Abstract

We present the analyses of surface plasmon polaritons (SPPs) coupling induced interference in metal/dielectric (M/D) multilayer metamaterials and techniques to improve the performance of sub-wavelength plasmonic lithography. Expressions of beam spreading angles and interference patterns are derived from analyses of numerical simulations and the coupled mode theory. The new understandings provide useful guidelines and design criteria for plasmonic lithography. With proper layer structure design, sub-wavelength uniform periodic patterns with feature size of 1/12 of the mask's period can be realized. High pattern contrast of 0.8 and large field depth of 80 nm are also demonstrated numerically by considering the SPPs coupling in the photoresist. Both high contrast and large image depth are crucial for practical application of plasmonic lithography.

© 2012 OSA

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. S. Thongrattanasiri and V. A. Podolskiy, “Hypergratings: nanophotonics in planar anisotropic metamaterials,” Opt. Lett. 34(7), 890–892 (2009).
    [CrossRef] [PubMed]
  2. W. S. Cai, D. A. Genov, and V. M. Shalaev, “Superlens based on metal-dielectric composites,” Phys. Rev. B 72(19), 193101 (2005).
    [CrossRef]
  3. X. B. Fan and G. P. Wang, “Nanoscale metal waveguide arrays as plasmon lenses,” Opt. Lett. 31(9), 1322–1324 (2006).
    [CrossRef] [PubMed]
  4. L. Verslegers, P. B. Catrysse, Z. F. Yu, and S. H. Fan, “Deep-subwavelength focusing and steering of light in an aperiodic metallic waveguide array,” Phys. Rev. Lett. 103(3), 033902 (2009).
    [CrossRef] [PubMed]
  5. X. Fan, G. P. Wang, J. C. W. Lee, and C. T. Chan, “All-angle broadband negative refraction of metal waveguide arrays in the visible range: theoretical analysis and numerical demonstration,” Phys. Rev. Lett. 97(7), 073901 (2006).
    [CrossRef] [PubMed]
  6. H. Shin and S. Fan, “All-angle negative refraction for surface plasmon waves using a metal-dielectric-metal structure,” Phys. Rev. Lett. 96(7), 073907 (2006).
    [CrossRef] [PubMed]
  7. T. Yang and K. B. Crozier, “Analysis of surface plasmon waves in metaldielectric- metal structures and the criterion for negative refractive index,” Opt. Express 17(2), 1136–1143 (2009).
    [CrossRef] [PubMed]
  8. X. F. Yang, B. B. Zeng, C. T. Wang, and X. G. Luo, “Breaking the feature sizes down to sub-22 nm by plasmonic interference lithography using dielectric-metal multilayer,” Opt. Express 17(24), 21560–21565 (2009).
    [CrossRef] [PubMed]
  9. W. Srituravanich, N. Fang, C. Sun, Q. Luo, and X. Zhang, “Plasmonic nanolithography,” Nano Lett. 4(6), 1085–1088 (2004).
    [CrossRef]
  10. Z. W. Liu, Q. H. Wei, and X. Zhang, “Surface plasmon interference nanolithography,” Nano Lett. 5(5), 957–961 (2005).
    [CrossRef] [PubMed]
  11. X. G. Luo and T. Ishihara, “Surface plasmon resonant interference nanolithography technique,” Appl. Phys. Lett. 84(23), 4780–4782 (2004).
    [CrossRef]
  12. T. Xu, Y. H. Zhao, J. X. Ma, C. T. Wang, J. H. Cui, C. L. Du, and X. G. Luo, “Sub-diffraction-limited interference photolithography with metamaterials,” Opt. Express 16(18), 13579–13584 (2008).
    [CrossRef] [PubMed]
  13. M. J. Weber, Handbook of Optical Materials (CRC Press, 2003), Chap. 4, 352–355.
  14. C. C. Yan, D. H. Zhang, Y. A. Zhang, D. D. Li, and M. A. Fiddy, “Metal-dielectric composites for beam splitting and far-field deep sub-wavelength resolution for visible wavelengths,” Opt. Express 18(14), 14794–14801 (2010).
    [CrossRef] [PubMed]
  15. B. Wang and G. P. Wang, “Surface plasmon polariton propagation in nanoscale metal gap waveguides,” Opt. Lett. 29(17), 1992–1994 (2004).
    [CrossRef] [PubMed]
  16. A. Yariv, “Coupled-mode theory for guided-wave optics,” IEEE J. Quantum Electron. 9(9), 919–933 (1973).
    [CrossRef]
  17. A. Locatelli, M. Conforti, D. Modotto, and C. De Angelis, “Diffraction engineering in arrays of photonic crystal waveguides,” Opt. Lett. 30(21), 2894–2896 (2005).
    [CrossRef] [PubMed]
  18. H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, “Discrete Spatial Optical Solitons in Waveguide Arrays,” Phys. Rev. Lett. 81(16), 3383–3386 (1998).
    [CrossRef]
  19. M. D. Arnold and R. J. Blaikie, “Subwavelength optical imaging of evanescent fields using reflections from plasmonic slabs,” Opt. Express 15(18), 11542–11552 (2007).
    [CrossRef] [PubMed]

2010

2009

2008

2007

2006

X. B. Fan and G. P. Wang, “Nanoscale metal waveguide arrays as plasmon lenses,” Opt. Lett. 31(9), 1322–1324 (2006).
[CrossRef] [PubMed]

X. Fan, G. P. Wang, J. C. W. Lee, and C. T. Chan, “All-angle broadband negative refraction of metal waveguide arrays in the visible range: theoretical analysis and numerical demonstration,” Phys. Rev. Lett. 97(7), 073901 (2006).
[CrossRef] [PubMed]

H. Shin and S. Fan, “All-angle negative refraction for surface plasmon waves using a metal-dielectric-metal structure,” Phys. Rev. Lett. 96(7), 073907 (2006).
[CrossRef] [PubMed]

2005

W. S. Cai, D. A. Genov, and V. M. Shalaev, “Superlens based on metal-dielectric composites,” Phys. Rev. B 72(19), 193101 (2005).
[CrossRef]

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

A. Locatelli, M. Conforti, D. Modotto, and C. De Angelis, “Diffraction engineering in arrays of photonic crystal waveguides,” Opt. Lett. 30(21), 2894–2896 (2005).
[CrossRef] [PubMed]

2004

B. Wang and G. P. Wang, “Surface plasmon polariton propagation in nanoscale metal gap waveguides,” Opt. Lett. 29(17), 1992–1994 (2004).
[CrossRef] [PubMed]

X. G. Luo and T. Ishihara, “Surface plasmon resonant interference nanolithography technique,” Appl. Phys. Lett. 84(23), 4780–4782 (2004).
[CrossRef]

W. Srituravanich, N. Fang, C. Sun, Q. Luo, and X. Zhang, “Plasmonic nanolithography,” Nano Lett. 4(6), 1085–1088 (2004).
[CrossRef]

1998

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, “Discrete Spatial Optical Solitons in Waveguide Arrays,” Phys. Rev. Lett. 81(16), 3383–3386 (1998).
[CrossRef]

1973

A. Yariv, “Coupled-mode theory for guided-wave optics,” IEEE J. Quantum Electron. 9(9), 919–933 (1973).
[CrossRef]

Aitchison, J. S.

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, “Discrete Spatial Optical Solitons in Waveguide Arrays,” Phys. Rev. Lett. 81(16), 3383–3386 (1998).
[CrossRef]

Arnold, M. D.

Blaikie, R. J.

Boyd, A. R.

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, “Discrete Spatial Optical Solitons in Waveguide Arrays,” Phys. Rev. Lett. 81(16), 3383–3386 (1998).
[CrossRef]

Cai, W. S.

W. S. Cai, D. A. Genov, and V. M. Shalaev, “Superlens based on metal-dielectric composites,” Phys. Rev. B 72(19), 193101 (2005).
[CrossRef]

Catrysse, P. B.

L. Verslegers, P. B. Catrysse, Z. F. Yu, and S. H. Fan, “Deep-subwavelength focusing and steering of light in an aperiodic metallic waveguide array,” Phys. Rev. Lett. 103(3), 033902 (2009).
[CrossRef] [PubMed]

Chan, C. T.

X. Fan, G. P. Wang, J. C. W. Lee, and C. T. Chan, “All-angle broadband negative refraction of metal waveguide arrays in the visible range: theoretical analysis and numerical demonstration,” Phys. Rev. Lett. 97(7), 073901 (2006).
[CrossRef] [PubMed]

Conforti, M.

Crozier, K. B.

Cui, J. H.

De Angelis, C.

Du, C. L.

Eisenberg, H. S.

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, “Discrete Spatial Optical Solitons in Waveguide Arrays,” Phys. Rev. Lett. 81(16), 3383–3386 (1998).
[CrossRef]

Fan, S.

H. Shin and S. Fan, “All-angle negative refraction for surface plasmon waves using a metal-dielectric-metal structure,” Phys. Rev. Lett. 96(7), 073907 (2006).
[CrossRef] [PubMed]

Fan, S. H.

L. Verslegers, P. B. Catrysse, Z. F. Yu, and S. H. Fan, “Deep-subwavelength focusing and steering of light in an aperiodic metallic waveguide array,” Phys. Rev. Lett. 103(3), 033902 (2009).
[CrossRef] [PubMed]

Fan, X.

X. Fan, G. P. Wang, J. C. W. Lee, and C. T. Chan, “All-angle broadband negative refraction of metal waveguide arrays in the visible range: theoretical analysis and numerical demonstration,” Phys. Rev. Lett. 97(7), 073901 (2006).
[CrossRef] [PubMed]

Fan, X. B.

Fang, N.

W. Srituravanich, N. Fang, C. Sun, Q. Luo, and X. Zhang, “Plasmonic nanolithography,” Nano Lett. 4(6), 1085–1088 (2004).
[CrossRef]

Fiddy, M. A.

Genov, D. A.

W. S. Cai, D. A. Genov, and V. M. Shalaev, “Superlens based on metal-dielectric composites,” Phys. Rev. B 72(19), 193101 (2005).
[CrossRef]

Ishihara, T.

X. G. Luo and T. Ishihara, “Surface plasmon resonant interference nanolithography technique,” Appl. Phys. Lett. 84(23), 4780–4782 (2004).
[CrossRef]

Lee, J. C. W.

X. Fan, G. P. Wang, J. C. W. Lee, and C. T. Chan, “All-angle broadband negative refraction of metal waveguide arrays in the visible range: theoretical analysis and numerical demonstration,” Phys. Rev. Lett. 97(7), 073901 (2006).
[CrossRef] [PubMed]

Li, D. D.

Liu, Z. W.

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

Locatelli, A.

Luo, Q.

W. Srituravanich, N. Fang, C. Sun, Q. Luo, and X. Zhang, “Plasmonic nanolithography,” Nano Lett. 4(6), 1085–1088 (2004).
[CrossRef]

Luo, X. G.

Ma, J. X.

Modotto, D.

Morandotti, R.

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, “Discrete Spatial Optical Solitons in Waveguide Arrays,” Phys. Rev. Lett. 81(16), 3383–3386 (1998).
[CrossRef]

Podolskiy, V. A.

Shalaev, V. M.

W. S. Cai, D. A. Genov, and V. M. Shalaev, “Superlens based on metal-dielectric composites,” Phys. Rev. B 72(19), 193101 (2005).
[CrossRef]

Shin, H.

H. Shin and S. Fan, “All-angle negative refraction for surface plasmon waves using a metal-dielectric-metal structure,” Phys. Rev. Lett. 96(7), 073907 (2006).
[CrossRef] [PubMed]

Silberberg, Y.

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, “Discrete Spatial Optical Solitons in Waveguide Arrays,” Phys. Rev. Lett. 81(16), 3383–3386 (1998).
[CrossRef]

Srituravanich, W.

W. Srituravanich, N. Fang, C. Sun, Q. Luo, and X. Zhang, “Plasmonic nanolithography,” Nano Lett. 4(6), 1085–1088 (2004).
[CrossRef]

Sun, C.

W. Srituravanich, N. Fang, C. Sun, Q. Luo, and X. Zhang, “Plasmonic nanolithography,” Nano Lett. 4(6), 1085–1088 (2004).
[CrossRef]

Thongrattanasiri, S.

Verslegers, L.

L. Verslegers, P. B. Catrysse, Z. F. Yu, and S. H. Fan, “Deep-subwavelength focusing and steering of light in an aperiodic metallic waveguide array,” Phys. Rev. Lett. 103(3), 033902 (2009).
[CrossRef] [PubMed]

Wang, B.

Wang, C. T.

Wang, G. P.

X. Fan, G. P. Wang, J. C. W. Lee, and C. T. Chan, “All-angle broadband negative refraction of metal waveguide arrays in the visible range: theoretical analysis and numerical demonstration,” Phys. Rev. Lett. 97(7), 073901 (2006).
[CrossRef] [PubMed]

X. B. Fan and G. P. Wang, “Nanoscale metal waveguide arrays as plasmon lenses,” Opt. Lett. 31(9), 1322–1324 (2006).
[CrossRef] [PubMed]

B. Wang and G. P. Wang, “Surface plasmon polariton propagation in nanoscale metal gap waveguides,” Opt. Lett. 29(17), 1992–1994 (2004).
[CrossRef] [PubMed]

Wei, Q. H.

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

Xu, T.

Yan, C. C.

Yang, T.

Yang, X. F.

Yariv, A.

A. Yariv, “Coupled-mode theory for guided-wave optics,” IEEE J. Quantum Electron. 9(9), 919–933 (1973).
[CrossRef]

Yu, Z. F.

L. Verslegers, P. B. Catrysse, Z. F. Yu, and S. H. Fan, “Deep-subwavelength focusing and steering of light in an aperiodic metallic waveguide array,” Phys. Rev. Lett. 103(3), 033902 (2009).
[CrossRef] [PubMed]

Zeng, B. B.

Zhang, D. H.

Zhang, X.

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

W. Srituravanich, N. Fang, C. Sun, Q. Luo, and X. Zhang, “Plasmonic nanolithography,” Nano Lett. 4(6), 1085–1088 (2004).
[CrossRef]

Zhang, Y. A.

Zhao, Y. H.

Appl. Phys. Lett.

X. G. Luo and T. Ishihara, “Surface plasmon resonant interference nanolithography technique,” Appl. Phys. Lett. 84(23), 4780–4782 (2004).
[CrossRef]

IEEE J. Quantum Electron.

A. Yariv, “Coupled-mode theory for guided-wave optics,” IEEE J. Quantum Electron. 9(9), 919–933 (1973).
[CrossRef]

Nano Lett.

W. Srituravanich, N. Fang, C. Sun, Q. Luo, and X. Zhang, “Plasmonic nanolithography,” Nano Lett. 4(6), 1085–1088 (2004).
[CrossRef]

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

Opt. Express

Opt. Lett.

Phys. Rev. B

W. S. Cai, D. A. Genov, and V. M. Shalaev, “Superlens based on metal-dielectric composites,” Phys. Rev. B 72(19), 193101 (2005).
[CrossRef]

Phys. Rev. Lett.

L. Verslegers, P. B. Catrysse, Z. F. Yu, and S. H. Fan, “Deep-subwavelength focusing and steering of light in an aperiodic metallic waveguide array,” Phys. Rev. Lett. 103(3), 033902 (2009).
[CrossRef] [PubMed]

X. Fan, G. P. Wang, J. C. W. Lee, and C. T. Chan, “All-angle broadband negative refraction of metal waveguide arrays in the visible range: theoretical analysis and numerical demonstration,” Phys. Rev. Lett. 97(7), 073901 (2006).
[CrossRef] [PubMed]

H. Shin and S. Fan, “All-angle negative refraction for surface plasmon waves using a metal-dielectric-metal structure,” Phys. Rev. Lett. 96(7), 073907 (2006).
[CrossRef] [PubMed]

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, “Discrete Spatial Optical Solitons in Waveguide Arrays,” Phys. Rev. Lett. 81(16), 3383–3386 (1998).
[CrossRef]

Other

M. J. Weber, Handbook of Optical Materials (CRC Press, 2003), Chap. 4, 352–355.

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 (6)

Fig. 1
Fig. 1

Schematic diagram of the multilayer Ag/ MgF2 waveguide with an air slit. All the components are treated as semi-infinite in the y direction.

Fig. 2
Fig. 2

(a) Intensity of total electrical field of the SPPs spreading in Ag/MgF2 multilayer waveguide, where the thicknesses of Ag are 30 nm, 20 nm and 15 nm in (i), (ii), (iii), respectively. (b) Comparison of the spreading angles calculated by the simulations of COMSOL and coupled mode theory

Fig. 3
Fig. 3

Total electrical field in the Ag/MgF2 multilayer waveguide with two slits.

Fig. 4
Fig. 4

(a) Theoretical electric field distribution expressed by Eq. (1) and plotted by Matlab. (b) Total electric field distribution of the MDMW with one air slit simulated by COMSOL 3.5a. (c) Theoretical electric field distribution expressed by Eq. (3) with five excitation ports. The dashed lines are the intersections of the spreading beams. (d) Electric field distribution of the MDMW with five air slits calculated by COMSOL 3.5a. The distance between the neighboring slits is 600 nm and the thicknesses of Ag/MgF2 are 30 nm/20 nm.

Fig. 5
Fig. 5

Intensity of total electrical field on the photoresist in structures with different thicknesses of Ag/MgF2, 28 nm/30 nm in (a) and 20 nm/30 nm in (b); (c) thicknesses of Al/ MgF2 are 16 nm/16 nm. (d) Profile of the electrical field at a distance to 20 nm from the top of the photoresist of interference patterns in (c).

Fig. 6
Fig. 6

(a) Intensity distribution of electrical field of the enhanced interference patterns with 50 nm feature size in the MDMW with a metal layer below photoresist;(b) Comparison of profiles of the cross section of the interference patterns with a distance of 40 nm from the top surface of photoresist in the structures with and without Al layer; (c) and (d) are the results for the interference patterns with feature size of 20 nm; (e) Schematic of the SPPs coupling in the photoresist. The red curve represents the coupled SPP modes on the top and bottom photoresist/metal interface. (f) Amplified intensity 2D electrical field distributions in the photoresist without and with metal film.

Equations (3)

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

i d dx E n +β E n +C( E n+1 + E n1 )=0,
E n (x)= E 0 (i) n exp(iβx) J n (2Cx),
E(x)= k=1 m E k ( x )= k=1 m A 0 (i) n exp(iβx) J n { 2C[xL(k)] } ,

Metrics