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One-dimensional diffractive optical element based fabrication and spectral characterization of three-dimensional photonic crystal templates Debashis Chandaa), Ladan Abolghasemi, Peter R. Herman Department of Electrical and Computer Engineering and Institute for Optical Sciences, University of Toronto Toronto, Ontario, Canada, M5S 3G4, Tel: 1-416-9787039, Fax: 1- 416- 9713020 [email protected])

Abstract: We demonstrate improved fabrication precision and provide the first spectral characterization of Woodpile-type photonic crystal templates formed by one-dimensional diffractive optical elements. The threedimensional periodic structures were produced in thick resist by sequential exposures of two orthogonal diffractive optical elements with an argon-ion laser. The observed crystal motif is shown to closely match the isointensity surfaces predicted by the interfering diffracted beams. Nearinfrared spectroscopic observations reveal the presence of both low and high energy photonic stopbands that correspond with theoretical predictions in several crystal directions. Numerous high-energy stop bands are further reported along very narrow crystallographic angles that attest to the high periodicity and uniformity of the crystal motif through the full resist thickness and over the large sample area. The optical characterization demonstrates the precise control and facile means of diffractive-opticalelement based holographic lithography in fabricating large-area threedimensional photonic crystal templates, defining a promising medium for infiltration with high-refractive-index materials to create photonic bandgap devices. ©2006 Optical Society of America OCIS codes: (090.0090) Holography; (110.5220) Photolithography; (260.3160) Interference; (220.4000) Microstructure fabrication

References and links 1. 2. 3. 4. 5. 6. 7. 8.

S. Lin, J. Flemming, D. Hetherington, B. Smith, R. Biswas, K. Hot, M. Sigalas, W. Zubrycki, S. Kurtz, and J. Bur, “A three-dimensional photonic crystal operating at infrared wavelengths,” Nature 394, 251253 (1998). S. Noda, K. Tomoda, N. Yamamoto, and A. Chutinan, “Full three-dimensional Photonic Bandgap Crystals at Near-Infrared Wavelengths,” Science 289, 604-606 (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). N. Tétreault, G. von Freymann, G. A. Ozin, “New route to three-dimensional Photonic Bandgap Materials: Silicon Double Inversion of Polymer Templates,” Adv. Mater. 18, 457-460 (2006). S. Shoji and S. Kawata, “Photofabrication of three-dimensional photonic crystals by multibeam laser interference into a photopolymerizable resin,” Appl. Phys. Lett. 76, 2668-2670 (2000). I. Divliansky, T. S. Mayer, K. S. Holliday, and V. H. Crespi, “Fabrication of three-dimensional polymer photonic crystal structures using single diffraction element interference lithography,” Appl. Phys Lett. 82, 1667-1669 (2003). 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,” PNAS 101, 12429 -12434 (2004). 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, 071117-071119 (2005).

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(C) 2006 OSA

Received 7 August 2006; revised 6 September 2006; accepted 10 September 2006

18 September 2006 / Vol. 14, No. 19 / OPTICS EXPRESS 8568

9.

D. Chanda, L. Abolghasemi, and P. Herman, “Diffractive optical elements based fabrication of photonic crystals,” in Conference on Lasers and Electro-Optics 2006 Technical Digest (Optical Society of America, Washington, DC, 2006), CMV7. 10. K. M. Ho, C. T. Chen, C. M. Soukoulis, R. Biswas, M. Sigalas, “Photonic Band Gaps in three dimensions: New layer-by-layer periodic structures,” Solid State Commun. 89, 413-416 (1994). 11. O. Toader, and S. John, Ph D thesis, University of Toronto, (2003). 12. C. T. Chan, S. Datta, K. M. Ho and C. M. Soukoulis, “A7 structure: A family of photonic crystals,” Phys. Rev. B 50, 1988-1991 (1994). 13. D. Chanda, L. Abolghasemi, and P. Herman, “Numerical band calculation of holographically formed periodic structures with irregular motif,” in Photonic Crystal Materials and Devices IV, A. Adibi, S.-Yu Lin, and A. Scherer, eds., Proc. SPIE 6128, 311-316 (2006). 14. 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). 15. M. Deubel, G. von Freymann, M. Wegener, S. Pereira, K. Busch, M. Soukoulis, “Direct laser writing of three-dimensional photonic-crystal templates for telecommunications,” Nat. Mater. 3, 444–447 (2004). ______________________________________________________________________________________________

1. Introduction Large-scale three-dimensional (3-D) micro-fabrication of photonic crystals using standard semiconductor lithographic technology remain tedious and costly [1,2], prompting development of lower-cost and simpler fabrication approaches. Laser holographic lithography (HL) is one such promising approach first introduced in 2000 by Campbell et al. [3] that generates photonic crystal templates by interference of multiple laser beams inside photosensitive media. Such low index media can be infiltrated [4] with high refractive index materials to form a complete photonic bandgap device. In this way, 3-D HL is the critical processing step offering advantages of rapid parallel 3-D imprinting, control of filling fraction, and flexible shaping of motif by means of tuning the relative beam intensities, polarizations, intercepting angles, and light source wavelength [3,5,6]. However, multi-beam HL requires stable and vibration-free alignment of multiple beam-splitting and steering optical components during the exposure. A diffractive optical element (DOE) is a promising alternative device for 3-D HL where one DOE creates multiple laser beams in various diffraction orders that are inherently phase-locked and stable for reproducible creation of 3-D interference patterns from a single laser beam. Rogers and coworkers [7] demonstrated the formation of various 3-D periodic nanostructures in thick photoresist using conformal phasemask DOEs. Our group was first to extend DOEs to the fabrication of 3-D photonic crystal templates , creating “Woodpile”-type structures in SU-8 photoresist by two sequential exposures of orthogonal one-dimensional DOEs (1D-DOE) with an Ar-ion laser [8, 9]. In this DOE approach, control parameters such as grating period, duty cycle and laser wavelength determine the periodic crystal structure while etch depth, laser intensity, polarization and photoresist threshold define the filling fraction and motif that together enables a wide variety of 3-D photonic crystal structures to be formed. The present paper builds on this sequential DOE-exposure method [8,9] by improving the fabrication precision of “Woodpile”-type photonic crystal templates and, for the first time, spectroscopically characterizing the templates to verify their 3-D structure against energy band models. Section 2 provides a theoretical guideline for fabricating “Woodpile”-type photonic crystal templates by sequential DOE laser exposures. Detail DOE design criteria are presented, for the first time, for creating templates that will support a complete stopband after inversion with high index media. Section 3 describes the formation of 3-D templates in SU-8 photoresist with telecom-quality 1D-DOEs. Thick, large-area periodic nano-structures are confirmed to have “Woodpile”-type structure closely matching the computed optical interference iso-intensity surfaces. In Section 4, spectroscopic characterization of the templates reveals numerous low and high energy stopbands along preferential crystallographic directions that are consistent with calculated band dispersion curves for the low-index media. The results demonstrate good structural uniformity through a relatively large resist thickness and over large exposure area.

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Received 7 August 2006; revised 6 September 2006; accepted 10 September 2006

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2. DOE design criteria In this section a general theoretical guideline for fabricating “Woodpile”-type photonic crystal templates by the double-exposure 1D-DOE method is presented. Laser exposure conditions and DOE design parameters are outlined for creating stable 3-D photonic crystal templates with wide bandgaps. 2.1. DOE-generated interference patterns Normal Incidence Laser Beam

Λ

DOE (nd)

d Incidence Medium (ni)

Resist (nr)

m = -1

.

m = +1

m=0

Fig. 1. Formation of multiple diffracted beams from a single laser beam by a 1-D DOE and arrangement for photoresist exposure.

Figure 1 shows the separation of an incident laser beam into m = +1st, 0th, and -1st diffraction orders after passing through a 1D-DOE of period, Λ. In the overlap volume immediately below the DOE, the diffracted beams interfere to create a 2-D log-pile type interference pattern as shown in Fig. 2(a). After solving interference equations it can be shown that the lateral and vertical periodicities of this structure are

a = Λ

and

λd / nr

c = 1−

1−

λd

2

,

(1)

(nr Λ )2

respectively, where λd is the free-space laser wavelength illuminating the DOE, and nr is the refractive index of the photoresist medium in which the interference occurs as shown in Fig. 1. Note that the refractive index of the DOE, nd, and the incidence medium, ni, do not affect the periodicity of the interference pattern. The 2-D periodic interference pattern can be accurately captured with a thick (>>c) negative photoresist placed in the beam overlap region of Fig. 1 and by applying a laser exposure that just exceeds the photo-polymerization threshold of the photoresist. Post exposure development then solidifies the polymerized volume and dissolves the under-exposed volume to replicate the interference pattern. A positive photoresist will generate an inverted structure to that shown in Fig. 2(a). To create a 3-D periodic structure, the first 1D-DOE exposure [Fig. 2(a)] is followed by a second exposure with an identical but orthogonal 1D-DOE, creating the rotated 2-D log-pile intensity pattern show in Fig. 2(b). The combination of two sequential exposures then yields an intensity pattern approximately described by the interlaced 3-D “Woodpile”-type structure as shown in Fig. 2(c). Although the figure depicts uniform elliptical-like cross-sections with asymmetric radii, Rx and Rz, as defined, the sum of two interference patterns are more complex than shown. A more precise representation of the intensity distribution can be easily generated with numerical computations that account for laser polarization together with the

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Received 7 August 2006; revised 6 September 2006; accepted 10 September 2006

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diffraction efficiencies and angles that depend on the groove depth and DOE period. The final structure of the photoresist is further governed by complex relations between laser exposure dose, photoresist exposure threshold, shrinkage and chemical diffusion.

a)

b)

c)

a c

Fig. 2. Periodic interference laser patterns created by (a) a single exposure with a 1DDOE, (b) a single exposure with a similar 1D-DOE rotated by 900, and (c) the resulting interlaced 3-D “Woodpile”-type structure due to combination of the two exposures in (a) and (b).

2.2. Interlacing of log-pile structures To form a stable interconnected “Woodpile”-type structure [Fig. 2(c)] that does not collapse on development, the two log patterns in Figs. 2(a) and 2(b) must be physically offset with displacement, S, while also having sufficient axial cross-section, Rz, defined in Fig. 2(c), that conservatively satisfy: c c (2) R z ≥ , a n d ( − 2 R z ) ≤ S ≤ 2 R z ; ∀{ R z , c} , 8 2 While Rz is defined by the laser exposure, the S offset requires precise alignment stages to vary the resist-to-DOE gap, d (see Fig. 1), used in each of the orthogonal DOE exposures. Rz = c/8 defines the lowest exposure threshold at which Eq. (2) demands an exact quarter period offset of S = c/4, while any offset value is acceptable for Rz > c/4. 2.3. Controlling structure dimensions A complete photonic bandgap in “Woodpile”-type structures is available only in a narrow range of axial-to-transverse periodicity ratios, c/a, that further depends on the refractive index of dielectric medium and the filling fraction [10, 11]. For example, a “Woodpile”-type structure made with dielectric material n = 3.45 will provide a complete photonic bandgap only for the range 0.6 < c/a < 2.1 for a given filling fraction of 26% [10, 11]. DOEs provide wide latitude here for varying the c/a ratio and thereby optimizing the bandgap properties. According to Eq. (1), c/a depends principally on the DOE period, refractive index of the photoresist, and laser wavelength, and is plotted in Fig. 3 as a function of the normalized wavelength, λd/Λ, for SU-8 photoresist (nr = 1.6). To produce a template offering a wide bandgap (after inversion), near-symmetric periodic structures with near unity c/a ratio are required. According to Fig. 2, this can be achieved with a small period DOE such that Λ ~ λd. However, this condition yields high diffraction angles for the first order beams that will only propagate inside the DOE substrate for periods larger than the optical wavelength, Λ > λd/nd. Total internal reflection at either of the DOE-incidence medium or the incidence mediumresist interfaces (Fig. 1) impose additional constraints of Λ > λd/ni and Λ > λd/nr, respectively, that together limit the valid range of the c/a data in Fig. 3 to a minimum value defined by the normalized wavelength

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Received 7 August 2006; revised 6 September 2006; accepted 10 September 2006

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λd

Λ

≤ m in {n d , n i , n r } ;

∀

c ≥1 a

(3)

By substituting this limit into Eq. (1), one obtains the minimum c/a value, for example, identified by the X-marks in Fig. 3, for different incidence media and assuming nd > ni. For air (ni =1), one can generate a minimum c/a ratio of only 2.85. Alternatively, in the limit of using an index matching fluid with ni = nr = 1.6, one obtains a symmetric periodic structure (c/a =1).

ni =1

X

ni =1.3 X n =1.6 X i

λd/Λ Fig. 3. Variation of c/a ratio in SU-8 photoresist (nr = 1.6) with normalized wavelength ,λd /Λ, for different refractive index values of the incidence medium (ni). To access the full c/a range of 1 ≤ c/a ≤ ∞, the refractive index of DOE (nd) and the incidence medium (ni) must exceed the refractive index of the photoresist and this has been expressed in Eq. (4). c (4) {nd , ni} ≥ nr ; 1 ≤ ≤ ∞ a Larger ni and nr values are attractive to reduce Fresnel losses, but c/a = 1 is the minimum ratio available by this DOE method for any value of nr. 2.4. Bandgap optimization From the ongoing development, it is evident that with suitable selection of optical materials and DOE design, a stable interconnected 3-D “Woodpile”-type structure can be fabricated by double-exposure based 1D-DOE holographic lithography. While such “Woodpile”-type structures can be classified as face centered cubic (FCC) or tetragonal (TTR) lattice symmetry [12, 11], the TTR irreducible Brillouin zone is known to be more appropriate symmetry [12, 11] for “Woodpile”-type structures and hence we base our band dispersion calculations on TTR symmetry. To determine the band positions, band dispersion curves were calculated for DOE-HL structured templates using the plane wave expansion (PWE) method as previously described in [13]. Calculations were carried out over a wide range of c/a ratios (1 < c/a < 3) and laser exposure levels (filling fractions of 10%