Fabrication of Silicon Inver Woodpile Photonic Crystals
M. Hermatschweiler, M. Wegener
骑虎难下是什么意思DFG-Center for Functional Nanostructures (CFN), Universität Karlsruhe (TH), D-76131 Karlsruhe, Germany
Institut für Angewandte Physik, Universität Karlsruhe (TH), D-76131 Karlsruhe, Germany
步步升迁E-mail: martin.hermatschweiler@physik.uni-karlsruhe.de
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G. A. Ozin
Department of Chemistry, University of Toronto, 80 St. George Street, Toronto, Ontario M5S 3H6, Canada
A. Ledermann, and G. von Freymann
Institut für Nanotechnologie, Forschungszentrum Karlsruhe in der Helmholtz-Gemeinschaft, D-76021 Karlsruhe, Germany
Abstract: We fabricate silicon inver woodpile structures for the first time. Direct lar writing
of polymeric templates and a novel silicon-single-inversion procedure lead to structures with
gap/midgap ratios of 14.2 % centered at 2.5 µm wavelength.
2007 Optical Society of America
OCIS codes:(160.4670) Optical materials; (220.4000) Microstructure fabrication
Soon after the introduction of the concept of photonic band gap materials Ho, Chan, and Soukoulis [1] reported in 1990 that certain structures with diamond-like symmetry can exhibit complete three-dimensional photonic band gaps (PBG). A prominent example of such a “miconductor for light” is the so-called woodpile or logpile structure. It reveals an 18% gap/midgap ratio if fabricated out of silicon with f = 30% volume filling fraction [2].
The inver woodpile structure shows a yet larger gap: For slightly ellipsoidal air rods (aspect ratio 5/肉段的家常做法
4) a gap/midgap ratio of 28% has been predicted theoretically for f = 18 % silicon volume filling fraction [2]. This record is standing.
So far, however, it has not been possible to actually fabricate inver Si woodpiles by any means in any frequency range. In this letter, we realize this important structure by employing direct lar writing of polymeric templates and a subquent silicon-single-inversion procedure (SSI) – which is introduced here for the first time.
In 2006, we introduced the silicon-double-inversion (SDI) procedure [3]: First, polymer templates are fabricated by direct lar writing (DLW) [4] or other means. Unfortunately, the polymeric templates (SU-8) alone do not stand the temperatures required for the infiltration with Si via chemical vapor deposition (CVD). Thus, we introduced an intermediate step, namely the inversion with silica via an atomic-layer-deposition (ALD) process at room temperature [5]. Next, the polymer is removed and Si is deposited in the silica inver structure. Finally, the silica is etched out, leading to a high-quality Si positive replica of the original polymer structure [3].
Fig. 1: Electron micrographs of a Si inver woodpile (LHS) and a silica coated SU-8 woodpile after heating to the
deposition temperature of Si (RHS). Both samples were cut by a focud ion beam to reveal the internal structure and
quality.
Here, we modify the SDI process to SSI: Rather than completely filling the polymer template with silica, we just provide a thin silica coating (Fig. 1, RHS). Next – without removing the polymer – we infiltrate the composite structure with Si via Si CVD. Amazingly, the thin silica coating provides sufficient and reliable stabilization for the high-temperature Si CVD process, in which the polymer melts but keeps its shape due to the silica coating.
Furthermore, the polymer cannot be calcined due to the lack of oxygen. Finally, the silica is etched out and the
三岛由纪夫作品polymer is calcined in air, leading to a Si inver of the previously silica-coated polymeric template (Fig. 1, LHS).
©OSA 1-55752-834-9
Accidentally, the intermediate silica-coating step very favorably reduces the aspect ratio of the elliptical woodpile rods made by DLW as well as the Si volume filling fraction of the final Si inver woodpile structure.
To asss the optical quality of our Si inver structures we have performed optical transmittance and reflectance experiments (Fig. 2, RHS). The instrument ud for this purpo is a commercial microscope Fourier-transform spectrometer. For reference, we u the bare glass substrate and a silver mirror, respectively. A pronounced transmittance dip at around 2.5 µm wavelength is obrved
with a minimum value of less than 10-3. This value is instrument-limited, as confirmed in independent control experiments on thick anodized metal plates (e gray noisy curve in Fig. 2 (RHS)). The structural parameters of the resulting Si inver woodpile are as follows: in-plane rod distance a =0.95 µm, lattice constant c along the stacking direction c = 1.344 µm, rod aspect ratio χ = 1.47, and Si volume filling fraction f = 33.5 %.
To allow for comparison with theory, we have performed band-structure and scattering-matrix calculations for the structural parameters given above. Note that any deposition of solids from gas pha leaves behind small air voids in 3D structures as soon as bottlenecks clo (e Fig. 1, LHS). We accounted for this by introducing a reduced effective Si refractive index n eff = 3.28 instead of the 3.95 for bulk amorphous Si. The resulting band structure shown in Fig. 2 (LHS) is consistent with our optical experiments along the ΓΧ’-direction and reveals a complete 3D PBG with a gap/midgap ratio of 14.2 %. Note, that in order to compare the band structure with experiment we also have to take into account the ΓW’’-direction. In addition, we have also performed scattering-matrix calculations for the sample consisting of 20 layers. We average the reflectance and transmittance data achieved for plane waves impinging onto the samples from different orientations, taking into account angles of incidence between 15 and 30 degrees. This mimics the experimental tup where
a Casgrain objective is ud for focusing light onto the sample. Clearly, the position of the stop band (e gray area in Fig. 2) must not be confud with that of the PBG. The obrved and calculated stop bands agree qualitatively. Deviations are likely due to sample imperfections and/or due to the simplicity of our modeling.
Finally, we have optimized the woodpile design by increasing the lattice constant c by 15 % along the stacking direction relative to fcc translational symmetry. Notably, gap/midgap ratios of up to 20.5 % are within reach.
Fig. 2: Calculated band structure (LHS) of a sample with parameters taken from an FIB cut. A complete 3D PBG with松原美食
14.2 % gap/midgap ratio can be en. On the RHS, scattering-matrix calculations (dashed curves) are compared to
measurements (solid curves). The minimum transmittance is instrument-limited as can be en by comparison of
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transmittance measurements from an opaque sample (gray noi, RHS).
[1] K. M. Ho, C. T. Chan, C. M. Soukoulis, “Existence of a Photonic Band Gap in Periodic Dielectric Structures”, Phys. Rev. Lett. 65,
3152-3155 (1990).
[2] K. M. Ho, C. T. Chan, C. M. Soukoulis, R. Biswas, and M. Sigalas, “Photonic band gaps in three dimensions: New layer-by-layer periodic structures,” Solid State Commun. 89, 413-416 (1994).
[3] N. Tétreault, G. von Freymann, M. Deubel, M. Hermatschweiler, F. Pérez-Willard, S. John, M. We
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gener, and G. A. Ozin, “New route to three-dimensional photonic bandgap materials: Silicon double inversion of polymer templates,” Adv. Mater. 18, 457-460 (2006).
[4] M. Deubel, G. von Freymann, M. Wegener, S. Pereira, K. Busch, and C. M. Soukoulis, “Direct lar writing of three-dimensional photonic-crystal templates for telecommunications,” Nature Mater. 3, 444-447 (2004).
[5] H. Míguez, N. Tétreault, B. Hatton, S. M. Yang, D. Perovic, and G. A. Ozin, “Mechanical stability enhancement by pore size and
connectivity control in colloidal crystals by layer-by-layer growth of oxide,” Chem. Commun., 2736-2737 (2002).
