Hyperuniform disordered networks belong to a peculiar class of structured materials predicted to display isotropic complete photonic bandgaps for a refractive index contrast larger than 3. The practical realization of such photonic designer materials is challenging, however, as it requires control over a multi-step fabrication process on optical length scales. Here we report the direct-laser writing of three-dimensional hyperuniform polymeric templates followed by a silicon double inversion procedure leading to high-quality network structures made of polycrystalline silicon. We observe a pronounced gap in the shortwave infrared centered at a wavelength of , in good agreement with numerical simulations. In the experiments the typical structural length scale can be varied between 2 and 1.54 μm, leading to a blueshift of the gap accompanied by an increase of the silicon filling fraction.
© 2017 Optical Society of America
Photonic crystal structures have drawn a lot of attention over the past decades due to their potential applications in optical circuits and photon guiding , improved laser sources , negative refractive index material properties , or tunable optical devices [4,5]. However, the routine design of full bandgap materials in three dimensions for optical wavelengths has proven elusive [3,6–10]. Recently, disordered and isotropic photonic materials have been suggested as an alternative [11–17]. A hyperuniform structure combined with short range order and an open network architecture is widely considered to be a strong candidate for an optimized photonic material design [13,14,18]. The isotropic structure should offer advantages such as the possibility to incorporate waveguides with arbitrary bending angles [1,19,20]. Numerical calculations in two and three dimensions suggest the presence of a full photonic bandgap in the near-infrared if the material is made out of a material with an refractive index in air, such as silicon [13,14]. Previous experimental studies of hyperuniform photonic materials have reported partial and full bandgaps for 2D hyperuniform network structures in the microwave regime [19,21]. Recently we demonstrated the fabrication of high refractive index three-dimensional (3D) hyperuniform materials by coating polymer templates with and silicon . The final materials contained some titania (, ), lowering the refractive index contrast slightly. The gold standard to achieve silicon photonic bandgap materials is the silicon double-inversion method, a rather complex multi-step process to transfer polymer templates into silicon replica [22,23]. Despite its complexity, it has been successfully applied to periodic structures [23–25]. Full photonic bandgaps have been reported for silicon woodpile photonic crystals in the shortwave infrared  and the near-infrared at telecom wavelengths . The application of this approach to open hyperuniform network structures is even more difficult. In particular, retaining the mechanical stability of the network is a challenging task considering the harsh conditions when removing the sacrificial material components after each processing step. Here we report the successful realization of a silicon double-inversion approach applied to hyperuniform network structures designed by direct-laser writing (DLW) into a polymer photoresist [23,25,27].
We first fabricate polymeric templates of height and a footprint of approximately with DLW into a liquid negative-tone photoresist as reported previously in [28,29]. As a seed pattern, we use the center positions of a jammed assembly of spheres , which is then numerically converted into a 3D hyperuniform (HU) network structure by following the procedure described in Ref. . The average distance between the points is set by the diameter of the jammed spheres and is denoted by . It sets the intrinsic length scale of the structure similar to the lattice constant of a photonic crystal. Consequently, determines the wavelength of the observed photonic features. The design protocol consists of mapping the seed pattern into tetrahedrons by performing a Delaunay tessellation. Then, the centers of mass of the tetrahedrons are connected, resulting in a tetravalent network structure of interconnected rods with the desired structural properties. The volume filling fraction and the mean rod diameter are linked by for . In the fabrication process, the rods acquire an ellipsoidal cross section, and an effective value of can be calculated by taking the square root of the product between the two axes of the ellipse. In the present work, the characteristic structural length scale is varied over a range . The resulting polymer templates are therefore very open structures with a volume filling fraction of only about 15% for a mean rod diameter of [28,29], Fig. 1(a). Next, these polymer structures are completely infiltrated with zinc oxide using atomic layer deposition (ALD) at a temperature of 110°C, low enough to preserve the integrity of the template. The sample is exposed to an Ar plasma to remove the excess of ZnO that forms on top of the structure. Then the polymer–ZnO composite material is heated to a temperature of 500°C for to thermally degrade the polymer. The ZnO inverse structure is infiltrated with amorphous silicon using chemical vapor deposition (CVD) at 480°C [1,25]. To obtain the positive replica, the ZnO is removed by wet etching with aqueous hydrochloric acid. At this stage, the photonic features in the optical spectrum are masked by the pronounced scattering from the Si overlayer (Fig. S3 in Supplement 1). Further tempering of the structure at 600°C for transforms the as-deposited amorphous silicon into its brittler polycrystalline phase . Subsequent plasma etching reduces the thickness of the Si overlayer up to a point at which it starts to break off. When doing so, the bare network structure becomes accessible [Fig. 1(b)].
A. Direct Laser Writing
Polymeric templates on the mesoscale are fabricated using a commercially available DLW system (Photonic Professional GT, Nanoscribe GmbH, Germany) in dip-In configuration. [28,29] The digitally designed structures with a height of 6 μm are written on infrared transparent substrates (Crystan, UK) by dipping an oil-immersion objective (, ) inside a liquid negative-tone photoresist (IP-DIP, Nanoscribe GmbH, Germany). The writing process is started in a virtual depth of approximately 0.5 μm inside the glass substrate, and thus the nominal height is 5.5 μm. The latter is needed to guarantee a continuous laser writing process along the axial direction, which is necessary to ensure the adhesion of the polymer template to the substrate. Moreover, the actual height of the sample is further reduced by 10%–20% due to polymer shrinkage in the development process and the subsequent etching steps. We thus estimate the actual height to be . Massive square walls are written around each structure to improve the mechanical stability during the development procedure and the post-processing. The photopolymerized samples are developed in two successive baths of propylene glycol monomethyl ether acetate (PGMEA) for twice 10 min and consecutively rinsed in a bath of isopropanol for 8 min. Gentle drying is ensured by redirecting a stream of through a bubbler filled with isopropanol onto the sample.
B. Silicon Double Inversion
The DLW-produced polymeric HU structures are infiltrated with ZnO using ALD. The deposition is carried out in a commercial ALD reactor (Savannah 100, Cambridge Nanotech, Inc.) operating in exposure mode at a moderate temperature of 110°C. Slow heating and cooling ramps are set to prevent thermal degradation of the polymer structure. Diethylzinc (Strem Chemicals, Inc., purity) and deionized (Milli-) water were chosen as metal and oxygen sources, respectively. Both precursors are kept in stainless steel reservoirs at room temperature and subsequently introduced by pneumatic valves under a carrier gas flow of 5 sccm (sccm denotes cubic centimeters per minute at standard temperature and pressure) 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 flow and a purge of 60 s under 20 sccm . With these parameters the nominal growth rate is 1.2 Å per cycle. Three-thousand ALD cycles are applied on the HU structures to guarantee complete infiltration. After the ALD process, the ZnO overlayer is removed by plasma etching (PE-100 Series, Plasma Etch, Inc.) with 20 sccm of Ar at a pressure of 0.4 torr () and a power of 200 W. The etch rate is approximately . Next, the polymeric fraction of the ZnO-photoresist composite structure is removed via calcination at 500°C for in a tube furnace [Gero, Type SR(A)]. Heating and cooling ramps of are chosen to avoid thermal deterioration and delamination of the structures. The ZnO inverse structures are subsequently infiltrated with amorphous silicon at 480°C by thermal CVD. The process is carried out in a custom built reactor operating at a base pressure of 9 Torr by slowly heating the structures with plateaus at 150°C, 250°C, 350°C, and 480°C and with a dwelling time between 15 and 30 min. This allows the structures to thermally stabilize. Disilane gas () (Linde, ) is used as precursor. The disilane flow is set to 2 sccm, yielding a growth rate of about . The flow is maintained for 35 min at a pressure of 17 torr to completely infiltrate the network structures. The silicon overlayer is partially removed by employing plasma etching with a gas mixture of 10 sccm of Ar and 3 sccm of sulfur hexafluoride () at a pressure of 0.3 torr and a power of 40 W. The etching rate is . The remaining ZnO is then wet etched by applying a few drops of aqueous hydrochloric acid (10 vol. %) on the sample. After 1 min the sample is rinsed with DI water and the procedure is repeated three times until no zinc oxide remains. The sample is dried in a gentle flow of . Next, the as-fabricated structures are tempered at 600°C for to transform the amorphous silicon into its polycrystalline phase. This procedure reduces the refractive index somewhat  but has also been suggested to lead to a lower residual absorption coefficient . Consecutive plasma etching results in a further reduction of the silicon overlayer until it was observed to break off revealing the bare network structure.
C. Electron Microscopy
The structures are analyzed by scanning electron microscopy (SEM) (Sirion FEG-XL30 S, FEI) between 5 and 10 kV. The complete silicon infiltration is confirmed by analyzing cross sections of a focused ion beam (FIB) cut, as well as by the presence of solid Si rods on the back side of a structure that detached and flipped over during the inversion process. The FIB cuts reveal that the silicon rods possess an elliptical cross section oriented in plane  with lengths of about 210 and 580 nm along the short and long axes, respectively [Fig. 1(c)]. These values correspond to a mean rod diameter of and a corresponding silicon volume fraction of for . The compositional analysis of the final structure by Energy Dispersive Spectroscopy (Fig. S4 and Table S1 in Supplement 1) indicates the presence of pure silicon.
D. Optical Characterization
The optical spectra of the hyperuniform disordered structures are recorded using a Fourier transform infrared spectrometer (Bruker Vertex 70, germanium-coated KBr beam splitter) connected to a microscope (Bruker Hyperion 2000, SiC globar light source, liquid -cooled InSb detector) [Fig. 2]. The employed objective is a Cassegrain with a numerical aperture of 0.52. Transmittance and reflectance of light incident under a cone of light between 10° and 30° relative to the surface normal are measured. Additional transmittance measurements with a reduced angular spread are performed by tilting the sample with an appropriate holder and shadowing part of the Cassegrain objective such that a probing illumination under 0°–10° with respect to normal incidence is achieved [Fig. 2(a)] . All spectra are normalized by a reference taken in air and on a gold pad for transmittance and reflectance measurements, respectively.
3. NUMERICAL SIMULATIONS OF LIGHT TRANSPORT
We perform 3D finite-difference time-domain (FDTD) simulations on hyperuniform silicon networks using the free software package MEEP (v.1.2) . The simulations provide the total transmittance () and reflectance () () as functions of frequency or wavelength. The hyperuniform dielectric networks are analyzed with a spatial discretization of 50 nm (Fig. S5 in Supplement 1). We take the elliptical cross section of the rods into account with an aspect ratio of 2.8, and the mean rod diameter is varied to simulate different filling fractions. The size of the simulated structure is chosen as . Periodic boundary conditions are applied along the and axes. Left and right of the sample, along the wave propagation direction , we place perfectly matched layer (PML) absorbers (Fig. S5 in Supplement 1). Moreover, we add a region of free space between the PMLs and the structure to allow any probable evanescent fields to decay before reaching the PML region. The thickness of the PML is set to 7 μm and we have verified that this choice effectively suppresses back reflections for wavelengths .
The structural and chemical characterization shows that the double inversion of the hyperuniform network structures into silicon has been successful. Moreover, we observe a pronounced gap in transmittance at a central wavelength of for a structure of height and , as shown in Figs. 2 and 3. The central position of the gap nor its width changes when measuring at oblique or normal incidence [Fig. 2(a)]. This is an important observation since disordered materials are structurally isotropic, and, therefore, the photonic features are expected to be nearly angularly independent . The gap extends from [Fig. 3(a)] while at the same time no specular reflections are observed for the corresponding wavelengths, as shown in Fig. 3(b). While a reflection peak is a characteristic feature of photonic crystals, it is notably absent here [8,9,26,33]. This means that the reflected light is diffusely distributed over the whole hemisphere. Residual oscillations in some of the reflectance spectra can be attributed to Fabry–Perot interference effects.
As shown in Fig. 2(b), we find good overall agreement between the experiment and the FDTD simulations for a refractive index of and a height of . Numerical calculations of the density of states of equivalent hyperuniform disordered network structures have shown that a complete photonic bandgap appears for filling fractions of and for refractive indices . The optimal filling fraction is predicted to be in the range . Indeed, it is in this region that we observe experimentally and numerically the most pronounced gaps.
To study different silicon filling fractions, we vary the typical structural length scale from down to (Fig. 3). Correspondingly, the central gap wavelength shifts from to . The cross section of the ellipsoidal rods remains unchanged as it is set by the DLW “pen.” This means that, by continuously reducing the parameter , the filling fraction increases from to 0.18. The increased filling fraction leads to an effectively increased background refractive index that partially counteracts the blueshift of when reducing . With FDTD simulations we can study a larger range of filling fractions . As shown in the inset of Fig. 3(a), we again observe a shift of the reduced gap wavelength due to the increased effective (background) refractive index. The numerical simulations are in quantitative agreement with the experimental data if we assume . The slight mismatch can be explained by shrinkage of the network material during development of the polymer templates and the double-inversion procedure .
The onset of the pseudo-gap observed in the FDTD simulations appears to be more abrupt in comparison to the experimental data. To verify possible reasons for this discrepancy, we first performed FDTD calculations for a smaller rod refractive index (, Fig. S6 in Supplement 1). As expected, this leads to a weaker gap; however, the overall shape of the spectra remains essentially unchanged. Moreover, the chemical analysis indicates pure silicon, electron microscopy and FIB etching do not indicate that the rods are porous, and we therefore believe the rods consist of pure silicon with for the wavelengths probed. Also, the position of the gap predicted by FDTD matches the experimental data well. We thus attribute the difference between the experimental and the numerical results to distortions in the structure, which lead to a smearing of the gap. Such distortions can be associated to uneven shrinkage and other imperfections, such as surface roughness, notable in Fig. 1(b), not taken into account in the numerical simulations.
For smaller wavelengths , the simulations and the experimental data deviate substantially. This is partially because, in the simulations, we calculate the total transmittance, whereas in the experiment, only light in a small cone is recorded. Moreover, the rough surface of the rods and other imperfections can lead to increased scattering in this regime. Similar deviations for are commonly observed in periodic photonic structures, as well [26,33].
5. SUMMARY AND CONCLUSION
In this work, we have demonstrated the feasibility of fabricating 3D hyperuniform silicon networks by double inversion, and we have shown that the optical properties of the materials match those obtained from numerical simulations. This suggests that macroscopic, three dimensional hyperuniform photonic materials with a full bandgap can be realized if the structures are engineered on larger length scales, while at the same time conserving the structural integrity. In future work it would be desirable to reduce the structural length scales even further to bring the photonic bandgap closer to telecommunication wavelengths. As we have shown here, this can be realized by only reducing the cross section of the laser writing pen. Otherwise, the silicon filling fraction will increase beyond and the photonic properties are expected to weaken . Indeed, the necessary higher resolution can be achieved, for example, by employing a DLW scheme based on a 405 nm wavelength diode laser for the fabrication of polymeric templates as reported in  or by stimulated emission depletion inspired direct laser writing . We believe the structural length scale could then be reduced to below , thereby opening the path toward a full isotropic bandgap at near-infrared wavelengths around .
Adolphe Merkle Foundation; Fonds National de la Recherche Luxembourg (FNR) (3093332); Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung (SNF) (149867, 169074, NCCR Bio-Inspired Materials).
The authors thank Bodo Wilts for technical support and discussions. JH acknowledges the use of the TeraACMIN cluster at the Academic Centre for Materials and Nanotechnology, AGH-UST, Krakow, Poland.
See Supplement 1 for supporting content.
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