OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 21, Iss. 9 — Sep. 1, 2004
  • pp: 1703–1713

Fully three-dimensional modeling of the fabrication and behavior of photonic crystals formed by holographic lithography

Raymond C. Rumpf and Eric G. Johnson  »View Author Affiliations

JOSA A, Vol. 21, Issue 9, pp. 1703-1713 (2004)

View Full Text Article

Enhanced HTML    Acrobat PDF (996 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



A comprehensive and fully three-dimensional model of holographic lithography is used to predict more rigorously the geometry and transmission spectra of photonic crystals formed in Epon® SU-8 photoresist. It is the first effort known to the authors to incorporate physics of exposure, postexposure baking, and developing into three-dimensional models of photonic crystals. Optical absorption, reflections, standing waves, refraction, beam coherence, acid diffusion, resist shrinkage, and developing effects combine to distort lattices from their ideal geometry. These are completely neglected by intensity-threshold methods used throughout the literature to predict lattices. Numerical simulations compare remarkably well with experimental results for a face-centered-cube (FCC) photonic crystal. Absorption is shown to produce chirped lattices with broadened bandgaps. Reflections are shown to significantly alter lattice geometry and reduce image contrast. Through simulation, a diamond lattice is formed by multiple exposures, and a hybrid trigonal–FCC lattice is formed that exhibits properties of both component lattices.

© 2004 Optical Society of America

OCIS Codes
(050.0050) Diffraction and gratings : Diffraction and gratings
(090.0090) Holography : Holography

Original Manuscript: November 21, 2003
Revised Manuscript: March 18, 2004
Manuscript Accepted: March 18, 2004
Published: September 1, 2004

Raymond C. Rumpf and Eric 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)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys. Rev. Lett. 58, 2059–2062 (1987). [CrossRef] [PubMed]
  2. S. John, “Strong localization of photons in certain disordered dielectric superlattices,” Phys. Rev. Lett. 58, 2486–2489 (1987). [PubMed]
  3. M. J. A. Dood, A. Polman, J. G. Fleming, “Modified spontaneous emission from erbium-doped, photonic, layer-by-layer crystals,” Phys. Rev. B 67, 115106 (2003).
  4. M. A. Kaliteevski, J. M. Martinez, D. Cassagne, J. P. Albert, “Appearance of photonic minibands in disordered photonic crystals,” J. Phys. Condens. Matter 15, 785–790 (2003).
  5. A. Mekis, J. C. Chen, I. Kurland, S. Fan, P. R. Villeneuve, J. D. Joannopoulos, “High transmission through sharp bends in photonic crystal waveguides,” Phys. Rev. Lett. 77, 3787–3790 (1996). [PubMed]
  6. T. Baba, N. Fukaya, J. Yonekura, “Observation of light propagation in photonic crystal optical waveguides with bends,” Electron. Lett. 35, 654–655 (1999).
  7. A. Talneau, L. Gouezigou, N. Bouadma, M. Kafesaki, C. M. Soukoulis, M. Agio, “Photonic-crystal ultrashort bends with improved transmission and low reflection at 1.55 μm,” Appl. Phys. Lett. 80, 547–549 (2002).
  8. T. D. Engeness, M. Ibanescu, S. G. Johnson, O. Weisberg, M. Skorobogatiy, S. Jacobs, Y. Fink, “Dispersion tailoring and compensation by modal interactions in OmniGuide fibers,” Opt. Express11, 1175–1196 (2003); www.opticsexpress.org . [PubMed]
  9. D. R. Solli, C. F. McCormick, R. Y. Chiao, J. M. Hickmann, “Experimental observation of superluminal group velocities in bulk two-dimensional photonic bandgap crystals,” IEEE J. Sel. Top. Quantum Electron. 9, 40–42 (2003).
  10. C. Luo, S. G. Johnson, J. D. Joannopoulos, “Negative refraction without negative index in metallic photonic crystals,” Opt. Express 11, 746–754 (2003). [PubMed]
  11. D. M. Chambers, G. P. Nordin, S. Kim, “Fabrication and analysis of a three-layer stratified volume diffractive optical element high-efficiency grating,” Opt. Express 11, 27–38 (2003). [PubMed]
  12. C. Cuisin, A. Chelnokov, J. M. Lourtioz, D. Decanini, Y. Chen, “Fabrication of three-dimensional photonic crystal structures with submicrometer resolution by x-ray lithography,” J. Vac. Sci. Technol. B 18, 3505–3509 (2000).
  13. Y. V. Miklyaev, D. C. Meisel, A. Blanco, G. Freymann, K. Busch, W. Kock, C. Enkrich, M. Deubel, 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).
  14. C. K. Ullal, M. Maldovan, M. Wohlgemuth, E. L. Thomas, C. A. White, S. Yang, “Triply periodic bicontinuous structures through interference lithography: a level-set approach,” J. Opt. Soc. Am. A 20, 948–954 (2003).
  15. T. J. Suleski, B. Baggett, W. F. Delaney, C. Koehler, E. G. Johnson, “Fabrication of high-spatial-frequency gratings through computer-generated near-field holography,” Opt. Lett. 24, 602–604 (1999).
  16. G. Witzgall, R. Vrijen, E. Yablonovitch, V. Doan, B. J. Schwartz, “Single-shot two-photon exposure of commercial photoresist for the production of three-dimensional structures,” Opt. Lett. 23, 1745–1747 (1998).
  17. Y. Ono, K. Ikemoto, “Fabrication of three-dimensional photonic crystals by holographic lithography,” in Diffractive Optics and Micro-Optics, Vol. 75 of OSA Technical Digest Series (Optical Society of America, Washington, D.C., 2002), pp. 205–207.
  18. X. L. Yang, L. Z. Cai, Q. Liu, “Theoretical bandgap modeling of two-dimensional triangular photonic crystals formed by interference technique of three noncoplanar beams,” Opt. Express11, 1050–1055 (2003); www.opticsexpress.org . [PubMed]
  19. A. Feigel, Z. Kotler, B. Sfez, “Scalable interference lithography alignment for fabrication of three-dimensional photonic crystals,” Opt. Lett. 27, 746–748 (2002).
  20. A. Yen, E. H. Anderson, R. A. Ghanbari, M. L. Schattenburg, H. I. Smith, “Achromatic holographic configuration for 100-nm-period lithography,” Appl. Opt. 31, 4540–4545 (1992). [PubMed]
  21. L. Z. Cai, X. L. Yang, 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]
  22. Y. Ono, K. Ikemoto, “Fabrication of arbitrary three-dimensional photonic crystals by four plane-waves interference,” in Micromachining Technology for Micro-optics and Nano-optics, E. G. Johnson, ed., Proc. SPIE4984, 70–78 (2003). [CrossRef]
  23. L. Z. Cai, X. L. Yang, Y. R. Wang, “All fourteen Bravais lattices can be formed by interference of four noncoplanar beams,” Opt. Lett. 27, 900–902 (2002). [CrossRef]
  24. J. M. Shaw, J. D. Gelorme, N. C. LaBianca, W. E. Conley, S. J. Holmes, “Negative photoresists for optical lithography,” IBM J. Res. Dev. 41, 81–94 (1997). [CrossRef]
  25. I. R. Matias, I. Villar, F. J. Arregui, R. O. Claus, “Comparative study of the modeling of three-dimensional photonic bandgap structures,” J. Opt. Soc. Am. A 20, 644–654 (2003). [CrossRef]
  26. A. Chutinan, S. Noda, “Effects of structural fluctuations on the photonic bandgap during fabrication of a photonic crystal,” J. Opt. Soc. Am. B 16, 240–244 (1999). [CrossRef]
  27. S. Fan, P. R. Villeneuve, J. D. Joannopoulos, “Theoretical investigation of fabrication-related disorder on the properties of photonic crystals,” J. Appl. Phys. 78, 1415–1418 (1995). [CrossRef]
  28. R. C. Rumpf, E. G. Johnson, “Micro-photonic systems utilizing SU-8,” in MOEMS and Miniaturized Systems IV, A. El-Fatatry, ed., Proc. SPIE5346, 64–72 (2004). [CrossRef]
  29. K. Busch, S. John, “Photonic band gap formation in certain self-organizing systems,” Phys. Rev. E 58, 3896–3908 (1998). [CrossRef]
  30. C. Xiaolan, S. H. Zaidi, S. R. J. Brueck, “Multiple exposure interference lithography—a novel approach to nanometer structures,” in Conference on Lasers and Electro-Optics, Vol. 9 of 1996 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1996), pp. 390–391.
  31. S. C. Kitson, W. L. Barnes, J. R. Sambles, “The fabrication of submicron hexagonal arrays using multiple-exposure optical interferometry,” IEEE Photonics Technol. Lett. 8, 1662–1664 (1996). [CrossRef]
  32. A. Taflove, S. C. Hagness, Computational Electrodynamics: the Finite-Difference Time-Domain Method, 2nd ed. (Artech House, Norwood, Mass., 2000).
  33. D. M. Sullivan, Electromagnetic Simulation Using the FDTD Method (Wiley–IEEE Press, Piscataway, N.J., 2000).
  34. A. Erdmann, C. Kalus, T. Schmoller, A. Wolter, “Efficient simulation of light diffraction from three-dimensional EUV masks using field decomposition techniques,” in Emerging Lithographic Technologies VII, R. L. Engelstad, ed., Proc. SPIE5037, 482–493 (2003). [CrossRef]
  35. A. Erdmann, N. Kachwala, “Enhancements in rigorous simulation of light diffraction from phase shift masks,” in Optical Microlithography XV, A. Yen, ed., Proc. SPIE4691, 1156–1167 (2002). [CrossRef]
  36. A. Vial, A. Erdmann, T. Schmoeller, C. Kalus, “Modification of boundary conditions in the FDTD algorithm for EUV masks modeling,” in Photomask and Next-Generation Lithography Mask Technology IX, H. Kawahira, ed., Proc. SPIE4754, 890–899 (2002). [CrossRef]
  37. Ref. 32, pp. 194–224.
  38. Ref. 33, pp. 85–89.
  39. Z. Ling, K. Lian, L. Jian, “Improved patterning quality of SU-8 microstructures by optimizing the exposure parameters,” in Advances in Resist Technology and Processing XVII, F. M. Houlihan, ed., Proc. SPIE3999, 1019–1027 (2000). [CrossRef]
  40. C. A. Balanis, Advanced Engineering Electromagnetics (Wiley, New York, 1989), pp. 28–32.
  41. A. Erdmann, W. Henke, S. Robertson, E. Richter, B. Tollkuhn, W. Hoppe, “Comparison of simulation approaches for chemically amplified resists,” in Lithography for Semiconductor Manufacturing II, C. A. Mack, T. Stevenson, eds., Proc. SPIE4404, 99–110 (2001). [CrossRef]
  42. J. G. Proakis, D. G. Manolakis, Digital Signal Processing (Prentice Hall, Englewood Cliffs, N.J., 1996), pp. 425–433.
  43. S. Robertson, E. Pavelchek, W. Hoppe, R. Wildfeuer, “Improved notch model for resist dissolution in lithography simulation,” in Advances in Resist Technology and Processing XVIII, F. M. Houlihan, ed., Proc. SPIE4345, 912–920 (2001). [CrossRef]
  44. “The SU-8 photoresist for MEMS,” http://aveclafaux.freeservers.com/SU-8.html .
  45. M. Khan, S. B. Bollepalli, F. Cerrina, “A semi-empirical resist dissolution model for submicron lithographies,” in MSM98: Technical Proceedings of the 1998 International Conference on Modeling and Simulation of Microsystems (Applied Computational Research Society, http://www.cr.org/index.html .), pp. 41–46.
  46. J. Malov, C. K. Kalus, H. Mullerke, T. Schmoller, R. Wildfeuer, “Accuracy of new analytical models for resist formation lithography,” in Optical Microlithography XV, A. Yen, ed., Proc. SPIE4691, 1254–1265 (2002). [CrossRef]
  47. R. E. Jewett, P. I. Hagouel, A. R. Neureuther, T. Duzer, “Line-profile resist development simulation techniques,” Polym. Eng. Sci. 17, 381–384 (1977). [CrossRef]
  48. I. Karafyllidis, P. I. Hagouel, A. Thanailakis, A. R. Neureuther, “An efficient photoresist development simulator based on cellular automata with experimental verification,” IEEE Trans. Semicond. Manuf. 13, 61–75 (2000). [CrossRef]
  49. E. W. Scheckler, N. N. Tam, A. K. Pfau, A. R. Neureuther, “An efficient volume-removal algorithm for practical three-dimensional lithography simulation with experimental verification,” IEEE Trans. Comput.-Aided Des. 12, 1345–1356 (1993). [CrossRef]
  50. Y. Hirai, S. Tomida, K. Ikeda, M. Sasago, M. Endo, S. Hayama, N. Nomura, “Three-dimensional resist process simulator PEACE (photo and electron beam lithography analyzing computer engineering system),” IEEE Trans. Comput.-Aided Des. 10, 802–807 (1991). [CrossRef]
  51. F. H. Dill, A. R. Neureuther, J. A. Tuttle, E. J. Walker, “Modeling projection printing of positive photoresists,” IEEE Trans. Electron Devices 22, 456–464 (1975). [CrossRef]
  52. S. D. Burns, G. M. Schmid, P. C. Tsiartas, C. G. Willson, L. Flanagin, “Advancements to the critical ionization dissolution model,” J. Vac. Sci. Technol. B 20, 537–543 (2002). [CrossRef]
  53. I. S. Maksymov, G. I. Churyumov, “2D computer modeling of waveguiding in 2D photonic crystals,” in Proceedings of Fourth Laser and Fiber Optical Networks Modeling Conference (Institute of Electrical and Electronics Engineers, New York, 2002), pp. 181–184.
  54. Ref. 29, pp. 614–616.
  55. B. Denecker, F. Olyslager, D. Zutter, L. Klinkenbusch, L. Knockaert, “Efficient analysis of photonic crystal structures using a novel FDTD-technique,” IEEE Trans. Antennas Propag. 4, 344–347 (2002).
  56. R. W. Ziolkowski, M. Tanaka, “Finite-difference time-domain modeling of dispersive-material photonic bandgap structures,” J. Opt. Soc. Am. A 16, 930–940 (1999). [CrossRef]
  57. R. M. Ridder, R. Stoffer, “Finite-difference time-domain modeling of photonic crystal structures,” in Proceedings of 2001 Third International Conference on Transparent Optical Networks (Institute of Electrical and Electronics Engineers, New York, 2001), pp. 22–25.
  58. Ref. 32, pp. 411–472.
  59. S. Dey, R. Mittra, “A locally conformal finite-difference time-domain algorithm for modeling three-dimensional perfectly conducting objects,” IEEE Microwave Guid. Wave Lett. 7, 273–275 (1997). [CrossRef]
  60. S. Dey, R. Mittra, “A modified locally conformal finite-difference time-domain algorithm for modeling three-dimensional perfectly conducting objects,” IEEE Microwave Opt. Tech. Lett. 17, 349–352 (1997). [CrossRef]
  61. S. Dey, R. Mittra, “A conformal finite-difference time-domain technique for modeling cylindrical dielectric resonators,” IEEE Trans. Microwave Theory Tech. 47, 1737–1739 (1999). [CrossRef]
  62. Ref. 29, p. 427.
  63. Ref. 29, pp. 413–415.
  64. P. Lalanne, “Effective medium theory applied to photonic crystals composed of cubic or square cylinders,” Appl. Opt. 35, 5369–5380 (1996). [CrossRef] [PubMed]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited