," Phys. Rev. B 6, 4370-4379 (1972).
    [CrossRef]
  22. K. Li, M. I. Stockman, and D. J. Bergman, "Self-similar chain of metal nanospheres as an efficient nanolens" Phys. Rev. Lett. 91, 227402 (2003).
    [CrossRef] [PubMed]
  23. M. I. Stockman, "Nanofocusing of optical energy in tapered plasmonic waveguides," Phys. Rev. Lett. 93, 137404 (2004).
    [CrossRef] [PubMed]

2007

X. Wei, X. Luo, X. Dong and C. Du, "Localized surface plasmon nanolithography with ultrahigh resolution," Opt. Express. 15, 14177-14183 (2007).
[CrossRef] [PubMed]

2005

Z. W. Liu, Q. H. Wei, and X. Zhang, "Surface plasmon interference nanolithography," Nano Lett. 5, 957-961 (2005).
[CrossRef] [PubMed]

Q1. V.  Zayats, I. I.  Smolyaninov, and A. A.  Maradudin, "Nano-optics of surface plasmon polaritons," Phys. Rep.  408, 131-314 (2005).
[CrossRef]

2004

M. I. Stockman, "Nanofocusing of optical energy in tapered plasmonic waveguides," Phys. Rev. Lett. 93, 137404 (2004).
[CrossRef] [PubMed]

X. Luo and T. Ishihara, "Surface plasmon resonant interference nanolithography technique," Appl. Phys. Lett. 84, 4780-4782 (2004).
[CrossRef]

X. Luo and T. Ishihara, "Subwavelength photolithography based on surface-plasmon polariton resonance," Opt. Express. 12, 3055-3065 (2004).
[CrossRef] [PubMed]

W. Srituravanich, N. Fang, C. Sun, Q. Luo, and X. Zhang, "Plasmonic nanolithography," Nano Lett. 4, 1085-1088 (2004).
[CrossRef]

2003

A. V. Zayats and I. I. Smolyaninov, "Near-field photonic: surface plasmon polaritons and locallized surface plasmons," J. Opt. A: Pure Appl. Opt. 5, S16-S50 (2003).
[CrossRef]

A. Bouhelier, J. Renger, M. R. Beversluis, and L. Novotny, "Plasmon-coupled tip-enhanced near-field optical microscopy", J. Microsc. 210, 220-224 (2003).
[CrossRef] [PubMed]

K. Li, M. I. Stockman, and D. J. Bergman, "Self-similar chain of metal nanospheres as an efficient nanolens" Phys. Rev. Lett. 91, 227402 (2003).
[CrossRef] [PubMed]

2002

J. G. Goodberlet and H. Kavak, "Patterning sub-50 nm features with near-field embedded-amplitude masks," Appl. Phys. Lett. 81, 1315-1317 (2002).
[CrossRef]

2001

M. Switkes and M. Rothschild, "Immersion lithography at 157 nm," J. Vac. Sci. Technol. B 19, 2353-2356 (2001).
[CrossRef]

M. I. Stockman, S. V. Faleev, and D. J. Bergman, "Localization versus delocalization of surface plasmons in nanosystems: Can one state have both characteristics?," Phys. Rev. Lett. 87, 167401-167404 (2001).
[CrossRef] [PubMed]

1999

J. A. Hoffnagle, W. D. Hinsberg, M. Sanchez, and F. A. Houle, "Liquid immersion deep-ultraviolet interferometric lithography", J. Vac. Sci. Technol. B 17, 3306-3309 (1999).
[CrossRef]

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

M. Rothschild, T. M. Bloomstein, J. E. Curtin, D. K. Downs, T. H. Fedynyshyn, D. E. Hardy, R. R. Kunz, V. Liberman, J. H. C. Sedlacek, R. S. Uttaro, A. K. Bates, and C. V. Peski, "157 nm: deepest deep-ultraviolet yet," J. Vac. Sci. Technol. B 17, 3262-3266 (1999).

1998

C. W. Gwyn, R. Stulen, D. Sweeney, and D. Attwood, "Extreme ultraviolet lithography," J. Vac. Sci. Technol. B 16, 3142-3149 (1998).
[CrossRef]

J. P. Silverman, "Challenges and progress in x-ray lithography," J. Vac. Sci. Technol. B 16, 3137-3141 (1998).
[CrossRef]

1997

M. A. McCord, "Electron beam lithography for 0.13 ?m manufacturing," J. Vac. Sci. Technol. B 15, 2125-2129 (1997).
[CrossRef]

1993

J. Melngailis, "Focused ion beam lithography," Nucl. Instrum. Methods Phys. Res. B 80, 1271-1280 (1993).
[CrossRef]

1972

P. B. Johnson and R. W. Christy, "Optical constants of the noble metals," Phys. Rev. B 6, 4370-4379 (1972).
[CrossRef]

Alkaisi, M. M.

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

Attwood, D.

C. W. Gwyn, R. Stulen, D. Sweeney, and D. Attwood, "Extreme ultraviolet lithography," J. Vac. Sci. Technol. B 16, 3142-3149 (1998).
[CrossRef]

Bates, A. K.

M. Rothschild, T. M. Bloomstein, J. E. Curtin, D. K. Downs, T. H. Fedynyshyn, D. E. Hardy, R. R. Kunz, V. Liberman, J. H. C. Sedlacek, R. S. Uttaro, A. K. Bates, and C. V. Peski, "157 nm: deepest deep-ultraviolet yet," J. Vac. Sci. Technol. B 17, 3262-3266 (1999).

Bergman, D. J.

K. Li, M. I. Stockman, and D. J. Bergman, "Self-similar chain of metal nanospheres as an efficient nanolens" Phys. Rev. Lett. 91, 227402 (2003).
[CrossRef] [PubMed]

M. I. Stockman, S. V. Faleev, and D. J. Bergman, "Localization versus delocalization of surface plasmons in nanosystems: Can one state have both characteristics?," Phys. Rev. Lett. 87, 167401-167404 (2001).
[CrossRef] [PubMed]

Beversluis, M. R.

A. Bouhelier, J. Renger, M. R. Beversluis, and L. Novotny, "Plasmon-coupled tip-enhanced near-field optical microscopy", J. Microsc. 210, 220-224 (2003).
[CrossRef] [PubMed]

Blaikie, R. J.

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

Bloomstein, T. M.

M. Rothschild, T. M. Bloomstein, J. E. Curtin, D. K. Downs, T. H. Fedynyshyn, D. E. Hardy, R. R. Kunz, V. Liberman, J. H. C. Sedlacek, R. S. Uttaro, A. K. Bates, and C. V. Peski, "157 nm: deepest deep-ultraviolet yet," J. Vac. Sci. Technol. B 17, 3262-3266 (1999).

Bouhelier, A.

A. Bouhelier, J. Renger, M. R. Beversluis, and L. Novotny, "Plasmon-coupled tip-enhanced near-field optical microscopy", J. Microsc. 210, 220-224 (2003).
[CrossRef] [PubMed]

Cheung, R.

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

Christy, R. W.

P. B. Johnson and R. W. Christy, "Optical constants of the noble metals," Phys. Rev. B 6, 4370-4379 (1972).
[CrossRef]

Cumming, D. R. S.

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

Curtin, J. E.

M. Rothschild, T. M. Bloomstein, J. E. Curtin, D. K. Downs, T. H. Fedynyshyn, D. E. Hardy, R. R. Kunz, V. Liberman, J. H. C. Sedlacek, R. S. Uttaro, A. K. Bates, and C. V. Peski, "157 nm: deepest deep-ultraviolet yet," J. Vac. Sci. Technol. B 17, 3262-3266 (1999).

Dong, X.

X. Wei, X. Luo, X. Dong and C. Du, "Localized surface plasmon nanolithography with ultrahigh resolution," Opt. Express. 15, 14177-14183 (2007).
[CrossRef] [PubMed]

Downs, D. K.

M. Rothschild, T. M. Bloomstein, J. E. Curtin, D. K. Downs, T. H. Fedynyshyn, D. E. Hardy, R. R. Kunz, V. Liberman, J. H. C. Sedlacek, R. S. Uttaro, A. K. Bates, and C. V. Peski, "157 nm: deepest deep-ultraviolet yet," J. Vac. Sci. Technol. B 17, 3262-3266 (1999).

Du, C.

X. Wei, X. Luo, X. Dong and C. Du, "Localized surface plasmon nanolithography with ultrahigh resolution," Opt. Express. 15, 14177-14183 (2007).
[CrossRef] [PubMed]

Faleev, S. V.

M. I. Stockman, S. V. Faleev, and D. J. Bergman, "Localization versus delocalization of surface plasmons in nanosystems: Can one state have both characteristics?," Phys. Rev. Lett. 87, 167401-167404 (2001).
[CrossRef] [PubMed]

Fang, N.

W. Srituravanich, N. Fang, C. Sun, Q. Luo, and X. Zhang, "Plasmonic nanolithography," Nano Lett. 4, 1085-1088 (2004).
[CrossRef]

Fedynyshyn, T. H.

M. Rothschild, T. M. Bloomstein, J. E. Curtin, D. K. Downs, T. H. Fedynyshyn, D. E. Hardy, R. R. Kunz, V. Liberman, J. H. C. Sedlacek, R. S. Uttaro, A. K. Bates, and C. V. Peski, "157 nm: deepest deep-ultraviolet yet," J. Vac. Sci. Technol. B 17, 3262-3266 (1999).

Goodberlet, J. G.

J. G. Goodberlet and H. Kavak, "Patterning sub-50 nm features with near-field embedded-amplitude masks," Appl. Phys. Lett. 81, 1315-1317 (2002).
[CrossRef]

Gwyn, C. W.

C. W. Gwyn, R. Stulen, D. Sweeney, and D. Attwood, "Extreme ultraviolet lithography," J. Vac. Sci. Technol. B 16, 3142-3149 (1998).
[CrossRef]

Hardy, D. E.

M. Rothschild, T. M. Bloomstein, J. E. Curtin, D. K. Downs, T. H. Fedynyshyn, D. E. Hardy, R. R. Kunz, V. Liberman, J. H. C. Sedlacek, R. S. Uttaro, A. K. Bates, and C. V. Peski, "157 nm: deepest deep-ultraviolet yet," J. Vac. Sci. Technol. B 17, 3262-3266 (1999).

Hinsberg, W. D.

J. A. Hoffnagle, W. D. Hinsberg, M. Sanchez, and F. A. Houle, "Liquid immersion deep-ultraviolet interferometric lithography", J. Vac. Sci. Technol. B 17, 3306-3309 (1999).
[CrossRef]

Hoffnagle, J. A.

J. A. Hoffnagle, W. D. Hinsberg, M. Sanchez, and F. A. Houle, "Liquid immersion deep-ultraviolet interferometric lithography", J. Vac. Sci. Technol. B 17, 3306-3309 (1999).
[CrossRef]

Houle, F. A.

J. A. Hoffnagle, W. D. Hinsberg, M. Sanchez, and F. A. Houle, "Liquid immersion deep-ultraviolet interferometric lithography", J. Vac. Sci. Technol. B 17, 3306-3309 (1999).
[CrossRef]

Ishihara, T.

X. Luo and T. Ishihara, "Surface plasmon resonant interference nanolithography technique," Appl. Phys. Lett. 84, 4780-4782 (2004).
[CrossRef]

X. Luo and T. Ishihara, "Subwavelength photolithography based on surface-plasmon polariton resonance," Opt. Express. 12, 3055-3065 (2004).
[CrossRef] [PubMed]

Johnson, P. B.

P. B. Johnson and R. W. Christy, "Optical constants of the noble metals," Phys. Rev. B 6, 4370-4379 (1972).
[CrossRef]

Kavak, H.

J. G. Goodberlet and H. Kavak, "Patterning sub-50 nm features with near-field embedded-amplitude masks," Appl. Phys. Lett. 81, 1315-1317 (2002).
[CrossRef]

Kunz, R. R.

M. Rothschild, T. M. Bloomstein, J. E. Curtin, D. K. Downs, T. H. Fedynyshyn, D. E. Hardy, R. R. Kunz, V. Liberman, J. H. C. Sedlacek, R. S. Uttaro, A. K. Bates, and C. V. Peski, "157 nm: deepest deep-ultraviolet yet," J. Vac. Sci. Technol. B 17, 3262-3266 (1999).

Li, K.

K. Li, M. I. Stockman, and D. J. Bergman, "Self-similar chain of metal nanospheres as an efficient nanolens" Phys. Rev. Lett. 91, 227402 (2003).
[CrossRef] [PubMed]

Liberman, V.

M. Rothschild, T. M. Bloomstein, J. E. Curtin, D. K. Downs, T. H. Fedynyshyn, D. E. Hardy, R. R. Kunz, V. Liberman, J. H. C. Sedlacek, R. S. Uttaro, A. K. Bates, and C. V. Peski, "157 nm: deepest deep-ultraviolet yet," J. Vac. Sci. Technol. B 17, 3262-3266 (1999).

Liu, Z. W.

Z. W. Liu, Q. H. Wei, and X. Zhang, "Surface plasmon interference nanolithography," Nano Lett. 5, 957-961 (2005).
[CrossRef] [PubMed]

Luo, Q.

W. Srituravanich, N. Fang, C. Sun, Q. Luo, and X. Zhang, "Plasmonic nanolithography," Nano Lett. 4, 1085-1088 (2004).
[CrossRef]

Luo, X.

X. Wei, X. Luo, X. Dong and C. Du, "Localized surface plasmon nanolithography with ultrahigh resolution," Opt. Express. 15, 14177-14183 (2007).
[CrossRef] [PubMed]

X. Luo and T. Ishihara, "Subwavelength photolithography based on surface-plasmon polariton resonance," Opt. Express. 12, 3055-3065 (2004).
[CrossRef] [PubMed]

X. Luo and T. Ishihara, "Surface plasmon resonant interference nanolithography technique," Appl. Phys. Lett. 84, 4780-4782 (2004).
[CrossRef]

Maradudin, A. A.

Q1. V.  Zayats, I. I.  Smolyaninov, and A. A.  Maradudin, "Nano-optics of surface plasmon polaritons," Phys. Rep.  408, 131-314 (2005).
[CrossRef]

McCord, M. A.

M. A. McCord, "Electron beam lithography for 0.13 ?m manufacturing," J. Vac. Sci. Technol. B 15, 2125-2129 (1997).
[CrossRef]

McNab, S. J.

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

Melngailis, J.

J. Melngailis, "Focused ion beam lithography," Nucl. Instrum. Methods Phys. Res. B 80, 1271-1280 (1993).
[CrossRef]

Novotny, L.

A. Bouhelier, J. Renger, M. R. Beversluis, and L. Novotny, "Plasmon-coupled tip-enhanced near-field optical microscopy", J. Microsc. 210, 220-224 (2003).
[CrossRef] [PubMed]

Peski, C. V.

M. Rothschild, T. M. Bloomstein, J. E. Curtin, D. K. Downs, T. H. Fedynyshyn, D. E. Hardy, R. R. Kunz, V. Liberman, J. H. C. Sedlacek, R. S. Uttaro, A. K. Bates, and C. V. Peski, "157 nm: deepest deep-ultraviolet yet," J. Vac. Sci. Technol. B 17, 3262-3266 (1999).

Renger, J.

A. Bouhelier, J. Renger, M. R. Beversluis, and L. Novotny, "Plasmon-coupled tip-enhanced near-field optical microscopy", J. Microsc. 210, 220-224 (2003).
[CrossRef] [PubMed]

Rothschild, M.

M. Switkes and M. Rothschild, "Immersion lithography at 157 nm," J. Vac. Sci. Technol. B 19, 2353-2356 (2001).
[CrossRef]

M. Rothschild, T. M. Bloomstein, J. E. Curtin, D. K. Downs, T. H. Fedynyshyn, D. E. Hardy, R. R. Kunz, V. Liberman, J. H. C. Sedlacek, R. S. Uttaro, A. K. Bates, and C. V. Peski, "157 nm: deepest deep-ultraviolet yet," J. Vac. Sci. Technol. B 17, 3262-3266 (1999).

Sanchez, M.

J. A. Hoffnagle, W. D. Hinsberg, M. Sanchez, and F. A. Houle, "Liquid immersion deep-ultraviolet interferometric lithography", J. Vac. Sci. Technol. B 17, 3306-3309 (1999).
[CrossRef]

Sedlacek, J. H. C.

M. Rothschild, T. M. Bloomstein, J. E. Curtin, D. K. Downs, T. H. Fedynyshyn, D. E. Hardy, R. R. Kunz, V. Liberman, J. H. C. Sedlacek, R. S. Uttaro, A. K. Bates, and C. V. Peski, "157 nm: deepest deep-ultraviolet yet," J. Vac. Sci. Technol. B 17, 3262-3266 (1999).

Silverman, J. P.

J. P. Silverman, "Challenges and progress in x-ray lithography," J. Vac. Sci. Technol. B 16, 3137-3141 (1998).
[CrossRef]

Smolyaninov, I. I.

Q1. V.  Zayats, I. I.  Smolyaninov, and A. A.  Maradudin, "Nano-optics of surface plasmon polaritons," Phys. Rep.  408, 131-314 (2005).
[CrossRef]

A. V. Zayats and I. I. Smolyaninov, "Near-field photonic: surface plasmon polaritons and locallized surface plasmons," J. Opt. A: Pure Appl. Opt. 5, S16-S50 (2003).
[CrossRef]

Srituravanich, W.

W. Srituravanich, N. Fang, C. Sun, Q. Luo, and X. Zhang, "Plasmonic nanolithography," Nano Lett. 4, 1085-1088 (2004).
[CrossRef]

Stockman, M. I.

M. I. Stockman, "Nanofocusing of optical energy in tapered plasmonic waveguides," Phys. Rev. Lett. 93, 137404 (2004).
[CrossRef] [PubMed]

K. Li, M. I. Stockman, and D. J. Bergman, "Self-similar chain of metal nanospheres as an efficient nanolens" Phys. Rev. Lett. 91, 227402 (2003).
[CrossRef] [PubMed]

M. I. Stockman, S. V. Faleev, and D. J. Bergman, "Localization versus delocalization of surface plasmons in nanosystems: Can one state have both characteristics?," Phys. Rev. Lett. 87, 167401-167404 (2001).
[CrossRef] [PubMed]

Stulen, R.

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Figures (4)

Fig. 1.
Fig. 1.

Schematic view of the composite structure with controllable localization energy.

Fig. 2.
Fig. 2.

(a). Electric field intensity distribution pattern in the case without grating. Electric field intensity distribution pattern in the case of l=0nm (b), l=70nm (c) and l=140nm (d) with grating. (e) Electric field intensity profiles at Δh=30nm (30nm below the interface of mask and photoresist). (f) Magnitude of the electric field intensity at constant X=0nm versus the vertical distance Z.

Fig. 3.
Fig. 3.

Relationship of localized energy versus the distance l. the red dash line with the value of 1 represents the energy value of a single taper structure without grating. Geometrical parameters are also w 1=600nm, w 2=160nm, h 1=60nm, h 2=240nm, p=280nm, n=4 and d=40nm.

Fig. 4.
Fig. 4.

(a). Electric field intensity distribution with four tapers. (b) Near-field intensity profiles at Δh=30nm. (c) Peak of the electric field intensity versus the vertical distance from the interface of the mask and the photoresist.

Equations (3)

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k sp = k 0 ε d · ε m ε d + ε m
k sp = k 0 n s sin θ ± m 2 π m = 1 , 2 , 3 . . . . . .
= 2 π k sp

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