Photonic hyperuniform networks by silicon double inversion of polymer templates
Nicolas Muller, Jakub Haberko, Catherine Marichy, Frank Scheffold
PPhotonic hyperuniform networks by silicon double inversion ofpolymer templates
Nicolas Muller, Jakub Haberko, Catherine Marichy, and Frank Scheffold ∗ Department of Physics, University of Fribourg, CH-1700 Fribourg, Switzerland Faculty of Physics and Applied Computer Science,AGH University of Science and Technology,al. Mickiewicza 30, 30-059 Krakow, Poland Universit´e de Lyon, Laboratoire des Multimat´eriauxet Interfaces, Villeurbanne Cedex, France, 69622
Abstract
Hyperuniform disordered networks belong to a peculiar class of structured materials predicted topossess partial and complete photonic bandgaps for relatively moderate refractive index contrasts.The practical realization of such photonic designer materials is challenging however, as it requirescontrol over a multi-step fabcrication process on optical length scales. Here we report the direct-laser writing of hyperuniform polymeric templates followed by a silicon double inversion procedureleading to high quality network structures made of polycrystalline silicon. We observe a pronouncedgap in the shortwave infrared centered at a wavelength of λ Gap (cid:39) µ m, in nearly quantitativeagreement with numerical simulations. In the experiments the typical structural length scale ofthe seed pattern can be varied between 2 µ m and 1.54 µ m leading to a blue-shift of the gapaccompanied by an increase of the silicon volume filling fraction. Keywords: Photonic bandgap materials; Photonic crystals; Scattering a r X i v : . [ phy s i c s . op ti c s ] A ug NTRODUCTION
Photonic crystal structures have drawn a lot of attention over the last two decades butthe routine design of full bandgap materials in three dimensions for optical wavelengthshas proven elusive [1–7]. Recently, disordered and isotropic photonic materials have beensuggested as an alternative [8–13]. A hyperuniform structure combined with short rangeorder and an open network architecture is widely considered to be a strong candidate foran optimized photonic material design [10, 11, 14]. Moreover the isotropic structure shouldoffer additional advantages such as the possibility to incorporate waveguides with arbitrarybending angles [15–17]. Numerical calculations in two and three dimensions suggest thepresence of a full photonic bandgap in the near infrared if the material is made out of siliconwith an refractive index n (cid:39) . , n (cid:39) . ETHODSDirect laser writing (DLW)
Polymeric templates on the mesoscale are then fabricated using a commercially availabledirect-laser writing (DLW) system (Photonic Professional GT, Nanoscribe GmbH, Germany)in Dip-In configuration. [25, 26] The structures are written on infrared transparent CaF substrates (Crystan, UK) by dipping an oil-immersion objective (63x, NA=1.4) inside aliquid negative-tone photoresist (IP-DIP, Nanoscribe GmbH, Germany). One should notethat the writing process is started in a virtual depth of approximately 0 . µ m inside the glasssubstrate to guarantee a continuous laser writing process along the axial direction which isnecessary to ensure the adhesion of the polymer template to the substrate. The actual heightof the structures is thus reduced by 0 . µ m as well. The highest resolution is achieved bytuning the laser power close to the photopolymerization threshold of the photoresist. Thephotopolymerized samples are developed in two successive baths of PGMEA (Propyleneglycol monomethyl ether acetate) for twice 10 min and consecutively rinsed in a bath ofisopropanol for 8 min. Gentle drying is ensured by redirecting a stream of N through abubbler filled with isopropanol onto the sample. Massive square walls are written aroundeach structure to improve the mechanical stability during the development procedure andthe post-processing. Silicon double inversion
The DLW produced polymeric HU structures are infiltrated with ZnO using atomic layerdeposition (ALD). The depositions is carried out in a commercial ALD reactor (Savannah100, Cambridge Nanotech, Inc.) operating in exposure mode at a moderate temperature of110 ◦ C. Slow heating and cooling ramps are set in order to prevent thermal degradation ofthe polymer structure. Diethylzinc (Strem Chemicals, Inc., ¿95 % purity) and DI (Milli-Q)water were chosen as metal and oxygen sources, respectively. Both precursors are kept instainless steel reservoirs at room temperature and subsequently introduced by pneumaticvalves under a carrier gas flow of 5 sccm N into the reactor chamber. For the depositions,pulse durations of 0.015 s are chosen for both the metal precursor and the oxygen source.Each pulse is followed by a dwelling time of 5 s without N flow and a purge of 60 s under30 sccm N . With these parameters the nominal growth rate is 1.2 ˚A per cycle. 3000 ALDcycles are applied on the HU structures in order to guarantee complete infiltration. Afterthe ALD process, the ZnO overlayer is removed by plasma etching (PE-100 Series, PlasmaEtch, Inc.) with 20 sccm of Ar at a pressure of 0.4 torr (1 torr ≈ − . Next, the polymeric fraction of theZnO-photoresist composite structure is removed via calcination at 500 ◦ C for ¿5 hours in atube furnace (Gero, Type SR(A)). Heating and cooling ramps of 100 ◦ C per hour are chosento avoid thermal deterioration and delamination of the structures.The zinc oxide inverse structures are subsequently infiltrated with amorphous silicon at 480 ◦ C by thermal chemical vapor deposition. The process is carried out in a custom built reactoroperating at a base pressure of 9 Torr by slowly heating the structures with plateaus at 150,250, 350 and 480 ◦ C and with a dwelling time between 15-30 min. This allows the structuresto thermally stabilize. Disilane gas (Si H ) (Linde, ≥ . − . The flow ismaintained for 35 min at a pressure of 17 torr in order to completely infiltrate the networkstructures. The silicon overlayer is partially removed by employing plasma etching with agas mixture of 10 sccm of Ar and 3 sccm of sulfur hexafluoride (SF ) at a pressure of 0.3 torrand a power of 40 W. The etching rate is 25-30 nm min − . The remaining ZnO is then wet-etched by applying a few drops of aqueous hydrochloric acid (10 vol.%) on the sample. After1 minute the sample is rinsed with DI water and the procedure is repeated three times untilno zinc oxide remains. The sample is dried in a gentle flow of N . Next, the as-fabricatedstructures are tempered at 600 ◦ C for ¿8 hours in order to transform the amorphous siliconinto its polycrystalline phase. This procedure reduces the refractive index slightly but alsoleads to a lower residual absorption coefficient [6]. Consecutive plasma etching results in afurther reduction of the silicon overlayer until it was observed to brake off revealing the barenetwork structure.
Electron microscopy
The structures are analyzed by scanning electron microscopy (SEM) (Sirion FEG-XL30S, FEI) between 5 and 10 kV. Cross-sections are realized by focused ion beam (FIB) milling(Dualbeam NOVA600 Nanolab, FEI) performed by accelerating a Ga ion beam (30 kV) at4 current of 3 nA onto the sample for several minutes. A consecutive ”cleaning” step at 1nA is used to further clean the etching area.
Optical characterization
The optical spectra of the hyperuniform disordered structures are studied using a Fouriertransform infrared spectrometer (Bruker Vertex 70, germanium coated KBr beamsplitter)connected to a microscope (Bruker Hyperion 2000, SiC globar light source, liquid N -cooledInSb detector). The employed objective is a 36x Cassegrain with a numerical aperture of0.52. Transmittance and reflectance of light incident under a cone of light between 10-30 ◦ relative to the surface normal are measured. Additional transmittance measurements witha reduced angular spread are performed by tilting the sample with an appropriate holderand shadowing the Cassegrain objective such that a probing illumination under 0-10 ◦ withrespect to normal incidence is achieved. Spectra are normalized by a reference taken in airand on a gold mirror for transmittance and reflectance measurements, respectively. We notethat the shifts of the gap wavelength λ Gap observed are well explained by the change in a and the effective refractive index of the material. This excludes that the observed featuresare due to chemical absorption bands. RESULTS AND DISCUSSION
We first fabricate polymeric templates with direct-laser writing (DLW) into a liquidnegative-tone photoresist as reported previously in [25, 26]. As a seed pattern, we use thecenter positions of a jammed assembly of spheres [27] which is then numerically convertedinto a three-dimensional hyperuniform (HU) network structure by following the proceduredescribed in reference [25]. The average distance between the points is set by the diameterof the jammed spheres and is denoted by a . It sets the intrinsic length scale of the structuresimilar to the lattice constant of a photonic crystal. Consequently, a determines the wave-length of the observed photonic features. The design protocol consists in mapping the seedpattern into tetrahedrons by performing a Delaunay tessellation. Then the centers of massof the tetrahedrons are connected, resulting in a tetravalent network structure of intercon-nected rods with the desired structural properties. It has been shown that an approximate5elation between the volume filling fraction φ and the rod diameter ¡ D ¿ can be derived asfollows [13] : φ ≈ . D ¿ /a ) . In the fabrication process the rods acquire an ellipsoidalcross section and an effective value of ¡ D ¿ can be calculated by taking the square root ofthe product between the two axes of the ellipse, Figure 1. The characteristic structurallength scale a is varied over a range a = 1 . − µ m. The resulting polymer templatesare therefore very open structures with a volume filling fraction of only about 15 % for amean rod diameter of ¡ D ¿ ≈
400 nm [25, 26]. Next, these polymer structures are completelyinfiltrated with zinc oxide using atomic layer deposition (ALD) at a temperature of 110 ◦ C,low enough to preserve the integrety of the template. Next the sample is exposed to anAr plasma in order to remove the excess of ZnO that forms on top of the structure. Thenthe polymer-ZnO composite material is heated to a temperature of 500 ◦ C for ¿5 hours tothermally degrade the polymer. Scanning electron microscopy images confirm the conser-vation of the network geometry after the thermal treatment. The ZnO inverse structure isinfiltrated with amorphous silicon (n ≈ ◦ C [16, 22]. In order to obtain the positive replica, the ZnO is removed by wet-etchingwith aqueous hydrochloric acid. At this stage, the photonic features in the optical spec-trum are masked by the pronounced scattering from the Si overlayer (Figure S-2). Furthertempering of the structure at 600 ◦ C for ¿8 hours transforms the as-deposited amorphoussilicon into its brittler poly-crystalline phase. Subsequent Ar-SF plasma etching reduces thethickness of the Si overlayer up to a point at which it starts to break off. When doing so thebare network structure becomes accessible, Figure 1(a). We note that this process is ratherpoorly controlled and the removal of the overlayer remains experimentally challenging. Weuse focussed ion beam (FIB) cutting to access the internal structure of the material. Thecomplete silicon infiltration is confirmed by analyzing cross sections of the FIB cut (Figure1(c)) as well as by the presence of solid Si rods on the back side of a structure which detachedand flipped over during the inversion process (Figure 1(b)). The rods possess an ellipticalcross section oriented in plane [26] with a length of about 210 nm and 580 nm along theshort and long axis, respectively. These values corresponding to a mean rod diameter of¡ D ¿ ≈ √ ·
580 nm= 350 nm and a corresponding silicon volume fraction of φ ≈ IG. 1. Scanning electron microscopy (SEM) of the fabricated hyperuniform disordered structures.(a) Top-view of a polymer structure with a =1.82 µ m and height h=5.5 µ m. (b) Image of the backside of a structure composed of poly-crystalline silicon acquired after the silicon double inversionprocess, revealing that the structure was completely infiltrated during the replication procedure.(c) Close-up view of a focused ion beam (FIB) cross-section of a Si-ZnO composite structure revealsthe bulk network structure of solid silicon rods. The dimensions of the rods in-plane is determinedto be approximatively 210x580 nm , resulting in a silicon volume filling fraction of φ ≈ .
13. Allscale bars indicate a length of 1 µ m. form infrared spectrometer coupled to a microscope. We use a pair of Cassegrain lenses withacceptance angles between 10 ◦ and 30 ◦ with respect to the surface normal, meaning that aset of reciprocal lattice vectors probe the sample simultaneously. Additional transmittancemeasurements with an angular spread between 0 ◦ -10 ◦ along normal incidence were realizedby shadowing the Cassegrain condenser objective partially and tilting the sample with acustom made holder similar to the one used in ref. [23]. A pronounced gap in transmittanceis observed at a central wavelength of λ Gap ≈ µ m for a structure of height h=5.5 µ mand a = 1.82 µ m as shown in Figure 3 (a). As expected for a nearly isotropic material wefind that that the central position λ Gap of the dip as well as its width do not change when7
IG. 2. Depiction of the double inversion procedure for fabricating silicon replica of a polymertemplate obtained by direct-laser writing lithography at the mesoscale. (a) Polymeric template ofa network structure produced by direct-laser writing (DLW). (b) Completely infiltrated polymertemplate using ZnO atomic layer deposition (ALD) at a moderate temperature of 110 ◦ C. (c)Ar plasma etching of the ZnO overlayer and polymer degradation at 500 ◦ C for ¿ 5 hours. (d)Infiltration of amorphous silicon using chemical vapor deposition (CVD) at 480 ◦ C. (e) DilutedHCl wet-etching of the remaining ZnO fraction. The Si overlayer is plasma etched using an Ar-SF gas mixture. Next, the sample is tempered at 600 ◦ C for ¿ 8 hours in order to transform theamorphous Si into its poly-crystalline phase. measuring at oblique or normal incidence. This is an important observation since disorderedmaterials are isotropic nature and therefore the photonic features are expected to be nearlyangular independent[10]. The dip extends from λ ≈ µ m while at the same time nostrong specular reflectance is observed for the corresponding wavelengths. This means thatthe light that is not transmitted is diffusely reflected over the whole hemisphere. Residualoscillations in some of the reflectance spectra can be attributed to Fabry-Perrot interferenceeffects.Next we study the evolution of the optical transmission spectra as a function of the typicalstructure length scale of the seed pattern a . To this end a discrete set of network structuresis designed and fabricated where the parameter a is reduced from a = 2 µ m down to a =1.54 µ m (Figure 3 (b,c)). Correspondingly the central gap wavelength shifts from λ Gap ≈ IG. 3. Infrared spectroscopy of silicon hyperuniform network structures performed by Fouriertransform infrared spectroscopy. (a) Transmittance and reflectance spectra for a hyperuniformstructure of a =1.82 µ m and height h=5.5 µ m are recorded using a pair of Cassegrain objectives.The resulting probing cone of light possesses an angular spread of 10-30 ◦ with respect to normalincidence. Additional transmittance measurements are performed with a reduced angular spread of0-10 ◦ with respect to the surface normal. Transmission (b) reflectance (c) spectra for h=5.5 µ m andfor different values of a . The data displays the blue-shift of the gap wavelength λ g upon reducingthe typical structure length scale of the seed pattern a = 2, 1.82, 1.67, 1.54 µ m. Inset: Electronmicrograph of the silicon material flipped by 180 ◦ during the final processing step revealing theinternal structure of the pure silicon network. µ m to λ Gap ≈ µ m. The cross section of the ellipsoidal rods remains unchanged asit is set by direct-laser writing ’pen’. Thus the effective rod diameter ¡ D ¿ remains constantas well. This means that by continuously reducing the parameter a , the filling fraction in-creases from φ =0.11 to 0.22. This reduces the blue-shift of λ Gap since the effective refractiveindex is increased as discussed in more detail in [13]. Numerical calculations on hyperuni-form disordered network structures have shown that a complete photonic bandgap appearsfor filling fractions of φ =0.15-0.4 and for refractive indices n ≥ φ =0.15-0.25. Indeed, it is in this region that weobserve experimentally the most pronounced gaps. For a = 1 . µ m we find experimentally9 Gap (cid:39) . µ m and we estimate a silicon filling fraction of φ = 0 .
13. For comparison, inthe numerical study a central gap wavelength for the silicon network (n=3.6, φ = 0 .
15) isfound at λ Gap (cid:39) . · a = 2 . µ m [11] which almost quantiatively matches our experimentalresult. The slight 10% difference can be attributed to the slightly lower filling fraction and toshrinking effects during the fabrication process. Similar shrinking effects have been reportedpreviously due to the thermal decomposition of the polymer and the high temperature sili-con chemical vapor deposition in the fabrication of silicon woodpile photonic crystals [29].It would be desirable to reduce the structural length scales even further in order to bringthe photonic band gap closer to telecommunication wavelengths. As we have shown herethis can only be realized if the cross section of the laser writing ’pen’ can be reduced sub-stantially. Otherwise the filling fraction will increase beyond φ = 0 .
25 and the photonicproperties are expected to weaken as shown in [11]. Indeed, such a higher resolution can beachieved for example by employing a direct-laser writing scheme based on a 405 nm wave-length diode laser for the fabrication of polymeric templates as reported in [30]. We believethe structural length scale a could be reduced to below a =1 µ m, thereby shifting the gapto the near-infrared wavelengths around λ Gap ≈ µ m. ACKNOWLEDGEMENTS
This project has been financially supported by the National Research Fund, Luxembourg(project No. 3093332), the Swiss National Science Foundation (projects 132736 and 149867),the National Centre of Competence in Research Bio-Inspired Materials and the AdolpheMerkle Foundation. We thank Bodo Wilts for help with the scanning electron microscopy. ∗ Frank.Scheff[email protected][1] S. John, “Strong localization of photons in certain disordered dielectric superlattices,” PhysicalReview Letters , 2486 (1987).[2] E. Yablonovitch, “Inhibited spontaneous emission in solid-state physics and electronics,” Phys-ical Review Letters , 2059 (1987).[3] A. Blanco, E. Chomski, S. Grabtchak, M. Ibisate, S. John, S. W. Leonard, C. Lopez,F. Meseguer, H. Miguez, J. P. Mondia et al. , “Large-scale synthesis of a silicon photonic rystal with a complete three-dimensional bandgap near 1.5 micrometres,” Nature , 437–440 (2000).[4] H. Mıguez, C. L´opez, F. Meseguer, A. Blanco, L. V´azquez, R. Mayoral, M. Ocana, V. Forn´es,and A. Mifsud, “Photonic crystal properties of packed submicrometric sio2 spheres,” AppliedPhysics Letters , 1148–1150 (1997).[5] E. Cubukcu, K. Aydin, E. Ozbay, S. Foteinopoulou, and C. M. Soukoulis, “Electromagneticwaves: Negative refraction by photonic crystals,” Nature , 604–605 (2003).[6] C. Becker, S. Linden, G. Von Freymann, M. Wegener, N. T´etreault, E. Vekris, V. Kitaev,and G. Ozin, “Two-color pump–probe experiments on silicon inverse opals,” Applied PhysicsLetters , 091111 (2005).[7] R. Rehammar, R. Magnusson, A. Fernandez-Dominguez, H. Arwin, J. M. Kinaret, S. Maier,and E. E. Campbell, “Optical properties of carbon nanofiber photonic crystals,” Nanotech-nology , 465203 (2010).[8] M. Reufer, L. F. Rojas-Ochoa, S. Eiden, J. J. S´aenz, and F. Scheffold, “Transport of light inamorphous photonic materials,” Applied Physics Letters , 171904 (2007).[9] K. Edagawa, S. Kanoko, and M. Notomi, “Photonic amorphous diamond structure with a 3dphotonic band gap,” Physical Review Letters , 013901 (2008).[10] M. Florescu, S. Torquato, and P. J. Steinhardt, “Designer disordered materials with large,complete photonic band gaps,” Proceedings of the National Academy of Sciences , 20658–20663 (2009).[11] S. F. Liew, J.-K. Yang, H. Noh, C. F. Schreck, E. R. Dufresne, C. S. O?Hern, and H. Cao,“Photonic band gaps in three-dimensional network structures with short-range order,” Phys-ical Review A , 063818 (2011).[12] D. S. Wiersma, “Disordered photonics,” Nature Photonics , 188–196 (2013).[13] N. Muller, J. Haberko, C. Marichy, and F. Scheffold, “Silicon hyperuniform disordered pho-tonic materials with a pronounced gap in the shortwave infrared,” Advanced Optical Materials , 115–119 (2014).[14] L. S. Froufe-P´erez, M. Engel, P. F. Damasceno, N. Muller, J. Haberko, S. C. Glotzer, andF. Scheffold, “Role of short-range order and hyperuniformity in the formation of band gapsin disordered photonic materials,” Physical Review Letters , 053902 (2016).
15] W. Man, M. Florescu, E. P. Williamson, Y. He, S. R. Hashemizad, B. Y. Leung, D. R.Liner, S. Torquato, P. M. Chaikin, and P. J. Steinhardt, “Isotropic band gaps and freeformwaveguides observed in hyperuniform disordered photonic solids,” Proceedings of the NationalAcademy of Sciences , 15886–15891 (2013).[16] K. Ishizaki, M. Koumura, K. Suzuki, K. Gondaira, and S. Noda, “Realization of three-dimensional guiding of photons in photonic crystals,” Nature Photonics , 133–137 (2013).[17] S. A. Rinne, F. Garc´ıa-Santamar´ıa, and P. V. Braun, “Embedded cavities and waveguides inthree-dimensional silicon photonic crystals,” Nature Photonics , 52–56 (2008).[18] W. Man, M. Florescu, K. Matsuyama, P. Yadak, G. Nahal, S. Hashemizad, E. Williamson,P. Steinhardt, S. Torquato, and P. Chaikin, “Photonic band gap in isotropic hyperuniformdisordered solids with low dielectric contrast,” Optics Express , 19972–19981 (2013).[19] M. Deubel, G. Von Freymann, M. Wegener, S. Pereira, K. Busch, and C. M. Soukoulis, “Directlaser writing of three-dimensional photonic-crystal templates for telecommunications,” NatureMaterials , 444–447 (2004).[20] N. T´etreault, G. von Freymann, M. Deubel, M. Hermatschweiler, F. Perez-Willard, S. John,M. Wegener, and G. A. Ozin, “New route to three-dimensional photonic bandgap materials:silicon double inversion of polymer templates,” Advanced Materials , 457–460 (2006).[21] K. M. Ho, C. Chan, C. Soukoulis, R. Biswas, and M. Sigalas, “Photonic band gaps in threedimensions: new layer-by-layer periodic structures,” Solid State Communications , 413–416(1994).[22] M. Hermatschweiler, A. Ledermann, G. A. Ozin, M. Wegener, and G. von Freymann, “Fab-rication of silicon inverse woodpile photonic crystals,” Advanced Materials , 2273–2277(2007).[23] I. Staude, M. Thiel, S. Essig, C. Wolff, K. Busch, G. Von Freymann, and M. Wegener, “Fab-rication and characterization of silicon woodpile photonic crystals with a complete bandgapat telecom wavelengths,” Optics Letters , 1094–1096 (2010).[24] A. Fr¨olich, J. Fischer, T. Zebrowski, K. Busch, and M. Wegener, “Titania woodpiles withcomplete three-dimensional photonic bandgaps in the visible,” Advanced Materials , 3588–3592 (2013).[25] J. Haberko and F. Scheffold, “Fabrication of mesoscale polymeric templates for three-dimensional disordered photonic materials,” Optics Express , 1057–1065 (2013).
26] J. Haberko, N. Muller, and F. Scheffold, “Direct laser writing of three-dimensional networkstructures as templates for disordered photonic materials,” Phys. Rev. A , 043822 (2013).[27] C. Song, P. Wang, and H. A. Makse, “A phase diagram for jammed matter,” Nature ,629–632 (2008).[28] M. Janai, D. Allred, D. Booth, and B. Seraphin, “Optical properties and structure of amor-phous silicon films prepared by cvd,” Solar Energy Materials , 11–27 (1979).[29] G. Von Freymann, A. Ledermann, M. Thiel, I. Staude, S. Essig, K. Busch, and M. Wegener,“Three-dimensional nanostructures for photonics,” Advanced Functional Materials , 1038–1052 (2010).[30] P. Mueller, M. Thiel, and M. Wegener, “3d direct laser writing using a 405 nm diode laser,”Optics Letters , 6847–6850 (2014)., 6847–6850 (2014).