Abstract

We present a quantitative study of the distortion from a three-term diamond-like structure fabricated in SU8 polymer by four-beam holographic lithography. In the study of the refraction effect, theory suggests that the lattice in SU8 should be elongated in the [111] direction but have no distortion in the (111) plane, and each triangular-like hole array in the (111) plane would rotate by ~30° away from that in air. Our experiments agree with the prediction on the periodicity in the (111) plane and the rotation due to refraction effect, however, we find that the film shrinkage during lithographic process has nearly compensated the predicted elongation in the [111] direction. In study of photonic bandgap (PBG) properties of silicon photonic crystals templated by the SU8 structure, we find that the distortion has decreased quality of PBG.

© 2007 Optical Society of America

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    [CrossRef] [PubMed]
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  35. D. C. Meisel, M. Wegener, and K. Busch, "Three-dimensional photonic crystals by holographic lithography using the umbrella configuration: Symmetries and complete photonic band gaps," Phys. Rev. B 70, 165104 (2004).
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2007

M. Thiel, M. Decker, M. Deubel, M. Wegener, S. Linden, and G. von Freymann, "Polarization stop bands in chiral polymeric three-dimensional photonic crystals," Adv. Mater. 19, 207-210 (2007).
[CrossRef]

S. R. Marder, J. L. Bredas, and J. W. Perry, "Materials for multiphoton 3D microfabrication," MRS Bull. 32, 561-565 (2007).
[CrossRef]

J. H. Moon, Y. Xu, Y. Dan, S. M. Yang, A. T. Johnson, and S. Yang, "Triply periodic bicontinuous structures as templates for photonic crystals: A pinch-off problem," Adv. Mater. 19, 1510-1514 (2007).
[CrossRef]

W. Haske, V. W. Chen, J. M. Hales, W. T. Dong, S. Barlow, S. R. Marder, and J. W. Perry, "65 nm feature sizes using visible wavelength 3-D multiphoton lithography," Opt. Express 15, 3426-3436 (2007).
[CrossRef] [PubMed]

J. Xu, R. Ma, X. Wang, and W. Y. Tam, "Icosahedral quasicrystals for visible wavelengths by optical interference holography," Opt. Express 15, 4287-4295 (2007).
[CrossRef] [PubMed]

2006

J. S. King, E. Graugnard, O. M. Roche, D. N. Sharp, J. Scrimgeour, R. G. Denning, A. J. Turberfield, and C. J. Summers, "Infiltration and inversion of holographically defined polymer photonic crystal templates by atomic layer deposition," Adv. Mater. 18, 1561-1565. (2006).
[CrossRef]

Y. Lin, D. Rivera, and K. P. Chen, "Woodpile-type photonic crystals with orthorhombic or tetragonal symmetry formed through phase mask techniques," Opt. Express 14, 887-892 (2006).
[CrossRef] [PubMed]

J. H. Moon, S. Yang, W. T. Dong, J. W. Perry, A. Adibi, and S. M. Yang, "Core-shell diamond-like silicon photonic crystals from 3D polymer templates created by holographic lithography," Opt. Express 14, 6297-6302 (2006).
[CrossRef] [PubMed]

T. Y. M. Chan, O. Toader, and S. John, "Photonic band-gap formation by optical-phase-mask lithography," Phys. Rev. E 73, 046610 (2006).
[CrossRef]

J. H. Moon, J. Ford, and S. Yang, "Fabricating three-dimensional polymer photonic structures by multi-beam interference lithography," Polym. Adv. Technol. 17, 83-93 (2006).
[CrossRef]

D. C. Meisel, M. Diem, M. Deubel, F. Perez-Willard, S. Linden, D. Gerthsen, K. Busch, and M. Wegener, "Shrinkage precompensation of holographic three-dimensional photonic-crystal templates," Adv. Mater. 18, 2964-2968 (2006).
[CrossRef]

2005

Y. Lin, P. R. Herman, and K. Darmawikarta, "Design and holographic fabrication of tetragonal and cubic photonic crystals with phase mask: toward the mass-production of three-dimensional photonic crystals," Appl. Phys. Lett. 86, 071117 (2005).
[CrossRef]

Y. C. Zhong, S. A. Zhu, H. M. Su, H. Z. Wang, J. M. Chen, Z. H. Zeng, and Y. L. Chen, "Photonic crystal with diamondlike structure fabricated by holographic lithography," Appl. Phys. Lett. 87, 061103 (2005).
[CrossRef]

Y. K. Lin, and P. R. Herman, "Effect of structural variation on the photonic band gap in woodpile photonic crystal with body-centered-cubic symmetry," J. Appl. Phys. 98, 063104 (2005).
[CrossRef]

T. Y. M. Chan, O. Toader, and S. John, "Photonic band gap templating using optical interference lithography," Phys. Rev. E 71, 046605 (2005).
[CrossRef]

T. Kondo, S. Juodkazis, and H. Misawa, "Reduction of capillary force for high-aspect ratio nanofabrication," Appl. Phys. A 81, 1583-1586 (2005).
[CrossRef]

K. K. Seet, V. Mizeikis, S. Matsuo, S. Juodkazis, and H. Misawa, "Three-dimensional spiral-architecture photonic crystals obtained by direct laser writing," Adv. Mater. 17, 541-545 (2005).
[CrossRef]

W. D. Mao, J. W. Dong, Y. C. Zhong, G. Q. Liang, and H. Z. Wang, "Formation principles of two-dimensional compound photonic lattices by one-step holographic lithography," Opt. Express 13, 2994-2999 (2005).
[CrossRef] [PubMed]

2004

G. M. Gratson, M. Xu, and J. A. Lewis, "Microperiodic structures - Direct writing of three-dimensional webs" Nature 428, 386 (2004).
[CrossRef] [PubMed]

S. Jeon, J.-U. Park, R. Cirelli, S. Yang, C. E. Heitzman, P. V. Braun, P. J. A. Kenis, and J. A. Rogers, "Fabricating complex three-dimensional nanostructures with high-resolution conformable phase masks," Proc. Nat. Acad. Sci. USA 101, 12428-12433 (2004).
[CrossRef] [PubMed]

C. K. Ullal, M. Maldovan, E. L. Thomas, G. Chen, Y. J. Han, and S. Yang, "Photonic crystals through holographic lithography: Simple cubic, diamond-like, and gyroid-like structures," Appl. Phys. Lett. 84, 5434-5436 (2004).
[CrossRef]

D. C. Meisel, M. Wegener, and K. Busch, "Three-dimensional photonic crystals by holographic lithography using the umbrella configuration: Symmetries and complete photonic band gaps," Phys. Rev. B 70, 165104 (2004).
[CrossRef]

2003

Y. V. Miklyaev, D. C. Meisel, A. Blanco, G. von Freymann, K. Busch, W. Koch, 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]

Y. Akahane, T. Asano, B. S. Song, and S. Noda, "High-Q photonic nanocavity in a two-dimensional photonic crystal," Nature 425, 944-947 (2003).
[CrossRef] [PubMed]

T. Prasad, V. Colvin, and D. Mittleman, "Superprism phenomenon in three-dimensional macroporous polymer photonic crystals," Phys. Rev. B 67, 165103 (2003).
[CrossRef]

P. V. Parimi, W. T. T. Lu, P. Vodo, and S. Sridhar, "Photonic crystals - Imaging by flat lens using negative refraction," Nature 426, 404-404 (2003).
[CrossRef] [PubMed]

C. K. Ullal, M. Maldovan, M. Wohlgemuth, E. L. Thomas, C. A. White, and S. Yang, "Triply periodic bicontinuous structures through interference lithography: a level-set approach," J. Opt. Soc. Am. A 20, 948-954 (2003).
[CrossRef]

2002

S. R. Kennedy, M. J. Brett, O. Toader, and S. John, "Fabrication of tetragonal square spiral photonic crystals," Nano Lett. 2, 59-62 (2002).
[CrossRef]

W. H. Zhou, S. M. Kuebler, K. L. Braun, T. Y. Yu, J. K. Cammack, C. K. Ober, J. W. Perry, and S. R. Marder, "An efficient two-photon-generated photoacid applied to positive-tone 3D microfabrication," Science 296, 1106-1109 (2002).
[CrossRef] [PubMed]

S. Yang, M. Megens, J. Aizenberg, P. Wiltzius, P. M. Chaikin, and W. B. Russel, "Creating periodic three-dimensional structures by multibeam interference of visible laser," Chem. Mater. 14, 2831-2833 (2002).
[CrossRef]

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, 900-902 (2002).
[CrossRef]

R. L. Sutherland, V. P. Tondiglia, L. V. Natarajan, S. Chandra, D. Tomlin, and T. J. Bunning, "Switchable orthorhombic F photonic crystals formed by holographic polymerization-induced phase separation of liquid crystal," Opt. Express 10, 1074-1082 (2002).
[PubMed]

2001

S. G. Johnson, and J. D. Joannopoulos, "Block-iterative frequency-domain methods for Maxwell's equations in a planewave basis," Opt. Express 8, 173-190 (2001).
[CrossRef] [PubMed]

Y. A. Vlasov, X. Z. Bo, J. C. Sturm, and D. J. Norris, "On-chip natural assembly of silicon photonic bandgap crystals," Nature 414, 289-293 (2001).
[CrossRef] [PubMed]

A. C. Edrington, A. M. Urbas, P. DeRege, C. X. Chen, T. M. Swager, N. Hadjichristidis, M. Xenidou, L. J. Fetters, J. D. Joannopoulos, Y. Fink, and E. L. Thomas, "Polymer-based photonic crystals," Adv. Mater. 13, 421-425 (2001).
[CrossRef]

2000

M. Campbell, 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] [PubMed]

1999

A. Chutinan and S. Noda, "Highly confined waveguides and waveguide bends in three-dimensional photonic crystal," Appl. Phys. Lett. 75, 3739-3741 (1999).
[CrossRef]

1998

S. Y. Lin, J. G. Fleming, D. L. Hetherington, B. K. Smith, R. Biswas, K. M. Ho, M. M. Sigalas, W. Zubrzycki, S. R. Kurtz, and J. Bur, "A three-dimensional photonic crystal operating at infrared wavelengths," Nature 394, 251-253 (1998).
[CrossRef]

1997

H. Lorenz, M. Despont, N. Fahrni, N. LaBianca, P. Renaud, and P. Vettiger, "SU-8: a low-cost negative resist for MEMS," J. Micromech. Microeng. 7, 121-124 (1997).
[CrossRef]

1996

A. Mekis, J. C. Chen, I. Kurland, S. H. Fan, P. R. Villeneuve, and J. D. Joannopoulos, "High transmission through sharp bends in photonic crystal waveguides," Phys. Rev. Lett. 77, 3787-3790 (1996).
[CrossRef] [PubMed]

1994

J. P. Dowling, M. Scalora, M. J. Bloemer, and C. M. Bowden, "The photonic band edge laser: a new approach to gain enhancement," J. Appl. Phys. 75, 1896-1899 (1994).
[CrossRef]

1987

E. Yablonovitch, "Inhibited spontaneous emission in solid-state physics and electronics," Phys. Rev. Lett. 58, 2059-2062 (1987).
[CrossRef] [PubMed]

S. John, "Strong localization of photons in certain disordered dielectric superlattices," Phys. Rev. Lett. 58, 2486-2489 (1987).
[CrossRef] [PubMed]

Adibi, A.

Aizenberg, J.

S. Yang, M. Megens, J. Aizenberg, P. Wiltzius, P. M. Chaikin, and W. B. Russel, "Creating periodic three-dimensional structures by multibeam interference of visible laser," Chem. Mater. 14, 2831-2833 (2002).
[CrossRef]

Akahane, Y.

Y. Akahane, T. Asano, B. S. Song, and S. Noda, "High-Q photonic nanocavity in a two-dimensional photonic crystal," Nature 425, 944-947 (2003).
[CrossRef] [PubMed]

Asano, T.

Y. Akahane, T. Asano, B. S. Song, and S. Noda, "High-Q photonic nanocavity in a two-dimensional photonic crystal," Nature 425, 944-947 (2003).
[CrossRef] [PubMed]

Barlow, S.

Biswas, R.

S. Y. Lin, J. G. Fleming, D. L. Hetherington, B. K. Smith, R. Biswas, K. M. Ho, M. M. Sigalas, W. Zubrzycki, S. R. Kurtz, and J. Bur, "A three-dimensional photonic crystal operating at infrared wavelengths," Nature 394, 251-253 (1998).
[CrossRef]

Blanco, A.

Y. V. Miklyaev, D. C. Meisel, A. Blanco, G. von Freymann, K. Busch, W. Koch, 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]

Bloemer, M. J.

J. P. Dowling, M. Scalora, M. J. Bloemer, and C. M. Bowden, "The photonic band edge laser: a new approach to gain enhancement," J. Appl. Phys. 75, 1896-1899 (1994).
[CrossRef]

Bo, X. Z.

Y. A. Vlasov, X. Z. Bo, J. C. Sturm, and D. J. Norris, "On-chip natural assembly of silicon photonic bandgap crystals," Nature 414, 289-293 (2001).
[CrossRef] [PubMed]

Bowden, C. M.

J. P. Dowling, M. Scalora, M. J. Bloemer, and C. M. Bowden, "The photonic band edge laser: a new approach to gain enhancement," J. Appl. Phys. 75, 1896-1899 (1994).
[CrossRef]

Braun, K. L.

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Figures (8)

Scheme 1.
Scheme 1.

Flow chart illustrating the step-by-step theoretical analysis.

Scheme 2.
Scheme 2.

Schematic illustration of light propagation from air to the dielectric medium.

Scheme 3.
Scheme 3.

Schematic illustration of the four-beam HL in the umbrella configuration.

Fig. 1.
Fig. 1.

Level surfaces of (a) three-term diamond-like structure in air described by Eq. (14), tair =0, the filling fraction of dielectric materials is 50%, and (b) distorted SU8 structure described by Eq. (15), t SU8=0, the filling fraction of SU8 is 48%. All surfaces belong to the {100} family planes. The unit length on the 3D frame of (a) is d/2, where the lattice constant, d=1.38 µm, and that of (b) is d’/2, and d’=1.78 µm. Insets: corresponding unit cells.

Fig. 2.
Fig. 2.

Level surfaces of (a) three-term diamond-like structure in air with filling fraction of the dielectric materials as 50% [Eq. (14), t air=0], and (b) distorted SU8 structure with the filling fraction of SU8 as 48% [Eq. (15), t SU8=0]. In both images, the top surface is the (111) plane, the left side is the (112) plane, and the right side is the (110) plane. The unit length in the 3D frames: d=1.38 µm. Insets: 2D cut of the top surfaces.

Fig. 3.
Fig. 3.

(a) Close-up SEM image of the fabricated SU8 structure with the top surface tilted by 30°. The cross-section is FIB milled perpendicular to the (111) plane. The green dotted lines indicate four adjacent (111) lattice planes. Taking into account the viewing angle (60°), the distance between the adjacent lattice planes in the [111] direction is h 111=0.81 µm. The top (111) plane is partially melted by the ion beam. Inset: the (111) plane before FIB milling. (b) Distorted SU8 structure described by Eq. (18) with a filling fraction of 48% (t’ SU8=0) by considering both refraction and film shrinkage. The top surface is the (111) plane, the left one is the (112⃗) plane, and the right one is the (1⃗10) plane. The unit length of the frame is d=1.38 µm. Inset: the unit cell. (c) The bottom layer of the SU8 structure. (d) 2D cut of the (111) plane from Fig. 3(b).

Fig. 4.
Fig. 4.

High-symmetry points of the Brillouin zone of the distorted structure [Eq. (15) and (18)] belonged to space group No.155 (R32).

Fig. 5.
Fig. 5.

PBG maps of silicon PCs templated from (a) three-term diamond-like structure [Eq.(14)] and (b) distorted structure by taking into account of both refraction and film shrinkage [Eq.(18)]. Insets: quality factor vs. filling fraction. Black lines: the gap between the second and third band, and blue lines: the gap between the seventh and eighth band. d fcc=1.38µm and c 0 is the light velocity in vacuum.

Tables (2)

Tables Icon

Table 1. Wave vectors and polarization vectors in air and SU8 using interference lithography with visible light (λ=532 nm).

Tables Icon

Table 2. Lattice parameters for the interference patterns in air and in SU8. (c = /d and d = 1.38µm.)

Equations (26)

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t = ( E ' E ) = 2 cos θ cos θ ' + n r cos θ
t = ( E ' E ) = 2 cos θ cos θ + n r cos θ '
E ' = E ' + E ' = [ E ' x , E ' y , E ' z ]
I ( r ) = l = 0 N 1 m = 0 N 1 E l · E m * exp [ i ( k l k m ) · r ]
I ( r ) = I 0 + 2 l , m = 0 l < m 3 { Re ( E l · E m * ) cos [ ( k l k m ) · r ] Im ( E l · E m * ) sin [ ( k l k m ) · r ] }
E 0 = E 0 2 a ̂ ± i E 0 2 b ̂
E j in A = E j ( E j . k 0 k 0 ) k 0 k 0
E 0 · E j * = E 0 2 E j in A ( cos [ θ j ] ± i sin [ θ j ] )
Re ( E 0 · E j * ) cos [ ( k 0 k j ) · r ] Im ( E 0 · E j * ) sin [ ( k 0 k j ) · r ]
= E 0 2 E j in A cos [ ( k 0 k j ) · r ± θ j ]
I ( r ) = I 0 + 2 { i = 1 3 E 0 2 E i in A cos [ ( k 0 k i ) · r ± θ i ] + i , j = 1 i < j 3 ( E i · E j ) cos [ ( k i k j ) · r ] }
( k 0 k i ) · ( r + ρ ) ± θ i = ( k 0 k i ) · ( r + j = 1 3 θ j η j ) ± θ i = ( k 0 k i ) · r θ i ± θ i = ( k 0 k i ) · r
( k i k j ) · ( r + ρ ) = ( k i k j ) · r + [ ( k 0 k j ) ( k 0 k i ) ] · s = 1 3 θ s η s = ( k i k j ) · r α i j
I ( r ) = I 0 + 2 * { i = 1 3 E 0 2 E i in A cos [ ( k 0 k i ) · r ] + i , j = 1 i < j 3 ( E i · E j ) cos [ ( k i k j ) · r α i j ] }
F air ( r ) = cos [ 2 π d ( x + y + z ) ] + cos [ 2 π d ( x y + z ) ] + cos⁡ [ 2 π d ( x + y z ) ]
F SUB ( r ) = cos [ 2 π d ( 1.140 x + 0.860 y + 0.860 z ) ] + cos [ 2 π d ( 0.860 x 1.140 y + 0.860 z ) ]
+ cos [ 2 π d ( 0.860 x + 0.860 y 1.140 z ) ] + 0.301 cos [ 2 π d · 2 ( x y ) π 3 ]
+ 0.301 cos [ 2 π d · 2 ( y z ) π 3 ] + 0.301 cos [ 2 π d · 2 ( z x ) π 3 ]
F ( r ) > t for dielectric , and F ( r ) < t for air
F SU 8 ( r r ) = cos ( 2 π d x r ) + cos ( 2 π d y r ) + cos ( 2 π d z r )
+ v { cos [ 2 π d ( x r y r ) ] + cos [ 2 π d ( y r z r ) ] + cos [ 2 π d ( z r x r ) ] }
q { sin [ 2 π d ( x r y r ) ] + sin [ 2 π d ( y r z r ) ] + sin [ 2 π d ( z r x r ) ] }
A ˜ 100 No . 155 + v A ˜ 1 1 × 0 No . 155 q B ˜ 1 1 ¯ 0 No . 155
F ' SUB ( r ) = cos [ 2 π d ( 1.006 x + 0.994 y + 0.994 z ) ] + cos [ 2 π d ( 0.994 x 1.006 y + 0.994 z ) ]
+ cos [ 2 π d ( 0.994 x + 0.994 y 1.006 z ) ] + 0.301 cos [ 2 π d · 2 ( x y ) π 3 ]
+ 0.301 cos [ 2 π d · 2 ( y z ) π 3 ] + 0.301 cos [ 2 π d · 2 ( z x ) π 3 ]

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