Abstract

Near-field nano-patterning greatly simplifies holographic lithography, but deformations in formed structures are potentially severe. A fast and efficient comprehensive model was developed to predict geometry more rigorously. Numerical results show simple intensity-threshold methods do not accurately predict shape or optical behavior. By modeling sources with partial coherence, unpolarized light, and an angular spectrum, it is shown that standard UV lamps can be used to form 3D structures.

© 2005 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Fully three-dimensional modeling of the fabrication and behavior of photonic crystals formed by holographic lithography

Raymond C. Rumpf and Eric G. Johnson
J. Opt. Soc. Am. A 21(9) 1703-1713 (2004)

Designing unit cell in three-dimensional periodic nanostructures using colloidal lithography

Joong-Hee Min, Xu A. Zhang, and Chih-Hao Chang
Opt. Express 24(2) A276-A284 (2016)

Accurate near-field lithography modeling and quantitative mapping of the near-field distribution of a plasmonic nanoaperture in a metal

Yongwoo Kim, Howon Jung, Seok Kim, Jinhee Jang, Jae Yong Lee, and Jae W. Hahn
Opt. Express 19(20) 19296-19309 (2011)

References

  • View by:
  • |
  • |
  • |

  1. John D. Joannopoulos, Robert D. Meade, and Joshua N. Winn, Photonic Crystals, (Princeton University Press, Princeton, New Jersy, 1995).
  2. Y. V. Miklyaev, D. C. Meisel, A. Blanco, G. Freymann, K. Busch, W. Kock, C. Enkrich, M. Deubel, and M. Wegener, “Three-dimensional face-centered-cubic photonic crystal templates by laser holography: fabrication, optical characterization, and band-structure calculations,” Appl. Phys. Lett. 82, 1284–1286 (2003).
    [Crossref]
  3. L. Z. Cai, X. L. Yang, and Y. R. Wang, ”Formation of three-dimensional periodic microstructures by interference of four noncoplanar beams,” J. Opt. Soc. Am. A 19, 2238–2244 (2002).
    [Crossref]
  4. L. Z. Cai, X. L. Yang, and Y. R. Wang, ”All fourteen Bravais lattices can be formed by interference of four noncoplanar beams,” Opt. Lett. 27(11), 900–902 (2002).
    [Crossref]
  5. S. Jeon, G. Wiederrecht, and J. A. Rogers, “Photonic systems formed by proximity field nanopatterning,” in Proceedings of SPIE Micromachining Technology for Micro-Optics and Nano-Optics III5720,E.G. Johnson, ed. (SPIE, Bellingham, WA, 2005), pp. 187–195.
  6. R. C. Rumpf and E. G. Johnson, “Fully three-dimensional modeling of the fabrication and behavior of photonic crystals formed by holographic lithography,” J. Opt. Soc. Am. A 21, 1703–1713 (2004).
    [Crossref]
  7. R. C. Rumpf and E. G. Johnson, “Modeling the formation of photonic crystals by holographic lithography,” in Proceedings of SPIE Micromachining Technology for Micro-Optics and Nano-Optics III5720, E. G. Johnson, ed. (SPIE, Bellingham, WA, 2005), pp. 18–26.
  8. S. Robertson, E. Pavelchek, W. Hoppe, and R. Wildfeuer, “Improved notch model for resist dissolution in lithography simulation,” in Proceedings of SPIE Advances in Resist Technology and Processing XVIII4345, F. M. Houlihan, ed., 912–920 (2001).
  9. M. G. Moharam, E. B. Grann, D. A. Pommet, and T. K. Gaylord, “Formulation for stable and efficient implementation of the rigorous coupled-wave analysis of binary gratings,” J. Opt. Soc. Am. A 12, 1068–1076 (1995).
    [Crossref]
  10. M. G. Moharam, D. A. Pommet, E. B. Grann, and T. K. Gaylord, “Stable implementation of the rigorous coupled-wave analysis for surface-relief gratings: enhanced transmittance matrix approach,” J. Opt. Soc. Am. A 12, 1077–1086 (1995).
    [Crossref]
  11. F. H. Dill, “Positive Optical Lithography,” Conf. IEEE International Solid-State Circuits, 54–55 (1975).
  12. Y. Shacham-Diamond, “Modeling of Novolak-Based Positive Photoresist Exposed to KrF Excimer Laser UV Radiation at 248 nm,” IEEE Trans. Semiconductor Manufacturing3(2), 37–44 (1990).
    [Crossref]
  13. Z. Ling, K. Lian, and L. Jian, “Improved patterning quality of SU-8 microstructures by optimizing the exposure parameters,” in Proceedings of SPIE Advances in Resist Technology and Processing XVII, 1019–1027 (2000).
  14. J. A. Sethian, Level Set Methods and Fast Marching Methods: Evolving interfaces in computational geometry, fluid mechanics, computer vision, and materials science, (Cambridge University Press, New York, New York, 1999).
  15. “The SU-8 photoresist for MEMS,” http://aveclafaux.freeservers.com/SU-8.html.
  16. EXFO Application Note 088, “High Power UV Light Sources,” (EXFO, 2005) http://www.exfo-uv.com/App Notes/High Power UV Light Sources.pdf.
  17. MicroChem Product Data Sheet for SU-8 2007, “NANOTM SU-8 2000 Negative Tone Photoresist Formulations 2002-2025,” (MicroChem, 2005), http://www.microchem.com/.

2004 (1)

2003 (1)

Y. V. Miklyaev, D. C. Meisel, A. Blanco, G. Freymann, K. Busch, W. Kock, C. Enkrich, M. Deubel, and M. Wegener, “Three-dimensional face-centered-cubic photonic crystal templates by laser holography: fabrication, optical characterization, and band-structure calculations,” Appl. Phys. Lett. 82, 1284–1286 (2003).
[Crossref]

2002 (2)

1995 (2)

Blanco, A.

Y. V. Miklyaev, D. C. Meisel, A. Blanco, G. Freymann, K. Busch, W. Kock, C. Enkrich, M. Deubel, and M. Wegener, “Three-dimensional face-centered-cubic photonic crystal templates by laser holography: fabrication, optical characterization, and band-structure calculations,” Appl. Phys. Lett. 82, 1284–1286 (2003).
[Crossref]

Busch, K.

Y. V. Miklyaev, D. C. Meisel, A. Blanco, G. Freymann, K. Busch, W. Kock, C. Enkrich, M. Deubel, and M. Wegener, “Three-dimensional face-centered-cubic photonic crystal templates by laser holography: fabrication, optical characterization, and band-structure calculations,” Appl. Phys. Lett. 82, 1284–1286 (2003).
[Crossref]

Cai, L. Z.

Deubel, M.

Y. V. Miklyaev, D. C. Meisel, A. Blanco, G. Freymann, K. Busch, W. Kock, C. Enkrich, M. Deubel, and M. Wegener, “Three-dimensional face-centered-cubic photonic crystal templates by laser holography: fabrication, optical characterization, and band-structure calculations,” Appl. Phys. Lett. 82, 1284–1286 (2003).
[Crossref]

Dill, F. H.

F. H. Dill, “Positive Optical Lithography,” Conf. IEEE International Solid-State Circuits, 54–55 (1975).

Enkrich, C.

Y. V. Miklyaev, D. C. Meisel, A. Blanco, G. Freymann, K. Busch, W. Kock, C. Enkrich, M. Deubel, and M. Wegener, “Three-dimensional face-centered-cubic photonic crystal templates by laser holography: fabrication, optical characterization, and band-structure calculations,” Appl. Phys. Lett. 82, 1284–1286 (2003).
[Crossref]

Freymann, G.

Y. V. Miklyaev, D. C. Meisel, A. Blanco, G. Freymann, K. Busch, W. Kock, C. Enkrich, M. Deubel, and M. Wegener, “Three-dimensional face-centered-cubic photonic crystal templates by laser holography: fabrication, optical characterization, and band-structure calculations,” Appl. Phys. Lett. 82, 1284–1286 (2003).
[Crossref]

Gaylord, T. K.

Grann, E. B.

Hoppe, W.

S. Robertson, E. Pavelchek, W. Hoppe, and R. Wildfeuer, “Improved notch model for resist dissolution in lithography simulation,” in Proceedings of SPIE Advances in Resist Technology and Processing XVIII4345, F. M. Houlihan, ed., 912–920 (2001).

Jeon, S.

S. Jeon, G. Wiederrecht, and J. A. Rogers, “Photonic systems formed by proximity field nanopatterning,” in Proceedings of SPIE Micromachining Technology for Micro-Optics and Nano-Optics III5720,E.G. Johnson, ed. (SPIE, Bellingham, WA, 2005), pp. 187–195.

Jian, L.

Z. Ling, K. Lian, and L. Jian, “Improved patterning quality of SU-8 microstructures by optimizing the exposure parameters,” in Proceedings of SPIE Advances in Resist Technology and Processing XVII, 1019–1027 (2000).

Joannopoulos, John D.

John D. Joannopoulos, Robert D. Meade, and Joshua N. Winn, Photonic Crystals, (Princeton University Press, Princeton, New Jersy, 1995).

Johnson, E. G.

R. C. Rumpf and E. G. Johnson, “Fully three-dimensional modeling of the fabrication and behavior of photonic crystals formed by holographic lithography,” J. Opt. Soc. Am. A 21, 1703–1713 (2004).
[Crossref]

R. C. Rumpf and E. G. Johnson, “Modeling the formation of photonic crystals by holographic lithography,” in Proceedings of SPIE Micromachining Technology for Micro-Optics and Nano-Optics III5720, E. G. Johnson, ed. (SPIE, Bellingham, WA, 2005), pp. 18–26.

Kock, W.

Y. V. Miklyaev, D. C. Meisel, A. Blanco, G. Freymann, K. Busch, W. Kock, C. Enkrich, M. Deubel, and M. Wegener, “Three-dimensional face-centered-cubic photonic crystal templates by laser holography: fabrication, optical characterization, and band-structure calculations,” Appl. Phys. Lett. 82, 1284–1286 (2003).
[Crossref]

Lian, K.

Z. Ling, K. Lian, and L. Jian, “Improved patterning quality of SU-8 microstructures by optimizing the exposure parameters,” in Proceedings of SPIE Advances in Resist Technology and Processing XVII, 1019–1027 (2000).

Ling, Z.

Z. Ling, K. Lian, and L. Jian, “Improved patterning quality of SU-8 microstructures by optimizing the exposure parameters,” in Proceedings of SPIE Advances in Resist Technology and Processing XVII, 1019–1027 (2000).

Meade, Robert D.

John D. Joannopoulos, Robert D. Meade, and Joshua N. Winn, Photonic Crystals, (Princeton University Press, Princeton, New Jersy, 1995).

Meisel, D. C.

Y. V. Miklyaev, D. C. Meisel, A. Blanco, G. Freymann, K. Busch, W. Kock, C. Enkrich, M. Deubel, and M. Wegener, “Three-dimensional face-centered-cubic photonic crystal templates by laser holography: fabrication, optical characterization, and band-structure calculations,” Appl. Phys. Lett. 82, 1284–1286 (2003).
[Crossref]

Miklyaev, Y. V.

Y. V. Miklyaev, D. C. Meisel, A. Blanco, G. Freymann, K. Busch, W. Kock, C. Enkrich, M. Deubel, and M. Wegener, “Three-dimensional face-centered-cubic photonic crystal templates by laser holography: fabrication, optical characterization, and band-structure calculations,” Appl. Phys. Lett. 82, 1284–1286 (2003).
[Crossref]

Moharam, M. G.

Pavelchek, E.

S. Robertson, E. Pavelchek, W. Hoppe, and R. Wildfeuer, “Improved notch model for resist dissolution in lithography simulation,” in Proceedings of SPIE Advances in Resist Technology and Processing XVIII4345, F. M. Houlihan, ed., 912–920 (2001).

Pommet, D. A.

Robertson, S.

S. Robertson, E. Pavelchek, W. Hoppe, and R. Wildfeuer, “Improved notch model for resist dissolution in lithography simulation,” in Proceedings of SPIE Advances in Resist Technology and Processing XVIII4345, F. M. Houlihan, ed., 912–920 (2001).

Rogers, J. A.

S. Jeon, G. Wiederrecht, and J. A. Rogers, “Photonic systems formed by proximity field nanopatterning,” in Proceedings of SPIE Micromachining Technology for Micro-Optics and Nano-Optics III5720,E.G. Johnson, ed. (SPIE, Bellingham, WA, 2005), pp. 187–195.

Rumpf, R. C.

R. C. Rumpf and E. G. Johnson, “Fully three-dimensional modeling of the fabrication and behavior of photonic crystals formed by holographic lithography,” J. Opt. Soc. Am. A 21, 1703–1713 (2004).
[Crossref]

R. C. Rumpf and E. G. Johnson, “Modeling the formation of photonic crystals by holographic lithography,” in Proceedings of SPIE Micromachining Technology for Micro-Optics and Nano-Optics III5720, E. G. Johnson, ed. (SPIE, Bellingham, WA, 2005), pp. 18–26.

Sethian, J. A.

J. A. Sethian, Level Set Methods and Fast Marching Methods: Evolving interfaces in computational geometry, fluid mechanics, computer vision, and materials science, (Cambridge University Press, New York, New York, 1999).

Shacham-Diamond, Y.

Y. Shacham-Diamond, “Modeling of Novolak-Based Positive Photoresist Exposed to KrF Excimer Laser UV Radiation at 248 nm,” IEEE Trans. Semiconductor Manufacturing3(2), 37–44 (1990).
[Crossref]

Wang, Y. R.

Wegener, M.

Y. V. Miklyaev, D. C. Meisel, A. Blanco, G. Freymann, K. Busch, W. Kock, C. Enkrich, M. Deubel, and M. Wegener, “Three-dimensional face-centered-cubic photonic crystal templates by laser holography: fabrication, optical characterization, and band-structure calculations,” Appl. Phys. Lett. 82, 1284–1286 (2003).
[Crossref]

Wiederrecht, G.

S. Jeon, G. Wiederrecht, and J. A. Rogers, “Photonic systems formed by proximity field nanopatterning,” in Proceedings of SPIE Micromachining Technology for Micro-Optics and Nano-Optics III5720,E.G. Johnson, ed. (SPIE, Bellingham, WA, 2005), pp. 187–195.

Wildfeuer, R.

S. Robertson, E. Pavelchek, W. Hoppe, and R. Wildfeuer, “Improved notch model for resist dissolution in lithography simulation,” in Proceedings of SPIE Advances in Resist Technology and Processing XVIII4345, F. M. Houlihan, ed., 912–920 (2001).

Winn, Joshua N.

John D. Joannopoulos, Robert D. Meade, and Joshua N. Winn, Photonic Crystals, (Princeton University Press, Princeton, New Jersy, 1995).

Yang, X. L.

Appl. Phys. Lett. (1)

Y. V. Miklyaev, D. C. Meisel, A. Blanco, G. Freymann, K. Busch, W. Kock, C. Enkrich, M. Deubel, and M. Wegener, “Three-dimensional face-centered-cubic photonic crystal templates by laser holography: fabrication, optical characterization, and band-structure calculations,” Appl. Phys. Lett. 82, 1284–1286 (2003).
[Crossref]

J. Opt. Soc. Am. A (4)

Opt. Lett. (1)

Other (11)

S. Jeon, G. Wiederrecht, and J. A. Rogers, “Photonic systems formed by proximity field nanopatterning,” in Proceedings of SPIE Micromachining Technology for Micro-Optics and Nano-Optics III5720,E.G. Johnson, ed. (SPIE, Bellingham, WA, 2005), pp. 187–195.

R. C. Rumpf and E. G. Johnson, “Modeling the formation of photonic crystals by holographic lithography,” in Proceedings of SPIE Micromachining Technology for Micro-Optics and Nano-Optics III5720, E. G. Johnson, ed. (SPIE, Bellingham, WA, 2005), pp. 18–26.

S. Robertson, E. Pavelchek, W. Hoppe, and R. Wildfeuer, “Improved notch model for resist dissolution in lithography simulation,” in Proceedings of SPIE Advances in Resist Technology and Processing XVIII4345, F. M. Houlihan, ed., 912–920 (2001).

John D. Joannopoulos, Robert D. Meade, and Joshua N. Winn, Photonic Crystals, (Princeton University Press, Princeton, New Jersy, 1995).

F. H. Dill, “Positive Optical Lithography,” Conf. IEEE International Solid-State Circuits, 54–55 (1975).

Y. Shacham-Diamond, “Modeling of Novolak-Based Positive Photoresist Exposed to KrF Excimer Laser UV Radiation at 248 nm,” IEEE Trans. Semiconductor Manufacturing3(2), 37–44 (1990).
[Crossref]

Z. Ling, K. Lian, and L. Jian, “Improved patterning quality of SU-8 microstructures by optimizing the exposure parameters,” in Proceedings of SPIE Advances in Resist Technology and Processing XVII, 1019–1027 (2000).

J. A. Sethian, Level Set Methods and Fast Marching Methods: Evolving interfaces in computational geometry, fluid mechanics, computer vision, and materials science, (Cambridge University Press, New York, New York, 1999).

“The SU-8 photoresist for MEMS,” http://aveclafaux.freeservers.com/SU-8.html.

EXFO Application Note 088, “High Power UV Light Sources,” (EXFO, 2005) http://www.exfo-uv.com/App Notes/High Power UV Light Sources.pdf.

MicroChem Product Data Sheet for SU-8 2007, “NANOTM SU-8 2000 Negative Tone Photoresist Formulations 2002-2025,” (MicroChem, 2005), http://www.microchem.com/.

Supplementary Material (1)

» Media 1: AVI (847 KB)     

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 (9)

Fig. 1.
Fig. 1.

(850 kb) Movie of near-field nano-patterning process.

Fig. 2.
Fig. 2.

(a) Phase grating design. (b) Spectral orders diffracted from grating.

Fig. 3.
Fig. 3.

Output of comprehensive model at various stages of simulation. Units are in nanometers. (a) Aerial image where blue represents most intense field. (b) Latent image where blue represents most absorbed energy. (c) Dissolution rate where black represents highest solubility. (d) Unit cell of photonic crystal.

Fig. 4.
Fig. 4.

Transmission and reflection spectra through 10 layers of photonic crystal. One layer is shown. (a) Comprehensive model. (b) Intensity-threshold model.

Fig. 5.
Fig. 5.

Approximation of “unpolarized” light source. LPx represents linear polarization in the x direction. LPy represents linear polarization in the y direction. CP indicates circular polarization.

Fig. 6.
Fig. 6.

Near-field nano-patterning using partially coherent light. (a) Typical i-line profile. (b) Bottom 10 μm of 100 μm film.

Fig. 7.
Fig. 7.

Near-field nano-patterning using unfiltered light from typical mercury-vapor lamp. (a) Overlay of lamp spectrum [16] and SU-8 absorption coefficient [13,17]. (b) Normalized weighted lamp spectrum after propagating through different thicknesses of SU-8. Weighted spectrum is defined as the product of absorption coefficient with irradiance. (c) Output of each stage of comprehensive simulation using unfiltered light.

Fig. 8.
Fig. 8.

Impact of angular spectrum. (a) Assumed angular spectrum. (b) Aerial images and lattices in 10 μm film.

Fig. 9.
Fig. 9.

Parametric curves for limiting angular spectrum. L min is smallest feature size that must be resolved.

Equations (18)

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

k m , n x = k inc x + ( m g 1 + n g 2 ) x ̂
k m , n y = k inc y + ( m g 1 + n g 2 ) y ̂
k i , m , n z = { k 0 2 ε i ( k m , n x ) 2 ( k m , n y ) 2 k 0 2 ε i ( k m , n x ) 2 + ( k m , n y ) 2 j ( k m , n x ) 2 + ( k m , n y ) 2 k 0 2 ε i k 0 2 ε i < ( k m , n x ) 2 + ( k m , n y ) 2
ξ ( r ) = α ( r ) I ( r ) T .
g ( r ) = 1 2 π ρ eff 2 exp ( r 2 2 ρ eff 2 )
Δ x′ = ( 1 s xx ) Δ x Δy = ( 1 s yy ) Δ y Δz = ( 1 s zz ) Δ z
R ( E ¯ ) = R max ( 1 E ¯ ) N [ ( a n + 1 ) ( 1 E ¯ ) N notch a n + ( 1 E ¯ ) N notch ] + R min [ R min E ¯ 1 R max E ¯ 1 ] [ 1 ( a n + 1 ) ( 1 E ¯ ) N notch a n + ( 1 E ¯ ) N notch ]
a n = N notch + 1 N notch 1 ( 1 E ¯ th ) N notch
T ( x , y , z ) R ( x , y , z ) = 1
max 2 ( D x , D x + , 0 ) + max 2 ( D y , D y + , 0 ) + max 2 ( D z , D z + , 0 ) = 1 / R i , j , k 2
D x = ( T i , j , k T i 1 , j , k ) / Δ x D x + = ( T i + 1 , j , k T i , j , k ) / Δ x
D y = ( T i , j , k T i , j 1 , k ) / Δy D y + = ( T i , j + 1 , k T i , j , k ) / Δ y
D z = ( T i , j , k T i , j , k 1 ) / Δz D z + = ( T i , j , k + 1 T i , j , k ) / Δ z
( T i , j , k new m x Δ x ) 2 + ( T i , j , k new m y Δ y ) 2 + ( T i , j , k new m z Δ z ) 2 = 1 R i , j , k 2
m x = min ( T i 1 , j , k , T i + 1 , j , k , T i , j , k old )
m y = min ( T i , j 1 , k , T i , j + 1 , k , T i , j , k old )
m z = min ( T i , j , k 1 , T i , j , k + 1 , T i , j , k old )
θ BW < n L min T

Metrics