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)

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]

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]

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

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]

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)

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]

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]

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]

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

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]

Frejlich, J.

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

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]

Joannopoulos, J. D.

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

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.

Meade, R. D.

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

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]

Winn, J. N.

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

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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