Abstract

2D hexagonal patterns can be generated by the superimposition of two or three fringe patterns that have been formed by two-wave interference and that have rotations of 60° between them. Superimposing three exposures solves the problem of asymmetry in the cross section of structures, which is caused by double exposure. The resulting structure, however, depends on the phase shift of the third fringe pattern in relation to the previous two. We propose a method for controlling the phase shift, and we demonstrate that three different lattice geometries of hexagonal photonic crystals can be recorded when the phase is chosen.

© 2006 Optical Society of America

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References

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  1. S. R. J. Brueck, "Optical and Interferometric Lithography Nanotechnology Enablers," Proc. IEEE 93, 1704 (2005).
    [CrossRef]
  2. A. Fernandez, J. Y. Decker, S. M. Herman, D. W. Phillion, D. W. Sweeney and M. D. Perry, "Methods for fabricating arrays of holes using interference lithography," J. Vac. Sci. Technol. B 15, 2439-2443 (1997).
    [CrossRef]
  3. L. Pang, W. Nakagawa and Y. Fainman, "Fabrication of two-dimensional photonic crystals with controlled defects by use of multiple exposures and direct write," Appl. Opt. 42, 5450-5456 (2003).
    [CrossRef] [PubMed]
  4. F. Quiñónez, J. W. Menezes, V. F. Rodriguez-Esquerre, H. Hernandez-Figueroa, R. D. Mansano and L. Cescato, "Band gap of hexagonal 2D photonic crystals with elliptical holes recorded by interference lithography," Opt. Express 14, 4873-4879 (2006)
    [CrossRef] [PubMed]
  5. M. Campbel, D. N. Sharp, M. T. Harrison, R. G. Denning and A. J. Turberfield, "Fabrication of photonic crystals for the visible spectrum by holographic lithography," Nature 404, 53-56 (2000).
    [CrossRef]
  6. D. N. Sharp, M. Campbell, E. R. Dedman, M. T. Harrison, R. G. Denning and A. J. Turberfield, "Photonic crystals for the visible spectrum by holographic lithography," Opt. Quantum Electron. 34, 3-12 (2002).
    [CrossRef]
  7. N. D. Lai, W. P. Liang, J. H. Lin, C. C. Hsu and C. H. Lin, "Fabrication of two- and three-dimensional periodic structures by multi-exposure of two-beam interference technique," Opt. Express 13, 9605-9611 (2005).
    [CrossRef] [PubMed]
  8. L. Cescato and J. Frejlich, Three-Dimensional Holographic Imaging (Wiley-Interscience Publication, 2002), Chap. 3.
  9. A. A. Talin, K. A. Dean and J. E. Jaskie, "Field emission displays: a critical review," Solid State Electron. 45, 963-976 (2001).
    [CrossRef]
  10. L. E. Gutierrez-Rivera, E. J. de Carvalho, M. A. Silva and L. Cescato, "Metallic submicrometer sieves fabricated by interferometric lithography and electroforming," J. Micromech. Microeng. 15, 1932-1937 (2005).
    [CrossRef]
  11. J. D. Joannopoulos, R. D. Meade and J. N. Winn, Photonic Crystals (Princeton University Press, 1995).
  12. N. D. Lai, W. P. Liang, J. H. Lin and C. C. Hsu, "Rapid fabrication of large-area periodic structures containing well-defined defects by combining holography and mask techniques," Opt. Express 13, 5331-5337 (2005).
    [CrossRef] [PubMed]
  13. C. A. Mack, "Development of positive photoresists," J. Electrochem. Soc. 134, 148-152 (1987).
    [CrossRef]
  14. B. A. Mello, I. F. Costa, C. R. A. Lima and L. Cescato, "Developed profile of holographically exposed photoresist gratings," Appl. Opt. 34, 597-601 (1995).
    [CrossRef]
  15. V. Berger, O. Gauthier-Lafaye and E. Costard, "Photonic band gaps and holography," J. Appl. Phys. 82, 60-64 (1997).
    [CrossRef]
  16. M. Breide, S. Johansson, L. E. Nilsson and H. Ahlèn, "Blazed Holographic Gratings", Opt. Acta 26, 1427-1441 (1979).
    [CrossRef]
  17. C. M. B. Cordeiro, A. A. Freschi, L. Li and L. Cescato, "Measurement of phase differences between the diffracted orders of deep relief gratings," Opt. Letters 28, 683-685 (2003).
    [CrossRef]
  18. A. A. Freschi, F. J. dos Santos, E. L. Rigon and L. Cescato, "Phase-locking of superimposed diffractive gratings in photoresists," Opt. Commun. 208, 41-49 (2002).
    [CrossRef]

2006 (1)

2005 (4)

2003 (2)

C. M. B. Cordeiro, A. A. Freschi, L. Li and L. Cescato, "Measurement of phase differences between the diffracted orders of deep relief gratings," Opt. Letters 28, 683-685 (2003).
[CrossRef]

L. Pang, W. Nakagawa and Y. Fainman, "Fabrication of two-dimensional photonic crystals with controlled defects by use of multiple exposures and direct write," Appl. Opt. 42, 5450-5456 (2003).
[CrossRef] [PubMed]

2002 (2)

D. N. Sharp, M. Campbell, E. R. Dedman, M. T. Harrison, R. G. Denning and A. J. Turberfield, "Photonic crystals for the visible spectrum by holographic lithography," Opt. Quantum Electron. 34, 3-12 (2002).
[CrossRef]

A. A. Freschi, F. J. dos Santos, E. L. Rigon and L. Cescato, "Phase-locking of superimposed diffractive gratings in photoresists," Opt. Commun. 208, 41-49 (2002).
[CrossRef]

2001 (1)

A. A. Talin, K. A. Dean and J. E. Jaskie, "Field emission displays: a critical review," Solid State Electron. 45, 963-976 (2001).
[CrossRef]

2000 (1)

M. Campbel, D. N. Sharp, M. T. Harrison, R. G. Denning and A. J. Turberfield, "Fabrication of photonic crystals for the visible spectrum by holographic lithography," Nature 404, 53-56 (2000).
[CrossRef]

1997 (2)

A. Fernandez, J. Y. Decker, S. M. Herman, D. W. Phillion, D. W. Sweeney and M. D. Perry, "Methods for fabricating arrays of holes using interference lithography," J. Vac. Sci. Technol. B 15, 2439-2443 (1997).
[CrossRef]

V. Berger, O. Gauthier-Lafaye and E. Costard, "Photonic band gaps and holography," J. Appl. Phys. 82, 60-64 (1997).
[CrossRef]

1995 (1)

1987 (1)

C. A. Mack, "Development of positive photoresists," J. Electrochem. Soc. 134, 148-152 (1987).
[CrossRef]

1979 (1)

M. Breide, S. Johansson, L. E. Nilsson and H. Ahlèn, "Blazed Holographic Gratings", Opt. Acta 26, 1427-1441 (1979).
[CrossRef]

Ahlèn, H.

M. Breide, S. Johansson, L. E. Nilsson and H. Ahlèn, "Blazed Holographic Gratings", Opt. Acta 26, 1427-1441 (1979).
[CrossRef]

Berger, V.

V. Berger, O. Gauthier-Lafaye and E. Costard, "Photonic band gaps and holography," J. Appl. Phys. 82, 60-64 (1997).
[CrossRef]

Breide, M.

M. Breide, S. Johansson, L. E. Nilsson and H. Ahlèn, "Blazed Holographic Gratings", Opt. Acta 26, 1427-1441 (1979).
[CrossRef]

Brueck, S. R. J.

S. R. J. Brueck, "Optical and Interferometric Lithography Nanotechnology Enablers," Proc. IEEE 93, 1704 (2005).
[CrossRef]

Campbel, M.

M. Campbel, D. N. Sharp, M. T. Harrison, R. G. Denning and A. J. Turberfield, "Fabrication of photonic crystals for the visible spectrum by holographic lithography," Nature 404, 53-56 (2000).
[CrossRef]

Campbell, M.

D. N. Sharp, M. Campbell, E. R. Dedman, M. T. Harrison, R. G. Denning and A. J. Turberfield, "Photonic crystals for the visible spectrum by holographic lithography," Opt. Quantum Electron. 34, 3-12 (2002).
[CrossRef]

Cescato, L.

F. Quiñónez, J. W. Menezes, V. F. Rodriguez-Esquerre, H. Hernandez-Figueroa, R. D. Mansano and L. Cescato, "Band gap of hexagonal 2D photonic crystals with elliptical holes recorded by interference lithography," Opt. Express 14, 4873-4879 (2006)
[CrossRef] [PubMed]

L. E. Gutierrez-Rivera, E. J. de Carvalho, M. A. Silva and L. Cescato, "Metallic submicrometer sieves fabricated by interferometric lithography and electroforming," J. Micromech. Microeng. 15, 1932-1937 (2005).
[CrossRef]

C. M. B. Cordeiro, A. A. Freschi, L. Li and L. Cescato, "Measurement of phase differences between the diffracted orders of deep relief gratings," Opt. Letters 28, 683-685 (2003).
[CrossRef]

A. A. Freschi, F. J. dos Santos, E. L. Rigon and L. Cescato, "Phase-locking of superimposed diffractive gratings in photoresists," Opt. Commun. 208, 41-49 (2002).
[CrossRef]

B. A. Mello, I. F. Costa, C. R. A. Lima and L. Cescato, "Developed profile of holographically exposed photoresist gratings," Appl. Opt. 34, 597-601 (1995).
[CrossRef]

Cordeiro, C. M. B.

C. M. B. Cordeiro, A. A. Freschi, L. Li and L. Cescato, "Measurement of phase differences between the diffracted orders of deep relief gratings," Opt. Letters 28, 683-685 (2003).
[CrossRef]

Costa, I. F.

Costard, E.

V. Berger, O. Gauthier-Lafaye and E. Costard, "Photonic band gaps and holography," J. Appl. Phys. 82, 60-64 (1997).
[CrossRef]

de Carvalho, E. J.

L. E. Gutierrez-Rivera, E. J. de Carvalho, M. A. Silva and L. Cescato, "Metallic submicrometer sieves fabricated by interferometric lithography and electroforming," J. Micromech. Microeng. 15, 1932-1937 (2005).
[CrossRef]

Dean, K. A.

A. A. Talin, K. A. Dean and J. E. Jaskie, "Field emission displays: a critical review," Solid State Electron. 45, 963-976 (2001).
[CrossRef]

Decker, J. Y.

A. Fernandez, J. Y. Decker, S. M. Herman, D. W. Phillion, D. W. Sweeney and M. D. Perry, "Methods for fabricating arrays of holes using interference lithography," J. Vac. Sci. Technol. B 15, 2439-2443 (1997).
[CrossRef]

Dedman, E. R.

D. N. Sharp, M. Campbell, E. R. Dedman, M. T. Harrison, R. G. Denning and A. J. Turberfield, "Photonic crystals for the visible spectrum by holographic lithography," Opt. Quantum Electron. 34, 3-12 (2002).
[CrossRef]

Denning, R. G.

D. N. Sharp, M. Campbell, E. R. Dedman, M. T. Harrison, R. G. Denning and A. J. Turberfield, "Photonic crystals for the visible spectrum by holographic lithography," Opt. Quantum Electron. 34, 3-12 (2002).
[CrossRef]

M. Campbel, D. N. Sharp, M. T. Harrison, R. G. Denning and A. J. Turberfield, "Fabrication of photonic crystals for the visible spectrum by holographic lithography," Nature 404, 53-56 (2000).
[CrossRef]

dos Santos, F. J.

A. A. Freschi, F. J. dos Santos, E. L. Rigon and L. Cescato, "Phase-locking of superimposed diffractive gratings in photoresists," Opt. Commun. 208, 41-49 (2002).
[CrossRef]

Fainman, Y.

Fernandez, A.

A. Fernandez, J. Y. Decker, S. M. Herman, D. W. Phillion, D. W. Sweeney and M. D. Perry, "Methods for fabricating arrays of holes using interference lithography," J. Vac. Sci. Technol. B 15, 2439-2443 (1997).
[CrossRef]

Freschi, A. A.

C. M. B. Cordeiro, A. A. Freschi, L. Li and L. Cescato, "Measurement of phase differences between the diffracted orders of deep relief gratings," Opt. Letters 28, 683-685 (2003).
[CrossRef]

A. A. Freschi, F. J. dos Santos, E. L. Rigon and L. Cescato, "Phase-locking of superimposed diffractive gratings in photoresists," Opt. Commun. 208, 41-49 (2002).
[CrossRef]

Gauthier-Lafaye, O.

V. Berger, O. Gauthier-Lafaye and E. Costard, "Photonic band gaps and holography," J. Appl. Phys. 82, 60-64 (1997).
[CrossRef]

Gutierrez-Rivera, L. E.

L. E. Gutierrez-Rivera, E. J. de Carvalho, M. A. Silva and L. Cescato, "Metallic submicrometer sieves fabricated by interferometric lithography and electroforming," J. Micromech. Microeng. 15, 1932-1937 (2005).
[CrossRef]

Harrison, M. T.

D. N. Sharp, M. Campbell, E. R. Dedman, M. T. Harrison, R. G. Denning and A. J. Turberfield, "Photonic crystals for the visible spectrum by holographic lithography," Opt. Quantum Electron. 34, 3-12 (2002).
[CrossRef]

M. Campbel, D. N. Sharp, M. T. Harrison, R. G. Denning and A. J. Turberfield, "Fabrication of photonic crystals for the visible spectrum by holographic lithography," Nature 404, 53-56 (2000).
[CrossRef]

Herman, S. M.

A. Fernandez, J. Y. Decker, S. M. Herman, D. W. Phillion, D. W. Sweeney and M. D. Perry, "Methods for fabricating arrays of holes using interference lithography," J. Vac. Sci. Technol. B 15, 2439-2443 (1997).
[CrossRef]

Hernandez-Figueroa, H.

Hsu, C. C.

Jaskie, J. E.

A. A. Talin, K. A. Dean and J. E. Jaskie, "Field emission displays: a critical review," Solid State Electron. 45, 963-976 (2001).
[CrossRef]

Johansson, S.

M. Breide, S. Johansson, L. E. Nilsson and H. Ahlèn, "Blazed Holographic Gratings", Opt. Acta 26, 1427-1441 (1979).
[CrossRef]

Lai, N. D.

Li, L.

C. M. B. Cordeiro, A. A. Freschi, L. Li and L. Cescato, "Measurement of phase differences between the diffracted orders of deep relief gratings," Opt. Letters 28, 683-685 (2003).
[CrossRef]

Liang, W. P.

Lima, C. R. A.

Lin, C. H.

Lin, J. H.

Mack, C. A.

C. A. Mack, "Development of positive photoresists," J. Electrochem. Soc. 134, 148-152 (1987).
[CrossRef]

Mansano, R. D.

Mello, B. A.

Menezes, J. W.

Nakagawa, W.

Nilsson, L. E.

M. Breide, S. Johansson, L. E. Nilsson and H. Ahlèn, "Blazed Holographic Gratings", Opt. Acta 26, 1427-1441 (1979).
[CrossRef]

Pang, L.

Perry, M. D.

A. Fernandez, J. Y. Decker, S. M. Herman, D. W. Phillion, D. W. Sweeney and M. D. Perry, "Methods for fabricating arrays of holes using interference lithography," J. Vac. Sci. Technol. B 15, 2439-2443 (1997).
[CrossRef]

Phillion, D. W.

A. Fernandez, J. Y. Decker, S. M. Herman, D. W. Phillion, D. W. Sweeney and M. D. Perry, "Methods for fabricating arrays of holes using interference lithography," J. Vac. Sci. Technol. B 15, 2439-2443 (1997).
[CrossRef]

Quiñónez, F.

Rigon, E. L.

A. A. Freschi, F. J. dos Santos, E. L. Rigon and L. Cescato, "Phase-locking of superimposed diffractive gratings in photoresists," Opt. Commun. 208, 41-49 (2002).
[CrossRef]

Rodriguez-Esquerre, V. F.

Sharp, D. N.

D. N. Sharp, M. Campbell, E. R. Dedman, M. T. Harrison, R. G. Denning and A. J. Turberfield, "Photonic crystals for the visible spectrum by holographic lithography," Opt. Quantum Electron. 34, 3-12 (2002).
[CrossRef]

M. Campbel, D. N. Sharp, M. T. Harrison, R. G. Denning and A. J. Turberfield, "Fabrication of photonic crystals for the visible spectrum by holographic lithography," Nature 404, 53-56 (2000).
[CrossRef]

Silva, M. A.

L. E. Gutierrez-Rivera, E. J. de Carvalho, M. A. Silva and L. Cescato, "Metallic submicrometer sieves fabricated by interferometric lithography and electroforming," J. Micromech. Microeng. 15, 1932-1937 (2005).
[CrossRef]

Sweeney, D. W.

A. Fernandez, J. Y. Decker, S. M. Herman, D. W. Phillion, D. W. Sweeney and M. D. Perry, "Methods for fabricating arrays of holes using interference lithography," J. Vac. Sci. Technol. B 15, 2439-2443 (1997).
[CrossRef]

Talin, A. A.

A. A. Talin, K. A. Dean and J. E. Jaskie, "Field emission displays: a critical review," Solid State Electron. 45, 963-976 (2001).
[CrossRef]

Turberfield, A. J.

D. N. Sharp, M. Campbell, E. R. Dedman, M. T. Harrison, R. G. Denning and A. J. Turberfield, "Photonic crystals for the visible spectrum by holographic lithography," Opt. Quantum Electron. 34, 3-12 (2002).
[CrossRef]

M. Campbel, D. N. Sharp, M. T. Harrison, R. G. Denning and A. J. Turberfield, "Fabrication of photonic crystals for the visible spectrum by holographic lithography," Nature 404, 53-56 (2000).
[CrossRef]

Appl. Opt. (2)

J. Appl. Phys. (1)

V. Berger, O. Gauthier-Lafaye and E. Costard, "Photonic band gaps and holography," J. Appl. Phys. 82, 60-64 (1997).
[CrossRef]

J. Electrochem. Soc. (1)

C. A. Mack, "Development of positive photoresists," J. Electrochem. Soc. 134, 148-152 (1987).
[CrossRef]

J. Micromech. Microeng. (1)

L. E. Gutierrez-Rivera, E. J. de Carvalho, M. A. Silva and L. Cescato, "Metallic submicrometer sieves fabricated by interferometric lithography and electroforming," J. Micromech. Microeng. 15, 1932-1937 (2005).
[CrossRef]

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

A. Fernandez, J. Y. Decker, S. M. Herman, D. W. Phillion, D. W. Sweeney and M. D. Perry, "Methods for fabricating arrays of holes using interference lithography," J. Vac. Sci. Technol. B 15, 2439-2443 (1997).
[CrossRef]

Nature (1)

M. Campbel, D. N. Sharp, M. T. Harrison, R. G. Denning and A. J. Turberfield, "Fabrication of photonic crystals for the visible spectrum by holographic lithography," Nature 404, 53-56 (2000).
[CrossRef]

Opt. Acta (1)

M. Breide, S. Johansson, L. E. Nilsson and H. Ahlèn, "Blazed Holographic Gratings", Opt. Acta 26, 1427-1441 (1979).
[CrossRef]

Opt. Commun. (1)

A. A. Freschi, F. J. dos Santos, E. L. Rigon and L. Cescato, "Phase-locking of superimposed diffractive gratings in photoresists," Opt. Commun. 208, 41-49 (2002).
[CrossRef]

Opt. Express (3)

Opt. Letters (1)

C. M. B. Cordeiro, A. A. Freschi, L. Li and L. Cescato, "Measurement of phase differences between the diffracted orders of deep relief gratings," Opt. Letters 28, 683-685 (2003).
[CrossRef]

Opt. Quantum Electron. (1)

D. N. Sharp, M. Campbell, E. R. Dedman, M. T. Harrison, R. G. Denning and A. J. Turberfield, "Photonic crystals for the visible spectrum by holographic lithography," Opt. Quantum Electron. 34, 3-12 (2002).
[CrossRef]

Proc. IEEE (1)

S. R. J. Brueck, "Optical and Interferometric Lithography Nanotechnology Enablers," Proc. IEEE 93, 1704 (2005).
[CrossRef]

Solid State Electron. (1)

A. A. Talin, K. A. Dean and J. E. Jaskie, "Field emission displays: a critical review," Solid State Electron. 45, 963-976 (2001).
[CrossRef]

Other (2)

J. D. Joannopoulos, R. D. Meade and J. N. Winn, Photonic Crystals (Princeton University Press, 1995).

L. Cescato and J. Frejlich, Three-Dimensional Holographic Imaging (Wiley-Interscience Publication, 2002), Chap. 3.

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Figures (6)

Fig. 1.
Fig. 1.

Iso-dose light patterns resulting from the superimposition of two single interference fringe patterns rotated of 60° between them.

Fig. 2.
Fig. 2.

Iso-dose light patterns resulting from the superimposition of three interference patterns rotated between them of 60° for a phase shift ϕ 3 =0 (a); ϕ 3 =π/2 (b) and ϕ 3 =π (c).

Fig. 3.
Fig. 3.

Top view of the simulated photoresist structures corresponding to the light patterns shown in Fig. 2(a); (b) and (c) respectively, for the same dose and development time. Each contour line corresponds to the same height of the photoresist structure.

Fig. 4.
Fig. 4.

Photograph of the sample holder showing the angle α and the outside reference ring.

Fig. 5.
Fig. 5.

Photographs of the Moiré-like pattern formed at the diffracted orders. The sequence shows the alignment of the grating with the maximum Moiré-like period corresponding to the best repositioning of the sample. The small curvature of the fringes indicates a small wave front distortion and for the best positioning of the sample that the same phase difference occurs along the whole sample.

Fig. 6.
Fig. 6.

Structures recorded in a positive photoresist on glass substrates using the superimposition of three exposures with rotations of 60° between them and phase-shifts of (a) ϕ3=0, (b) ϕ3=π/2 and (c) ϕ3=π.

Equations (2)

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E R = i = 1 n ( Δ t i ) I Ri
I Ri = 2 I { 1 + cos [ 2 π Λ i ( cos ( α i ) x sin ( α i ) y ) + ϕ i ] }

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